text stringlengths 1.23k 293k | tokens float64 290 66.5k | created stringdate 1-01-01 00:00:00 2024-12-01 00:00:00 | fields listlengths 1 6 |
|---|---|---|---|
ArgumenText: Argument Classification and Clustering in a Generalized Search Scenario
The ArgumenText project creates argument mining technology for big and heterogeneous data and aims to evaluate its use in real-world applications. The technology mines and clusters arguments from a variety of textual sources for a large range of topics and in multiple languages. Its main strength is its generalization to very different textual sources including web crawls, news data, or customer reviews. We validated the technology with a focus on supporting decisions in innovation management as well as customer feedback analysis. Along with its public argument search engine and API, ArgumenText has released multiple datasets for argument classification and clustering. This contribution outlines the major technology-related challenges and proposed solutions for the tasks of argument extraction from heterogeneous sources and argument clustering. It also lays out exemplary industry applications and remaining challenges.
Introduction
Argument mining (AM) has become an established field of research in Natural Language Processing (NLP) with numerous works published over the last years [8,12,16]. AM is used with growing success to automatically detect argumentative structures in textual discourse, including student essays [8] and web forums [11]. Argumentative structures which can be automatically resolved include claims [6] and premises, argument relations [8], or pro-and con-arguments [22]. As such, AM can be used to support decision making by retrieving the most important arguments for and against controversial matters.
The current contribution details how we addressed the challenging task of argument search in heterogeneous data in the ArgumenText project. 1 ArgumenText has pioneered the generalization of AM at sentence level and created important resources for both argument classification and argu-1 www.argumentext.de. Johannes Daxenberger<EMAIL_ADDRESS>1 Ubiquitous Knowledge Processing Lab, Department of Computer Science, Technische Universität Darmstadt, Darmstadt, Germany ment clustering. To achieve this goal, we had to overcome several research challenges: (1) Generalizing AM to heterogeneous sources (e.g. news as well as web content): to extract relevant arguments from all sources available, we need to ensure that the AM model is able to detect arguments from any type of text. (2) Scaling AM technology to big data (e.g. millions of web pages): to be able to work on large datasets or data streams, the extraction must be fast as in other information retrieval (IR) scenarios. (3) Clustering similar arguments (if they refer to the same reasoning): to better present long lists of arguments to users, it is necessary to detect similar and dissimilar arguments.
In the following, we explain those challenges in more depth and show how they were solved in the ArgumenText project.
Argument-based Search
AM offers the perfect ground to combine machine learning with human decision making, as it is supposed to detect viewpoints (in the form of argumentative structures) using machine intelligence. Given a controversial topic (e.g. "wind energy") and a large enough text collection to search Table 1 Argumentative search engines. Sources: document collections from which the arguments are extracted; Argument Classification: argument detection at query (online) or indexing (offline) time.
Reference
Name Sources Arg. Class. Prototype [26] args.me debate portals offline www.args.me [21] ArgumenText generic web crawl online www.argumentsearch.com [4] PerspectroScope curated online sources offline and online www.perspectroscope.com [10] IBM Debater news articles, Wikipedia online not available in (e.g. a web crawl), the ideal AM system should be able to extract all relevant reasoning from previous debates about the topic of interest. For example, AM-supported decision making has been investigated in the context of evidencebased reasoning [19], where AM is used to detect and distinguish kinds of evidence with applications in the medical domain [14]. Given the subjective nature of evidence evaluation [1], initial applications of AM-supported decision making quickly converged into the creation of argumentative search engines [26]. Inspired by manually curated online debating portals such as kialo.com, procon.org or idebate.org, this line of research frames automatic AM as a retrieval task, aiming to maximize the relevance of search results with respect to the input query [17]. As opposed to standard web search engines, argumentative search engines need to detect the most relevant arguments given query term(s) and document collections to search in. Most approaches divide arguments into statements supporting (pro) or attacking (con) the input query, motivated by the goal to avoid biased or one-sided retrieval [2]. Arguments themselves are typically defined as "text expressing evidence or reasoning that can be used to either support or oppose a given topic" [22] where the topic may be equal or highly relevant to the input query. The first case, in which arguments are classified as such based on the query itself, can be referred to as online argument classification [2]. In the latter case, arguments are classified regardless of the query (i.e. offline). Table 1 lists recently proposed argumentative search engines. We only list search engines dividing arguments by (binary) stance (pro vs. con). Further AM-driven search engines such as MARGOT [13] and TARGER [5] provide online interfaces for argument tagging, i.e. argument component detection on token-level [8]. Fig. 1 shows the ArgumenText search engine results for the query "wind energy".
The ArgumenText search engine was created as part of our effort to demonstrate the applicability of AM-driven approaches to decision-making, in particular to unrestricted and unstructured text collections. To date, ArgumenText is the only publicly available argumentative search engine retrieving English and German arguments in realtime from completely uncurated web sources (see Table 1). Recent work in the context of the IBM Debater project [10] presents a similar system extracting arguments from news and Wikipedia articles -however, they only release the Wikipedia portion of the dataset and do not offer a public search engine. The methodological details of our proposed solution to this problem are described in Sect. 3. For the project goal of testing the usefulness of AM technologies for real-world applications (see Sect. 1), we needed to go beyond argument search and develop end-user applications. This resulted in two additional requirements: the technology needed to be able to work on dynamic data streams (e.g. social media) and the clustering of recurring arguments (to reveal and quantify reasoning strategies for given topics). These two challenges are detailed in Sects. 4 and 5.
Extracting Arguments from Heterogeneous Sources
Early work on AM in NLP research used highly structured argumentation schemes to parse argumentative discourse [16,20]. These argumentation schemes make rather strong assumptions on the argumentative nature of the input documents they can be applied to; e.g. the claim-premise scheme proposed by [20] relates premises (evidence) to claims which in turn refer to major claims. While it has been shown that such discourse-level approaches to AM can also be applied to web data [11], it remains doubtful whether they can be reliably applied to certain kinds of usergenerated web content such as customer reviews [15]. Furthermore, for the purpose of training deep learning models, it is also necessary to collect large amounts of training data, which is much more difficult for fine-grained hierarchical schemes as the one proposed by [20]. We also found that often the major claim or even the claims themselves are not given explicitly, but must be inferred from the context or by using world knowledge. For example, an argument explicitly attacking coal energy could also serve as a supporting argument for wind energy implicitly.
As a remedy to this, [22] suggest information-seeking AM, which is "general enough for use on heterogeneous data sources, and simple enough to be applied manually by untrained annotators at a reasonable cost" [22]. The work shows that reliable annotation via crowdsourcing and automatic inference across eight topics is possible, when using a given controversial topic (e.g. "minimum wage") to Fig. 1 The first few hits for the search query "wind energy" as displayed by the argument search engine ArgumenText. ArgumenText ranks arguments by the confidence score of its argument extraction algorithm [21] classify isolated sentences into either non-, pro-, or conargument. The resulting dataset is released as part of the ArgumenText project. 2 Training and inference is performed by a Contextual BiLSTM architecture ("biclstm") which integrates the information about the topic into some of the LSTM gates, such that a sentence and topic can be processed jointly. Another advantage of the simpler annotation scheme is that the training data which was originally created on English sources can be translated into other languages using state-of-the-art machine translation (as exemplary shown for German by [23]). The translated data can then be used to directly train a model in the target language, which has been recognized as a very efficient way to create cross-lingual models for AM [9].
Our later work on argument classification [18] shows that the biclstm approach of [22] is largely outperformed by a transformer-based architecture using contextualized BERT-large embeddings [7]. In [21], we showed that when training on a larger set of topics, the performance of the sentence classification into non-, pro-, or con-argument can be further improved. We further showed that this kind of argument classification can also be performed on word level, allowing to decompose sentence-level arguments into more fine-grained units [24]. This approach requires token-level 2 https://www.ukp.tu-darmstadt.de/sent_am. annotations for training a sequence labeling method, which we also release as part of the ArgumenText project. 3 For the public version of the ArgumenText search engine, we indexed more than 400 million English and German web pages from the CommonCrawl project and segmented all documents into sentences [21]. For English and German queries, the system first retrieves a limited number of relevant documents ranked by a BM25 score, and second classifies all sentences from these documents with the above described classifier. Only arguments which have been identified as pro-or con-arguments are displayed and ranked by classifier confidence. Using this two-stage approach for argument search in heterogeneous sources, the ArgumenText system yields a coverage as high as 89% when comparing top-ranked search results to expert-curated lists [21].
Scaling AM to Big Data
The ArgumenText search engine described in Sect. 3 extracts arguments from a static web crawl. To be able to validate the technology beyond generic argument search, we built a service-oriented infrastructure around the core components. In particular, we wanted to be able to extract arguments from any given source, including arbitrary document Fig. 2 Overview of the ArgumenText service infrastructure. The document storage (left) can process and store content from static or dynamically growing document collections. The core components (middle) are responsible for argument processing and storage. Two graphical interfaces allow to interact with the system (right) Fig. 3 Excerpt from the Ar-gumenText dashboard. The argument graph for the topic "e-scooter" reveals an initial positive trend in June 2019, which turned negative in later months. Green and red bars indicate the number of pro and con arguments on the time axis collections specified by end users. For that purpose, we decoupled argument classification from document retrieval and wrapped it as service available via REST APIs. 4 This service accepts arbitrary textual input and -given a topic which is used to decide on the argumentativeness of the sentences -returns sentence-level arguments from that input.
As direct queries to the REST APIs can only process a limited number of documents in order to prevent timeouts, we connected the argument classification API with a queuing functionality which handles query monitoring and execution in the background. The queuing component is connected to a graphical frontend which records search queries by registered users and pulls novel arguments pe-4 api.argumentsearch.com. riodically from the queue. The overall infrastructure is illustrated in Fig. 2. Fig. 3 shows the output of the graphical frontend for the query "e-scooter", as extracted from a web crawl. 5
Argument Clustering
Arguments retrieved from multiple sources as in the above described scenarios often repeat similar reasoning. For example, on the topic of "nuclear energy", arguments referring to the problem of radioactive waste (an argumentative aspect) can be phrased in many ways. While it can be insightful to compare multiple instances of arguments from Fig. 4 Word clouds and example arguments for three exemplary clusters for the topic "abortion". a "Fetuses are incapable of feeling pain when most abortions are performed." b "Abortion is the killing of a human being, which defies the word of God." c "Allowing abortion conflicts with the unalienable right to life recognized by the Founding Fathers of the United States." the same argumentative aspect, smart AM decision-supporting systems should provide end-users with argument clusters rather than unsorted lists of arguments. Multiple lines of research have addressed this problem, including unsupervised learning of semantic similarities of arguments [3,27].
However, as we have shown in [18], unsupervised methods are outperformed by supervised methods for the task of argument similarity assessment. Unsupervised learning methods rely on semantic overlap between pairs of arguments, which is not ideal for arguments that already discuss the same topic. Instead, we propose to train dedicated argument similarity models to provide similarity scores for the clustering approach. For this purpose, we released a corpus of sentence-level argument pairs extracted from heterogeneous web sources across 28 topics (ASPECT corpus). 6 The pairs were annotated on a range of three degrees of similarity, according to their overlap with regard to the argumentative aspect they address. Following the experiments described in [18], we only distinguish between related and unrelated arguments which enables to evaluate similarity prediction methods with F1 scores. The best supervised model (fine-tuned BERT-base) performs almost 10pp better than an unsupervised model based on BERT embeddings. Using agglomerative hierarchical clustering with stopping threshold, we are able to aggregate all arguments retrieved for a topic into clusters of aspects. Fig. 4 visualizes three example clusters that were produced using the above procedure.
Applications
We identified two promising applications for AM in supporting decisions: innovation assessment and advanced customer feedback analysis.
Technology and Innovation Assessment: Innovative technology often goes along with overly positive reasoning ("hype") at an early stage, such that it is difficult to identify potential risks. AM-based decision support can help this dilemma as it seeks to retrieve a balanced representation of supporting and attacking arguments on early or more mature innovative technologies. When applied to real-time news collections reporting about innovation and technology (e.g. online magazines), AM can help taking smarter investment decisions. Furthermore, novel trending aspects can be detected and quantified early on, using a combination of the technologies described in Sects. 4 and 5.
Advanced Customer Feedback Analysis: Companies with a broad product range in the consumer sector are often unable to accurately evaluate the large amount of customer feedback on different products and from multiple channels. Existing automatic methods to analyze the customer feedback rely on sentiment mining or unsupervised methods (clustering). While sentiment analysis might be able to separate positive from negative feedback or to distinguish degrees of criticality, it cannot reveal reasons behind the feedback which would be helpful for product development. Thus, the AM technologies as explained in Sects. 4 and 5 can be used to discover and quantify problematic aspects of existing products, to increase productmarket-fit and decrease time-to-market.
Future Directions
We presented challenges and solutions for AM-based decision support in the context of the ArgumenText project. Some remaining open challenges include: (a) Sorting arguments by quality: Current argument search engines rank arguments by classifier confidence or by IR-based ranking functions. However, end users might prefer arguments of high quality [25] over arguments with high relevance to search query. (b) End-to-end argument clustering evaluation: A largescale benchmark dataset which contains sentence-level arguments for multiple topics and further groups them into subtopics is urgently required. (c) Labeling argument clusters: Interpreting clusters is a difficult task which can be approximated by specifying predominant word lists (e.g. using LDA) or word frequency clouds. However, to clearly identify and label argument clusters, dedicated methodologies to extract aspect identifiers are required.
Acknowledgements This work has been supported by the German Federal Ministry of Education and Research (BMBF) under the promotional reference 03VP02540 (ArgumenText).
Funding Open Access funding provided by Projekt DEAL.
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://creativecommons.org/licenses/by/4. 0/. | 3,878 | 2020-06-16T00:00:00.000 | [
"Computer Science",
"Business"
] |
Azimuthal Anchoring Strength in Photopatterned Alignment of a Nematic
: Spatially-varying director fields have become an important part of research and develop-ment in liquid crystals. Characterization of the anchoring strength associated with a spatially-vary-ing director is difficult, since the methods developed for a uniform alignment are seldom applicable. Here we characterize the strength of azimuthal surface anchoring produced by the photoalignment technique based on plasmonic metamsaks. The measurements used photopatterned arrays of topological point defects of strength +1 and −1 in thin layers of a nematic liquid crystal. The integer-strength defects split into pairs of half-integer defects with lower elastic energy. The separation distance between the split pair is limited by the azimuthal surface anchoring, which allows one to determine the strength of the latter. The strength of the azimuthal anchoring is proportional to the UV exposure time during the photoalignment of the azobenzene layer.
Introduction
Anisotropy of molecular interactions at bounding surfaces of liquid crystals leads to the phenomenon of surface anchoring, i.e., a preferred "easy axis" of the director specifying the average orientation of the molecules. Surface anchoring is characterized by geometrical parameters, such as the polar and azimuthal direction of the easy axis. Using the energy parameters, the so-called anchoring coefficients measure the work needed to deviate the director from the easy axis [1]. For planar alignment, with the easy axis parallel to a certain direction in the plane of a substrate, one distinguishes azimuthal and polar anchoring coefficients, related to the in-plane and out-of-plane director tilts, respectively.
For decades, the prime mode of liquid crystal alignment was a uniform one, with the director independent of spatial coordinates. There is a growing interest in alignment modes with the director varying from point to point. The patterned alignment is used, for example, in planar optics [2][3][4][5][6], bistable switching [7], shaping liquid crystal elastomers [8][9][10][11], controlling dynamics of microswimmers [12,13], and living tissues [14]. The patterned surface alignment is difficult to achieve by traditional approaches, such as mechanical rubbing [15]. Early works reported that alignment patterns could be produced by scribing the substrate with the atomic force microscope's stylus [16,17]. The most popular current approach to produce patterned director fields is photoalignment, based on photosensitive molecules that adjust their orientation with respect to the polarization direction of impinging light [6,15,18,19]. Photoalignment is less prone to problems such as the introduction of dust particles [15]. One of the most widely used mechanisms of photoalignment is the orientational ordering of azobenzene molecules that experience transcis isomerization and reorientation under illumination with linearly polarized light [15].
Isomerizations and reorientations result in the alignment of long axes of trans-isomers along the direction of minimum light absorption, i.e., perpendicularly to the polarization of light [15,18,19]. There have been many different implementations of azobenzene-based photoalignment. For example, McConney et al. [20] used a laser beam with a controllable direction of polarization to irradiate a rotating substrate with a photosensitive azobenzene layer, thus producing axially-symmetric patterns, also known as q-plates [21][22][23][24]. Culbreath et al. [25] introduced a maskless digital micromirror photopatterning technique that allows one to create an array of disclinations. Most recently, Guo et al. [26][27][28] introduced a method based on plasmonic metamasks (PMMs), which allows one to imprint the entire pattern of director alignment in a single exposure, with a high spatial resolution of 1 μm. Besides high speed of production and high resolution, the advantage is that the same mask can be used repeatedly for multiple exposures with a steady long-term performance.
Most of the research on photoalignment emphasizes the geometrical features such as the direction of the easy axis, while studies on anchoring strength and its dependence on the conditions of substrate preparation are less common. Previous reports on surface anchoring coefficients characterizing the photoalignment technique have dealt with a uniform alignment of liquid crystals, (see for example [29][30][31][32][33][34]). However, the anchoring strength established in a patterned director field is not necessarily the same as in a cell with a uniform director, one of the reasons being the difference in photomasks. In this work, we present the experimental study of the in-plane (azimuthal) surface anchoring coefficient in spatially-varying director patterns produced by the PMM technique. A key question is how strong this anchoring is and how its strength depends on the irradiation time. The measurements of are based on the recently proposed analysis of splitting defect cores of integer disclinations at patterned substrates [14]. The experimental cells are of a sandwich type with both substrates photoaligned through the same PMMs to form surface director patterns in the form of square lattices of alternating +1 and −1 disclinations. The cells are very thin, in the order of 1 μm, to assist the bulk director to remain parallel to the bounding plates. If the azimuthal anchoring were infinitely strong, these patterns would preserve the imposed director field with well-defined +1 and −1 core regions. However, when the surface anchoring is finite, the pre-patterned defects' cores split into pairs of ±1/2 defects for energetic reasons. The value of is deduced by measuring the separation distance between the split ±1/2 defect cores.
Cell Preparation
We used clean indium tin oxide (ITO) coated glass plates as cell substrates. A solution of 0.5 wt% azo-dye Brilliant Yellow (BY), Figure 1a, in dimethylformamide (DMF) (both purchased from Sigma Aldrich) was spin-coated onto the glass substrates. The coated substrates were baked on a hotplate at 80 °C for 30 min. The preparation was performed inside a glovebox with the humidity level controlled to be at 20%. The cells were sealed using epoxy glue NOA 65 without any spacers to achieve the thickness of around 1 μm. The cell thickness, h, was measured by an interferometric technique using a UV/VIS spectrometer, Lambda 18 (Perkin Elmer). The separation distance of half-strength defect cores, , depends on the photopatterning time duration and the thickness ℎ of the nematic layer. It was expected that d might be a function of the cell thickness h; in particular, in very thick samples, h >> d, such as cylindrical capillaries, the escape into the third dimension is a preferred equilibrium state [35,36]. Even when the integer strength line splits into two half-integer lines, their elastic interactions might yield curved shapes, which would be detrimental for the surface anchoring measurements. To avoid these effects, the experiments were designed with very thin cells, (0.9-1.3) μm. In thin samples, one would expect the core splitting as a prevailing director structure [37]. To verify whether d depends on h, different thin cells were explored. In weakly anchored cells (irradiation time 2 min), the value of d remained constant (10.9 ± 0.1) μm in the cells with ℎ = 1.39 and 4.04 μm. For irradiation time 6 min, = (5.2 ± 0.2) μm for the three cells of thicknesses ℎ = 1.12, 1.15, and 1.22 μm. We conclude that the data on collected for cells of the thickness less than 1.3 μm are not affected by h and thus can be used for the determination of .
Photopatterning Method
The director field was patterned using the PMM technique [26]. A PMM represents a 150 nm thick Al film with an array of nanoslits, each of a length 220 nm and width 100 nm. The nanoslits are arranged in the form of square lattices with long axes forming +1 and −1 defects (Figure 2a). An unpolarized light beam passing through the nanoslit becomes polarized along the short axis of the local aperture. When the optical pattern with spatially-varying linear polarization of light irradiates the azobenzene layers on the inner surfaces of the cell, it aligns the BY molecules perpendicular to the local polarization of the impinging light. In other words, the molecules align parallel to the long axes of the nanoslits, and the desired surface director pattern of the azobenzene layer reproduces the pattern of nanoslits. A nematic in contact with the patterned azo-dye layer acquires the same molecular orientation pattern with the director being tangential to the interface. We used a light source EXFO X-Cite with a spectral range of (320-750) nm to irradiate empty cells formed by two parallel glass plates with inner BY coatings. The plates acquired the same alignment pattern as the pattern of nanoslits in PPM, enlarged by a factor of 10 by a pair of objectives [26], Figure 2a,b. The light beam propagated along the normal to both the PMM and the cell, and the intensity is ~ 7.1 × 10 Wm at the location of the cell. The distance between +1 and −1defects in the cells was 200 μm, which assured that the splitting distance of defects, which was on the order of 10 μm or less in the experiments, was not influenced by the proximity of other defects.
Two periodic square lattices of defects with strength +1 and −1 were designed, with the director field written using a superposition rule as = n , n , 0 = [cos φ, sin φ, 0], where φ = ∑ ∑ (−1) arctan ( ) + , x and y are Cartesian coordinates, p and q are the numbers of defects in rows and columns, respectively, = = 10; = = 200 μm was the distance between the defects along the x and y directions, respectively, and the phase defines the prevailing director deformation, splay or bend, around the +1 defects. Two types of lattices were used. In the first, which we call a radial array, = 0, the director field around the cores of +1 defects was radial, experiencing mostly splay. In the second pattern, called a circular array, the director around +1 defect was circular, = /2, with a prevalent bend.
Nematic Material
The cells with photopatterned substrates were filled by capillary action with 4-butyl-4-heptyl-bicyclohexyl-4-carbononitrile (CCN-47), Figure 1b, in the isotropic state at the temperature 64 °C. The material showed the following phase diagram upon heating: Smectic A 29.9 °C Nematic 58.5 °C Isotropic. After the cells were filled, they were kept at 45 °C for the duration of the experiments.
The nematic phase of CCN-47 was chosen because of the following two reasons. First, at 45 °C, the elastic constants of splay and of bend of CCN-47 are equal, = = = 8 pN [38], which allows one to use the superposition rule for the director field and to analyze the elastic properties of the patterns in the so-called one-constant approximation [1]. Second, CCN-47 is of a negative dielectric anisotropy, ∆ = ∥ − = −4.2, where ∥ and are dielectric permittivities parallel and perpendicular to the director, respectively. An AC electric field (frequency 4 kHz) applied across the cell using the top and bottom transparent ITO electrodes stabilized the director patterns in the plane parallel to the bounding plates, thus preventing [37] the potential escape of the ±1 defects into the third dimension [35][36][37].
A full-wavelength (530 nm) optical compensator helped to reconstruct the director field in the nematic cells, Figure 2c. The regions in which the director was parallel to the slow axis of the compensator acquired a blue interference color. When the director was perpendicular to the slow axis, that area appeared yellow. The left defect in Figure 2c was a +1 radial defect, while the right one was a −1defect.
Cell preparation, photopatterning, filling with CCN47, and imaging were done on the same day to prevent any aging effect. It was expected that the temperature [39] and humidity [40] during the sample preparation and irradiation would affect the values of W. W would also be a function of temperature after the cell is assembled [41]. To avoid these effects, all experiments were performed at fixed conditions. Humidity and temperature were kept at 20% and 22-23 °C respectively, until the cells were filled with the nematic CCN-47. During the measurements of W, the cells' temperature was fixed at 45 °C.
Optical Retardance of the Patterns
For accurate determination of the director alignment and splitting distance we used Exicor MicroImager (Hinds Instruments, Inc.) mapping of optical phase retardation. For the director in the plane of the cell, the optical phase retardance is = ( − )ℎ, where = 1.50 and = 1.47 are the extraordinary and ordinary refractive indices of CCN-47 at 45 °C, respectively. The expected retardance for 1 μm cell is thus = 30 nm. The defect cores show a steep decrease in retardation.
Results
The ±1 defects in the observed textures clearly split into pairs of ±½ defects, Figures 2b,c, 3, and 4. The split distance was determined as the distance between the minima of the optical retardance, Figure 3a. To verify whether the director remained mainly in plane, we monitored how the phase retardance of the cell changes in the presence of the electric field applied along the -axis normal to the cell. Neither the optical retardance ΔΓ, Figure 3b, nor d, Figure 3c changed when the electric field was applied. The result verifies that the director was confined in the plane of the cell and showed no significant escape into the third dimension: since ∆ < 0, a significant escape would lead to an increase of ΔΓ when the field is applied, which was not observed. The separation distance between the ±½ defect cores was measured as the distance between the minima in the optical retardance maps, Figure 3a, and the polarizing optical microscopy (POM) images of the patterns, Figures 2b,c and 4. The POM images were analyzed using the open-source software package Fiji/ImageJ. The distance d was calculated by averaging the data measured for all 50 defects of the same sign in the array. The error for d value was calculated as the standard deviation [42]. The separation distance between the ±1/2 defects was more significant for smaller irradiation times, Figure 4. The behavior was consistent with the expectation that a shorter exposure yields a weaker azimuthal anchoring and thus a wider splitting. We have deliberately chosen the regime of relatively weak surface anchoring, in which is larger than about 5 μm and thus could be measured accurately by optical microscopy, Figures 3 and 4.
The measured could be used to determine the in-plane anchoring coefficient, since it is determined by the balance of elastic repulsive force, , of two half-integer defects, and surface anchoring force, that tends to keep a single ±1 core as specified by the photopatterning. The energy per unit length of a planar disclination with the director normal to the line is proportional to , where is the strength of the defect, thus a = ±1 defects are of a higher elastic energy than a pair of half-integer defects [1]. Two defects of the same repel each other elastically, with the force = − = ℎ/2 , where = ln , ℎ is the thickness of the cell, and is the radius of the disclination core [1,14]. The surface anchoring energy can be found by integrating the Rapini-Papoular potential, ≈ 0.184 is a numerical coefficient; ( ) is the complete elliptic integral of the second kind [14].
Therefore, the surface anchoring force that tends to keep the half-integer defects as a single core is = − = −2 . At the balance point, + = 0 , which leads to the expression for the azimuthal anchoring coefficient, = ( ℎ)/ (4 ). With the known = 8 pN, = 0.184 and measured ℎ, , we found as a function of irradiation time, Figure 5b.
The surface anchoring grew stronger as the photopatterning time increased (Figure 5b). For irradiation times below 1 hr, increased linearly with . The least squares fit of the experimental data in Figure 5b yields = + , where = 0.035 × 10 Jm min , and = 0.27 × 10 Jm . A non-vanishing value of could be associated with the residual surface anchoring at the BY layer that was not photopatterned, for example, because of the local orientational order of a polydomain type. As demonstrated by Clark [43], local interactions are capable of producing local "easy" axis that remains in place even after the nematic is heated to the isotropic phase and then cooled down.
Conclusions
Most of the existing techniques to measure the azimuthal surface anchoring energy are applicable to surfaces with unidirectional alignment [44][45][46][47][48][49][50]. In this work, we demonstrate a method to measure the azimuthal anchoring coefficient of a nematic with a patterned director field. The method is based on the idea that the integer-strength disclinations split into half-integer disclinations and the resulting separation depends on the elastic and in-plane anchoring forces. The approach is valid when the director remains parallel to the bounding plates. A mechanism competing with the defect core splitting is the escape into the third dimension [35][36][37], in which the director realigns parallel to the disclination, thus removing the singular core. The competing tendencies were analyzed by Chiccoli et al. [37]. The escaped configuration was found to be energetically more stable than the planar singular disclination at cell thicknesses exciding some critical value, ℎ > ℎ , estimated to be submicron, ℎ = (0.2 − 0.5)μm. In an apparent contradiction, our experiments, including those with the applied electric field, did not show the escape in thicker cells, ℎ = (1 − 4) μm. The discrepancy might be rooted in the fact that the model assumes isotropic singular cores of disclinations with the core energies of the integer and half-integer disclinations being equal. However, the core energy of half-integer disclinations might be reduced by biaxial modifications of the order parameter [51,52]. Such a biaxial core was observed experimentally for half-integer disclinations in lyotropic nematics [53]. Furthermore, the studied nematic CCN-47 showed an enhanced susceptibility to biaxial distortions in experiments with an applied electric field [54]. Therefore, one expects that in CCN-47 the escape into the third dimension does not occur in cells used to find . Since CCN-47 yields a supramicron value of ℎ , it should allow one to explore the transition between the splitting and escape in detail, especially because the splitting scenario can be enhanced by the applied electric field. These experiments are in progress.
We found that the azimuthal anchoring energy of a nematic liquid crystal on photoaligned azo-dye substrates increases with the light irradiation time : increased from 0.1 × 10 Jm to 2.2 × 10 Jm when increased from 0.5 min to 45 min. As already stated, we deliberately used weakly anchored substrates to measure the corresponding splitting distances and thus with a better accuracy. However, the resulting strength of anchoring turned out to be reasonably strong when compared to the available literature data. For example, Clare et al. [55] have reported for oligo-terminated selfassembled monolayers supported on obliquely deposited gold films in contact with the nematic 4-cyano-4′-pentylbiphenyl (5CB) to be in the range (1.4 − 5.5) × 10 Jm . The azimuthal anchoring coefficient at the interface of a rubbed polyimide PI2555 layer has been reported to be 44 × 10 Jm [56], and for a surface coated with polyisoprene or polystyrene to be smaller than 3 × 10 Jm [57,58]. Shen et al. [34] reported the azimuthal anchoring 0.2 × 10 Jm at a uniformly aligned photoalignment layer SD1.
The proposed technique to measure the azimuthal anchoring strength is conceptually simple and should allow one to expand it to the studies of the memory phenomenon described by Clark [43], to explore how W is affected by irradiation intensity, temperature, multiple cycles of photopatterning, phase transitions, thickness of the photoalignment layer, parameters of the PPMs and nanoslits in PPMs, substrate aging, etc. We use this opportunity to congratulate Prof. Noel A. Clark on the anniversary.
Data Availability Statement:
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. | 4,593.4 | 2021-06-11T00:00:00.000 | [
"Geology"
] |
The Citrus flavanone naringenin prolongs the lifespan in C. elegans and slows signs of brain aging in mice
Aging is one of the main risk factors for neurodegenerative disorders, which represent a global burden on healthcare systems. Therefore, identifying new strategies to slow the progression of brain aging is a compelling challenge. In this article
Introduction
Aging is a main risk factor for neurodegenerative disorders, which are associated with neurological deficits and impaired cognitive abilities.A chronic low-grade production of pro-inflammatory mediators and reactive oxygen species (ROS), termed ox-inflammation, has been identified as a major mechanism of aging.Indeed, ox-inflammation can alter cell function and metabolism, ultimately causing cell death (Santoro et al., 2020).In this context, the enzyme sirtuin 1 (SIRT1) and multiple downstream targets are crucial in the senescence process.SIRT1 plays a central role in the regulation of cellular homeostasis (Chen et al., 2020).Indeed, SIRT1 activates the antioxidant transcription factor Nrf2 (Xu et al., 2021), inhibits the nuclear translocation of the proinflammatory transcription factor NF-κB (Song et al., 2022), and activates the transcription factor forkhead box O-3 (FOXO3) (Bordbari et al., 2022) which is involved in stress resistance and metabolism (Morris et al., 2015).SIRT1 also regulates cellular energy metabolism and mitochondrial function through activation of AMP-activated protein kinase (AMPK) and peroxisome proliferator-activated receptor-gamma coactivator (PGC1-α) (Canto and Auwerx, 2009).Finally, SIRT1 reduces the expression of senescence-associated genes, such as p16, thus slowing down cellular senescence (Duan et al., 2022), extending lifespan and preventing the development of age-related diseases, including neurological disorders (Song et al., 2022;Razick et al., 2023).However, a progressive reduction of SIRT1 expression and activity has been reported during aging in several tissues (Testai et al., 2020;Xu et al., 2020).
In this context, many nutraceuticals have attracted great interest as they can reduce oxidative stress, improve cognitive abilities, prolong lifespan and promote healthspan in aged animals (Musillo et al., 2021).Among them, polyphenols have been largely studied for the antioxidant, anti-inflammatory and anti-senescence properties (Maria and Ingrid, 2017;Gurau et al., 2018), as well as for the ability to reduce some key components of senescence-associated secretory phenotype (SASP) (Maria and Ingrid, 2017).Resveratrol, but also the Citrus flavanone naringenin (NAR), are two of the most known polyphenols among SIRT1 activators (Borra et al., 2005;Testai et al., 2020).Several studies have demonstrated the preventive effects of NAR against cardiovascular and neurodegenerative disorders (Da Pozzo et al., 2017;Nouri et al., 2019;Piano et al., 2019;Testai et al., 2020;Kesh et al., 2021;Salman et al., 2022;Wang et al., 2023), as well as against the senescence process in the cardiovascular system (Da Pozzo et al., 2017;Testai et al., 2020;Wang et al., 2023).In the study by Testai and colleagues, daily treatment with the SIRT1 activator NAR significantly reduced oxidative stress, inflammation and fibrosis in the myocardium of aged mice (Testai et al., 2020).
In previous work, daily administration of bergamot juice, containing naringin (precursor of NAR), promoted antioxidant and anti-senescence effects in the myocardium of 12-month-old mice, potentially through increased expression of SIRT1 (Da Pozzo et al., 2018).However, other mechanisms could contribute to the potential effects of polyphenols against the aging process.The Citrus flavanone NAR led to the opening of large-conductance calcium-activated potassium channels in mitochondria (mitoBKCa) in young-adult and aged rats (Testai et al., 2017), while hesperetin prevented the senescence process through activation of the CISD2 gene in aged mice (Yeh et al., 2022) and reduction of oxidative stress in Saccharomyces cerevisiae (Guo et al., 2019;Xiao et al., 2023).Finally, several flavonoids have been shown to slow the progression of age-related neurodegenerative diseases through cholinesterase inhibition (Khan et al., 2018;Li et al., 2022).To this regard, NAR promoted positive effects on memory consolidation (Liaquat et al., 2018) and exhibited preventive effects against neurodegenerative processes (Ghofrani et al., 2015;Piano et al., 2019;Kesh et al., 2021;Piano et al., 2022;Salman et al., 2022).Also, an 8-week treatment with flavanone-rich orange juice provided benefits for cognitive function in healthy volunteers (Kean et al., 2015) while long-term dietary flavonoid intake was associated with a lower risk of cognitive decline in men and women (Yeh et al., 2021).Therefore, natural flavonoids could have a high translational potential in clinical practice for the prevention of age-related neurodegenerative diseases, but the molecular mechanisms should be better elucidated.
In this study, based on the promising results on the anti-senescence effects of the SIRT1 activator NAR in the mouse myocardium (Testai et al., 2020), we investigated the potential effects of NAR in slowing down the signs of brain aging in vivo.Many animal models are commonly used to study the potential anti-aging effects of new compounds and/or nutraceuticals, such as the nematode Caenorhabditis elegans (C.elegans) which has about 60-80 % genes with homologs in humans (Caldwell et al., 2020).In fact, many intracellular pathways participating in the onset and progression of age-related neurodegenerative disorders are conserved from C. elegans to mice and humans (Markaki and Tavernarakis, 2020).Recently, it was reported that lifespan timing can affect brain and cognitive functions (Walhovd et al., 2023).Therefore, we first evaluated the effects of daily treatment with NAR on lifespan and healthspan in the short-living nematode C. elegans.Then, we investigated the molecular mechanisms through which daily NAR supplementation could slow down the signs of brain aging in longlived vertebrates with human-like organs and systems (i.e., middle-aged mice) (Brunet, 2020).In particular, we focused on the SIRT1/Nrf2 axis and evaluated the effects of NAR on both mitochondrial function and expression of the senescence marker p16 and SASP-related markers interleukin (IL)-6 and IL-18 (Idda et al., 2020;Saul et al., 2022).
Experiments in C. elegans 2.1.1. C. elegans cultivation and treatment
Wildtype (N2) nematodes were kept at 20 • C on NGM plates supplemented with ampicillin (0.01%w/v) and tetracycline (0.0005%w/v).E. coli HT115 (L4440) was used as a food source.HT115 (L4440) was obtained from Ahringer C. elegans RNAi feeding library (Kamath and Ahringer, 2003) and grown in LB medium supplemented with ampicillin (0.01%w/v) and tetracycline (0.0005%w/v) at 37 • C overnight before spotting on NGM plates.NAR was solubilized in DMSO in a concentration 50-times higher than the final concentration.The compound was then spread on the NGM plates seeded with E. coli HT115 (L4440) to obtain the final desired concentration considering the final volume of the NGM plates.
Lifespan and healthspan
Lifespan and healthspan assays (movement) were carried out in three biological replicas (each with at least 60 animals).Age-synchronous populations of animals were recorded from egg-lay on NGM plates containing NAR 100-400 μM.The treatment with NAR was continued for the entire lifespan.Starting from 1-day-adulthood, the worms were transferred to fresh NGM plates every day (during the fertile period) or every other day (after the fertile period) and the numbers of dead, alive and censored animals were scored.Animals not moving, moving (spontaneously or upon prodding) and censored were scored for the healthspan analysis.Animals with internal hatching, an exploded vulva or which died desiccated on the wall were censored.Survival analysis of pooled populations was performed in OASIS 2 (Schiavi et al., 2015;Han et al., 2016).
Chronic treatment of mice in vivo
All procedures were performed in accordance with Italian (D.L. March 2014 n.26) legislation and European (EEC Directive 2010/63).The experimental protocols were reported as indicated by the ARRIVE guidelines (McGrath and Lilley, 2015).
Male 6-month-old C57BL/6J mice (ENVIGO, Italy) were housed in cages (3 mice per cage), and they had free access to food pellets and drinking water, at 22 • C.After the acclimation period, they were divided into two groups (12 mice per group): the first group was treated with NAR (100 mg/kg/day; Sigma-Aldrich, MO, USA) administered in drinking water, while the second one received vehicle (1 % DMSO; Sigma-Aldrich, MO, USA) for 6 months.The allocation of mice in both groups was random.During the whole treatment, water intake was daily monitored, and mice were weekly weighted.NAR was daily prepared by dissolving the powder in DMSO (40 mg/ml) and diluting in drinking water up to a final concentration of 0.4 mg/ml.The selected daily dosage of NAR (100 mg/kg) has been used in previous in vivo experiments, and it was not associated with toxic effects (Testai et al., 2017;Piano et al., 2019).At the end of the 6-month treatment, mice were anesthetized with urethane (30 % w/w, i.p.; Sigma-Aldrich, MO, USA) and quickly sacrificed by collecting blood from the heart; then, brains were taken and stored in liquid nitrogen for functional and biochemical analyses.Untreated 6-, 9-and 12-month-old mice (12 mice per group; mice per cage) represented controls and were used to assess the timecourse of: i) the enzymatic activity of citrate synthase and cytochrome C oxidase; ii) mRNA expression of Sirt1 and Nrf2 and their downstream targets, namely antioxidant (Ho-1, Foxo3), inflammatory (Il-6, Il-18) and anti-senescence (p16) genes.
Measurement of cytochrome C oxidase activity
The oxidation of cytochrome C by the enzyme cytochrome C oxidase (CcO) was detected with a spectrophotometric assay.Briefly, cytochrome C was reduced with a solution of 1,4-dithiothreitol (DTT; Sigma-Aldrich, MO, USA) 10 − 1 M for 15 min at room temperature (1:200).Reduction of cytochrome C appeared as a change in colour from dark red to light purple, and it was confirmed by measuring the ratio between λ = 550 nm and λ = 465 nm with a spectrophotometer (EnSpire; Perki-nElmer, MA, USA).Reduction was considered complete if the calculated ratio ranged from 10 to 20.Then, supernatants were diluted in Assay Buffer (composed by Tris HCl 10 mM and KCl 120 mM, pH 7.0) and reaction was initiated by adding reduced cytochrome C (1:6) in each well.Absorption was measured at 30 • C for 15 min with 30 s intervals (λ = 550 nm) with a microplate reader (EnSpire; PerkinElmer, MA, USA).CcO activity was calculated in brains of 4-6 animals per group by interpolating results with a calibration curve of standard CcO (Sigma-Aldrich, MO, USA) diluted in enzyme dilution buffer (Tris HCl 10 mM, sucrose 250 mM, pH 7.0).
Real-time RT-PCR
Brain tissues from 6-, 9-and 12-month-old untreated mice and 12month-old treated mice (3 mice per group) were lysed with Phenol/ Guanidine-Based QIAZol Lysis Buffer (Qiagen, Germany) and total RNA was extracted by using Rneasy Mini Kit® (Qiagen, Germany) following the manufacturer's protocol.RNA purity was assessed with NanoDrop™ Lite Spectrophotometer (Invitrogen, CA, USA).The cDNA was obtained by retro transcription from extracted RNA by using the iScript cDNA Synthesis Kit (Bio-Rad, CA, USA).50 ng of cDNA, 10 μl of SsoAdvanced Universal SYBR Green Supermix (Bio-Rad, CA, USA) and 300 nM each of the forward and reverse primers (Table 1) were used for Real-Time PCR Reaction.Steps temperatures were as following: 95 • C for 15 s (enzyme activation), 98 • C for 30 s (initial denaturation), and primer-specific annealing and extension temperatures for 30 s. Denaturation, annealing and extension phases were repeated for 40 cycles.GAPDH was used as the housekeeping gene to normalize Ct values. 2 − Δct method was used for a relative quantification of mRNA expression.
C. elegans experiments
C. elegans survival assays were performed in triplicate (each trial with at least 60 animals) if not differently specified.Statistical analysis of C. elegans in vivo treatments was executed using the log-rank test.The p-values were corrected for multiple comparisons using the Bonferroni method.Data were expressed as mean ± SEM (see Table in Fig. 1).
Mouse experiments
Each experiment was performed in triplicate in the brains of 3-6 animals per group (N = 3 for gene and protein analysis, N = 4-6 for measurement of CS and CcO activity).Statistical data analysis and graphical presentations were realized with GraphPad Prism® (Graph-Pad Software Inc., San Diego, CA, USA).Statistical analysis was performed by Mann-Whitney t-test for two-group analyses and with oneway analysis of variance (ANOVA) with Bonferroni's corrected test for analyses with three or more groups.A p-value < 0.05 was considered statistically significant.Data were expressed as mean ± SEM.
NAR displays anti-aging properties in vivo in C. elegans
To evaluate the potential anti-aging effect of NAR in vivo, we first used the nematode C. elegans, a powerful 3R-compliant model organism for aging and intervention studies.Dose-response analysis was initially carried out to select the optimal concentration of NAR (data not shown).
Despite having a mild effect, NAR 100 μM consistently showed the highest anti-aging efficacy, since it significantly extended C. elegans lifespan (Fig. 1A).Of note, given that parameters associated with animals' health during aging (healthspan), such as neuromuscular features (e.g.motility or sensory functions) or resistance to stressors, have been shown in C. elegans to correlate with lifespan in a context-dependent manner (Maglioni et al., 2014;Banse et al., 2024), we also analyzed the effect of NAR on animals' ability to move during aging.Consistent with the effect on lifespan, 100 μM NAR also mildly but significantly promoted animals' healthspan (movement ability, Fig. 1B).
NAR enhances CS ad CcO activities in the brain of middle-aged mice
Based on the promising effects observed in the nematode C. elegans, the potential anti-aging properties of NAR were then investigated in longer-lived animals, i.e. middle-aged mice.No systemic toxicity was evident in mice during the 6-month treatment with NAR (100 mg/kg/ day) (data not shown).Then, a preliminary mechanistic investigation of NAR was performed, evaluating the effects on the activity of two key enzymes of cellular metabolism (i.e., CS and CcO) in the brains of middle-aged mice.
CS is a well-recognized marker of the mitochondrial metabolism, whose activity is reported to decrease during aging (Brys et al., 2010;Pellegrini et al., 2020;Testai et al., 2020;Yan et al., 2021).A similar trend was observed in our experimental conditions; indeed, CS activity in brains from 12-month-old mice was about halved than that from 6month-old mice.More in detail, CS activity in the brain tissue was 118.1 ± 18.7 mU/ml in 6-month-old mice, 117.3 ± 18.1 in 9-month-old mice, and 66.0 ± 8.7 mU/ml in 12-month-old mice.Interestingly, CS activity in brains from mice daily receiving NAR for 6 months was significantly higher (117.9 ± 9.5 mU/ml) compared to that of 12month-old mice treated with vehicle, and almost superimposable with that of 6-month-old mice (P = 0.049, F(3,14) = 3.314, DF = 17) (Fig. 2A).
CcO is a mitochondrial enzyme whose activity decrease during aging (Curti et al., 1990;Paradies et al., 1993).CcO activity showed an age-dependent decline also in our study, being 568.3 ± 45.5 mU/ml in 6month-old mice, 445.7 ± 61.8 mU/ml in 9-month-old mice, and 346.7 ± 48.2 mU/ml in 12-month-old mice.As previously observed for CS, also CcO activity was significantly lower (about 50.0 %) in brains from 12-month-old mice compared to that of 6-month-old mice.Conversely, brains from 12-month-old mice receiving NAR for 6 months showed a CcO activity (574.7 ± 57.8 mU/ml) significantly higher if compared with controls of the same age.Once again, this value was almost superimposable with that measured in younger controls (P = 0.0324, F (3,16) = 3.755, DF = 19) (Fig. 2B).
NAR increases the expression of antioxidant response-related genes and proteins in the brain of middle-aged mice
Given NAR promising effects on mitochondrial activity in the brain of middle-aged mice, a time course of transcriptional levels of genes involved in the antioxidant response was performed and the effects of NAR on their mRNA expression were evaluated.In particular, the Sirt1 and Nrf2 pathways were investigated.Indeed, it has been shown that SIRT1 counteracts increased ROS levels by regulating the mitochondrial electrons transport chain (Guo et al., 2014;Wan and Garg, 2021) and promotes Nrf2 transcription, thus exerting an antioxidant effect (Shah et al., 2017).
The results of the time-course transcriptional analysis revealed that NAR treatment increases mRNA expression of genes that showed an agerelated decrease in mRNA levels (Sirt1 and Foxo-3) or, in general, with lower mRNA levels in untreated mice (Nrf2 and Ho-1).For this reason, focusing on groups of mice fed with NAR compared with the untreated 12-month-old mice, protein analysis by Western Blot was performed to confirm the antioxidant effects of the NAR-supplemented diet in 12month-old mice.
Discussion
The increase in life expectancy raised the number of people over 60 and, then, of age-related pathologies, such as metabolic, cardiovascular and neurodegenerative disorders, making aging an important issue worldwide (Franceschi et al., 2018).Many studies have shown that healthy aging is the result of multiple factors, including genetics (or not modifiable) and environmental ones (or modifiable); to this regard, nutrition can represent a powerful strategy for modulating the aging process (Leitao et al., 2022).
In this study, we investigated the potential anti-aging activity of the Citrus flavanone NAR in both invertebrates (C.elegans) and vertebrates (mice).In the short-lived, 3R-compliant model (Brunet, 2020), we observed that daily treatment with 100 μM NAR significantly promoted lifespan and healthspan.Then, we investigated the possible effects of NAR in slowing the aging process in the brain of middle-aged mice to give more clinical translatability to our findings, since mice are longlived vertebrates with human-like organs and systems (Brunet, 2020).6-month-old mice were treated for 6 months with NAR (100 mg/kg/day) to simulate a nutraceutical intervention in middle-aged people.No signs of toxicity were highlighted during the treatment, as the intake of water and food did not change during the experimental protocol and the body weight gain was comparable to that of control and in line with a physiological increase (data not shown).As previously reported (Curti et al., 1990;Paradies et al., 1993;Brys et al., 2010;Pellegrini et al., 2020; E. Piragine et al.Testai et al., 2020;Yan et al., 2021), CS and CcO activities showed an age-dependent decline; in the brains of 12-month-old mice their activity was almost halved compared to that of young animals.Interestingly, NAR supplementation prevented this trend, suggesting its ability to preserve mitochondrial function and integrity, potentially ensuring adequate energy production for the cell.The mechanisms underlying these NAR-mediated protective effects may be related to those previously demonstrated in the myocardium of senescent animals (Testai et al., 2020).Therefore, we hypothesized that activation of SIRT1 enzyme may play a crucial, but not exclusive, role also in this tissue.Based on this idea, we measured mRNA expression of Sirt1, and downstream genes closely related to Sirt1 (i.e., Nrf2, Ho-1 and Foxo3).We observed a marked decline in the expression of these hallmarks of aging; on the contrary, these levels were significantly increased in the brains of NAR-treated animals.Of note, these transcriptional factors are known to be involved in the antioxidant defences of cells (Li et al., 2014).In agreement with the mRNA results, the protein assessment conducted on brain homogenates, by western blot method, confirmed the increasing trends, both for SIRT1 and for the proteins involved in the antioxidant response, namely Nrf2 and PGC1-α.Indeed, Nrf2 is an evolutionary conserved redox transcription factor, which plays a central role in the modulation of antioxidant responses and has been shown to be involved in the aging process in the nematode C. elegans (Blackwell et al., 2015;Tullet et al., 2017).PGC1-α is instead a transcription coactivator, also known to regulate the aging process in C. elegans (Corton and Brown-Borg, 2005).In particular, it regulates cellular energy metabolism by promoting the mitochondrial biogenesis and modulating both carbohydrate and lipid metabolism (Liang and Ward, 2006).
Therefore, these results agree with our previous findings and suggest a possible contribution of SIRT1 in the anti-aging effects of NAR in the brain.Indeed, SIRT1, regulates several pathophysiological processes, such as senescence and antioxidant response, through the deacetylation of different transcriptional factors or proteins (Chung et al., 2010;Grabowska et al., 2017).SIRT1 activates the FOXO3 pathway to reduce oxidative stress (Kops et al., 2002), as well as the expression of PGC1-α, which is involved in mitochondrial biogenesis and protection from mitochondrial dysfunction (Lin et al., 2004;St-Pierre et al., 2006) that occurs during aging, as confirmed by our data on CS and CcO.Finally, coactivation of Nrf2 promoting mRNA expression of its target gene Ho-1, confirms that NAR increases the antioxidant defence in cells.
Given the increased levels of proteins involved in the antioxidant response, we decided to study the anti-senescence effects of NAR treatment on p16, whose upregulation is involved in cell cycle arrest and, therefore, cellular senescence (Zindy et al., 1997;Krishnamurthy et al., 2004).Through a p16-mediated manner, senescent cells develop a SASP, which is characterized by increased mRNA expression of critical pro-inflammatory cytokines capable of establishing and worsening the chronic inflammation typical of aging and age-related functional alterations, including cognitive decline and shortened lifespan (Saul et al., 2022).The results on the mRNA expression of the senescence marker p16 and of the SASP-related proteins IL-6 and IL-18 seem to confirm the anti-senescence effects of the Citrus flavanone NAR, which can potentially prevent the p16-dependent cell cycle arrest and the release of the cytokines IL-6 and IL-18, whose levels are increased in senescent cells (Saul et al., 2022).
To the best of our knowledge, this is the first study aimed at evaluating the potential effects of chronic treatment with the SIRT1-activator NAR in preventing "physiological" brain aging rather than specific neurodegenerative diseases.Our data provide new evidence on the effects of NAR on lifespan and healthspan in C. elegans, previously reported only for the precursor glycoside-conjugated naringin (Zhu et al., 2020).Furthermore, our results not only confirm the neuroprotective effects shown by NAR in animal models of neurodegenerative diseases (Zbarsky et al., 2005;Ghofrani et al., 2015;Nouri et al., 2019;Salman et al., 2022) but also describe additional mechanisms of action (i.e., improved mitochondrial function and increased expression of Sirt1, Foxo3 and p16 genes) in the brain of middle-aged, healthy mice.Therefore, our findings open new perspectives in the prevention of agerelated cognitive decline and reduced neuronal function, which are prodromal to the development of neurodegenerative disorders in older adults.
Conclusions
Our results demonstrate that daily treatment with NAR prolongs the lifespan and improves the healthspan in short-lived nematodes (C.elegans).In long-lived animals (mice), dietary supplementation with NAR promotes the activity of enzymes involved in cellular metabolism (CS and CcO), prevents the age-dependent decrease of Sirt1 and Foxo3 mRNA expression, and improves that of Nrf2 and Ho-1 in the brain of middle-aged mice.Consistently, NAR treatment increases SIRT1, NRF2 and PGC1-α protein levels and restores mRNA expression of the senescence marker p16 and the pro-inflammatory genes Il-6 and Il-18.In conclusion, daily supplementation with NAR could represent a potential nutraceutical approach to slow the signs of brain aging and prevent the decline in neuronal and metabolic plasticity that occurs during aging.Indeed, from a translational point of view, this work focused on middleaged mice to mimic "preventive" NAR supplementation in young-adult people, aimed at slowing the first signs of cognitive decline and neuronal deterioration.Therefore, studying the effects of NAR administration in aged mice for a shorter period, when neuronal and metabolic plasticity are already compromised, could represent a future direction of our work.Furthermore, studies evaluating functional parameters and behavioural patterns in mouse models of brain aging are also needed to confirm our findings.
Fig. 1 .
Fig. 1.NAR promotes lifespan (A) and healthspan (B) extension in the nematode C. elegans.Mantel-cox survival analysis of wild-type animals treated with vehicle (DMSO) or NAR 100 μM.C. elegans assays were performed in triplicate (each trial with at least 60 animals).Abbreviations: SEM: standard error of the mean; CI: confidence interval.
Fig. 2 .
Fig. 2. NAR increases the activity of metabolic enzymes and the mRNA expression of antioxidant genes in the brain.Histograms show the CS activity (A) and the CcO activity (B), expressed in mU/ml, in the brain of animals of different ages (6-, 9-and 12-month-old) and of 12-month-old mice daily treated for 6 months with NAR (100 mg/kg) (N = 4-6 for each group).Histograms (C-F) show the mRNA expression of Sirt1, Foxo3, Nrf2 and Ho-1 in the brain of animals of different ages (6-, 9-and 12-month-old) and of 12-month-old mice daily treated for 6 months with NAR (100 mg/kg).Each bar represents the mean ± SEM (N = 3 for each group) (* significant vs 12-month-old; * p < 0.05; ** p < 0.01¸ *** p < 0.001).
Table 1
Sequences, annealing temperature and product amplicon size of primers used in RT-PCR. | 5,488 | 2024-06-17T00:00:00.000 | [
"Medicine",
"Biology",
"Environmental Science"
] |
Mechanism Research of Arch Dam Abutment Forces during Overload
This paper presents research on the abutment forces of a double-curvature arch damduring overload based onnumerical calculation results obtained through finite element method by Ansys. Results show that, with an increase in elevation, the abutment forces and bending moment of the arch dam increase first and then decrease from the bottom to the top of the dam. Abutment forces and bendingmoment reach theirmaximum at themiddle ormiddle-down portion of the dam.The distributions of abutment forces and moment do not change during overload.The magnitude of each arch layer’s forces and moment increases linearly during overload. This result indicates that each arch layer transmits bearing loads to the rocks of the left and right banks steadily. This research explains the operating mechanism of an arch dam under normal and overload conditions. It provides a simple method to calculate the distribution of forces F x and F y and a new method to calculate the overload factor of an arch dam through the estimation of arch layers based on the redistribution characteristic of arch abutment forces.
Introduction
The development of arch dams has a long history that dates back to 1st century BC [1].Relative uniformity was achieved in the 20th century after several designs and techniques were developed.The first known arch dam, Glanum Dam, was built by the Romans in France [2].Arch dam is a type of dam curved in the shape of an arch, with the top of the arch pointing back into the reservoir.Thus, the force of the water against it, known as hydrostatic pressure, presses against the arch.An arch dam is most suitable for narrow gorges with stable rocks.Considering that arch dams are thinner than any other dam type, they require much less construction materials, which make them economical and practical in remote areas.Arch dams are built all over the world because they are safe and involve minimal cost [3].China has the most number of arch dams [4].Many numerical methods are currently applied to the analysis of the structure of arch dams.Some examples of these methods are finite element method [5][6][7], discrete element method [8,9], block element method [10,11], discontinuous deformation analysis [12], fast Lagrange analysis of continua [13], and interface element method [14].Self-adapt element [15][16][17], meshless [18], and extended finite element methods [19][20][21] are utilized to simulate the development of cracks in the structure analysis of arch dams.The arch dam is a highly statically indeterminate structure.Through an arching action, arch layers transmit upstream water pressure to bank rocks on two sides.Arch layers play an important role in the safe operation of such dams, which transfers the loads to two banks.It makes large areas of arch dam body under compression through arch layer.This type of structure can make full use of compression strength of concrete.Limit equilibrium method is usually employed in the safety evaluation of arch dams [22,23].Little attention is paid to abutment forces in arch dam safety analysis.The mechanical characteristics of a structure can be determined through research on arch abutment forces during overload.It shows that thrust angles at different elevations increase during overload through abutments force analysis [24,25].Studying abutment force would thus provide a comprehensive understanding of the overload mechanism of arch dams.
Concrete Cracking Simulation of Arch Dam during Overload [26]
2.1.Concrete Cracking Mode.Before the failure of concrete under tensile condition, a linear relationship exists between stress and strain.The stiffness matrix is where is Young's modulus for concrete and ] is Poisson's ratio for concrete.
The following conditions apply to cracks in one direction only.
If principal stress in one direction is greater than the failure tensile stress, tensile failure occurs.After developing cracks, the concrete becomes an orthotropic material.Given that the stiffness and shear stiffness reduce the normal plane, the stress-strain matrix will change.After the destruction of the concrete, the presence of a crack at an integration point is represented through modification of the stress-strain relations by introducing a plane of weakness in a direction normal to the crack face.A shear transfer coefficient is introduced to represent a shear strength reduction factor for subsequent loads that induce sliding (shear) across the crack face.The stress-strain relationship is built in the direction of the failure surface and the direction perpendicular to it.When principal stress is greater than the tensile breaking stress in only one direction, the stress and strain of the new matrix are where the superscript signifies that the stress-strain relations refer to a coordinate system parallel to principal stress directions with the axis perpendicular to the crack face. works with adaptive descent and diminishes to 0.0 as the solution converges.
In Figure 1, is uniaxial tensile cracking stress and is the multiplier for the amount of tensile stress relaxation.
If the crack closes, then all compressive stresses normal to the crack plane are transmitted across the crack.Only shear transfer coefficient for a closed crack is introduced.[ ] can then be expressed as The stress-strain relations for concrete that has cracked in two directions are If both directions reclose The stress-strain relations for concrete that has cracked in all three directions are If the crack is closed again in three directions, formula (5) will be selected. and values have the following relationship: 1 > > > 0. (7)
Distinguishing between Crack Opening and Closing.
The open or closed status of integration point cracking is based on strain value , which is called the crack strain.For the case of a possible crack in the direction, this strain is evaluated as where , , are three normal component strains in crack orientation.
Vector { } is computed by where { } is modified total strain (in element coordinates).{ } is defined as where is the substep number, { el −1 } is the elastic strain from the previous substep, {Δ } is the total strain increment (based on {Δ }, the displacement increment over the substep), {Δ th } is the thermal strain increment, and {Δ pl } is the plastic strain increment.
If is less than zero, the associated crack is assumed to be closed.
If is greater than or equal to zero, the associated crack is assumed to be open.When cracking first occurs at an integration point, the crack is assumed to be open for the next iteration.
Numerical Model and Parameters
Many constitutive models of concrete exist at present.In 3D finite element numerical calculations, the most preferred model is D-P criterion mainly because model parameters can be easily obtained with this model.D-P criterion has a smooth yield surface and is easy to use.This model can be easily utilized in elastic-plastic analyses for concrete and other materials with similar properties.The Drucker-Prager yield function is where and are material parameters, 1 is the first invariant of the stress tensor, and 2 is the partial stress tensor for the second invariant.They can be calculated as where 2. The -axis positive direction of the model is along the right banks.The positive direction of -axis is downstream along the river, and the positive direction of -axis is along the dam's increasing height.The range of the numerical model is as follows: 230 m width on the two sides, 270 m depth under the riverbed, 150 m length upstream, and 360 m length downstream.The bottom of the numerical model is subjected to a three-direction constraint, the boundary of the left and right banks is subjected to an direction constraint, and the boundary of the upstream and downstream is subjected to a direction constraint.The model has 28,296 elements and 33,830 nodes in total.It will take much more time in numerical calculation with the elastic damage model for computer.So this model is used only in elements of dam body, the elastic-plastic model is used in other parts elements.
Parameters and Loads.
The loads of each case include water pressure, temperature load, and dam gravity.The overload process was implemented by gradually adjusting the density of water and keeping the water level and other loads unchanged.Overload factor is defined as = / 0 , where is the current water density of the dam and 0 is the normal water density.In Case 1, the value of water density is 9.8 kg/m 3 .In Case 2, the magnitude of water density is twice the normal value (19.6 kg/m 3 ) and so on.The relevant parameters are listed in Table 1.
Calculation Results
The abutment forces were obtained through the integration of abutment element nodes.The directions of abutment forces are similar to those in the coordination of the numerical model.The direction of the bending moment complies with the right-hand rule.The following is an analysis of abutment , , and bending moment.Abutment forces , and bending moment are discussed under normal loads and overloads separately.To express the results clearly, analysis is first performed on the distribution characteristic of abutment forces , and bending moment under normal loads.Then, the abutment forces changing rule during overload are discussed.A simple method is then provided to determine the distribution of abutment forces and .Arch layers 1 to 8 are arch layers from the bottom to the top of the dam.The calculated cases are shown below.The finial failure pattern is shown in Figure 3. 2).
Case 2. It is as follows: 2 times water load + gravity + temperature load (Table 3).
Case 3. It is as follows: 3 times water load + gravity + temperature load (Table 4).
Case 4. It is as follows: 4 times water load + gravity + temperature load (Table 5).
Distribution of Abutment Forces under Normal Loads.
The abutment force of (Figure 4) increases gradually from the bottom to the middle of the dam as the elevation increases.It reaches the maximum at the middle and then decreases from the middle to the top of the arch dam.The maximum of is at approximately 80 m of the height of the dam.The left and right banks are symmetrical because of the symmetry of the dam body shape.
With regard to the distribution of force , force gradually increases as elevation increases; the maximum is reached at the middle-down portion of the arch dam (about 60 m high, Figure 5).The left and right banks are almost similar because of the symmetry of the arch dam.The distribution of and has a similar feature to that from [24,25].The relation between bending moment and increasing elevation is similar to that in .The only difference is that the maximum bending moment is at approximately 100 m of the dam height (Figure 6).The abutment bending moment of the left and right banks is also symmetrical.The results of abutment forces show that the arch dam transmits loads to rocks on the two sides through an arching action.Most of the loads are transferred to the rocks in the middle and downside of the two banks.The rocks in this location have an important function in the safety of the arch dam.Bending moment is calculated by force multiplied with distance.Compared with distance, the magnitude of force is much larger; thus, the distribution of bending moment mainly reflects the feature of force.Such is the reason why bending moment (Figure 6) appears somewhat similar to abutment force (Figure 4).
Abutment 𝐹 𝑥 and 𝐹 𝑦 and Bending Moment of Each Arch
Layer during Overload.The above calculation and analysis are results of the arch dam being subjected to normal loads.The following presents the results during overload.Analysis of the arch dam during overload would improve the understanding of the overloading mechanism of the arch dam.The feature of each arch layer during overload is shown (Figures 7, 8, and 9).The line of each arch layer during overload is straight (Figure 7). is the force that dam abutment applies on the left and right bank rocks.Each arch layer transfers the excess loads to the rocks in the valley.This condition can explain why arch dams usually have a comparatively high tolerance for overloading.The arch plays a key role in overload transfer.In Figures 7, 8, and 9, the axis is the overload factor.The overload process ensues by gradually adjusting the density of water and keeping the water level and other loads unchanged.The gradient of the lines signifies the transfer coefficient of each arch layer and shows the capacity of an arch layer to transmit overloads to bank rocks.As shown in Figures 7 to 9, the line of each arch layer is straight; thus, the transfer coefficient is a constant.Arch layer 4 has the largest coefficient followed by arch layers 3, 5, 2, 6, 7, 1, and 8.The arch layer of the middle and lower portions of the dam has a large transfer capacity because the middle and lower arch layers have a large central angle and suitable arc length.The rule for force during overload is similar to that for (Figure 8).For , arch layer 3 has the largest coefficient followed by arch layers 2, 4, 5, 1, 6, 7, and 8.For bending moment, the size of the transfer coefficient (from large to small) is 4, 5, 3, 6, 2, 7, 1, and 8.
The arch layers located in top and bottom portions of arch dam usually have a smaller transfer coefficient, and the arc lengths of these arch layers are either too long or too short.The axes of these arch layers are approximately straight lines, which goes against the role that an arch layer is playing.Arch layers located in the middle and lower portions of arch dam have relatively suitable arc length and central angle, which make them have a larger transfer coefficient.The central angle of arch layer is mainly affecting the magnitude of and .Engineers usually hope that arch dam can transfer loads to two banks as much as possible and a larger transfer coefficient of arch layer is always preferred.Therefore, much attention should be specially paid to the determination of arc length and central angel of each arch layer during its designing process.to that of the right bank.The distribution of , , and bending moment does not change in different cases.The different abutment forces increase linearly under conditions of overload.Once the distribution of abutment forces in the normal case is determined, the distribution in different overload cases can also be determined.The unchanged distribution provides a good suggestion to arch dam designs.Engineers can modify the arch dam shape according to the distribution of abutment forces.The arch should not transmit a large force to weak rocks in a valley.The distribution also helps evaluate the abutment stability of arch dams.Abutment forces differ at different elevations.For an arch layer with larger abutment forces, more abutment forces are required during overload; hence, the rock mass at this location should be stable (Figures 10 and 11).
Simple Method to Determine the Distribution of Abutment Forces.
Unchanged distribution is helpful to arch dam designers.The use of finite element method in the calculation is inconvenient and complex.For convenience, a simple method is necessary.Vertical force contributes little to the distribution of abutment forces because and are horizontal forces.Temperature load is much smaller than water load.Thus, the main factor that affects abutment force distribution is water load.Arch layers differ in terms of the length of the arch, magnitude of water load, height of the arch, and central angle.The first three factors affect the magnitude of force on the upstream face, and the last one affects the value where 1 and 2 are the water pressure of the upstream face, 1 and 2 are arch layer length, ℎ is arch layer height, and is the central angle of an arch layer.All parameters are shown in Figure 13. and distributions were obtained with the simple method (Table 8).The results are shown in Figures 14 and 15.The distribution is similar to that obtained with finite element method.
The above mentioned method is an approximate means to calculate and ; the absolute magnitudes of and are different from that obtained from finite element method.The simple method mainly aims to determine the distribution characteristic.To compare the accuracy of results obtained from the simple method and those from finite element method, each result of the two methods is utilized to divide the maximum value obtained through the two methods.The results are shown in Figures 16 and 17.The results of the simple method are consistent with those of finite element method.
Discussions
The distribution of abutment forces is determined by the special body shape of an arch dam.The deeper the dam is, the greater the pressure is.The distribution of water pressure forms a triangle.The force acting on an upstream layer is equal to the product of water pressure and the acting area.The upstream area of different arch layers differs.Usually, the arch layer area changes from small to large from the bottom to the top of the arch dam.Conversely, water pressure changes from large to small from the bottom to the top.Thus, the product of water pressure and area increases from the bottom to the middle section of the arch dam and decreases from the middle to the top section of the dam.arch dam site that has a large quantity of strong rock mass on both banks.At the least, arch layers with large arch abutment forces should not be placed in an area where the two banks of a valley cannot offer a sufficiently large quantity of strong rock mass.Thus, distribution can provide valuable information to arch dam design.It also reminds us that the safety evaluation of arch dams may be conducted from two aspects.First, estimate whether the two banks of the valley offer sufficient rock mass in the evaluation of each arch layer according to the distribution of abutment forces because different abutment forces are required at different elevations.Second, ascertain the design of an arch layer to ensure that the arch layer is sufficiently strong because various arch layers bear different load magnitudes.The distribution of abutment forces indicates that arch layers with large abutment forces are usually located in the middle and lower sections of the arch dam.These parts of the dam and rocks bear a large force.Hence, the dam body or the rock mass of the two banks should be sufficiently strong.
Conclusions
(1) Abutment force increases from the bottom to the middle section of the arch dam.It reaches the maximum at the middle of the dam and then decreases from the middle to the top of the dam. and bending moment have a similar distribution feature under normal loads.The only difference is that the maximum of , , and bending moment is at different heights of the dam.The and bending moment of the left and right banks exhibit good symmetry.The distribution of , , and bending moment does not change during overload.
(2) With regard to the distribution of abutment force along the elevation, attention should be paid to the design process.On the one hand, this condition would ensure that both sides of the bank can provide sufficient force to meet the force requirements at different elevations.Given that each abutment along the elevation requires a different magnitude of force, bank rocks must offer sufficient force.On the other hand, the arch layer should be designed in accordance with the load because arch layers in different elevations bear different magnitudes of load.
(3) The left and right bank rocks must have sufficient force storage to ensure the safety of the arch dam during overload.Different arch layers require different magnitudes of rock force.Abutment force increases linearly during overload.The arch layer with the maximum abutment forces will require a large rock force during overload.
(4) A simple method to ascertain the distribution characteristic is provided through formula (13).This simple method can only get a precise distribution characteristic of and , and the absolute magnitude of and got by simple method is different from that by finite element method.This simple method can help to choose a suitable dam site.By the distribution of abutment forces got with simple method, engineers will know which layer will bear the largest force.They must choose a better site where the rock is stable enough at the elevation of the layer that has the largest abutment forces.Second, it helps to design a stronger arch dam.The layer that has the largest abutment forces usually bears large water pressure.So, it reminds engineers that dam body at this elevation should be built strong enough.
(5) The safe operation of an arch dam relies mainly on the arch.The arch transfers loads to the rocks of the bank.Arch layers play a key role in the safe operation of arch dams.If an arch layer is destroyed under normal loads or overloads, the dam would fail.The overload capacity of an arch dam can be ascertained through the estimation of arch layers.An arch dam's overload capacity is determined by the weakest arch layer.The overload factor of an arch dam can be simply defined as where is the maximum value of the bearing capacity of all arch layers. is the capacity of an arch layer in normal loads, and is the number of different arch layers.An arch layer's overload factor can be evaluated from two aspects.One is the overload capacity of an arch layer, and the other is the force storage of the bank rocks.The overload factor is the minimum of the two aspects mentioned above.
Figure 3 :
Figure 3: Typical damage pattern of dam body (Case 6: the black zone is the damage area of dam body.).
Figure 11 :
Figure 11: distribution in each case.
Figure 12 :
Figure 12: Bending moment distribution in each case.
Figure 16 :
Figure 16: Comparison of obtained with the simple method and FEM.
Figure 17 :
Figure 17: Comparison of obtained with the simple method and FEM.
Table 2 :
Results of Case 1.
Table 3 :
Results of Case 2.
Table 4 :
Results of Case 3.
Table 5 :
Results of Case 4.
Table 6 :
Results of Case 5.
Table 7 :
Results of Case 6.
Table 8 :
Abutment forces by simple method. | 5,069.4 | 2015-03-09T00:00:00.000 | [
"Engineering"
] |
Charged-particle Multiplicity Density at Midrapidity in Central Pb-pb Collisions at Root S(nn)=2.76 Tev 0 0 0 0 2 0 0 0 5 1 0 0 0 0 1 0 0 0 5 Vzero Amplitude (charge Arb. Units) Data Glauber Mc 0%-5% Centrality
The first measurement of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV is presented. For an event sample corresponding to the most central 5% of the hadronic cross section, the pseudorapidity density of primary charged particles at midrapidity is 1584 AE 4ðstatÞ AE 76ðsystÞ, which corresponds to 8:3 AE 0:4ðsystÞ per participating nucleon pair. This represents an increase of about a factor 1.9 relative to pp collisions at similar collision energies, and about a factor 2.2 to central Au-Au collisions at ffiffiffiffiffiffiffiffi s NN p ¼ 0:2 TeV. This measurement provides the first experimental constraint for models of nucleus-nucleus collisions at LHC energies. The theory of strong interactions, quantum chromody-namics (QCD), predicts a phase transition at high temperature between hadronic matter, where quarks and gluons are confined inside hadrons, and a deconfined state of matter, the quark-gluon plasma. A new frontier in the study of QCD matter opened with the first collisions of 208 Pb ions in November 2010, at the Large Hadron Collider (LHC) at CERN. These collisions are expected to generate matter at unprecedented temperatures and energy densities in the laboratory. The first step in characterizing the system produced in these collisions is the measurement of the charged-particle pseudorapidity density, which constrains the dominant particle production mechanisms and is essential to estimate the initial energy density. The dependence of the charged-particle multiplicity density on energy and system size reflects the interplay between hard parton-parton scattering processes and soft processes. Predictions of models that successfully describe particle production at RHIC vary by a factor of 2 at the LHC [1,2]. This Letter reports the measurement of the charged-particle pseudorapidity density produced in Pb-Pb collisions at the LHC, utilizing data taken with the ALICE detector [3] at a center-of-mass energy per nucleon pair ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV. The primary charged-particle density, dN ch =d, in central (small impact parameter) Pb-Pb collisions is measured in the pseudorapidity interval jj jÀln tanð=2Þj < 0:5, where is the polar angle between the charged-particle direction and the beam axis (z). We define primary particles as prompt particles produced in the collision, including decay products, except those from weak decays of strange particles. The present measurement extends the study of particle densities in nucleus-nucleus collisions into the TeV regime. We make comparisons to model predictions [4–16] and …
The theory of strong interactions, quantum chromodynamics (QCD), predicts a phase transition at high temperature between hadronic matter, where quarks and gluons are confined inside hadrons, and a deconfined state of matter, the quark-gluon plasma.A new frontier in the study of QCD matter opened with the first collisions of 208 Pb ions in November 2010, at the Large Hadron Collider (LHC) at CERN.These collisions are expected to generate matter at unprecedented temperatures and energy densities in the laboratory.
The first step in characterizing the system produced in these collisions is the measurement of the charged-particle pseudorapidity density, which constrains the dominant particle production mechanisms and is essential to estimate the initial energy density.The dependence of the chargedparticle multiplicity density on energy and system size reflects the interplay between hard parton-parton scattering processes and soft processes.Predictions of models that successfully describe particle production at RHIC vary by a factor of 2 at the LHC [1,2].
This Letter reports the measurement of the chargedparticle pseudorapidity density produced in Pb-Pb collisions at the LHC, utilizing data taken with the ALICE detector [3] at a center-of-mass energy per nucleon pair ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV.The primary charged-particle density, dN ch =d, in central (small impact parameter) Pb-Pb collisions is measured in the pseudorapidity interval jj jÀln tanð=2Þj < 0:5, where is the polar angle between the charged-particle direction and the beam axis (z).We define primary particles as prompt particles produced in the collision, including decay products, except those from weak decays of strange particles.
A detailed description of the ALICE experiment is given in Ref. [3].Here, we briefly describe the detector components used in this analysis.The silicon pixel detector (SPD) is the innermost part of the inner tracking system.It consists of two cylindrical layers of hybrid silicon pixel assemblies positioned at radial distances of 3.9 and 7.6 cm from the beam line, with a total of 9:8 Â 10 6 pixels of size 50 Â 425 m 2 , read out by 1200 electronic chips.The SPD coverage for particles originating from the center of the detector is jj < 2:0 and jj < 1:4 for the inner and outer layers, respectively.Each chip provides a fast signal if at least one of its pixels is hit.The signals from the 1200 chips are combined in a programmable logic unit which supplies a trigger signal.The fraction of SPD channels active during data taking was 70% for the inner and 78% for the outer layer.The VZERO detector consists of two arrays of 32 scintillator tiles placed at distances z ¼ 3:3 m and z ¼ À0:9 m from the nominal interaction point, covering the full azimuth within 2:8 < < 5:1 (VZERO-A) and À3:7 < < À1:7 (VZERO-C).Both the amplitude and the time signal in each scintillator are recorded.The VZERO time resolution is better than 1 ns, allowing discrimination of beam-beam collisions from background events produced upstream of the experiment.The VZERO also provides a trigger signal.The zero degree calorimeters (ZDCs) measure the energy of spectators (noninteracting nucleons) in two identical detectors, located AE114 m from the interaction point.Each ZDC consists of two quartz fiber sampling calorimeters: a neutron calorimeter positioned between the two beam pipes downstream of the first machine dipole that separates the two charged-particle beams and a proton calorimeter positioned externally to the outgoing beam pipe.The energy resolution at beam energy is estimated to be 11% for the neutron and 13% for the proton calorimeter, respectively.
For the data analyzed, beams of four bunches, with about 10 7 Pb ions per bunch, collided at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV, with an estimated luminosity of 5 Â 10 23 cm À2 s À1 .The trigger was configured for high efficiency for hadronic events, requiring at least two out of the following three conditions: (i) two pixel chips hit in the outer layer of the SPD, (ii) a signal in VZERO-A, (iii) a signal in VZERO-C.The threshold in the VZERO detector corresponds approximately to the energy deposition of a minimum ionizing particle.The luminous region had a rms width of 5.9 cm in the longitudinal direction and 50 m in the transverse direction.The estimated luminosity corresponds to a hadronic collision rate of about 4 Hz.The observed rate was about 50 Hz, mainly due to electromagnetically induced processes [33].These processes have very large cross sections at LHC energies but generate very low multiplicities and therefore do not contribute to the high particle multiplicities of interest for the present analysis.The trigger rate without beam was negligible and the rate in coincidence with bunches of only one beam was about 1 Hz.This beam background is eliminated from the triggered event sample using the VZERO timing information, as well as the correlation between the number of tracks reconstructed in the time projection chamber and the number of hits in the SPD.
Off-line event characterization utilizes global event observables that are intrinsically correlated over different regions of phase space through the initial collision geometry.Figure 1 (upper) shows the measured correlation between the energy deposited in the ZDC and the sum of amplitudes in the VZERO detector.The VZERO response is proportional to the event multiplicity, and the ZDC energy to the number of noninteracting nucleons close to beam rapidity.As events become more central, with smaller impact parameter, they generate larger multiplicity in VZERO and less energy forward in the ZDC.This behavior is understood based on collision geometry and nuclear breakup [34].For small ZDC response the VZERO signal has two distinct values corresponding to peripheral and central collisions.However, the VZERO signal alone can be used to discriminate on centrality.Figure 1 (lower) shows the distribution of the VZERO amplitude for all triggered events after beam background removal.The distribution is fit using the Glauber model [35] to describe the collision geometry and a negative binomial distribution to describe particle production [34].In addition to the two parameters of the negative binomial distribution, there is one free parameter that controls the power-law dependence of particle production on the number of participating nucleons (N part ).To avoid the region contaminated by electromagnetic processes, which constitutes over 90% of the triggered events, the fit is restricted to the VZERO amplitude region above 150, where the trigger for hadronic collisions is fully efficient.The fraction of the hadronic cross section from the model fit corresponding to this cut, 87%, allows the determination of the cross section percentile for any more-central VZERO cut by integrating the measured distribution.The most central 5% fraction of the hadronic cross section was determined in this way.
The analysis is based on the VZERO event selection as described above.Among the triggered sample of about 650 000 events, 3615 events correspond to the most central 5% of the hadronic cross section, indicated by the shaded region in Fig. 1 (lower).The first step in the measurement of the charged-particle multiplicity is the determination of the primary vertex position by correlating hits in the two SPD layers.All events in the central sample are found to have a well-constrained primary vertex.To minimize edge effects at the limit of the SPD acceptance we have only used events with reconstructed vertex at jz vtx j < 7 cm, reducing the sample to 2711 events.Tracklet candidates [25] are formed using information on the position of the primary vertex and of hits on the SPD layers.A tracklet is defined by a pair of hits, one on each SPD layer.Using the reconstructed vertex as the origin, we calculate the differences in azimuthal (Á', bending plane) and polar (Á, nonbending direction) angles for pairs of hits [31].Only hit combinations satisfying a selection on the sum of the squares of Á' and Á, each normalized to its estimated resolution (60 mrad in Á' and 25sin 2 mrad in Á), are selected as tracklets.If multiple tracklet candidates share a hit, only the combination with the smallest sum of squares of Á' and Á is kept.The cut imposed on Á' efficiently selects charged particles with transverse momentum (p t ) above 50 MeV=c.Particles below 50 MeV=c are mostly absorbed by material.
The charged-particle pseudorapidity density dN ch =d is obtained from the number of tracklets within jj < 0:5 according to dN ch =d ¼ Â ð1 À ÞdN tracklets =d, where is the correction factor for the acceptance and efficiency for a primary track to generate a tracklet and is the probability to form a background tracklet from uncorrelated hits.The corrections and are determined as a function of the z position of the primary vertex and the pseudorapidity of the tracklet.The simulations used to calculate the corrections are based on the HIJING [36] event generator and a GEANT3 [37] model of the detector response.Three different methods have been used to estimate the combinatorial background.
The main method to estimate the combinatorial background relies on the event simulation using a sample of events with similar multiplicities (SPD hits) as in the real data.In Fig. 2 the Á' distribution for candidate tracklets is compared for data and simulation.The distributions are very similar, practically identical in the background dominated tails.The second method is based on the injection of random background hits in the real event, in order to evaluate the probability of creating fake tracklets by combinatorics.In the third method events are modified by rotating hits in the inner SPD layer by 180 in ', thereby destroying real correlations, but preserving global event features.In all cases, the absolute amount of combinatorial background is obtained by matching the tracklet and background distributions in the tails.For the main method, which ideally provides both the shape and the normalization, an adjustment of 1% is needed to match the tails.The estimated combinatorial background is about 14%.In order to account for the effect of the correlated background, the same background subtraction procedure is also applied to the simulation (i.e., without relying on the event generator information).The correction for the acceptance and efficiency, , is obtained by the ratio of the number of generated primary charged particles to the number of reconstructed tracklets after subtraction of the combinatorial background.In this way, accounts for geometrical acceptance, detector and reconstruction efficiencies, contamination by weak decay products of strange particles, conversions, secondary interactions, and undetected particles below 50 MeV=c transverse momentum.The overall correction factor varies slightly depending on vertex position and , and is about 2.
We have considered the following sources of systematic uncertainties: background subtraction estimated as 2% by comparing the results of different methods; particle composition estimated as 1% by changing the relative abundances of protons, pions, kaons by a factor of 2; contamination by weak decays estimated as 1% by changing the relative contribution of the yield of strange particles by a factor of 2; low-p t extrapolation estimated as 2% by varying the amount of undetected particles at low p t by a factor of 2; event generator estimated as 2% by using HIJING [36] with and without jet quenching, as well as DPMJET [38] for the corrections; centrality definition estimated as 3% by using an alternative event selection based on the SPD hit multiplicities, and by varying the range of the Glauber model fit.All other sources of systematic errors considered (tracklet cuts, vertex cuts, material budget, detector efficiency, background events) were found to be negligible.The total systematic errors amounts to 4.8%.Independent cross-checks performed using tracks reconstructed in the time projection chamber and the inner tracking system yield results consistent within the systematic uncertainty.
In order to compare bulk particle production in different collision systems and at different energies, and to compare with model calculations, the charged-particle density is scaled by the number of participating nucleons, determined using the Glauber model fit described above (Fig. 1).The average number of participants for the 5% most central events is found to be hN part i ¼ 381 with a rms of 18 and a systematic uncertainty of 1%.The systematic uncertainty was obtained by varying the parameters of the Glauber calculation within the experimental uncertainty and by AE8% around 64 mb for the nucleon-nucleon cross section, by using different fit ranges, and by comparing results obtained for different centrality variables (SPD hits or combined use of the ZDC and VZERO signals).We measure a density of primary charged particles at midrapidity dN ch =d ¼ 1584 AE 4ðstatÞ AE 76ðsystÞ.Normalizing per participant pair, we obtain dN ch =d= ð0:5hN part iÞ ¼ 8:3 AE 0:4ðsystÞ with negligible statistical error.In Fig. 3, this value is compared to the measurements for Au-Au and Pb-Pb, and nonsingle diffractive pp and p " p collisions over a wide range of collision energies [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].It is interesting to note that the energy dependence is steeper for heavy-ion collisions than for pp and p " p collisions.For illustration, the curves / s 0:15 NN and / s 0:11 NN are shown superimposed on the data.A significant increase, by a factor 2.2, in the pseudorapidity density is observed at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV for Pb-Pb compared to ffiffiffiffiffiffiffiffi s NN p ¼ 0:2 TeV for Au-Au.The average multiplicity per participant pair for our centrality selection is found to be a factor 1.9 higher than that for pp and p " p collisions at similar energies.
Figure 4 compares the measured pseudorapidity density to model calculations that describe RHIC measurements at ffiffiffiffiffiffiffiffi s NN p ¼ 0:2 TeV, and for which predictions at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV are available.Empirical extrapolation from lower energy data [4] significantly underpredicts the measurement.Perturbative-QCD-inspired Monte Carlo event generators, based on the HIJING model tuned to 7 TeV pp data without jet quenching [5], on the dual parton model [6], or on the ultrarelativistic quantum molecular dynamics model [7], are consistent with the measurement.Models based on initial-state gluon density saturation have a range of predictions depending on the specific implementation [8][9][10][11][12] and exhibit a varying level of agreement with the measurement.The prediction of a hybrid model based on hydrodynamics and saturation of final-state phase space of scattered partons [13] is close to the measurement.A hydrodynamic model in which multiplicity is scaled from p þ p collisions overpredicts the measurement [14], while a model incorporating scaling based on Landau hydrodynamics underpredicts the measurement [15].Finally, a calculation based on modified PYTHIA and hadronic rescattering [16] underpredicts the measurement.
In summary, we have measured the charged-particle pseudorapidity density at midrapidity in Pb-Pb collisions at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV, for the most central 5% fraction of the hadronic cross section.We find dN ch =d ¼ 1584 AE 4ðstatÞ AE 76ðsystÞ, corresponding to 8:3 AE 0:4ðsystÞ per participant pair.These values are significantly larger than those measured at RHIC, and indicate a stronger energy dependence than measured in pp collisions.The result presented in this Letter provides an essential constraint for models describing high energy nucleus-nucleus collisions.
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex.The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: Calouste Gulbenkian
FIG. 1 (
FIG.1(color online).Upper panel: Correlation of ZDC and the VZERO response in hadronic collisions.Lower panel: Distribution of the sum of amplitudes in the VZERO scintillator tiles (black histogram); inset shows the low amplitude part of the distribution.The gray (red) line shows the fit of the Glauber calculation to the measurement.The fit was performed above the cut indicated in the inset, avoiding the region at low amplitudes dominated by the electromagnetic processes.The shaded area corresponds to the most central 5% of hadronic collisions.
FIG. 2 (
FIG. 2 (color online).Distribution of the azimuthal separation (Á') of all candidate tracklets in data, simulation, and the background contribution that is estimated from the simulation. | 4,277 | 2010-12-13T00:00:00.000 | [
"Physics"
] |
Prediction of vitamin interacting residues in a vitamin binding protein using evolutionary information
Background The vitamins are important cofactors in various enzymatic-reactions. In past, many inhibitors have been designed against vitamin binding pockets in order to inhibit vitamin-protein interactions. Thus, it is important to identify vitamin interacting residues in a protein. It is possible to detect vitamin-binding pockets on a protein, if its tertiary structure is known. Unfortunately tertiary structures of limited proteins are available. Therefore, it is important to develop in-silico models for predicting vitamin interacting residues in protein from its primary structure. Results In this study, first we compared protein-interacting residues of vitamins with other ligands using Two Sample Logo (TSL). It was observed that ATP, GTP, NAD, FAD and mannose preferred {G,R,K,S,H}, {G,K,T,S,D,N}, {T,G,Y}, {G,Y,W} and {Y,D,W,N,E} residues respectively, whereas vitamins preferred {Y,F,S,W,T,G,H} residues for the interaction with proteins. Furthermore, compositional information of preferred and non-preferred residues along with patterns-specificity was also observed within different vitamin-classes. Vitamins A, B and B6 preferred {F,I,W,Y,L,V}, {S,Y,G,T,H,W,N,E} and {S,T,G,H,Y,N} interacting residues respectively. It suggested that protein-binding patterns of vitamins are different from other ligands, and motivated us to develop separate predictor for vitamins and their sub-classes. The four different prediction modules, (i) vitamin interacting residues (VIRs), (ii) vitamin-A interacting residues (VAIRs), (iii) vitamin-B interacting residues (VBIRs) and (iv) pyridoxal-5-phosphate (vitamin B6) interacting residues (PLPIRs) have been developed. We applied various classifiers of SVM, BayesNet, NaiveBayes, ComplementNaiveBayes, NaiveBayesMultinomial, RandomForest and IBk etc., as machine learning techniques, using binary and Position-Specific Scoring Matrix (PSSM) features of protein sequences. Finally, we selected best performing SVM modules and obtained highest MCC of 0.53, 0.48, 0.61, 0.81 for VIRs, VAIRs, VBIRs, PLPIRs respectively, using PSSM-based evolutionary information. All the modules developed in this study have been trained and tested on non-redundant datasets and evaluated using five-fold cross-validation technique. The performances were also evaluated on the balanced and different independent datasets. Conclusions This study demonstrates that it is possible to predict VIRs, VAIRs, VBIRs and PLPIRs from evolutionary information of protein sequence. In order to provide service to the scientific community, we have developed web-server and standalone software VitaPred (http://crdd.osdd.net/raghava/vitapred/).
Background
A protein individually utilizes only a limited range of functionality present in its natural amino acid side chains, and the catalytic activity of many enzymes requires the involvement of a small-molecule that acts as a co-factor. These are required in almost all important metabolic pathways because they are specialized in certain types of reaction. One particular cofactor can be involved in several pathways and, conversely, several cofactors can be required in one particular pathway [1,2]. Many vitamins have diverse biochemical functions but they are primarily known to assist enzyme-substrate reactions by playing the role of an enzyme cofactor [3,4]. Some vitamins have hormone-like function as regulators of mineral metabolism (e.g. vitamin D), or regulators of cell and tissue growth and differentiation (e.g. some forms of vitamin A). The function of vitamin D as anti-infectious and anti-inflammatory is well-established [5,6] and other functions as antioxidants (e.g. vitamin E and sometimes vitamin C). The majority of vitamins (e.g. B complex vitamins) function as precursors of enzyme cofactor that helps enzyme in their work as catalysts in metabolism [7].
As most vitamin biosynthetic pathway enzymes are not present in mammals and present in many of the pathogens [8], these enzymes have become attractive drug targets in several disease including tuberculosis [8,9] and malaria [10,11]. Several investigators have targeted Ornithine decarboxylase (ODC) for different diseases like African trypanosomiasis, Pneumocystis carinii pneumonia, ischemia, autoimmune diseases and hyperplasia [12]. Nonetheless, many groups are targeting Serine hydroxyl-methyltransferase (SHMT) as antitumor target knowing that enhanced levels of SHMT activity have been found in rapidly proliferating tumor cells [13]. A constitutive ODC activity observed in cancer cells, where its uncontrolled expression confers a cancer phenotype to the cells so ODC has been targeted in antitumor drugs [14]. In past, several studies have been done to identify the cofactor binding cleft and interacting residues in various enzymes. Pyridoxal 5'-phosphate (PLP)-dependent enzymes like 3,4-dihydroxyphenylalanine decarboxylase (DDC) [15,16], Cystathionine beta-synthase (CBS) [17], 8-amino-7oxononanoate synthase [18], Aminobutyrate aminotransferase [19], ODC and SHMT etc. have been investigated in various studies for identification of PLP and substrate interacting residues. These studies helped them to investigate the underlying mechanism and develop strategies for inhibitor designing. Similarly enzymes involved in folate (Vit-B9) metabolism such as Dihydropteroate synthase [20], Dihydrofolate synthase [21] and thiamin (Vit-B1) pathway [22] like Pyruvate dehydrogenase [23] and Oxoglutarate dehydrogenase [24] have also been taken as drug targets. In addition, binding of PLP also inhibits the activity of aminoacyl-tRNA synthetases [25]. Therefore, computational tool for the prediction of PLP and other vitamin-interacting site is highly desirable.
The advancement of genome sequencing produces huge amount of sequence data but reliable in-silico annotation of these sequences still remains a challenge. There are several prediction tools available for the functional annotation of proteins. Broadly, the existing computational method can be divided in two categories; (i) protein level prediction, where function of whole protein is predicted [26][27][28] and (ii) residue level prediction where function of each residue in a protein is predicted [29][30][31]. The protein level prediction provides overall function of protein whereas residue level predictions are advancement over protein level and provides the information of functional residues. The residue level predictions mainly deal with prediction of interaction with other proteins, DNA, RNA and ligands. There are various methods to predict different interacting residues from the structure of protein but the major challenge is to predict interacting residues when only protein sequence is known. Several prediction methods have been developed for carbohydrates [32,33], lipids [34,35], DNA [29,[36][37][38][39] and RNA [30,38,40] interacting residues in protein sequence. Some methods have been developed for specific ligands such as ATP [41,42], GTP [43], NAD [44], FAD [45] and mannose [46].
In this study, preliminary investigations revealed differential binding patterns of vitamins and other small-molecules. These differential patterns suggested that each ligand has specific residual preference for their binding with protein. Therefore, it becomes important to develop vitamin-specific interacting residue prediction methods. In this study, we developed different models for the sequence-based prediction of vitamin-interacting residues (VIRs), vitamin-A interacting residues (VAIRs), vitamin-B interacting residues (VBIRs) and PLP-interacting residues (PLPIRs). We utilized various classifiers and finally selected Support Vector Machines (SVMs) for developing the prediction models. SVM is a very powerful machine learning technique, which has been used for developing various bioinformatics methods in the past [38,[47][48][49][50]. It has been shown that the evolutionary information provided more information [40,43,45] than protein sequence, therefore we applied evolutionary information in the form of Position-Specific Scoring Matrix (PSSM) profile for developing a prediction method. This vitamin binding site prediction will be very useful for the study of enzyme activity and further advancement of drug development technologies.
Analysis of protein-binding patterns of various ligands
It is important to analyze protein-binding patterns of different ligands in order to understand binding specificity of each ligand. Previously published datasets of different ligand-binding patterns for example ATP, GTP, NAD, FAD and mannose, were used to look at the preference of interacting residues. We analyzed the ligand-binding patterns for ATP (Additional file 1: Figure S1), GTP (Additional file 1: Figure S2), NAD (Additional file 1: Figure S3), FAD (Additional file 1: Figure S4) and mannose (Additional file 1: Figure S5) FAD and mannose ligands respectively. We further analyzed and observed that significant differences were also present in the neighboring residues surrounding these preferred and non-preferred sets. This suggests the existence of different binding pockets for each small molecule ligand in the proteins. In order to predict these potentially differing binding pockets, there should be ligand specific binding site tools.
Analysis of different protein-interacting residues of different vitamin classes
After analysis of various ligand-protein interactions, we compared vitamins-interacting patterns with other ligands and found that significant differences were present. The Tyr, Phe, Ser, Trp, Thr, Gly and His are preferred as VIRs whereas Glu, Ala, Pro, Leu, Lys, Gln, Val and Asp are nonpreferred. We analyzed amino acid compositions of the vitamin binding protein residues grouped by the sub-class to which the binding protein belonged: VIRs, VAIRs, VBIRs and PLPIRs ( Figure 1). The interacting site of Vitamin A, Vitamin B and PLP preferred {Phe, Ile, Trp, Tyr, Leu, Val}, {Ser, Tyr, Gly, Thr, His, Trp, Asn, Glu} and {Ser, Thr, Gly, His, Tyr, Asn} whereas the non-preferred residues were {Glu, Pro, Asp, Asn, Ser, Arg, Gln}, {Leu, Glu, Ala, Pro, Val, Ile, Lys} and {Leu, Glu, Ala, Pro, Val, Ile, Ala} respectively. This implies that differences do exist at the proteinvitamin interaction sites even within vitamins sub-classes.
In this study, we initially developed a model for the prediction of vitamin-interacting residues and then further classified VIRs into vitamin A, vitamin B and pyridoxal-5-phosphate (vitamin B6; PLP) interacting residues. Four different types of prediction methods were developed, one for each of the interacting residues: VIRs, VAIRs, VBIRs and PLPIRs. All the models developed in this study were evaluated using five-fold cross validation technique. In all cases, we used 10 times more negative instances than positive instances.
Prediction of vitamin-interacting residues (VIRs)
Here we developed the comprehensive prediction method for all VIRs. By generating sliding patterns and creating Two Sample Logo, we found that Phe, Gly, His, Ser, Thr, Trp and Tyr were more abundant in VIRs as compared to non-VIRs (See Additional file 1: Figure S6). These patterns were converted into binary patterns and different kernels/parameters of SVM were employed to optimize the discrimination power between VIR and non-VIR patterns. We achieved 68.57% sensitivity, 64.88% specificity, 65.22% accuracy and 0.20 MCC. Preferences for neighboring amino acids between VIRs and non-VIRs patterns were also observed in the TSL (See Additional file: 1 Figure S6). Thereafter, evolutionary information obtained from PSI-BLAST was used for the discrimination between VIRs and non-VIRs. Applying different machine learning algorithms of WEKA revealed that IBk method achieved maximum 50 Figure 2). The performance increased significantly when PSSM was used as input instead of the binary patterns approach.
Prediction of vitamin A interacting residues (VAIRs)
We also developed prediction method for the VAIRs. The TSL of sliding patterns showed that Phe, Ile, Leu, Val and Trp were more abundant in VAIRs than in non-VAIRs (See Additional file 1: Figure S7). These patterns were converted into the binary profile of patterns in order to develop the SVM-based prediction model. Table 2 shows performances of all applied classifiers. As shown in ROC graph, binary (SVM), PSSM (IBk) and PSSM (SVM) achieved 0.70, 0.70 and 0.83 AUC values, respectively ( Figure 3). The PSSM based approach enhanced the prediction performance with SVM.
Prediction of vitamin B interacting residues (VBIRs)
The TSL analysis of VBIRs and non-VBIRs showed that Gly, His, Asn, Ser, Thr, Trp and Tyr were more abundant in VBIRs (See Additional file: 1 Figure S8). Table 3. Prediction of pyridoxal-5-phosphate interacting residues (PLPIRs) The compositional and TSL analysis of PLPIRs and non-PLPIRs found that Gly, His, Asn, Ser, Thr and Tyr were more abundant in PLPIRs (See Additional file 1: Figure S9). Figure 5). Table 4 shows performances of all applied classifiers. Here also PSSM profile based evolutionary information enhanced the prediction performance of SVM model.
Performance of balanced datasets
We also developed the SVM-based prediction models on the balanced datasets using both binary and PSSM approaches. The binary approach achieved 0.32, 0.24, 0.37 and 0.52 MCC for VIRs, VAIRs, VBIRs and PLPIRs respectively ( Table 5). The PSSM approach improved the prediction performance significantly and achieved 0.53, 0.47, 0.63 and 0.80 MCC for VIRs, VAIRs, VBIRs and PLPIRs respectively (Table 5). Table S1). The performance enhanced significantly while using PSSM approach and achieved highest 0.38, 0.37, 0.35 and 0.63 MCC for the prediction of VIRs, VAIRs, VBIRs and PLPIRs respectively ( Table 6).
Surface accessibility based prediction
Most of binding residues reside inside the surface pockets and predicting these pockets is therefore important. For these predictions, it is required to firstly predict the surface accessibility (SA) of each residue from the protein sequence. Therefore, we used SARpred method [51] for the prediction of surface accessibility of all residues. On the basis of these surface accessibility values, we tried to develop SVM-based models but as shown in the Additional file 1: Table S2). The performance of PLPIRs predictor was better than the performance from this study. This may be because of the presence of more than one ligand in the other predictors (VIR, VAIR, VBIR). There may be chances that binding pockets were very different for each ligand and therefore difficult to model. Sometime, it is better to combine more than two features, in order to achieve good prediction results. In-spite of a combined PSSM-surface accessibility approach, we were unable to achieve any improvement in performance measures over The values of standard errors are also given with performances.
the single PSSM-based approach for both the realistic and balanced datasets (See Additional file 1: Table S2). These results suggest that PSSM-based individual approach performances were as good as combined approach with both PSSM and surface accessibility features.
Quality of PSSM profiles
The number of homology sequences can affect the quality of PSSM profiles; therefore it is important to check the quality of PSSM profiles. Earlier this type of analysis has been done for the prediction of DNA-binding proteins in the DNAbinder method [27]. The number of homology sequences depends on total number of the protein sequences in the database. We Table S3.
As the total numbers of homology sequences were different for each query sequence; by default it varied from the 0-500 sequences. On the basis of total PSI-BLAST hits, we divided each dataset into five different categories (overall 0-500, 0-10, 11-100, 101-400 and 401-500). As mentioned in the Additional file 1: Table S3, it was observed that performances increased with the increment of number of homolog sequences. Prediction performances were poor for the 0-10 and 11-100 ranges of query sequences in all four cases whereas average for the 101-400 range and good for the 401-500 homolog sequences. These results suggested that the quality of PSSM profiles depends on the number of homolog sequences. In most of cases, the major fraction of sequences ranged between 401-500 (PSI-BLAST hit range). The overall performances of simple binary-based approach (Additional file 1: Table S1) were higher than the PSSM-based prediction that had range values between 0-10 (Additional file 1: Table S3).
Datasets
In this study, we collected data from SuperSite documentation [52] and extracted 1061 PDB IDs of protein having contact with vitamins in PDB. We downloaded the sequence of all chains of these PDB Ids from Protein Data Bank [53]. In next step, we used these PDB IDs in Ligand Protein Contact (LPC) web-server [54] and get total 2720 chains that interact with vitamins with their corresponding interacting residues and its position. We used a cut-off of 5.0 Å to define the vitamin interacting residues. A residue was considered to be vitamin-interacting if the closest distance between atoms of the protein and the partner vitamin was within the cut-off (5 Å). The 25% non-redundant dataset of protein chains was created by using BLASTCLUST and finally retrieved a total 187 interacting chains with a total 3004 vitamin-interacting residues (VIRs) and remaining all residues are non-vitamin-interacting residues (non-VIRs). This step was repeated for the dataset development of vitamin A, vitamin B and PLP (vitamin B6-derived) interacting residue prediction and retrieved 538, 2207 and 1092 interacting residues in 31, 141 and 71 chains respectively. The interacting and noninteracting residues were used as positive and negative instances respectively. The number of non-interacting residues was very large than interacting residues so we have randomly picked up 10 times more non-interacting than interacting residues in order to create realistic dataset. The balanced datasets of equal positive and negative were also created, where equal numbers of random negative instances was taken from the total negative window patterns.
We independent datasets were less than 25% similar than sequences of main datasets.
Window patterns and size
We generated sliding (overlapping) patterns of 17-residue size, for each interacting chain sequence. In past, several studies have adopted this strategy for the interacting residue tools development [40,45]. If the central residue of pattern was interacting, then we classified the pattern as interacting or positive pattern; otherwise it was termed as non-interacting or negative pattern. To generate the pattern corresponding to the terminal residues in a protein sequence, we have added (L-1)/2 dummy residue "X" at both terminals of protein (where L is the length of pattern).
Here the length of pattern is 17 so we have added 8 "X" before N-terminal and 8 "X" after C-terminal, in order to create equal number of patterns from sequence length.
Position-Specific Scoring Matrix (PSSM)
We performed PSI-BLAST (position-specific iterative BLAST) search (default parameter) against the nonredundant (NR) database available at Swiss-Prot [55]. After three iterations, PSI-BLAST generated the PSSM profiles with the highest score from multiple alignments of the high-scoring hits by calculating the position-specific scores for each position in the alignments. The PSSM profile contains the occurrence probability of all amino acids at each position along with insertion/deletion and provides the evolutionary information for all amino acids. The final PSSM was normalized using a sigmoid function.
Surface accessibility
We calculated surface accessibility value for each residue of the all sequences using SARpred method [51]. We normalized these values (between minimum to maximum) and assigned a value for the each residue of the 17-length window patterns. We used these 17 input features for the SVM-based prediction of VIRs, VAIRs, VBIRs and PLPIRs.
In the hybrid approach with PSSM, we combined these 17 input features with the PSSM features.
Support vector machine
In this study, a highly successful machine learning technique termed as a Support Vector Machine (SVM) was used. SVM is a machine-learning tool and based on the structural risk minimization principle of statistics learning theory. SVMs are a set of related supervised learning methods used for classification and regression [56]. The user can choose and optimize number of parameters and kernels (e.g. Linear, polynomial, radial basis function and sigmoidal) or any user-defined kernel. In this study, we implemented SVM light Version 6.02 package [57] of SVM and machine learning was carried out using three different (linear, polynomial and radial basis function) kernels. SVM takes a set of fixed length input features, along with their output, which is used for training of model. After training, learned model can be used for prediction of unknown examples [58]. We optimized different parameters and kernels for all approaches and developed efficient prediction tools.
WEKA package
WEKA is a large collection of various machine-learning algorithms as single package [59]. We applied WEKA 3.6.4 version, which integrates different classifiers such as BayesNet, NaiveBayes, ComplementNaiveBayes, NaiveBayesMultinomial, RandomForest and IBk. All algorithms have been applied and optimized for different prediction tool development.
Five-fold cross validation
The validation of any prediction method is very essential part. In this study, we have used a five-fold cross-validation technique [60] for training, testing and evaluating our prediction methods. The protein sequences/patterns of positive and negative instances were randomly divided into five parts. Each of these five sets consists of one-fifth of positive and one-fifth of negative instances. In this technique, the training and testing was carried out five times, each time using one distinct set for testing and the remaining four sets for training.
Evaluation parameters
To assess the performance of various modules developed in this study, we calculated the sensitivity, specificity, accuracy and Matthew's correlation coefficient (MCC). These calculations were routinely used in these types of prediction-based studies [61,62]. These parameters were calculated using following equations (1-4): Specificity The standalone version of VitaPred gives prediction results with probability score instead of SVM score. We have calculated probability score by using following equation - We rescaled the SVM scores with maximum 1.5 and minimum −1.5, where more than 1.5 and less than −1.5 both scores were used as 1.5 and −1.5 respectively. The probability score varies from 0-9 for each residue of protein sequence. The probability scores ranges between 0-4 and 5-9 predicted as non-interacting and interacting residues respectively at default 0.0 thresholds. The five fold cross-validation technique created five test sets and calculated performance for each test set. The final performance of prediction model is an average performance of these five test sets. In this average performance, we also calculated standard error of the performance of these five test set. MCC is considered to the most robust parameters for the evaluation of any prediction method [63]. The MCC value ranges between +1 to −1. The MCC value of 1 corresponds to a perfect prediction, whereas 0 corresponds to a completely random prediction. The −1 MCC value indicates total disagreement between prediction and actual examples. The evaluation parameters of SVM performances are threshold-dependent and require parameters/kernels optimization for the better results. The complete optimization of all parameters is key step in SVM based machine learning. We manually optimized all parameters and selected the highly performed prediction models for different tasks. In order to have a threshold independent evaluation of our method, we also created ROC and calculated AUC value for the threshold independent evaluation using SPSS statistical package.
Two sample logo (TSL)
In this study, we have created Two Sample Logo (http://www.twosamplelogo.org/) for the graphical representation of positive and negative patterns [64]. It is a web-based application to calculate and visualize position-specific differences between positive and negative samples.
Web-server
A user-friendly web-server VitaPred developed for the prediction of VIRs, VAIRs, VBIRs and PLPIRs in protein sequence. The VitaPred is freely available from http://crdd.osdd.net/raghava/vitapred/ web-address. It requires protein sequence in standard FASTA format. There are four different type of options provided for the prediction of VIRs, VAIRs, VBIRs and PLPIRs. We have also provided our datasets and other supplementary materials, which were used for the development of VitaPred web-server.
Standalone version of VitaPred
In the era of genomics, it is essential to develop computational tools for the huge amount of sequence data. We have developed standalone version of VitaPred by using Visual Basic .NET technologies. This is available from the site of web-server. User can download and install it in their system. This software gives the results with probability scores (Equation 5) for each residue of protein sequences. The multiple sequences can efficiently proceed with this software.
Discussion
The experimental determination of vitamin binding sites is very difficult task because of their complex chemical nature, and the fact that they are often made in very small amounts, making detection of the enzyme activities and intermediates difficult [4]. So there is a need to develop alternate technique, such as computational techniques for predicting vitamin-binding sites in a protein. The comparative analysis of different ligands with VIR (Additional file 1: Figure S6) such as ATP (Additional file 1: Figure S1), GTP (Additional file 1: Figure S2), NAD (Additional file 1: Figure S3), FAD (Additional file 1: Figure S4) and mannose (Additional file 1: Figure S5) revealed that each ligand has different protein-binding patterns (See all Figures in Additional file 1). Thus, it is important to develop a separate vitamin-interacting residues prediction tool.
We have used available structural information (knowledge-based) for the prediction model development using different machine learning algorithms. The structural information of protein-vitamin complexes extracted from SuperSite [52]. We found total 1061 protein-vitamin complexes, in which 181 and 843 complexes proteins are bind with vitamin A and B respectively. Out of these total 843 complexes of vitamin B binding complexes, 553 are bind to vitamin B(6)-derived pyridoxal 5'-phosphate (PLP) binding protein. The structural availability of vitamin C, D, E and K binding protein complexes are very low in PDB. Thus, we have developed four different methods for the prediction of VIRs, VAIRs, VBIRs and PLPIRs. We identified interacting and non-interacting residues using Ligand Protein Contact (LPC) web server [54]. The interacting residues analysis suggested that Phe, Gly, His, Ser, Thr, Trp and Tyr amino acids are preferred in the vitamin binding pockets of Vitamin Binding Proteins (VBPs) (Figures 1). The preference of interacting and neighboring residues is vitamin class-specific (See Additional file 1: Figure S6-S9). In the past, it has been shown in some studies that multiple sequence alignment based evolutionary information provides more comprehensive detail about the protein instead of single sequence [51,65]. Thus, all sequences of datasets were created into PSSM profiles and used for the prediction tool development. The comparative analysis between vitamin A and B interacting sites showed that Phe, Ile, Leu, Val and Trp are abundant in VAIRs whereas Asp, Glu, Gly, His, Lys, Asn. Arg, Ser and Thr are abundant in VBIRs (Figure 1, See Additional file 1: Figure S7-S8). The vitamin B(6)-derived pyridoxal 5'-phosphate (PLP) is the cofactor of enzymes catalyzing a large variety of chemical reactions (more than 140 enzymes are PLP-dependent) mainly involved in amino acid metabolism [66]. According to the Enzyme Commission, about 4% of enzyme-catalyzed reactions are PLP-dependent (EC; http://www.chem.qmul.ac.uk/iubmb/enzyme/). Therefore, it was very important to develop a separate prediction model for the PLPIRs in protein sequence. The PSSM based approach achieved maximum performance for PLPIRs because of separate model for a single PLP molecule. The VIRs, VAIRs and VBIRs modules performed relatively low because each class comprises more than one molecule. It means the overall prediction performance of VIRs is an approximately combined performance of all vitamins.
The performances of all the used classifiers are also provided in the Tables 1, 2, 3, and 4. It was observed that PSSM feature based SVM classifier performed better in all cases, in term of balancing between sensitivity and specificity. The threshold-independent performance of SVM is better than IBk for all modules (Figures 2, 3, 4 and 5). In the 5-fold cross validation, we got total five prediction performances corresponding to five test sets and computed average performance and standard error (SE) from these 5 performances. In most of cases, we found low value of SE, which is variation in the performance over five sets (it is not performance of variation on individual protein/chain). As patterns were divided randomly in five sets so it is expected that performance in each set will be nearly same. In other words, low SE values show that distribution of patterns in sets is not biased. Moreover, SE is not affected by similarity between patterns or protein chains, as this SE only measures biasness in distribution of patterns in five sets.
The prediction performances on the different independent datasets show that these modules can predict interacting residues of all vitamin classes with reasonably good accuracy ( Table 6). The quality of PSSM profiles were also investigated and found that protein sequences in our dataset have fairly high number of hits. Furthermore we also found PSSM approach based prediction performances increase with the increasing number of PSI-BLAST hits of the query sequence. As discussed, vitamins are crucial for the activation of many enzymes and crystal structures of many VBPs are unsolved. Furthermore, many vitamin-dependent enzymes have been used as a potential drug targets, thus residue level study of vitamin-interacting and non-interacting sites will be use for the further drug discovery processes.
Conclusions
In order to assist the biologists in assigning the vitamininteracting residues of VBPs, a systematic attempt has been made for predicting the vitamin-binding sites (VIRs, VAIRs, VBIRs and PLPIRs) from the amino acid sequence of VBPs. This study demonstrates that PSSM evolutionary information can be use to predict vitaminbinding sites in a protein sequence.
Additional file
Additional file 1: Figure S1-S5. The TSL representation of sliding patterns (17-residues length) of ATP, GTP, NAD, FAD and mannose. The central residue (9 th position) is showing interacting (positive) and noninteracting (negative) residues. Figure S6-S9. The TSL representation of sliding patterns (17-residues length) for prediction of VIRs, VAIRs, VBIRs and PLPIRs. The central residue (9 th position) is showing VIRs (positive) and non-VIRs (negative). Table S1. SVM-based prediction performances of surface accessibility (SA) and Hybrid (PSSM + SA) approaches for four different types of prediction methods on both realistic and balanced datasets. The values of standard errors are also given with performances. Table S2. SVM-based prediction performances (at the default threshold) of PSSM approach; according to their total number PSI-BLAST hits of different independent datasets. Table S3. SVM-based prediction performances (at the default threshold) of binary approach on the different independent datasets. | 6,587 | 2013-02-07T00:00:00.000 | [
"Biology",
"Computer Science"
] |
Synergistic Photothermal Therapy and Chemotherapy Enabled by Tumor Microenvironment-Responsive Targeted SWCNT Delivery
As a novel therapeutic approach, photothermal therapy (PTT) combined with chemotherapy can synergistically produce antitumor effects. Herein, dithiodipropionic acid (DTDP) was used as a donor of disulfide bonds sensitive to the tumor microenvironment for establishing chemical bonding between the photosensitizer indocyanine green amino (ICG-NH2) and acidified single-walled carbon nanotubes (CNTs). The CNT surface was then coated with conjugates (HD) formed by the targeted modifier hyaluronic acid (HA) and 1,2-tetragacylphosphatidyl ethanolamine (DMPE). After doxorubicin hydrochloride (DOX), used as the model drug, was loaded by CNT carriers, functional nano-delivery systems (HD/CNTs-SS-ICG@DOX) were developed. Nanosystems can effectively induce tumor cell (MCF-7) death in vitro by accelerating cell apoptosis, affecting cell cycle distribution and reactive oxygen species (ROS) production. The in vivo antitumor activity results in tumor-bearing model mice, further verifying that HD/CNTs-SS-ICG@DOX inhibited tumor growth most significantly by mediating a synergistic effect between chemotherapy and PTT, while various functional nanosystems have shown good biological tissue safety. In conclusion, the composite CNT delivery systems developed in this study possess the features of high biocompatibility, targeted delivery, and responsive drug release, and can achieve the efficient coordination of chemotherapy and PTT, with broad application prospects in cancer treatment.
Introduction
Photothermal therapy (PTT) uses photothermal conversion agents (PTAs) to obtain energy from near-infrared (NIR) light [1], which is converted into heat to increase the temperature of the surrounding environment to approximately 46 • C, resulting in tumor cell death and tumor necrosis [2].Most chromophores inherent in the body, such as oxygenated hemoglobin, deoxygenated hemoglobin, and melanin, are relatively weakly absorbed in the range of NIR light, allowing it to penetrate deep tissue and thus be highly efficient for PTT [3,4].However, PTT always leads to poor efficacy when used alone due to damage to the normal tissue around the tumor, the limited depth of light penetration leading to the incomplete ablation of tumors outside the irradiation range, and difficulties in the delivery of PTA.Therefore, PTT must be combined with other treatments to compensate for its inherent shortcomings.
Despite killing tumor cells and inhibiting their growth and reproduction, chemotherapy inevitably produces a certain degree of toxicity to normal human cells [5], especially those with rapid division and proliferation.Heat shock proteins (HSPs) are overexpressed in tumor tissues, which participate in protein folding and enhance protein stability, promote the proliferation and metastasis of tumor cells, maintain cell survival through various ways, and inhibit cell apoptosis.Synergistic therapy (NIR irradiation) can inhibit the expression of HSP, thereby improving the efficacy.Combining PTT and chemotherapy can reduce the required dose of chemotherapeutic drugs and decrease adverse reactions [6].When NIR radiation is applied to the tumor site, the photothermal effect will generate heat energy, and the increase in temperature can promote the release of chemotherapy drugs from carriers to increase their accumulation in the tumor site, thus realizing the effective combination of PTT and chemotherapy [7].Therefore, the combination of PTT and chemotherapy could be a promising cancer treatment strategy.Previously, graphene oxide, indocyanine green (ICG), and doxorubicin hydrochloride (DOX) nanoparticle cores were coated with erythrocyte membrane and folic acid [8].The system combined PTT with chemotherapy to effectively reduce tumor size.Thus, PTT combined with chemotherapy was shown to be more effective than either PTT or chemotherapy alone.However, because of their strong phototoxicity, low dark toxicity (low cytotoxicity under dark conditions) [9], and rapid clearance by the liver and kidney, it is still challenging to load PTAs, especially ICG, onto delivery platforms such as single-walled carbon nanotubes (SWCNTs) to form a vector with controlled release.
Nanomaterials commonly used as delivery carriers of chemotherapeutic drugs and PTAs include carbon nanotubes (CNTs), quantum dots, gold nanoparticles, and gold nanorods, among others.CNTs have the advantages of high chemical stability, large specific surface area, good drug adsorption, and ease of functionalization [10].Among them, SWCNTs have garnered extensive application in the development of versatile nanoplatforms because of their remarkable photothermal conversion ability and sizable drug loading capacity.Furthermore, the strong NIR absorption of SWCNTs makes it an effective absorbent for the photothermal ablation of cancer cells [11,12].SWCNTs have an adjustable hollow chemical structure, and the drug can be loaded onto their surface through covalent bonds or π-π interaction and the adsorption complexation of charged surfactants [13].The surface functional modification of SWCNTs improves their dispersion, cell uptake, and intratumoral aggregation while reducing their cytotoxicity [14].Although SWCNTs have already been applied in some studies for synergistic tumor treatment through PTT coupled with chemotherapy, the poor targeting delivery of SWCNT carriers needs to be further addressed [15].
Disulfide bonds exist naturally in the human body and play an important role in stabilizing protein structures [16].Glutathione (GSH) has the ability to convert disulfide bonds into sulfhydryl groups.When ICG is conjugated onto the surface of a nanocarrier by a disulfide bond, the nanocarrier can rapidly release ICG under a tumor microenvironment (TME).This modification can enhance the hydrophilicity and stability of ICG; meanwhile, the photothermal conversion performance of the nanocarrier is also improved.GSH concentrations in tumor cells are high; therefore, SWCNTs and ICG can be grafted by disulfide bonds to form a drug delivery carrier that is sensitive to TME.Responsive and "intelligent" drug delivery systems (DDSs) provide a new mechanism to control cargo (such as ICG) release through internal or external stimuli [17].Adaptation to internal oxidative stress in tumor cells usually leads to an increase in the antioxidant capacity of the surrounding tumor tissue, causing selective internal stimulation to trigger the responsive release of ICG, thus avoiding their photolysis and premature release and maximizing the photothermal effect at the tumor site [18].Redox-sensitive delivery carriers that contain a disulfide bond are widely used in intracellular drug delivery towards tumors due to degradation from the sulfhydryl exchange reaction in the reducing environment of tumors [19].Some studies have reported the use of disulfide bonds to control drug release.For example, camptothecin (CPT) was linked to polyethylene glycol (PEG) to design a CPT-SS-PEG-SS-CPT delivery carrier, which releases the drug into TME, improving the antitumor effect and reducing the side effects of drugs.
In our previous study, we showed that a conjugate (HD) of hyaluronic acid (HA) and a 1,2-tetragacylphosphatidyl ethanolamine coating can increase nanosystems' targeting affinity to tumors.Herein, Dithiodipropionic anhydride (DTDPA) was synthesized by the dehydration of dithiodipropionic acid (DTDP), which provides a disulfide bond connecting CNTs and ICG.A HD-coated SWCNT delivery system was further developed to load the chemotherapeutic drug, DOX.The DOX and ICG co-loaded system (HD/CNTs-SS-ICG@DOX) can responsively release ICG under TME and achieve synergistic antitumor effects by mediating chemotherapy and PTT [20].After HD/CNTs-SS-ICG@DOX reach the tumor site by the targeted action of HA, they first penetrate the cell membrane and reach the lysosome through endocytosis.At this stage, high concentrations of GSH in TME will break disulfide bonds, thus rapidly releasing ICG.At the same time, external NIR light will be used to convert light energy into high-temperature thermal energy to maximize the photothermal effect of ICG.The acidic microenvironment and the increase in temperature promote the release of DOX from CNTs, and then lysosomal escape occurs, which makes small molecules enter the cytoplasm and nucleus, there realizing an effective coordination between PTT and chemotherapy.This tumor-targeting and microenvironment-responsive nanosystem has broad application potential for PTT synergistic chemotherapy.
Characterization of Various SWCNT Nanocarriers
The preparation procedure and antitumor mechanism of HD/CNTs-SS-ICG@DOX are shown in Scheme 1 and Figure S1.To improve the biocompatibility, pristine SWCNTs were treated with nitric acid to obtain CNTs with carboxyl groups on their surface [21].After acidification, the particle size of CNTs decreased from 164.2 nm to approximately 122.4 nm (Figure 1C and Table 1).The results listed in Table 2 show that the melting point of DTDP was in the range of 152.5-155.8• C, and that of DTDPA was in the range of 67.5-73.2• C. According to reports in the literature [5], the melting point of DTDP is 153-155 • C, and the change in melting point confirmed the successful preparation of DTDPA.TEM images showed that the acidified CNTs had a larger diameter, stretched length, and improved dispersity, with the removal of most impurities (Figure 1A).Despite the various treatments, SWCNT samples maintained a hollow tubular structure, indicating that the addition of each modified component did not destroy its basic structure.Moreover, numerous nodules appearing on the surface of HD/CNTs-SS indicated that HD was conjugated onto CNT samples.SEM images of different SWCNTs are shown in Figure S2.
The characteristic peaks of DTDP, DTDPA, NH 2 -PEG-OH, and NH 2 -PEG-SS-COOH were assessed using a nuclear magnetic resonance hydrogen spectrometer (Figure 1B).DTDP and DTDPA had the same two peaks at δ = 2.88 ppm (-CH 2 -SS-CH 2 -) and δ = 2.60 ppm (-CH 2 -CH 2 -SS-CH 2 -CH 2 -), respectively, and the carboxyl hydrogen in DT-DPA disappeared after the dehydration of DTDP to DTDPA.The carboxyl hydrogen at δ = 12.36 ppm (-COOH) disappeared in DTDPA.The peaks at δ = 2.94 ppm (-CH 2 -SS-CH 2 -) and δ = 2.83 ppm (-OOC-CH 2 -CH 2 -SS-CH 2 -CH 2 -COOH) showed the successful synthesis of NH 2 -PEG-SS-COOH [5].The FT-IR spectra in Figure 1E show that DTDP had the characteristic peaks of C=O and -OH at 3400 cm −1 and 1600-1700 cm −1 , whereas DTDPA only had a vibration peak at 1689 cm −1 , indicating that DTDP had been completely dehydrated to DTDPA.NH 2 -PEG-SS-COOH had characteristic peaks of C=O and -OH, respectively.Compared with CNT, after conjugation with NH 2 -PEG-SS-COOH, the C=O peak of the CNTs-SS became weak and the absorption peaks from the carboxyl group and the disulfide bond were notably enhanced.These results verified the successful synthesis of NH 2 -PEG-SS-COOH and surface modification for CNT samples.notably enhanced.These results verified the successful synthesis of NH2-PEG-SS-COOH and surface modification for CNT samples.Scheme 1. Schematic diagram of the preparation procedure and antitumor mechanism of HD/CNTs-SS-ICG@DOX DDS.A drug delivery system (HD/CNTs-SS-ICG@DOX) was developed by conjugating ICG-NH2 on the surface of CNTs through S-S, loading chemotherapy drug DOX inside the lumen, and finally coating the surface with targeting agent HD.The drug delivery system can release drugs in the TME to realize the synergistic antitumor effect by mediating chemotherapy and PTT.The efficient loading of ICG and DOX by CNT carriers was demonstrated by ultraviolet-visible spectrophotometry (UV-Vis) (Figure 1F).HD/CNTs-SS-ICG@DOX showed in- The efficient loading of ICG and DOX by CNT carriers was demonstrated by ultravioletvisible spectrophotometry (UV-Vis) (Figure 1F).HD/CNTs-SS-ICG@DOX showed intense UV absorption peaks from DOX and ICG at 480 nm and 780 nm, respectively, indicating the presence of DOX and ICG on CNT carriers.The zeta potential analysis results indicated that, compared with the pristine SWCNTs, the surface charge of CNTs decreased from −21.8 mV to −41.7 mV due to the large number of carboxyl groups on their surface (Figure 1D and Table 1).After modification with NH 2 -PEG-SS-COOH, an increase in the electric potential to −18.5 mV for CNTs-SS was observed, attributing the neutralization of the carboxyl group during the amide reaction and its strong adsorption capacity.Finally, HD/CNTs-SS-ICG@DOX had the potential of −18.5 mV.In Raman spectra, the D peak at 1340 cm −1 and the G peak at 1575 cm −1 represented the disordered vibration and stretching vibration of the C-C single bond, respectively, indicating that the modified CNTs retained their basic structure (Figure 1G).After modification with NH 2 -PEG-SS-COOH, the I G /I D value increased, indicating an increase in the degree of graphitization.The enhancement of the G peak was mainly caused by the enlarged diameter of CNTs and the enhanced stretching vibration of the C-C single bond.For HD/CNTs-SS, their I G /I D value further increased from 3.2392 to 3.8246, which was likely attributed to the strong interaction between the phosphatidyl chains in HD and SWCNTs, resulting in a change in the force constants of C-C single bonds in the wall structure.XRD patterns showed that the most typical diffraction peaks at 26 • and 44 • indicated that the modified CNTs still retained their basic structure (Figure 1H).
Additionally, the dispersion stability of SWCNTs@DOX and HD/CNTs-SS@DOX are shown in Figure S3A.Regardless of which dispersion medium was used, SWCNTs@DOX always tended to be rapidly clustered.In contrast, HD/CNTs-SS@DOX exhibited better dispersion stability in various mediums.In X-ray photoelectron spectroscopy (XPS) spectra, CNTs-SS and HD/CNTs-SS showed the N1s peaks at 400 eV, and only HD/CNTs-SS had the characteristic P peaks at 132 eV and 188 eV, indicating that NH 2 -PEG-SS-COOH and HD were conjugated onto the surface of CNTs (Figure S3B-F).The thermogravimetric analysis (DSC) results showed that SWCNTs transformed from an amorphous to crystalline state at 252.56-264.09• C, while the temperature range for acidified CNTs to transform was 107.87-161.91 • C. The significant decrease in phase transition temperature was caused by the thermal decomposition of the hydroxyl and carboxyl groups on the surface of CNTs into CO 2 and H 2 O (Figure S3G).The DSC curves of CNTs-SS and HD/CNTs-SS were similar, and the decomposition temperature was higher than that of CNTs, indicating that modification with NH 2 -PEG-SS-COOH and HD could increase the thermal stability of CNTs.
Loading Efficiency and In Vitro Release of ICG and DOX
The ICG loading efficiencies of CNTs-SS-ICG and HD/CNTs-SS-ICG were 90.64% and 88.43%, respectively.The DOX encapsulation efficiency and loading efficiency of various delivery systems are listed in Table 3.For example, the encapsulation efficiency and loading efficiency of HD/CNTs-SS-ICG@DOX were 88.40% and 55.82 µg/mg, respectively.
To assess the redox responsiveness of the nanosystem, the release of ICG from HD/CNTs-SS-ICG was investigated at different concentrations of GSH (Figure 2A).In the medium free of GSH, the release rate of ICG was 36.22%within 120 h, whereas in the medium with a high concentration of GSH, the released ICG reached 74.50%.This result indicated that, with increasing GSH concentration, the cleavage speed of the disulfide bond in HD/CNTs-SS-ICG was accelerated, leading to the rapid release of ICG from the nanosystem.The release of DOX from HD/CNTs-SS-ICG@DOX was evaluated under different temperatures and pH conditions.This nanosystem exhibited a dual-temperature and pH-sensitive drug release property.In the medium simulating normal conditions (at 25 • C and pH 7.4), the release rate of DOX was only 29.41% after 120 h, while under the conditions with a high temperature and low pH (at 45 • C and pH 5.0), the release rate was up to 94.25% (Figure 2B).These results imply that DOX release could be enhanced by photothermal effects on the local tumor environment.Furthermore, the DOX release profiles of various nanosystems are shown in Figure 2C,D.The Higuchi model was used to fit the drug release curve.It was found that the release rate constants (K) of SWCNTs@DOX, CNTs@DOX, CNTs-SS@DOX, and HD/CNTs-SS@DOX were 0.1644, 0.6606, 2.5381, and 5.6345, respectively, at pH 7.4.The K of these nanosystems was 0.9711, 1.6665, 1.8658, and 7.2762 at pH 5, respectively.All the nanosystems exhibited a more rapid drug release at pH 5.0 than that at pH 7.4, and the functionalized systems had a higher release amount than unmodified samples within 120 h. and pH-sensitive drug release property.In the medium simulating normal conditions (at 25 °C and pH 7.4), the release rate of DOX was only 29.41% after 120 h, while under the conditions with a high temperature and low pH (at 45 °C and pH 5.0), the release rate was up to 94.25% (Figure 2B).These results imply that DOX release could be enhanced by photothermal effects on the local tumor environment.Furthermore, the DOX release profiles of various nanosystems are shown in Figure 2C,D.The Higuchi model was used to fit the drug release curve.It was found that the release rate constants (K) of SWCNTs@DOX, CNTs@DOX, CNTs-SS@DOX, and HD/CNTs-SS@DOX were 0.1644, 0.6606, 2.5381, and 5.6345, respectively, at pH 7.4.The K of these nanosystems was 0.9711, 1.6665, 1.8658, and 7.2762 at pH 5, respectively.All the nanosystems exhibited a more rapid drug release at pH 5.0 than that at pH 7.4, and the functionalized systems had a higher release amount than unmodified samples within 120 h.
Photothermal Performance Verification
Photothermal analysis was performed at an excitation wavelength of 808 nm due to its advantages of efficient tissue penetration, minimal absorption by water molecules, cells, and tissue components, as well as its biosafety [22,23].The photothermal conversion property of ICG was verified under NIR irradiation of 5 W/cm 2 ; the result indicated that the heating rate increased with increasing ICG concentration (Figure 3A).After 210-240 s of irradiation, the high temperature induced by free ICG with different concentrations
Photothermal Performance Verification
Photothermal analysis was performed at an excitation wavelength of 808 nm due to its advantages of efficient tissue penetration, minimal absorption by water molecules, cells, and tissue components, as well as its biosafety [22,23].The photothermal conversion property of ICG was verified under NIR irradiation of 5 W/cm 2 ; the result indicated that the heating rate increased with increasing ICG concentration (Figure 3A).After 210-240 s of irradiation, the high temperature induced by free ICG with different concentrations rapidly decreased, owing to the photolysis property.Thus, it was crucial to load ICG by nanocarriers to improve its photothermal stability.The HD/CNTs-SS-ICG solution exhibited an excellent response to an irradiation intensity of 5 W/cm 2 (Figure 3B,C), and the temperature increased to 45 • C within 30 s after NIR irradiation at this intensity.The tumor cells could undergo thermal ablation at this temperature, inducing further necrosis.
nanocarriers to improve its photothermal stability.The HD/CNTs-SS-ICG solution exh ited an excellent response to an irradiation intensity of 5 W/cm 2 (Figure 3B,C), and t temperature increased to 45 °C within 30 s after NIR irradiation at this intensity.The t mor cells could undergo thermal ablation at this temperature, inducing further necrosi The photothermal properties of HD/CNTs-SS and HD/CNTs-SS-ICG@DOX were al verified under NIR irradiation of 5 W/cm 2 (Figure 3D).HD/CNTs-SS had an inferior ph tothermal conversion performance, which only increased the environmental temperatu to 35.2 °C at 300 s.Conversely, HD/CNTs-SS-ICG@DOX could rapidly increase the te perature to above 40 °C, and the final temperature reached approximately 43.5 °C.The results demonstrated that it was indispensable to incorporate ICG to manufacture nanosystem to trigger PPT effects, and that the loading of DOX almost did not affect t photothermal conversion performance of HD/CNTs-SS-ICG.Furthermore, HD/CNTs-S ICG solutions maintained a good photothermal performance in four heating-cooling c cles, with photothermal conversion efficiencies greater than 60% (η1 = 63.89%,η2 = 73.05η3 = 85.51%, η4 = 90.64%).The incremental η values could result from the accumulative released ICG with increasing cycles (Figure 3E).The photothermal properties of HD/CNTs-SS and HD/CNTs-SS-ICG@DOX were also verified under NIR irradiation of 5 W/cm 2 (Figure 3D).HD/CNTs-SS had an inferior photothermal conversion performance, which only increased the environmental temperature to 35.2 • C at 300 s.Conversely, HD/CNTs-SS-ICG@DOX could rapidly increase the temperature to above 40 • C, and the final temperature reached approximately 43.5 • C.These results demonstrated that it was indispensable to incorporate ICG to manufacture a nanosystem to trigger PPT effects, and that the loading of DOX almost did not affect the photothermal conversion performance of HD/CNTs-SS-ICG.Furthermore, HD/CNTs-SS-ICG solutions maintained a good photothermal performance in four heating-cooling cycles, with photothermal conversion efficiencies greater than 60% (η1 = 63.89%,η2 = 73.05%,η3 = 85.51%, η4 = 90.64%).The incremental η values could result from the accumulatively released ICG with increasing cycles (Figure 3E).
Cell Viability Assessment
Herein, the cytotoxicity of various SWCNTs against MCF-7 cells was assessed within 24 h (Figure 4A).Free ICG showed higher cytotoxicity than SWCNT nanoparticles.At concentrations of 50 µg/mL or 100 µg/mL, functionalized HD/CNTs-SS-ICG had a higher cell survival rate compared with other SWCNTs (above 85%).The hemolysis rate results shown in Figure 4C,E indicated that the hemolysis rates of various SWCNTs were all less than 5% at 10-100 µg/mL, showing good biological safety.
Cell Viability Assessment
Herein, the cytotoxicity of various SWCNTs against MCF-7 cells was assessed within 24 h (Figure 4A).Free ICG showed higher cytotoxicity than SWCNT nanoparticles.At concentrations of 50 μg/mL or 100 μg/mL, functionalized HD/CNTs-SS-ICG had a higher cell survival rate compared with other SWCNTs (above 85%).The hemolysis rate results shown in Figure 4C,E indicated that the hemolysis rates of various SWCNTs were all less than 5% at 10-100 μg/mL, showing good biological safety.
In the HD/CNTs-SS-ICG@DOX treatment group, after 5 W/cm 2 of NIR irradiation for 5 min, the cell survival rate decreased to 42.66%.The cell lethal rate was nearly 3.61% and 13.55% higher than that of HD/CNTs-SS@DOX and HD/CNTs-SS-ICG+NIR treatment, respectively, verifying the superior synergistic tumor inhibitory effect over chemotherapy or PTT alone (Figure 4D).The survival rate of IPEC-1 cells by free DOX treatment was approximately 55.17%, suggesting that chemotherapy drugs had an inhibitory effect on normal cell growth.By the same treatment with HD/CNTs-SS@DOX, the survival rate of IPEC-1 cells was much higher compared to that of MCF-7 cells (by approximately 40%), which was likely due to the enhanced targeting effect of nanocarriers originating from HD modification towards tumor cells.Similarly, in the HD/CNTs-SS-ICG@DOX+NIR treatment group, the viability of IPEC-1 cells was nearly 30% higher than that of MCF-7 cells, indicating that synergistic chemotherapy and PTT had higher biological safety in normal cells (Figure 4B).In the HD/CNTs-SS-ICG@DOX treatment group, after 5 W/cm 2 of NIR irradiation for 5 min, the cell survival rate decreased to 42.66%.The cell lethal rate was nearly 3.61% and 13.55% higher than that of HD/CNTs-SS@DOX and HD/CNTs-SS-ICG+NIR treatment, respectively, verifying the superior synergistic tumor inhibitory effect over chemotherapy or PTT alone (Figure 4D).The survival rate of IPEC-1 cells by free DOX treatment was approximately 55.17%, suggesting that chemotherapy drugs had an inhibitory effect on normal cell growth.By the same treatment with HD/CNTs-SS@DOX, the survival rate of IPEC-1 cells was much higher compared to that of MCF-7 cells (by approximately 40%), which was likely due to the enhanced targeting effect of nanocarriers originating from HD modification towards tumor cells.Similarly, in the HD/CNTs-SS-ICG@DOX+NIR treatment group, the viability of IPEC-1 cells was nearly 30% higher than that of MCF-7 cells, indicating that synergistic chemotherapy and PTT had higher biological safety in normal cells (Figure 4B).
Cellular Uptake and Intracellular Distribution
The cellular fluorescence of ICG and DOX was observed using a fluorescence microscope to analyze the uptake of the nanosystem by MCF-7 cells.As shown in Figure 5A-C, only a weak fluorescence signal was detected in cells treated with free DOX or ICG, owing to the fact that free drug molecules were transferred into cells only by passive mobility or diffusion.Conversely, as the nanocarriers, functionalized SWCNTs were apt to be internalized by cells via direct penetration or endocytosis.Thus, various nano-samples exhibited a more efficient cellular uptake than free drugs, and the fluorescence intensity was increased gradually with the improvement in surface modification for nanocarriers.Furthermore, FCM was used to quantitatively assess the intracellular fluorescence intensity.As shown in Figures 5D and S4A, various nanosystems could be effectively internalized by cells in a time-dependent manner, indicating the gradual accumulation of delivery carriers in tumor cells.HD/CNTs-SS-ICG@DOX showed a higher uptake efficiency compared with other formulations; the fluorescence intensity at 24 h was almost 4.0-fold that of free DOX.This result should be attributed to the fact that surface modification would enhance the water dispersion of SWCNTs and improve their targeting affinity to tumor cells, being conducive to efficient delivery and subsequent intracellular drug release.
The intracellular distribution of FITC-labeled HD/CNTs-SS nanoparticles in MCF-7 cells was investigated by confocal microscopy.As shown in Figure S4B, most of the green fluorescence of FITC colocalized with the red fluorescence of Lyso-tracker after treatment with HD/CNTs-SS@FITC for 4 h.After 16 h of co-incubation, it could be observed that HD/CNTs-SS@FITC gradually translocated from the lysosome to the cytoplasm, and a small number of nanoparticles accumulated into the nucleus.At 24 h, FITC fluorescence overlapped with Hochest blue fluorescence, becoming higher; meanwhile, the intensity of red fluorescence was significantly reduced, implying that the nano-samples achieved lysosomal escape and could locate the nucleus to exert an antitumor effect.
Cell Apoptosis and Cell Cycle Variation Analysis
The apoptosis rate in MCF-7 cells treated with various formulations was investigated by FACS (Figure 6A-D).After 16 h of treatment, the apoptosis rate of cells treated with free DOX was 2.41%, while that of the HD/CNTs-SS@DOX treatment group increased to 2.64% and that of the HD/CNTs-SS-ICG+NIR group further increased by nearly 18%.More notably, the apoptosis rate of the HD/CNTs-SS-ICG@DOX+NIR treatment reached 44.1%,
ROS Measurement
The effects of various formulations on ROS levels in MCF-7 cells were assessed and the results are shown in Figure 5E-G.The 2 ′ ,7 ′ -dichlorodihydrofluorescein (DCF) fluorescence of free DOX was relatively weak when compared to CNT nano-formulations, and the red fluorescence from DOX was slightly enhanced under NIR irradiation, indicating that irradiation was helpful for the cellular uptake of drugs [24].After treatment with HD/CNTs-SS@DOX and HD/CNTs-SS-ICG+NIR for 24 h, the green fluorescence of DCF increased.However, after 24 h of treatment with HD/CNTs-SS-ICG@DOX+NIR, both the red and green fluorescence reached their highest intensity.This result suggested that synergistic therapy can effectively increase DOX uptake and ROS production, leading to triggering cell apoptosis and the necrosis pathway.The enhanced intracellular fluorescence of DCF with the extension of the treatment time indicated that the synergistic antitumor effect of chemotherapy and PTT was also time-dependent.
Cell Apoptosis and Cell Cycle Variation Analysis
The apoptosis rate in MCF-7 cells treated with various formulations was investigated by FACS (Figure 6A-D).After 16 h of treatment, the apoptosis rate of cells treated with free DOX was 2.41%, while that of the HD/CNTs-SS@DOX treatment group increased to 2.64% and that of the HD/CNTs-SS-ICG+NIR group further increased by nearly 18%.More notably, the apoptosis rate of the HD/CNTs-SS-ICG@DOX+NIR treatment reached 44.1%, and the total cell death rate (apoptosis rate + necrosis rate) was 48.62%, indicating that highintensity light irradiation led to necrosis and the rapid ablation of tumor cells.Similarly, the apoptosis rate in the HD/CNTs-SS@DOX and HD/CNTs-SS-ICG+NIR groups after 48 h of treatment was 28.37% and 36.42%,respectively, whereas the total death rate caused by the HD/CNTs-SS-ICG@DOX+NIR treatment was up to 70.2%.It could be concluded that synergistic therapy mediated by HD/CNTs-SS-ICG@DOX systems had a better antitumor effect than chemotherapy or PTT alone to achieve a 1 + 1 > 2 efficacy.
FACS was used to investigate the cell cycle distribution of MCF-7 cells after different treatments (Figure 7A-D).Compared with the control group, the S-phase fraction (SPF) of cells treated with HD/CNTs-SS@DOX for 16 h and 48 h increased by 40% and 47%, respectively, indicating that loading DOX by CNT carriers could affect the cycle distribution of MCF-7 cells significantly.Furthermore, the SPF of the HD/CNTs-SS-ICG+NIR group increased by 10%.In particular, the SPF and G2 phase cells after HD/CNTs-SS-ICG@DOX+NIR treatment increased more markedly, which implied that synergistic treatment with PTT and chemotherapy increased the number of MCF-7 cells in the S phase and arrested the cell cycle in the G2 phase.Therefore, the number of cells in the M phase was reduced to achieve an antitumor effect by interfering with cell division and decreasing DNA synthesis.
ICG@DOX+NIR treatment increased more markedly, which implied that synergistic treatment with PTT and chemotherapy increased the number of MCF-7 cells in the S phase and arrested the cell cycle in the G2 phase.Therefore, the number of cells in the M phase was reduced to achieve an antitumor effect by interfering with cell division and decreasing DNA synthesis.
Evaluation of the Antitumor Efficacy In Vivo
Model animals were established using MCF-7 cells to explore the photothermal properties of the nanosystems for in vivo therapy (Figure 8A,B).Female BALB/c nude mice were randomly divided into five groups: blank control (NS), free DOX, HD/CNTs-SS@DOX, HD/CNTs-SS-ICG+NIR, and<EMAIL_ADDRESS>photothermal effects of each sample after exposure to NIR light for 5 min were then evaluated.The temperature of the HD/CNTs-SS-ICG and HD/CNTs-SS-ICG@DOX groups rose obviously within the first 1 min of NIR irradiation, reaching 48 °C and 45 °C, respectively.Then, the temperature rose slowly and stabilized at about 50 °C after 2 min.In the free ICG group, the temperature was stable at 40 °C after NIR irradiation, indicating that ICG combined with CNTs could synergistically improve their photothermal conversion capacity.There was no significant temperature variation at the tumor site in the NS treatment group, and treatment with HD/CNTs-SS-ICG and HD/CNTs-SS-ICG@DOX rapidly led to a temperature rise at the tumor site, reaching the optimal temperature for triggering the photothermal effect.
Evaluation of the Antitumor Efficacy In Vivo
Model animals were established using MCF-7 cells to explore the photothermal properties of the nanosystems for in vivo therapy (Figure 8A,B).Female BALB/c nude mice were randomly divided into five groups: blank control (NS), free DOX, HD/CNTs-SS@DOX, HD/CNTs-SS-ICG+NIR, and<EMAIL_ADDRESS>photothermal effects of each sample after exposure to NIR light for 5 min were then evaluated.The temperature of the HD/CNTs-SS-ICG and HD/CNTs-SS-ICG@DOX groups rose obviously within the first 1 min of NIR irradiation, reaching 48 • C and 45 • C, respectively.Then, the temperature rose slowly and stabilized at about 50 • C after 2 min.In the free ICG group, the temperature was stable at 40 • C after NIR irradiation, indicating that ICG combined with CNTs could synergistically improve their photothermal conversion capacity.There was no significant temperature variation at the tumor site in the NS treatment group, and treatment with The procedure for the in vivo assessment of antitumor therapy is shown in Figure 9A.The tumor volume of the mice was measured and photographed every 3 days (Figure 9B,G).In the chemotherapy group (free DOX), the tumor volume decreased in the first six days, and then increased to some extent, which may be due to the increased drug resistance of the tumor after repeated administration.The tumor volume of nude mice in the chemotherapy group (HD/CNTs-SS-ICG@DOX) and PTT group (HD/CNTs-SS-ICG+NIR) did not change significantly, which further confirmed that both chemotherapy and PTT could inhibit tumor growth.On the contrary, in the HD/CNTs-SS-ICG@DOX+NIR group, the tumor volume continued to decrease within 15 days, which proved that synergistic therapy could stably inhibit tumor growth and had a good antitumor effect.At the endpoint of the experiments, the tumor was resected and weighed to evaluate the in vivo antitumor effect by different treatments.As shown in Figure 9D-F, simultaneous chemotherapy and PTT mediated by the HD/CNTs-SS-ICG@DOX system had a more potent inhibitory activity against tumor growth, as tumor eradication in one mouse and a dramatically decreased tumor size in other four mice were observed after 15 The procedure for the in vivo assessment of antitumor therapy is shown in Figure 9A.The tumor volume of the mice was measured and photographed every 3 days (Figure 9B,G).In the chemotherapy group (free DOX), the tumor volume decreased in the first six days, and then increased to some extent, which may be due to the increased drug resistance of the tumor after repeated administration.The tumor volume of nude mice in the chemotherapy group (HD/CNTs-SS-ICG@DOX) and PTT group (HD/CNTs-SS-ICG+NIR) did not change significantly, which further confirmed that both chemotherapy and PTT could inhibit tumor growth.On the contrary, in the HD/CNTs-SS-ICG@DOX+NIR group, the tumor volume continued to decrease within 15 days, which proved that synergistic therapy could stably inhibit tumor growth and had a good antitumor effect.At the endpoint of the experiments, the tumor was resected and weighed to evaluate the in vivo antitumor effect by different treatments.As shown in Figure 9D-F, simultaneous chemotherapy and PTT mediated by the HD/CNTs-SS-ICG@DOX system had a more potent inhibitory activity against tumor growth, as tumor eradication in one mouse and a dramatically decreased tumor size in other four mice were observed after 15 days of treatment.Furthermore, the tumor weight of the HD/CNTs-SS-ICG@DOX+NIR group was less and the TGIR was much higher than other treatments (up to 83.77%, Figure 9E).These results confirmed that synergistic therapy with chemotherapy and PTT could stably inhibit tumor growth and achieve a better therapeutic effect.
(Figure S5), no intense damage to normal organs and tumor tissues was observed after NIR irradiation, indicating that PTT had little effect on normal tissues and thus verifying the biosafety of NIR irradiation used in PTT.Finally, free DOX and various nano-drug treatments inflicted no remarkable organ damage on nude mice; only the synergistic treatment group exhibited a marked necrosis effect on tumor tissues, which favored achieving a better antitumor effect (Figure 8C).The body weight changes in nude mice during the entire treatment were monitored to further assess the biosafety of various nanosystems (Figure 9C).With the extension of treatment time, the body weight in each treatment group increased slightly, suggesting that the different treatment schemes did not lead to significant systemic toxicity.Compared to the HE staining of normal organs and NIR-irradiated organs in the blank control (Figure S5), no intense damage to normal organs and tumor tissues was observed after NIR irradiation, indicating that PTT had little effect on normal tissues and thus verifying the biosafety of NIR irradiation used in PTT.Finally, free DOX and various nano-drug treatments inflicted no remarkable organ damage on nude mice; only the synergistic treatment group exhibited a marked necrosis effect on tumor tissues, which favored achieving a better antitumor effect (Figure 8C).
Cell Culture
In this study, MCF-7 breast cancer cells obtained from American Type Culture Collection (ATCC, Manassas, VA, USA) were used as the model.The cells were cultured in RPMI-1640 medium supplemented with 9% FBS and incubated under the following culture conditions: 5% CO 2 , 90% humidity, and a constant temperature of 37 • C. IPEC-1 porcine small intestine epithelial cells were used as the control model.
Experimental Animals
All animal experiments followed the guidelines of the National Institutes of Health and the rules and guidelines approved by the Ethics Committee of the Animal Center of Zhengzhou University.BALB/c female mice aged 4-6 weeks (body weight: 14-15 g) were purchased from Beijing WeitongLihua Experimental Animal Technology Co., Ltd.MCF-7 cells (1 × 10 7 ) and 0.2 mL of NS were subcutaneously injected (s.c.) into the right forelimb of mice to establish the tumor-bearing nude mouse model [25].First, 50 mg of SWCNTs was added into nitric acid, then the sample was ultrasonicated (200 W, 53 kHz) for 3 h and left to rest overnight.Subsequently, it was heated at 90 • C for 24 h and the supernatant was removed by centrifugation at 24,000 rpm for 30 min.The precipitate was washed to neutral with ultrapure water, and CNTs were obtained after vacuum-drying.
Preparation of CNTs-SS-ICG
Synthesis of DTDPA: The 1 g of DTDP was added into 5 mL of acetyl chloride in an oil bath at 65 • C for 5.5 h.The sample was rotary-evaporated at 50 • C, and white flocculent appeared after 20 mL of glacial ether was added.Afterward, the suspension was suction-filtered and washed with glacial ether.The residue was collected and subjected to vacuum-drying at 30 • C, and the white precipitate obtained was DTDPA.
Preparation of NH 2 -PEG-SS-COOH: DTDPA, NH 2 -PEG-OH, DMAP, and TEA were dissolved in DMF.The above mixture was reacted at 600 rpm at either 37 • C or 45 • C for 24 h.Subsequently, ice ether (50 mL) was added into the mixture and further subjected to centrifugation at 1000 rpm for 8 min and then maintained at 4 • C; the procedure was repeated twice.The white precipitate, which was NH 2 -PEG-SS-COOH, was collected and dried under a vacuum at 25 • C.
Preparation of CNTs-SS: The 30 mg of CNTs was dispersed in DMSO (9 mL) and further ultrasonicated (200 W, 53 kHz) with an ultrasonic cleaner for 3 h.The 1 mL of NHS and 1 mL of DCC (dissolved in DMSO) were introduced to a CNT suspension to activate carboxyl groups.After 12 h, 1 mL of NH 2 -PEG-SS-COOH (31 mg/mL in DMSO) and 1 mL of DMAP (150 mg/mL in DMSO) were added to the activated CNT solution.After reacting at 600 rpm and 37 • C for 24 h, the final mixture was dialyzed and freeze-dried to obtain CNTs-SS.
Preparation of CNTs-SS-ICG:
The 20 mg of CNTs-SS was dispersed in DMSO (9 mL) and then activated by 50 mg of NHS and 40 mg of DCC.The ICG-NH 2 (1 mg/mL in DMSO) and DMAP (1 mL; 25 mg/mL DMSO solution) were catalyzed and allowed to react with CNTs-SS in the absence of light for 24 h.After that, the mixture was centrifuged at 12,000 rpm for 20 min and the supernatant was collected to determine the loading efficiency of ICG by high-performance liquid chromatography (HPLC).CNTs-SS-ICG were obtained after the precipitation was lyophilized.
Synthesis of HA-DMPE:
The 20 mg of HA and 11.4 µL of EDAC were dissolved in ultrapure water (5 mL) and stirred at 37 • C for 2 h.Subsequently, HA was activated by adjusting the pH to 8.4 with 0.1 M borate buffer.The 50 mg of DMPE was dissolved in ether (5 mL) and further rotary-evaporated to form the lipid membrane.The activated HA solution was poured into the lipid membrane.After ultrasonication (200 W, 53 kHz) for 30 min, the mixture was further reacted at 37 • C for 24 h.The final mixture was dialyzed and freeze-dried to obtain HA-DMPE (HD).
Preparation of HD/CNTs-SS-ICG@DOX: The 10 mg of CNTs-SS-ICG was dispersed in PBS (20 mL).After 2 h of ultrasonication (200 W, 53 kHz), DOX solution (1 mg/mL) was added and allowed to react at 37 • C for 4 h.The resulting products (CNTs-SS-ICG@DOX) were centrifuged at 12,000 rpm for 20 min.The precipitation was collected and mixed with HD solution (1 mg/mL in PBS).After ultrasonic dispersion, the mixture was reacted at 37 • C for 2 h and further centrifugated at 12,000 rpm for 20 min.The amount of free DOX in the supernatant was determined and the precipitation was collected and lyophilized to obtain HD/CNTs-SS-ICG@DOX.
Powder samples (0.2 g) of SWCNT, CNT, CNT-SS, and HD/CNT-SS were weighed and tested with a BRUCKER D8 ADVANCE X-ray diffractometer (Bruker AXS, Berlin, Germany).The scanning range was set between 5 and 80 • , with a scanning step of 0.02 • and scanning speed of 5 • /min.Various samples were uniformly laid on glass slides, pressed, and smoothed.Raman scattering was measured using a Renishaw on a Via Raman spectrometer at an excitation wavelength of 633 nm in the range of 100-3500 cm −1 .Two flat stainless-steel modules were pressed and measured on the sample table of a Thermo escalab250XiX X-ray photoelectron spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) with double-sided adhesive.The narrow scan elements were carbon (C), oxygen (O), nitrogen (N), and sulfur (S), which were used to determine the types of elements present on the sample surface.
Photothermal Effect Analysis
The temperature curves of the PBS and HD/CNTs-SS-ICG were drawn under 808 nm NIR irradiations of 4 W/cm 2 , 5 W/cm 2 , and 6 W/cm 2 for 5 min, respectively.Temperature changes in the four cycles were recorded, and the photothermal conversion efficiency was obtained from the heat transfer curves [29].The photothermal conversion efficiency was calculated according to the following formula: η = hA(△Tmax − △Tmax.PBS)/I(1 − 10 −Aλ ), where h = 0.59 W/(m 2 .K), A is the surface area of the container (4.5 × 10 −4 m 2 ), Tmax is the temperature change in the sample solution at the highest steady temperature, Tmax.PBS is the temperature change in PBS at the highest steady temperature, I is the laser power, and Aλ is the absorbance of the sample solution at 808 nm, respectively [30,31].
Drug Loading and Encapsulation Efficiency
Following the synthesis of CNTs-SS-ICG and HD/CNTs-SS-ICG, the supernatant was collected to determine ICG using HPLC.The load efficiency of ICG was calculated according to the following formula: load efficiency (%) = (Total ICG − Free ICG )/Total ICG × 100%.SWCNTs, CNTs, CNTs-SS, CNTs-SS-ICG, and CNTs-SS-ICG (10 mg) were suspended in 20 mL of PBS.After ultrasonication for 2 h, 2 mg of DOX solution at a concentration of 1 mg/mL was added and ultrasonicated for another 2 h [32].The mixture was centrifuged at 12,000 rpm for 20 min and the supernatant was taken to measure the amount of free DOX using UV-vis at 480 nm.DOX encapsulation efficiency and drug loading were calculated according to the following formulas: encapsulation rate (%) = (Total DOX − Free DOX )/Total DOX × 100%, drug loading (%) = (Total DOX − Free DOX )/(Total amount of carrier + Total DOX ) × 100%.
In Vitro Drug Release
The HD/CNTs-SS-ICG was dispersed in PBS containing 0, 2, 5, or 10 mM GSH and oscillated at 160 rpm and room temperature.ICG concentration was determined by HPLC at preset time intervals.
The HD/CNTs-SS-ICG@DOX was dispersed in 5 mL of PBS and then suspended in 50 mL of PBS at different temperatures and pH, respectively.Furthermore, SWCNTs@DOX, CNTs@DOX, CNTs-SS@DOX, CNTs-SS@DOX, and HD/CNTs-SS-ICG@DOX were suspended in PBS at pH 5.0 or 7.4, respectively.All the samples were oscillated at 160 rpm and at preset time intervals, 2 mL of supernatant was taken out, and the percentage of released DOX was determined by UV-vis.
Cytotoxicity and Hemolysis of Nanoparticles
The cytotoxicity of SWCNTs, CNTs, CNTs-SS, ICG, CNTs-SS-ICG, and HD/CNTs-SS-ICG towards MCF-7 cells was assessed by MTT assay [33].The cells were cultured in 96-well plates overnight; then, the culture medium was replaced by fresh medium containing different nanoparticles.After 24 h, 20 µL of MTT solution was added for further incubation for 4 h.Subsequently, the medium was removed and 100 µL of DMSO was added to disperse the formazan precipitate, and the multi-functional plate reader (Varioskan Flash, ThermoFisher Scientific, Waltham, MA, USA) was used to measure the optical density of the solution at 490 nm [34,35].Hemolysis of various nanoparticles was evaluated using 1% Triton and NS as positive and negative control, respectively.The hemolysis rate was calculated using the following formula: hemolysis rate = (Experimental group A540 − Negative control A540)/(Positive control A540 − Negative control A540) × 100%.
In Vitro Antitumor Activity
The inhibitory effect of DOX, HD/CNTs-SS@DOX, ICG (2.0 µg/mL), HD/CNTs-SS-ICG, and HD/CNTs-SS-ICG@DOX against MCF-7 cells and IPEC-1 cells was also evaluated by MTT assay.Lastly, the absorbance of each well was measured at 490 nm to calculate cell viability, as mentioned above.The cells incubated with nano-formulations were exposed to NIR laser irradiation (5 W/cm 2 , 808 nm) for 5 min, and the cells were incubated for another 4 h to investigate the photothermal influence on cytotoxicity.
Cellular Uptake
The cellular uptake of various nano-formulations was determined by fluorescence microscope and flow cytometry (FCM).The MCF-7 cells were cultivated overnight at a density of 2 × 10 5 cells per well in 12-well plates.After incubating each sample for different times (4 h or 24 h), the cells were washed twice with PBS and centrifuged at 1000 rpm for 5 min to collect cells.Finally, the cells were resuspended in PBS, and the average fluorescence intensity of DOX and ICG was quantified using a flow cytometer (Thermo Fisher Scientific, Waltham, MA, USA) and the cellular uptake was observed by a fluorescence microscope [36].
Intracellular Reactive Oxygen Species (ROS) Assessment
The MCF-7 cells were seeded in 12-well plates overnight at a density of 2 × 10 5 cells per well at 37 • C.Then, the cells were treated with free DOX, HD/CNTs-SS@DOX, free ICG, HD/CNTs-SS-ICG, HD/CNTs-SS-ICG+NIR, and HD/CNTs-SS-ICG@DOX+ NIR, respectively.After 4 h or 24 h of incubation, the cells in the last two treatment groups were irradiated with an 808 nm NIR laser at 5 W/cm 2 for 5 min.Next, the serum-free medium containing 10 µM of DCFH-DA was added into each well.The cells were incubated for another 20 min in darkness and then washed with PBS and trypsinized.Lastly, the cell suspension was used to detect intracellular ROS levels using Fluorescence-activated Cell Sorting (FACS) and a fluorescence microscope, respectively.
Cell Apoptosis and Cell Cycle Distribution Detection
The MCF-7 cells were treated with NS, free DOX, HD/CNTs-SS@DOX, ICG+NIR, HD/CNTs-SS-ICG+NIR, and HD/CNTs-SS-ICG@DOX+NIR, respectively.After coincubation for 16 h or 48 h, the cells in the last three treatment groups were irradiated with an 808 nm NIR laser.Next, the cells were incubated for another 4 h and then washed with PBS, trypsinized, and centrifugated at 1000 rpm.Afterward, 500 µL of binding buffer containing PI/Annexin V staining solution was added for further incubation.The cell apoptosis ratio was determined by FACS.The cells in NS treatment group were used as the control group.The experimental procedure of cell cycle measurement was similar to the above process.The collected cells were resuspended in cold anhydrous ethanol overnight to avoid structural damage to the cytomembrane [37].The cell suspensions were subsequently centrifugated to remove ethanol, and 500 µL of PI buffer solution was added for incubation at 37 • C in darkness.The cells in yjr NS treatment group were used as the control group to determine the cell cycle variation.
In Vivo Antitumor Effect Evaluation
The MCF-7 cell suspension was injected subcutaneously into the mice.When the tumor size reached 50-80 mm 3 , the mice were randomly divided into five groups.Mice in each group were subcutaneously injected with 50 µL of NS, DOX (3 mg/kg), HD/CNTs-SS@DOX (15 mg/kg), HD/CNTs-SS-ICG (15 mg/kg), or HD/CNTs-SS-ICG@DOX (15 mg/kg).The latter two groups of mice were anesthetized with a mixture of tribromoethanol and tert-amyl alcohol and their tumor sites were exposed to an 808 nm laser (5 W/cm 2 , 5 min).Temperature variations at the tumor site were recorded and photographed by infrared thermal imaging.After continuous treatment for 15 days, the antitumor effect on each group of mice was evaluated by monitoring tumor volume and body weight every 3 days [38].The tumor volume was calculated according to the following formula: tumor volume= (length × width 2 )/2.Lastly, the mice were sacrificed to remove the tumor and major organs, and the resected tumor was weighed and photographed.The tumor growth inhibition rate (TGIR) was calculated according to the following formula: where W c and W t represent the average tumor weight of the control group and treatment group, respectively [39].The major organs and tumor tissues after perfusion were fixed overnight in 4% paraformaldehyde.The tissues were soaked in a mixture of xylene and molten paraffin (volume ratio 1:1) and soaked overnight.The organized wax blocks were sliced with a slicer and affixed to the slide.After dewaxing, the wax blocks were stained with hematoxylin and eosin (HE).
Statistical Analysis
All data are prepared as mean ± SD and the mean values were considered significantly different when p* < 0.05, p** < 0.01, or p*** < 0.001.ANOVA was used for the statistical analysis of all the treatment groups by SPSS software (version 9.1).
Scheme 1 .
Scheme 1. Schematic diagram of the preparation procedure and antitumor mechanism of HD/CNTs-SS-ICG@DOX DDS.A drug delivery system (HD/CNTs-SS-ICG@DOX) was developed by conjugating ICG-NH 2 on the surface of CNTs through S-S, loading chemotherapy drug DOX inside the lumen, and finally coating the surface with targeting agent HD.The drug delivery system can release drugs in the TME to realize the synergistic antitumor effect by mediating chemotherapy and PTT.
Figure 3 .
Figure 3. Photothermal performance verification of ICG and various nanosystems.(A) Thermal images of different concentrations of ICG under 5 W/cm 2 of NIR irradiation for 5 min.(B) Thermal
Figure 4 .
Figure 4. Cytotoxicity and biosafety assessment results of various SWCNT carriers or DDSs.(A) Cytotoxicity of various SWCNT carriers.(B) Cell viability of various DDSs towards IPEC-1 cells.
Figure 8 .
Figure 8. (A) Thermal images in mice treated with different samples irradiated by NIR.(B) Temperature curves of different samples under NIR irradiation.(C) HE staining images of tumors and main organ slices collected from mice in different groups.
Figure 8 .
Figure 8. (A) Thermal images in mice treated with different samples irradiated by NIR.NIR irradiation time was set at 0-5 min.(B) Temperature curves of different samples under NIR irradiation.(C) HE staining images of tumors and main organ slices collected from mice in different groups.
Figure 9 .
Figure 9. (A) Treatment procedure.(B) Tumor growth curves of mice after different treatments.(C) Body weight variation in mice after different treatments.(D) Tumor weight of mice after different treatments.(E) Tumor inhibition rate of mice in different treatment groups.(F) Tumor images of mice after 15 days of treatment.(G) Tumor variation in mice in different treatment groups assessed
Figure 9 .
Figure 9. (A) Treatment procedure.(B) Tumor growth curves of mice after different treatments.(C) Body weight variation in mice after different treatments.(D) Tumor weight of mice after different treatments.(E) Tumor inhibition rate of mice in different treatment groups.(F) Tumor images of mice after 15 days of treatment.(G) Tumor variation in mice in different treatment groups assessed every 3 days up to 12 days.(In (D,E) a: NS, b: DOX, c: HD/CNTs-SS@DOX, d: HD/CNTs-SS-ICG+NIR, e: HD/CNTs-SS-ICG@DOX+NIR).
Table 3 .
Encapsulation efficiency and drug loading of various SWCNT vehicles. | 11,201.4 | 2024-08-23T00:00:00.000 | [
"Medicine",
"Engineering",
"Materials Science"
] |
Exploring the Usage of Fast Carry Chains to Implement Multistage Ring Oscillators on FPGAs: Design and Characterization
Ring oscillators (ROs) serve as basic building blocks in a lot of application scenarios, where they must ensure high reliability, flexibility, and low-area/energy footprint. With the recent advances of the Internet-of-Things (IoT) technology, in particular, the necessity to endow interconnected devices with security facilities has increased as well. In this context, the efficient implementation of ROs on field-programmable gate arrays (FPGAs) is crucial, even though it hides some pitfalls. This article presents a new design strategy for multistage ROs relying on the carry chains (CCs) available into modern FPGA devices. Several configurations of ROs designed as proposed here have been characterized in terms of hardware costs, jitter, and temperature/voltage sensitivity. In all the evaluated cases, the proposed design allows to achieve predictable routing schemes through the automatic place and route (P&R), while reducing slice occupancy and energy consumption by up to 50% and 44%, respectively, in comparison with the traditional lookup table (LUT)-based ROs. When realized on a Artix-7 device, the basic version of the proposed oscillator realized using 33 inverting stages allows obtaining multiphase outputs oscillating at 29.7 MHz with a standard deviation less than 10 kHz. The analysis conducted also demonstrates the high flexibility of the novel circuits, such as the possibility to easily change their behavior depending on the target application requirements. As an example, by exploiting additional pass-through elements, the proposed scheme achieves a sensitivity of 49 kHz/°C that is more than 4 times higher than that shown by the corresponding traditional LUT-based competitor, thus making it more suitable for thermal monitoring applications.
Abstract-Ring oscillators (ROs) serve as basic building blocks in a lot of application scenarios, where they must ensure high reliability, flexibility, and low-area/energy footprint.With the recent advances of the Internet-of-Things (IoT) technology, in particular, the necessity to endow interconnected devices with security facilities has increased as well.In this context, the efficient implementation of ROs on field-programmable gate arrays (FPGAs) is crucial, even though it hides some pitfalls.This article presents a new design strategy for multistage ROs relying on the carry chains (CCs) available into modern FPGA devices.Several configurations of ROs designed as proposed here have been characterized in terms of hardware costs, jitter, and temperature/voltage sensitivity.In all the evaluated cases, the proposed design allows to achieve predictable routing schemes through the automatic place and route (P&R), while reducing slice occupancy and energy consumption by up to 50% and 44%, respectively, in comparison with the traditional lookup table (LUT)-based ROs.When realized on a Artix-7 device, the basic version of the proposed oscillator realized using 33 inverting stages allows obtaining multiphase outputs oscillating at 29.7 MHz with a standard deviation less than 10 kHz.The analysis conducted also demonstrates the high flexibility of the novel circuits, such as the possibility to easily change their behavior depending on the target application requirements.As an example, by exploiting additional pass-through elements, the proposed scheme achieves a sensitivity of 49 kHz/ • C that is more than 4 times higher than that shown by the corresponding traditional LUT-based competitor, thus making it more suitable for thermal monitoring applications.
With the rapid expansion of the Internet-of-Things (IoT) network, the need for miniaturized objects embedded with electronics, software, and sensors is increased as well [2].In this context, the field-programmable gate array (FPGA) technology has nowadays consolidated as one of the most popular realization platform because of its high flexibility and attractive computation capabilities, especially for the implementation of heterogeneous systems-on-chips (SoCs) that exploit both programmable logic fabric and microprocessors [14].In the near future, it is expected that in several application fields, such as smart cities, connected vehicles, healthcare systems, and even data centers, more and more infrastructures would benefit from the synergy between the IoT approach and FPGA technologies.This increase of interconnected devices pushes the demand for preserving the information down to the chip level.Indeed, despite of the incessant progresses in the fabrication of logic programmable devices, security is nowadays a crucial issue.As an example, preventing hard faults due to either external attacks or FPGA performance degradation caused by aging mechanism is mandatory before enabling such infrastructures in our daily lives.Also, FPGA bitstream encryption is essential for anticounterfeiting purpose.However, conventional nonvolatile memory (NVM)-based approach for storing the secret key suffers from reverse engineering and sidechannel attacks.In this regard, several approaches have gained popularity in the last decade.Most common solutions in the literature include physically unclonable function (PUF) for hardware authentication [1], [2], [3], true random number generator (TRNG) on the fly free session keys generation [4], [5], voltage sensors for remote side-channel attacks detection [7], and ON-chip aging estimation circuits [9], [10].All these methods rely on ROs that have to be efficiently implemented within the FPGA device.
Although the functionality of an RO is based on a quite simple circuitry, its desired hardware characteristics, and consequently its design, are strongly target application-dependent.Just as an example, ROs used to implement a PUF circuit must be ideally no sensitive to different environmental conditions (e.g., voltage variations) [15], which is exactly the opposite of the behavior expected by a voltage sensor [7].Often, such designs make use of multiple RO instances, for which ensuring nominally identical frequency behaviors is mandatory [16], [17].Therefore, achieving a relatively good prediction of the nominal RO frequency as a function of its length, at design stage, is crucial.However, as it is well known, SRAM-based FPGAs rely on programmable logic and configurable routing resources: during the implementation phase, unless of specific user's constraints, the place and route (P&R) tool explores the available design space relative to the target chip and adopts the default floor-planning strategy to automatically select the most proper resources, place them onto specific sites, and configure interconnections between logic blocks accordingly.As a result, implementing ROs on such devices with easy-totune, predictable, and repeatable behaviors is not trivial.
The above considerations motivate the focus of this work.Furthermore, many previous research works confirm that FPGA-based ROs designed by exploiting lookup table (LUT) primitives require manual P&R, in order to achieve reliable and effective implementations [7], [16], [17], [18], [19].In addition, due to its circuitry consisting just of chained LUTs and routing resources, the conventional RO design demonstrates poor adaptability to different application requirements and relatively low flexibility in fine-tuning the oscillator behavior.With the aim to overcome these limitations, this article presents a new design methodology to efficiently deploy ROs on FPGA devices.It adopts in an unconventional manner dedicated fast carry chain (CC) resources available within modern FPGA chip families [20], [21] in place of configurable LUTs.As a result, the automatic P&R is driven by a dedicated interconnection scheme, thus ensuring predictable and repeatable behaviors without any user's constraint.To the best of our knowledge, this is the first proposal of using CCs to realize multistage and multiphase ROs.The proposed solution significantly simplifies the design and allows better frequency fine-tuning and higher flexibility to achieve the specific application requirements.A comprehensive study, including hardware characterization, intra-/inter-die analysis, and evaluation of sensitivity to voltage/temperature variations, has been conducted to demonstrate the effectiveness of the proposed RO design methodology.Results highlight that, in addition to the advantages in terms of reduced design complexity, high flexibility, and independence of performance of the output load, an RO designed as proposed here is cheaper and less energy consuming compared with the traditional LUT-based counterpart.The rest of this article is organized as follows.Section II provides a brief background and overviews the state of the art.Section III introduces the proposed RO design methodology, whereas its mathematical model for frequency estimation is described in Section IV.Section V presents experimental results obtained for ROs at different lengths based on the conventional and new design methodologies.An application case study exploiting ROs based on the proposed design methodology is also discussed in Section VI.Finally, conclusions are drawn in Section VII.
II. BACKGROUND AND RELATED WORKS
According to the literature review from [22], LUTs are the most commonly adopted resources in order to implement ROs on FPGAs.These hardware primitives can be properly configured at design time to map possibly any m-input Boolean function, with m depending on the target FPGA technology.In order to implement an N -stage RO, many LUTs are cascaded connected, as shown in Fig. 1(a).In such a case, with the generic LUTi being configured, as depicted in Fig. 1(b), not(I0) is outputted, regardless of the value assumed by the I1 and I2 inputs.The frequency of the RO combinatorial loop depends on the propagation delay τ p across the overall path, including logic τ logic and net τ net contributions.The latter is, in turn, influenced by the FPGA sites selected for placement, the length of routed interconnections, and the number of pass transistors (PTs) enabled through the programmable switch matrices.
One of the major challenges in designing these architectures relies on the fact that the layout obtained by the P&R phase is not known a priori, unless of specific user's constraints.The automatic P&R floor-planning strategy exploits complex heuristic searches aimed at identifying a limited design space with balanced characteristics in terms of delay and interconnection density [24].Interfering with this process in order to drive the P&R toward a desired and predictable implementation is not easy to put into practice.The complexity of the problem significantly increases for those applications that involve the usage of multiple identical ROs [1], [4], [7], [8], [9], [10], [11], running at a specific frequency and in conjunction with surrounding logic circuitry [25].In such a case, specific placement constraints responsible for assigning RO resources to a locked region within the FPGA chip could be used in order to avoid undesired packing of multiple LUTs.However, such a strategy could be not enough.Indeed, neither the position of the generic LUTi nor the configured interconnections are locked within the constrained region, potentially leading to different RO frequencies at each new implementation run.As a result, the design of LUT-based ROs with predictable and repeatable frequency behaviors must necessarily pass through manual P&R [7], [16], [17], [18], [19].Moreover, given that the RO output is usually retrieved by interfering with the combinatorial loop, the propagation delay τ p is also influenced by the load capacitance [26], [27], [28].This aspect represents a further challenge for many applications.Just as an example, in the case of PUFs, multiple ROs must have identical nominal characteristics, as well as marginal and balanced contributions due to the load capacitance, so that the small frequency difference due to the process variations can be detected adequately [26].
In the recent past, various alternatives to conventional LUT-based oscillators have been demonstrated [8], [22], [29], [30], [31].Burgiel et al. [29] proposed to use input/output buffer (IOBUF) primitives available in Xilinx FPGAs inside a loop of a conventional LUT-based multistage RO.As illustrated in Fig. 2(a), this proposal uses the IOBUF element to drive the I/O pad pin, thus allowing the RO frequency to be tuned by changing the drive strength and slew rate.However, the usage of an IOBUF element makes the RO more sensitive to temperature variations, still requires manual P&R, and does not allow granular fine-tuning of the RO frequency.In fact, changing the slew rate of the IOBUF from SLOW to FAST introduces a scaling of approximately 3-10 MHz that cannot be modulated (similar considerations arise for the changes of the drive strength).
All other alternative proposals discuss the realization of single-stage oscillators.Some of them [8], [30], [31] implement noncombinatorial loops by using sequential elements.Their main advantages are compactness and simplicity of the circuitry that, in its most basic design, consists of just one feedback latch/flip-flop (FF).However, the effectiveness of this architecture has been successfully demonstrated just for TRNG applications [30], where the metastability produced by the feedback latch is exploited as entropy source.On the contrary, La et al. [22] evaluated the possibility to implement combinatorial loop ROs by using digital signal processing (DSP) and Mux resources available within modern FPGA devices, as schematized in Fig. 2(b) and (c).Both these schemes rely on dedicated resources that allow reducing the design effort mainly because of their compactness, but, as a drawback, they are suitable only for the implementation of single-stage ROs having fixed frequency.On the contrary, the design methodology proposed in this article exploits CCs in a more effective manner and enables the realization of multistage ROs whose behavior can be easily configured to comply with the requirements of the target application.
III. PROPOSED RO DESIGN
Nowadays, CCs are available in various extents in most FPGA devices produced by many vendors [20], [21].They consist of hard-wired resources specialized for efficient ON-chip implementation of arithmetic operations, such as additions and multiplications.A CC typically consists of k internal stages of cascaded multiplexers that, in combination with auxiliary XOR gates, implement as many full adders each exploiting the basic 1-bit carry look-ahead logic.Most importantly, CCs are placed neatly within the chip, so that longer chains can be implemented by cascading multiple instances through dedicated routing.Our proposal aims at exploiting this unique property for the implementation of ROs.Indeed, during the automatic P&R step, the position of the first CC can be used as the "anchor point" for the whole design; then, both cascaded CCs and nets are placed and routed through a delay-deterministic scheme, thus avoiding the need for manual P&R.
According to the above consideration, the design illustrated in Fig. 3 (in the following, named CC_ROv1) is here proposed as the basic configuration to enable the CC unit to operate as an oscillator.Without loss of generality, the architecture includes x CCs, each composed by k = 4 internal stages.In order to enable the propagation of the oscillating signal along the circuit, all the internal stages must be used for each CC, except for the last one where the designer can choose the convenient number of stages to be exploited.Thereby, the selectors of multiplexers MXs, the first one excepted, are properly set to constant values following the scheme shown in Fig. 3. Thus, while the multiplexers MXs in the even positions propagate the signal coming from the previous multiplexer, those in the odd ones transfer on the carry line the signal coming from the XOR gate in the previous stage.In this way, a chain of XOR gates, each acting as an inverter stage, is formed.Finally, to make odd the number of inverting stages, the first LUT, highlighted in gray, maps a NAND function: the low-to-high transition of the en signal triggers the first inversion through the LUT, which is then propagated to the XOR gate in order to produce O 0 .It is important to note that the function mapped within the first LUT has to be chosen based on the configuration of other components (e.g., selectors and inputs of the multiplexers).We verified that such kind of changes in the first LUT content does not significantly affect the behavior of the RO architecture.In the subsequent chain positions, the proposed scheme allows the oscillating signal to be propagated to the next stage by alternating the outputs from the XOR gate and the multiplexer, respectively.As a result, the CC_ROv1 configuration actually includes y = 2x + 1 inverting stages, highlighted in gray in Fig. 3.
From the schematic of Fig. 3, it can be observed that the remaining LUTs are not necessary to produce the oscillation, but they could be exploited as pass-through elements to fine-tune the RO period.In such a case, the external multiplexers aligned to the CC even positions can be used to select the corresponding LUT outputs, as depicted in Fig. 4.This choice expands the design space, leading to the new configurations CC_ROv2 and CC_ROv3, where one or two LUTs per CC are enabled, respectively.As deeply analyzed in the following, the proposed configurations exhibit different characteristics in terms of oscillation frequency and sensitivity to voltage/temperature variations.Besides the interesting properties mentioned above, as shown in Fig. 3, the proposed scheme can provide the oscillating output RO out through one or more of the unused XOR gates, such as that at the position kx − 1, thus avoiding interference with the interconnect loop.This allows realizing efficient multiphase oscillators suitable for applications that need load-independent RO frequencies [1], [26], [28].
IV. MODELING THE PROPAGATION DELAY
In this section, we introduce the mathematical model for the frequency estimation of the proposed RO scheme.Let us consider the path involved in the combinatorial loop of the CC_ROv1 configuration, as highlighted in blue in Fig. 5.Then, the RO frequency f RO can be computed as 1/2τ p by applying (1) and (2) for modeling τ p .Therefore, τ i→ j represents the delay contribution associated with the generic segment i → j in the path, τ LUT is the LUT access delay, and τ loop is the interconnection delay due to the net named loop in Fig. 5 τ According to the adopted FPGA technology, the delay switching characteristics at the nominal conditions are provided by the vendor for most of the contributions highlighted in Fig. 5, except τ O 0 →B 1 , τ O 2 →B 3 , and τ loop .Table I summarizes the values of each contribution τ i→ j , with reference to the FPGA chips belonging to the Xilinx Artix-7 (speed grade −1) family; a similar approach could be adopted with different devices.The four examined cases, in the following, named fast-fast (FF), fast-slow (FS), slow-fast (SF), and slow-slow (SS), take into account, respectively, the process corner (first letter) and the standard delay format (SDF) adopted for delay modeling (second letter).
Table II, instead, reports the τ O 0 →B 1 and τ O 2 →B 3 delays related to the specific tracks illustrated in Fig. 5.Although related to programmable routing, such contributions can be considered as constants, regardless of the RO length, since the start point and the endpoint of the interconnection are fixed by the adopted architecture, as it will be detailed later.
It is worth noting that the τ loop delay depends not only on how many stages are involved in the oscillator, but also on the interconnection length and the number of pass transistors crossed along the loop path.Without loss of generality, the dependence between τ loop and the number of inverting stages y is here derived for the proposed RO design by adopting a procedure similar to [32].
The above model has been validated by comparing its prediction with results obtained by postimplementation timing reports, for several CC_ROv1 samples, with y ranging from 3 to 33.On average, the achieved error is lower than 0.25%.It is worth noting that the model discussed in this section relies on production level devices specifications furnished by the manufacturer.To provide high accuracy, such parameters are released once enough production silicon of a particular device family member has been characterized; thus, no significant risk of underestimation of delays exists.
A. Hardware Implementation
The CC-and LUT-based designs with various lengths have been implemented by using the Vivado 2018.3Development Tool.As an example, Fig. 7 illustrates the layout obtained for the proposed RO_CCv1 configuration with y = 5 when the Xilinx xc7a100tcsg324-1 FPGA is selected as the target device.In all analyzed cases, using the same hardware description language coding, the P&R tool operates without any additional manual constraints and achieves a predictable routing scheme.This property comes from the carry-chain itself that autoconstraints both the placement and the routing paths between the internal nodes of the oscillator architecture.On the contrary, conventional LUT-based designs require each stage of the oscillator to be carefully placed and routed using a regular distribution over consecutive slices, by means of manual designer action.In particular, from Fig. 7, it can be noted that, while the connection between adjacent CCs is based on hard-wired routing (blue line), the interconnections between the XOR gates and the multiplexers rely on fast neighborhood routing tracks and proceed through identical paths across multiple CC stages (purple lines).On the other hand, interconnections external to the CCs, i.e., O 0 →B 1 , O 2 →B 3 , and the loop, rely on the programmable routing.However, as visible in Fig. 7, such nets connect neighbor elements through a substantially (and automatically) constrained path.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.⃝ and 5 ⃝ are actually the only programmable junction points.However, under default routing order rules, the P&R tool selects them as preferred way points.In very congested layouts, as a common practice, a physical block (PBlock) that inhibits other nets to be routed through the switchboxes used by the oscillator could be easily exploited.
Table III summarizes nominal frequency at the four corners, area occupancy, and energy per transition (EPT) of the proposed RO designs.The latter exhibits different energy/area characteristics at a given y, depending on the number of additional LUTs used in the various configurations.In general, the higher the number of stages of the RO, the higher the cost to fine-tune the behavior of the oscillator.Just as an example, the energy overheads of the CC_ROv2 configuration with respect to CC_ROv1 one are 26%, 34.8%, and 38.79%, for y = 5, y = 9, and y = 17, respectively.Similarly, when moving from the CC_ROv2 to the CC_ROv3 design, the 22.2%, 25.4%, and 28.2% energy overheads must be payed for the y = 5, y = 9, and y = 17 lengths, respectively.Table III also compares the new ROs with the LUT-based counterparts considering different lengths.At a glance, it can be observed that the proposed CC-based ROs reduce both the amount of occupied slices and the energy consumption with respect to the LUT-based counterparts at similar frequencies.Just as an example, the CC_ROv2 (y = 5) design runs at a frequency close to the nine-stage LUT-based RO, but it uses 33.3% less slices and dissipates 13% lower energy.Overall, the slice and energy savings exhibited by the proposed CC_ROv1 and CC_ROv2 over the LUT-based implementations span, respectively, from 11.1% to 50% and from 13% to 44%.On the other hand, the CC_ROv3 circuits allow expanding the space of possible frequencies without requiring additional slices, in contrast to the conventional RO designs.To achieve
B. Test Setup
In the next subsections, in order to characterize the behavior of both CC-and LUT-based ROs and to appreciate the general validity of the proposed methodology, we report results of experimental tests performed on 28-nm CMOS Artix-7 xc7a 100tcsg324-1, 28-nm CMOS Zynq xc7z045ffg900-2, 40-nm CMOS Virtex-6 xc6vlx240tffg1156-1, and 16-nm Fin-FET Ultrascale+ xck26sfvc784-2lvc devices.To this purpose, a Tektronix MSO64 mixed signal oscilloscope (2.5 GHz) has been used to capture and analyze output signals.A Keithley precision measurement dc supply 2280S-60-3 has been exploited to power supply the devices under test, also monitoring the current drawn by the FPGA boards.For the purpose of a reliable analysis, frequency measurements were repeated for at least 10 5 cycles; then, the average values and the standard deviations were recorded, thus avoiding artifacts due to the stochastic fluctuation.An oscilloscope screenshot is depicted in Fig. 8.In this case, the configuration under test is the CC_ROv1 with y = 33, obtained by cascading x = 16 CCs.Two phase-shifted output signals are retrieved from the XOR gates in the 31th and 63rd positions within the chain, as shown in Fig. 8(c).As expected, these signals have the same frequency, with mean value µ around 29.7 MHz and a standard deviation σ of ∼10 kHz.The histogram plot in Fig. 8(b) reports the Gaussian frequency distribution retrieved from 115 080 repetitive measurements that achieves σ /µ(%) of ∼0.03%.The latter is in line with the literature [33] for conventional LUT-based ROs.In the analyzed case, the time difference between the two output signals is ∼7.6 ns, and the histogram plot in Fig. 8(a) illustrates the
C. Temperature Sensitivity
As it is well known, temperature variations have a twofold impact on MOSFET devices, with the carrier mobility and the threshold voltage decreasing as the temperature increases due to the scattering and to the Fermi level and bandgap energy shift, respectively.At the device level, such mechanisms coexist impacting the current in opposite directions.But, while in static CMOS gates operating in the above threshold region, the first one is dominant, thus leading to an increase of the delay as the temperature increases; in PT logic circuits, they balance out quite differently.In such a case, the carrier mobility reduction is significantly contrasted by the lower threshold voltage, which, in turn, lead to a propagation delay reduction.This behavior is expected to be much more evident when ROs are realized on FPGA platforms exploiting a massive usage of PT logic circuits [34], [35].By transistor-level simulations performed by using a standard CMOS process technology, we investigated the effects of the coexistence of PT and static CMOS logic stages, typically occurring in the target platform.Although based on some speculations on the FPGA internal architecture [36], simulation results show that, in such a case, the temperature influences the RO frequency quite differently than in traditional static CMOS circuits.Fig. 9 illustrates the implementation of the single LUT [36] adopted in the simulations and the plots of the RO frequency under temperature changing.It can be observed that, due to the massive usage of PT stages within the FPGA fabric, initially, the effect of the threshold voltage prevails.Then, as the temperature increases, the two phenomena tend to balance each other out, until the carrier mobility reduction becomes the dominant effect.Moreover, from our simulation, we verified that increasing the number of PT stages in the RO path moves the local maximum toward higher temperatures.
In order to evaluate the impact of temperature on the analyzed ROs, we performed a measurement campaign using the ACS DY16-T climatic chamber, varying the temperature from 5 • C to 75 • C. The acquisition of the ROs outputs was always performed after the thermal transient was concluded.To this purpose, the die temperature was monitored through the internal sensor and the precision measurement dc supply that also allowed verifying that the standard deviation of the absorbed current is below 10 nA.Besides the LUT-based reference designs, the CC_ROv1, CC_ROv2, and CC_ROv3 configurations have been characterized for y = 3, 5, 9, and 17 at the temperatures Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The latter is here defined as ( 4) and provides a synthetic metric that allows evaluating how, in the ranges of observation, the RO frequency changes as a consequence of the operating temperature with respect to the nominal condition As the evidence of the fact that more logic and routing resources contribute to the RO frequency, Fig. 10 highlights that the VI temp increases with the RO length for both the CC_ROv1 and LUT-based designs.Even more interesting are the results obtained for the proposed CC_ROv2 and CC_ROv3 configurations.As shown by the preliminary analysis dis-cussed at the beginning of this section, the synergy between CCs and LUTs could be exploited to modulate the behavior in temperature of the RO by using some LUTs as passthrough elements, as shown in Fig. 4. In such a case, the additional PT stages are responsible of the flipped trend within the range 25 • C-50 • C. As illustrated in Fig. 10, depending on the number of additional pass-through LUTs, the behavior in temperature can be relatively fine-tuned to increase or decrease the RO sensitivity with respect to the CC_ROv1 circuit.Indeed, the CC_ROv3 configuration exhibits a VI temp up to 0.4% and a sensitivity of 0.049 MHz/ • C (y = 3 in the range 5 • C-50 • C), which is 4.45 times higher than the five-stage LUT-based counterpart.As a consequence, such a design is ideal for those applications that aim at monitoring performance degradation due to the temperature [8], [9], [10], [11].Whereas, the CC_ROv2 configuration allows achieving the lowest VI temp , regardless of the target length, thus becoming an effective candidate for the implementation of circuits requiring high resilience to the temperature variations [1], [2], [3].
For the purpose of a deep analysis, we investigated also the impact of using different types of slices to implement the proposed ROs.The Xilinx FPGA devices from the Series-7, for example, are organized in configurable logic blocks (CLBs) that include two slices for each switch matrix, placed up and down, as shown in Fig. 7.Moreover, they account for only logic slices (type L) and more complex slices that can also be used as distributed memory (type M).While the above characterization refers to the usage of slices L positioned at the bottom of the CLBs, Table IV reports the RO frequency measured at different temperature points when the placement schemes Up-L and Down-M are chosen on the xc7a100tcsg324-1 chip.It can be appreciated that, even though the three implementations are located within the same die region, the RO frequencies differ, in accordance with the slice type.This is more evident in the case Up-L, since the connections between each slice and the corresponding switch matrix follow different paths.
An intradie analysis has been also carried out by considering the Down-L placement for the proposed CC_ROv2 configuration within four different FPGA regions (i.e., 1: X0Y3, 2: X1Y2, 3: X1Y1, and 4: X0Y0).Fig. 11 plots the σ /µ (%) metric as a function of the temperature and points out two important observations.The former is that, as expected, different sites exhibit different absolute RO frequencies.Moreover, each site has its proper characteristic under different temperature conditions, which suggests an uniqueness related to the process variations.The latter is that, for a given site, the standard deviation σ remains almost stable, indicating that temporal fluctuation has little impact on the measured frequency.It is important underlying that this behavior has not been verified for the LUT-based RO, which demonstrated σ values up to 36% higher at the parity of placement and temperature conditions.
In order to investigate the interdie behavior, the new CC_ROv2 design has been characterized on ten xc7a100tcsg324-1 chips at different temperatures.The resulting statistics are summarized in Fig. 12, where the point indicates the mean frequency value, computed by averaging the µ results from the ten chips, and the bars report the distance with respect to the highest/lowest observed frequency.At a glance, it can be noted that the mean frequency follows a trend similar to that noticed until now.The range given by the bars, instead, demonstrates that the RO frequency may vary significantly from die-to-die as the result of global variations [33].At the same time, when looking at different temperature conditions, the frequency range seems to be unchanged, thus suggesting that the temperature equally affects all the chips.Finally, with the aim of generalizing the applicability of the proposed strategy, and to show its thermal behavior on very different process technology nodes, Fig. 13 plots the temperature sensitivity of the 40-nm CMOS Virtex-6, 28-nm CMOS Artix-7, and 16-nm FinFET Ultrascale+ implementations of the CC_ROv1 design with y = 5.It can be clearly observed that the sensitivity to temperature variations is significantly reduced when advanced technologies, such as the Ultrascale+, are employed.This finding is in accord with the conclusions achieved in previous works [38], [39].
D. Jitter Analysis
To evaluate the jitter behavior of the proposed ROs, we analyzed the variations of the running period within a certain interval time, i.e., long-term jitter [37].Table V reports the relative standard deviation of the RO period (σ p /µ p ) measured for the proposed circuits at length y = 17 and for a 35-stage LUT-based sample, considering the xc7a100tcsg324-1 FPGA device.All the ROs under analysis have shown a Gaussian distribution of the oscillation period, which typically identifies random jitter.In general, it can be observed that the compared designs exhibit quite similar characteristics, with the CC_ROv2 and CC_ROv3 configurations able to slightly reduce the σ p /µ p over the LUT-based counterpart, regardless of the temperature.
E. Voltage Sensitivity
To perform the voltage sensitivity analysis, we used the TI UCD90120A power controller in order to modify the internal core voltage within the range 0.8-1.12V, with 1 V being the nominal condition.Because of the aggressive voltage scaling, the frequency variation measured for the new and LUT-based RO designs spans also within few tens of MHz.To better highlight the different behaviors exhibited by the referenced Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.VI.The latter also shows the VI volt defined in (5).From this metric, it can be noted that the frequency of each implementation changes following a similar trend.The CC_ROv1 sensitivity to voltage variations appears to be slightly lower than the LUT-based counterparts at N = 5, 9, 17, and 35.The opposite trend is exhibited by the CC_ROv2 designs compared with the LUT-based ROs at N = 7 11, 21, and 41.We speculate that this is due to the higher number of PT stages used in the path of the latter configuration
VI. CASE STUDY: THE CC_ROV1 DESIGN FOR TRNGS
As an example of applications and to verify the effectiveness of the proposed architecture, we utilized the CC-based RO in the realization of a TRNG.To this purpose, we slightly modify the design presented in [23] to accommodate a CC_ROv1 oscillator with y = 9.According to results in Table V, such a configuration indeed exhibits a jitter quite similar to that of the oscillators, which can be exploited as entropy source to generate random bit sequences.Fig. 15 illustrates the block diagram of the realized TRNG.The CC_ROv1 block used to generate seven multiphase oscillating outputs at 108 MHz.Such output signals are sampled by FFs receiving a clock signal formed by the DCM.The basic idea exploited in [23] is to tune the phase of such clock through the DCM in order to force on one or more FFs to enter the metastability region.The input clock clk_in running at 62.5 MHz is sent to the DCM that, according to the control signal psen given by the FSM block, performs a phase shifting each 20 cycles to produce the clk_out used as clock signal for the sampling FFs.The phase shifting performed by the DCM continues until the signal T resulting from the XOR operation changes its value, meaning that a violation is occurred at the first stage of FFs.Random bits are, therefore, generated and stored within a 32-bit shift register that is responsible to feed the ON-chip postprocessing circuit demonstrated in [23].
Table VII summarizes the results obtained by the NIST SP800-22 statistical tests for 64 M random bits acquired as 64 consecutive 1 M bit sequences.All the statistical tests show a proportion and a P value T higher than the minimum pass threshold set by the NIST SP800-22 standard, demonstrating that the proposed oscillator can be effectively employed in the design of a TRNG able to produce a random bit sequence through a very low complex design consisting of 37 LUTs, 124 FFs, 4 CCs, and 1 DSPs.Finally, we performed the AIS-31 T8 test that measures the randomness of the output bitstream in terms of byte entropy.The AIS test shows that the TRNG architecture of Fig. 15 achieves a byte entropy of 8.0 overcoming the recent LUT-based competitor scheme [6] that reaches a byte entropy of 7.996, with a somewhat similar energy efficiency.
VII. CONCLUSION
This work presented a new design methodology to realize multistage ROs by means of the CC resources available within modern FPGA chip families.ROs realized as proposed here show the following benefits.
1) They enable automatic P&R while ensuring predictable and repeatable behaviors because of the dedicated interconnection scheme relying on.Furthermore, their oscillation frequency is not affected by the load on the output node.These results are in contrast to those discussed in several prior works dealing with tedious manual layout actions of LUT-based ROs [7], [16], [17], [18], [19].2) Because of the possibility to strategically add pass-through elements to the oscillating path, they can be easily configured to adjust their thermal/voltage behavior and/or their nominal frequency to comply with the specific application requirements.For instance, our experiments show that one of the proposed configurations is more suitable to work as temperature sensor, whereas the other two solutions can better fit a PUF application because of the reduced temperature sensitivity.
3) The hardware description of the proposed ROs is straightforward, and its portability is ensured.To demonstrate this aspect, we characterized it on different chip technologies, including 40-nm CMOS Virtex-6, 28nm CMOS Artix-7 and Zynq-7000, and finally 16-nm FinFET Ultrascale+.4) As a final remark, the above benefits are achieved by reducing the LUTs count and the energy consumption by up to 83% and 44%, respectively, with respect to the LUT-based solution.
Fig. 3 .
Fig. 3. Proposed CC-based multistage RO design (CC_ROv1 configuration).Inverting stages are realized through the XOR gates and the LUT highlighted in gray.Shadowed LUTs are exploited to permanently set the selectors of corresponding multiplexers.Forward propagation of the oscillation signal relies on the chain of MX elements.
Fig. 4 .
Fig. 4. Proposed CC-based multistage RO design.(a) CC_ROv2.(b) CC_ROv3.Additional LUTs are used as pass-through elements to enable fine-tuning of the RO characteristics.O ′ i signals are delayed copy of O i .
Fig. 5 .
Fig. 5. Propagation delay path for the CC_ROv1 design.Red labels identify the interconnection segments as reported in the technical documentation for delay estimation purpose.
Fig. 6 .
Fig. 6. τ loop as a function of y at different corners.
Fig. 14 .
Fig. 14.Frequency plot obtained for the CC-and LUT-based ROs under different supply voltages (xc7z045ffg900-2 FPGA device).Subplots refer to different lengths and similar nominal frequencies: y = 3 (top left), y = 5 (top right), y = 9 (bottom left), and y = 17 (bottom right).For reference LUT-based designs, the number of inverting stages that best fits the nominal frequency of the corresponding CC_ROv1 and CC_ROv2 was chosen.
Exploring the Usage of Fast Carry Chains to Implement Multistage Ring Oscillators on FPGAs: Design and Characterization Fanny Spagnolo , Member, IEEE, Stefania Perri , Senior Member, IEEE, Massimo Vatalaro , Member, IEEE, Fabio Frustaci , Senior Member, IEEE, Felice Crupi , Senior Member, IEEE, and Pasquale Corsonello , Senior Member, IEEE
FREQUENCY VALUES IN MHZ the frequency around 65 MHz at the FF corner, for instance, a 43-stage LUT-based RO would occupy 11 slices and consume 5.57 pJ, which is 37.5% wider and 11.4% more energy consuming than the CC_ROv3 configuration with y = 17.
TABLE V σ
p /µ p (%) MEASURED UNDER DIFFERENT TEMPERATURE CONDITIONS
TABLE VII NIST
RANDOMNESS TEST RESULTS | 8,878.8 | 2024-08-01T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Effect of Different Initial Light Intensity by the Soft-Start Photoactivation on the Bond Strength and Knoop Hardness of a Dental Composite
This study evaluated the bond strength (push-out method) and Knoop hardness of Z250 composite resin, photoactivated with XL 2500 curing unit, using different protocols: continuous mode (700mW/cm2 for 20s) (CO); soft-start (50 mW/cm2 for 5 s, followed by 700 mW/cm2 for 15 s) (SS1); soft-start (100 mW/cm2 for 5 s, followed by 700 mW/cm2 for 15 s) (SS2); soft-start (150 mW/cm2 for 5 s, followed by 700mW/cm2 for 15s) (SS3); soft-start (200mW/cm2 for 5s, followed by 700mW/cm2 for 15s) (SS4); soft-start (250mW/ cm2 for 5 s, followed by 700 mW/cm2 for 15 s) (SS5); soft-start (300 mW/cm2 for 5 s, followed by 700 mW/cm2 for 15 s) (SS6). For the push-out test, the specimens were tested in a universal testing machine at a crosshead speed of 0.5 mm/min. For the hardness test, the specimens were polished for the hardness measurements, using a 50 g load for 15 s. Data were submitted to ANOVA and Tukey’s test (α=5%). The results of bond strength showed that the SS3 group obtained the highest bond strength when compared to the CO group. There were no significant differences among the other modes in relation to the other groups. Regarding the other results in hardness, there were no significant differences among the groups in the surface region and up to 4 mm depth.
INTRODUCTION
Composite resins are the most widely used direct restorative dental materials. Current dental composites are expected to have optical and mechanical properties comparable to those of tooth enamel and dentin and provide a service life of 10 years or more. However, the polymerization shrinkage still remains the main problem of dental composites. Regardless of composite resin formulation, polymerization shrinkage occurs due to covalent bond between monomer molecules, leading to polymeric chain shortening (1). Walls et al. (2) reported that polymerization shrinkage is influenced by the molecular weight of monomer, the filler content, the degree of conversion and the monomer formulation.
This creates contraction stress, leading to marginal gap, invasion of oral fluids and bacteria, determining the composite longevity (1). However, several factors limit the performance of this material, especially depth of cure and degree of conversion (DC). Light of an appropriate wavelength initiates polymerization of methacrylate groups producing a highly cross-linked polymer matrix. Light from the curing source must be able to adequately polymerize deeper composite regions than just the top, irradiated surface. However, as light passes through the composite, it is absorbed and scattered, reducing its effectiveness to initiate polymerization, and consequently resulting in variation of the cure with depth (3). Although high irradiance provides higher DC values, it also produces greater polymerization shrinkage, which may cause gap formation and further microleakage, compromising the longevity of the restoration. Another problem is that the insufficient polymerization with high residual monomers. The amount of residual monomers depends on the light source and the photoactivation method (4). This monomer may be released within the first days in oral conditions. The unreacted monomers result in inferior physical properties, and can be leached of polymeric matrix (5). Marginal integrity can be increased by absorbing stress materials under restorative materials; adhesive systems with high bond strength to tooth structure, incremental technique filling, and flowing control by light modulation during photoactivation (6).
Several methods of light modulation have been used for the photoactivation of composites with the objective of minimizing the stress generated by the polymerization shrinkage. These photoactivation methods have been suggested to initiate the composite cure reactions, maintaining DC values similar to that found using high light intensity, whilst reducing the polymerization shrinkage (7). Soft-start polymerization adopts an initially low irradiance followed by a final cure with high irradiance. A slower rate of conversion allows for better flow of the material, which in turn decreases contraction stresses, leading to better marginal adaptation. The complement of photoactivation with high irradiance is used for the composite to achieve the maximum degree of conversion (6). Irradiance diminishes as the curing tip is moved away from composite restorative material, and can be used for two-step photoactivation methods. Furthermore, the viscoelastic nature of the polymerizing composite must also be considered. During polymerization there is an irreversible increase in the elastic modulus of the composite. The moment when the loss of the flowing capacity of the material occurs is called gel-point. Prior to the gelpoint, polymerization contraction will not create stress at the restoration margins or within the material, as it is compensated by flow. However, rigid contraction after the gel-point has received much attention and has been responsible for the induction of stress at the bonding interface (8). Kinomoto et al. (9) demonstrated that the speed of the polymerization reaction has a great effect on the generation of stress. The ideal photoactivation method is primordial to optimal marginal adaptation, mechanical properties and depth of cure of composite resin (10). By using a lower irradiance, free radical formation will be lower than when a higher irradiance is used. A lower free radicals formation means that linear polymerization will initially occur to a greater extent, thus the propagating chain comes close to an adjacent free radical or initiated chain as cross-linkage can occur. This study evaluated the ideal initial irradiance using soft-start photoactivation methods to produce the highest bond strength (push-out test) and Knoop hardness for a composite resin.
Push-out test
Seventy round metallic matrices (3 mm height) with a round cavity with 6 mm in the lower diameter and 9 mm in the upper diameter were used (Fig. 1).
These matrices were internally sandblasted with 40-μm aluminum oxide using a micro-etcher (Danville Eng. Inc., San Ramon, CA, USA). After sandblasting, the matrices were etched with 37% phosphoric acid for 15 s, rinsed and dried. The silane bonding agent (Ceramic Primer) was applied and dried for 5 s. The adhesive system (Single Bond, 3M/ESPE) was applied, air-dried for 20 s and photoactivated for 10 s.
During the application of composite resin, the matrices were set on a Mylar strip positioned on a glass slab. Z250 composite resin was bulk inserted and a Mylar strip was seated on the specimen surface and manually pressed using a microscope slab to remove composite excesses. The material was light cured with a halogen lamp XL2500 (3M/ESPE). The maximum irradiance checked with a radiometer (Demetron Research Corp., Danbury, CT, USA), was 700 mW/cm 2 . Composite resin were photoactivated according to the following methods: continuous mode (700 mW/cm 2 for 20 s) (CO); softstart (50 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS1); soft-start (100 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS2); soft-start (150 mW/ cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS3); soft-start (200 mW/cm 2 for 5 s, followed by 700 mW/ cm 2 for 15 s) (SS4); soft-start (250 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS5); soft-start (300 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS6). For reduced irradiances, the tip of curing units was moved away from composite surface. To standardize the photo-activation distance, self-cure acrylic resin spacers (JET; Artigos Odontológicos Clássico, São Paulo, SP, Brazil) were made with 0.5 cm, 0.8 cm, 1.5 cm, 2.4 cm, 3.2 cm, and 3.7 cm heights ( Fig. 2A). A hole at the center of the spacers (Fig. 2B) was made to permit the light pass through, which was measured by a radiometer, establishing the different irradiances used to each photoactivation groups (Fig. 2C).
After light curing, the specimens were stored in an incubator at 37ºC ± 1 for 24 h ± 1, in a dark and dry container, before the push-out test. The top and bottom surfaces of restorations were ground using 400-grit sandpapers (Carborundum, Saint-Gobain Abrasivos Ltda, Cruz de Rebouças, Igaraçu, PE, Brazil) on an automated polisher under water cooling to remove the composite excess, promoting the correct positioning of specimen while testing.
For the push-out test an acrylic resin apparatus containing a central hole was attached to a universal testing machine (Instron model 4411, Instron Ltd, Buckinghamshire, England, UK). A sphere-shaped rod attached to a compression load cell (500 N) was used to load the composite restorations until failure at a crosshead speed of 0.5 mm/min. The push-out bond strength was determined by computing the quotient of maximum load (N) and adhesion area (equation for calculation of truncated cones; mm 2 ). Data was submitted to one-way ANOVA, followed by Tukey's HSD test at 5% significance level.
A B C
(250 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS5); soft-start (300 mW/cm 2 for 5 s, followed by 700 mW/cm 2 for 15 s) (SS6). For reduced irradiances, the tip of the curing units was moved away from the composite surface. To standardize the photoactivation distance, acrylic resin (JET; Artigos Odontológicos Clássico) spacers were interposed between the composite surface and the tip of the light curing units. After light curing, the specimens were stored in incubator at 37ºC ± 1 for 24h ± 1, in a dark and dry container. Elapsed 24 h, the specimens were embedded in polystyrene resin for grinding and polishing. After curing of the polystyrene resin, the specimens were wet ground and polished using 320-, 400-, 600-and 1200grit sandpapers (Carborundum, Saint-Gobain Abrasivos Ltda.) on an automated polisher. The specimens were dried and submitted to Knoop hardness measurements in a hardness tester (HMV 2, Shimadzu, Tokyo, Japan) with load of 50 g for 15 s. For each specimen, 5 readings were taken in different depths (top and 1, 2, 3, 4 and 5 mm) and the average was calculated.
Data was submitted to two-way ANOVA (photoactivation mode x depth) and Tukey's test at the 5% significance level. Table 1 displays the means (SD) for bond strength results. The SS3 group had significantly higher bond strength than CO groups. There were no statistically significant differences among the different soft-start methods. There were no significant differences among groups SS1, SS2, SS4, SS5, SS6 and CO. Table 2 displays the means (SD) for Knoop hardness. There were no significant differences for Knoop hardness from top up to 4 mm depth between soft-start method and control group. At 5 mm, group SS4 presented statistically significant higher Knoop hardness means than groups SS2 and SS3 (p<0.05).
Knoop Hardness Test
Comparisons among depths (Table 2) show that at 2 mm depth, Knoop hardness of groups SS1, SS2, SS5 and SS6 was statistically significant lower than that of top surface. Knoop hardness for all groups at 3 mm depth was significantly lower than that of top surface. Different letters indicate statistically significant difference at 5%.
DISCUSSION
The test design for this study was a push-out model. Extrusion testing in dentistry was first described by Roydhouse in 1970 (11). This author proposed pushing out dental material cylinders from tooth discs. Previous studies using a conical version of the push-out design demonstrated the different bonding properties of direct and indirect restorations with highly reproducible measurements (12). In addition, the cavity-like configuration of the bonding area allows the determination of both composite bond strength and marginal adaptation on the same specimen (12). Independently of the photoactivation method applied, the DC must be as high as possible, ensuring that the material achieves the best properties. It has been demonstrated a good correlation between DC and hardness of composites and, hence, hardness is useful as an indicator of DC (5).
Composite polymerization is a complex phenomenon that involves innumerous factors. The magnitude of stress development depends on the volume fraction of fillers, filler geometry, ratio of modulus between polymer and particle, adhesion between polymer and particle, inherent shrinkage of the particle, and degree of polymer cure. The shrinkage stress has great importance to longevity and success composites, and depends on the polymerization rate, composition of polymeric matrix, specimen geometry, filler volume fraction, photoinitiator concentration, and curing method. The rate of polymerization is influenced by the photoinitiator concentration, monomer reactivity, molecular weight of monomer, leading to different viscosities and mobility (13). Moreover, characteristics related to light curing unit, such as energy density and spectral flow, also alter final material properties (3). Energy density is the product of irradiance and the duration of light exposure, whilst spectral flow represents the optical power output from the light-curing unit, in mW, at each given wavelength (14). In a photoactivated composite, DC depends on the total energy density, at the correct wavelength, supplied to the photoinitiator. Reduction of this initial speed can be obtained by using low irradiance units that produce few free radicals (15). This lower speed gives the composite more time for molecular rearrangement, reducing the stress caused by polymerization shrinkage (16).
The soft-start method described by Uno and Asmussen (17) uses the premise that a short pulse of light allows the relief of stresses prior to inducing additional stresses during the continuing polymerization (18). In this work, the amount of photons supplied to composite within the same exposure time was changed. If the polymerization reaction depends on the generation of free radicals, the speed reaction would be changed for different irradiances during photoactivation. The results showed the soft-start method using 150 mW/ cm 2 initial irradiance (SS3) produced significantly higher bond strength than the control group (CO). The low irradiance during the photoactivation cycle makes the polymerization reaction to proceed slowly, allowing the relief of shrinkage stresses and decreasing the stress at tooth-restorative material interface. In addition, SS3 presented Knoop hardness means similar to CO group (p>0.05). This means that, in those specimens, less stress occurred at bond interface, whilst the DC was maintained. According to Sakaguchi et al. (18), the maximum contraction force rate occurs within the first 10 s of photoactivation. The contraction force can lead to rupture at the bond interface, promoting lower bond strength. When soft-start method is used, the initial irradiance has a great importance for bond strength. When low irradiance was used, SS1 and SS2 groups, bond strength was similar to CO group. It was expected that by using low-irradiance photoactivation, the bond strength would be increased. However, it seemed that in those specimens the energy density of the initial photoactivation was not enough to effectively initiate the polymerization reaction. The reaction only became effective when the second high irradiance exposure occurred. Thus, the reaction occurred under high intensity similar to CO, leading to gap formation and lower bond strength (19). This may be seen in the Knoop hardness test, in which SS1 and SS2 groups had Knoop hardness means similar to those of CO.
There were no statistical differences among SS4, SS5, SS6 and CO for bond strength. The speed reaction has been decreased to give the composite more time for molecular rearrangement, reducing the stress caused by polymerization shrinkage (16). Maybe, the high energy density during the first curing cycle for SS4, SS5, and SS6 produced high conversion of double bonds, leading to high polymerization shrinkage and contraction force. This can be seen in the similar bond strength results to CO. Regardless of the light modulation method, it has been recommended that energy densities similar those supplied by conventional photoactivation (continuous mode) be used. This is recommended because previous studies reported that the degree of conversion depends on the energy density that is supplied to the composite and the photoactivation method (20). Koran and Kurschner (7) found that the increase in energy density led to an increase in the hardness values until photoactivation with 17 J/cm 2 , after which there was no significant alteration in hardness values. However, the ideal energy density for photoactivation is composite dependent. In this study the energy density variations (10.95-14.00 J/cm 2 ) have no effect on DC, seen on Knoop hardness values.
In conclusion, the initial irradiance variations for the soft-start photoactivation method influence on bond strength, but do not have any effects on Knoop hardness values of Z250 composite resin. The best alternative for the traditional mode (continuous mode) is the soft-start mode with 150mW/cm 2 initial pulse. | 3,763.2 | 2007-01-01T00:00:00.000 | [
"Materials Science",
"Medicine"
] |
On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties
: In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace–Carson transform for the two-variable matrix Bessel polynomial analogue.
Introduction
In modern mathematics, special functions play a crucial role in various disciplines.Special versions of these functions have proven invaluable in various fields, including probability theory, computer science, mathematical physics, engineering, and many other areas (see [1,2]).
Bessel polynomials are important due to their natural occurrence in seemingly unrelated situations.For example, they appear in the solution of the wave equation in spherical polar coordinates (see [3]), in network synthesis and design (see [4]), in the analysis of the Student t-distribution (as shown in [5]), and in the development of a matrix approach suitable for solving differential equations with multiple orders and fractions of orders.In addition, Bessel polynomials play a role in the representation of the energy spectrum functions for a family of isotropic turbulence fields (see [6]).
In 1949, Krall and Frink [3] presented an article on what they termed Bessel polynomials.Within this work, they introduced the elementary Bessel polynomials in the following manner: where 2 F 0 is the Gauss hypergeometric function of a two-numerator as The generalized Bessel polynomials, denoted as Y ϵ (µ, ν; x) and extending the Bessel polynomials Y ϵ by introducing two parameters, are defined based on the research by Krall and Frink [3] as follows: ). ( where (µ) k is the Pochhammer symbol, defined by They also obtained certain recurrence relations between these polynomials and one generating function for the Bessel polynomials proper and also provided some of their qualities including orthogonality and the linkages between them and Bessel functions.
The Laplace-Carson transform of the function G(s) for all s ≥ 0 is defined as [12] L where L is Laplace-Carson transform operator.The field of generalized special matrix functions has undergone significant development in recent years.This interest is due to various reasons.Focusing on practical applications, one realizes that the use of new classes of special matrix functions in certain physical problems has led to solutions that are difficult to obtain using traditional analytical and numerical methods.In this context, Hermite, Chebyshev, Jacobi, Laguerre, and Gegenbauer matrix polynomials have been introduced and studied (see, e.g., [13][14][15][16][17]).
The objective of this paper is to present a novel two-variable analogue, denoted as (z, w), and to derive specific outcomes related to the two-variable matrix Bessel polynomials Y (θ,ϑ) ϵ (z, w).Additionally, we explore applications involving the Laplace-Carson transform of functions.
The structure of this article is outlined as follows: In Section 2, we give a brief introduction to certain matrix functions that are important for the further development of the article.In Section 3, we introduce a novel extension of Bessel matrix polynomials called Y (θ,ϑ) ϵ (z, w) and state several theorems on recurrence relations and the derivation formula for this extension.Section 4 deals with various integral formulas for the Bessel matrix polynomials Y (θ,ϑ) ϵ (z, w).In Section 5, we give theorems on the Laplace-Carson transform of functions containing the new extension of the matrix Bessel polynomials Y (θ,ϑ) ϵ (z, w).The concluding remarks and future work are presented in Section 6.
Some Definitions and Notations
Let C r be the r-dimensional complex vector space and C r×r denote all square complex matrices of order r.A positive stable matrix θ in C r×r is denoted as Re(λ) > 0 for all λ ∈ σ(θ), where σ(θ) is the set of all Eigenvalues of θ and θ n ̸ = 0, then we call a matrix polynomial in z of degree n.
In the matrix complex space C r×r , we use I to represent the identity matrix and O for the zero matrix.
The spectrum of a matrix θ in C r×r is defined as the set of all its Eigenvalues and is denoted by σ(θ).If g(z) and h(z) are holomorphic functions defined on an open set D ⊆ C and θ is a matrix in C r×r , such that σ(θ) ⊂ D, then the commutative property g(θ)h(θ) = h(θ)g(θ) holds ( [18,19]).
Laguerre matrix polynomials may be defined in [16] by The Whittaker matrix function W θ,−θ+I/ϵ+2 (z) is defined [26] by the matrix function W θ,−θ+I/ϵ+2 (z) defined [26] by We also see that the Whittaker matrix functions and Laguerre's matrix polynomials are the fundamental components of the generalized Bessel matrix polynomials.In fact, we have and The integral representation is an immediate result of ( 12) as The orthogonality of the generalized Bessel matrix polynomials on the unit circle with regard to the weight matrix function ((cf.[26]): This is satisfied by the associated matrix nonhomogeneous equation For n ̸ = ϵ, we have Now, a few features of the Pochhammer symbol are needed in our present study.
The Matrix Bessel Polynomial
In this section, we introduce the matrix Bessel polynomial Y (θ,ϑ) ϵ (z, w) of two variables and discuss some important basic properties of it as follows.
Definition 1.Let θ and ϑ be positive stable matrices in C r×r satisfying the condition (9), then the matrix Bessel polynomials of two variables Y Remark 1.The following lists some particular results on matrix Bessel polynomials: 2. Also, from (27), we can deduce that 3.
If we put w = 0 in (27), we find that 4.
If putting w = 0 and ϑ = O in (27), we obtain the relation: Theorem 1. Suppose that θ and ϑ are matrices in C r×r satisfying the condition (9) such that ϵ, s, and r are non-negative integer numbers and where all matrices are commutative, then we have Proof.Using the R.H.S. of (32), we determine that By using (24), we have Putting ϵ − r − s = v and rearranging the terms, we obtain This complete the proof.
Theorem 2. If we assume that θ and ϑ are matrices in C r×r satisfying the condition (9) such that ϵ, p, q, and r are non-negative integer numbers and where all matrices are commutative, then we have that Proof.By using the definition in (27), we obtain Now, we find that By using (20), we have and this finish the proof.
Theorem 3. Let parameters θ and ϑ be positive stable matrices in C r×r satisfying the condition (9), where ϵ and r are non-negative integer numbers and where all matrices are commutative, then we obtain Proof.The Bessel matrix polynomials are expanded in double series using (27) in this case, and it is sufficient to show that the coefficient of z v w r is the same on both sides of Equation (34).Form the definition in (27), we have the L.H.S. as then, we find the coefficient of z v w r given by Also, we see the R.H.S. of Equation (34) as follows: The coefficient of z v w r of the R.H.S is We find this from (36) as Hence, from (35) and (37), the coefficient of z v w r is the same on both sides of Equation (34), and this complete the proof.
Some Integrals Involving the Matrix Bessel Polynomial
In this section, our attention is directed towards presenting integral representations for the matrix Bessel polynomial Y (θ,ϑ) m (z, w) in the form of theorems.
Theorem 4. Let θ, ϑ, and R be positive stable matrices in C r×r satisfying the condition (9) and where all matrices are commutative, then we obtain Where a, b > 0 Proof.By using the definition (27) in the L.H.S., we obtain By substituting p = v + r, rearranging the terms, and using (1), we obtain This concludes the proof.
Theorem 5.For θ andϑ, R and K are matrices in C r×r such that RK = KR and satisfying the condition (9), then we obtain where a, b > 0 Proof.By using the L.H.S. of ( 39) and (27), we find that By putting v + r = p and rearranging the terms, we have This complete the proof.
Theorem 6.If θ and ϑ are positive stable matrices in C r×r such that θϑ = ϑθ and satisfy the condition (9), then the matrix Bessel polynomials Y (θ,ϑ) ϵ (z, w) satisfy the following integral representation as where a, b > 0.
Proof.By using the L.H.S. of (40) and (27), we obtain This leads to the assertion (40).
Theorem 7. Let θ and ϑ be positive stable matrices in C r×r such that θϑ = ϑθ satisfies the condition (9), then we have where a, b > 0 Proof.By using the L.H.S. of ( 41) and (27), we obtain Substituting z = tu, we obtain and this complete the proof.
The Laplace-Carson Matrix Transform
In this section, we introduce the Laplace-Carson transform of the extended matrix Bessel polynomial.Initially, we provide the definition of the Laplace-Carson transform for matrix functions.Definition 2. Let F(u, s) be a function defined on the collection of all the positive stable matrices observed in C r×r , then the two-dimensional Laplace-Carson transform is provided by: such that the integral on the right side of the equation exists.
Theorem 8. Suppose that θ and ϑ are in C r×r satisfying the condition (9) and where all matrices are commutative, then we obtain the Laplace-Carson transform as where Re(u) > 0, Re(s) > 0.
Proof.By using Definition 2, we find that where K = (θ + I) ϵ (ϑ + I) ϵ .Putting uz = t and sw = n, we have which is the required proof.
Theorem 10.Let θ and ϑ be matrices in C r×r , satisfying the condition (9) and where all matrices are commutative, then we obtain where A = (θ + I) ϵ (ϑ + I) ϵ , and the Humbert matrix function ψ 1 (θ, ϑ; R, R ′ ; z, w) of two complex variables is given in [29] as This concludes the proof of Theorem 10.
Conclusions
The article examines a two-variable counterpart of matrix Bessel polynomials and investigates specific differential formulas and recurrence relations associated with them.Part of the integral formula for this new extension of matrix Bessel polynomials is also presented.In addition, we presented the Laplace-Carson transform for the analogous matrix Bessel polynomial with two variables.Future research efforts could be devoted to unveiling further properties and features of these polynomials.This could include the exploration of extended and generalized forms, as well as integral representations.The analysis of these facets may contribute to a deeper understanding of the polynomials and their behavior. | 2,500.4 | 2024-03-17T00:00:00.000 | [
"Mathematics"
] |
Comparing Physicochemical Properties and Sorption Behaviors of Pyrolysis-Derived and Microwave-Mediated Biochar
: Biochar’s ability to amend and remediate agricultural soil has been a growing interest, though the energy expenses from high-temperature pyrolysis deter the product’s use. Therefore, it is urgent to improve the pyrolysis efficiency while ensuring the quality of produced biochar. The present study utilized three types of feedstock (i.e., switchgrass, biosolid, and water oak leaves) to produce biochar via conventional slow pyrolysis and microwave pyrolysis at different temperature/energy input. The produced biochar was characterized and comprehensively compared in terms of their physiochemical properties (e.g., surface functionality, elemental composition, and thermal stability). It was discovered that microwave-mediated biochar was more resistant to thermal decomposition, indicated by a higher production yield, yet more diverse surface functional groups were preserved than slow pyrolysis-derived biochar. A nutrient (NO 3 -N) adsorption isotherm study displayed that microwave-mediated biochar exhibited greater adsorption (13.3 mg g − 1 ) than that of slow pyrolysis-derived biochar (3.1 mg g − 1 ), proving its potential for future applications. Results suggested that microwaves pyrolysis is a promising method for biochar production.
Introduction
Biochar is the thermochemical product converted from biomass in the absence of oxygen at high temperature [1]. The process has been deemed "charring" or "pyrolysis". When biochar was first investigated, it was widely used as a method to sequester carbon in soil [2,3]. Consequently, instead of suffering from rapid decomposition, the residues of plants and compost were recycled for biochar production and retained in the format of aromatic carbon [4]. Biochar is not a narrowly defined material. Because the utilization of the various feedstocks and the different pyrolysis conditions, biochar can exhibit different beneficial characteristics. As the interest in biochar research consistently grows, the extensive benefits of biochar contribute to a wide range of strategies: Agronomic improvement, mitigation of climate change, waste management, and energy production [4,5]. Large progress in each strategic scenario has been recorded in the previous studies. For example, Hangs et al. [6] demonstrated that the biochar produced from shrub willow feedstock enhanced the urease activity and nitrification rate of urea fertilizer which consequently increased the crop yield. Greenhouse gas (GHG) emissions, such as N 2 O, CO 2 , and NH 3 , have been largely reduced because of the addition of biochar [7]. The nutrient-rich temple floral refuse was processed to a biochar in the Singh et al. study, and the potential application in the dye removal was evidenced by a series of adsorption experiments [4]. Lastly, with regard to energy production, slow pyrolysis not only produces biochar, but it also presents comparable energy production. Besides the high efficiency for energy production, 30% lower energy input and 2-5 times of CO 2 emission elimination can be achieved [8].
The yield of biochar, its physical and chemical characteristics vary depending on the pyrolysis conditions (e.g., temperatures, retention times, and heat fluxes) and the raw materials. Processed via relatively higher temperatures, biochar is more recalcitrant and resistant to microbial and chemical decomposition. Elements like hydrogen (H) and oxygen (O) are largely depleted during pyrolysis. At the same time, the increased carbon (C) concentration indicates that C-related compounds have been condensed and mostly existed as the form of stable aromatic C in the biochar [9]. In addition, high temperatures provide benefits not limited to: Larger porosity and surface area, which are vitally important in the application related to biochar adsorption capacity [10]. However, high residue ashes and metal volatilization from high temperature charring get caught in the micropores [11]. In contrast, an atmosphere with a low temperature reserves most of the elements. Benefits including increased biochar yield and water adsorption make the low-temperature pyrolysis unignorable. Biochar under low-temperature pyrolysis (<500 • C) is recognized to be more favorable for plant growth and more easily decomposed [12].
The biochar derived from relatively high-temperature pyrolysis is more depleted of H and O, but possesses a larger proportion of aromatic C in comparison with that from a lower temperature [13] and consequently, has great chemical recalcitrance and resistance to microbial and chemical decomposition in soil. The organic matter presents in feedstocks, composed of mostly hydrocarbons, amino-acids, or lipids, and with a small presence of lignin or cellulose [14], can lead to an amelioration of soil physical properties, including an improvement in soil structure or attenuating the potential for surface runoff and erosion. The mineralization of the organic matter releases macro and micronutrients essential for crop development, reducing mineral fertilizer use [15]. Organic matter contributes as an energy source for micro-organisms inhabiting in soil. Therefore, feedstocks with these qualities may increase soil microbial population and activity [16]. Furthermore, different soil constraints require different biochar properties by also recognizing the different crop needs; for example: Legume or cereal crops [17]. As a result, not all biochar have demonstrated improved crop yield in all instances [18,19], and there are significant differences in stability between biochar [20]. In addition, biochar properties change over time in soil and these changes may also be affected by the initial properties of the biochar [21]. Therefore, the differences between biochar properties have to be well understood as a function of production conditions and feedstock type, in order to match soil needs with the appropriate biochar type.
Slow pyrolysis has been a well explored and trusted method of biochar production, providing a proficient baseline for comparisons. The pyrolysis-derived suffered from the long heating duration, damage to the reactor wall, and even an undesired secondary reaction. Slow pyrolysis requires time for the furnace to reach the desired temperature, as well as the desired time of pyrolysis at the desired temperature. To address these problems, the microwave irradiation has been explored as an innovative alternative heating source for these two main reasons. Compared to a furnace, the amount of time required to meet a comparable pyrolysis temperature is achieved in a fraction of the time [22]. Secondly, the merit of microwave mediation is that the rotation of molecules through high frequency and the penetration depth of the microwaves into the materials consequently provide sufficient heat to the materials [23]. During such process, the interactions between polar functional groups and free surface charges on the biochar surface and water molecular will concretely transfer the microwave energy to heat energy, facilitated with the mechanism such as interfacial polarization, ionic conduction, and dipole polarization [24,25]. Previous studies on various biomass example feedstocks also explored feasibility of microwave radiation in the biochar synthesis with continuous N2 gas and a vacuum [25].
This study is unique in two ways. First, it has attempted an alternative method in which the procedure of the irradiation was by covering the vessel containing the feedstock and purged with N 2 providing an alternative method to produce biochar via microwave. A second distinction is testing NO 3 − sorption capacity rather than ammonium nitrogen (NH 4 + ). The implications of these two are documented in the end of the discussion. The hypothesis is that this method of producing microwave-mediated biochar through a faster means will yield a quality biochar at a reduced energy demand.
The objectives of this study were to: 1.
Develop an alternative method of microwave biochar production, 2.
produce microwave-mediated biochar from three feedstocks that exhibit similar characteristics to that of pyrolysis-derived biochar, and 3.
compare characteristics of slow pyrolysis-derived biochar and microwave pyrolysisderived biochar via elemental composition, thermogravimetric structure, porous and surface structure, as well as sorption capacities of nitrate (NO 3 − ).
Feedstocks of biosolid, water oak leaves (Quercus virginiana), and switchgrass (Panicum virgatum) were utilized to produce biochar at several pyrolysis temperatures and energy levels. The takeaways aim at providing evidence of a biochar alternative method that can have increased use in future agricultural industry at a significantly lower energy requirement.
Biochar Feedstock and Production
To maximize the economic benefits of biochar in agronomic fields, three feedstocks that are easily accessible were used in this study: Switchgrass (SG), biosolids (BS), and water oak leaves (L). All feedstocks were dried at 60 • C for 48 h until no significant weight change was observed. It was then crushed to 0.5-1 cm in size.
Conventional Slow Pyrolysis
During slow pyrolysis, pure N 2 gas with purity > 99.99% was used at temperatures 300, 500, and 700 • C in a bench scale pyrolysis apparatus described in a previous study [26]. In brief, between 10-14 g of preprocessed feedstock was centered in a quartz tube (inner diameter: 2 cm, length: 45 cm). The tube was fitted with airtight connectors and rubber O-rings with continuous N 2 gas purge at 80 mL/min, heated in a controllable S-line single-zone split tube furnace (Thermcraft Inc., Wiston-Salem, NC, USA) at heat ramp of 10 • C/min until the desired temperature and was kept at final temperature for 60 min. The quartz tube was purged with N 2 gas during heating and cooling to prevent rapid oxidation and/or auto-ignition.
Microwave Pyrolysis
A Domestic Electric microwave (General Electric, Boston, MA, USA) with maximum power output of 1650 W and 2.45 GHz frequency was utilized for microwave mediation. Preprocessed feedstock (between 10-15 g) was evenly distributed in a leakproof glass container. Before being completely sealed, pure N 2 gas with purity > 99.99% sparged the container for minutes to prevent oxidation during the following process. Two power levels, Level 8 (1320 W) and Level 10 (1650 W) were used to synthesize the biochar. A 60-min duration was used for both power levels, and a third product was synthesized at 1650 W for 30 min, producing a total of 9 microwave-mediated biochar samples. Whence half the time was reached, the vessel was shaken to disperse the contents. Because the vessel was enclosed, it became pressurized with N 2 gas as well as biogas from the breakdown of the feedstock.
The yield of biochar was estimated by proportion of solid product to the original weight (wt/wt). The produced biochar from two methods were grinded to a fine composition with a mortar and pestle (<0.5 mm). They were then stored in sealed plastic containers at room temperature to prevent moisture absorption. Different pyrolysis conditions and biochar labels are listed in the Table 1.
MESTA Ultimate Analysis and Thermogram
The multi-element scanning thermal analysis (MESTA) was performed using a carrier gas of 33% O 2 in helium [27]. The loaded sample (15 mg) at ambient temperature (22 ± 1 • C) was heated to 750 • C at a 50 • C/min temperature ramp. Integration of thermograms of carbon (C), nitrogen (N), hydrogen (H), and sulfur (S) were used to determine the elemental composition (wt%) of biochar. Mass balance was performed to estimate the oxygen (O) content (wt%): O = 100 − (C + N + H + residual ash). Elemental compositions allow us to calculate significant parameters such as the atomic H/C and atomic O/C ratios, as well as the polarity index.
Thermogravimetric Analysis
The feedstock and biochar samples were analyzed by TGA thermalgravimetric analyzer (GA 550, TA Instrument, New Castle, DE) under the flow of argon (50 mL/min). The sample was weighed to approximately 5-7 mg. Before the sample was placed, a tare was performed so that only the sample weight was measured in the thermal weight-change analysis. The temperature ramp was set as follows: 1.
Porous Structure Analysis
The Brunauer, Emmett, and Teller (BET) test was performed using an autosorb iQ automated gas sorption analyzer (Boynton Beach, FL, USA) to determine the specific surface area of the biochar samples within the 0.01-0.30 relative pressure (P/P o ) range of N 2 sorption isotherm. Degassing of the sample was done as a pretreatment by heating the tube around the sample to 120 • C for 4 h and vacuuming any remaining gas out of the vessel. Polanyi theory (P/P o = 0.98) was used to calculate the total pore volume [28]. The built-in Non-Local Density Functional Theory determined the pore size distribution in the pressure region (0.01-0.98). NovaWin 11.0 (Quantachrome Instruments, Boynton Beach, FL, USA) performed the data analysis.
Surface Morphology Analysis
The scanning electron microscopy (SEM) imaging was performed on all biochar and feedstocks utilizing a FEI Nova 400 Nano SEM (Hillsboro, OR, USA). Samples were first coated with Iridium (Ir) via sputter coater (Cressington HR208 Sputter Coater, Ted Pella, Inc.) with N 2 gas purging to dissipate charging artifacts and minimize the beam damage. A 4 nm coat was applied to each sample. Images were taken on samples under vacuum following the standard procedures at scales 50 µm, 10 µm, and 5 µm, which was magnifications of 1000, 5000, and 10000, respectively. Characterization of surface morphology was performed using the SEM detector (ETD) at a voltage of 5 kV, 10 kV, or 15 kV, current of 96 pA, and focal length of 5 mm to 10 mm.
FTIR Analysis
Fourier transform infrared (FTIR) spectroscopy using a PerkinElmer 100 spectrometer (Waltham, MA, USA) was performed to analyze the structure of biochar using the noncontact reflectance imaging method. For the FTIR spectra, there were 16 scans performed on each sample with a spectral resolution of 4 cm −1 and in the mid-infrared range of 4000 to 650 cm −1 . Broad-bands within the detection ranges include aromatic C-H rings, O-H stretch of phenolic compounds, aromatic and olefinic C = C vibrations, C-H alkyl structures, and H-bonded O-H stretch vibrations of hydroxyl groups from alcohols, phenols, and organic acids [9].
Nitrate Adsorption Isotherm Experiments
Batch sorption experiments were conducted to investigate the ability of different biochar to adsorb NO 3 − . A series of polyethylene centrifuge tubes with 15mL volume containing 100 mg of biochar sample and 12 mL NaNO 3 solutions (10, 25, 50, 75, and 150 mg L −1 NO 3 − ) were agitated on a wrist action shaker (Model 75, Burrel Scientific, Pittsburgh, PA, USA) to reach sorption equilibrium. Tests were triplicated with each trial beginning with a blank at each concentration to gain a calibration curve (R 2 = 0.998). The samples suspension were then centrifuged for 15 min at 2500 rpm. Concentrations of NO 3 − in 6 mL of sample supernatant were estimated by ion chromatography (Dionex Aquion, Thermo Scientific, Waltham, MA, USA). A 4-mm AS15 analytical column set at 40 • C was coupled with a 4-mm AG15 guard column, and a 4-mm AMMS Micromembrane suppressor to take measurements of NO 3 − (Thermo Scientific, Waltham, MA, USA). During the test, 38 mM NaOH was used as an eluent at a flow rate of 1.2 mL/min.
The amount of NO 3 − adsorbed on the biochar was calculated via Equation (1): where, q (mg g −1 ) is the amount of NO 3 − adsorbed onto the biochar at equilibrium; C 0 and C e (mg L −1 ) are the initial and equilibrium concentrations of NO 3 − ; V (L) is the volume of the aqueous solution; and M (g) is the mass of the added biochar.
The Freundlich model in Equation (2), a widely utilized sorption model, was fitted to the sorption data.
where K F and n are experimentally derived constants.
Statistical Analysis
Statistical analyses for means and errors of the data were executed using Microsoft Excel for Windows 10 (Microsoft Office, Redmond, WA, USA) and SigmaPlot (Version 10.0, Systat Software, Inc., San Jose, CA, USA).
Yield of Biochar
The biochar yield observed from the slow pyrolysis from the different feedstocks showed that BS had the largest yield across the three different temperatures (Figure 1). This might because the higher concentration of inorganic compounds and lower volatile organic contents in BS [29]. Both SG and L had yields between 20% and 30% for temperatures of 500 • C and 700 • C, but then increased to almost 40% and 50% at 300 • C, respectively. There was an interesting commonality among the three feedstocks: The 300 • C biochar had high variability (3-10 times more) in yield compared to the 500 • C and 700 • C. The microwave pyrolysis derived biochar had a similar trend of decreased yield when a higher power level was applied for the same duration. Although, when the feedstock was radiated at 1.65 kW for half the time as the other specimens, it had a similar yield to that of 1320-60M biochar. There was 150-200% increase in yield from microwave-mediated biochar yield compared to the pyrolysis-derived biochar. Additionally, the minimum yield of microwave-mediated biochar, found at 1.65 kW for 60 min, was observed to be the same or higher than the maximum yield observed from the pyrolysis-derived biochar, i.e., 300 • C.
Knowledge on measured temperature from previous studies during the microwave pyrolysis-derived biochar synthesis was used in this study. A recent study observed temperature for microwave biochar synthesis at 700 W; their findings showed that after 15 min, a temperature of at least 650 • C was achieved [22]. Another study measured 400 • C in a microwave at 750 W [23]. Ge et al., 2020, also observed that there was an average 60 • C min −1 increase in temperature within the first 5 min, but dropped to roughly a 30 • C min −1 increase for the remainder of the synthesis, with signs of plateauing in the last 2 min of synthesis [22].
Elemental Composition of Biochar
Elemental composition of biochar exhibited great dependence on the feedstock types. Since the initial benefit of biochar was carbon sequestering, it was expected that the percent composition of C increased with temperature/power increase [9]. This expected result was only not evident for BS biochar (Table 2). Relatively high carbon contents (>50%) were found in the L and SG biochar, proving that the feedstocks have the potential to provide carbon-rich biochar [30]. The variation of C consequently led to the variation of O content, even though increased dehydrogenation and condensation were to promote significant decreases in both H and O [31]. BS raw materials and resulting biochar consistently composed most of elemental N among three feedstocks. This indicates that heterolytic N-containing structure may be formed as a result of pyrolysis [32]. According to previous study, the formed N-functional group may affect nutrient such as NH4-N and organic-N adsorption, which consequently resulting in N immobilization [33]. Element S, as one of essential plant nutrients and soil amendment [34], was detected in very low concentration (<1.0 wt%) in BS and SG-300P biochar. Atomic O/C ratios of the biochar ranged from 0.19-1.34 (Table 2). Higher O/C ratios have been attributed to hydrophilic surfaces from more O-containing functional groups [9]. When applied in agricultural fields, lower atomic O/C ratios may provide larger halflives (>1000 years), allowing it to be retained in the soil and providing its other benefits perpetually [35]. Atomic H/C ratios of biochar, which specify degree of original organic carbon preserved, varied from 0.19-1.52, with lower ratios occurring at higher temperatures and power outputs, though more uncertainty was evident with the microwave-mediated biochar. BS1320-60M had the highest atomic H/C ratio. Higher ratios eluded that increased filtering efficiency of inorganic contaminants could be achieved [36]. The atomic H/C ratio is a key factor when associated with agricultural fields as it has been found to impact the intensity of reducing N 2 O emissions, where lower H/C ratios were observed having higher capacity for reduction of N 2 O emissions [37].
The gradation of recalcitrance and aromaticity of biochar was approximated by the data from Table 2, developed as a van Krevelen diagram ( Figure 2). Generally, the lower H/C and O/C ratios occurred at SG and L biochar, attributed to the formation of aromatic rings, increase of single C-bonds, decrease in H-C and O-C bonds, and reduction of easily biodegradable organic compounds [31]. However, BS biochar has a relatively high O/C and H/C producing from both pyrolysis methods. This indicates SG and L biochar may mineralize slower than BS biochar, contributing to higher biochar stability in the application [32]. Compared to slow pyrolysis, microwave pyrolysis resulted in similar ratios for SG and L feedstocks, while biosolid exhibited less predictable results from two pyrolysis procedures. The lack of gas circulation and the heating of water particles in the microwave-mediated biochar process may resulted in less dehydration, which could account for difference in ratio trends.
Thermogravimetric Characteristics of Biochar
The decomposition stability of the slow and microwave pyrolysis-derived biochar and their respective feedstocks were analyzed by TG decomposition and derivative thermogram (DTG) curves (Figures 3-5). DTG curves were derived from data obtained from TG decomposition data, which displayed differences in thermal peak quantity, temperature occurrence, and magnitude/shape of peak across each feedstock and its respective temperature or radiation applied, indicating differences in structure by all types of biochar. Compared to microwave pyrolysis, slow pyrolysis exhibited great carbon sequestration of all feedstocks evidenced from less pronounced and less amounts of thermal peaks. The first dominant thermal peaks occurred between 200 and 400 • C on original feedstocks and microwave pyrolysis biochar, resulting from the combustion of cellulose and hemicellulose [38]. All of the microwave-mediated had significant increased weight reduction within 350-550 • C, mainly attributed to the breakdown of lignin and autocatalytic reactions [39]. Lignin has been suggested to begin showing loss of mass beginning at 200 • C, but at small increments, as is the most difficult component to decompose compared to cellulose and hemicellulose, due to its complex chemical composition [38]. The differences in decomposition that occurred across the feedstocks as well as by methods of pyrolysis show that there was a clear difference of structural integrity of the samples, with generally more stability in the samples that occurred at higher temperature or power.
Surface Structure Analysis of Biochar
Surface structures were observed from the infrared spectra of the biochar and their respective feedstock at the various slow and microwave pyrolysis syntheses ( Figure 6). The spectral peaks enabled the diverse functional groups in the raw feedstock, microwavemediated, and low temperature samples to be evident. The raw feedstocks, all microwavederived biochar, and slow pyrolysis at 300 • C (except for SG) detected the unstable functional groups of O-H (~3400 cm −1 ) and alkyl C-H (~3000 cm −1 ). This occurrence was attributed to the breaking of hydroxyl groups of aliphatic groups which occur between 120 and 200 • C. The further increasing of temperature to 400 • C cause the breaking of the aliphatic methoxyl, methyl, and methylene groups [9]. For most feedstocks and biochar except at 700 • C, and in BS-and SG-500 • C, broadbands near 1000 and 1700 cm −1 were still evident. The only broadbands that seemed to disappear for the microwave-mediated biochar were the C-H stretching and O-H stretching near 3000 cm −1 and 3400 cm −1 , respectively, indicating that half the functional groups were released through microwave irradiation. At 3200-3400 cm −1 , non-detection of the hydroxyl group signified a release of hydroxylcontaining compounds (phenolic or aliphatic alcohol) as volatile matter [5]. Additionally, alkyl-hydroxyl chain cracking within lignin [2] potentially cracked (within the carbonization process), attributing to the release of the hydroxyl groups [40]. In the 2850-2950 cm −1 range, C-H stretching functional groups were released partly due to demethylation [41] and methyl group transforming into species containing carbon (CO and/or CO 2 ) by means of ether bond breaking [30]. The band of C-O-C stretching near 1000 cm −1 were more pronounced for both 1.65 kW biochar for BS and L, corresponding to the increased C and O elements found from the MESTA results in Section 3.2. The dehydration of cellulosic materials and ligneous compounds occurring at temperatures > 400 • C attribute to the increased pronunciation [2].
Structural Porosity and Morphology of Biochar
The surface area and porosity of biochar have been noted as two of the most critical properties for nutrient sorption of biochar [42]. The greater surface area the biochar contains per gram can promote increased space for adsorption along with more microbial communities to grow and assist in crop growth [30]. There were many similarities discovered in the surface area between the different specimens ( Figure 7). For slow pyrolysis-derived biochar at 500 • C, the highest surface area was recorded for L and BS at 42 m 2 g −1 and 29 m 2 g −1 , respectively. Whereas the 700 • C biochar had the most surface area for SG at 18 m 2 g −1 .
The feedstocks showed varied results. SG was collectively the feedstock with the least surface area among all the variations of slow and microwave pyrolysis derived. The other two feedstocks had similar surface areas which were contained between 2-10 m 2 g −1 , with the exception of the 500 and 700 • C samples. Higher temperature/energy input was expected to yield a more porous/increased surface area biochar due to more mesopores and micropores being formed from the intensified structural condensation [26]; however, decreased pore size is a consequence of high temperature/energy input pyrolysis. The microwave pyrolysis-derived biochar for SG showed consistent results (0.5-2 m 2 g −1 ), despite the increase in power or time. While the highest specific surface area for BS was 1650-60M (8.3 m 2 g −1 ) and L 1650-30M (7.2 m 2 g −1 ), respectively. Compared to the feedstocks, there was at least a 350% increase in specific surface area as energy was used to heat the feedstocks. The elevated power level increased heat energy that led to enhanced carbonization, which allowed more volatile matter to be released, theorized to create more pores in remaining non-volatile parts [30]. Therefore, results showed promise to be a successful soil amendment to adsorb N nutrients and facilitate plant growth. BS specimens were expected to contain the highest surface area as the temperature and radiation level increased (Figure 7), as well as by the evident amount of pore space shown from the SEM images ( Figure 8). The BS feedstock showed the most visual surface area from SEM. L surface was primarily smooth across all versions of the biochar species, but there was an area that showed capacity for an increased amount of surface are. For the SG biochar, there was primarily strings of parallel rods that ran the length of the sample. Within these rods there were strings of silicon bands that remained within the biochar (found via Energy Dispersive Spectroscopy detector). Between SG 1320-60M and SG 1650-60M, the increased energy dissipation onto the biochar provided clear deterioration of the surface, creating grooves along the length of the specimen, indicating an increased surface area when energy was increased.
NO 3 − Adsorption Isotherms and Characteristics
Like NH 4 + , NO 3 − is a species of N required for adequate and/or enhanced crop growth. NO 3 -N is a key component in the nitrogen cycle, specifically starting the denitrification process, and ending up as N 2 O, a GHG. Previous studies have looked primarily at NH 4 + adsorption on biochar [26], while few investigated NO 3 − [43], and mainly found that little or no NO 3 − adsorption capacity was evident for biochar. Additionally, there has not been much exploration of NO 3 − sorption on microwave-mediated biochar [44]. Vital information of nutrient sorption by slow and microwave pyrolysis-derived biochar was observed through the equilibrium isotherm of NO 3 − (Figure 9). Biochar derived from two pyrolysis methods shared similar NO 3 − adsorption capacities. In addition, there was a significant increase of N nutrient adsorption for SG 1650-30M, where 6.2 mg g −1 NO 3 − -N showed more than a 200% increase than all other feedstocks for an initial concentration of 150 mg L −1 NO 3 − (Figure 9f). However, there was considerable variability among all SG samples derived from both pyrolysis methods. There was a difference of behavior from the different pyrolysis temperatures as well as the microwave power dispersion; i.e., for pyrolysis-derived and microwave-mediated, the adsorption of NO 3 − was 500P > 300P > 700P and 1320-60M > 1650-30M > 1650-60M for BS, respectively, 300P > 700P > 500P and 1650-60M > 1320-60M > 1650-30M, for L respectively, and 300P > 500P > 700P and 1650-30M > 1320-60M > 1650-60M for SG, respectively. In these differences, it is clear that lower temperatures and lower irradiation concluded with more NO 3 − adsorbed by biochar, due to the reduced amount of dehydrogenation and dehydration that occurred at higher temperatures and radiation. It is suggested that increased sorption of NO 3 − is possible when an acid activation with hydrochloric acid is performed to reduce negative surface charge of biochar, as indicated in a previous study [44].
There were certain samples of the biochar, namely all derivations of SG and L1320-60M that were not able to comply with the Freundlich model from the experimental data of NO 3 − adsorption (R 2 < 0.72). In relation to increased sorption intensity and capacity, the constants 1/n and k F tend to have higher values [26]. However, a decrease in R 2 -value occurred with an increased k F and decreased, implying that increased variability occurred with decreased intensity. The high correlations with low SE values of the Freundlich model indicates that the adsorption of NO 3 − follows a heterogeneous behavior [4] for BS and L, while SG is assumed to follow a homogenous behavior [26].
Implications of the Study and Future Work
One of the studies pointed out that energy consumption, chemicals, and reactors running cost required 50% of the total processing cost [45]. Therefore, the involvement of microwave irradiation could be beneficial because of less energy requirement and equipment installation. Furnaces, such as the one used in this study, required time to warm up, to ramp to the desired temperature, and to hold that temperature to produce the biochar, which demands increasingly more amounts of energy for each stage. Costs associated with ramping alone were shown to increase four-fold for a biochar specimen of 600 • C (400 USD ton −1 ) compared to one at 400 • C (~100 USD ton −1 ) [9]. With a microwaveirradiated instrument, however, there is no/little additional energy or time requirement for warming and ramping, only time to produce the product at the desired energy level. Additionally, the biochar yield of microwave-mediated biochar was on average about 50% more than what the yield of pyrolysis-derived biochar (Figure 1), potentially allowing for higher production in addition to the reduced energy costs. Therefore, perfecting the microwave mediation process of biochar can open new opportunities for a cost-effective soil additive by reducing the production time and energy input required. Although temperature was not measured during the microwave pyrolysis in this study, the amount of power from the microwave can be used as a pseudo-variable to measure temperature if the specific heat capacity of the feedstock is known. However, the specific heat capacity of the feedstock used in this study is not available. This brings out the need for estimating specific heat capacity of alternative feedstocks and is deferred for future work. The ash content of the original feedstock was not measured in this study. However, it can help understand reasons of high oxygen content in some of the biochar specimens. Raw material analysis from an earlier study using the same feedstock was used to estimate ash content.
Further laboratory experiments, field application studies, as well as techno-economical estimation are needed to display realistic conditions and the ability for microwave-mediated biochar to confirm its ability for N adsorption via fertilizer application and its ability to enhance crop production for cost driven farmers [46]. A prior study had found that pyrolysis-derived biochar would not be economically feasible without the additional application of fertilizer products [47], whereas it is still unknown whether this requirement also applies to microwave-mediated biochar. Studies also need to increase exploration on additional feedstock materials and their respective product properties to determine the scale of variability that microwave-mediated biochar can have across various regions. Though feedstock dependent, there may be obvious trade-offs for this method of synthesis, i.e., a low-cost production versus a high specific surface area and carbon sequestration. Such knowledge can remove the lingering uncertainty for biochar products and potentially provide a variety of cost-effective method of biochar application.
Conclusions
This study indicated that microwave irradiation is a promising pyrolysis method. Carbon content of all produced biochar were similar, except biosolid, where variation was found between different pyrolysis methods. Higher yield from microwave-mediated biochar can benefit in large scale production and reduce cost. Specific surface area was a characteristic that greatly differentiated between the two pyrolysis, in which the microwave pyrolysis-derived biochar exhibited smaller surface area compared to slow pyrolysisderived biochar (500 • C or higher). The biggest difference was the considerable adsorption of NO 3 − observed in all biochar, and in the case of switchgrass, exceptionally more adsorption from microwave pyrolysis-derived biochar than slow pyrolysis-derived biochar. Such high adsorbency might be because of the more hydrophilic functional groups on the biochar surface, which was also indicated by the FT-IR and TGA results. The application of microwave pyrolysis-derived biochar in agricultural fields may provide a potential soil additive to incorporate increased N retention for enhanced crop production. Indicating from previous studies, the significant reduction in energy requirement and cost increases the likelihood for future use; however, in situ experiments and techno-economical assessment to expand on the application potential of microwave pyrolysis-derived biochar are required in future study.
Data Availability Statement:
The data presented in this study are available on request from the corresponding author. | 7,806.4 | 2021-02-22T00:00:00.000 | [
"Environmental Science",
"Agricultural and Food Sciences",
"Materials Science",
"Chemistry"
] |
A speedup technique for (l, d)-motif finding algorithms
Background The discovery of patterns in DNA, RNA, and protein sequences has led to the solution of many vital biological problems. For instance, the identification of patterns in nucleic acid sequences has resulted in the determination of open reading frames, identification of promoter elements of genes, identification of intron/exon splicing sites, identification of SH RNAs, location of RNA degradation signals, identification of alternative splicing sites, etc. In protein sequences, patterns have proven to be extremely helpful in domain identification, location of protease cleavage sites, identification of signal peptides, protein interactions, determination of protein degradation elements, identification of protein trafficking elements, etc. Motifs are important patterns that are helpful in finding transcriptional regulatory elements, transcription factor binding sites, functional genomics, drug design, etc. As a result, numerous papers have been written to solve the motif search problem. Results Three versions of the motif search problem have been proposed in the literature: Simple Motif Search (SMS), (l, d)-motif search (or Planted Motif Search (PMS)), and Edit-distance-based Motif Search (EMS). In this paper we focus on PMS. Two kinds of algorithms can be found in the literature for solving the PMS problem: exact and approximate. An exact algorithm identifies the motifs always and an approximate algorithm may fail to identify some or all of the motifs. The exact version of PMS problem has been shown to be NP-hard. Exact algorithms proposed in the literature for PMS take time that is exponential in some of the underlying parameters. In this paper we propose a generic technique that can be used to speedup PMS algorithms. Conclusions We present a speedup technique that can be used on any PMS algorithm. We have tested our speedup technique on a number of algorithms. These experimental results show that our speedup technique is indeed very effective. The implementation of algorithms is freely available on the web at http://www.engr.uconn.edu/rajasek/PMS4.zip
Background
Pattern search in biological sequences has numerous applications and hence a large amount of research has been done to identify patterns. Motifs are fundamental functional elements in proteins vital for understanding gene function, human disease, and may serve as therapeutic drug targets. Three versions of the motif search problem have been identified by researchers: Simple Motif Search (SMS), Planted Motif Search (PMS)also known as (l, d)-motif search, and Edit-distance-based Motif Search (EMS) (see e.g., [1]).
PMS problem takes as input n sequences of length m each and two integers l and d. The problem is to identify a string M of length l such that M occurs in each of the n sequences with a Hamming distance of at most d. For example, if the input sequences are GCGCGAT, CACGTGA, and CGGTGCC; l = 3 and d = 1, then GGT is a motif of interest.
EMS is the same as PMS, except that edit distance is used instead of the Hamming distance. SMS takes as input n sequences and an integer l. The problem is to identify all the patterns of length l (with up to l/2 wild card characters), together with a count of how many times each pattern occurs.
Two kinds of algorithms can be found in the literature for the solution of PMS. The first kind of algorithms identify all the motifs always. This kind of algorithms are called exact algorithms. The second kind of algorithms may not always identify the motif(s). Numerous algorithms of each kind can be found in the literature.
The exact version of the PMS problem is known to be NP-complete.
Several exact algorithms are also known for solving the PMS problem: [10][11][12][13][14][15][16], and [17]. PMS algorithms are typically tested on random benchmark data generated as follows: Twenty sequences each of length 600 are generated randomly from the alphabet of interest. The motif M is also generated randomly and planted in each of the input sequences within a Hamming distance of d. The motif instances are also generated randomly. Certain instances of the (l, d)-motif problem have been identified to be challenging. An instance is challenging if the expected number of (l, d)-motifs that occur by random chance (in addition to the planted one) is one or more. For example, the following instances are challenging: (9, 2), (11,3), (13,4), (15,5), (17,6), (19,7), etc. The performance of PMS algorithms are customarily shown only for challenging instances.
The exact algorithm MITRA of [8] can solve the challenging instance (15,4). It cannot solve (15,5) or any larger instances. On these instances it takes either too much time or too much space. Three exact algorithms PMS1, PMS2, and PMS3 have been given in [18]. These algorithms are faster than MITRA. Other exact algorithms are: Voting of [19], RISOTTO of [20], and PMSprune of [21].
In this paper we present a speedup technique that can be used for any PMS algorithm. Before presenting details of our technique, we provide a brief summary of the following algorithms: PMS1, Voting, RISOTTO, and PMSprune. We have employed these algorithms to demonstrate the efficacy of our technique.
A Summary of Known Algorithms PMS0 and PMS1
PMS0 and PMS1 are two exact algorithms given in [18]. PMS0 works as follows. Let S 1 , S 2 , ..., S n be the given input sequences and let m be the length of each input sequence. For any two l-mers u and v let H.D.(u,v) stand for the Hamming distance between u and v. Let u be any l-mer. We define the d-neighborhood of u (denoted as D u ) as the set of l-mers that are at a distance of ≤ d from u. In other words, D u is nothing but {v: H.D.(u, v) ≤ d}. Let C be the collection of l-mers in S 1 . Note that C has (ml + 1) l-mers. PMS1 is an exact algorithm that works as follows. For each input sequence S i (1 ≤ i ≤ n) it generates a list of d-neighbors. In particular, for each l-mer u in S i , it generates D u . It merges all such D u 's and eliminates duplicates to get L i . The output (l, d)-motifs will be ∩ n i=1 L i . More details follow.
Algorithm PMS1 1. Generate all possible l-mers from out of each of the n input sequences. Let C i be the collection of lmers from out of S i for 1 ≤ i ≤ n.
2. For all 1 ≤ i ≤ n do: . Sort all the l-mers in every C i , 1≤ i ≤ n, in lexicographic order, and eliminate duplicates in every C i . An integer sorting algorithm can be used (see e.g., [22]). Let L i be the resultant sorted list corresponding to C i . 4. Merge all the L i 's (1 ≤ i ≤ n) and output the generated (in step 2) l-mers that occur in all the L i 's.
The following theorem results.
where w is the word length of the computer.
Voting
The Voting algorithm proposed in [19] is very similar to PMS1. In this algorithm also, the potential motifs considered are the d-neighbors of each l-mer in the input sequences. In particular, they employ a hash table V of d-neighbors. Each such d-neighbor collects votes. Let v be a d-neighbor of some l-mer in the input. Then, v will receive a vote from the input sequence i (for if v is a d-neighbor of some l-mer in the input sequence S i . They ensure that v will not get multiple votes from any sequence using another hash table R. The algorithm builds both V and R by processing each l-mer u in each input sequence, generating the d-neighborhood of u, and hashing the d-neighbors into V and R. After processing all the input l-mers in this fashion, the algorithm outputs all those d-neighbors that receive a vote of n.
Clearly, the asymptotic run time of this algorithm is O mn l d | | d assuming that l is a constant. If l is not of constant size, there could be a linear dependence on l as well in the run time.
RISOTTO
An exact algorithm for PMS has been given by [23] that For each such neighbor v the algorithm of [23] walks through the suffix tree to check if v is a valid motif (i.e., it has a d-neighbor in each input sequence). This walking step is referred to as 'spelling'. The spelling operation takes a total of O(n 2 ml d (|Σ| -1) d ) time using an additional O(nm) space. An improved version of the above algorithm, called RISOTTO, has been given by [20]. The algorithm of [23] makes use of a trie called the motif tree. The root of this tree corresponds to the empty string. The algorithm grows this string one symbol at a time and for each such string checks if it is a valid motif (i.e., the string is of the right length and it occurs in every sequence within a Hamming distance of d).
A key observation that [20] make use of in their algorithm is the following. Let q be a string that occurs in all the input sequences (up to a Hamming distance of d). Let its maximum extensibility be MaxExt(q).
MaxExt(q) refers to the maximum number of symbols that can be appended to q so that the resultant string will occur in all the input sequences (within a Hamming distance of d). If q' is another string such that q is a suffix of q', then MaxExt(q') cannot be more than MaxExt (q). As a result, if MaxExt(q') + |q'| <l, then we don't have to consider augmenting q' further. In other words, we can prune the subtree rooted at q' in the motif tree [20]. show that the average performance of RISOTTO is better than that of [23].
PMSprune
PMSprune follows the same strategy as PMS0: for every l-mer y in S 1 it generates the set of neighbors of z and for each one of them checks whether this is a valid (l, d)-motif or not. However it improves the performance of PMS0 in a significant way. Salient features of this algorithm are: 1. It generates the neighborhood of every l-mer u in a branch and bound manner. In this method, these l-mers will correspond to nodes in a tree of height at most d. The root (which is at level zero) of this tree will be u. At level i of this tree they generate lmers that are at a distance of i from u (for 1 ≤ i ≤ d). its worst case run time is worse than that of PMS0, PMSprune has a better expected run time and it does better in practice [21].
Our Speedup Technique Summary
We refer to our speedup technique as PMS4 and it can be used in conjunction with any PMS algorithm. The idea of PMS4 is also based on PMS0. We can think of PMS0 as consisting of two stages. In the first stage, we generate all the l-mers of S 1 and for each such l-mer generate its d-neighborhood. All of these d-neighborhoods are then merged to get the list L 1 of l-mers. In the second stage, for each l-mer v in L 1 , check if v is a valid (l, d)-motif or not. In other words, in stage 1 we come up with a list of candidate motifs. In the second stage, for each candidate motif we check if it is a valid motif or not. For each candidate motif it takes O(mnl) time to check if it is a valid motif or not. This is rather a large amount of time. PMS0 does not perform well since there are a large number of candidate motifs and for each candidate motif it takes a long time to check its validity. We can speedup its performance if we can reduce the number of candidate motifs (and/or if we can speedup the validity checking for each candidate motif).
PMS4 reduces the number of candidate motifs by first running the PMS algorithm on a small number of input sequences. It then verifies the validity of each candidate. Let A be the PMS algorithm under concern. A pseudocode for PMS4 follows.
Algorithm PMS4 1. Run the algorithm A on k input sequences (where k <n). An optimal value of k can be determined empirically. We could pick the k sequences in a number of ways. For example, they could be the first k sequences, random k sequences, and so on. Let C be the collection of (l, d)-motifs found in these k sequences.
A probabilistic analysis
The problem of planted motif search is complicated by the fact that, for a given value of l, if the value of d is large enough, then the expected number of motifs that occur by random chance could be enormous. For instance, when n = 20, m = 600, l = 9, d = 2, the expected number of spurious motifs (that occur in each input sequence at a hamming distance of d) is 1.6. On the other hand for n = 20, m = 600, l = 10, d = 2, the expected number of spurious motifs is only 6.1 × 10 -8 . A probabilistic analysis to this effect can be conducted as follows (as shown in [3]). Let S k be any input sequence 1 ≤ k ≤ n and let u be any l-mer. Probability that u occurs in S k at a Hamming distance of d starting from a specific position is Thus, probability that u occurs in S k starting from at least one of the positions in S k is 1 -(1p) m-l+1 . Here it is assumed that the occurrence of u is independent of the starting position (which is clearly not true). Buhler and Tompa argue that this assumption nearly holds in practice [3]. This means that the expected number of l-mers that occur in each of the input sequences (at a hamming distance of d) is 4 l [1 -(1p) m-l+1 ] n . A slightly different valid analysis has been presented in [24]. Let S k be any input sequence 1 ≤ k ≤ n and let u The run times of many of the known PMS algorithms are linearly dependent on the number of input sequences. Examples include PMS0, PMS1, RISOTTO, Voting, and PMSprune. Any reduction in the number of input sequences will result in a corresponding reduction in the run time. If the number of resultant motifs is small then the overall run time will be reduced. We have to strike a balance between the time it takes for the first stage and the second stage. A good starting point for the value of k is ⌈n/2⌉. We could then work around this value to optimize the time.
Results and Discussion
We have tested the performance of PMS1, PMSprune, and RISOTTO for various values of (l, d), and k. The improvements in performance are shown next. We have not included Voting in this comparison since the Voting program takes a very long time when we decrease the number of sequences. When we decrease the number of sequences the number of motifs increases. The Voting program sorts these motifs and outputs them. We suspect that the sorting program used could be the reason for the long run times. However, since the asymptotic run time of Voting is linear in the number of sequences, PMS4 is expected to result in a speedup of Voting similar to that in PMS1 and RISOTTO. All the times reported in this section are averages over 10 random instances (fixing the values of k, l, and d). Each instance is a benchmark set of 20 random sequences of length 600 as mentioned in the Background Section The case of (9, 2) Results for the case of l = 9 and d = 2 are shown in Table 2. In this table, we display the time taken by each algorithm for k = 20 (denoted as T 20 ) in column 2. Note that these algorithms, by default, work with 20 sequences. The best times found using PMS4 (denoted as T b ) are shown in column 3. The ratio T 20 /T b (called the speedup) is shown in column 4. It is clear from this table that each of these algorithms benefits from PMS4. In particular, RISOTTO benefits the most with a speedup of close to 2. Figure 1 shows the performance of these algorithms for various values of k starting from 5.
The case of (11,3) Results for the case of l = 11 and d = 3 are shown in Table 3. For this case also RISOTTO benefits the most with a speedup of more than 2. The speedup for PMSprune has decreased and that for PMS1 has also decreased but not by the same amount as PMSprune. Figure 2 shows the performance of these three algorithms for different values of k.
The case of (13, 4) Table 4 summarizes the performance of PMS1, PMSprune and RISOTTO. The speedup for RISOTTO has increased. In general, the performance of RISOTTO increases with an increasing value of l. The performance of PMS1 also increases with an increasing value of l. However, the performance of PMSprune seems to be stable. Figure 3 displays the performance of all the three algorithms.
The case of (15,5) In Table 5 and Figure 4, we show the results for PMS1 and PMSprune. RISOTTO takes too much time for this case and hence we have not included it in this comparison. As has been observed before, the speedup of PMS1 increases with an increasing value of l and the speedup for PMSprune stays nearly the same (at around 1.4). Based on the experimental results, we suggest that the best value of k should be chosen around 0.4n to have maximum speedup.
Conclusion
In this paper we have presented a speedup technique that can be used on any PMS algorithm. We have tested our speedup technique on a number of algorithms. These experimental results show that our speedup technique is indeed very effective. | 4,254.6 | 2011-03-08T00:00:00.000 | [
"Computer Science"
] |
On the holographic phase transitions at finite topological charge
Exploring the significant impacts of topological charge on the holographic phase transitions and conductivity we start from an Einstein–Maxwell system coupled with a charged scalar field in Anti-de Sitter spacetime. In our set up, the corresponding black hole (BH) is chosen to be the topological AdS one where the pressure is identified with the cosmological constant (Kubiznak and Mann in JHEP 7:33, 2012), then the AdS BH undergoes the phase transition from small to large BHs, which is totally similar to the transition from gas to liquid in the van der Waals theory. Our numerical computation shows that the process of condensation is favored at finite topological charge, in particular, the phase transition from small to large BHs in the bulk generates a mechanism for changing the order of phase transition in the boundary: the second order phase transitions occur at pressures higher than the critical pressure of the phase transition from small to large BHs while they become first order at lower pressures. This property is confirmed with the aid of holographic free energy. Finally, the frequency dependent conductivity exhibits an energy gap when the phase transition is second order and when the phase transition becomes first order this gap is either reduced or totally lost.
Introduction
It is known that the AdS/CFT duality [1] formulated by Maldacena and developed independently by Witten [2] and Gubser, Klebanov and Polyakov [3] in the form of the GKPW relation has opened up a new direction of connecting gravity with other branches of physics. At present the GKPW relation turns out to be a powerful formalism for this purpose. In this respect, the study of holographic phase transitions has been developed strongly and gained great successes associated with superconductors and related topics [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, to our understanding, up to now maybe Ref. [16] was a e-mail<EMAIL_ADDRESS>(corresponding author) solely the one which suggested that the Einstein-Maxwell system coupled with a charged scalar field in the topological AdS BH could yield superconductivity. Therefore inspired by [16], we will investigate systematically in this paper the holographic phase transitions at finite topological charges. Our main aim is to look for the new effects which could emerge when there occurs the phase transition from small to large BHs in the bulk.
Then let us start from the model of a Abelian Higgs field and a Maxwell field in the four-dimensional spacetime Einstein gravity. The bulk action reads where G N is the Newton constant. In the uncondensed phase, the solutions to Eq. (1) are the Reissner-Nordstrom black hole (BH) where and here the horizon radius, r 0 , is the largest solution of the equation: In Eq. (1), dΩ 2 2,k is the metric of a two-sphere of radius 1/ √ k for k > 0. Note that the parameters M and Q are different from the mass and the charge of BH by corresponding factors. The Hawking temperature T and entropy of BH are respectively given by It is very interesting to mention that adopting the relation between pressure P and the cosmological constant of BH one discovered the total analogy between the small-large BH phase transition and the liquid-gas phase transition of the van der Waals theory for k > 0 [11,12] . In this set up M becomes the enthalpy of the system and k is interpreted as the measure of a new charge, the topological charge [13,14].
Then the extended first law [15] of BH reads where T and S are given in Eq. (4a), ε = 4π k is the topological charge and its conjugate potential ω = r 0 /8π , the pressure P conjugates to the volume V = 4 3 πr 3 0 , the charge Q conjugates to the potential φ = Q/r 0 .
In term of ε from Eqs. (3), (4b) and (5), it is easily derived the isobaric specific heat which yields the critical values for pressure, temperature and horizon event radius where, for simplicity we set G N = Q = 1 from now on. Equation (6) shows that at fixed ε the transition from liquid to gaz takes place at P ≤ P c and T ≥ T c and the bigger values of ε lead to the smaller values of P.
The present paper is organized as follows. Section 2 deals with the holographic phase transitions at finite topological charges and the free energy, respectively. Section 3 is devoted to the calculations of frequency dependent conductivity in different phase transitions. The conclusion and outlook are given in Sect. 4.
A. Basic set up
At first let us set up the frame work for the whole study of holographic phase transitions. We begin with the following ansatz and at the same time we choose which is above the Breitenlohner-Freedman bound [18]. Inserting Eq. (7)) into Eq. (1) we derive the equations of motion for matter fields where the prime denotes derivative with respect to r . For the fields to be regular at horizon we impose the condition Inserting Eq. (11) into Eq. (10), and expand near r → r 0 , we arrive at the condition at horizon for scalar field At the AdS boundary, the large r behaviors of φ and ψ take the form where μ and ρ are chemical potential and the corresponding density associated with the expectation value of charge density, ρ = J 0 , with a source term in the boundary action of the form Due to the holographic duality there are two possibilities for identifying the sources and condensates of the dual field theory ψ 1 is the source which vanishes at infinity and ψ 2 is the source which vanishes at infinity and ψ 1 is condensate ψ 1 ∼ O 1 .
B. Free energy
In order to analyse the order of phase transitions we have to calculate the holographic free energy. This quantity is holographically evaluated by calculating the corresponding on-shell value of the Abelian-Higgs sector of the Euclidean action. Plugging the ansatz, Eq. (7), into the action, Eq. (1), we arrive at Here we have made a change of variable, z = 1/r , to better formulate the system of equations of motion for numerical evaluations and to simplify various expressions.
Applying the boundary condition, Eq. (11), and the Eqs. (9, 10), we obtain the on-shell value of the Euclidean action Substituting the asymptotic behaviors of φ and ψ into the above action we get The divergence term in the foregoing expression will be removed by adding the counter term [8] where h is the determinant of the induced metric on the AdS boundary. With the aid of the asymptotic behavior of ψ it is easily found that The renormalised free energy of the boundary field theory is obtained (18) which corresponds to the O 1 quantization , V 2 is the volume of two-sphere with radius 1/ √ k. Analogously, the renormalised free energy in O 2 quantization reads which is the Legendre transform of Ω 1 . From Eqs. (18) and (19), it is clear that This is exactly what we assumed that only one of ψ 1 and ψ 2 is non-vanishing for physical solutions. The free energy corresponding to non-condensed state reads From Eq. (20), we get the free energy difference This is our expected result.
C. Numerical results
In this subsection we focus on the impacts of the topological charge in the holographic phase transitions. To this end, let us proceed to the numerical calculation which will be implemented in the following cases: The scalar condensation is plotted in Fig. 1, where the onset of second order phase transitions occur at T c = 0.113μ and 0.050μ, respectively.
After fitting the curves in Fig. 1 near T → T c , we obtain approximately the expressions Fig. 1 The condensation of O 1 (a) and O 2 (b) as T → T c = 0.113μ and as T → T c = 0.050μ. Figure 1 and the foregoing expressions characterise one of the typical properties of superconductors in mean-field approximation. It is worth to note that the phase transition takes place at L = 1, corresponding to pressure P L=1 = 3 8π L 2 L=1 which is bigger than the critical pressure P c = 3 8π L 2 L=6 given in Eq. (6). Now let the pressure decrease to lower values which corresponds to bigger values of L. In Fig. 2a, b are shown the phase diagrams for L =1, 4, 6, and 9. It is clear that at critical pressure P c = 3 8π L 2 L=6 , the first order phase transition begins to appear.
In order to confirm exactly the exhibition of first order phase transitions let us calculate numerically the free energy difference, Eq. (21), between the condensed and uncondensed phases for O 1 and O 2 , respectively. They are plotted in Fig. 3a, b which indicate that at L = 6, 9 the free energy difference is not analytical at corresponding critical temperatures.
2. ε = 16π and L = 0.5, 1.5, 2 Next we consider the case when the topological charge takes bigger value. The phase diagrams plotted In Fig. 4 tell that at L ≥ 1.5 the first order phase transitions emerge. Figure 4 demonstrate again that the first order phase transitions always emerge at critical pressure P c = 3 8π L 2 L=1,5 and moreover when the topological charge gets bigger values the first order phase transitions manifest at higher pressures. The existence of the first order phase transitions in Fig. 4 are confirmed again in Fig. 5 the free energy is not analytical at corresponding temperatures.
Conductivity
Let us finally proceed to the conductivity of superconductor in the dual CFT as a function of frequency. For this purpose, we must solve the equation for the fluctuations of the vector potential A x (r, t) in the bulk. Let this potential take the form
from which we get the equation of A x (r ) in our set up
which is rewritten in new variable z = 1/r as where ψ was solved in Sect. 2. In order to determine the solution to Eqs. (22,23) we need two boundary conditions. The first one is given by the on going condition at horizon and the second boundary condition is set at large r . To do this, A x is expanded in term of z near z → 0. This gives Therefore the second boundary condition is The AdS/CFT duality dictionary tells that b x determines the boundary current j x = b x . Then the Ohm law gives us the conductivity Equation (27) numerical computation provides the graphs of the frequency dependent conductivity corresponding respectively to the phase diagrams given in subsection C. They are presented in accordance with different items in subsection C: 1. ε = 4π, Q = 1, L = 1, and 9 We plot the real part of frequency dependent conductivity Reσ (ω) derived from the numerical calculations of Eqs. (22,23) at Q = k = L = 1 in Fig. 6a, b which exhibit a gap determined by condensate and, furthermore Reσ (ω) contains a delta function which is recognized from the imaginary part Imσ (ω) having a pole at ω = 0 (it is not shows up here). Therefore the real part and imaginary part of ω = 0 are related by the Kramers-Kronig relations. At L = 9 we have correspondingly Fig. 7a, b which tell that the foregoing gap disappears. This means that the superconductivity is totally lost.
2. ε = 16π, Q = 1, L = 0.5, and 2 Corresponding to L = 0.5 we depict the graphs in Fig. 8a, b which prove clearly that the gap is really reduced even when the phase transition is second order, this implies that a mixture of normal and conductive states emerges. At L = 2 the gap totally disappears as seen in Fig. 9a, b, the superconductivity is totally lost. Thus, the conductivity of superconductor is greatly affected by topological charge. These features are similar to those of some strongly coupled superconductors [19][20][21].
Conclusion and discussion
Before summarizing this paper it is worth to emphasize again that the existence of the topological charge leads to the phase transitions from small to large BHs which totally similar the phase transition from liquid to gas in the van der Waals theory. Within this framework we studied the significant impact of the topological charge on the holographic phase transitions and what we obtained can be brefly written as follows.
1. The phase transition from small to large BHs in the bulk created a mechanism for changing the holographic phase transitions from second order to first order in the boudary. In other words, the holographic phase transitions in the boundary are closely associated with the phase transition from liquid to gaz in the van der Waals theory. This effect was confirmed by the free energy difference.
2. When the phase transitions are second order the frequency dependent conductivity σ (ω) exhibits an energy gap and, moreover, its real and imaginary parts fulfill the Kramers -Kronig relation while the phase transition becomes first order the gap is either reduced or totally lost. Our set up provides a new types of holographic superconductivity in which the topological charge plays the crucial role. The foregoing results exactly express the novelty of our paper, they do not exist for BHs without topological charge. Therefore they express the significant impacts of topological charge.
It is very interesting to remark that there exists a formal analogy between our present paper and Ref. [9] although our starting points are different, namely, The holographic phase transitions studied in our paper is associated with the transition from small to large BHs in the bulk while in Ref. [9] the holographic phase transitions is associated with the Hawking-Page transition in the bulk because the AdS-soliton decays into AdS BH via Hawking-Page transition.
We start from the charged AdS BH in four dimensional spacetime with finite topological charge while Ref. [9] started from the AdS-soliton in five dimensional spacetime without topological charge, as a consequence, the holographic transition is solely second order.
The analogous effect was also presented in other papers, for example, Refs. [6,7] with different mechanisms. In Ref. [7] the charged scalar field is forced to condense by another neutral scalar field and in Ref. [6] the nonlinear interaction of charged scalar field was employed F = 4 2 c i |ψ| i . One found that first order phase transitions occurred for c 4 ≥ 1 and, moreover, the gap becomes narrower as c 4 increases from 0 to 1.
Reference [22] dealing with the unbalanced Stackelberg holographic superconductors the authors showed that depending on the values of the Stackelberg model's parameters the phase transitions also change from second to first order and, at the same time, the conductivity gaps are affected strongly.
Last but not least it is clear that the results found above allows us to have a better understanding on the physical meaning of topological charge. In this regard, we need to explore more and more the the impacts of this charge on various physical processes. The backreaction of matter fields will be the subject of our next 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://creativecomm ons.org/licenses/by/4.0/. Funded by SCOAP 3 . | 3,780 | 2020-04-25T00:00:00.000 | [
"Physics"
] |
Inverse Modeling Using Taylor Expansion Approach and Jacobi Matrix on Magnetic Data (Dike/Magma Intrusion Cases)
The mathematical modeling of dike or magma intrusion has been done, based on magnetic data with inversion techniques using MatLab. The magnetic equation was done using a linear approach to non-linear mathematical models of magnetic data using the Taylor expansion approach and Jacobi Matrix. The first step, we made a synthetic data forward modeling from the magnetic equation of dike or magma intrusion cases without errors, and then add errors to the data. The next step was to do an inversion to get the parameters sought, i.e., depth and angle of the magma intrusion, by giving initial guesses, and then recorrect solution iteratively until obtained the convergent results. Finally, parameters of dike/magma intrusion slope orientation and its depth can be determined, and this technique can be used to get the physical parameters of these geological cases.
INTRODUCTION
The objective of measuring using geophysical methods is to get a subsurface model of observational field data, i.e., magnetic susceptibility, density, resistivity, and others [1]. A magnetic method is one of the geophysical methods based on measuring the variation of magnetic field intensity on the surface of the earth caused by differences in the distribution of magnetized sub-surface objects [2], using magnetic sensors, in order to determine the rocks magnetic susceptibility [3]. This difference in susceptibility can occur when a rock is broken through by other rocks as well as a magmatic intrusion of maar and cinder cone [4] as well as at Mount Lamongan area [5]. A mathematical formulation is needed to connect the sub-surface susceptibility model and observation data at the surface [6], using forward and inversion modeling [7]. Forward modeling is done by calculating the anomaly of the model and comparing it with the anomaly data from the measurement results, while inversion modeling calculates the value of physical parameters from the existing observation data based on the mathematical model. The main difficulty occurs when we do inversion modeling at non-linear mathematical equations such as mathematical magmatic intrusion equations so that the solution no longer uses a linear approach [8]. Some solutions to this problem can be done using the simulated annealing approach [9] and Taylor-Jacobi expansion [7]. In this paper, we use Taylor-Jacobi expansion iteratively to solve non-linear equations of dike/magmatic intrusion formula in order to determine its parameters, i.e., slope orientation and depth.
METHODS
The mathematical equations formulated by [10] were then modified by [11], and Almantouq [12] used to get synthetic data on geological structures, i.e., dike or magma intrusion. From this synthetic data, a subsurface structure model, i.e., orientation and depth, can be determined using the inversion method with Taylor Expansion Approach and Jacoby Matrix.
Anomaly magnetic field formulation due to dike/magmatic intrusion
Dike and magma intrusion is a sheet of rock that fills or breaks through existing rock bodies [12]. Frozen rocks shaped flat in the form of these plates occur because of the process of intrusion of magma between existing rock layers either with upright or tilted directions. [10] in [8] explain the relationship of magnetic anomaly field F(x) caused by an infinite dike with a certain depth, can be written as, F(x) is a magnetic field profile measured along x, and perpendicular to the strike direction of the magma intrusion. For charts with tiny widths and depths, equation (1) above written as [10,11], With α is the angle formed by horizontal to dike or thin magma column, x is the position of the measurement offset data, h is the depth of the dike, and C is the constant (3225 nT). Using equation (2) above, we can calculate the magnetic field caused by forward modeling along with the offset of x measurement.
Mathematical Equations of Inversion Method
In general, inversion techniques are formulated in the following relationships [7,14], The above equation then we multiply the two sections again with ( ) and we get, The Equation (5) is an inversion for linear cases, while Equation (2) used for magnetic data forward modeling geological case studies are a case of non-linear equations. The kernel matrix, which is a function of forward modeling, no longer contains the predicted model parameters, which is then carried out by the process of matching the model parameters. Suppose the solution of inversion in Equation (3) is m which is the initial model m0 which matched with ∆m in order to obtain a better match of the response of the model to the data [7], then = 0 + ∆ (6) and from equation (3), by applying equation (6) for this case can be written as, and if the equation (15) rewritten at its components, with i = 1,2,3 ... N is the amount of data, and j = 1,2,3, ..., m is the model parameter.
The first-order Taylor Expansion of G(m) function around the model from equation (16) and ignore the residual tribe, then produce, [6], with is the Jacobi mabtrix, = by substituting an equation (10) into equation (9) and rearranging equation (9) again, it will obtain, − ( 0 ( ) ) = (11) So, the equation (19) can be written in matrix notation as follow, or, or, Furthermore, 0 is the Jacobi matrix which evaluated at = 0 . The equation (13) is similar to = ( ), so by analogy with the same formula differentiation in equations (10) to (13), by multiplying the two segments of ∆ 0 = 0 ∆ 0 (equation 21) with 0 , then we get, by multiplying two segments in equation (15) with ( 0 0 ) −1 , then obtained, (16) is an identity matrix, so that it equation can be rewritten as, then, by substituting the equation (15) to (17), it is obtained, By doing iteratively matching equation (25) to the initial model m0 so that a better model obtained ( = 0 + ∆ 0 ). The model response is expected to be more appropriate and fit with subsurface geological features. The G which is the Jacobi matrix in the magmatic intrusion case (equation 2) consists of, with is a transpose matrix for each parameter in the n iteration, d is data and ( 0 ) is the inverse calculation model result. Jacobi matrix G1 and G2 expressed as equation (20) and (21).
Magnetic data inversion step
The first step is to make synthetic data ( ) at field data by carrying out a forward technique using equation (2) by using specific α and h model parameters. The data from the forward modeling then added to a random error. The second step is to make the same data as the first step (data ) by making an initial guess at the model parameters α and h. The next step calculates the difference between dan . If there is a difference (within specified limits), modifications are made to the stages of the model parameter values until appropriate. The step is shown by the flow chart of the image (1). When the difference between the actual parameters and the inversion results is very small and the inversion result parameters are correct, the α (dike/magma intrusion angle) and h (dike/magma intrusion depth) parameters obtained from the inversion process will be obtain.
RESULT AND DISCUSSION
After the algorithm and script program completed, the test is carried out with several stages; the first step is to create synthetic data from equation (2) in forward modeling. And verify the pattern of the forward model made with existing software that, in this case, we use Mag2DC to prove it. The next step is to create a forward model that added to a random error that seems to represent a field data. After that, we do an inversion script test by inversion the forward data that has not been given an error, assuming that if the program script created correctly, the result will be the same as the data forward. The last step is to test by inverting the forward data that has given a random error.
Forward Modeling and verification
After the algorithm and script program completed, several stages of the test were carried out. The first step is to create synthetic data from equation (2) in forward modeling to make a magnetic data of a simple dike case or thin magma intrusion/dike, verify the pattern of the forward model made with existing software that, in this case, we use Mag2DC to verify it. Mag2dc is software for modelling magnetic data and make a sub-surface model of magnetic data. First, the model made with α simple dike with an orientation of 60 0 and 90 0 at 160 meters depth, offset x from -5000 meters to 5000 meters with interval measuring points as far as 150 meters. Output, the results of the forward modeling are shown in figure (1) and (2). There is a suitability of the results of forward modeling with angular parameters of 60 0 and 90 0 at a depth of 160 meters (figures 1(a) and 2(a)), with the results of the forward model with the same parameters using the MAG2DC software (figures 1(a) and 2(b)). The forward yield graph pattern built using equation (2) produces results data known as synthetic observation.
Forward Modeling added an error
Because there is no direct field data/observation data, an error is added to the forward model data in the previous step as if it were field data or substitute for field data. The assumption used here is that field data is usually not ideal as a model formulation, but there is an error due to measurement. The forward result that has added to this error presented by a figure (3), Data from the addition of errors is not smooth or not as ideal as the data before an error added. The model parameters used are at angle α = 60 0 and depth of dike (h) = 160 meters. The same can done for several different parameters.
Forward Data and Inversion Result without Error
The next step is testing from the inversion process that has been made by making forward data and then making an inversion process. The inversion step will be correct if the final result of the model parameter inversion calculated is the same as the model parameter used during the forward process, and the data graph plot coincides. In figure 4 is the result of a forward with an angle α = 60 0 and a depth of h = 160 meters. From the results of inversion with initial guessing approaching the forward value with α = 65 0 and h = 155 meters, the inverse results are α = 60,01 and h = 160 with a misfit of 0.000005 and 4 iteration processes. With the same parameters (α = 60 0 and depth ( h) = 160) then inversion is done by using a rather distant guess that is α = 80 0 and depth is h = 150 meters. With this guess, the model parameters obtained from the inversion results are α = 59.89, and the depth is h = 159.90 meters, with misfit = 0.73 and need 7 iteration processes it. In the inversion process with different initial guessing parameters, the inversion results are almost the same but have differences in terms of misfit and time of the iteration process. In a distorted initial guess, the obtained misfit is more significant and requires a longer iteration time. At this stage, the inversion algorithm built can be used to guess the parameters of the slope angle and depth of the subsurface object with a simple dike or thin magma intrusion scenario in ideal conditions without the addition of errors in the data.
Inversion Result with Error
In this test, data forward is used, which has added an error in substitute for field data. At this stage, the first test is carried out by varying the different angles and fixed h, guessing with fixed angles and h depth varies, and both are varied. In this first case example a trial with parameters α = 100 0 and h = 300 m, with an initial guess α = 30 0 and h = 100 m. The results of this inversion shown in figure 5. The result of these processes shown that the model parameters obtained from inversion α = 99.88; h = 299,57 m, with misfit equal to 0.58 and the five iterations. This parameter occurs until the inversion model has a parameter similar to the forward parameter. The first iteration satisfaction is 4.40, the second iteration = 3.40, the third iteration = 2.38, the fourth iteration = 1.40 and the fifth iteration is obtained misfit = 0.58. This misfit decays until the value of the misfit below one is obtained.
CONCLUSION
The mathematical equation of the non-linear model can be solved using a linear approach with the Taylor expansion and the Jacobi Matrix iteratively. The inversion value at a far estimate of the model parameter will be valid if the initial guess is not too far away. At a far estimate of the initial parameter input, more iterations are needed to converge and need a more extended time to process it. Using this method, the simple sub-surface model of magmatic intrusion/dike parameters, i.e., orientation and depth, can be determined. | 3,096.8 | 2019-12-01T00:00:00.000 | [
"Geology",
"Physics"
] |
A New Integrated Approach Based on the Iterative Super-Resolution Algorithm and Expectation Maximization for Face Hallucination
: This paper proposed and verified a new integrated approach based on the iterative super-resolution algorithm and expectation-maximization for face hallucination, which is a process of converting a low-resolution face image to a high-resolution image. The current sparse representation for super resolving generic image patches is not suitable for global face images due to its lower accuracy and time-consumption. To solve this, in the new method, training global face sparse representation was used to reconstruct images with misalignment variations after the local geometric co-occurrence matrix. In the testing phase, we proposed a hybrid method, which is a combination of the sparse global representation and the local linear regression using the Expectation Maximization (EM) algorithm. Therefore, this work recovered the high-resolution image of a corresponding low-resolution image. Experimental validation suggested improvement of the overall accuracy of the proposed method with fast identification of high-resolution face images without misalignment.
Introduction
Super-resolution (SR) is the process of improving a low resolution (LR) image to a high resolution (HR) image without altering the originality of the image.This super-resolution is also called hallucination [1].The process of converting a low-resolution image to a high-resolution image is necessary during image processing [2], and it has a wide range of applications.In satellite image processing, image restoration and image enhancement require super-resolution to remove distortions and for enhancement of satellite images [3].Super-resolution has wide applications in medical image processing for improving the quality of medical images, such as MRI CT scan, which requires more contrast and fine enhancements [4].Its multimedia applications are also increasing, wherein all multimedia, e.g., images, videos, and animation require high definition when the SR functionality is involved [5].Face hallucination must have the following constraints: 1.
Data constraints: The output image of face hallucination must be similar to the input after completion of smoothening and downsampling.2.
Global constraint: It must have the same features of the human face, e.g., mouth, nose, and eyes.
The face features must be steady.
3.
Local constraint: The final image must have the exact characteristics of a face image with the local feature.
Video surveillance cameras are used widely in many places, such as banks, stores, and parking lots, where intensive security is critical [6].Details of facial features obtained from the surveillance video are essential in identifying personal identity [7].However, in many cases, the images obtained from the surveillance cameras cannot be well identified due to the low resolution of facial images that cause the loss of facial features [8].Thus, to obtain detailed facial features for personal recognition, it is necessary to infer a low-resolution (LR) facial image to a high-resolution (HR) using by face hallucination or face super-resolution [9].
Such techniques are applied in a variety of essential sectors, e.g., medical imaging, satellite imaging, surveillance system, image enlarging in web pages, and restoration of old historic photographs [10].Due to limited information on image identification, reconstruction and expression analysis is a challenge to both humans and computers.Under some circumstances, it is impossible to obtain image sequences [11].Several super-resolution reconstruction (SRR) researches have been proposed, relying on two approaches: reconstruction-based and learning-based approach [12].The reconstruction-based approach employs multiple LR images of the same object as an input for reconstructing an HR image.
In contrast, the learning-based approach uses several training samples from the same domain with different objects to reconstruct the HR image [13].An advantage of the learning-based approach is its ability to reconstruct the HR image from the single LR image.Learning-based super-resolution is applied to human facial images [14].Several related facial hallucination methods have been proposed in recent years.Learning-based methods have acquired more considerable attention as they can achieve high magnification factors and produce positive super-resolved results compared to other methods [15].
The related facial hallucination methods may be used on position-patches to improve image quality [16].Such methods perform a one-step facial hallucination based on the position-patch instead of neighbor-patch.A patch position is one of the learning-based approaches that utilize the facial image, as well as image features, to synthesize high-resolution facial images from low-resolution ones [17].In comparison, neighbor patches are used widely in face hallucination.The reconstruction of a high-resolution facial image could be based on a set of high and low-resolution training image pairs [18].The high-resolution image is generated using the same position image patches of each training image [19].This method can be extended using bilateral patches [20].The local pixel structure is learned from the nearest neighbors (KNN) faces.However, there are some uncontrollable problems regarding this method, i.e., the facial images captured by the camera (i.e.LR and facial hallucination) are limited to frontal faces [21].Therefore, it is practically significant to study how to create HR multi-viewed faces from LR non-frontal images.
As a sequence, a method called the multi-viewed facial hallucination method based on the position-patch was developed in [22].It is a simple face transformation method that converts an LR face image to a global image, predicting the LR multiple views of that given LR image.Based on the synthesized LR faces, facial details are incorporated using the local position-patch.Meanwhile, the traditional locally linear embedding (LLE) [23] technique, when applied in such a hallucination method still faces a problem related to the determination of the optimal weights.Such weights are defined using a fixed number of neighbors for every point [24].This is not practical for real-world data because the number of neighbors in each point is not equal to the other point.In that study, multi-view face hallucination using an adaptive locally linear embedding technique was proposed for efficiently reconstructing high-resolution face images from a single low-resolution image [25].The optimal weights determination was applied to manipulate the non-frontal facial details.By feeding a single LR face in one of up, down, left, or right views to the proposed method, the HR images are generated in all views [26].
The critical value of the mapping coefficient in LR to HR is computed in the TRNR [27].Accuracy is maintained in the training vector using subspace matching, and data with dissimilar scales are computed for representation.The weighted coding methodology is used to evaluate the noisy image as input.Generalized adversarial related networks are used to evaluate the quality of the image using the super-resolution strategy [28].Dissimilar types of global priority related methodologies prevent the data from segregating into tiny decomposed elements from the input image [29].The neighbor embedding [30] methodology was used to resolve the natural images, according to the geometry LR patch space construction.The LR training set may be applied to the HR space to demonstrate the image patch.The least-square regression methodology was used to implement location-based patches to regularize coefficient representation to get the most accuracy [31].
The drawbacks of the related methods include not being suitable for global face images while performing super resolving generic image patches.They have minimized accuracy and are time-consuming.While processing the minimized resolution image, the guaranteed output is not achieved.Therefore, the main objectives of that proposed method are: (a) Using a hybrid methodology, where low-resolution images can be converted into high-resolution based images.(b) Reducing misalignment variations using the local geometric co-occurrence matrix model.(c) Every image with random transformation for each pixel will minimize the computational complexity and minimize the loss to avoid degenerate solutions.(d) Maintaining a high amount of accuracy.
Therefore, this paper proposed a new integrated approach based on the iterative super-resolution algorithm and expectation-maximization for face hallucination.Training global face sparse representation was used to reconstruct images with misalignment variations after a local geometric co-occurrence matrix.In the testing phase, we propose a hybrid method, which is a combination of the global sparse representation and local linear regression using the Expectation Maximization (EM) algorithm.Therefore, this work recovers the high-resolution image of a corresponding low-resolution image.Simulation results proved that the proposed work performed well in various performance metrics compared to related works.
The paper is organized as follows: The proposed system with modules such as global face model learning, local geometric co-occurrence model learning, and the expectation-maximization algorithm is introduced in Section 2. The results and discussions are in Section 3, and finally, the conclusion and the future enhancements are given in Section 4.
Main Ideas
Sparse representation is the existing method for super-resolution, which is not appropriate for global face images, as we need to explore non-linear information hidden in the data.Moreover, the available Eigenface model and Markov network model have very low accuracy.The processing step starts when the low-resolution image is interpolated to the size of the target high-resolution image [11].The low-resolution interpolated image is a blurred image that is deficient in high-frequency information, and it is used as a preliminary estimation of the target HR image.Then, the image will be divided further into non-overlapping image patches that are not separate.The framework uses the generated patches to identify the image, which is most matched by searching a training data set of low-resolution and high-resolution image patches.The selected high-resolution image is generated to study high-resolution information.Finally, the trained high-resolution image and the interpolated images are combined to estimate the high-resolution target image.The embedded space is learned for producing solutions with representation, distinct solutions for the same functionality, and picking the group of embedding vectors.Therefore, mapping within the embedding spaces is restricted.Figure 1 demonstrates the block diagram of SR based face hallucination.
available Eigenface model and Markov network model have very low accuracy.The processing step starts when the low-resolution image is interpolated to the size of the target high-resolution image [11].The low-resolution interpolated image is a blurred image that is deficient in high-frequency information, and it is used as a preliminary estimation of the target HR image.Then, the image will be divided further into non-overlapping image patches that are not separate.The framework uses the generated patches to identify the image, which is most matched by searching a training data set of low-resolution and high-resolution image patches.The selected high-resolution image is generated to study high-resolution information.Finally, the trained high-resolution image and the interpolated images are combined to estimate the high-resolution target image.The embedded space is learned for producing solutions with representation, distinct solutions for the same functionality, and picking the group of embedding vectors.Therefore, mapping within the embedding spaces is restricted.Figure 1 demonstrates the block diagram of SR based face hallucination.
The proposed algorithm was employed to discover the non-linear structure in the data.The algorithm was developed under the assumption that any object is "nearly" flat on small scales.The initial object was to map data from one space globally to another space by embedding the locations of the neighbors for each point.For face hallucination, it was about LR and HR face image spaces.The main idea of the proposed methodology was minimizing the reconstruction error of the set of all local neighborhoods in the data set.The reconstruction weights were computed by reducing the reconstruction error using the cost function in Equation (1).For face hallucination, such reconstruction weights are computed in the LR face image space and then applied to the HR space to reconstruct the HR face image that corresponds to the LR input.The proposed method normally contains the weight matrix computed from the neighborhood in the same space as the training samples.Similar to LLE, the ALLE (Adaptive locally linear embedding) computes the weights from the space of training samples, which is built adaptively from only the neighborhood of each input, not all training samples.Since some information contained in all training samples can make the optimizer misleading to another optimal value, the threshold of similarity is defined for building each subspace in Equation ( 2).
Face image is represented as a column vector of all pixel values.Based on structural similarity, the face image can be synthesized using the linear combination of training objects.In other words, a face image at an unfixed view can also be reconstructed using a linear combination of other objects in the same view aligned as computed using Equation (3).The proposed algorithm was employed to discover the non-linear structure in the data.The algorithm was developed under the assumption that any object is "nearly" flat on small scales.The initial object was to map data from one space globally to another space by embedding the locations of the neighbors for each point.For face hallucination, it was about LR and HR face image spaces.The main idea of the proposed methodology was minimizing the reconstruction error of the set of all local neighborhoods in the data set.The reconstruction weights were computed by reducing the reconstruction error using the cost function in Equation (1).
For face hallucination, such reconstruction weights are computed in the LR face image space and then applied to the HR space to reconstruct the HR face image that corresponds to the LR input.The proposed method normally contains the weight matrix W computed from the neighborhood in the same space as the training samples.Similar to LLE, the ALLE (Adaptive locally linear embedding) computes the weights from the space of training samples, which is built adaptively from only the neighborhood of each input, not all training samples.Since some information contained in all training samples can make the optimizer misleading to another optimal value, the threshold of similarity θ is defined for building each subspace in Equation (2).
Face image is represented as a column vector of all pixel values.Based on structural similarity, the face image can be synthesized using the linear combination of training objects.In other words, a face image at an unfixed view can also be reconstructed using a linear combination of other objects in the same view aligned as computed using Equation (3).
There is no information to determine the construction coefficients at other views.After obtaining the LR in all views, these LR images are hallucinated to the HR face images of all views using the position-patch methodology.The proposed framework for multi-view face hallucination is to replace the linear combinations in all processes to improve the performance of hallucinating face images in multiple views.The framework means the number of the neighbors can be adapted for each input patches, and this would relieve the deviation from optimal values.The symbols used to construct the proposed framework are demonstrated in Table 1.
AIHEM Algorithm
Step 1: Consider a set of starting parameters in incomplete data.
Step 2: (E-step): Using the observed data from the data set approximates the values of the lost data.
Step 3: (M-Step): the complete data generated after the E-step is used for updating the parameters.
The proposed model consists of 3 phases: • Global face model learning.
•
Local geometric co-occurrence model learning • Iterative sparse representation optimization.
The training phase consists of two parts: The first part is the global face model learning and local geometric co-occurrence model learning.We use a Gaussian mixture model-based estimator for expectation-maximization, as the Gaussian mixture model uses a combination of probability distribution and estimates the mean and standard deviation parameters, as demonstrated in Figure 2.
Step 1: Consider a set of starting parameters in the incomplete data, with a hypothesis that the observed data is generated from a precise model.
Step 2: E-step-Using the observed data from the data set, approximate the values of the lost data, which are used to update the variables.
Step 3: M-Step-the complete data generated after the E-step is used to update the parameters, i.e., for updating the hypothesis.
Step 4: Checks whether the values are converged, where the concept of convergence is an intuition based on probabilities.When the probability of the variables has a tiny difference, then we say it has converged, i.e., the values are matched.If it is matched, the process stops, otherwise Steps 3 and 4 are iterated until convergence.
Global Face Model Learning
First, we provide the input HR face images with misalignment and apply the online dictionary to create the dictionary H for the HR face images.Figure 3 demonstrates the global face model learning.To construct a dictionary to obtain face image "sparsity prior," face images are preferentially represented by the basis vectors of the same misalignment variation so that the superresolved HR face images are constrained in a subspace of certain misalignment variation.
HR face images are always highly dimensional (the dimension is 127 × 158 for an HR image and 50 × 62 for an LR image in this paper), and the training set needs to be large enough for training the redundant dictionary.However, in practical applications, the computational complexity of the sparse problem is very high with an extensive dictionary.Generally speaking, the computational cost is proportional to the size of the dictionary H, i.e., a size of ¼ nm, where n is the dimension of the HR face image, and m is the number of basis vectors in the dictionary.Since the solutions are usually an iterative method dealing with a large dictionary matrix, the storage requirements and computational cost are significant.In our case, if all images with different misalignment variations were selected to compose a dictionary, it would be difficult to solve the super-resolution problem.Thus, we considered dictionary learning to compress a dictionary to reduce the operational burden.Batchbased methods have problems dealing with an extensive training matrix effectively.This paper employed an online dictionary learning method to process the images, one at a time, with low memory consumption and lower computational costs.The number of basis vectors in the dictionary was 1024.The following steps were required to perform online dictionary learning.
1. Assume the training set, such as the first dictionary and number of iterations.2. Reset the past information.3. Find the sparse coding using LARS (least angle regression coefficient).
Here is dictionary coefficient is Lagrange's multiplier.
Global Face Model Learning
First, we provide the input HR face images with misalignment and apply the online dictionary to create the dictionary H for the HR face images.Figure 3 demonstrates the global face model learning.To construct a dictionary to obtain face image "sparsity prior," face images are preferentially represented by the basis vectors of the same misalignment variation so that the super-resolved HR face images are constrained in a subspace of certain misalignment variation.
HR face images are always highly dimensional (the dimension is 127 × 158 for an HR image and 50 × 62 for an LR image in this paper), and the training set needs to be large enough for training the redundant dictionary.However, in practical applications, the computational complexity of the sparse problem is very high with an extensive dictionary.Generally speaking, the computational cost is proportional to the size of the dictionary H, i.e., a size of 1 4 nm, where n is the dimension of the HR face image, and m is the number of basis vectors in the dictionary.Since the solutions are usually an iterative method dealing with a large dictionary matrix, the storage requirements and computational cost are significant.In our case, if all images with different misalignment variations were selected to compose a dictionary, it would be difficult to solve the super-resolution problem.Thus, we considered dictionary learning to compress a dictionary to reduce the operational burden.Batch-based methods have problems dealing with an extensive training matrix effectively.This paper employed an online dictionary learning method to process the images, one at a time, with low memory consumption and lower computational costs.The number of basis vectors in the dictionary was 1024.The following steps were required to perform online dictionary learning.
1.
Assume the training set, such as the first dictionary and number of iterations.
2.
Reset the past information.
3.
Find the sparse coding using LARS (least angle regression coefficient).
Here δ is dictionary coefficient ϑ is Lagrange's multiplier.
χ is an Original data.
Di is the created dictionary.Suffix 2 is a normalization factor.4.
Compute the learned dictionary, Here i is loop iteration.5.
Get the updated dictionary.
Appl.Sci.2020, 10, x FOR PEER REVIEW 7 of 23 4. Compute the learned dictionary, Here i is loop iteration.
5. Get the updated dictionary.
Local Geometric Co-Occurrence Model Learning
The following steps are required to perform the local geometric co-occurrence model learning: 1. Consider the training set LR and HR face residue.
2. Get the local geometric feature representation for each patch.
Local Geometric Co-Occurrence Model Learning
The following steps are required to perform the local geometric co-occurrence model learning: 1.
Consider the training set LR and HR face residue.
2.
Get the local geometric feature representation for each patch.
3.
Connect the HR and the corresponding LR geometric feature vectors for jointly learning the HR and LR visual vocabularies.4.
Apply the affinity propagation clustering algorithm.
5.
All data points are considered simultaneously as candidate cluster centers.
6.
Messages are transmitted between the data points until an appropriate set of cluster centers and corresponding clusters emerge.7.
The number of clusters also depends on a prior specification of how preferable each data point is as a cluster center.8.
Consider all data points that have equal potential to be the cluster centers, so the preferences of all data points are set to the same value that can be controlled to produce different numbers of clusters.
In the testing phase, there were three steps to be followed.In the first step, we chose the LR image.Then, the initialization and the optimization process were performed.The LR image was given as input and it was initialized by interpolation.That image was compared to the global face image and processed to the M-step.Hence, the initialized image was compared to the local geometric co-occurrence model image, where that image was a process in the E-Step.Finally, the M-step and the E-step image was optimized.The geometrical feature that was defined in this section represented the high-frequency structures that are due to various intensity changes.
Demonstration of Execution Steps of the Proposed Method
Figure 4 demonstrates the execution steps for the proposed method.
Step 1: The modules are selected from the graphic user interface.In the training phase, there is global face model learning and local geometric co-occurrence model learning.Here, two modules can be selected.The first module is the training phase, and the second module is the testing phase.Figure 5 illustrates the GUI (Graphical User Interface) of Module Selection.
Step 2: Selection of training phase, the second page opens, which is the GUI of the Training Phase, which contains global face model learning and local geometric co-occurrence model learning.Figure 6 demonstrates the GUI of the training phase.
Step 3: Selection of the global face model learning.Two directories can be chosen as the high-resolution directory, and they create the dictionary.Figure 7 illustrates the GUI of the global face model learning phase.
Step 4: Choosing a directory for training the GUI for every image.Three poses are created so that it will be easy to compare the images with the testing phase.Figure 8 illustrates the GUI for directory selection.
Step 5: All images with different misalignment variations are selected to compose a dictionary.This output shows that the dictionaries are created for each directory using online dictionary learning.Figure 9 demonstrates the GUI of the HR face sparse representation dictionary.
Step 6: Steps in local geometric co-occurrence model learning.The first step chooses the LR images and extracts features from the LR patches, and the second step chooses the HR images and extracts the features of the HR patches.Figure 10 illustrates the GUI of global face model learning.
Step 7: The given global face input image is divided into LR (Low resolution) and HR (High Resolution) patches that include individual parts such as the eye and nose region.Figure 11 demonstrates the selection of the LR image.Figure 12 illustrates feature extraction from the LR image.Figure 13 demonstrates the selection of the HR image.Figure 14 illustrates feature extraction from the HR Image.Step 8: On extraction of the HR and LR features from the input image, visual words are created for both the LR and HR, separately.Figure 15 demonstrates the creation of visual words.
Step 9: Applying linear regression to the HR and LR visual words, the regression coefficients are determined.The regression coefficients are calculated by finding the mean value of the RGB (Red-Green-Blue) of the HR and LR image gradient features.Figure 16 demonstrates the application of linear regression on visual words.Testing Phase: Step 1: Choosing an LR Image. Figure 17 demonstrates choosing the LR image from the directory.
Step 2: The LR image should be applied for initialization by interpolation for resizing the LR image, which is easy to compute using the global face model.Figure 18 demonstrates initialization for interpolation.Figure 19 illustrates applying interpolation.After applying the initialization, the same LR image is split into patches.Figure 20 demonstrates initial image extraction.The LR image should extract the features and give the gradient of the features.Then, the feature is compared to the local geometric co-occurrence model of the training phase.
Step 3: Optimization.Testing Phase: Step 1: Choosing an LR Image. Figure 17 demonstrates choosing the LR image from the directory.
Step 2: The LR image should be applied for initialization by interpolation for resizing the LR image, which is easy to compute using the global face model.Figure 18 demonstrates initialization for interpolation.Figure 19 illustrates applying interpolation.After applying the initialization, the same LR image is split into patches.Figure 20 demonstrates initial image extraction.The LR image should extract the features and give the gradient of the features.Then, the feature is compared to the local geometric co-occurrence model of the training phase.
Step 3: Optimization.Testing Phase: Step 1: Choosing an LR Image. Figure 17 demonstrates choosing the LR image from the directory.
Step 2: The LR image should be applied for initialization by interpolation for resizing the LR image, which is easy to compute using the global face model.Figure 18 demonstrates initialization for interpolation.Figure 19 illustrates applying interpolation.After applying the initialization, the same LR image is split into patches.Figure 20 demonstrates initial image extraction.The LR image should extract the features and give the gradient of the features.Then, the feature is compared to the local geometric co-occurrence model of the training phase.
Step 3: Optimization.The input LR image is initialized, and then the E-step is applied.In this step, the LR image is given as the input and it is initialized by interpolation.The image is compared to the global face image, and then it is processed to the M-step.Hence, the initialized image is compared to the local geometric co-occurrence model image, and that image is processed to the E-Step.Finally, the M-step and the E-step image is optimized.Figure 21 demonstrates the optimized image of the input LR image.The technique works perfectly with an RGB image like the black and white image shown in Figure 22.The input LR image is initialized, and then the E-step is applied.In this step, the LR image is given as the input and it is initialized by interpolation.The image is compared to the global face image, and then it is processed to the M-step.Hence, the initialized image is compared to the local geometric co-occurrence model image, and that image is processed to the E-Step.Finally, the M-step and the E-step image is optimized.Figure 21 demonstrates the optimized image of the input LR image.The technique works perfectly with an RGB image like the black and white image shown in Figure 22.The input LR image is initialized, and then the E-step is applied.In this step, the LR image is given as the input and it is initialized by interpolation.The image is compared to the global face image, and then it is processed to the M-step.Hence, the initialized image is compared to the local geometric co-occurrence model image, and that image is processed to the E-Step.Finally, the M-step and the E-step image is optimized.Figure 21 demonstrates the optimized image of the input LR image.The technique works perfectly with an RGB image like the black and white image shown in Figure 22.The input LR image is initialized, and then the E-step is applied.In this step, the LR image is given as the input and it is initialized by interpolation.The image is compared to the global face image, and then it is processed to the M-step.Hence, the initialized image is compared to the local geometric co-occurrence model image, and that image is processed to the E-Step.Finally, the M-step and the E-step image is optimized.Figure 21 demonstrates the optimized image of the input LR image.The technique works perfectly with an RGB image like the black and white image shown in Figure 22.This method consists of training testing phases.The training phase consists of two parts.The first part is global face sparse representation learning in which an online dictionary is used to learn the face prototype dictionary.The second part is a local geometric co-occurrence before learning, where we jointly clustered the HR and LR image residue patches and learned the regression coefficients from the LR to HR visual vocabulary.
In the testing phase, when the LR face image is presented, an initial image was generated by simple interpolation.An iterative sparse representation model using the learned dictionary was proposed to generate an HR image.The representation coefficients were iteratively optimized using the EM algorithm, in which local residue compensated to the global face using linear interpolation.
The training phase consisted of two parts.The first part was the global face model learning, and the second was the local geometric co-occurrence model learning.In global face model learning, two directories choose the high-resolution directory and create the dictionary.The images are selected from the directory for training.In the database for every image, three poses were created so that it would be easy to compare the images with the testing phase.All images with different misalignment variations were selected to compose a dictionary.This output showed that dictionaries were created for each directory using online dictionary learning.In the local geometric co-occurrence model learning, the first step was to choose the LR images and extract the features from the LR patches.The second step involved choosing the HR images and extracting the features of the HR patches.
The given global face input image was split into LR (low-resolution) patches that included unique parts such as the eye and nose region.It showed the features of the LR image and that the images should extract the gradient features.The given global face input image was split into HR (high-resolution) patches that included unique parts such as the eye and nose region.It showed the features of the HR image and that images should be extracted from the gradient features.The visual word was the collection of all local geometric features.The visual words were created for both HR and LR images separately.HR and corresponding LR geometric features were joined together for learning the HR and LR visual words.Regression coefficients were determined by applying linear regression to the HR and LR visual words.The regression coefficients were calculated by finding the mean value of the HR and LR image gradient features.In the testing phase, the global and local geometric features are involved.During the testing phase, three steps should be followed.The first step is choosing the LR image.Then the initialization and the optimization processes are performed.
The LR image should be applied for the initialization by interpolation, for resizing the LR image.It is used to compute the global face model.After applying the initialization, that same LR image is split into patches.The LR image should be extracted from the features, and it gives the gradient of the features.Then the feature is compared to the local geometric co-occurrence model of the training phase.The input LR image is initialized, and then the E-step is applied.In this step, the LR image is given as input, and that is initialized by interpolation.Then the image is compared to the global face image, after that the image is processed to the M-step.Hence, the initialized image is compared to the local geometric co-occurrence model image, where that image is processed to the E-Step.Finally, the M-step and the E-step image are optimized.The Kalman filter is used during the image optimization process.It is very effective in performing computational operations with linear filter modeling.It can produce an estimation of the current states of the system to remove the noise in the image.The main goal of utilizing the Kalman filter is to predict the position of a particular area of an image to be evaluated during the image optimization process.The expected position measures the prediction for the identifying area and it is identified using the variance and the confidence level.Building robust dictionaries is required to recover the high-resolution images and remove the dark regions of the images.
Performance Evaluation
The implementation requires an i3 processor with a 4GB RAM on MATLAB R2018b using the Windows 7 operating system.The proposed method was compared to related methods, e.g., SRGAN [28], TRNR [27], and LSR [26].Here, the time taken analysis is denoted by the training phase image value.Each individual has five different views (left, right, up, down, and frontal views) under the same light conditions.These face images were aligned manually using the locations of three points: centers of the left and right eyeballs and the center of the mouth.Some aligned face images were cropped to 32 × 24 pixels for low-resolution face images, and to 128 × 96 pixels for high resolution face images.Based on the same training sets, the proposed method was compared to related methods.Each input face image was generated into five different outputs of LR, synthesized LR face images, and HR face images according to the framework.Table 2 demonstrates the list of PSNR values of the hallucinated image with an input face image on the frontal view.The value of K is 100 and θ = 0.1.Table 3 demonstrates the list of PSNR values of the hallucinated image with an input face image on the up view.The value of K was 200 and θ = 0.2.Table 4 demonstrates the list of PSNR values of the hallucinated image with an input face image on the down view.The value of K was 200 and θ = 0.2.Table 5 demonstrates the list of PSNR values of the hallucinated image with an input face image on the left view.The value of K was 200 and θ = 0.2.Table 6 demonstrates the list of PSNR values of the hallucinated image with an input face image on the right view.The value of K was 200 and θ = 0.2.The threshold of similarity was used to find the similarity within a collection of objects.It contained several factors to determine scalability and minimize computational cost.In the testing phase, it generated the low-resolution input images to high-resolution images.The semantic class of the image was essential for solving within the inherent class to achieve the improved result.In-depth features can be implemented to increase the accuracy.In Figure 23, the accuracy is high because all images are performed by the training phase so that there is no error rate.The precision rate and recall rates are also equally high.Running time for evaluating the efficiency of the proposed methodology was compared to the related methodologies.The proposed method ran faster than the related methods because of its fast optimization techniques.Figure 24 demonstrates the running time.The experimental results showed the higher quality of reconstructed images of the proposed framework over the enhanced methods with interpolation.High-resolution face images of five different views were generated from a single low-resolution face image.According to the experimental results, the reconstructed image was more accurate if the view of the input image was the same as that of the output.Particularly, frontal, up, and down views achieved better estimations than others.The results of the proposed method showed superior reconstruction quality of the HR face image over other related methods in both visualization and PSNR values.The proposed AIHEM methodology was based on the EM algorithm, which is nondeterministic; thus, the performance evaluation was performed multiple times using standard deviation values.The standard deviation value was measured to obtain the PSNR value for the proposed method, as compared to the related methods.The performance results may vary in several iterations of continued evaluation, and the results are shown in Figures 25 and 26.The results showed a standard deviation of 10 and a standard deviation of 100, respectively.The proposed AIHEM methodology was based on the EM algorithm, which is non-deterministic; thus, the performance evaluation was performed multiple times using standard deviation values.The standard deviation value was measured to obtain the PSNR value for the proposed method, as compared to the related methods.The performance results may vary in several iterations of continued evaluation, and the results are shown in Figures 25 and 26.The results showed a standard deviation of 10 and a standard deviation of 100, respectively.
The proposed method was a very effective technique and required fewer computational resources, so the processing was easy to produce the solutions for the optimization problems.It is useful to recognize and tune the data with predictable output.The performance improved compared to the related methods, and it was straightforward to train the dataset.The measurement of accuracy is an integral part of image classification when validating the proposed work.The vectors were used to extract the features to achieve the highest amount of accuracy.The iteration model was used to classify the image based on the similarity parameter from a pixel by pixel.The proposed AIHEM methodology was based on the EM algorithm, which is nondeterministic; thus, the performance evaluation was performed multiple times using standard deviation values.The standard deviation value was measured to obtain the PSNR value for the proposed method, as compared to the related methods.The performance results may vary in several iterations of continued evaluation, and the results are shown in Figures 25 and 26.The results showed a standard deviation of 10 and a standard deviation of 100, respectively.The proposed method was a very effective technique and required fewer computational resources, so the processing was easy to produce the solutions for the optimization problems.It is useful to recognize and tune the data with predictable output.The performance improved compared to the related methods, and it was straightforward to train the dataset.The measurement of accuracy is an integral part of image classification when validating the proposed work.The vectors were used to extract the features to achieve the highest amount of accuracy.The iteration model was used to classify the image based on the similarity parameter from a pixel by pixel.
The computational complexity of the proposed system was analyzed using the big oh notation O(n K M), for the face hallucination methodology.The pre-processing and alignment methods were crucial to reducing computational complexity.The performance was analyzed using a thresholdbased similarity that was 35 times faster than the other methods.The running time for the image in the testing phase was 13.5 s while using the proposed mechanism.The proposed method had a considerable development that attained a steady performance at a size of 20 20 pixel frame.
Whenever the size increases, the running time will also increase.To minimize the computational complexity of the proposed algorithm, we maintained the size of the pixel frame as 20 20 pixels for performance evaluation.
Conclusions
This paper proposed a new iterative face hallucination using the expectation-maximization based iterative super-resolution algorithm.The M-step is a global face sparse representation model for adaptively selecting proper basis vectors of misalignment variation to input an LR image.The Estep uses an alignment-robust local geometric co-occurrence before compensating for the error generated by the sparse global representation in the first step.The global and local methods are combined iteratively.This iterative method not only takes advantage of both global and local approaches, but it also combines two different strategies to handle the same misalignment problem.Experimental results showed that the proposed method outperformed face super-resolution methods in terms of visual quality.Using the existing system (i.e., sparse representation), the accuracy of the HR image was 80%, but using the proposed method (global face sparse representation), the accuracy of the HR image was 85-90%.In the future, we will study various methods [32][33][34][35][36][37][38][39][40][41][42][43] and enhance the algorithm on posed face images.
Figure 4 .
Figure 4. Execution steps of the proposed method.Figure 4. Execution steps of the proposed method.
Figure 4 .
Figure 4. Execution steps of the proposed method.Figure 4. Execution steps of the proposed method.
Figure 4 .
Figure 4. Execution steps of the proposed method.
Figure 5 .
Figure 5. GUI of Module Selection.Figure 5. GUI of Module Selection.
Figure 7 .
Figure 7. GUI of global model learning.
Figure 7 .
Figure 7. GUI of global model learning.
Figure 7 .
Figure 7. GUI of global model learning.
Figure 7 .
Figure 7. GUI of global model learning.
Figure 8 .
Figure 8. GUI of directory selection.Figure 8. GUI of directory selection.
Figure 10 .
Figure 10.GUI of global face model learning.
Figure 9 .
Figure 9. GUI of the high-resolution (HR) face sparse representation dictionary.
Figure 9 .
Figure 9. GUI of the high-resolution (HR) face sparse representation dictionary.
Figure 10 .
Figure 10.GUI of global face model learning.
Figure 10 .
Figure 10.GUI of global face model learning.
Figure 10 .
Figure 10.GUI of global face model learning.
Figure 11 .
Figure 11.Selection of the low-resolution (LR) image.Figure 11.Selection of the low-resolution (LR) image.
Figure 13 .
Figure 13.Selection of the HR image.
Figure 13 .
Figure 13.Selection of the HR image.Figure 13.Selection of the HR image.
Figure 13 .
Figure 13.Selection of the HR image.Figure 13.Selection of the HR image.
Figure 13 .
Figure 13.Selection of the HR image.
Figure 14 .
Figure 14.Feature extraction from the (HR) image.Figure 14.Feature extraction from the (HR) image.
Figure 16 .
Figure 16.Linear regression on visual words.
Figure 16 .
Figure 16.Linear regression on visual words.
Figure 16 .
Figure 16.Linear regression on visual words.
23 Figure 17 .
Figure 17.Choosing an LR image from the directory.
Figure 17 . 23 Figure 17 .
Figure 17.Choosing an LR image from the directory.
Figure 21 .
Figure 21.Optimized image of the input LR image.
Figure 21 .
Figure 21.Optimized image of the input LR image.
Figure 21 . 23 Figure 20 .
Figure 21.Optimized image of the input LR image.
Figure 21 .
Figure 21.Optimized image of the input LR image.
Figure 23 .
Figure 23.Comparison of Existing and Proposed Method.
Figure 23 .
Figure 23.Comparison of Existing and Proposed Method.
Figure 25 .
Figure 25.PSNR values for a standard deviation of 10.
Figure 25 .
Figure 25.PSNR values for a standard deviation of 10.Figure 25.PSNR values for a standard deviation of 10.
Figure 25 .
Figure 25.PSNR values for a standard deviation of 10.Figure 25.PSNR values for a standard deviation of 10.
Figure 26 .
Figure 26.PSNR values for a standard deviation of 100.
Table 3 .
List of PSNR values of the hallucinated image-up view, K = 200, and θ = 0.2.
Table 4 .
List of PSNR values of the hallucinated image-down view, K = 200, and θ = 0.2.
Table 6 .
List of PSNR values of the hallucinated image-right view, K = 200, and = 0.2. | 9,867.2 | 2020-01-20T00:00:00.000 | [
"Computer Science"
] |
The Application of Various Bark Species as a Fillers for UF Resin in Plywood Manufacturing
The aim of the presented study was to apply various bark species (birch, beech, maple, pine and spruce) as fillers for urea-formaldehyde (UF) resin in three-layer plywood manufacturing. For this purpose, all types of bark were ground and added to the adhesive mixture. The resultant plywood was subjected to investigations of the following: tensile strength, modulus of elasticity (MOE), bending strength (MOR) and formaldehyde emission. The results indicate a reduction in the tensile strength. Moreover, the lack of significant improvement in strength parameters can be explained by too high a load of the filler (20 wt%). In the case of formaldehyde emissions, a reduction was observed for birch (B-1), beech (B-2), maple (B-3) and pine bark (B-4). In addition, an increase in the emission of formaldehyde was recorded only for spruce bark.
Introduction
The adhesive mixtures used for the production of plywood usually contain some additives called fillers [1]. Their role is usually to adjust the rheological properties of the resin in order to reduce the cost of the raw material and improve the properties of the resultant panels, for example, by causing a reduction in formaldehyde emission [2][3][4].
Current trends focus on the use of most industry by-products. Following this tendency, it is worth emphasizing that the wood industry generates huge amounts of by-products, such as bark, sawdust and dust [5]. Annual global bark production is estimated to be 359,111,200 m 3 [6], which makes it an excellent raw material that can be used in several ways. Generally, bark is used in horticulture as a mulch [7] or is considered a natural source of chemicals [8].
Due to the chemical composition of bark and the presence of numerous organic compounds, such as tannins, catechins, galocatechins, falwonoids, proanthocyaninidins, it can be used as a potential formaldehyde-scavenging filler in the production of plywood. The chemical compounds of bark, such as lignin or tannins, seem to be able to react with formaldehyde. This phenomenon may reduce the toxic effects of formaldehyde on humans by reducing hazardous emissions occurring in the indoor environments [9][10][11][12].
Formaldehyde is the simplest aldehyde, and it is widely used in the synthesis of the resins. Unfortunately, it is a harmful compound with a known carcinogenic effect. Studies on the reduction in formaldehyde emissions through the use of various types of fillers are continuously being conducted globally [1,[13][14][15][16][17][18][19].
Therefore, it is worth looking at bark as a natural filler with a formaldehyde bonding ability. The use of bark can therefore contribute to a reduction in formaldehyde emissions from wood-based materials such as plywood. Currently, a lot of scientific research is focusing on the possibility of producing environmentally friendly materials. There are already existing scientific references from the literature regarding the use of larch bark to reduce formaldehyde emissions from decorative boards [20]. Moreover, Medved et al. [21] conducted studies showing that the bark of spruce and pine can be used as a substitute for wooden particles in the production of particleboard. Research on the use of the bark was also conducted by Sahin and Arslan [22], Réh et al. [23], Ružiak et al. [24]. The results of these studies also indicate that the bark species could have a significant impact on the effectiveness of reducing formaldehyde emissions.
There are many issues associated with the production of plywood that are constantly being researched. Formaldehyde emissions are a very important aspect; however, mechanical properties should also be considered as crucial for potential applications. Aydin et al. [25] reported that an amount of bark higher than 12.25% has a negative influence on formaldehyde release, thickness swelling, and mechanical strength, whereas research conducted by Mirski et al. [14] showed that the addition of oak bark at a concentration of 15% made it possible to produce plywood panels characterized by reduced formaldehyde release and improved bonding quality, which is the main goal when establishing the potential industrial application. Another important aspect is the influence of the particle size on the parameters of the produced plywood. Different sizes of particles were previously tested, and it was found that the dimensional fraction of 0.315 mm showed the best result [26]. Furthermore, the increase in bending strength and Young's modules of elasticity was observed when 15% of beech bark was added to a urea-formaldehyde adhesive [24].
The aim of the study was to use the selected, various bark species commonly processed in Polish sawmills that were not studied before as fillers for UF resin in plywood manufacturing.
Materials
Plywood was produced using rotary cut birch veneer sheets with dimensions of 320 × 320 mm, moisture content of 6% ± 1%, and average thickness of 1.5 mm. An industrial UF resin with the following characteristics was used: pH 9.5 to 10.7, solids content of 64 to 69%, and gel time at 100 • C of 63 s. Ammonium nitrate (20 wt%) was introduced to the adhesive mixture as a hardener. The rye flour and bark powders differing in species were used as a fillers. For this purpose, birch (Betula L.), beech (Fagus L.), maple (Acer L.) pine (Pinus L.) and spruce (Picea A. Dietr.) bark particles were ground to obtain a fraction of 0.315-0.4 mm. Moisture content of added bark was~9.0 %. The compositions and pH of adhesive mixtures are presented in Table 1.
Methods
The plywood panels were manufactured in the three-layer system. The adhesives mixtures were spread on the surface of veneer sheets in the amount of 170 g/m 2 . The pressing parameters, such as temperature, unit pressure and time were 120 • C, 1.4 MPa and 4 min, respectively. The moisture content of manufactured plywood was determined according to EN 322 [27]. The thickness, density and moisture content of produced plywood are given in Table 2.
The manufactured plywood were subjected to an evaluation in terms of mechanical properties, including bonding quality according to EN 314-1 (2004) [28] after soaking (10 repetitions) and modulus of elasticity (MOE) and bending strength (MOR) in a per-pendicular and parallel direction to the grains of the face veneer layer (12 repetitions), according to EN 310 [29]. The results were subjected to a statistical analysis using HSD Tukey test on the significance level of α = 0.05 with Statistica 13.0 software (StatSoft Inc., Tulsa, OK, USA). Moreover, formaldehyde emissions were also determined. For this purpose, plywood samples were tested using a flask method in accordance with PN EN 717-3 [30] (2 repetitions).
SEM pictures were taken with a Hitachi SU 3500 Electron Microscope (Hitachi, Japan) under high-vacuum conditions. The plywood samples were covered with gold. Au sputtering was performed with a Cressington Sputter Coater 108 auto sputtering machine (Ted Pella, Redding, CA, USA).
Tensile Strength
The changes in tensile strength depending on the resin formulation are presented in Figure 1. As can be seen, all variants (control and plywood with bark particles) fulfilled the standard requirements for tensile strength (values exceeded 1 N/mm 2 ). Moreover, a statistical analysis was carried out and homogeneous groups were distinguished. They are marked with letters above the bars. The highest values were obtained for both the control variant and maple-bark-containing one. Between them, no statistically significant differences were observed. This means that the addition of maple bark to the UF resin gave comparable results with the control variant. The lowest tensile strength value was shown by variant B-5; however, there are no statistical differences between this variant and variants B-1, B-2 and B-4. Similar results, where a reduction in tensile strength was observed due to the addition of the bark, were presented by Aydin et al. [25]. This phenomenon can be explained by the pH of the environment and its effect on the adhesive curing process. Elbadawi et al. [31] reported that the curing rates of formaldehyde-based resins are strongly dependent on the pH of the curing environment. According to Xing et al. [32], when the pH rises above 7 the reactivity of adhesive considerably slows down and it affects bonding strength. On the other hand, if the pH is too low then a pre-curing process may occur. They also observed that as the content of tannins increased (which are included in bark composition), the mechanical properties of the pro- This phenomenon can be explained by the pH of the environment and its effect on the adhesive curing process. Elbadawi et al. [31] reported that the curing rates of formaldehyde-based resins are strongly dependent on the pH of the curing environment. According to Xing et al. [32], when the pH rises above 7 the reactivity of adhesive considerably slows down and it affects bonding strength. On the other hand, if the pH is too low then a pre-curing process may occur. They also observed that as the content of tannins increased (which are included in bark composition), the mechanical properties of the produced panels decreased. Furthermore, the similar results were also observed by Nemli et al. [33]. The phenomenon of lowering tensile strength can be explained by the presence of tannins, which affect the resin curing process. If there is a too major a decrease in the pH, it can lead to the pre-curing of the adhesives before pressing, and thus it can cause a deterioration in the properties of boards [25,31].
Modulus of Elasticity (MOE) and Bending Strength (MOR)
The MOR and MOE parameters were tested in two directions (longitudinal and perpendicular) (Figures 2 and 3). In the case of the perpendicular direction, the statistically significant differences were observed between the individual variants ( The lack of significant improvement in strength parameters-and in the case of the B-5 variant, their significant reduction-can be explained by too high a proportion of the filler used. According to the literature, an addition of more than 15% significantly increases the viscosity of the resin [23,24,34]. Réh et al. [35] also observed that the addition of 20% (based on the dry weight of the resin) of bark particles increases the viscosity of [38] reported that lignin is able to react with formaldehyde in an acidic medium. Moreover, tannins are characterized by their phenolic nature, and condensed polyflavonoid tannins are able to react with HCHO [39,40]. Only in the case of spruce bark (B-5), an increase in the emission of formaldehyde was recorded. This can be explained by the weakening of the bonding quality, which was confirmed by the results for the mechanical properties. According to Hogger et al. [41], the hindrance in polymer network formation and a deterioration in bonding quality can result in an increase in formaldehyde emission from UF resin-bonded plywood. The lack of significant improvement in strength parameters-and in the case of the B-5 variant, their significant reduction-can be explained by too high a proportion of the filler used. According to the literature, an addition of more than 15% significantly increases the viscosity of the resin [23,24,34]. Réh et al. [35] also observed that the addition of 20% (based on the dry weight of the resin) of bark particles increases the viscosity of the resin. This can result in an uneven application of glue.
Formaldehyde Emission
Another important aspect is the presence of tannins and lignin in the bark, which influences the properties of the resin. Various explanations can be found in the literature, which still remain inconclusive. On the one hand, a high proportion of these compounds can lead to an improvement in mechanical properties [35]. On the other hand, in some cases, a high proportion of these compounds affects their reactivity, which leads to a rapid increase in viscosity, which in turn translates into a short resin pot life and affects intermolecular cross-linking [36,37]. The observations of Nemli et al. [33] confirm that, in this case, the MOE results can be lowered. Figure 3 presents the results of MOE and MOR in the longitudinal direction. It was observed that MOR parameters for the variants REF, B-1, B-2 and B-3 were at a similar level, and there were no statistically significant differences. Only in the case of B-4 and B-5 variants was there a slight decrease, which may have been observed due to the decreased veneer quality. In the case of MOE, the differences were noticeable, and statistically significant differences were observed. As in the case of the MOR, the MOE was the lowest for the B-4 variant. [38] reported that lignin is able to react with formaldehyde in an acidic medium. Moreover, tannins are characterized by their phenolic nature, and condensed polyflavonoid tannins are able to react with HCHO [39,40]. Only in the case of spruce bark (B-5), an increase in the emission of formaldehyde was recorded. This can be explained by the weakening of the bonding quality, which was confirmed by the results for the mechanical properties. According to Hogger et al. [41], the hindrance in polymer network formation and a deterioration in bonding quality can result in an increase in formaldehyde emission from UF resin-bonded plywood.
SEM Analysis
The cross-sections of plywood characterized with SEM at different magnifications of ×100 and ×1000 are presented at Figure 5. Compared with REF resin plywood (Figure 5a,d), the glue line of B-1 and B-5 adhesive plywood was characterized by larger free spaces (Figure 5b,c,e,f). This could be caused by the fact that bark fillers contained adhesive B-1, and B-5 was characterized by larger particle size. However, these changes affected the mechanical parameters (MOR and MOE in perpendicular direction) and formaldehyde emissions only in the case of the B-5 sample when compared to the REF sample.
SEM Analysis
The cross-sections of plywood characterized with SEM at different magnifications of ×100 and ×1000 are presented at Figure 5. Compared with REF resin plywood (Figure 5a,d), the glue line of B-1 and B-5 adhesive plywood was characterized by larger free spaces (Figure 5b,c,e,f). This could be caused by the fact that bark fillers contained adhesive B-1, and B-5 was characterized by larger particle size. However, these changes affected the mechanical parameters (MOR and MOE in perpendicular direction) and formaldehyde emissions only in the case of the B-5 sample when compared to the REF sample.
SEM Analysis
The cross-sections of plywood characterized with SEM at different magnifications of ×100 and ×1000 are presented at Figure 5. Compared with REF resin plywood (Figure 5a,d), the glue line of B-1 and B-5 adhesive plywood was characterized by larger free spaces (Figure 5b,c,e,f). This could be caused by the fact that bark fillers contained adhesive B-1, and B-5 was characterized by larger particle size. However, these changes affected the mechanical parameters (MOR and MOE in perpendicular direction) and formaldehyde emissions only in the case of the B-5 sample when compared to the REF sample.
Conclusions
In the case of maple bark, there were no statistically significant differences compared to the reference sample. In other cases, the reduction in the tensile strength was observed after the addition of the bark when compared to the reference variant. The phenomenon of lowering tensile strength can be explained by the chemical composition of bark, which could affect the resin curing process. Moreover, when the pH is considerably lowered, the pre-curing process could occur and consequently affect the bond lines strength.
The lack of significant improvement in strength parameters (MOR, MOE) can likely be explained by too high a proportion of filler (20 wt%).
The results of the experiment clearly indicate that the replacement rye flour with birch (B-1), beech (B-2), maple (B-3) and pine (B-4) bark led to a decrease in formaldehyde emissions. The observed reduction in emissions can be explained by the high lignin and tannins content. Only in the case of spruce bark (B-5), an increase in the emissions of formaldehyde was recorded. These results can be explained by the noted deterioration in the bonding quality, which is in agreement with the results of mechanical properties.
The most important conclusion is that the use of 20% (wt) bark powder is too much, and a lower load of filler should be used in the future studies. | 3,722.6 | 2022-10-01T00:00:00.000 | [
"Materials Science"
] |
Broken wholeness: A critical analysis of Henri JM Nouwen’s spirituality of vulnerability and its possible value for the current discourse on health and wholeness.
This essay investigates whether the counter-cultural spiritual formation theology of Henri Nouwen could make a significant contribution to the current discourse on an inclusive, gender-equitable, spirituality-based approach to holistic health. Three main relationships feature in the majority of Nouwen’s works: the relationship to self, the relationship to others and the relationship to God. This foundational framework of Nouwen is used to structure this inquiry into the possible enduring value of certain core concepts that Nouwen developed within his triad of ‘movements’ toward wholeness. In his thinking about the movement of Reaching Out to our Fellow Human Beings, the concept of Vulnerability emerges as a key component of his theology and it will be the focus of this article. In a second article the value of Nouwen’s seminal thinking on Embodiment (the movement of Reaching Out to our Innermost Self) and in a third his lifelong engagement with Mystery (the movement of Reaching Out to our God) will also be brought into discussion with current thinking.
the Dutch Henri Nouwen Stichting in Rotterdam, admits that he had not fully comprehended the extent and significance of his brother's work and artistry until after his death. Since then he has come to see him as a very special kind of artist, almost like Vincent van Gogh, whose true talent was only discovered after his death.
Henri was a little like Vincent van Gogh in the way that he taught us to look differently. After Van Gogh we looked at the world differently. Henri is also a person who gave us a different view. We can look with his eyes as well. He provides us with an alternative way of looking at reality. We can describe Henri as a theological artist. And sometimes an artist is ahead of his time. I am most interested in why he is still read so widely. Therefore I am more interested in the reader than in the author. What is the reader looking for today? Why is there such a positive response to his simple writings? 1 Part of the reason for Nouwen's continuing popularity today might be that, as a true artist, he discerned in his time certain core ideas that would inform the theological discourse for the foreseeable future. This article hopes to investigate the current relevance of one of the rich spiritual veins that Henri Nouwen tapped into that is increasingly emerging as part of a new way of thinking about health and wholeness. Henri Nouwen's sensitive and honest theological and existential journey into 'vulnerability' could possibly add value and deepen the level of the current discourse on what wholeness (and holiness) comprises.
In the current discourse on global health care there seems to be a strong movement towards recognizing and including the essential role of religion and spirituality. In an important contribution Christoph Benn, on behalf of the Global Fund to Fight Aids, TB and Malaria, speaks about 'The Continued Paradigm Shift in Global Health and the Role of the Faith Community' (Benn 2011:10). In an equally significant contribution, Gillian Paterson, Research Fellow at Heythrop College, University of London, presents us with a persuasive argument for this inclusion in "Discovering Fire: Changes in International Thinking on Health Care -The Challenges for Religion" (Paterson 2011:16). A number of researchers in the fields of theology, psychology, medicine and whole-person caring present convincing arguments concerning the vital importance of integrated bodymind-spirit healing in a whole-systems approach. 2 From an African perspective James Cochrane, one of the three co-principals of the African Religious Health Assets Program, is very positive about the shift in theory formation that is slowly taking place away from "utilitarian, or market-based, or rational choice theories of the human good, all of which are anthropologically superficial and relevant only within strict limits". He discerns a movement towards a slowly developing new kind of intellectual paradigm and formulates his position as follows: …signs of a paradigm shift are now everywhere, partly impelled by the failures of current models, and partly by the collapse of the radical secularization thesis that dominated most of the scientific community, across disciplines, through the latter half of the 20 th century. In the new paradigm that is emerging, we will recognize that every aspect of applied health sciences has a dynamic link to religious health worlds and religious assets, and that every aspect of religious phenomena has a health relevance and health implication (Cochrane, Schmid & Cutts 2006:72).
Cochrane pointedly gives the following illustration of the typical African way of thinking about health and religion: "In Sesotho for example, as in isiXhosa, Bemba and other related African languages, there are no direct equivalents for either 'religion' or 'health', at least not if they are understood separately from each other. The only appropriate Sesotho word is bophelo (imphilo in isiXhosa, ubumi in Bemba). This word combines both our sense of what religion is and what health is, and also extends to include not just the individual body, but also the social body from which the individual's health is inseparable" (Cochrane, Schmid & Cutts 2006: 68,69).
It is clear that this wider frame of reference and more inclusive point of departure for thinking about health matters offers new momentum for broadening the understanding of the concept of what holistic health comprises, and ways in which healing can be nurtured, promoted and maintained. "Healing" takes on a whole new meaning if the very definition of what health entails is changing. The inclusion of the religious dimension as an important factor in thinking about health enriches the whole area of health research and praxis in profound ways. Among other things, it means that certain aspects of religion and spirituality need to be carefully explored and weighed to determine in which ways they could possibly add value to the current discourse on health and wholeness.
The innovative, counter-cultural spiritual formation theory of Henri J.M. Nouwen could present such fertile ground from which fresh perspectives and new dimensions of praxis might arise in fields such as health, theology, development, gender, and integral well-being. The gradual worldwide philosophical "paradigm shift" away from an exclusively modernist scientific approach asks for a different kind of spiritual and theological approach to issues of private and public health. Without discounting the important contributions gained from the modernist world of "scientific" calculations and measurements, and without uncritically adopting "postmodernism" as philosophical frame of reference 3 , one could argue that the more "non-dualistic" approach of someone like Henri Nouwen provides an important alternative theological approach to life, health and well-being.
A brief survey of recent literature and current opinions about Henri Nouwen's life and writings reveals that his legacy is still widely judged to be extraordinarily relevant for the current theological discourse. Richard Rohr, in his foreword to Wil Hernandez's third book in a trilogy on the legacy of Henri Nouwen, affirms that Nouwen's life, spirituality and theology have enduring relevance for us today as "an excellent seer, inviting us into the same seeing" (Hernandez 2012: Kindle location 106).
He concurs with Hernandez's framing of Nouwen's thought in terms of his natural ability to be a nondualistic thinker, and his ability to hold wouldbe tensions in a very creative balance At the end of his third book on Nouwen, Hernandez summarises the value of Nouwen's way of thinking in the movement towards wholeness and integration as follows: "Henri Nouwen saw things differently and operated out of a different framework of thinking because he personified the non-dualistic consciousness characteristic of the contemplative mystics" (Hernandez 2012: Kindle Location 2006. In the opinion of Michael Higgins and Kevin Burns, who in 2012 constructed a radio series and published a book on the life and legacy of Nouwen under the title Genius Born of Anguish, the fact that Nouwen represented "the quintessential post-modern quester" accounts for much of his continuing relevance today (Higgens & Burns 2012: Kindle location 117). Michael Ford, another researcher into the life and enduring legacy of Henri Nouwen, also describes the surprising continuing global impact of this Wounded Prophet: "In the time since Nouwen's death, there has been an upsurge of interest in his books, which are selling around the world in greater numbers than ever before. The Henri Nouwen Literary Centre, set up in his memory at Daybreak, deals daily with inquiries from people in many different countries and is clearly witnessing the fruits of his lifelong endeavours. Henri Nouwen Societies have been formed in North America and Holland, while retreats and conferences are doing much to evaluate his work and legacy" (Ford 1999: 208). In a recent reconstruction and publication of Henri Nouwen's unpublished class notes and other writings on spiritual formation, we are presented with a fresh and creative approach to formation for whole-person health. The lasting value of Nouwen's approach is described as follows: "The fruit of Nouwen's creative and integrative work in the field of pastoral psychology is a new, transformative, non-systematic approach to spiritual formation". Some interpreters have called Nouwen's approach a "spirituality of imperfection" (Nouwen, Christensen & Laird 2010: Kindle Location 2147).
In the previously mentioned personal interview with Laurent Nouwen, the younger brother of Henri Nouwen, he responded to this researcher's question about the contemporary relevance and popularity of his brother Henri Nouwen's work in the following way: I am quite amazed by it. I cannot really say about the rest of the world, but I have a good picture of sales of his books in Holland and Germany, because I represent the estate. What I see is that book sales are still today more or less on an equal level. Even last Sunday there was a Protestant TV show about Henri, 18 years after his death. They repeat it every year. I was also interviewed on the program by Bobby Schuller. There is still this amazing interest across all denominations. I am very amazed. So it must touch a deeper cry. 4 Obviously Henri Nouwen still speaks the language of many people looking for integral wholeness, not just in America or Europe, but worldwide. This article hopes to make a contribution to his lasting legacy by responding to the challenge of theologically analysing one of the crucial aspects in the current discourse on holistic health, viz. the role of spirituality and, specifically, vulnerability. As the most widely read author in the field of Christian spirituality at the time of his death in 1996 (Beumer 1997:13) and still one of the most influential voices in the field of spirituality and theology in recent times 5 Henri JM Nouwen embodied a spirituality of compassionate vulnerability that touched and healed the lives of millions worldwide.
Therefore, thorough analysis and critical evaluation of core aspects of Henri Nouwen's thinking about healing and wholeness seems indicated. However, if this is merely to be attempted from a modernistic epistemological framework of so-called "objective science" we would do the legacy of Henri Nouwen grave injustice. His approach to spirituality and spiritual formation does not involve minute distinctions and the construction of rigid schemes. Henri Nouwen's caustic observation in this regard was: Many great saints have described their religious experiences, and many lesser saints have systematized them into different phases, levels or stages. These distinctions can be helpful for those who write books and for those who use them to instruct, but it is of great importance that we leave the world of measurements behind when we speak about the life of the spirit (Nouwen 1987: 18).
Nouwen chooses not to speak about steps or stages on the way to perfection. He prefers using the dynamic metaphor of movements towards full, mature humanity. In their recent reconstruction of the class notes of Nouwen's formerly unpublished course on spiritual formation when he was a professor at Yale, two of his former students recorded Nouwen's own words on this matter: Spiritual formation, I have come to believe, is not about steps or stages on the way to perfection. It's about the movements from the mind to the heart through prayer in its many forms that reunites us with God, each other, and our truest selves (Nouwen, Christenson & Laird 2013: Kindle Location 139). 6 The academic surmise upon which this investigation is undertaken is that the spiritual "movements" towards wholeness that Henri Nouwen identified might hold promise for the current discourse on growth, healing and holistic health. The structure of this paper is an attempt to honour Nouwen's way of doing theology. From amongst the various movements colourfully described by Nouwen in a number of his books, this study identifies three as representative of his spiritual formation theory and which may be significant for today's circumstances. 7 They have been synthesized from various sources and renamed for the current context in a style that Henri Nouwen might possibly have employed today. In broad terms the study is constructed to reflect a pattern that Nouwen makes use of in many 6 Nouwen returns to this image of a movement "from the head to the heart" in many of his books. Referring to the mystic Theophan the Recluse, he sees prayer as "standing in the presence of God with the mind in the heart -that is, in the point of our being where there are no divisions or distinctions and where we are totally one within ourselves, with God, and with others and the whole of creation" (Nouwen, Christiansen & Laird 2013: Kindle Location 149). 7 Jurjen Beumer, a close Dutch friend of Henri Nouwen, also sees the three movements described by Nouwen in Reaching Out (Open Uw Hart) as representative of the core of his theology: " Er komen in dit boek een aantal lijnen van zijn denken, voelen en ervaren bij elkaar", in Onrustig zoeken naar God: de spiritualiteit van Henri Nouwen, (Beumer 1997:40).
of his books, in describing the "outward" movement to find God in others, the "inward" movement to find God our deepest being, and the journey "upward" or "beyond" to find God in all things. This article investigates the implications of the first of these: the outward movement toward vulnerability. Embodiment and mysticism, representing the "inward" and "upward" movements will be considered in further articles.
2. The way of vulnerability: From hostility to hospitality. The "way of vulnerability" that Nouwen embodied and opened up for many through his writings seems to gain in significance with the passing years after his death. Nouwen's name came to be associated with the phrase "The Wounded Healer" ever since the publication of his foundational book with that title in 1979. Nouwen's life story, literary legacy and theological contribution is very aptly summed up in this phrase. In his inimitable way Nouwen popularised "The Wounded Healer" as a metaphor for ministers who are called not only to care for other people's wounds but to make their own wounds into an important source of healing. He explains the deeper meaning of this phrase as follows:
Nouwen's theology of weakness
Making one's own wounds a source of healing, therefore, does not call for a sharing of superficial personal pains but for a constant willingness to see one's own pain as rising from the depth of the human condition which all men (sic) share (Nouwen 1979: 88).
Only by facing and embracing our woundedness and weakness and moving away from the illusion of being able to control life through gaining more and more power can we discover the healing potential of the way of vulnerability. According to Nouwen, a "Theology of Weakness" is necessary to counter the lust for power that has entrapped and corrupted the human spirit in the western world. The response of God to this "diabolic power" was to choose powerlessness. God chose to enter human history in complete weakness, as a vulnerable, dependent human baby. In Jesus of Nazareth the powerless God appeared among us to unmask our illusion of power. The movement from abusive power to power through powerlessness is what we are called to. A theology of weakness is a theology of divine empowering, not a theology for weaklings. It is movement from the illusion of being in control to complete surrender to the power of God. The all-pervading conviction in western society is that power is a good thing. But more power, in the form of money, connections, fame, intellectual ability, skills, is only a way to get some sense of security and control and strengthen the illusion that life is ours to dispose of.
Nouwen develops the Judeo-Christian concept of hospitality 8 as a healing ministry, because it takes away the illusion that wholeness can simply be given by one person to another. The pain and loneliness is not taken away, but when the host feels at home in his or her own house they can "create a free and fearless space" for others where they can recognize their pain on a level where it can be shared. Shared pain is no longer paralyzing but mobilizing. A true healing ministry helps to clear away the false supposition that there should be no fear or loneliness, no confusion or doubt. These sufferings can only be dealt with creatively when they are understood as wounds integral to our human condition. The wounds and pains are not necessarily cured or alleviated, but they become openings or occasions for a new vision.
In order to be a hospitable host, we need to embrace poverty. Nouwen advocates a "poverty of mind" and a "poverty of heart". In order for us to be able to really listen, to be open to discover the gift of the other, we need a spiritual attitude of growing willingness to recognize the incomprehensibility of the mystery of life. We need a docta ignorantia, a learned ignorance, an articulate not-knowing, so that we can mature in giving up our illusion of control in order to be controlled by God. Poverty of mind makes one able to receive the word from others and the Other with great attention.
The more mature we become, the more we will become able to give up our inclination to grasp, catch and comprehend the fullness of life and the more we will be ready to let life enter into us (Nouwen 1975: 96).
God is not only greater than our mind, he is also greater than our heart. So a "poverty of the heart" is also necessary for us to be a good host and make room for the stranger. Just as we have to avoid the temptation to adapt God to our small concepts we have to avoid adapting God to our small feelings.
An inflated heart can make us very intolerant. But when we are willing to detach ourselves from making our own limited experience the criterion for our approach to others, we may be able to see that life is greater than our life, history is greater than our history, experience greater than our experience, God greater than our God (Nouwen 1975:98).
Nouwen appeals to what he regards as the core of the Christian message: God's self-revelation in the kenosis of Jesus Christ (Phil 2:6-8). God does not reveal Godself as the powerful other, unapproachable in omniscience, omnipotence and omnipresence, but God is revealed in the incarnation. He came to us in the vulnerable way of Jesus Christ. Nouwen argues that God thereby also reveals to us the movement of our spiritual life. It is not a movement from weakness to power, but a movement in which we become less and less defensive and ever more open and vulnerable. Part of the mystique that still surrounds the legacy of Henri Nouwen is that he not only lucidly wrote about this "downward" movement throughout his career, but that his own life story dramatically illustrates the agony and ecstasy of embarking on this "Way of Vulnerability".
A brief exploration of the current discourse on vulnerability could reveal fertile links to the theology of Nouwen.
The fragile discourse on vulnerability
One of the major influences on Henri Nouwen's thinking and the course of his life story was Jean Vanier, founder of L'Arche, the international network of communities where "core members", people with intellectual and other disabilities, and "assistants", people without intellectual disabilities, share life together as fellow human beings. Vanier initially, and unexpectedly, invited Nouwen to spend some time with him, his mother and the L'Arche community at Trosly in France at a time when Nouwen needed to make major decisions and life changes. This eventually led to Nouwen's move from being a prestigious professor at universities like Yale and Harvard to spending the last ten years of his life as assistant and pastor to the disabled at the Daybreak L'Arche community in Toronto, Canada. Vanier and Nouwen became good friends and continued to be friends until Nouwen's death in 1996. Vanier delivered a moving eulogy at Henri Nouwen's funeral. Jean Vanier, along with the respected theologian Stanley Hauerwas, 9 represent leading voices in the current discourse on vulnerability, disability and the Christian tradition.
In the defining book that Vanier and Hauerwas co-authored in 2008, Living Gently in a Violent World: The Prophetic Witness of Weakness, both the authors take as their point of departure the fundamental gospel principle that the weakest and least presentable people are indispensable to the church (1 Cor 12:22). For the major paradigm shift that is implied in really taking this principle seriously, the L'Arche communities provide a much needed exemplar.
Henri Nouwen was attracted to the L'Arche ideal and was eventually convinced that this represented the type of "home" where he wanted to spend the last years of his life: not in the power-hungry, success-driven academic world where the bottom line is always achievement and competition, but in the gentle world of mutual trust and caring of L'Arche. Working as physical assistant and pastor for the Daybreak L'Arche community in Toronto, Canada, Nouwen introduced to his huge readership the L'Arche concept of the importance of the so-called handicapped and marginalized members of society.
The L'Arche communities with their ethos of "living with" rather than "doing for", provide a unique model of profound inclusive spirituality. Jean Vanier in his gentle but convincing way explains the mystery of God's choice for the people at the bottom of society, "to shame the clever and the powerful" (1 Cor 1:18-31).
The mystery of people with disabilities is that they long for authentic and loving relationships more than for power. They are not obsessed with being well-situated in a group that offers acclaim and promotion. They are crying for what matters most: love. And God hears their cry because in some way they respond to the cry of God, which is to give love (Hauerwas & Vanier 2008: 30).
Stanley Hauerwas, speaking on "The Politics of Gentleness", uses Vanier's example and embodiment of vulnerability and gentleness at L'Arche to develop a fiery critique of contemporary assumptions about wholeness, ethics and politics. 10 His main point of criticism is that liberal political theory per definition excludes people with mental disabilities. He refers to Hans Reinders to explain that liberal political theory is based on the assumption that individual persons are free to live their own lives as they prefer, provided that they allow other people equal freedom to do the same. "Persons", according to liberal democracy, are constituted by the powers of reason and free will. Only persons, in the sense of rational moral agents, can receive equal concern and respect, which causes a problem with respect to the inclusion of severely handicapped people. Approaching the area of disability along the way of vulnerability might help us to adopt a proper mode of humility when trying to unravel aspects of inscrutable mystery. We would do well to keep in mind that we are engaging with one aspect of the matter, which does not enable us to grasp the whole.
In the evolving academic field of theological disability studies 11 there is a growing consensus about the necessity of changing the conversation on "disability" and "normalcy" away from a binary "us-them" way of thinking, especially as couched in terms of "normal" versus "abnormal". Thomas Reynolds sees two major changes that need to happen in this discourse. The first is that we should shift away from seeing disability as a "tragic flaw". The social construct of "normality", which creates the difference between bodies that are "able" and those that are "disabled", should be challenged. The second is that there is a need to move away from representing disability merely as a problem to be included according to the good graces of a community.
If we grant that "normal" is a standard that is socially constructed, we are brought to recognise that it can also be critiqued and deconstructed. The basis for this, I believe, lies in something all human beings share, which undercuts the "us-them" binary: vulnerability (Reinders, in Claassens, Schwartz & Hansen (Eds) 2013: 20).
Another influential voice concerning vulnerability and dependence is that of the philosopher Alisdair MacIntyre. In his Dependent Rational Animals: Why Human Beings Need the Virtues, MacIntire makes a strong case for "the virtues of acknowledged dependence". (MacIntire 1999:119). His argument is that human beings must be understood first as animals, but then as a special sort of animal. He discusses in detail those aspects of our nature that are shared with other intelligent species such as dolphins, particularly the dependence and vulnerability that mark every period of our life. According to MacIntyre, disability should be taken seriously as a natural fact of life from which no one is exempt. There is a scale of disability on which we all find ourselves in different periods of our life. In order to "flourish" and to protect themselves from many dangers, dolphins need each other. In order for human beings to "flourish" like dolphins, but then as independent, reasoning animals, we need certain "virtues" which we cannot acquire without the sustained help of others on whom we depend, especially, but not exclusively, our parents. We will need not only the virtues that help us grow toward independence (such as risk-taking, patience, courage and temperateness), but also the virtues of "acknowledged dependence" (such as gratitude, courtesy, and forbearance). MacIntyre asserts that human life is a life of reciprocal indebtedness. Political community exists not only to adjust competing interests or to provide goods and services (as in liberal democracy theory). It exists to make possible the kind of community in which joint deliberation about life can take place within the framework of reciprocal indebtedness and just generosity.
Thomas Reynolds, in his overview of the current discourse on disability and vulnerability, quotes Jean Vanier, Stanley Hauerwas, Michel Foucault, Jurgen Moltmann and Nancy Eiesland in support of his conviction that in the end there is no hard and fast line between ability and disability and that every life has its limitations, vulnerabilities and weaknesses.
Thus I contend that disability is both anthropologically and redemptively fundamental. It signifies vulnerability as a condition of the gift of sharing life with one another. Yet there is a need for healing, not because disability signifies "bodies gone wrong", but because it entails real suffering, sometimes bodily, and in many cases communal in the form of alienation, exclusion and assimilation. (Reynolds, in Claassens, Schwartz & Hansen (Eds), 2013: 20).
In her insightful analysis of the biblical story of Job, Juliana Claassens concludes with Reynolds that all humans are "only partially and temporarily able-bodied" (Claassens, in Claassens, Swartz & Hansen (eds.) 2013: 64). Only when we realize our own vulnerability and accept various degrees of disability as part of life will we be able to grant true hospitality to those who are equally vulnerable.
In his inimitable way Henri Nouwen, years ago, opened up this new kind of thinking about what health comprises, suggesting a new paradigm from which to consider what wholeness is, which will continue to influence the discourse on healing for many years to come: A Christian community is therefore a healing community not because wounds are cured and pains are relieved, but because wounds and pains become openings or occasions for a new vision. Mutual confession then becomes a mutual deepening of hope, and sharing weakness becomes a reminder to one and all of the coming strength (Nouwen 1994: 94).
Nouwen referred to himself as a "hyphenated priest": a psychologist-priest. Yolanda Dreyer investigated the underlying epistemology of Nouwen's theological model to ascertain whether he was working primarily from a psychological or a theological frame of reference. This is important because of the distinctive epistemologies underlying the psychological and theological discourses. Referring to the strong influence that Heidegger had on Nouwen's thinking she observes that Nouwen's spirituality incorporates, but then goes beyond, the epistemology of psychology. Since much of psychology today is still essentialist, empiricist and positivist, Nouwen opened a way of moving beyond an empiricist epistemology "that assumes the accumulation of knowledge is only gained by information gathered via the techniques and methods of the senses: objectified and empirical data" (Dreyer 2003:715-733).
Henri Nouwen's movement away from the modernist values of being an individualist, an upwardly mobile achiever at Ivy League universities, to becoming a dependent, downwardly mobile servant, at home with the mentally wounded at L'Arche, will continue to challenge prevailing attitudes and practices concerning health and wholeness for a long time. In a posthumous publication of the content of a workshop that was recorded near the end of his life, Nouwen made it clear that he considered following the fragile way of vulnerability, "choosing the way of Jesus", as the way to a different, broken, but beautiful kind of wholeness: This way takes us on a path through the desert of suffering to our hidden wholeness and to our utter beauty in the eyes of the One we name God (Nouwen 2009:111).
In a foreword that Henri Nouwen wrote for a pamphlet that Parker J. Palmer composed as a "celebration of the contradictions in Thomas Merton's thought" 12 we can sense Nouwen's joy in the hidden, paradoxical, broken but beautiful wholeness that he sees reflected in the lives of people like Thomas Merton and Parker Palmer. "This essay is short, fresh, and obviously written with a twinkle in the eye. And the greatest surprise of all is that it not only leads us closer to the spirit of Merton, but closer to Him in whose service Merton juggled contradiction and paradox. It is a reason for joy to see these two kindred spirits together!" (Nouwen, in Palmer 2004: 2) | 7,130.2 | 2016-12-31T00:00:00.000 | [
"Philosophy"
] |
Coupling function from bath density of states
Modelling of an open quantum system requires knowledge of parameters that specify how it couples to its environment. However, beyond relaxation rates, realistic parameters for specific environments and materials are rarely known. Here we present a method of inferring the coupling between a generic system and its bosonic (e.g., phononic) environment from the experimentally measurable density of states (DOS). With it we confirm that the DOS of the well-known Debye model for three-dimensional solids is physically equivalent to choosing an Ohmic bath. We further match a real phonon DOS to a series of Lorentzian coupling functions, allowing us to determine coupling parameters for gold, yttrium iron garnet (YIG) and iron as examples. The results illustrate how to obtain material-specific dynamical properties, such as memory kernels. The proposed method opens the door to more accurate modelling of relaxation dynamics, for example for phonon-dominated spin damping in magnetic materials.
Introduction. -Quantum technologies face many challenges, often arising due to the unavoidable coupling of any system to its environment. The prediction of their dynamics requires open quantum system methods that include such coupling effects, for example the Caldeira-Leggett model [1] and the spin-boson model [2]. These methods are successfully employed in many physical contexts, e.g., quantum optics [3][4][5], condensed matter [6][7][8][9][10][11], quantum computation [12][13][14], nuclear physics [15] and quantum chemistry [16]. For instance, modelling circuit quantum electrodynamics with the spin-boson model shows that the heat transport of a superconducting qubit within a hybrid environment changes significantly, depending on the qubit-resonator and resonator-reservoir couplings [6].
In the mathematical treatment of an open quantum system, a coupling function C ω is typically introduced that describes how strongly the system interacts with bath degrees of freedom (DoF). Its functional form determines the temporal memory of the bath and whether the noise is coloured or not [1,2,17], critically affecting the system dynamics [8,18,19]. A large body of theoretical results exist for various toy models that make specific assumptions on the coupling function C ω [1,2,20]. However, a major drawback is a somewhat lacking connection to system-or material-specific characteristics to which these methods could be applied: for a given DoF, in a given material, which coupling function C ω should one choose to model its dynamics?
An alternative approach is taken in the condensed matter literature, where open quantum systems are usually characterized by the density of states (DOS) of their environ-ment [21]. Measurement of, for example, the phonon DOS is well-established using different inelastic scattering techniques [22,23]. Modes in the environment typically couple to the system with a wave vector-dependent strength g k [2,24,25], which in many cases can be captured by a frequency-dependent g ω .
In this paper, we present a useful relation that translates the coupling function C ω of an open quantum system into an experimentally measurable DOS D ω , and vice versa. While a similar relation has previously been reported for onedimensional quantum spin impurities [26,27], the relation obtained here is valid for a generic system coupled to a bosonic bath, capturing dimensionality and anisotropy. It paves the way to parametrizing realistic coupling functions for a range of applications, for example, for spins in a magnetic material that experience damping through the coupling to the crystal lattice [17,28] or for nitrogen vacancy centers, a solid-state analogue of trapped atoms, whose coherence lifetime in optical transitions is also limited by interaction with phonons [29,30]. The link is explicitly established for a generic quantum system that couples locally to a bosonic environment. Extensions to other environments, such as fermionic environments, will be possible using similar arguments.
The paper is organised as follows: we first introduce the two approaches involving D ω and C ω , respectively. Setting up the dynamics of the environment, we evaluate its memory kernel and establish the link between D ω and C ω , allowing for general g ω . In the second part of the paper, we choose a flat g for simplicity, and illustrate the application of the relation with a few examples. We demonstrate that the widely p-1 arXiv:2112.04001v2 [quant-ph] 15 Dec 2022 used Debye approximation is equivalent to the well-known Ohmic coupling function. While this approximation suffices at low frequencies, experimental DOS show peaks at higher frequencies, leading to non-trivial dissipation regimes. We parametrize two measured phonon DOS, those of gold and iron (see Supplementary Material (SM)), and one theoretically computed phonon DOS of yttrium iron garnet (YIG) and extract key parameters for the corresponding coupling functions C ω . These give direct insight into the impact of memory for any phonon-damped dynamics in these materials.
Two approaches. -The Hamiltonian of a quantum system in contact with a bath iŝ where the bath HamiltonianĤ B and the system Hamiltonian H S may contain the internal interactions among their own components. The system-bath interaction is assumed to be of product form,Ĥ whereŜ is a (Hermitian) system operator andB is a bath operator, each with d s components. The form of the bath HamiltonianĤ B and of the bath operatorB depends on the context. We consider here a bosonic bath, i.e. an infinite set of harmonic oscillators. In the literature, one can broadly distinguish two representations of the bath, working either in wave vector (WV) or frequency (F) space, as illustrated in Fig. 1.
The wave vector approach is common in condensed matter physics [2,21] where the bath Hamiltonian is expressed as a sum over all possible modes k Here ω = ω k gives the dispersion relation of a normal mode with wave vector k andb k (b † k ) are bosonic annihilation (creation) operators of a mode excitation with commutation relations [b k ,b † k ] = δ kk . Usually one considers a three-dimensional (3D) structure with wave vectors k = (k x , k y , k z ). For example, in a cubic 3D lattice with number of lattice sites N , lattice constant a and volume V = N a 3 , each component of k runs through the range − , . . . , 0, . . . , For large N and V , and for any function f (ω k ) that only depends on the frequency ω k , one can approximate sums over the wave vectors as This equation defines D ω as the DOS per unit volume of bath modes at frequency ω [21]. For bosonic baths, we choose the standard interaction [2] where the bath operatorB is linear in the bosonic mode operators (single phonon processes), where ξ k = k hg 2 k /(2ω k ) 1/2 with k a d s -dimensional unit polarisation vector [1] and g k the wave vector-dependent coupling, see Fig. 1. Eq. (2) may be generalized to the situation that several system componentsŜ m are located at different positions R m , and sum over interaction terms, i.e. H SB = − mŜ m ·B(R m ). The field operators would then be R-dependent, i.e.B W V (R) = 1 √ V k ξ kbk e ik·R +h.c.. For simplicity, we will concentrate in the following on just one system site and drop summation over m again.
Another approach to setting up the bath HamiltonianĤ B and the interactionĤ SB is based on a frequency expansion often employed in the open quantum systems literature [1,2]. In contrast to Eq. (3), hereĤ B is written directly as a sum or integral over frequencies, whereP ω andX ω are 3D [in general, d-dimensional (dD)] momentum and position operators, respectively, for the bath oscillator with frequency ω. Their components obey [X ω,j ,P ω ,l ] = ih δ jl δ(ω − ω ). In this approach, the bath operator in Eq. (2) is often chosen as [17] where the coupling function C ω (in general a d s × d tensor) is weighting the system-bath coupling at frequency ω. The p-2 Coupling Function From Bath Density Of States system operators couple isotropically to the bath if C ω C T ω = 1 ds C 2 ω . The scalar coupling function C ω is related to the bath spectral density J ω , which alternatively quantifies the effect of the environment on the system as J ω ∝ C 2 ω /ω [1,2]. The bath dynamics can be categorised [2] based on the low-ω exponent of the spectral density, J ω ∝ ω s , into three different classes, called Ohmic (s = 1), sub-Ohmic (s < 1), and super-Ohmic (s > 1).
The difference between wave vector approach and frequency approach is that at a fixed frequency ω, there is in Eq. (7) just one bath operatorX ω that couples to the system, while according to Eq. (5), the interaction is distributed over several wave vector modes k with weighting factors ξ k , their number being set by the DOS D ω (see Fig. 1).
We now want to address the question of the connection between the DOS D ω and the coupling function C ω . To achieve this, we consider one relevant quantity in both approaches and equate the corresponding formulas. In the following, we choose the memory kernel K which encodes the response of the bath to the system operatorŜ. Note that the choice ofB in Eq. (5) restricts the discussion to the linear response of the bath, as is reasonable for a bath that is thermodynamically large [1,2].
Memory kernel in both approaches. -To find an explicit relation in the wave vector approach for the dynamics of the bath operatorB W V in Eq. (5), the starting point is the equation of motion forb k , whose retarded solution contains two termŝ Therefore, the time evolution of the bath operator can be written asB W V (t) =B W V induced (t) +B W V response (t). The first term represents the internally evolving bath which is contains information about the system's past trajectory, where K W V (t − t ) is the memory kernel (a tensor), Here, the ξ k have been expressed by the unit polarisation vectors k [see after Eq. (5)] and Θ(t − t ) is the Heaviside function, which ensures that the bath responds only to the past state of the system, i.e. t < t. For large volume V , the summation over k in Eq. (11) can be transformed into a frequency integration as in Eq. (4). The projection on polarization vectors, averaged over an isofrequency surface Ω, is taken into account by a (d s × d s ) positive Hermitian matrix g 2 where the matrix M ω is normalized to unit trace and g 2 ω is a scalar. With these notations, the memory tensor in the wave vector approach is Turning now to the frequency approach, the dynamics of the bath operatorX ω in Eq. (7) follows a driven oscillator equation Its exact solution iŝ where Green's function. Inserting this solution in Eq. (7) leads again to induced and response evolution parts given, respectively, Comparing with Eq. (10) one can identify the memory kernel tensor in the frequency approach as Coupling function C ω versus DOS D ω . -Since Eqs. (12) and (16) describe the same memory effects, we may set them equal, leading to This relation links the system-bath couplings in the two approaches, i.e. the DOS D ω is proportional to the Hermitian "square" of the coupling function C ω . This is the first result of the paper. The result (17) may be applied to any quantum system that interacts linearly with a bosonic bath. For instance, magnetic materials in which spinsŜ relax in contact with a phonon reservoir have been studied extensively [13,17,31]. The noise-affected occupation of fermionic modes in a double quantum dot [32], and the behaviour of an impurity in a Bose-Einstein condensate environment [33] are other examples.
Note that in Eq. (17) the dimension of the system is either smaller or equal to the dimension of the bath, i.e. d s ≤ d.
A rectangular (d s × d) coupling matrix C ω may model a graphene-on-substrate structure, where the electronic system (d s = 2) is in contact with a 3D phononic bath [34]. An example for equal dimensions is a 3D spin vector that couples to a 3D phononic environment [17].
p-3
Specific examples. -In this second part of the paper, we wish to use Eq. (17) to obtain coupling function estimates from experimentally measurable quantities. To do so we have to drop generality and make a number of simplifying assumptions.
First, we assume isotropic coupling to an isotropic bath, and set C ω = 1 ds C ω with scalar C ω , and M ω = 1 ds /d s .
Second, for simplicity, we assume a frequency-independent g so that the frequency-dependent impact of the coupling is captured by D ω alone. This is a common approximation for quantum optics systems [35,36], while examples of condensed matter systems where this approximation holds over a range of frequencies are limited [2]. Whenever a non-trivial g ω is known for a specific context, such as a power law behaviour ∝ ω p , this can be included in Eq. (17) separately from the DOS' ω-dependence. To establish such g ω requires microscopic models for specific physical situations, which make several approximation steps. For example, a derivation of the electron-phonon interactions in quantum dots [25] was given in [24]. These assumptions reduce Eq. (17) to the scalar equation with system dimension d s . We will base the following discussion of examples for the coupling functions C ω on this simpler scalar form.
Debye approximation. -In condensed matter physics, the Debye model is used to describe the phonon contribution to a crystal's thermodynamic properties. It assumes an acoustic dispersion, i.e. ω = c|k| with an averaged sound speed c, resulting in 3D in [21] D Deb Here ω D is the Debye frequency, i.e. the maximum bath frequency, which in practice is taken to be near the edge of the Brillouin zone. For example, for gold, see Fig. 2 The scaling of C Deb ω implies that the spectral density J(ω) ∝ C 2 ω /ω is Ohmic, i.e. J(ω) ∝ ω. Hence, the 3D Debye model with constant coupling g in the wave vector approach captures the same relaxation dynamics as an Ohmic bath in the frequency approach.
Beyond 3D cubic lattices, D ω will depend on the dimensionality and lattice symmetry. What happens if the lattice is effectively two-or one-dimensional? To answer this, let us imagine a dD isotropic lattice with volume V = N a d . The volume element of such a lattice in k-space corresponds to )) and two-peak Lorentzian DOS (blue solid line, Eq. (22)) fitted to a measured phonon DOS for gold (red dots) reported as in Ref. [37]. The Debye frequency for gold is ωD/2π = 3.54 THz given in Ref. [21]. Fit specified peak frequencies ω0,j, widths Γj and peak ratios Aj/A1 are given in Table 1. The grey dashed lines separate three frequency regimes discussed in the main text. (b) Memory kernels K(t − t ) corresponding to Debye DOS and two-peak Lorentzian DOS.
Analogously to the 3D lattice, using the acoustic dispersion with an averaged sound speed c, one finds the dD Debye DOS Via Eq. (18) we obtain the power-law C ω ∝ ω (d−1)/2 for the corresponding coupling functions which implies spectral densities J(ω) ∝ ω d−2 . Thus, isotropic baths in 2D or 1D behave in a distinctly sub-Ohmic way.
Inferring coupling functions from DOS data. -Here we wish to go beyond the conceptually useful Debye model, and fully specify the functional form of C ω , given experimentally accessible DOS data that characterise the phononic environment.
A generic feature of real materials is a structured DOS, which shows several peaks [37,38]. Sums of Lorentzian or Gaussian functions are two convenient candidates to approximate such peaky shaped densities [39]. Here, we fit experimentally measured DOS for gold [37] (and iron [38] in SM) and theoretically computed DOS for YIG [40] to a function consisting of multiple Lorentzians, The fits, see Figs. 2 (a), 3 and figure in SM, reveal the material specific peak frequencies ω 0,j , peak widths Γ j and peak ratios A j /A 1 , see Table 1 and tables in SM, while the first peak amplitude A 1 remains undetermined. Fixing A 1 would require information additional to the DOS, such as the system's relaxation rate due to interaction with the phonon bath. Note that phonon DOS are generally slightly temperature dependent [38]. Hence the fit parameters in Eq. (22) will be (usually weak) functions of temperature, a dependence that only matters when a large range of temperatures is considered. The peak widths in Eq. (22) determine a characteristic memory time 1/Γ j . However, beyond this single timescale number, the functional dependence of the memory is fully determined by the kernel Eq. (12), which for multi-peak Lorentzians is proportional to with ω 1,j = ω 2 0,j − Γ 2 j /4. The degree of memory introduced by this kernel into a system's dynamics could be quantified in terms of several non-Markovianity measures, see e.g. [41][42][43][44].
For gold, Fig. 2 (a) shows the phonon DOS measured by Muñoz et al. [37], together with our two-peak Lorentzian fit. The fit gives good agreement in all frequency regimes, with a slightly slower decay in region III than the measured DOS. For a system coupled to phonons in gold, the peak widths (see Table 1) immediately imply a characteristic memory time in the picosecond range. The relevant kernel is shown (blue) in Fig. 2 (b) for the two-peak fitted DOS of gold shown in (a). Using the Debye model instead would give a qualitatively different behaviour: the pink curve shows a distinctly slower long-time tail, due to the sharp cutoff at the Debye frequency. Note also that without any cutoff, the kernel would be K(t − t ) ∝ ∂ t δ(t − t ), implying no memory [17]. In contrast, the Lorentzian fit (blue) provides a quantitatively accurate memory kernel.
Our approach may provide a more realistic picture of the magnetization dynamics based on actual material data. YIG Theo. [40]. The grey dashed line shows a single-peak Lorentzian fit. The fitted peak frequencies ω0,j, widths Γj and amplitude ratios Aj/A1 can be found in Table 2 in the SM. [45,46] is a typical magnetic insulator in which the relaxation of a spin DoFŜ is dominated by the coupling to phonons [47], similar to magnetic alloys like Co-Fe [48], while in metallic materials, the coupling to electrons is more relevant [49]. Fig. 3 illustrates a theoretically computed DOS for YIG [40] with a fit that contains eighteen Lorentzians. (Parameters are displayed in Table 2 in the SM.) In this fit, a few negative amplitudes A j in Eq. (22) are needed to reproduce the gap near 16 THz, however, the total D ω remains positive. Using additional information of the typical Gilbert damping parameter for this material [50], also the peak amplitude A 1 can be determined (see the SM).
18-Lor Fit
More generally, via Eq. (18) the parameters of the multipeak DOS (22) immediately specify the functional form of the coupling C ω of a system to a phononic bath in real materials. This second result of the paper will be useful for modelling the Brownian motion of spins [17,51] and in applications such as quantum information processing with solid-state spin systems [52].
Conclusion. -We have derived the general relation (17) that translates the function C ω , determining the coupling of a generic system to a bosonic bath at various frequencies, into the density of states D ω of the latter. This was achieved by evaluating the memory kernel of dynamical bath variables in two equivalent approaches. Several applications of the relation were then discussed. We demonstrated how for systems damped by phonons in 3D with a frequency-independent g, Debye's quadratic DOS captures the same physics as a linear coupling function C ω which corresponds to an Ohmic spectral density. Secondly, we have established how to infer C ω from the measured DOS of a material, such that it reflects the specific properties of the material. Given that real materials have densities of states with multiple peaks, the typical picture which emerges from our general relation (17) is that the coupling function is non-Ohmic and memory effects in the system dynamics become important. The corresponding time scales (in the ps range, e.g., for gold in Fig. 2 (b)) can be conveniently determined by fitting multiple Lorentzians to the bath DOS.
Future work could address how to extend relation (17) to systems interacting with multiple independent baths. This should be suitable for non-equilibrium settings involving different temperatures [53], as used in heat transport [54]. The impact of memory may also change the behaviour of systems like superconducting qubits or two-level systems that are in contact with two baths [55,56]. [57]. Experimental data are shifted vertically for clarity. The fit parameters for the Lorentzian peaks are given in Table 2.
Supplementary Material. -Fig. 4 shows the phonon DOS for iron, a well-known magnetic conductor. In this figure, we use experimental data reported in Ref. [38] and microscopic theoretical results calculated in Ref. [57]. Fig. 4 (22) with a single peak]. The Debye cut-off frequency is taken from the Debye temperature (420 K) according tohω D = k B T D . Both models reproduce the quadratic scaling at low frequencies, but the Lorentzian also captures the first two peaks. It does not properly capture the data for large frequencies, however.
In Fig. 4 (b), a three-peak Lorentzian [Eq. (22)] fits the measured DOS spectrum remarkably well. It slightly deviates at higher frequencies because the Lorentzians decay less rapidly. Therefore, one can conclude that all three models are reliable fits to the measured data at low frequencies. However, if details are required in a broader frequency range (i.e. at shorter time scales), the three-peak Lorentzian DOS will be the better choice. Fig. 4(c) illustrates the additional structure in the DOS that becomes visible when fitting to the theoretical DOS of Ref. [57]. Here, we fitted a five-peak Lorentzian [see Table 2] to reproduce two additional shoulders. Compared to the experimental data, these are probably hidden by the finite resolution of the measurement. Taking experimental data with such a broadening at face value, one would therefore produce a fitted coupling function with a somewhat shorter memory time compared to the real material. Fit parameters are given in Table 2.
In Table 3, we give the fitting parameters for the DOS of the material Yttrium Iron garnet (YIG). This is a magnetic material which has phonon-damped spin dynamics. Here, an absolute magnitude for the peak amplitudes can be extracted using the known Gilbert damping parameter η 5 × 10 −4 [50] and the electron gyromagnetic ratio γ e 28×10 9 Hz/T [58]. We consider for the system operatorŜ in Eq. (2), as in Ref. [17], a spin vector s multiplied by the gyromagnetic ratio γ e (with |s| =h/2). For the eighteen-peak fit, in Fig. 3 of the main paper, we determine the absolute peak height to be A 1 71.14 (rad THz T) 2 /meV. The other fit parameters are given in Table 3. For the single-peak fit, which is easier to use in simulations, the absolute peak height is A 1 1194.19 (rad THz T) 2 /meV and the other fit parameters are given in Table 3. Table 3: Fit parameters of single-peak and eighteen-peak Lorentzians -shown in Fig. 3 of the paper -matched to the theoretical DOS for YIG reported in Ref. [40]. | 5,559.4 | 2021-12-07T00:00:00.000 | [
"Physics"
] |
Detecting High-Frequency Gravitational Waves with Microwave Cavities
We give a detailed treatment of electromagnetic signals generated by gravitational waves (GWs) in resonant cavity experiments. Our investigation corrects and builds upon previous studies by carefully accounting for the gauge dependence of relevant quantities. We work in a preferred frame for the laboratory, the proper detector frame, and show how to resum short-wavelength effects to provide analytic results that are exact for GWs of arbitrary wavelength. This formalism allows us to firmly establish that, contrary to previous claims, cavity experiments designed for the detection of axion dark matter only need to reanalyze existing data to search for high-frequency GWs with strains as small as $h\sim 10^{-22}-10^{-21}$. We also argue that directional detection is possible in principle using readout of multiple cavity modes. Further improvements in sensitivity are expected with cutting-edge advances in superconducting cavity technology.
I. INTRODUCTION
The first direct observations of gravitational waves (GWs) by the ground-based interferometers LIGO and Virgo [1] have ushered in the era of GW astronomy.While the central focus of such experiments has been on the Hz − kHz frequency range, an exploration across a much wider spectrum is warranted.The Universe is expected to be populated by GWs over many decades in frequency, analogous to electromagnetic (EM) radiation [2], carrying information that may revolutionize our understanding of Nature.This fact has spurred the development of a large array of observational efforts with the aim of detecting much lower frequency signals compared to current interferometers.These include future ground-based [3][4][5] and space-based [6,7] laser interferometers, atom interferometers [8][9][10], pulsar timing arrays [11,12], and CMB observations [13,14], as well as new types of astrophysical signatures [15].
In this work, we focus on how GWs couple to electromagnetism, highlighting in particular the role of small-scale laboratory experiments for the detection of GHz-frequency signals.A GW propagating through a static background EM field sources a feeble EM field that oscillates at the frequency of the GW.Resonant detectors are well-suited to the detection of such oscillating fields provided that the GW is coherent over many oscillation cycles.In fact, similar signals arise from other new physics sources, most notably in the case of ultralight axion dark matter that couples to electromagnetism.Motivated by the tremendous progress in small-scale technology targeting dark matter detection, we focus on setups that are either identical or similar to existing experiments (such as ADMX [46], HAYSTAC [47], ORGAN [48], and CAPP [49]), which feature a resonant conducting cavity of size L det ∼ O(cm) − O(m) immersed in a strong static magnetic field.Since the resonant frequencies of conducting cavities are comparable to their inverse geometric size, such setups are naturally sensitive to GWs in the GHz regime.Our results also apply to other electromagnetic resonators, such as LC circuits [50].
From a more general perspective, a second goal of this work is to provide a description of how GWs couple to electromagnetism in a manner that is largely agnostic to the particular experimental setup.In performing such calculations, great care must be taken to preserve gauge invariance (equivalent to consistently incorporating the signal within a particular choice of frame).In particular, GW signals are often computed in the so-called transverse-traceless (TT) gauge, since the spacetime metric is especially simple in this case.However, in this frame, the background EM field and the cavity modes do not coincide with those in flat space.This has not always been taken into account in previous calculations, which has led several studies to conclude that no EM signal is generated when the background magnetic field is aligned with the GW's direction of propagation.As we show in this paper, this statement is at odds with gauge invariance.Our treatment illustrates that existing experiments targeting axions, such as ADMX and HAYSTAC, already have sensitivity to high-frequency GWs and need only to reanalyze existing data with a different signal template.
For the detectors considered in this work, complications arising from gauge artifacts are avoided by noting that the laboratory defines a preferred frame, the so-called proper detector (PD) frame [51][52][53].For this reason, the majority of our calculations adopt the PD frame.However, in order to demonstrate gauge invariance, we also perform a simple toy example calculation in both the TT and PD frames to show that they yield identical results.More generally, the use of the PD frame has typically been restricted to situations where the GW wavelength λ g is much larger than the size of the detector L det [51,52], such that it suffices to keep only the leading O(L 2 det /λ 2 g ) corrections to the flat spacetime metric.Here, we further improve upon such calculations by resumming the GW perturbation to the metric to all orders in L det /λ g , allowing for the use of the PD frame even when the GW is on resonance with the cavity, which occurs when L det /λ g ∼ O (1).
The rest of this paper is organized as follows.In Sec.II, we provide a conceptual overview of the class of experimental signals discussed here and derive the GW-EM coupling in the form of an effective current.We also demonstrate gauge invariance between the TT and PD frames with a simple toy example consisting of a GW impinging on a background magnetic field in empty space.This lays the foundations for applying this formalism to a more realistic setup consisting of a resonant cavity immersed in a magnetic field, for which we motivate the optimally-coupled cavity modes in Sec.III.Following a brief survey of possible GW sources in Sec.IV, in Sec.V we discuss the overall sensitivity of setups identical or similar to existing dark matter haloscopes and catalog the GW-cavity coupling coefficient for various resonant modes, GW propagation directions, and GW polarizations.Finally, in Sec.VI we conclude and give an outlook on future detection possibilities.Appendix A contains additional details about cavity mode functions and energy densities.
II. GW ELECTRODYNAMICS IN THE PROPER DETECTOR FRAME
In this section, we provide a detailed discussion of GW electrodynamics, paying particular attention to the role of gauge invariance.Before presenting the technical details, we give a conceptual overview of the signal strength and the process of graviton-photon conversion in the language of classical fields.As we show in the following sections, we find this formalism particularly convenient at the level of identifying optimal cavity modes and quantifying the dependence of the signal on the GW's direction of propagation.Our notation and conventions follow those of Ref. [53].
The GW-EM coupling is encapsulated in the Einstein-Maxwell action where F µν is the EM field strength.To isolate the effect of a GW, we first linearize the metric as g µν = η µν + h µν + O(h 2 ), where η µν = diag(−1, 1, 1, 1) is the flat-space metric, h µν is the dimensionless GW strain, and O(h n ) denotes a quantity order-n in strain h µν .In the presence of a static external B-field B 0 , the action contains O(h) terms schematically of the form ∼ h B • B 0 .This implies that a GW of frequency ω g can generate an EM field of typical magnitude h B 0 at the same frequency.Inside an EM cavity, this signal will ring up coherently if ω g matches the cavity's resonant frequency.At the level of single quanta, this effect can be interpreted as graviton-photon mixing in a background magnetic field, known as the inverse-Gertsenshtein effect [54][55][56].We can also describe this effect in terms of a classical effective current, which as we show below is parametrically of size j eff ∼ ω g h B 0 when the cavity size is of order L det ∼ 1/ω g .Because the graviton is described by a spin-2 tensor field, the direction of this effective current is non-trivially determined by the polarization of the GW.
As mentioned above, we make use of the PD frame throughout this work.This frame utilizes so-called Ferminormal coordinates [51,57,58], which describe GWs according to a freely-falling inertial observer (see footnote 3) and are written as an expansion in the proper distance from the detector's center of mass.The lowest order terms in this expansion were derived in Refs.[51,[59][60][61] and to all orders in Refs.[62,63].As we illustrate below, the EM signals generated by GWs in resonant cavities are most simply described using such coordinates.Regardless, this computation is non-trivial when the GW wavelength λ g is comparable to the cavity size L det , in which case the expansion parameter is L det /λ g ∼ O(1) and the series expansion cannot be approximated by the first few terms [64][65][66][67][68].As far as we are aware, a closed-form expression for the metric, including terms to all orders in L det /λ g , has not been presented previously.In particular, we show below that resumming the metric in the PD frame is possible for a monochromatic GW of any wavelength traveling along a fixed direction.
A. Analogies with Axion Dark Matter Detection
Though it is not strictly necessary for the logic of the paper, it is useful at this point to make an analogy with axionphoton conversion, since this will allow us to derive a quick back-of-the-envelope estimate for the sensitivity of existing axion experiments to GWs.Indeed, the similarity of the phenomenology of axions and gravitons interacting with EM < l a t e x i t s h a 1 _ b a s e 6 4 = " L / / v Q R K t 1 h y q T 2 y 3 A cartoon illustrating the differences between GW-EM conversion (left) and axion-EM conversion (right) in the presence of an external magnetic field B0.The GW effective current is proportional to ωghB0, with a direction dependent on the GW polarization and a typical quadrupole pattern, yielding a signal field with amplitude hB0.The axion effective current is proportional to ωaθaB0, with a direction parallel to the external field B0, yielding a signal field with amplitude θaB0.The differing geometry of the effective current yields different selection rules for coupling the GW and axion to cavity modes.
fields has been noted since the seminal paper of Raffelt and Stodolsky [69], and the effective current formalism [70] is often used when studying axion dark matter signals in the low-frequency (quasistatic) limit [71,72].The Lagrangian for an axion dark matter field a interacting with EM fields is L = −1 4 g aγγ a F µν F µν = g aγγ a E • B, where g aγγ is the dimensionful axion-photon coupling.Taking B = B 0 to be a static external B-field, the Lagrangian now contains the bilinear g aγγ a E, which allows an axion field at frequency ω a to convert to an E-field that oscillates at the same frequency, with typical magnitude g aγγ a B 0 .This is reflected in the equations of motion for the axion and EM fields, which can be written so that the time derivative of a non-relativistic axion background field sources an effective current term j eff ⊃ g aγγ ∂ t a B 0 ω a θ a B 0 on the right-hand side of Ampère's Law.Here, we defined the effective dimensionless field θ a ≡ g aγγ a, which will allow for a useful comparison to the GW case discussed above.Since axion dark matter is described by a a non-relativistic spin-0 field, the direction of the effective current is determined straightforwardly by the external field B 0 , independent of the axion. 1 A schematic illustration of this axion vs. GW comparison is shown in Fig. 1.The effective current formalism helps elucidate the fact that the cavity modes which couple most strongly to GWs will in general be different from those excited by axions.Nonetheless, we will show below that for certain geometries, GWs do indeed have a non-zero coupling to the TM 010 cavity mode currently employed in, e.g., the ADMX and HAYSTAC axion detectors, meaning that these experiments already have some sensitivity to GWs in their resonant frequency ranges.Momentarily ignoring very important differences in the spectral characteristics of the axion dark matter and GW fields, we can derive a conservative estimate for the sensitivity of axion dark matter experiments to coherent high-frequency GWs by comparing the respective forms of the effective currents.In particular, identifying θ a ∼ h and noting that ADMX is currently sensitive to the QCD axion parameter space, corresponding to θ a ∼ several × 10 −22 , implies that such experiments are sensitive to similar values of the strain h (as well as smaller values for GW signals that are more coherent than axion dark matter).A more precise sensitivity estimate will be provided in Sec.V.
Aside from the difference in cavity mode selection rules, there is a second important conceptual difference between axions and gravitons related to the role of reference frames.The axion dark matter field is assumed to have a Maxwellian speed distribution in the galactic rest frame, and moving to the laboratory frame where the cavity fields are defined is a simple Galilean boost which does not parametrically affect the signal strength.On the other hand, the large gauge freedom of linearized general relativity allows the GW signal to be computed in different reference frames, but a gauge transformation will also transform the background EM fields at the same order as the signal strength.We explore these issues in detail below.
B. General Formalism
The equations of motion can be derived straightforwardly from the action of Eq. (1).In particular, after linearizing in h µν and integrating by parts, the O(h) terms in the action are where j µ eff ∼ O(h) is an effective 4-current and h ≡ η µν h µν is the trace of h µν .It is important to emphasize that j µ eff is not a true 4-current; for instance, it does not transform covariantly between frames.This stands in contrast to other tensors, such as the Riemann tensor R µνρσ ∼ O(h), which upon transforming between frames behaves schematically as R µνρσ → R µνρσ +O(h2 ) and is thus frame-independent to O(h) [64,74].Hence, although j µ eff is O(h), it is not invariant between frames.At a technical level, this arises from the fact that in linearized theory, the form of h µν is not unique, up to a residual gauge freedom in the choice of coordinates x µ → x µ = x µ + ξ µ (x), where ∂ µ ξ ν ∼ O(h).From the usual transformation properties of a tensor we can conclude that an O(h n ) tensor transforms as O(h n ) → O(h n ) + O(h n+1 ), which implies that a covariant O(h) tensor is gauge-invariant in linearized theory.This transformation, applied to h µν and F µν , can also be used to show explicitly that j µ eff is not invariant at O(h).That being said, j µ eff does couple to the EM potential as a 4-current does, and so sources signal EM fields when a GW encounters a background EM field. 2 The remainder of this section is dedicated to further illustrating this point in a manner that is largely agnostic to the particular experimental setup.
To evaluate Eq. ( 3), we must choose a frame.The preferred frame of the laboratory is the aforementioned PD frame, which generalizes the notion of an inertial observer to curved space-time and reduces to the flat space-time metric in the ω g → 0 limit [51][52][53].Furthermore, unlike in other frames, experimental parameters, such as the applied EM fields, are naturally defined in the PD frame.In most applications of the PD frame, the metric is written to leading order in ω g L det 1, where L det is the characteristic size of the detector.However, this is not suitable for the experimental setup explored in this study, which instead requires ω g L det ∼ O(1).In our calculations, we thus employ the full set of higher-order terms in the metric, which has been derived in, e.g., Refs.[62,63].Adapting these results, we find that for R µνρσ ∝ e iωg(t−z) in the form of a monochromatic plane wave traveling along the +ẑ direction, the metric in the PD frame can be obtained exactly by resumming the full set of terms from Ref. [62], where the symbol i denotes a spatial index only when appearing as a superscript or subscript of a vector or tensor; otherwise it is understood to be the imaginary unit. 3In Eq. ( 4), the Riemann tensor R µνρσ is evaluated at the spatial origin x i = 0, which is chosen to coincide with the detector's center of mass, keeping the time-dependence R µνρσ = R µνρσ (ω g t) intact.Note that the second factor in each line of Eq. ( 4) is equal to unity in the limit that ω g → 0 and so smoothly matches on to the well-known long-wavelength expressions [53].To proceed, we take advantage of the fact that R µνρσ is frame-independent to leading order in strain [53].For convenience, we can thus choose to evaluate R µνρσ in the TT frame, in which case Eq. ( 4) becomes where h TT ab ∝ e iωgt is the GW in the TT frame evaluated at the spatial origin, and the indices a, b = x, y run over the spatial components that are perpendicular to the GW's direction of propagation.Substituting Eq. ( 5) into Eq.( 3) yields j µ eff in terms of h TT µν for a monochromatic plane wave. 4As a result, the physical effects of the GW, as well as our projected sensitivity, will be phrased in terms of h TT µν , which can be regarded as the strain sourced by some cosmological or astrophysical event in the TT frame, decomposed in terms of its plus-or cross-polarized components h TT + and h TT × [53].To simplify the notation, we will drop the "TT" superscript on the strain polarizations, h +,× ≡ h TT +,× , for the remainder of this work.
C. Toy Example
We conclude this section with a simple toy example calculation involving a GW impinging on a longitudinal magnetic field.As we will see below, this calculation highlights the importance of keeping track of frame-dependent aspects of the signal, some of which have been overlooked in the past literature but are necessary to preserve gauge invariance.Generally, we aim to illustrate the important point that laboratory parameters, such as the EM-field configuration or motion of a sensor, cannot be held fixed in both the PD and TT frames.At the level of this toy example, we concretely define the experimental setup, and then transform the relevant quantities into the frame of interest in order to calculate an approximately gauge-invariant observable in the form of an O(h) covariant vector (see the discussion below Eq. ( 3)).
For simplicity, we begin by considering a low-frequency plus-polarized GW of amplitude h + traveling along the +ẑ direction over a region of space that contains a magnetic field B 0 .To proceed with the calculation, we must specify a detector, two examples of which are discussed here.One such detector is an ideal conductor.In this case, we expect the oscillating EM fields generated by the GW to drive a small signal current that scales as J sig ∝ σ h + B 0 , where σ is the conductivity of the detector.Let us take the background magnetic field to be static, spatially uniform, and pointing along the +ẑ direction in the TT frame, B TT 0 = B 0 ẑ.Though real experimental B-fields will usually be static in the PD frame, this choice allows us to most easily compare to previous calculations (which work solely in TT gauge [69]) and to demonstrate the frame dependence.For concreteness, we take the position of the conducting detector to be approximately fixed in the PD frame.This is physically motivated and can be ensured by fixing the detector in the laboratory to an arbitrarily stiff mount that can resist the tidal forces induced by the GW.
It is instructive to compare the signal current J sig as derived in either the TT or PD frame.In the TT frame, the trace and divergence pieces of the metric vanish, in which case only the third term of Eq. ( 3) contributes to the effective current of the previous section, such that where we took the GW to be a monochromatic plane wave traveling along the +ẑ direction, h TT µν ∝ e iωg(t−z) .The last equality shows that in the TT frame the effective current vanishes in the case that the background magnetic field is aligned with the GW's direction of propagation.
To illustrate the signal, we adopt from Ref. [63] the coordinate transformations from the PD frame (denoted with x µ ) to the TT frame (denoted as x µ TT ), which to leading order in the long wavelength limit are5 Eq. ( 7) can be used to transform the 4-velocity U µ of the conducting detector in the PD frame to the TT frame.Since the conductor is assumed to be stationary in the PD frame U µ = (1, 0, 0, 0), this implies that it moves with a small U i TT ∼ O(h + ) velocity in the TT frame.Such movement in the stationary background magnetic field B TT 0 generates a Lorentz force, driving a small oscillating signal current.More concretely, the covariant generalization of Ohm's law [75], which yields to leading order in ω g × length.Hence, as expected, we see that the effect of the GW is to drive an oscillating current in the conductor at the same frequency as the GW.The calculation proceeds in a similar manner in the PD frame, in which case the coordinates of the conductor are fixed.However, transforming the EM field-strength from the TT to PD frame shows that the EM fields pick up an oscillating component from the GW, From the above expression for the electric field, we see that the signal current in the PD frame, J i sig = σ E i , agrees with the same result in the TT frame in Eq. ( 8) (we have also checked that this agreement holds to all orders in ω g × length).
Another example of a simple detector is a wire that is prepared by driving a current along the +ẑ direction, parallel to the applied magnetic field, such that the wire experiences zero Lorentz force in the absence of a GW.However, we expect a signal to arise in the form of an oscillating Lorentz force, distinct from the usual tidal force, when the GW sources small EM fields perpendicular to the direction of the wire.As before, we take the background magnetic field to be B TT 0 = B 0 ẑ in the TT frame, and for concreteness, we assume that the applied current density J 0 in the wire is constant in time in the PD frame, J µ 0 = (0, 0, 0, J 0 ).For a GW propagating in the +ẑ direction, j µ eff,TT = 0, as in the previous example, and one might be tempted to conclude that no EM signal is generated.However, using the transformations of Eq. ( 7), the current density in the wire picks up additional oscillating components in the TT frame, which induce small Lorentz forces.In particular, from the covariant form of the Lorentz force density, In the PD frame, we calculate the force density obtained by the corrections to the EM fields in Eq. ( 9).As expected, we find that this agrees with the TT force density of Eq. (11).From the calculations above, we see that the signal, as described by the O(h) covariant current or Lorentz force density, is invariant between the TT and PD frames.Generally, the EM signal sourced by a GW interacting with a background EM field has individual contributions that differ between frames but whose sum enters into a gaugeinvariant observable.In the remaining sections, our calculation differs somewhat from the toy example presented < l a t e x i t s h a 1 _ b a s e 6 4 = " X k Proper detector frame: w S t 4 s 5 6 s F + v d + p i 3 V q x y 5 h D 8 g f X 5 A 5 z M l c E = < / l a t e x i t > @ t B0 = 0 < l a t e x i t s h a 1 _ b a s e 6 4 = " a X l l d W 2 9 t F H e 3 N r e 2 X X 3 9 l t a J g q T J p Z M q k 6 I N G F U k K a h h p F O r A j i I S P t c H w 7 9 d s P R G k q R c N M Y h J w N B Q 0 o h g Z K / X d w x 4 P 5 W P a U E j o S C q e y 9 c Z 7 L s V r + r l g < l a t e x i t s h a 1 _ b a s e 6 4 = " J 2 7 w v s q / S N G C U K N M W q z s J k s n u N w 4 q e 0 R i 9 o w / r x X q 1 P q 2 v a W v O m s 3 s o z + y v n 8 A q K + q m w = = < / l a t e x i t > FIG. 2. A heuristic sketch of our experimental setup in the PD and the TT frames, as well as the transformations between them.The EM signal arises from a GW-induced effective current in the PD frame, where the external magnetic field B0 is static.In the TT frame the effective current vanishes for specific B-field geometries, but there is nonetheless a signal from an O(h) oscillating correction to B0.To avoid these gauge artifacts, we work entirely in the PD frame, which corresponds to the experimental situation where the EM fields are set up in a frame where the detector and the applied B-field are static.
above, in that the applied magnetic field B 0 is considered to be spatially uniform and static in the PD frame (instead of the TT frame).In this case, in the TT frame the effective current vanishes for a GW propagating in the direction of B 0 , and instead the signal arises from the transformation of the background EM fields between the PD and TT frames.Previous studies have neglected the latter contribution by taking the background EM field in the TT frame to be the same as in the laboratory; in this case, one is led to mistakenly conclude that the signal vanishes for a magnetic field aligned with the GW's direction of propagation (see, e.g., Refs.[76][77][78]).
For a more general geometrical configuration, the signal in the TT frame has contributions both from the effective current and the transformation of EM fields between frames.On the other hand, for a rigid detector in the PD frame the signal solely arises from the effective current, since the background EM fields are defined with respect to the laboratory.Since the isolation of the effective current as a source simplifies the analysis for more general geometries, we work solely in the PD frame for the remainder of this work.In the next section, we develop this formalism further, by evaluating j eff and the resulting signal for an experimental setup consisting of a static magnetic field inside a cylindrical cavity.
To conclude, we note that the main lesson from our toy example is simple and well-known: we can measure only gauge-invariant quantities.Above, we computed two quantities, J µ sig and f µ sig , which are frame-independent at O(h).Going beyond this, the Lorentz force, for instance, projected onto the 4-velocity of an observer f µ sig U µ = F µν J ν U µ is frame-independent to all orders in h.In the remainder of the paper, we implicitly compute gauge-invariant observables, with the contraction with U µ understood.Appropriate probes in the laboratory (and so in the PD frame), such as test-currents J ν and observers U µ , are sensitive to the different F µν components that we compute below.
III. RESONANT EXCITATION OF CAVITIES
In this section, we calculate the EM signal that arises in a resonant cavity immersed in a magnetic field B 0 .As emphasized above, in a realistic experimental setup, B 0 is static and spatially uniform in the PD frame.Note that this is essentially the reverse of the toy example discussed above, where B 0 was instead taken to be static in the TT frame.By contrast, our calculational setup, as illustrated in Fig. 2, corresponds to the physical situation of turning on a static and spatially-uniform magnetic field in the PD frame.
We begin in Sec.III A by discussing the general form of the signal for an arbitrary cavity, which admits a decomposition of the EM fields into resonant modes [79].We continue in Sec.III B by focusing on cylindrical cavities that are already employed in searches for axion dark matter.In this case analytic expressions for the cavity modes are tractable, and considerations of the EM signal greatly simplify if the external magnetic field is oriented along the symmetry axis of the cavity.
A. General Formalism
The components of the effective current j µ eff = (ρ eff , j eff ) enter as additional source terms in the inhomogeneous Maxwell equations, where ρ and j are physical charge and current densities.The piece of j independent of h µν sources, for example, the external B-field: ∇ × B 0 = j 0 .In the following we subtract all such zeroth-order pieces from Eq. ( 13) such that all fields are O(h).On the other hand, the homogeneous Maxwell equations (Gauss' law for magnetism, ∇ • B = 0, and Faraday's law, ∇ × E + ∂ t B = 0) are not modified by the GW.Indeed, this is because these Maxwell equations come from a topological equation of motion dF = 0 (where d is the exterior derivative and F is the field-strength two-form) which does not involve the metric g µν .This will be of practical importance because the homogeneous Maxwell equations determine the resonant cavity modes, and thus we will see that the change in the modes induced by the tidal force of the GW affects our signal only at O(h 2 ).Combining Eq. ( 13) with Faraday's law yields the standard form of the wave equation The electric field in the cavity is expanded in terms of the resonant modes E n (x) as [75,79,80]: where n indexes the various modes and e n is a dimensionless time-dependent coefficient.In general, the sum over the modes E n includes both solenoidal (∇ • E n = 0) and irrotational (∇ × E n = 0) contributions.Since irrotational modes are not resonantly enhanced (see Appendix A 1), they are omitted from our analysis below.Note also that we assume any degenerate modes have been diagonalized into orthogonal mode functions and indexed separately in the sum.
The spatial mode functions E n satisfy the relations Vcav where ω n is the resonant frequency of mode n and V cav is the volume of the cavity.The above relations are supplemented by the boundary condition n × E n = 0 over the surface of the cavity, where n is the unit vector normal to the boundary.Note that formally this boundary condition is unchanged even in the presence of the GW, since it follows from the standard form of Faraday's law, as mentioned above.The boundary of the cavity can oscillate in the presence of a GW, but as we will see below this only affects the signal at O(h 2 ).Using Eqs. ( 15)-( 17), the wave equation in Eq. ( 14) can be rewritten in terms of the mode coefficients e n .In the absence of external physical current sources, this gives where the mode-dependent quality factor Q n appears from losses in the cavity.In principle, ω n and V cav appearing in the above equation are perturbed by the tidal force of the GW at O(h).However, if in the absence of the GW there is no power in the cavity modes, this effect corrects our signal only by terms of O(h e n ) and O(h j eff ), both of which are O(h 2 ).
Taking the GW to be monochromatic and on resonance with the cavity mode, i.e., j eff (x, t) = e iωgt j eff (x) where the GW frequency is ω g ω n , the solution to Eq. ( 18) is enhanced by the large quality factor Q n 1.The steady-state form of the excited signal electric field E sig = e n E n is then given by where for convenience, we will drop the subscript from the quality factor, Q ≡ Q n , from now on.Note that if there are multiple degenerate modes at ω g , we must sum over all such modes with their own time functions e n (t) to obtain the total signal field; we will see such an example for cylindrical cavities in Sec.III B below.Since the effective current scales as j eff ∝ ω 2 g in both the high-and low-frequency limits (see Sec. III B), we decompose it into a dimensionful amplitude and two spatially-dependent dimensionless functions ĵ+ (x) and ĵ× (x) that describe the spatial profile and polarization of the GW signal, as follows: The steady-state signal power delivered to the cavity can then be expressed as which follows from the energy density stored in resonant cavity modes (see Appendix A 3).Note from Eq. ( 19) that when both polarizations in j eff are present, the power will generically have cross-terms between the two polarizations.However, for simplicity of presentation, we will often consider the case where only one of the polarizations is present at a time.In this case, we can can define a dimensionless coupling coefficient in terms of which the signal power can be written as where h 0 = h + or h × is the magnitude of the GW strain.Eq. ( 23) illustrates the scaling of the power in a transparent way; when both polarizations are present, the power should be computed directly from Eqs. ( 20) and ( 21).In the next section, we evaluate Eq. ( 22) for different configurations, corresponding to various cavity modes, GW polarizations, and orientations of the GW's direction of propagation with respect to the symmetry axis of the cavity.
B. Selection Rules for Cylindrical Cavities
The discussion in the previous section is valid for cavities of any shape.In the following, we focus specifically on cylindrical cavities in part because existing experiments use this geometry.For concreteness, we will consider such a cavity of equal radius and length, R det = L det .The solenoidal modes of a cylindrical cavity are classified into transverse magnetic (TM) and transverse electric (TE) modes.For cylindrical cavities, the generic mode number n, introduced in the previous section, is represented by three integers n = (m, n, p) and a ± index, where m, n, and p stand for the azimuthal, radial, and longitudinal mode indices, and the ± indexes a pair of degenerate modes for m = 0 with distinct azimuthal dependence.The explicit form of the mode functions, along with expressions for the corresponding resonance frequencies ω mnp , are provided in Appendix A 2.
As illustrated by the coupling coefficient of Eq. ( 22), it is advantageous to have a large overlap between the electric field mode and the GW-induced effective current j eff .A cross-sectional view of ĵ+ is shown in the xy-plane in the left-panel of Fig. 3, taking both the GW's direction of propagation and the applied magnetic field B 0 to be along the cavity axis.We define our coordinate system such that the center of the cavity is located at the origin and the cavity axis is along the z-axis.The black arrows illustrate the direction of ĵ+ , while the lighter/darker colored regions FIG. 3. A cross-sectional view of the dimensionless effective current ĵ+ (left) and electric field of the TE212− signal-mode Esig (right).The black arrows denote the direction of ĵ+ or Esig projected onto the xy-plane (in units of the cavity radius Rcav) near z = 0 (corresponding to the cavity's center of mass) where the symmetry axis of the cylindrical cavity, the applied magnetic field, and the gravitational wave's direction of propagation are chosen to align with the z-axis (not shown).The lighter/darker colored regions correspond to smaller/larger magnitudes of ĵ+ or Esig.The geometrical coupling between the gravitational wave and the cavity (encapsulated by the coupling coefficient ηn) is O(1), as can be inferred from the similar spatial profiles of ĵ+ and Esig.
correspond to smaller/larger magnitudes | ĵ+ |.The effective current exhibits a quadrupolar structure in the xy-plane, due to the spin-2 nature of the gravitational field (see the discussion below).An optimally-coupled cavity mode is one that possesses the same spin-2 structure along the azimuthal direction.This is shown in the right-panel of Fig. 3, which displays the vector field for the electric component of the TE 212− mode.As is evident by comparing both panels of Fig. 3, the effective current and the electric field of the TE 212− mode have a similar spatial dependence and therefore a large overlap, as quantified by Eq. ( 22).In Sec.V B, we confirm this statement by numerically evaluating the coupling coefficient η n for different cavity modes and find that η n ∼ O(0.1) is generic for various geometrical configurations, including this one.
For this specific example, the direction of the GW and the applied magnetic field preserve the cylindrical symmetry of the cavity.As a result, the form of j µ eff vastly simplifies, and one can derive simple cavity mode selection rules.This is made manifest by rewriting j µ eff in cylindrical coordinates, i.e., j µ eff = (ρ eff , j r eff , j φ eff , j z eff ), such that where is a dimensionless function that obeys lim x→0 f (x) = 1 and lim x→∞ f (x) = −3.Above, we have introduced the GW helicity components h ±2 ≡ (h + ± ih × )/ √ 2, which transform under a rotation by ∆φ about the cavity/GW axis as h ±2 → e ±2i∆φ h ±2 .From the explicit form of the current in Eq. ( 24), we can understand our choice of normalization for j eff in Eq. (20).Indeed, the spatial components of the current scale as j eff ∝ h 0 B 0 ω 2 g r, where the typical size of r cav .Since resonant modes parametrically have r ∼ 1/ω g , this recovers the naive scaling j eff ∼ h 0 B 0 ω g presented in Sec.II.
For a fixed GW polarization, the effective current in Eq. ( 24) is only invariant under rotations about z for φ → φ+qπ, q ∈ Z, reflecting the spin-2 nature of the tensor field h µν . 7The background field B 0 , being uniform and aligned with the cylindrical axis, is a scalar under the cylinder's U (1) rotational symmetry.The EM fields of a cylindrical cavity can be decomposed into a sum over modes with definite transformations under the cylindrical U (1) symmetry, E ∝ e ±imφ (see Appendix A 2).Thus, from Eq. ( 22), only modes with m = ±2 couple to the effective current for this particular example.This matches the intuition garnered from Fig. 3, where the angular overlap of j eff with an m = 2 mode is visually apparent.It is also instructive to apply this argument to the case where the GW remains coaxial with the cylinder, while B 0 is not aligned with the cavity axis.In this example, the direction of the applied magnetic field does not preserve the symmetry of the cavity.Since B 0 is a pseudo-vector under the cavity's U (1), along with the spin-2 GW, this yields an effective current with a spin-1 component, which can couple to m = ±1 cavity modes.The coupling coefficient for such geometries is evaluated numerically in Sec.V B.
IV. SOURCES
Before moving on to calculating the sensitivity of an EM cavity to a generic GW in Sec.V, we first briefly survey the kinds of sources which could give rise to spatially-localized (on the sky) high-frequency monochromatic GWs.
Our main examples are mergers of sub-solar mass objects -including primordial black holes (PBHs) and other exotic compact objects -and boson clouds from PBH superradiance.As we will see below, for binary mergers to generate inspiral signals in the GHz regime, the merging objects must be much lighter than a solar mass.Exotic compact objects [82] can be considerably lighter than a solar mass and therefore can emit GWs at high frequencies.Examples of such exotic compact objects are boson and fermion stars [82][83][84][85], gravitino stars [86], gravistars [87], and dark matter blobs [88].In general, the GW waveforms generated by merging exotic compact objects and PBHs are distinct, though this difference is small when the orbital radius is much larger than the spatial size of the merging objects; for simplicity, in our analysis we treat the merging objects as point-like.
The frequency of the GW emitted by a merging binary increases during the inspiral phase as the two compact objects approach each other.There is an upper bound on the frequency of GWs emitted by a binary in a quasi-circular orbit in the weak-field limit, corresponding to the GW frequency at the innermost stable circular orbit (ISCO).For a binary consisting of compact objects of equal mass M b , at sufficiently early times such that the orbital radius r b is greater than the ISCO radius r ISCO = 12G N M b , the GW frequency evolves as ω g 14 GHz × (10 . Thus, only very light binaries, such as sub-Earth mass PBHs [89][90][91], can generate GW signals in the GHz regime well before reaching the ISCO. However, such GW signals are highly transient near the ISCO, as the frequency of the emitted GW evolves in time according to dω g /dt ∝ (M b /r b ) 11/6 , which can limit the sensitivity of resonant experiments.In particular, GWs from the merger of light binaries can typically only resonantly excite a cavity for a short amount of time that decreases for heavier masses.This is quantified by the number of orbital cycles N cyc a binary spends emitting GWs within the resonator bandwidth ω g /Q, given by N cyc ∼ 10 −3 ×(10 −6 M /M b ) 5/3 (10 5 /Q) for ω g ∼ GHz.Requiring that a typical cavity is fully rung up by the GW signal, i.e., N cyc Q ∼ 10 5 , requires that M b 10 −11 M , which, amusingly, is a scenario where PBHs could constitute an O(1) fraction of the cosmological dark matter abundance [92][93][94][95].The expected strain from inspirals at a distance D from Earth is The best case strain can be estimated under the assumption that the PBHs are 100% of the dark matter and all PBHs are paired in binaries.In this case we get D = 10 −3 pc and hence a best case sensitivity of h 0 ∼ 10 −26 .
A more realistic study [96] finds that the average distance where one expects one merger event per year is D = 0.21 kpc . Note hat the merger rate is used as an approximation for the number of events where the GHz frequency band is crossed by a source nearby.Plugging the more realistic value for the distance D into eq.( 26) The experimental setup we discuss in Sec.V below has parametrically reduced sensitivity to sources that only spend a much smaller number of cycles exciting the cavity, which makes detecting heavier binaries (with correspondingly larger strain) difficult.On the other hand, since transient mergers sweep through a large range of frequencies, the resultant GWs will hit multiple resonant frequencies of the cavity.Therefore, unlike searches for axion dark matter, one does not have to scan different cavity frequencies by tuning the cavity when looking for GWs from such signals; the frequency sweeping is done by the merger itself.
High-frequency GWs can also arise from the annihilation of boson clouds generated by black hole superradiance [97][98][99][100][101][102][103][104][105][106].For instance, bosons of mass m a ∼ µeV × (10 −4 M /M PBH ) accumulate in large numbers outside a PBH of mass M PBH .When such bosons annihilate into gravitons in the background gravitational field, the frequency of the emitted GW is ω g = 2m a ∼ GHz × (m a /µeV).Thus, if such PBHs and sub-eV bosons both exist, superradiant clouds emit very high-frequency GWs.From the point of view of the experimental signals discussed here, the advantage of this GW source is that the associated waveform is monochromatic and coherent over very long timescales.The coherence time is limited by the change in gravitational potential energy of the boson cloud as it annihilates, which leads to a small positive drift in frequency, dω g /dt > 0 [106].This drift is small, such that the signal is effectively coherent for much longer than the cavity ring-up time ∼ Q/ω g .However, the masses of such hypothetical bosons and PBHs are unknown, so unlike the case of a transient inspiral signal, a scanning strategy must be implemented.The expected strain of such signals arising from a PBH a distance D from Earth is [107] where we have used that the fraction of PBH mass that the axion cloud carries is = 10 −3 and α = GM b ma = 0.5, where G is the gravitational constant and is the orbital quantum number.
In agreement with all current constraints on PBH dark matter we can assume that PBHs constitute 1% of the dark matter density.This enables us to estimate the average distance to be D ≈ 1 pc from what we estimate h 0 ≈ 10 −23 .Note that this is a best case scenario and the actual strain might be orders of magnitude worse [96] because we have not taken into account how the PBHs attained the spin which is necessary to generate the boson clouds via the superradiance mechanism.
While we do not focus heavily on non-coherent sources in this paper, there are also interesting sources of highfrequency stochastic GWs.The most prominent examples include GWs arising from first-order phase transitions [108,109], cosmic strings [110,111], inflation [112][113][114][115], preheating [116,117], and the thermal plasma (the so-called Cosmic Gravitational Microwave Background) [118][119][120]; for a review see, e.g., Ref. [121].We briefly discuss the detection of stochastic GWs with EM cavities below and will return to this issue in future work.
V. SENSITIVITY ESTIMATES AND CAVITY COUPLING COEFFICIENTS
In this section, we apply the formalism developed in Sec.III to a concrete experimental setup.We begin in Sec.V A with a general discussion of the sensitivity of a resonant cavity to coherent or stochastic GW sources, assuming an optimal cavity-GW coupling coefficient η n ∼ O(0.1), and illustrate how this sensitivity scales with the assumed experimental parameters.In Sec.V B, we then examine the angular dependence of η n with respect to the direction of an incoming monochromatic GW for different cavity modes and GW polarizations.We find that for various cavity modes, η n is O(0.1) over a large fraction of solid angle, including the TM 010 and TM 020 modes, which are already employed by existing axion dark matter experiments, such as ADMX and ORGAN.The strong dependence of the coupling coefficient on the incident direction of the GW makes a plausible case for directional detection.
We note that our estimates are purely based on the signal induced by the direct coupling of the GW to photons that we described in the previous sections.In principle, the GW can also induce other effects.We have already discussed how deformations of the cavity walls are not observable in these setups, since they generate an EM signal at O(h 2 ).The GW can in principle also induce a relative motion between the laboratory apparatus generating the background B-field and the cavity itself.This relative motion can produce an additional oscillating EM field in the rest frame of the cavity.The resulting O(h) oscillating component of the background electromagnetic field is shielded by the cavity itself (even in the absence of additional electromagnetic shielding).In practice only the static component penetrates the cavity walls efficiently and can produce an O(h) signal within the cavity after interacting with the wave.Thus, any electromagnetic "signal" generated by deformations of the external B-field source generate a signal only at O( × h) h where depends on the electromagnetic shielding of the cavity.An alternative justification for ignoring such effects is that the time-dependent electromagnetic fields generated by the GW interacting with the external electromagnetic source can only couple to the electromagnetic modes of the cavity by driving currents along the cavity walls.Such currents do not resonantly couple to the electromagnetic modes of the cavity since, by definition, the electric components of these modes vanish at the cavity wall.
A. Sensitivity Estimate
The signal power P sig due to a coherent GW on resonance with the cavity is given by Eq. ( 23).The signal-to-noise ratio (SNR) is then given by the Dicke radiometer equation as where T sys is the effective noise temperature, t int is the measurement integration time, and ∆ν is the signal frequency bandwidth.The sensitivity is estimated by taking SNR 1, which after using Eqs.( 23) and ( 28) yields 3/2 0.1 where we have adopted experimental parameters similar to those of ADMX [122].Recent advances in superconducting cavity technology suggest that achieving Q = 10 7 with B 0 = 6 T may be possible in the near future [123], and of course a longer integration time is possible for a dedicated GW search.
In a realistic setup, the signal bandwidth ∆ν will be determined by a combination of factors.For instance, ∆ν is bounded from below by, e.g., the intrinsic frequency spread of the GW source or the drift of the cavity resonant frequency, and it is bounded from above by the cavity bandwidth ∼ ω g /(2πQ).Our conservative benchmark of ∆ν = 10 kHz corresponds to the cavity bandwidth for Q = 10 5 and ω g /2π = 1 GHz, similar to that of the ADMX cavity.The fundamental lower bound on the bandwidth is given by the frequency resolution ∆ν 1/t int , which is saturated for a sufficiently monochromatic source with infinite coherence time in a phase-sensitive measurement scheme such as a lock-in amplifier.In this case, the SNR scales linearly with t int , resulting in a sensitivity of Indeed, this technique is already used in the GW detection community in the form of "matched filtering" [53], which ensures that the SNR scales as t int as long as the precise waveform of the signal is known.The sensitivity estimate from Eq. ( 29) is illustrated in Fig. 4 for various existing axion experiments, as well as for superconducting cavities being developed at the SQMS Center at Fermilab which can support both large B-field and high Q factors [123].Note that the sensitivity is generally weaker at higher frequencies because the cavity volume typically scales with the signal mode frequency as V cav ∝ ω −3 g .After taking the volume scaling into account, we find that the sensitivity to h 0 is proportional to ω g , which degrades linearly at large frequencies.One might overcome this by using higher modes if the coupling coefficient for such modes does not decrease (discussed further below), though Projected Sensitivities of Axion Experiments FIG. 4. Projected sensitivity of axion experiments to high-frequency GWs, assuming an integration time of tint = 2 min for ADMX, HAYSTAC and CAPP, tint = 4 day for ORGAN, and tint = 1 day for the SQMS parameters.These integration times are characteristic of data-taking runs in each experiment.The GW-cavity coupling coefficient is fixed to ηn = 0.1 for each experiment, and the signal bandwidth ∆ν is conservatively fixed to the linewidth of the cavity.Dark (light) blue regions indicate the sensitivity at the lowest (highest) resonant frequency of the tunable signal mode.For ADMX [46,122,124], HAYSTAC [47], and CAPP [125], the signal mode is TM010, but for ORGAN [48] the signal mode is TM020.The system temperature Tsys defining the thermal noise floor of each experiment is given in the figure, along with relevant experimental parameters including the loaded cavity quality factor Q.
at very high mode numbers the Q factor will tend to decrease and mode-crossings make isolating the signal mode difficult.Alternatively, one could consider a multiplexing strategy with N cavities each of a fixed volume V cav , in which case the sensitivity would improve as 1/ √ N .Indeed, this sort of strategy is being pursued by ADMX for their small "sidecar" cavities [124].A similar approach could be implemented in multi-cell cavities of the type typically used for RF acceleration [126].
Although not the main focus of this study, we conclude this subsection with a brief discussion of stochastic GW signals and leave a more detailed investigation to future work.A stochastic GW background is described by the average strain power per unit frequency, i.e., the strain power spectral density S h (ω).For a stochastic GW background of cosmological origin, this determines the energy density in GWs per logarithmic frequency, normalized by the critical energy density today, as Ω g (ω g ) ∼ ω 3 g S h (ω g )/H 2 0 , where H 0 is the present-day Hubble expansion parameter.Such a non-coherent signal appears as an additional noise source in the detector, such that the SNR is given by the ratio of the signal and noise power spectral densities, independent of the integration time [53,127].For the experimental setup described here, this amounts to where η 2 stoch is the effective stochastic GW-cavity coupling coefficient.Although a stochastic signal does not resonantly excite the cavity, the SNR in Eq. ( 31) scales linearly with the quality factor since larger values of Q correspond to suppressed intrinsic thermal fluctuations.Experimental parameters similar to those adopted above lead to projected sensitivities that are cosmologically meaningless Ω g 1, although our setup may be applicable to stochastic sources of non-cosmological origin, such as populations of merging PBHs.FIG. 5. Geometry of a GW incident on a cylindrical cavity from an arbitrary direction in the yz-plane of the cavity.The angle between the GW direction and the cavity symmetry axis is β.The external B-field is rotated with respect to the cavity symmetry axis by an angle α.The GW propagation direction is ẑ , and we take the coordinates in the GW frame to be a rotation of the yz-plane by β.The x-axis is not shown.
B. Evaluation of the Coupling Coefficient
In the above estimates, we used an approximate value of the coupling coefficient, η n ∼ 0.1.In this subsection, we demonstrate that this is indeed a typical value for various mode choices in a cylindrical cavity, using the intuition gained from the selection rules of Sec.III to help identify optimally-coupled resonant modes.In a realistic setup, the only aspect of the geometry which we could hope to control is the relative orientation of the cavity axis and the applied magnetic field, which we denote by the angle α.The angle of the incoming GW with respect to the cavity axis is denoted by β.This is shown explicitly in the schematic illustration of the experimental setup in Fig. 5.For simplicity, the applied external magnetic field B 0 is taken to be coplanar with the GW wavevector and the cavity symmetry axis ẑ, but we will also discuss the more general case below.For concreteness, we take cavity dimensions of equal radius and length, R det = L det .
The resummed metric is given in Eq. ( 4) assuming a GW propagating along the ẑ-direction.In our calculations, we evaluate the effective current j eff assuming the GW is traveling along the ẑ direction, which we define as a rotation of the ẑ axis in the yz-plane by an angle β, as in Fig. 5.After determining the effective current in the cavity frame, we numerically evaluate the coupling coefficient η n , as in Eq. (22).Note that η n includes contributions from both azimuthal polarizations of the EM mode (added in quadrature), denoted as the ± modes mentioned at the beginning of Sec.III B (see Appendices A 2 and A 3).
Before explaining the structure of our numerical results in detail, let us consider the coupling of a GW to the cavity mode typically used for axion detection, TM 010 . 8This will enable us to gain some intuition as to why ADMX, HAYSTAC, and other axion experiments only need to re-analyze their existing data to set a limit on GWs, and in doing so why using the full resummed metric in the PD frame is necessary.The electric field component of the TM 010 mode is E 010 ∝ J 0 (r x 01 /R cav ) ẑ, where x 01 is the first root of the Bessel function J 0 (x).From the E * 010 • ĵ+,× integrand of the coupling coefficient in Eq. ( 22), it is clear that we need only consider the ẑ component of the effective current.Taking the orientation of the background magnetic field to be aligned with the cavity axis (α = 0, as is typical for p = 1 p = 2 axion experiments), and keeping only the first few terms in the long wavelength limit, we find ĵ× where we have switched from Cartesian to cylindrical coordinates.Using the above expression in Eq. ( 22), we see that the volume integral of the leading-order contribution to the coupling coefficient η 010 vanishes, owing to the integration of sin φ between 0 and 2π.However, the next-to-leading-order term contributes to even powers of sin φ in the integrand of Eq. ( 22), yielding η 010 > 0. If we had instead considered ĵ+ , then we would have obtained a non-zero result only by including even higher order terms.This example clearly shows that keeping the entire series of terms in j eff (and hence in the metric), rather than only the leading-order term in the expansion, is necessary to see that the TM 010 mode can be excited by the incoming GW.In Figs. 6 and 7, we numerically evaluate the coupling coefficients for various TE and TM modes, respectively.The plots are presented in polar coordinates, for simplicity taking the cavity axis, GW wavevector, and external B-field to be coplanar.The radial coordinate is the magnitude of η n and the azimuthal coordinate is the angle β of the GW with respect to the cavity axis (see Fig. 5).Each row shows a different m mode for a particular choice of GW polarization.In the left (right) columns we take the external B-field to be perpendicular (parallel) to the cavity symmetry axis.These results confirm that the typical value of η n for an optimally-coupled mode is O(0.1); we leave an exhaustive investigation of all possible modes and polarizations to future work.
The coupling coefficient is shown in Fig. 6 for various TE mnp modes, including the m = 2 TE modes that were discussed in Sec.III B. In particular, the bottom-right panel of Fig. 6 verifies that this is the only class of modes that couples to a GW when both the external B-field and GW wavevector are on-axis with the cavity (α = β = 0).This selection rule was derived previously from the spin-2 azimuthal dependence of the effective current in Eq. (24).We also investigate more general geometrical configurations in the remaining panels of Figs. 6 and 7, taking the external B-field and/or GW wavevector to be unaligned, but still coplanar, with the symmetry axis of the cavity (α, β = 0).In this case, the lack of cylindrical symmetry implies that a larger set of modes can optimally couple to GWs of various polarizations, while still obeying certain selection rules in the coplanar limit.For instance, the m = 0 TM mnp modes of Fig. 7 only couple to h × for the geometries shown.While such selection rules do not generally apply outside of the coplanar limit, these results illustrate the general fact that different modes have different sensitivities to h + and h × , potentially enabling the determination of the polarization of a putative GW signal.
An important point, evident from Figs. 6 and 7, is that different modes have different directional sensitivity.Therefore, if the direction of the GW source is constant over the measurement time, one can in principle spatially localize the GW source by looking at multiple modes, which may be possible if the signal arises from a compact object merger which is continuously scanning over frequencies (see Sec. IV).We leave a detailed examinization of a multi-cavity setup's ability to efficiently characterize GW properties (including the possible role of degeneracies between different polarizations and directions of propagation) to future work.
C. Coupling Coefficient in the Quasistatic Regime
More generally, we may also consider resonant conversion of GWs to EM fields with a lumped-element LC circuit, where, unlike a cavity, the resonant frequency of the circuit is not tied to the geometrical size of the detector.In this setup, the magnetic field volume can remain large, providing an increased sensitivity for low-frequency signals in the quasistatic limit ω g L det 1, where L det is the characteristic size of the experiment.9Indeed, this has already been demonstrated as a promising strategy to search for kHz-MHz axions with ABRACADABRA [72,[128][129][130], ADMX-SLIC [71,131], and DM Radio [50,132].
However, we briefly argue here that the GW-EM signal decouples much faster in the quasistatic limit than an axion signal, leading to poor sensitivities at lumped-element experiments.As we showed in Sec.III B, in the lowfrequency limit the GW effective current scales as j eff ∼ ω 2 g B 0 h L det , while as discussed in Sec.II A, the axion effective current scales as j eff ∼ ω a B 0 θ a .In the limit ω g L det 1, the GW effective current is therefore suppressed by an additional power of ω g L det compared to an equivalent axion signal with θ a ∼ h.For, e.g., ABRACADABRA-10cm with L det = 10 cm and ω g = 10 kHz, this amounts to a suppression of ∼ 3 × 10 −6 .That being said, this low-frequency suppression may in fact be a feature for transient signals in quasistatic experiments with broadband capabilities, since the signal strength of a frequency-scanning signal, such as a merger, would grow rapidly even for fixed strain, and could manifest as a chirp-like signal.This parametric suppression motivates considering alternative strategies for GW detection in the kHz-MHz range, including up-conversion of GWs in an oscillating EM background of a driven cavity [26][27][28][29][30][31][32][33], induced by either the GW-EM or mechanical-EM coupling.We will return to these possibilities in future work.
VI. OUTLOOK AND CONCLUSIONS
In this work, we have analyzed the interaction between GWs and EM fields.By consistently working in the proper detector frame, which is the reference frame relevant for laboratory experiments, we have shown that axion dark matter haloscope experiments have sensitivity to GHz-scale GWs and only need to reanalyze existing data to set the current best bound on such signals.A generic feature of these setups is that the detailed structure of the signal is strongly tied to the incoming direction and polarization of the GW.Thus, the use of multiple cavities or multiple readout modes of a single cavity may enable the ability to localize the source and determine the polarization of a tentative signal.We have identified sub-solar mass binary mergers and GW emission from superradiant boson clouds as two possible sources in the GHz range to which our setup could theoretically have some sensitivity, though the immediate prospects for detection are not strong.Throughout, we have focused predominantly on EM conversion of GWs in a static background B-field using resonant cavity readout, since the signal is parametrically suppressed by ω g L det 1 for experiments targeting much lower frequencies.Along these lines, we have noted that most axion experiments designed for lower frequency signals are not favorable for GW detection.
There is, however, at least one important exception to this parametric statement.For instance, using microwave cavities pumped with an oscillating B-field considerably improves the low-frequency scaling of the signal.This technique was proposed to detect the mechanical signal induced by GWs through the vibration of the cavity walls in Refs.[25][26][27][28][29][30][31][32][33].A similar concept was subsequently applied to the EM signals generated by axion dark matter in Refs.[133][134][135][136].In a future companion paper, we will extend previous studies to include the direct GW-EM coupling with an oscillating background field, which gives rise to a visible signal also in the idealized case where the cavity is completely isolated from external vibrations.It would also be interesting to compare the generic sensitivity of such a heterodyne detection scheme to the sensitivity of interferometers such as LIGO, extrapolated into the kHz-MHz regime.More generally, we plan to explore the applicability of other axion experimental setups to GW detection, such as those planned for broadband readout at high frequencies [137].
A wealth of precious information on the fundamental laws of Nature is encoded in GWs spanning orders of magnitude in frequency and strain.The high-frequency regime, well above known astrophysical sources, is particularly interesting to extract information on early times (and extremely high energies) in the history of the Universe.The interactions of GWs with electromagnetism have long been proposed as a possible avenue towards detection in this frequency regime.In this work, we have further fleshed out details of this approach, leveraging cutting-edge advances in high-Q cavity technology, and we have set the foundations to study future experimental setups that can target this important new frontier in GW detection.
When going from Eq. (A31) to Eq. (A32) we have used that the B-field fulfills Maxwell's equations and we have assumed that we are on resonance, where ω ≡ ω g is the resonance frequency of the solenoidal cavity mode that we consider.In the second step (Eq.(A32) to Eq. (A33)) we have used that ∇ × E (1) • ∇ × E (1) * = ijk ∂ j E (1) k ilm ∂ l E (1) m * PI = − ijk ilm E (1) m * ∂ l ∂ j E k + ijk ilm ∂ l E (1) m * ∂ j E (1) k = E (1) * • ∇ × ∇ × E (1) + ∇ • E (1) * × (∇ × E (1) ) where we have used a partial integration (PI) by going from the first to the second equation.Finally when going from Eq. (A33) to Eq. (A34) we used ∇ × ∇ × E (1) = ω 2 E (1) for a solenoidal mode; here S is the surface of the cavity.Furthermore we used Gauss's theorem.In the last step we used that on the surface of a perfect conductor dS is parallel to E (1) and therefore the last term vanishes.
To summarize, the total energy that is stored in the cavity and due to the interaction with GWs is: In the case that E (1) is the sum of two E ± modes, cf.Eq. (A11) to Eq. (A16), W (2) is the squared sum of both contributions since E ± modes are orthogonal: B g I B n e I U 3 T 3 s v 3 r v 3 M W t d 8 v K Z A / g D 7 / M H 8 o W Q g A = = < / l a t e x i t > GW < l a t e x i t s h a 1 _ b a s e 6 4 = " M z A 0 y 0 Y 8 r 7 U O t y B x o 9 B B 2 k N T K V I = " > A A A B 8 3 i c b Z D L S g M x F I b P 1 F u t t 6 p L N 8 E i u C o z o u i y 6 M Z l B X u B z l A y a d q G 5 j I k G W k Z + h p u X C j i 1 p d x 5 9 u Y t r P Q 1 h 8 C H / 8 5 h 3 P y x w l n x v r + t 1 d Y W 9 / Y 3 C p u l 3 Z 2 9 / Y P y o d H T a N S T FIG.1.A cartoon illustrating the differences between GW-EM conversion (left) and axion-EM conversion (right) in the presence of an external magnetic field B0.The GW effective current is proportional to ωghB0, with a direction dependent on the GW polarization and a typical quadrupole pattern, yielding a signal field with amplitude hB0.The axion effective current is proportional to ωaθaB0, with a direction parallel to the external field B0, yielding a signal field with amplitude θaB0.The differing geometry of the effective current yields different selection rules for coupling the GW and axion to cavity modes.
5 B u 5 R s m m 1 D k 8 2 S Z I t l 6 T / x 4 k E R r / 4 T b / 4 b 0 3 Y P 2 v p g 4 P H e D D P z w o Q z b T z v 2 y m s r W 9 s b h W 3 S z u 7 e / s H 7 j b / i x o U i b t 2 6 8 2 + c t F l o 6 4 E L h 3 P u 5 d 5 7 / J h R q S z r 2 1 h a X l l d W y 9 t l D e 3 t n d 2 z b 3 9 t o w S g U k L R y w S X R 9 J w i g n L U U V I 9 1 Y E B T 6 j H T 8 0 U 3 u d 8 Z E S B r x B z W 5 C X 3 d m Z 8 p 5 7 1 c / M / r J S q 4 c l P K 4 0 Q R j m e L g o R B F c E 8 H N i n g m D F J p o g L K i + F e I h E g g r H W F Z h 2 D P v 7 x I 2 m c 1 + 6 J m 3 Z 9 X 6 o 0 i j h I 4 B E e g C m x w C e r g F j R B C 2 D w C J 7 B K 3 g z n o w X 4 9 3 4 m L U u G c X M A f g D 4 / M H b N m b n Q = = < / l a t e x i t > @t B0 = O(h) < l a t e x i t s h a 1 _ b a s e 6 4 = " U m M 5 R M 4 Z J p M B 9 f c F b n H f n Y 9 a 6 5 B Q z B + A P n M 8 f P 0 y W 0 A = = < / l a t e x i t > Transformation: < l a t e x i t s h a 1 _ b a s e 6 4 = " u a K h e c w + v f U d v c m F z n H z 9 R 3 l w u 0 = " > A A A B 7 3 i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B U 0 l E 0 W O p F 4 8 V b C 2 0 o W y 2 k 3 b p Z h N 3 N 4 U S + i e 8 e F D E q 3 / H m / / G b Z u D t j 4 Y e L w 3 w 8 y 8 I B F c G 9 f 9 d g p r 6 x u b W 8 X t 0 s 7 u 3 v 5 B + f C o p e N U M W y y W M S q H V C N g k t s G m 4 E t h O F N A o E P g a j 2 5 n / O E a l e S w f z C R B P 6 I D y U P O q L F S u z t G R u o 9 t 1 e u u F V 3 D r J K v J x U I E e j V / 7 q 9 m O W R i g N E 1 T r j u c m x s + o M p w J n J a 6 q c a E s h E d Y M d S S S P U f j a / d 0 r O r N I n Y a x s S U P m 6 u + J j E Z a T 6 L A d k b U D P W y N x P / 8 z q p C W / 8 j M s k N S j Z Y l G Y C m J i M n u e 9 L l C Z s T E E s o U t 7 c S N q S K M m M j K t k Q v O W X V 0 n r o u p d V d 3 7 y 0 q t n s d R h B M 4 h X P w 4 B p q c A c N a A I D A c / w C m / O k / P i v D s f i 9 a C k 8 8 c w x 8 4 n z 8 Z G I 9 Z < / l a t e x i t > B0 < l a t e x i t s h a 1 _ b a s e 6 4 = " u a K h e c w + v f U d v c m F z n H z 9 R 3 l w u 0 = " > A A A B 7 3 i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B U 0 l E 0 W O p F 4 8 V b C 2 0 o W y 2 k 3 b p Z h N 3 N 4 U S + i e 8 e F D E q 3 / H m / / G b Z u D t j 4 Y e L w 3 w 8 y 8 I B F c G 9 f 9 d g p r 6 x u b W 8 X t 0 s 7 u 3 v 5 B + f C o p e N U M W y y W M S q H V C N g k t s G m 4 E t h O F N A o E P g a j 2 5 n / O E a l e S w f z C R B P 6 I D y U P O q L F S u z t G R u o 9 t 1 e u u F V 3 D r J K v J x U I E e j V / 7 q 9 m O W R i g N E 1 T r j u c m x s + o M p w J n J a 6 q c a E s h E d Y M d S S S P U f j a / d 0 r O r N I n Y a x s S U P m 6 u + J j E Z a T 6 L A d k b U D P W y N x P / 8 z q p C W / 8 j M s k N S j Z Y l G Y C m J i M n u e 9 L l C Z s T E E s o U t 7 c S N q S K M m M j K t k Q v O W X V 0 n r o u p d V d 3 7 y 0 q t n s d R h B M 4 h X P w 4 B p q c A c N a A I D A c / w C m / O k / P i v D s f i 9 a C k 8 8 c w x 8 4 n z 8 Z G I 9 Z < / l a t e x i t > B0 < l a t e x i t s h a 1 _ b a s e 6 4 = " m z m 4 5 g o p n 7 K y J d r D G x r r a s K y G c j j x L y k f 5 8 C Q f 3 B z n C h e T O j K w B / t w C C G c Q g G u o Q g l I P A I z / A K b 9 6 T 9 + K 9 e x / j 0 T l v s r M D f + B 9 / g B i D 5 d a < / l a t e x i t > GW: Riemann tensor < l a t e x i t s h a 1 _ b a s e 6 4 = " k 1 9 A 7 2 Z m L + Y E q q a T v + f j v n E s I Y I = " > A A A C L 3 i c b Z D L S s N A F I Y n 9 V b r r e r S z W |j e↵ | |j e↵ | ⇠ O(1) < l a t e x i t s h a 1 _ b a s e 6 4 = " 9 s e C l l f 1 N X 5 q P D x h j r L h s D i i G 0 0 = " > A A A C K 3 i c b Z D L S g M x F I Y z 9 V b r r e r S T b A I d V N m R N F l q R t 3 V r A X 6 J Q h k 8 m 0 o U l m S D J C m c 7 7 u P F V X O j C C 2 5 9 D z N t F 9 r 6 Q + D n O + e Q c 3 4 / Z l R p 2 / 6 w C i u r a + s b x c 3 S 1 v b O 7 l 5 5 / 6 C t o k R i 0 s I R i 2 T X R 4 o w K k h L U 8 1 I N 5 Y E c Z + R j j + 6 z u u d B y I V j c S 9 H s e k z 9 F A 0 J B i p A 3 y y g 0 3 l A i n b k C Y R n A C G 5 7 L k R 5 K n t r Z J E s X A X Q V 5 X B K M G L p b V Y d n n r l i l 2 z p 4 L L x p m b C p i r 6 Z V f 3 C D C C S d C Y 4 a U 6 j l 2 r P s p k p p i R r K S m y g S I z x C A 9 I z V i B O V D + d 3 p r B E 0 M C G E b S P K H h l P 6 e S B F X a s x 9 0 5 l v q R Z r O f y v 1 k t 0 e N V P q Y g T T Q S e f R Q m D O o I 5 s H B g E q C N R s b g 7 C k Z l e I h 8 i E p 0 2 8 J R O C s 3 j y s m m f 1 Z y ωg/2π ∈ [0.65, 1.02] GHz Q ∼ 8 × 10 4 , B 0 = 7.5 T Vcav = 136 L, Tsys ∼ 0.6 K ωg/2π ∈ [5.6, 5.8] GHz Q ∼ 3 × 10 4 , B 0 = 9 T Vcav = 2 L, Tsys ∼ 0.13 K ωg/2π ∈ [1.6, 1.65] GHz Q ∼ 4 × 10 4 , B 0 = 7.3 T Vcav = 3.47 L, Tsys ∼ 1.2 K ωg/2π = 26.531GHz Q ∼ 1.3 × 10 4 , B 0 = 7 T Vcav ∼ 0.0078 L, Tsys ∼ 4 K ωg/2π ∈ [1, 2] GHz Q ∼ 10 6 , B 0 = 5 T Vcav = 100 L, Tsys ∼ 1 K
FIG. 6 .
FIG.6.The GW-cavity coupling coefficient ηmnp (the radial component in the polar plane) as a function of the angular direction of the GW propagation (β) in degrees, for various TE modes and GW polarizations.The notation for the mode index is defined in Eqs.(A11)-(A13).Left: the external B-field is orthogonal to the cavity symmetry axis (α = π 2 ).Right: the external B-field is aligned with the cavity symmetry axis (α = 0).
FIG. 7 .
FIG.7.The GW-cavity coupling coefficient ηmnp (the radial component in the polar plane) as a function of the angular direction of the GW propagation (β) in degrees, for various TM modes and GW polarizations.The notation for the mode index is defined in Eqs.(A11)-(A13).Left: the external B-field is orthogonal to the cavity symmetry axis (α = π 2 ).Right: the external B-field is aligned with the cavity symmetry axis (α = 0). | 19,664.4 | 2021-12-21T00:00:00.000 | [
"Physics"
] |
Cluster-randomized controlled trial of the effects of free glasses on purchase of children's glasses in China: The PRICE (Potentiating Rural Investment in Children's Eyecare) study
Background Offering free glasses can be important to increase children’s wear. We sought to assess whether “Upgrade glasses” could avoid reduced glasses sales when offering free glasses to children in China. Methods In this cluster-randomized, controlled trial, children with uncorrected visual acuity (VA)< = 6/12 in either eye correctable to >6/12 in both eyes at 138 randomly-selected primary schools in 9 counties in Guangdong and Yunnan provinces, China, were randomized by school to one of four groups: glasses prescription only (Control); Free Glasses; Free Glasses + offer of $15 Upgrade Glasses; Free Glasses + offer of $30 Upgrade Glasses. Spectacle purchase (main outcome) was assessed 6 months after randomization. Results Among 10,234 children screened, 882 (8.62%, mean age 10.6 years, 45.5% boys) were eligible and randomized: 257 (29.1%) at 37 schools to Control; 253 (28.7%) at 32 schools to Free Glasses; 187 (21.2%) at 31 schools to Free Glasses + $15 Upgrade; and 185 (21.0%) at 27 schools to Free Glasses +$30 Upgrade. Baseline ownership among these children needing glasses was 11.8% (104/882), and 867 (98.3%) children completed follow-up. Glasses purchase was significantly less likely when free glasses were given: Control: 59/250 = 23.6%; Free glasses: 32/252 = 12.7%, P = 0.010. Offering Upgrade Glasses eliminated this difference: Free + $15 Upgrade: 39/183 = 21.3%, multiple regression relative risk (RR) 0.90 (0.56–1.43), P = 0.65; Free + $30 Upgrade: 38/182 = 20.9%, RR 0.91 (0.59, 1.42), P = 0.69. Conclusions Upgrade glasses can prevent reductions in glasses purchase when free spectacles are provided, providing important program income. Trial registration ClinicalTrials.gov Identifier: NCT02231606. Registered on 31 August 2014.
Introduction Under-corrected refractive error (URE) accounts for 90% of visual disability among rural Chinese children [1][2][3][4][5][6], and among the 13 million children in the world visually impaired from URE, some half live in China [7]. Despite the fact that glasses wear is a safe and effective means of correcting refractive error [8], and is associated with significant, trial-proven increases in educational outcomes [9], only 15-20% of Chinese children in rural [9,10] and urban migrant [11,12] population studies who need glasses have them.
Various explanations exist for this situation [13]. Many stakeholders, including children, families and teachers, believe incorrectly that wearing glasses will harm children's eyes [14,15], despite randomized trial evidence to the contrary [8]. The quality of available glasses in rural China is poor: half of children wearing glasses have a power inaccurate by > 1 diopter [16], while two-thirds of rural refractionists practicing in private optical shops have a high school education or less [17].
Cost of glasses also remains a critical barrier: providing free spectacles more than doubled the rates of use 6 months later, compared to providing prescriptions alone [9]. By contrast, educational interventions alone, without free glasses, have been un-successful in increasing rates of wear [18]. However, providing free glasses may not be sustainable. School vision screening programs needed to identify children requiring glasses depends on profits from glasses sales for entities such as rural county hospitals in order to sustain them. Large-scale government programs providing free glasses would be likely to drive such practitioners out of business. A model combining the advantages of free glasses (lack of financial barriers) and glasses sales (sustainability) is needed.
We carried out a cluster-randomized, controlled trial in rural Guangdong and Yunnan Provinces, China, to evaluate the effect of providing "upgrade spectacles" (having stylish designs and scratch-free coatings) on the purchase (main outcome) and wear (secondary outcome) of spectacles among primary school children. We hypothesized that providing free glasses would reduce spectacle purchase, but that the offer of upgrade spectacles for sale at the point of distribution at county hospitals would prevent this reduction, that is, rates of spectacle purchase would not differ between the Control and two Upgrade groups.
Ethics, consent and permissions
This study was approved by the institutional review boards at the Zhongshan Ophthalmic Center (Guangzhou, China) and Yunnan Red Cross Hospital (Kunming, China). Permission was received from local boards of education in each region and the principals of all schools. Written informed consent was obtained from at least one parent of all participating children.
The presented data are anonymized and risk of identification is low. The principles of the Declaration of Helsinki were followed throughout.
Trial design
This was a cluster-randomized, investigator-masked, controlled trial.
Setting, sampling and eligibility criteria
The study was carried out in Guangdong and Yunnan Provinces, China. Guangdong ranked in the top third (9 th ) among China's 31 administrative divisions in per capita Gross Domestic Product in 2014 (US$ 10,330), while Yunnan was 29 th (US$4438) [19]. We selected 9 counties or county-level cities, five from Yunnan and four from Guangdong, on the basis of having a County-level hospital capable of providing refractive services and willing to participate in the study. All of these hospitals had comparable levels of capacity to refract and dispense glasses due to their current or previous involvement in programs with international non-government development organizations. Spectacles were available for purchase from other, non-study sources in all 9 counties, but no other free spectacle programs were on-going in these counties during the study. We obtained a list of all 601 primary schools (362 in Guangdong and 239 in Yunnan) in the sample counties from local bureaus of education. Bureau officials also provided information on the number of classes in each school and the number of students per class. For logistical reasons we excluded those schools with average class sizes <20 or >60 students (19% of the sample frame). These criteria were adopted because screening at larger schools could not be reliably completed in a day, which would have interfered with the screening schedule, and smaller schools would be expected to have <7 children requiring glasses, the minimum number required in our power calculations. From the list of 601 schools, we randomly selected 107 (57 schools in Guangdong and 50 in Yunnan), with the number of schools selected in each county being determined by population size.
At the time of our initial screening visit to all schools, we discovered the prevalence of refractive error was lower than expected, requiring an increase in the number of schools in order to achieve adequate power for the study. An additional 31 schools were randomly selected as above, for a total of 138 schools (88 in Guangdong and 50 in Yunnan). Within each sampled school, we randomly selected one class in each of the fourth and fifth grades (likely age range 9-12 years), if there was more than one class per grade level.
Visual acuity assessment
Children underwent baseline visual acuity screening at school by two trained volunteers. Visual acuity was tested separately for each eye without refraction at four m using early treatment diabetic retinopathy study charts [20] (Precision Vision, La Salle, IL) in a well-lighted, indoor area. If children correctly identified the orientation of at least four of five optotypes on the 6/60 line, they were examined on the 6/30 line, then the 6/15 line, and then line by line to 6/3. We defined visual acuity for an eye as the lowest line on which four of five optotypes were read correctly. If the top line could not be read at four m, the participant was tested at one m and the measured visual acuity was divided by four.
Refraction
Children with uncorrected visual acuity 6/12 in either eye underwent cycloplegia with up to three drops of cyclopentolate 1% in each eye after anesthesia with topical proparacaine hydrochloride 0.5%. Children then underwent automated refraction (Topcon KR 8900, Tokyo, Japan) with subjective refinement by an experienced optometrist. Participating optometrists were from Zhongshan Ophthalmic Center in Guangdong and the Second People's Hospital in Yunnan, both tertiary referral facilities, and all had extensive experience in the refraction of children. Children of parents refusing permission for cycloplegia (274/882 = 31.1%) underwent subjective refinement of the non-cycopleged value from the auto-refractor by an experienced optometrist in each eye using a target at four meters distance.
Children in selected classes were eligible for the study if they met the following criteria: • Uncorrected (without glasses) visual acuity of 6/12 in either eye; • Refractive error in a range previously demonstrated to be associated with significantly greater improvement with visual acuity when corrected: myopia −0.75 diopters (D), hyperopia !2.00 D, or astigmatism (non-spherical refractive error) !1.00 D [21]; • Visual acuity could be improved to >6/12 in both eyes with glasses.
Questionnaires
At baseline (September 2014, beginning of the school year), enumerators administered questionnaires to children, including questions on race (Han versus various minority groups), age, sex, glasses wear, awareness of refractive status, belief that wearing glasses harms children's vision, parental living condition and education, and ownership of a list of 16 selected items as an index of family wealth. At endline (June 2015, end of the school year), questionnaires were administered on glasses ownership, glasses wear, parental attitude toward wearing glasses and subjective evaluation of project glasses. All questionnaires used in the current study have been validated by our research team in previous publications [8,9].
Randomization and interventions
This was a cluster-randomized, controlled trial, with schools as the clusters (Fig 1).
In October 2014, after the baseline survey and vision screening but before refraction, eligible children were randomized by school to receive one of the following four interventions: • A glasses prescription and letter to the parents informing them of the refractive status of their child. (Control group: 42 schools assigned, 4 schools eliminated in Yunnan due to lack of eligible students, leaving 38 schools.) These children received free spectacles at the end of the trial, although this was not previously announced. Families could elect to purchase glasses at study hospitals or elsewhere if they wished during the study.
• Vouchers bearing the child's name, school, and refractive power in each eye, exchangeable for free glasses at the local county hospital. (Free group; 32 schools) • Vouchers exchangeable for free glasses at the local county hospital, where "upgrade glasses" (with scratch-proof lenses and popular designs based on previous research [22] on the style preferences of Chinese children) were also offered for sale to study participants at a price of US$15. (Free + $15 Upgrade group; 32 schools assigned, 1 school eliminated in Yunnan due to lack of eligible students, leaving 31 schools).
• Vouchers for free glasses at the county hospital, where upgrade glasses identical to those above were also offered, at a price of US$30. (Free + $30 Upgrade group; 32 schools assigned, 4 schools eliminated in Yunnan due to lack of eligible students, leaving 28 schools).
The figures of $15 and $30 (25 th and 75 th percentiles respectively of the amount paid for glasses in a previous study of glasses wear in rural China [9]) were selected as typical for the area. Vouchers were color-coded by study group and valid only at study hospitals, so that families were offered only the spectacle selection appropriate for their allocated study group. Randomization was carried out to allocate all but ten schools. These remaining ten schools were all allocated to the control group, in order to maximize power and minimize the accumulated probability of type II error [23,24]. Our study hypothesis was that providing free glasses would reduce spectacle purchase, but that the offer of upgrade spectacles would prevent this reduction, that is, rates of spectacle purchase would not differ between the Control and two Upgrade groups.
County hospitals were located at a median distance of 27 km (Guangdong: Range 3-63 km; Yunnan: Range 4-113 km) from the children's township of residence. Schools were stratified by three variables, information on which was collected during baseline vision screening: county; the total number of students in grades four and five; and the number of students failing vision screening in grades four and five. Stratification and randomization were carried out by an investigator (XM) at a central location (Stanford University, Stanford, CA) using R software (R Foundation for Statistical Computing, Vienna, Austria). Participants (students, parents, and teachers) and enumerators were not informed of either the overall design of the study or the explicit treatment arm assignment. Participants were told only that this was a study of vision care among rural, school aged children.
Assessment of outcomes
Purchase of glasses (main outcome): Records at the participating county hospitals were used to determine family's acceptance of free glasses and selection of upgrade glasses (where provided) given by the study within each group. Children's self-report on questionnaires at the endline examination provided data on purchase of spectacles outside of the study.
Wear of glasses (Secondary outcome): At closeout, spectacle wear was assessed through unannounced direct examinations, with only those children actually wearing their glasses qualifying. Study staff were unaware of the spectacle designs offered in the different groups, and were masked to group assignment.
Sample size and power
Power calculations were performed using Optimal Design software (http://sitemaker.umich. edu/group-based/optimal_design_software) for cluster-randomization and binary outcome (purchase vs non-purchase, wear vs non-wear). We determined that a sample size of 108 schools (27 per group) with a minimum of seven eligible students per school conferred 80% power, with an α of 0.05, intraclass correlation of 0.15 (based on our previous similar studies), and explained variation by covariates (R2) of 0.50, to detect a difference of 7.5% in eyeglasses purchase and wear rates between intervention arms and the control group. As noted above, the figure of 7 children per school was based on the refractive error prevalence encountered in our previous studies, and the true number per school was closer to 6. We calculated an additional 31 schools were needed to confer the above power under the same assumptions given this smaller number of myopic students per school.
Statistical methods
Results were presented as mean (SD, standard deviation) for continuous data and frequency (percentage) for categorical data. Baseline wear of glasses was defined as having glasses at school, having been told previously to bring them. We calculated family wealth by summing the value, as reported in the China Rural Household Survey Yearbook (Department of Rural Surveys, National Bureau of Statistics of China, 2013), of household items owned by the family from a previously-defined list of 13 common objects.
Refractive power was defined throughout as the spherical equivalent, that is, the spherical power plus half the cylindrical power. In view of the relatively high rate of parental refusal for cycloplegia, various baseline characteristics were compared between children with and without cycloplegic refraction, using linear regression for continuous variables, logistic regression for binary variables, multinomial logistic regression for nominal categorical variables and ordinal logistic regression for ordinal variables, all with adjustment for cluster effects within schools.
Generalized linear models with Poisson regression were used to estimate the relative risk by intervention arms for purchase and wear of glasses. All variables significant at the p< = 0.2 level in simple regression models were included in the multiple regression model. Regression analyses were performed separately for all children, and only including children undergoing cycloplegic refraction. Statistical analyses were performed using a commercially available software package (Stata 13.1, StataCorp, College Station TX, USA).
To satisfy the requirements of intention to treat analysis that all randomized participants should be included in analyses, we used multiple imputation in Stata to carry out the imputation of missing data [25], selecting the independent variables based on predictive value and availability of data: family wealth (n = 4), having friends wearing glasses (n = 13), purchase of glasses (n = 15) and wear of glasses (n = 15). We used logistic regression for binary variables, ordinal logistic regression for ordinal variables, and multinomial logistic regression for nominal variables. The multiple imputation approach created 20 copies of the data in which missing values were imputed by chained equations [25]. Final results were obtained by averaging these 20 datasets using Rubin's rules, which ensured that the standard errors for all regression coefficients took into account uncertainty in the imputations, as well as uncertainty in the estimation [25].
Results
Fig 1 details the enrollment and progression of children through the study. Among 882 children allocated to the four study groups and analyzed here, 608 (68.9%) received parental consent for cycloplegic refraction. Acceptance of cyclopegia was a higher in Yunnan (149/ 182 = 81.4%) than Guangdong (459/700 = 65.6%, P = 0.01), but children undergoing cycloplegia did not differ significantly by other baseline characteristics, including group assignment, from children who did not (data not shown). Children of families refusing cycloplegia underwent subjective refinement by an experienced refractionist of the power provided by automated refraction, and are included in all analyses. Table 1 gives the baseline demographic and clinical information, as well as other potential predictors of spectacle purchase and wear, for each of the four study groups. The mean (SD) age among all eligible children was 10.6 (1.0) years, 45.5% (401/882) were boys, and these characteristics varied little across groups. Only 11.8% (104/882) of these children, all of whom would benefit visually from spectacle wear, actually owned glasses at baseline. Refractive error was < = -2.0 D (that is, more myopic than -2.0D) in 36.6% (323/882), and the uncorrected visual acuity was < 6/18 in the better-seeing eye among 35.3% (311/882). Roughly equal numbers of parents had out-migrated to seek work (17.5%, 154/882) and wore glasses (19.5%, 172/ 882). (Table 1) Six month follow up was completed by 867 (98.3%) of children, and no group had lower than 97% follow-up. (Fig 1) The correct intervention as allocated was received by 99.2% Table 2) Significant predictors of having purchased spectacles in multiple regression models included: membership in the Free Glasses group (significantly reduced purchase: Relative Risk [RR] = 0.54, 95% Confidence Interval [95% CI] 0.34, 0.87, P = 0.01); Yunnan residence (significantly increased purchase: RR = 1.67, 95% CI 1.13, 2.45, P = 0.010); and studying for more than two hours per day (significantly increased purchase: RR = 1.65, 95% CI 1.07, 2.53, P = 0.02). Membership in the two Free + Upgrade groups, wearing glasses at baseline, uncorrected visual acuity and family wealth were unassociated with glasses purchase in the multivariate model. (Table 3).
Significant predictors of observed glasses wear at endline in multiple models included wearing glasses at baseline (increased wear: RR = 3.01, 95% CI 2.32, 3.89, P < 0.001) and uncorrected visual acuity (children with better visual acuity were less likely to wear glasses: RR = 0.24, 95% CI 0.11, 0.50, P < 0.001). Parental education and glasses wear, both parents being away from home the majority of the time, ownership of glasses by friends, and family wealth were unassociated with glasses wear in the multivariate models, though several of these were significantly associated in univariate analyses. (Table 4) Sensitivity analyses were performed excluding children undergoing non-cyclopegic refraction with adjustment by the refractionist, and our main study findings were unchanged (data not shown).
Discussion
As hypothesized, providing free glasses in this trial did significantly reduce purchase in the Free Glasses group (12.7% rate of purchase versus 23.6% among Controls who received no free glasses), but offering the opportunity to purchase upgrade glasses negated this effect (21.3% and 20.9% rates of purchase in the two Upgrade groups). At this price range of US$15-30 (chosen as the interquartile range of price paid for glasses in our previous studies) [9], demand for glasses was relatively inelastic. The results of this trial have important implications for spectacle programs: evidence suggests that free glasses can significantly increase rate of wear [9,26], but without the potential for glasses sales, these programs are likely to be unsustainable. This trial suggests that offering free glasses need not undercut sales. In China, for example, distribution of free spectacles by the government might go forward without undermining the profitability of spectacle sales by local hospitals, needed to support school screenings to identify children with refractive error. It is particularly encouraging in this context that rates of purchase (40%) were actually significantly higher in Yunnan, one of China's poorest provinces, when compared to far richer Guangdong. Further research is needed to calibrate cost versus demand curves in order to maximize income without reducing adherence. Observed spectacle wear rates in this setting were low (23.2% at endline even with provision of free spectacles). This is comparable with our previous results using the identical protocol, among similar-aged children in Shaanxi (19.5%) and Gansu (16.8%) [9]. In part, this is due to our choice of a conservative definition of spectacle wear, only counting those children observed to have glasses on their face at the time of an un-announced examination. This almost certainly under-estimated true rates of wear among children, but was felt to be more reliable than asking children about their own glasses use, and more practical than asking teachers to record wear over time. The principal goal of the current study was to better understand factors impacting on spectacle purchase and not wear, particularly the use of upgrade glasses. Our recent trial in urban migrant communities in eastern China [12] has already demonstrated that teacher incentives offer an effective means of optimizing children's long-term spectacle use in the classroom, achieving wear in nearly three-quarters of children over the course of a school year. Had such interventions been used in the current study, it is likely that wear rates would have been higher.
Strengths of this study include its randomized controlled design, population-based sampling in the selected areas, high rates of follow-up and of accurate implementation of interventions, programmatically relevant choice of county hospital as distribution points for spectacles and the inclusion of both rich and poor provinces. Weaknesses include having chosen only counties in two provinces where local hospitals interested to take part in the study could be found, which may limit generalizability to other regions of China. Further, we did not attempt in the current paper to calculate the proportion of program costs which sale of upgrade spectacles might support in these settings, which may be valuable to attempt in the future. A proportion of children underwent non-cyclopegic refraction, due to their parents failing to give permission for cycloplegia. These children had their automated refraction values adjusted by experienced refractionists using targets at a distance of 4 meters in order to remove the effects of accommodation. An alternative might have been to use retinoscopy with a distant target to reduce the effects of instrument accommodation, but this technique is not widely used in rural China and was not practical under the circumstances. Sensitivity analyses showed that the impact on our conclusions of using non-cycloplegic refraction on some children appears to have been minimal. Finally, the study was not designed to explore in depth the economic models employed by optical shops in these areas.
We searched PubMed in April 2014, using the terms "refractive error" and "myopia," crossindexed with "glasses" and "spectacles," and "sale, "purchase" and "distribution" for articles published in any language since Jan 1, 1970. We found no previous randomized trials designed to examine the effect of providing free glasses on families' purchase of children's spectacles. Previous trials in China [9], Tanzania [13] and India [27] have shown that providing free spectacles increases rates of wear significantly, when compared to providing prescriptions and depending on families to purchase glasses themselves. Other hybrid pricing models have been examined in non-trial settings, including a study in Timor-Leste [28] demonstrating that cross-subsidization could cover most costs of a rural spectacle program.
Conclusions
The PRICE model of "free glasses for all with an optional upgrade" may be an important one for China and other countries with a high prevalence of refractive error and a growing middle class, where spectacle sales may potentially be important to sustain programs of distribution. | 5,538.4 | 2017-11-21T00:00:00.000 | [
"Economics",
"Medicine"
] |
Riboregulators: Fine-Tuning Virulence in Shigella
Within the past several years, RNA-mediated regulation (ribo-regulation) has become increasingly recognized for its importance in controlling critical bacterial processes. Regulatory RNA molecules, or riboregulators, are perpetually responsive to changes within the micro-environment of a bacterium. Notably, several characterized riboregulators control virulence in pathogenic bacteria, as is the case for each riboregulator characterized to date in Shigella. The timing of virulence gene expression and the ability of the pathogen to adapt to rapidly changing environmental conditions is critical to the establishment and progression of infection by Shigella species; ribo-regulators mediate each of these important processes. This mini review will present the current state of knowledge regarding RNA-mediated regulation in Shigella by detailing the characterization and function of each identified riboregulator in these pathogens.
INTRODUCTION
Shigella are bacterial pathogens highly adapted for colonizing the human gut, a process that is facilitated by their unique lifestyle. The bacteria are passed from host to host via the fecal oral route of transmission. After surviving the acidic environment of the stomach, Shigella species travel the length of the intestinal tract to the site of infection at the colonic epithelium (Jennison and Verma, 2003). Once at the colon, Shigella transverse the colonic epithelium by passage through M-cells and are subsequently presented to, and engulfed by, macrophages. Once inside the macrophage, Shigella species induces lysis of the phagocytic cell, releasing the bacteria to the basal-lateral surface of the epithelium. (Wassef et al., 1989) Next, Shigella invade human intestinal epithelial cells using a type three secretion system (TTSS) and begin to replicate within the eukaryotic cytoplasm. (Schroeder and Hilbi, 2008) Finally, the bacteria utilize host actin to spread from one eukaryotic cell to the next, a process that destroys intestinal epithelial cells thus contributing directly to the development of symptoms of a Shigella infection, namely bloody diarrhea (Jennison and Verma, 2003;Schroeder and Hilbi, 2008). The gene encoding any factor that directly or indirectly facilitates the ability of Shigella species to complete one or more process essential for pathogenesis must themselves be considered virulence-associated genes.
To establish and progress an efficient infection, Shigella species precisely regulate the expression of virulence-associated genes in response to specific environmental conditions encountered within the host; a collection of complex processes in which regulatory RNA molecules play critical, and ever increasingly recognized roles (Figure 1). Their ability to mediate a rapid, specific response makes riboregulators ideal molecules to mediate the regulation of virulence-associated gene expression in response to changes within a pathogen's micro-environment. Riboregulators characterized thus far in Shigella include several regulatory small RNAs (sRNAs) and one RNA thermometer (Murphy and Payne, 2007;Giangrossi et al., 2010;Gore and Payne, 2010;Africa et al., 2011;Tran et al., 2011;Broach et al., 2012;Kouse et al., 2013). Despite the fact that they function to regulate the expression of different target genes and that they utilize a variety of molecular mechanisms, all riboregulators described in Shigella to date share two important features; (1) they each respond, directly or indirectly, to changes in specific environmental conditions, and (2) they all are nestled within large regulatory networks that impact pathogenesis (Table 1 and Figure 1). This review will examine all characterized riboregulators in Shigella, with special emphasis placed on a discussion of how each was discovered, as well as their functions and impact on pathogenesis.
CsrB AND CsrC
Two sRNAs which are important regulatory molecules for carbon metabolism in E. coli are the carbon storage regulators CsrB and CsrC (Liu et al., 1997;Romeo, 1998;Weilbacher et al., 2003). CsrB and CsrC belong to a unique class of sRNAs which bind and sequester multiple copies of their target protein to inhibit its activity (Liu et al., 1997;Romeo, 1998;Weilbacher et al., 2003). In this case, CsrB and CsrC bind to and inhibit CsrA, a protein that promotes the production of other proteins necessary for glycolysis while inhibiting the production of proteins required for gluconeogenesis (Romeo et al., 1993;Sabnis et al., 1995;Yang et al., 1996;Liu et al., 1997;Weilbacher et al., 2003). CsrA also indirectly up-regulates the production of CsrB and CsrC through the UvrY/BarA two-component system, thus regulating FIGURE 1 | sRNA Network Involved with Shigella Virulence. All sRNAs which have been characterized in Shigella thus far are interconnected within the virulence network. RyhB inhibits VirB which can lead to inhibition of invasion. CsrB/C can inhibit CsrA which is needed for invasion. RnaG inhibits icsA transcription and limits spread. ShuA is important for heme uptake and survival of the pathogen during the infection process.
its own activity (Gudapaty et al., 2001;Suzuki et al., 2002). Key genes involved with carbon regulation in E. coli, including those encoding CsrA, CsrB, and CsrC as well as UvrY and BarA, are conserved in Shigella.
Interestingly, researchers have demonstrated that CsrA activity is linked to virulence in S. flexneri (Gore and Payne, 2010). Specifically, a mutation in csrA inhibits the ability of S. flexneri to invade eukaryotic cells and to spread from one eukaryotic cell to the next within a monolayer (Gore and Payne, 2010). Additionally a mutation in csrB or csrC which, in turn, indirectly increases the amount of free CsrA, allows S. flexneri to invade slightly more effectively than the wildtype strain (Gore and Payne, 2010). When CsrB or CsrC are over-produced, CsrA activity is inhibited as expected, and S. flexneri is no longer able to invade host cells (Gore and Payne, 2010). CsrA is hypothesized to impact Shigella virulence by two mechanisms. By the first mechanism, CsrA facilitates the activity of phosphofructokinase A (PfkA), which in turn upregulates production the master virulence regulator in Shigella, VirF (Adler et al., 1989;Gore and Payne, 2010). By the second mechanism, CsrA and PfkA may impact glycosylation of LPS on the surface of Shigella. Changes in LPS structure, mediated by alterations in the degree of glycosylation, impact the exposure of the type III secretion system (T3SS) on the surface of Shigella (West et al., 2005). Given these observations, changes in the Csr regulatory pathway could influence exposure of the Shigella T3SS (Hong and Payne, 1997;West et al., 2005;Gore and Payne, 2010). Regardless of the underlying molecular mechanism, CsrA clearly impacts pathogenesis in Shigella (Gore and Payne, 2010). As RNA molecules that function to regulate CsrA activity, CsrB and CsrC are thus implicated in the control of Shigella virulence.
Although different in size, no unique functions for CsrC and CsrB have been found thus far in either E. coli or Shigella. Investigating CsrB and CsrC under a number of different environmental could reveal unique activity and/or production patterns for these regulators (Weilbacher et al., 2003). In general, the biological significance of sibling sRNAs with apparent functional redundancies remains unclear (Caswell et al., 2014). It has been suggested that the extremely short half-life of CsrB and CsrC contributes to the speed by which the sRNAs can regulate CsrA, and that CsrB and CsrC allow for fine-tuning of gene expression in response to changes of carbon sources (Romeo, 1998). The short half-life of CsrB and CsrC could also contribute to the rapid responses needed for the regulation of pathogenesis based on environment specific alterations in carbon source availability.
RyhB
Another sRNA indirectly influenced by an environmental factor is RyhB. Originally discovered and characterized in E. coli, RyhB has been demonstrated to be an important regulator of iron metabolism (Massé and Gottesman, 2002). Bacteria need iron for survival, but too much iron can kill the organism, thus the production of iron uptake systems and iron storage systems are tightly regulated (Andrews et al., 2003). Studies in E. coli have demonstrated that RyhB plays an important role in maintaining the critical balance between the strict requirement and potential toxicity of iron (Massé and Gottesman, 2002;Andrews et al., 2003) Specifically, the production of RyhB itself is regulated in response to iron availability via the activity of the iron-responsive transcriptional regulator Fur (Bagg and Neilands, 1987;De Lorenzo et al., 1988;Hantke, 2001;Massé and Gottesman, 2002). Under conditions of high iron, Fur functions to inhibit RyhB production. Fur-dependent repression of RyhB production in turn relieves the RyhB-mediated repression of genes encoding various iron containing enzymes and iron storage proteins (Massé and Gottesman, 2002). RyhB is conserved between E. coli and Shigella where, as in E. coli, production of the sRNA is regulated by Fur, and activity of the sRNA impacts the expression of several targets conserved between the two genus (Murphy and Payne, 2007). In addition to the role that RyhB plays in iron metabolism, RyhB has been implicated in the regulation of virulenceassociated gene expression in S. dysenteriae (Murphy and Payne, 2007;Africa et al., 2011;Broach et al., 2012). Specifically, RyhB inhibits the transcription of virB, a gene encoding a protein that functions to promote the expression of several virulenceassociated genes in Shigella. (Adler et al., 1989;Beloin et al., 2002;Murphy and Payne, 2007;Africa et al., 2011;Kane and Dorman, 2012). Although the exact molecular mechanism underlying RyhB-dependent inhibition of virB transcription remains unknown, complementarity between the template DNA strand within the virB open reading frame and RyhB exists, and is required for the observed regulation; data that suggests a novel regulatory mechanism may be at play (Broach et al., 2012).
RyhB allows for iron responsive regulation of the Shigella virulence cascade. In the relatively iron-rich environment of the human gut, Fur is likely active and functioning to repress the production of RyhB. With decreased production of RyhB, VirB production proceeds and the protein functions to promote the expression of several virulence-associated genes including icsP (Wing et al., 2004;Castellanos et al., 2009;Broach et al., 2012).
IcsP protease limits IcsA (a protein required to polymerize the actin tail used by Shigella to spread from one eukaryotic cell to the next) from being produced prior to invasion into the host cell (Makino et al., 1986;Bernardini et al., 1989;Lett et al., 1989;Goldberg and Theriot, 1995;Egile et al., 1997;Shere et al., 1997;Steinhauer et al., 1999;Wing et al., 2005;Africa et al., 2011). Once Shigella enter the host cell, iron conditions become limiting, and as a result Fur-mediated repression of RyhB production is relieved. Once produced in the low iron environment RyhB functions to represses virB expression, which in turn limits IcsP production (Wing et al., 2004;Africa et al., 2011). Decreased IcsP production results in increased activity of IcsA which in turn facilitates host actin polymerization and cell to cell spreading by the bacterium (Makino et al., 1986;Bernardini et al., 1989;Lett et al., 1989;Goldberg et al., 1993;Goldberg and Theriot, 1995).
Inhibition of virB transcription is not the only way by which RyhB influences pathogenesis in Shigella. In addition to its role in modulating VirB production, RyhB also indirectly regulates the expression of genes encoding factors required for acid resistance, an essential aspect of infection initiation by this pathogen (Oglesby et al., 2005).
Evolutionarily, as an sRNA RyhB is likely a more adapt regulator than a protein would be. To compensate for small changes in iron availability within the human host, the synthesis of RyhB can quickly be inhibited by Fur. RyhB can also become a fully active regulator after only transcription, giving it an edge over a protein regulator which would require more energy and time to synthesize (Beisel and Storz, 2010). Its fundamental features as an iron-regulated ribo-regulator allow for quick, efficient modulation of target gene expression by RyhB in response to the subtle changes of environmental iron availability experienced by the pathogen throughout the course of a natural infection.
RnaG
RnaG is unique among Shigella sRNA in that, unlike the others, it was first identified and characterized in Shigella, and it is encoded on the large virulence plasmid. Similar to other Shigella sRNAs however, is the fact that production of RnaG is regulated in response to a specific environmental cue and that once produced, it functions to impact pathogenesis. Specifically, RnaG production is indirectly controlled in response to environmental temperature, and once produced functions to regulate the transcription of icsA, a virulence-associated gene required for actin-based motility of Shigella species (Bernardini et al., 1989;Giangrossi et al., 2010;Tran et al., 2011). Two coordinated mechanisms allow RnaG to mediate transcriptional control of icsA. First, rnaG and icsA have convergent promoters in close proximity to each other (Giangrossi et al., 2010). As such, activity of the rnaG promoter results in decreased activity of the icsA promoter through promoter interference (Giangrossi et al., 2010). Second, as a result of their over-lapping arrangement, and thus nucleic acid complementarity, RnaG can bind directly to the icsA transcript via kissing complexes, alter the structure of the growing transcript, and lead to early transcriptional termination (Giangrossi et al., 2010). Through these two, nonmutually exclusive molecular mechanisms, transcription of the important virulence factor IcsA is inhibited by RnaG, thus directly implicating this small RNA in controlling Shigella pathogenesis.
RnaG is likely produced during the time Shigella first enters the host until the pathogen reaches the site of infection. During this time, RnaG would inhibit premature expression of icsA, thus preventing the production of proteins required for host actin polymerization (Giangrossi et al., 2010). At 37 • C (the environmental temperature within the host), VirF is produced and functions to promote the transcription of icsA, thus inhibiting that of rnaG (Tran et al., 2011). During the initial stages of infection, however, it is possible that VirF levels are not high enough to induce icsA transcription to levels required for efficient actin polymerization and, due to specific environmental factors such as pH and osmolarity, may not be high enough until Shigella reaches the colonic epithelium (Porter and Dorman, 1994;Nakayama and Watanabe, 1995;Kane and Dorman, 2012). In this case, RnaG production during these initial stages of infection would inhibit aberrant icsA expression between the time that Shigella first enters the host and when the pathogen reaches the site of infection. Such temporal timing would prevent premature production of IcsA and possibly damper any immune system alarms which may be set off in the presence of the protein.
ShuA
The final Shigella ribo-regulator is an RNA thermometer located within the 5' untranslated region (UTR) of S. dysenteriae shuA (Shigella heme uptake), a gene encoding an outer-membrane heme receptor that is essential for the utilization of heme as a source of nutrient iron by the pathogen Payne, 1995, 1997). RNA thermometers function to modulate translation efficiency from the transcript on which they are housed by the formation of an inhibitory structure(s) that physically blocks binding of the ribosome to the transcript at non-permissive (low) temperatures (Kortmann and Narberhaus, 2012). As the environmental temperature rises the inhibitory structure is destabilized, the ribosomal binding site is exposed and translation of the regulated gene proceeds. The shuA RNA thermometer represents the first RNA thermometer characterized in any Shigella species (Kouse et al., 2013). Although identified initially in Shigella, an identical regulator functions to control expression of the orthologous gene chuA in pathogenic E. coli where this gene product is a virulence determinant (Wyckoff et al., 1998;Hoffmann et al., 2001;Torres et al., 2001;Okeke et al., 2004). Transcription of shuA is subject to iron-dependent regulation by the protein Fur while translation from the shuA transcript is subject to temperature-dependent regulation by the activity of the cis-encoded RNA thermometer Payne, 1995, 1997;Kouse et al., 2013). It is important to note, that for bacterial pathogens increased environmental temperature can act as an important signal that the organism has entered the host, the environment where production of virulence-associated factors will provide the most benefit.
Only under particular environmental conditions will ShuA be efficiently produced. Under conditions where iron is abundant, shuA transcription will be repressed by the activity of Fur, regardless of environmental temperature. Conditions where iron is depleted, but the environmental temperature is relatively low, the FourU RNA thermometer will inhibit translation of shuA. Only in iron-limiting and at temperatures corresponding to that within the human body (37 • C), will ShuA be produced (Kouse et al., 2013). The transcriptional and translation regulation mediated by Fur and the shuA RNA thermometer, respectively, function together to ensure maximal production of ShuA under conditions of poor iron availability and increased temperature, precisely the condition encountered within the human body; the only environment in which Shigella will encounter heme as a potential source of essential nutrient iron.
DISCUSSION
The riboregulators in Shigella, described in this review, all respond (directly or indirectly) to environmental changes, and all of them function within larger regulatory networks to influence pathogenesis of these species. CsrB/CsrC are regulated in response to carbon availability, RnaG is regulated in response to temperature, RyhB is regulated in response to iron availability, and finally the activity of the shuA RNA thermometer is regulated in response to temperature. Importantly, every Shigella ribo-regulator characterized to date functions to influence the production of factors involved in one or more processes required for pathogenesis, and thus must themselves be considered virulence determinants. This observation raises the question, why are some virulence-associated processes in Shigella controlled by protein-based regulation while others are controlled, at least in part, by the activity of riboregulators? In all sRNA found in Shigella thus far, proteins (VirF, H-NS, Fur, and UvrY) seem to be the initial regulator controlling a given step of a specific virulence-associated process. In each case, the ribo-regulator functions to modulate a specific virulence-associated activity for some duration of time, and then due to an environmental trigger, quickly switches off and allows Shigella to proceed to the next stage of pathogenesis (Figure 1). Perhaps Shigella evolved to favor riboregulators over protein regulators in conditions under which rapid specific changes to the production of one or just a few genes would be more beneficial to the organism than turning on/off an entire large regulon. Perhaps, processes required for the initial induction of pathogenesis in Shigella is controlled by protein regulators rather than riboregulators because quick reactions to false positive signals for pathogenesis could be detrimental to the survival of the bacteria, while a lag in protein regulation may temper those signals, thus reducing the frequency of such detrimental events. (Beisel and Storz, 2010).
More research needs to be done on riboregulators in Shigella to fully understand their functions and roles in virulence regulation (Storz et al., 2011). Such studies are likely to be fueled by genomic-based analyses that suggest the presence of additional ribo-regulators in Shigella, regulators for which function(s) have not yet been elucidated (Peng et al., 2011;Skippington and Ragan, 2012). Additionally, many putative sRNAs should be examined to see if they have small proteins missed by predictor programs (Storz et al., 2014). Lastly, once sRNAs and riboregulators are fully understood, it is possible that their function could be targeted as novel treatments for shigellosis.
FUNDING
Studies in the Murphy lab have been supported by the National Institutes of Health, the American Heart Association, Ohio University, and Ohio University College of Osteopathic Medicine. | 4,354 | 2016-01-27T00:00:00.000 | [
"Biology",
"Medicine"
] |
Effects of High Hydrostatic Pressure on Expression Profiles of In Vitro Produced Vitrified Bovine Blastocysts
High hydrostatic pressure (HHP) has been used to pre-condition embryos before essential, yet potentially detrimental procedures such as cryopreservation. However, the mechanisms for HHP are poorly understood. We treated bovine blastocysts with three different HHP (40, 60 and 80 MPa) in combination with three recovery periods (0, 1 h, 2 h post HHP). Re-expansion rates were significantly higher at 40 and 60 but lower at 80 MPa after vitrification-warming in the treated groups than controls. Microarray analysis revealed 399 differentially expressed transcripts, representing 254 unique genes, among different groups. Gene ontology analysis indicated that HHP at 40 and 60 MPa promoted embryo competence through down-regulation of genes in cell death and apoptosis, and up-regulation of genes in RNA processing, cellular growth and proliferation. In contrast, 80 MPa up-regulated genes in apoptosis, and down-regulated protein folding and cell cycle-related genes. Moreover, gene expression was also influenced by the length of the recovery time after HHP. The significantly over-represented categories were apoptosis and cell death in the 1 h group, and protein folding, response to unfolded protein and cell cycle in the 2 h group compared to 0 h. Taken together, HHP promotes competence of vitrified bovine blastocysts through modest transcriptional changes.
Scientific RepoRts | 6:21215 | DOI: 10.1038/srep21215 gamma growth arrest and DNA-damage-inducible (GADD45G) were found to be significantly up-regulated by HHP treatment 12 . Further investigation revealed that pressure changed protein structures 19,20 and enhanced the production of heat shock proteins (HSP), such as HSP70 14,19,20 . In bovine blastocysts subjected to HHP treatment, several candidate stress genes have also been examined. These include stress related genes SOD2, glutathione peroxidase 4 (GPX4) and heat shock 70 kDa protein 1 A (HSPA1A). Cumulative analysis of these genes revealed a similar pattern of expression, with a tendency for peak transcript abundance 1 h after HHP treatment 14 . This information is insufficient for explaining the molecular mode of action of the beneficial effects of HHP, therefore, the molecular mechanisms have yet to be elucidated. Without many known definitive candidate genes, genome-wide expression profiling by DNA microarray is highly effective for the high-throughput examination of transcriptomes. Accordingly, the aim of the present study was to evaluate the effects of HHP treatments at three different levels with two different recovery times on the gene expression of bovine in vitro produced (IVP) vitrified blastocysts. To our knowledge, this is the first report of transcriptional profiling of bovine blastocysts treated by HHP. Pathways such as apoptosis, protein folding, cell cycle regulation, RNA processing and translation were found to be affected by HHP.
Results
The Effect of HHP on Re-expansion Rates of Cryopreserved Bovine IVP Blastocysts. Blastocyst re-expansion is a predictive metric for implantation of frozen-thawed blastocysts. We first investigated the postthaw survival of vitrified IVP bovine blastocysts. Because the re-expansion rate of blastocysts after 0 and 1 h recovery time had been studied previously 13 , only 2 h recovery was assessed (Fig. 1). Re-expansion rates were significantly affected by HHP and recovery time, but not by temperature (data not shown). Therefore data for the two temperatures (24 °C and 39 °C) were combined. Application of appropriate HHP (40 or 60 MPa) followed by 2 h of recovery proved to be superior with regard to re-expansion. Specifically, re-expansion rates were significantly (P < 0.05) higher in the 40-MPa (90% ± 4.5%) and 60-MPa (87% ± 3.3%) groups compared with the controls (63.5% ± 4.5%) (Fig. 2). These data demonstrated that application of defined sublethal HHP stress promoted the in vitro developmental competence of the vitrified bovine embryos. However, HHP treatment at 80 MPa resulted in significantly reduced re-expansion rates (43.5% ± 4.0%) compared to controls (63.5% ± 4.5%; Fig. 2), suggesting that 80 MPa was detrimental to the bovine blastocysts.
Hierarnchical Clustering of Expression Profiles of Pressure-Treated and Cryopreserved Bovine IVP blastocysts.
Building upon the previous notion and our observation that vitrified embryos re-expanded better when appropriate HHP treatment is combined with a short recovery period, a comprehensive genome-wide transcriptomic investigation was conducted. All microarray data from this study have been submitted to NCBI under the accession number of GSE7559. Hierarchical clustering of all treatments (expression data were combined for the two temperature treatments) based on 12,274 analyzed transcripts, clearly showed an effect of pressure and recovery time on gene expression profiles (Fig. 3a). Specifically, the 40-and 60-MPa groups were separated from the 80-MPa and control groups (Fig. 3a). Within each HHP level, 1 h and 2 h clustered together separate from 0 h with the exception in 80 MPa group (Fig. 3a). This overall gene expression clustering pattern was consistent with the re-expansion results.
A total of 399 transcripts (254 unique genes) were identified as differentially expressed among the different treatment groups (P < 0.05) (Supplementary Table S1). The hierarchical clustering of all differentials (Fig. 3b) was most influenced by pressure, further suggesting that pressure played a significant role in the gene expression changes.
Effects of HHP on Gene Expression. Among the 399 total differentially expressed transcripts, 340 were caused by HHP while 59 were not related to pressure changes. Of the 340, 83 and 182, 84 and 44, were down-and up-regulated in cryopreserved embryos treated with 40 MPa or 60 MPa HHP, respectively (Fig. 4a, Table S2). The common down-regulated transcripts in both the 40 MPa and 60 MPa HHP-treated embryos were involved in the cell death and/or apoptosis (Table 1), among these were heat shock 22 kDa protein 8 (HSPB8), death inducer-obliterator 1 (DIDO1), neuroepithelial cell-transforming gene 1 (NET1), coagulation factor III (F3) and caspase 7 (CASP7). Interestingly, CASP7, a protein of the caspase family and considered to be an important executioner protein of apoptosis, and HSPB8, a common heat shock protein involved in regulation of cell proliferation and apoptosis, were both down-regulated upon HHP treatment (Fig. 5). Moreover, DIDO1 and NET1, both activated early in apoptosis (pro-apoptotic) were also down-regulated by HHP (Fig. 5). The expression changes of these genes upon 40 and 60 MPa HHP treatment are supportive of their potential role in the higher survival rates of these groups. Conversely, the up-regulated transcripts, such as serine/arginine-rich splicing factor 7 (SFRS7), SFRS9, DNA-directed RNA polymerase II subunit G (POLR2G), POLR2F, POLR2L, small nuclear ribonucleoprotein D3 (SNRPD3), SNRPD2, eukaryotic translation initiation factor 4B (EIF4B), ribosomal protein L38 (RPL38) and mitochondrial ribosomal protein L43 (MRPL43) ( Table 1), are involved in RNA processing and transcription, as well as regulation of protein synthesis, and likely promoted embryo survival. Collectively, these results suggested that stress caused by elevated HHP induced the embryos to degrade apoptotic transcripts and increase RNA transcription and translation. These effects, while not necessarily specific for pressure resistance or cryo-tolerance, potentially allowed the embryos to resist insults and survive more robustly. However, when pressure was further increased to 80 MPa, 25 and 92 transcripts were down-and up-regulated, Table S2). The biological processes significantly represented among down-regulated transcripts included protein folding and cell cycle, which including BAG family molecular chaperone regulator 4 (BAG4), DBF4 zinc finger A (DBF4), mitogen-activated protein kinase phosphatase 1 (DUSP1), and serine/threonine-protein kinase SNK (PLK2; Table 1). Whereas, the up-regulated transcripts significantly over-represented were cell death, apoptosis, and chromatin assembly/disassembly, and included genes such as EIF4B, hexokinase 1 (HK1), histone cluster 1, H1e (HIST1H1E) and histone deacetylase 8 (HDAC8; Table 1). Some of these changes are opposite to those seen at 40 or 60 MPa. These results suggest that high HHP disturbs cell structure and proliferation and could be detrimental to bovine embryo survival.
Among genes up-and down-regulated at each pressure level, 136, 21 and 39 transcripts were uniquely differentially expressed in the 40-, 60-or 80-MPa treated groups compared to the controls, respectively ( Table S4). These include down-regulated transcripts, CASP7 and NET1, which is involved in cell death and apoptosis, and up-regulated transcripts, SFRS7, SFRS9, POLR2G, POLR2F, POLR2L, SNRPD2 and amyloid beta (A4) precursor-like protein 1 (APLP1), which are involved in RNA processing and translation. Twenty-six transcripts were differentially expressed in all pressure treated groups compared to un-pressured controls. These include DIDO1, HSPH1, HSPB8, HK1 and EIF4B (Fig. 4b, Supplementary Table S5) and may represent essential genes for pressure stress response.
Effects of Different Recovery Time on Gene Expression.
The duration of the recovery period is particularly important because HHP induces gene changes in cellular metabolism and functions and time is needed for the synthesis of related RNA and proteins. In a previous study, allowing bovine embryos to recover for 1 h after HHP increased embryo survival compared to 2 h or HHP alone without recovery 13 . Here, we compared gene expression at these three time points. Among the total of 399 differentially expressed transcripts, 167 were caused by recovery duration. We identified 49 and 98 down-regulated, and 16 and 33 up-regulated transcripts at 1 h and 2 h compared to controls (0 h), respectively (Fig. 4c, Supplementary Table S6). Gene ontology analysis of the down-regulated transcripts revealed apoptosis, proteolysis and phosphate metabolic process in the 1 h group, and protein folding, cell cycle and cell death in the 2 h group as significantly overrepresented (Table 2). Up-regulated transcripts were involved in cellular growth and proliferation, cell morphology, and cellular function and maintenance in the 1 h group, cellular growth and proliferation, DNA replication and G1/S transition of mitotic cell cycle in the 2 h group ( Table 2). Of special interest was the dramatically higher number of differentially expressed transcripts in the 0 vs. 2 h comparison than that of the 0 vs. 1 h comparison, suggesting that 2 h of recovery allowed more gene expression changes to occur. Among the differentially expressed genes unique to the 0 vs. 1 h and 0 vs. 2 h comparisons, 20 and 41 transcripts were identified, respectively (Fig. 4d, Supplementary Table S7). A total Table S8), including CASP7, DUSP1 and F3, which are involved in apoptosis and cell death.
It is noteworthy that although a 2 h recovery induced more gene expression changes, it did not promote better embryo re-expansion than 1 h. The additional changes in gene expression during the second hour of recovery may have corrected changes already taken place during the first hour, thereby canceling some of the changes needed to resist insults from the subsequent cryopreservation. we performed qRT-PCR on eight genes, namely CASP7, NET1, APLP1, EIF4B, HSPH1, HSPB8, DIDO1 and F3, which were significantly affected by HHP treatments and play crucial roles in cell death and apoptosis. In nearly all cases, the qRT-PCR detected greater fold changes and substantiated results of the microarray analysis (Fig. 6a,b).
Discussion
In the bovine embryo transfer industry, vitrification is the most common method to cryopreserve IVP embryos 21 . Sublethal HHP was reported to enhance stress tolerance and increase post-thaw survival of sperm, embryos or stem cells after cryopreservation in murine, porcine and bovine 12 . Different HHP conditions (pressure level, recovery time and temperature) have been explored on gametes and embryos subjected to various assisted reproductive technologies 22 . HHP treatment at 60 MPa for 1 h has been shown to increase the in vitro development of bovine blastocysts 13,14 . In the present study, we extended previous findings by testing 40 and 80 MPa and found that 80 MPa was not well-tolerated. Additionally, we also found that HHP at 40 MPa prior to vitrification resulted in a higher re-expansion rate than the previously tested 60 MPa and the non-treated control group. The results in cattle are also in accordance with previous reports in mice and sheep 15 .
Despite advances in morphological studies, limited information on the molecular mechanisms behind the positive effect of HHP are available. Without clear candidates, comparing the transcriptomes of the treated and control embryos was the approach of choice. Interestingly, transcriptomic changes were reflective of the re-expansion data, specifically that the best treatment condition, 40 MPa, elicited the most changes in gene expression compared to controls. Most of the down-regulated genes found in the beneficial treatment levels of HHP, 40 and 60 MPa, belonged to cell death and apoptosis, while up-regulated genes were involved in RNA processing, cellular growth and proliferation, however, some of these changed in the opposite direction by the harmful level of 80 MPa HHP. The majority of the genes reported here are newly identified in HHP-treated, vitrified embryos. Collectively, it appears that while the embryos responded to HHP stress by changing gene expression, these changes prepared them for the upcoming insult of vitrification. However, when too much stress was applied (80 MPa for bovine blastocysts), embryo lethality occurred. By the candidate approach it was previously reported that sublethal stress such as heat, affects the embryos through apoptosis 2,3,23 by influencing the expression of development 24 and stress-related genes 25,26 . In this study, the same pathways were revealed for HHP stress. It appears that the embryos have limited pathways available to resist stress and use the same mechanisms for different external insults.
In accordance with the finding that a short recovery period after HHP was shown to be beneficial for cell/ embryo survival 8,13,27 , we identified genes that were affected by different lengths of recovery. Similar to the effects of pressure treatment, genes involved in regulation of cell death, apoptosis and protein folding were down-regulated, while up-regulated genes belonged to cell morphology, DNA replication and cellular growth and proliferation categories after either a 1 h or 2 h recovery period. HHP and recovery seem to affect the same developmental pathways because avoiding cell death is essential for embryonic development.
In addition to the well-known apoptotic events induced by stress, we also identified many new pathways involved in potential protective mechanisms. These include RNA processing, translation, cell cycle, oxidative phosphorylation and cellular growth and proliferation. A closer look at the gene lists revealed members of the above-mentioned pathways, such as CASP7, DIDO1, NET1, HSPH1, and HSPB8, which may be responsible for possible protective mechanisms induced by HHP. In particular, CASP7, a member of caspase family, HSPH1 and HSPB8, members from the heat shock gene family, and DIDO1 and NET1 were down-regulated by HHP (40 and 60 MPa). CASP7 has been shown to be an important executioner protein of apoptosis 28,29 . HSPH1 prevents the aggregation of denatured proteins in cells under severe stress 30,31 . HSPB8 belongs to the superfamily of small heat-shock proteins and is involved in regulation of cell proliferation and apoptosis through the activation of transforming growth factor-β activated kinase 1 (TAK1) 32 . In addition, DIDO1 and NET1 are activated early in apoptosis through regulation of BCL-2 33,34 . Sequential activation of these essential genes in response to pressure stress could play a central role in improving the stress tolerance of vitrified bovine embryos. Furthermore, EIF4B was up-regulated in HHP treated bovine blastocysts. EIF4B is required for cell proliferation and survival through regulation of protein synthesis [35][36][37] . Its up-regulation suggests that 40-and 60-MPa requires the synthesis of new proteins to promote embryo survival. However, the well-known HSP70 (HSPA1A on our microarray) which was induced by sublethal pressures in microorganisms 38 was not significantly regulated by HHP in our study. This observation is consistent with a previous report employing the candidate approach 13 . It is possible that, instead of the HSP70, the bovine embryos activate alternative proteins such as HSPH1 and HSPB8, to respond to pressure stress. A recent study of the transcriptome of porcine oocytes after HHP treatment revealed 44 HHP-responsive genes related to developmental process and genomic imprinting 18 . In our study, the most represented biological processes showed that apoptosis events were down-regulated while RNA processing, cellular growth and proliferation were up-regulated by 40 and 60 MPa, and a short recovery time. HHP and recovery time seem to help embryos avoid cell death and accelerate cell growth, which are essential for embryonic development. However, translation and chromatin assembly associated genes were up-regulated by appropriate HHP, which suggests that embryos go back to normal faster after warming/thawing through the assembly of important functional proteins. Interestingly, another recent study of the transcriptome of 4-cell embryos derived from HHP-treated mice oocytes showed a massive down-regulation of translation-related genes 17 . It seems that HHP puts the oocytes into energy saving mode by reducing protein synthesis. A possible reason for this discrepancy could be the difference in the dynamics of transcription across embryo development and the timing of genome activation in these three species. Also, the beneficial genes are transcribed in response to stress in a very short period in our study. This is the first high-throughput study on HHP-treated and cryopreserved blastocysts. It should be noted that our microarray represents 10,991 genes, about half of the bovine expressed genome 39 . Of the approximately 12,000 genes expressed by the bovine blastocysts 39 , 6,086 were represented on the microarray used. Therefore, half of the blastocyst's transcriptome is not studied here. However, we were able to identify multiple HHP-induced pathways and gene ontology categories and some that were commonly used by cells to resist other stresses, such 3). In all cases, real time RT-PCR results substantiated the differential gene expression patterns from microarray. as heat. These data suggest that the cells are limited to only a number of pathways to counteract external stress and it is therefore likely that this study identified all pathways, albeit not all genes, involved in HHP stress resistance. Application of the more powerful RNA-seq technology may help to identify additional differentially expressed genes, but it is unlikely that additional pathways will be revealed.
Previous studies mainly focused on the development of embryos from HHP-treated oocytes as well as the gene expression in treated oocytes [7][8][9][12][13][14]27 . These studies together with ours revealed that only a moderate number of genes were changed by HHP. Changes at the protein level such as folding, post-translation modifications 19 and protein levels likely represent major responses induced by HHP. To date, proteomic analysis has only been applied in the analysis of HHP-treated microorganisms 40 . Such a study with embryos, however, is currently unfeasible due to the small number of cells that can be isolated from embryos and the high expense associated with proteomic analysis.
In summary, our results showed: 1) bovine cryopreserved embryos exhibit higher developmental competance after treatment of HHP at 40 or 60 Mpa, however, 80 MPa is not well-tolerated; 2) HHP treatments induced modest transcriptional changes in bovine embryos; and 3) HHP affected the expression of genes involved in cell death and survival, RNA processing, as well as cell cycle and cell proliferation.
Materials and Methods
Microarray Design and Annotation. The Cattle Array-Ready oligonucleotides were designed at the University of Illinois, Urbana-Champaign and described in detail by Everts et al. 41 . The microarray contained 13,254 70-mer oligonucleotide probes that were synthesized at Illumina (www.illumina.com, San Diego, CA, USA). All probes were printed in duplicate on glass slides at Microarrays Inc. (Nashville, TN, USA). In total, these oligonucleotide probes represent 10,991 unique genes.
Collection of IVP blastocysts.
In vitro bovine blastocysts were produced as described previously 13,42 .
Briefly, in vitro fertilization (Day 0) was performed using abattoir bovine oocytes and embryos were immediately placed in CR1aa medium supplemented with BSA for Days 1 and 2 of culture. Cleaved embryos were transferred to CR1aa + 10% FBS and cultured at 38.5 °C in 5% CO 2 in humidified air until Day 7/expanded blastocyst stage. Embryos were examined and staged under light microscopy and only morphologically intact embryos meeting the standards of Grade 1 by the International Embryo Transfer Society (IETS) were used in the following experiments.
High Hydrostatic Pressure Treatment of Bovine IVP Blastocysts. Blastocysts were randomly distributed into the control and HHP treated groups as shown in Fig. 1. To apply HHP, groups of embryos were transferred to 0.25 ml straws in embryo holding medium (TCM-199; Gibco, Grand Island, NY, USA) without air bubbles. Straws were sealed with plastic plugs and were then placed into a pre-warmed stainless steel pressure machine (HHP machine 100; Applied Cell Technology Ltd., Hungary) with distilled water as the pressure medium. The following treatments were included ( Fig. 1): (1) Control embryos were left untreated in the incubator (one atmospheric pressure or 0.1 MPa); (2) treatment groups were assigned to 40, 60 and 80 MPa HHP for 1 h at either 24 °C (room temperature) or 39 °C (body temperature), followed by three different recovery time periods (0, 1 and 2 h) post-HHP in the holding medium. The embryos were then vitrified using the Solid Surface Vitrification (SSV) method 43 . The cryopreserved blastocysts were then thawed by immersing the straws into 0.5 M sucrose solution for 5 min at 39 °C, after which the blastocysts were transferred into TCM-199 medium and cultured in an incubator at 39 °C, 5% CO 2 and humidified air. For recorded re-expansion rates, 120 embryos were used. The re-expansion rates of the embryos were assessed after 2 h of recovery and morphological survival was determined 24 h after warming. For gene expression analysis, a total of 360 embryos were examined; pools of 5 vitrified embryos from each treatment were washed twice in D-PBS and stored in RNAlater (Ambion, Grand Island, NY, USA) in liquid nitrogen. All treatments were repeated three times (n = 3).
The re-expansion rates were analyzed using One Way ANOVA with Tukey's HSD test. A P-value < 0.05 was considered statistically significant.
RNA Isolation, Linear Amplification, Labeling and Microarray Hybridization.
Following the reproducible procedures of RNA extraction and linear amplification from our previous study 42 , we isolated total RNA from each pool of 5 blastocysts using TRIzol reagent (Invitrogen, Grand Island, NY) and linear acrylamide as a carrier (Ambion, Grand Island, NY). The quality of the total RNA was examined with the Aglient RNA 6000 Pico kit (Aglient Technologies, Santa Clara, CA) using the Aglient Bioanalyzer 2100. The mRNA underwent two rounds of amplification using the TargetAmp 2-round aminoallyl-aRNA amplification kit 1.0 (Epicentre, Madison, WI) according to the manufacturer's instructions. From 5 blastocysts, we were able to generate an average of 60 μ g of amplified RNA. Amplified RNA was stored at − 80 °C until utilization on the microarray.
The reference microarray design, in which the embryonic expression profiles were compared to a standard reference RNA, was used. The reference RNA was isolated from brain, kidney, liver and lung tissues of a naturally reproduced heifer and pooled in equal proportion. More than 90% of the probes on the microarray were hybridized by the standard reference. Two micrograms of amplified RNA from each sample and the reference were reverse transcribed, labeled, and hybridized to each microarray as previously described for single embryos 42 . In total, 144 microarrays were used including dye-swap hybridizations.
Microarray Data Analysis. The microarrays were scanned with GenePix 400B (Molecular Devices, Union City, CA, USA) and normalization of fluorescence intensities was accomplished by using the GenePix Pro 6.0 scanning software (Axon Instruments, Union City, CA, USA). Each scanned image was examined thoroughly and dust particles and spots with high background were flagged and removed from analysis. The background and standard deviation were calculated for each raw data file after scanning, and only those spots with intensities three standard deviations above background were considered "expressed" and loaded into Genespring 12.1 (Agilent Technologies Palo Alto, CA, USA). Loess normalization was applied to all microarrays before statistical comparisons. In the analysis, each probe was considered individually.
In the post-normalization evaluation of the probes on the microarrays, 12,274 probes present in either the standard reference or the sample on 90% of the microarrays underwent further analysis. We wished to quantify the effect of temperature, recovery time, and HHP on the gene intensities. As these factors are all categorical, an ANOVA model was the natural choice. Considering a combination of the nature of the experiment and the biological focus, we decided to omit one variable from consideration to simplify the analysis. A separate ANOVA model was fit each of the possible covariates: HHP, recovery time and temperature. We looked at two metrics, firstly the number of genes for which we found that factor significant using a significance level of 0.01 and secondly the sum of the P-values for all probes. By taking into consideration both significant factors and that the re-expansion rates were not significantly affected by temperature, we chose to combine the data from the two temperatures to increase the statistical power and allow for a comprehensive analysis. We fit an ANOVA model with the covariates of HHP and recovery time. The ANOVA model returned a single P-value per probe. In order to account for multiple comparisons, we used the Benjamini Hochberg procedure to control for a false discovery rate (FDR) of 0.05. Hierarchical clusters were generated using Genespring GX 12.1 with the K-means clustering algorithm. Heatmaps and Venn diagrams of differentially expressed genes were developed with R.
Gene Ontology Analysis. Functional annotation enrichment analysis for Gene Ontology (GO) was conducted using DAVID 44 . GO terms shown in this study summarized all similar sub-terms into an overarching term, and Benjamani-Hochberg adjusted P-values are shown for the representative term.
Quantitative Real Time-Reverse Transcription Polymerase Chain Reaction (qRT-PCR)
Analysis. qRT-PCR was performed to validate differential expression of eight selected genes using amplified RNA that used for microarray hybridization. Amplified RNA was reverse transcribed to cDNA with SuperScript III Reverse Transcriptase (Invitrogen) and amplified with specific primers designed by using Primer 3.0 (Supplementary Table S9). The qRT-PCR was performed using SYBR Green PCR Master Mix (ABI) and an ABI 7500 Fast instrument. The data were analyzed using the 7500 software version 2.0.2 provided with the instrument. All values were normalized to the internal control, β-ACTIN. The efficiency of each primer pair was calculated over a 3.5 log dilution range and the relative gene expression values were calculated using the 2 −ΔΔCt method. The same standard reference amplified RNA used in the microarray analysis was used as the calibrator sample. Expression levels that were relative to those in the standard reference were calculated and the mean for each group was determined and compared for an overall fold change. Data from qRT-PCR were analyzed as described above for re-expansion rates. | 6,101.2 | 2016-02-17T00:00:00.000 | [
"Biology"
] |
Two-Step Resist Deposition of E-Beam Patterned Thick Py Nanostructures for X-ray Microscopy
Patterned elements of permalloy (Py) with a thickness as large as 300 nm have been defined by electron beam lithography on X-ray-transparent 50 nm thick membranes in order to characterize their magnetic structure via Magnetic Transmission X-ray Microscopy (MTXM). To avoid the situation where the fragility of the membranes causes them to break during the lithography process, it has been found that the spin coating of the resist must be applied in two steps. The MTXM results show that our samples have a central domain wall, as well as other types of domain walls, if the nanostructures are wide enough.
Introduction
Nowadays, there is wide interest in the exploration of the 3D magnetization configuration of patterned magnetic structures [1,2], as some of these structures might be topologically protected, which is important for subsequent applications. The interest in the study of microscopic magnetic structures lies in the possibility of the development and fabrication of sensors for numerous applications, including optics, memory devices, and biology [3][4][5][6][7]. On the other hand, it is important to note that the three-dimensional aspect ratio of the patterned structures usually implies a large thickness of the material.
Additionally, once the patterned elements with 3D magnetic configuration have been obtained, it is necessary to perform their appropriate characterization. In this sense, among other methods, Magnetic Transmission X-ray Microscopy (MTXM) has been shown to be a suitable technique to analyse the magnetic structure, as it provides a high spatial resolution of the sample, as well as element-specific magnetic information [8]. In addition, the data acquired with MTXM can be later processed by tomographic methods in order to obtain a magnetic tomographic reconstruction, which can allow us to resolve the threedimensional magnetization within the sample volume [9]. In fact, transmission methods are excellent for the visualization of magnetic states in a sample, while they require probes with high enough penetration depths [10]. Thus, in order to take advantage of the MTXM technique, it is mandatory to use membrane substrates with low X-ray absorption. In particular, the membranes must be thin enough to let through a considerable amount of light, since a large signal-to-noise ratio is crucial for these transmission measurements [11]. Then, completing the patterning process on top without damaging them becomes a challenge. While the magnetic properties of Py films can vary depending on the substrates [12], we have seen that our nanostructures share the same behaviour when they are patterned on the membranes or on the Si substrates.
In this work, the electron beam lithography (EBL) process for MTXM membranes is described. In particular, the article is focused on how the fabrication of large-thickness elements (permalloy microstructures) drives the division of the spin coating of the resist in two steps, which helps to avoid the membrane breaking during the patterning process. In this way, several series of lithographed structures have been patterned on the membranes, and the MTXM results of some of them that we already measured at the MISTRAL beamline of the ALBA synchrotron will be shown.
Materials and Methods
Several nanostructures have been made using electron beam lithography (EBL) on membrane substrates. EBL is a method that uses a tightly focused beam of electrons scanned over the surface of the substrate. The samples include Si 3 N 4 transparent membranes for MTXM measurements, with a window area of 750 µm × 750 µm and a very small thickness of 50 nm, where the nanostructures must be patterned ( Figure 1). In the measurements, the focused X-rays-which have a fixed energy-impact on the sample, before passing through the membrane and creating the image in the detector after being diffracted by a Fresnel zone plate.
Micromachines 2022, 13, x FOR PEER REVIEW 2 of 7 the substrates [12], we have seen that our nanostructures share the same behaviour when they are patterned on the membranes or on the Si substrates. In this work, the electron beam lithography (EBL) process for MTXM membranes is described. In particular, the article is focused on how the fabrication of large-thickness elements (permalloy microstructures) drives the division of the spin coating of the resist in two steps, which helps to avoid the membrane breaking during the patterning process. In this way, several series of lithographed structures have been patterned on the membranes, and the MTXM results of some of them that we already measured at the MISTRAL beamline of the ALBA synchrotron will be shown.
Materials and Methods
Several nanostructures have been made using electron beam lithography (EBL) on membrane substrates. EBL is a method that uses a tightly focused beam of electrons scanned over the surface of the substrate. The samples include Si3N4 transparent membranes for MTXM measurements, with a window area of 750 μm × 750 μm and a very small thickness of 50 nm, where the nanostructures must be patterned ( Figure 1). In the measurements, the focused X-rays-which have a fixed energy-impact on the sample, before passing through the membrane and creating the image in the detector after being diffracted by a Fresnel zone plate. In order to perform the EBL process, it is necessary beforehand to extend a resist over the sample (250 ± 20 nm). In our case, a PMMA 950K A4 resist from Microchem is used, which is spin coated at 4800 rpm for one minute, and then it is baked at 150 °C in an oven for more than 2 h. After the exposure of the pattern in a scanning electron microscope, the development of the resist (≈45 s) takes place. Due to the thinness of the membrane, the whole process must be performed very carefully in order to avoid any possible break. In our case, each pattern has several elements. In particular, the nanostructures are designed to have a curved (hyperbolic) shape to easily set a magnetic domain wall in the bent region after the application of an external magnetic field.
After the development, a permalloy (80% Ni and 20% Fe alloy) is deposited by sputtering at an Ar working pressure of 3 × 10 −3 mbar, as reported before [10], to obtain smooth surfaces. One remarkable characteristic of Py is that it is a soft magnetic material, and, In order to perform the EBL process, it is necessary beforehand to extend a resist over the sample (250 ± 20 nm). In our case, a PMMA 950K A4 resist from Microchem is used, which is spin coated at 4800 rpm for one minute, and then it is baked at 150 • C in an oven for more than 2 h. After the exposure of the pattern in a scanning electron microscope, the development of the resist (≈45 s) takes place. Due to the thinness of the membrane, the whole process must be performed very carefully in order to avoid any possible break. In our case, each pattern has several elements. In particular, the nanostructures are designed to have a curved (hyperbolic) shape to easily set a magnetic domain wall in the bent region after the application of an external magnetic field.
After the development, a permalloy (80% Ni and 20% Fe alloy) is deposited by sputtering at an Ar working pressure of 3 × 10 −3 mbar, as reported before [10], to obtain smooth surfaces. One remarkable characteristic of Py is that it is a soft magnetic material, and, therefore, its magnetic properties can be controlled by structural engineering on the nanoscale that results in a variety of behaviours [13][14][15]. The key to the process is the Py thickness. To contain 3D magnetic configurations, it must be wide and thick enough to leave some room for the formation of complex domain walls; otherwise, only ordinary walls (transverse/vortex walls, typically appearing in thin films) would be present, as there would not be enough space in the nanostructures to allow the creation of more complex walls. In fact, according to the characterization that we have carried out via Magnetic Force Microscopy (MFM) in structures patterned on Si substrates, we have determined that a width of at least 1 µm is needed. Finally, lift-off with acetone is performed to remove the remaining resist, leaving Py only in the already-exposed zone.
Gold particles with a diameter of 100 nm were sprinkled onto the sample to favour the alignment of the images acquired with MTXM. Element-specific magnetic Transmission soft X-ray Microscopy (TXM) imaging of the Fe absorption energy (706.8 eV) has been performed with the microscope installed at the Mistral beamline of the ALBA synchrotron [16]. There, X-ray Magnetic Circular Dichroism (XMCD), which consists of a magnetic material absorbing X-rays differently according to the helicity of the circularly polarized X-rays, is used [17].
Results and Discussion
The purpose of this research is to look for the appropriate curvature and the suitable electronic dose to obtain the desired magnetic walls. To perform this efficiently, several arrays of nanostructures are disposed in every membrane, so we have in each sample different curvatures and different electronic doses, the highest dose being around one hundred times higher than the lowest one. This layout gives a great variety of structures. The nanostructures have a curved shape similar to a boomerang, as sketched in Figure 2. The "boomerang" widths range from 0.1 µm to 2.5 µm in the lithographed samples, whereas they have an approximate length of 8-12 µm, depending on the curvature and on the Py thickness. An example is shown in Figure 3, where SEM images of some 100 nm thick Py nanostructures can be seen.
As was indicated in Section 2, we have performed Magnetic Force Microscopy measurements in samples grown on Si substrates, which have different Py thicknesses. In view of the MFM images, a wide "boomerang" is needed in order to see special features in the magnetization. As it can be seen in Figure 4, in an 80 nm Py "boomerang", the magnetization just "goes" from one end of the strip to the other, while different types of domain walls can be seen in a 140 nm Py "boomerang". That is the reason to increase the Py thickness. Unfortunately, due to the characteristic shape of the membranes and their inherent fragility, breaks are not unusual. In fact, Py layers of up to 100-120 nm were made with relative ease, but the common method seemed not to be the proper way to deal with samples with thicker Py layers, since all of them broke. In fact, the aim is to have a good aspect ratio in the thickness axis and, therefore, a larger resist thickness in the lithography process is needed. therefore, its magnetic properties can be controlled by structural engineering on the nanoscale that results in a variety of behaviours [13][14][15]. The key to the process is the Py thickness. To contain 3D magnetic configurations, it must be wide and thick enough to leave some room for the formation of complex domain walls; otherwise, only ordinary walls (transverse/vortex walls, typically appearing in thin films) would be present, as there would not be enough space in the nanostructures to allow the creation of more complex walls. In fact, according to the characterization that we have carried out via Magnetic Force Microscopy (MFM) in structures patterned on Si substrates, we have determined that a width of at least 1 μm is needed. Finally, lift-off with acetone is performed to remove the remaining resist, leaving Py only in the already-exposed zone. Gold particles with a diameter of 100 nm were sprinkled onto the sample to favour the alignment of the images acquired with MTXM. Element-specific magnetic Transmission soft X-ray Microscopy (TXM) imaging of the Fe absorption energy (706.8 eV) has been performed with the microscope installed at the Mistral beamline of the ALBA synchrotron [16]. There, X-ray Magnetic Circular Dichroism (XMCD), which consists of a magnetic material absorbing X-rays differently according to the helicity of the circularly polarized X-rays, is used [17].
Results and Discussion
The purpose of this research is to look for the appropriate curvature and the suitable electronic dose to obtain the desired magnetic walls. To perform this efficiently, several arrays of nanostructures are disposed in every membrane, so we have in each sample different curvatures and different electronic doses, the highest dose being around one hundred times higher than the lowest one. This layout gives a great variety of structures. The nanostructures have a curved shape similar to a boomerang, as sketched in Figure 2. The "boomerang" widths range from 0.1 μm to 2.5 μm in the lithographed samples, whereas they have an approximate length of 8-12 μm, depending on the curvature and on the Py thickness. An example is shown in Figure 3, where SEM images of some 100 nm thick Py nanostructures can be seen. As was indicated in Section 2, we have performed Magnetic Force Microscopy measurements in samples grown on Si substrates, which have different Py thicknesses. In view of the MFM images, a wide "boomerang" is needed in order to see special features in the magnetization. As it can be seen in Figure 4, in an 80 nm Py "boomerang", the magnetization just "goes" from one end of the strip to the other, while different types of domain walls can be seen in a 140 nm Py "boomerang". That is the reason to increase the Py thickness. Unfortunately, due to the characteristic shape of the membranes and their inherent fragility, breaks are not unusual. In fact, Py layers of up to 100-120 nm were made with relative ease, but the common method seemed not to be the proper way to deal with samples with thicker Py layers, since all of them broke. In fact, the aim is to have a good aspect ratio in the thickness axis and, therefore, a larger resist thickness in the lithography process is needed. In light of this problem, a different approach was used. Instead of depositing a thick layer of resist with the total thickness needed for the lithography process (which drives the breaking of the membranes), two thinner PMMA 950K A4 resist layers (each one with 250 nm in thickness) were consecutively extended and baked as sketched in Figure 5. By doing so, it is possible to make thicker samples. This result indicates that the deposition and baking of the first PMMA layer improves the mechanical response of the membrane before the deposition of the second layer and, therefore, it does not break in the second step. The width rises from about 400 nm to more than 2 μm, as can be seen in Figure 6, hence giving more space for domain walls to form. As was indicated in Section 2, we have performed Magnetic Force Microscopy measurements in samples grown on Si substrates, which have different Py thicknesses. In view of the MFM images, a wide "boomerang" is needed in order to see special features in the magnetization. As it can be seen in Figure 4, in an 80 nm Py "boomerang", the magnetization just "goes" from one end of the strip to the other, while different types of domain walls can be seen in a 140 nm Py "boomerang". That is the reason to increase the Py thickness. Unfortunately, due to the characteristic shape of the membranes and their inherent fragility, breaks are not unusual. In fact, Py layers of up to 100-120 nm were made with relative ease, but the common method seemed not to be the proper way to deal with samples with thicker Py layers, since all of them broke. In fact, the aim is to have a good aspect ratio in the thickness axis and, therefore, a larger resist thickness in the lithography process is needed. In light of this problem, a different approach was used. Instead of depositing a thick layer of resist with the total thickness needed for the lithography process (which drives the breaking of the membranes), two thinner PMMA 950K A4 resist layers (each one with 250 nm in thickness) were consecutively extended and baked as sketched in Figure 5. By doing so, it is possible to make thicker samples. This result indicates that the deposition and baking of the first PMMA layer improves the mechanical response of the membrane before the deposition of the second layer and, therefore, it does not break in the second step. The width rises from about 400 nm to more than 2 μm, as can be seen in Figure 6, hence giving more space for domain walls to form. In light of this problem, a different approach was used. Instead of depositing a thick layer of resist with the total thickness needed for the lithography process (which drives the breaking of the membranes), two thinner PMMA 950K A4 resist layers (each one with 250 nm in thickness) were consecutively extended and baked as sketched in Figure 5. By doing so, it is possible to make thicker samples. This result indicates that the deposition and baking of the first PMMA layer improves the mechanical response of the membrane before the deposition of the second layer and, therefore, it does not break in the second step. The width rises from about 400 nm to more than 2 µm, as can be seen in Figure 6, hence giving more space for domain walls to form.
In fact, with this new method to prepare the PMMA resist on the 50 nm thick MTXM membranes, it is even possible to pattern Py elements with a thickness up to 300 nm, as shown in Figure 7. In fact, with this new method to prepare the PMMA resist on the 50 nm thick MTXM membranes, it is even possible to pattern Py elements with a thickness up to 300 nm, as shown in Figure 7. Once the patterned samples have been obtained, a magnetic field has been applied to them to favour the appearance of domain walls, and then MTXM measurements at the MISTRAL beamline in the ALBA synchrotron have actually been performed with several Py nanostructures. The measurements, as depicted in Figure 8, show the appearance of several domain walls. In fact, a central domain wall extends all over each sample, showing black-and-white contrast colours. That means different out-of-plane magnetization orientations, because these images were collected at a normal incidence. Besides the central wall, a rhomboid structure appears in wide structures, where the wall bifurcates. Further analysis, out of the scope of this work, will be needed to see what types of domain walls are present in these samples and what their microscopic configuration is. In fact, with this new method to prepare the PMMA resist on the 50 nm thick MTXM membranes, it is even possible to pattern Py elements with a thickness up to 300 nm, as shown in Figure 7. Once the patterned samples have been obtained, a magnetic field has been applied to them to favour the appearance of domain walls, and then MTXM measurements at the MISTRAL beamline in the ALBA synchrotron have actually been performed with several Py nanostructures. The measurements, as depicted in Figure 8, show the appearance of several domain walls. In fact, a central domain wall extends all over each sample, showing black-and-white contrast colours. That means different out-of-plane magnetization orientations, because these images were collected at a normal incidence. Besides the central wall, a rhomboid structure appears in wide structures, where the wall bifurcates. Further analysis, out of the scope of this work, will be needed to see what types of domain walls are present in these samples and what their microscopic configuration is. Once the patterned samples have been obtained, a magnetic field has been applied to them to favour the appearance of domain walls, and then MTXM measurements at the MISTRAL beamline in the ALBA synchrotron have actually been performed with several Py nanostructures. The measurements, as depicted in Figure 8, show the appearance of several domain walls. In fact, a central domain wall extends all over each sample, showing blackand-white contrast colours. That means different out-of-plane magnetization orientations, because these images were collected at a normal incidence. Besides the central wall, a rhomboid structure appears in wide structures, where the wall bifurcates. Further analysis, out of the scope of this work, will be needed to see what types of domain walls are present in these samples and what their microscopic configuration is.
Conclusions
The results of this work show how the spin coating resist thickness is a key factor in the fabrication of micro-and nanostructures on fragile MTXM Si3N4 membranes (50 nm thick) when analysing their microscopic 3D magnetic configuration. In fact, the new method applied to these nanostructures indicates that the spin coating in two steps allows a successful lift-off process when the membranes are used in the experiment, and it is even possible to obtain 300 nm thick patterned elements. In fact, it has been already possible to characterize, at normal incidence, some of the patterned elements via MTXM measurements, which shows that the formation of domains and domain walls is actually favoured by the width and thickness of the structure.
Conclusions
The results of this work show how the spin coating resist thickness is a key factor in the fabrication of micro-and nanostructures on fragile MTXM Si 3 N 4 membranes (50 nm thick) when analysing their microscopic 3D magnetic configuration. In fact, the new method applied to these nanostructures indicates that the spin coating in two steps allows a successful lift-off process when the membranes are used in the experiment, and it is even possible to obtain 300 nm thick patterned elements. In fact, it has been already possible to characterize, at normal incidence, some of the patterned elements via MTXM measurements, which shows that the formation of domains and domain walls is actually favoured by the width and thickness of the structure. | 5,075 | 2022-01-28T00:00:00.000 | [
"Materials Science",
"Physics"
] |
Robot Trajectories Comparison: A Statistical Approach
The task of planning a collision-free trajectory from a start to a goal position is fundamental for an autonomous mobile robot. Although path planning has been extensively investigated since the beginning of robotics, there is no agreement on how to measure the performance of a motion algorithm. This paper presents a new approach to perform robot trajectories comparison that could be applied to any kind of trajectories and in both simulated and real environments. Given an initial set of features, it automatically selects the most significant ones and performs a statistical comparison using them. Additionally, a graphical data visualization named polygraph which helps to better understand the obtained results is provided. The proposed method has been applied, as an example, to compare two different motion planners, FM2 and WaveFront, using different environments, robots, and local planners.
Introduction
The task of planning a collision-free trajectory from a start to a goal position is fundamental for an autonomous mobile robot. Although path planning has been extensively investigated since the beginning of robotics, there is no agreement on how to measure the performance of a motion algorithm. Measuring the performance of a motion planner is not an easy task. On the one hand, the existing motion planning approaches are different in nature and their implementations heavily depend on the underlying environment representation. Whether a motion planner performs well or not depends on a large number of factors, often related with the task for which the method is being used. On the other hand, another issue when evaluating a motion planner is that robot motion task is an active task: it is not possible to collect logs and then run algorithms off-line, since the decisions taken by the algorithm in each step determine a new situation and thus new sensor readings and possibilities.
Many scientific disciplines take advantage of widely accepted comparison methodologies, performance metrics, and benchmark databases. Some examples are the PASCAL Object Recognition Database Collection for vision (http:// pascallin.ecs.soton.ac.uk/challenges/VOC/databases.html), UC Irvine Machine Learning repository (http://archive.ics. uci.edu/ml/) for the empirical analysis of machine learning al gorithms, and Radish (http://radish.sourceforge.net/) (Robotic Data Set Repository), focused on localization and mapping. It is of vital importance for any evaluation framework to identify some performance metrics, define a comparison methodology, and offer a set of benchmark problems.
In this paper, we present a method to compare different navigation approaches, with the aim of helping decide which of them would be better for the purposes in which the robot is to be used. The approach we present is mainly based on statistical measures for the trajectories performed and automatically selects the most significant features among a set of initial features to measure the goodness of a trajectory. The proposed method is used to compare two motion planners, the Fast Marching Square (FM 2 ) planner [1] and the WaveFront planner [2]. The FM 2 planner has been integrated as a plug-in driver in the Player/Stage multirobot simulation tool [3] and compared with the already existing WaveFront planner. The algorithms have been applied under the same conditions and tested in different environments and for two different robots combined with two local planners. 2 The Scientific World Journal The rest of the paper is organized as follows: after reviewing the related works (Section 2), Section 3 focuses on the proposed approach; Section 4 is devoted to the experimental setup; obtained experimental results are shown in Section 5, and finally in Section 6 the conclusions are presented and the future work lines are pointed out.
Related Works
The field of robot motion planning has been an active area of research over the last forty years, yielding many motion planning approaches. For example, Berg et al. present LQG-MP (linear-quadratic Gaussian motion planning) [4], a new approach to robot motion planning that takes into account the sensors and the controller that will be used during the execution of the robots path. LQG-MP is based on the linearquadratic controller with Gaussian models of uncertainty and explicitly characterizes in advance (i.e., before execution) the a priori probability distributions of the state of the robot along its path. Wei and Liu [5] present a novel evolutionary G3continuous (continuous-differentiable curvature) path planner for nonholonomic wheeled mobile robots.
Smith et al. [6] present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modelled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied.
Montemerlo et al. [7] present the architecture of Junior, a robotic vehicle capable of navigating urban environments autonomously. In doing so, the vehicle is able to select its own routes, perceive and interact with other traffic, and execute various urban driving skills including lane changes, U-turns, parking, and merging into moving traffic. The vehicle successfully finished and won second place in the DARPA Urban Challenge.
There is also lot of research devoted to path selection and trajectory optimization approaches. Adouane et al. [8] show a method based on elliptic trajectories to perform robot navigation, and Willms and Yang [9] present a robot path planning approach based on a dynamic propagation system.
Other approaches try to obtain optimal trajectories for manipulators: Constantinescu [10] presents a method to obtain smooth and time-optimal paths under some constraints; Gasparetto and Zanotto [11] present an approach to obtain trajectory plans based on an objective function which takes into account the integral of the squared jerk along the trajectories; Zanotto et al. [12] propose a methodology to compare trajectory planning algorithms for robotic manipulators, considering both the execution time and the squared jerk along the trajectory.
There are many other path planners found in the literature: Dolgov and Thrun [13] present a path planning algorithm that generates smooth paths for an autonomous vehicle settled on an unknown environment; Chang and Yamamoto [14] present a hybrid path planning based on Potential Field method and Voronoi Diagram approach whose aim is to concurrently navigate and perform map-building in a mobile robot.
Although lots of planning algorithms have been proposed over these years, a measurement of their performance only recently gained significant attention by the research community. Some examples of the efforts made to build common test environments are the collection of benchmark problems of the Algorithm and Application Group at Texa s A&M University (https://pwww2.cse.tamu.edu/dsmft/benchmarks/) and the MOVIE project (http://www.cs.uu.nl/centers/ give/movie/index.php), whose outcome is a database that contains many different test scenes that can be used to benchmark different motion planning techniques.
Calisi and Nardi [15] concentrate on pure-motion tasks: tasks that require moving the robot from one configuration to another, either as an independent subtask of a more complex plan or as a goal itself. After characterizing the goals and the tasks, they describe the commonly used problem decomposition and different kinds of modelling that can be used, from accurate metric maps to minimalistic representations. The contribution of their paper is an evaluation framework that they adopt in a set of experiments showing how the performance of the motion system can be affected by the use of different kinds of environment representations. In the same line, Calisi et al. [16] present a framework of benchmarks (MoVeME) (http://www.dis.uniro-ma1.it/calisi/index.php?page=moveme) for evaluating and comparing motion algorithms for autonomous mobile robots and vehicles. Karaman and Frazzoli [17] present an attempt to compare path planning algorithms from the quality point of view.
Many recent research papers address the problem of motion planning for self-driving vehicles, a context in which navigation evaluation methodologies become important. Werling et al. [18] deal with the trajectory generation problem faced by an autonomous vehicle in moving traffic. They propose a semireactive planning strategy that realizes all required long-term maneuver tasks (lane-changing, merging, distance-keeping, velocity-keeping, precise stopping, etc.) while providing short-term collision avoidance. Rastelli et al. [19] present a smooth trajectory generator computationally efficient and easily implementable, which considers Bezier curves and circumference parametric equations for a real vehicle. Moreover, this new trajectory generator reduces the control actions, generated with to a fuzzy controller.
Proposed Approach
The approach we present in this paper is mainly based on statistical measures for the trajectories performed. In this way, we first decide which set of features could be useful to measure the quality of a trajectory; then, we automatically select the most significant features among them; afterwards, we collect the selected features for a set of different trajectories, and finally we use these feature values to compare, from a statistical point of view, which of the used navigation techniques show a greater quality in the trajectories made.
The Scientific World Journal 3 The new approach works as follows.
(1) Decide the feature set which could help in the statistical measure of the trajectory quality.
Depending on the environment, goal, sensors provided by the robot, and the amount of possible dynamic obstacles expected, it is not supposed to be a unique set of features to be used. Nevertheless, the proposed approach could be used almost in any situation in which a navigation method has to be selected (semistructured environments, outdoor ones, UAV, submarine robots, etc.).
(2) Collect the values of these features for a set of trajectories.
It is noteworthy that the data can be obtained with the real robot in its appropriate environment or by a simulation software.
(3) Select the subset of features which maximizes the information.
This is the first thing to be done by a statistical analysis of the data. There are several ways to obtain this subset, but we have selected to use the Friedman test statistic [20], which is used as fitness value in an Estimation of Distribution Algorithm (EDA) [21] guided search. Friedman test has been found as a very sound method to compare the joint probability behaviour when different approaches are to be tested [22].
(4) Perform a statistical comparison using the selected features.
In this step, a statistical hypothesis test is carried out for each of the selected features to identify the statistically significant differences; obtained results are visualized graphically in the next step.
(5) Visualize the data. We present a new approach to show the results of the tests and to decide, for each type of environment, which is the navigation technique that performs best.
Using this new approach an experiment has been performed in order to make a comparison between two global navigation algorithms. Next sections present the experimental design and the obtained results.
The self-driving vehicles framework is a context of interest for the proposed approach to be applied, due to its increasing interest during last years. Different kind of sensors, such as Kineck RGB-D [23], and different environments in which real-time trajectory calculation is needed have been presented in the literature [24,25]. The approach introduced in this paper can be used as well in these scenarios; a specific feature selection is needed: the procedure to be used is the one presented in this paper.
Simulation Setup
We tested the proposed approach using two motion planners.
(i) Fast Marching Square (FM 2 ). The Fast Marching Square (FM 2 ) planner is a potential field based path planning algorithm whose main goal is to drive the robot to the goal in a smooth and safe way. The FM 2 method is based on the way electromagnetic waves propagate in nature, because the potential and its associated vector field have good properties desired for the trajectory, such as smoothness and absence of local minima. The FM 2 method makes use of the Fast Marching (FM) method, an efficient numerical algorithm to represent the front propagation proposed by Sethian [26]. It is a particular case of the Level Set methods [27], designed for problems in which the speed function never changes sign, so that the front is always moving forward or backward. The FM 2 method is a two-step algorithm. In the first step, a wave is propagated using FM starting from the points representing the obstacles. The result of this step is a greyscale potential map where obstacles are black, and the farther a location is from an obstacle, the lighter it becomes. This map is known as a refraction index map because it can be seen as a varying refraction index environment where a new wave will draw a trajectory. In the second step, a new wave is emitted from the goal point over the refraction index map using FM. This way a unique field is obtained and its associated vector field is attracted to the goal point and repulsed from the obstacles. Finally, the shortest time trajectory is calculated in this potential surface by using the gradient method.
(ii) WaveFront. This planner shares some similarities with the FM 2 method in the way the wave is propagated. Besides, it is offered as a planner driver within the Player/Stage software set. The WaveFront planner works as follows: it first creates a configuration space of grid cells from the map that is given, treating both occupied and unknown cells as occupied. Then, based on their distance to the nearest obstacle the planner assigns a cost to each of the free cells (the nearer the obstacle, the higher the cost). When the planner is given a new goal, it starts from the goal cell and assigns plan costs to the cells as it expands like a WaveFront. The plan cost in each cell is dependent on its distance from the goal, as well as the obstacle cost assigned in the previous step. Once the plan costs for all the cells have been evaluated, the robot can simply follow the gradient of each lowest adjacent cell all the way to the goal.
Usually, global planners should be combined with some obstacle avoidance strategy or local planner in order to cope with dynamic environments and reduce the need and hence the computational payload of replanning when changes in the environment make the original path unfeasible. Therefore, we used the stated global planners in combination with two local planners (also available within Player/Stage): the Vector Field Histogram Plus (VFH+) [28] and the Nearness Diagram (ND) [29]; the local planners were used in order to see how the local method affects the performance of the whole system.
Tests were made in simulation environments as the first step towards the application in the real world. Simulation tools allow analysis of the behavior of the methods with respect to a wide spectrum of situations and collect a great amount of data for statistical analysis. The stage simulator of the Player/Stage package was chosen for this experiment because it is widely used by the scientific community and is also included in some Linux distributions. Tests were made using two simulated robots, the popular Pioneer 2DX and our Segway RMP 200.
Environments Used.
To test the proposed approach, six simulation environments were used with the Player/Stage software. Three of these environments were created by us (a synthetic test room, an office indoor environment of Carlos III University and Teknikers laboratory) and the other three were taken from the "Mobile robots and Vehicles Motion algorithms Evaluation" (MoVeME) benchmark database (hospital, minguez00nd2, and ulrich00vfh). Figure 1 shows these environments, as well as the size of each of them. The idea behind the selected environments is to test the motion methods under typical and critical situations. Thus, room, uc3m, tmm, and hospital correspond to typical office-like indoor scenarios whereas minguez00nd2 and The Scientific World Journal
Trajectories.
The data collection is made based on ten trajectories performed by the robots in each of the six environments using FM 2 and WaveFront as global planners and in both of them the local navigation algorithms VFH+ and ND. In order to ensure the soundness of the experiments, the robot start position was fixed in each environment and 10 goal positions were randomly selected. For comparison purposes the same targets were commanded to both FM 2 and WaveFront motion planners. Figure 2 shows an example of the different trajectories performed in order to achieve a randomly obtained goal.
Data Collection.
It seems logical to characterize the trajectories using the data provided by the sensors on the robot. In the experiment performed, we use a laser device as leading sensor for the navigation system, and hence the laser readings are used for comparison purposes. First of all, four different regions of the laser reading area were defined (see (iv) Right side angle 1, from 60 to 90 degrees.
Once these regions were defined, the data collection consisted of measuring, for each trajectory, the 11 features shown in Table 1.
As the proposal is to compare two global navigation algorithms, we performed 10 random trajectories in each of the 6 environments, using two robots and two local navigation algorithms, which sum up a total of 10 × 6 × 2 × 2 = 240 trajectories, and the values of these 11 variables were collected for all the trajectories performed.
It is worth mentioning that, in the experiments carried out, some of the trajectories (48, all of them with the WaveFront planner) did not arrive to the commanded final location. Although this fact could give some information for the comparison, we decided to remove the data of the failed trajectories. The reason to do so is that it could be considered as a specific problem of the used environment/goals, and we aim to present a general comparison approach in any situation. Nevertheless, in any comparison to be done, the amount of nonending paths for each of the compared approaches is a matter to be taken into account, as it could indicate that one of the used methods outperforms the other in the amount of completed trajectories, even though in completed ones the performance of the worst approach seems to be better.
Feature Subset Selection.
Not all the initially selected features are going to be used for the performance comparison activity; a feature selection is made previously, in order to obtain the feature subset which gives more information about the differences between the used global navigation algorithms. The selection is based on the Friedman test value (see the Appendix), while the search is made using and evolutionary algorithm called Estimation of Distributions Algorithm (EDA), as explained below.
Searching Method.
Feature Subset Selection (FSS) can be viewed as a search problem [30], with each state in the search space specifying a subset of the possible features of the task. Exhaustive evaluation of possible feature subsets is usually infeasible in practice due to the large amount of computational effort required.
Estimation of Distribution Algorithms (EDAs) have successfully been developed for combinatorial optimization [31,32]. They combine statistical learning with populationbased search in order to automatically identify and exploit certain structural properties of optimization problems. EDAs typically work with a population of candidate solutions to the problem, starting with the population generated according to the uniform distribution over all admissible solutions. The population is then scored using a fitness function. This fitness function gives a numerical ranking for each string, so that the higher the number the better the string. From this ranked population, a subset of the most promising solutions are selected by the selection operator. An example selection operator is truncation selection with threshold = 50%, which selects the 50% best solutions. The algorithm then constructs a probabilistic model which attempts to estimate the probability distribution of the selected solutions. Once the model is constructed, new solutions are generated by sampling the distribution encoded by this model. The new solutions are then incorporated back into the old population, possibly replacing it entirely. The process is repeated until termination criteria are met (usually when a solution of sufficient quality is reached or when the number of iterations reaches some threshold), with each iteration of this procedure usually referred to as one generation of the EDA.
Selected Attributes.
After the search process, we obtain as the most valuable feature subset that composed by the variables { 3 , 4 , 7 , 8 , 11 } (see Table 2), that is, the length of the trajectories, the mean of the five minimum values (right and left), and the mean of the front laser readings (right, left). These are the variables to be used in the experimental phase below, to establish a comparison between different global navigation algorithms, and to be able to select the most suitable navigation method for each environment. As a result, the remaining variables are discarded by the Friedman test guided EDA selection approach.
The Scientific World Journal 7 Main Idea. If neither condition has an effect, then not only should the differences be equally distributed on either side of 0, but also the distance from 0 should be the same on either side. Consider the following: (1) let be the rank of | | (absolute value of difference); (2) restore signs of to the ranks → signed ranks; (3) calculate either Using this nonparametric test we can compare couples of values obtained for the values of some variable (feature) by two different methods. Table 3 shows the obtained value results of the Wilcoxon test using all the data collected in the performed trajectories. The first row presents the results obtained using all the collected data (six environments, two robots, two navigation algorithms for each of the compared methods). The rest of the rows show the results obtained for each of the environments. As it can be seen, differences appear in some of the selected variables, but it is still needed to visualize which of the methods obtains better result (i.e., which method is the difference for). With this goal in mind, a graphical data visualization has been depicted in order to obtain a more clear view of the obtained results.
Data Visualization: All the Selected Variables in One Single
Picture. The proposed method to visualize the obtained results after applying the Wilcoxon test is a graphical one. More precisely, it is a polygon in which the obtained results for each individual test are shown. As five are the selected variables for the proposed comparison, pentagons are used for this case, but the number of sides could vary, as it depends on the proposed experiment, resulting in general in a polygon of sides, where is the number of selected variables. The selected value to be shown graphically is the 1 − significance of the Wilcoxon test. The reason is that the aim of the comparison is to stress the differences-if any-between the compared two approaches. If we directly plot values, the appearance of differences results in values placed in the centre of the pentagon, making visualization more difficult and thus the finding of clear conclusions. By contrast using 1 − , if there exist differences they are placed close to the perimeter and the figure results more visual.
In this way, and aiming at highlighting the significance of the test made over each edge, we inscribe an internal pentagon which has a 0.8 length in each edge-that is, a value of 0.2. The idea is that the values over that inscribed pentagon are those to be taken into consideration for the comparison. It could be seen as a "trajectory" of the values over 0.8, which show the differences. Figure 4 shows the defined visualization approach named as polygraph; the pentagon is shown in the left side. The order of the five edges has been set for clarity, and therefore the right edges correspond to the 5 minimum values mean (up) and −60 to 0 values mean (bottom) while the left edges refer to the 0 to 60 values mean (bottom) and 5 minimum values mean (up); the central edge depicts the differences between the length of the performed paths. In addition, differences could favor the first or the second method. For instance, if our purpose is to reach the goals as soon as possible, shortest trajectories are desired. To clarify that, as shown in the right Therefore, what is important to take into account is the surface obtained (both in area and in shape) after the five edge values are given. Figure 5 shows several pentagon shapes that can be obtained depending on the results of the comparison. Hence, the pentagon should appear clean if no differences are identified ( Figure 5(a)), full signigicant differences appear in all the variables ( Figure 5(b)), and the different shapes it can take depending on the source of the differences, as shown in Figures 5(c), 5(d), 5(e), and 5(f).
Regarding the differences which appear as it has been stated above, it has to be shown which of the compared methods obtains better results. For that purpose a symbol has been defined as shown in Figure 5. The defined symbol is only used when differences are present, so it is only drawn in those 1 − values over 0.8. For instance, Figure 5(b) is an example in which one of the compared methods (the first one, M1) outperforms on all aspects of laser readings, while it obtains worse result for the length of the performed trajectories. In this case, the selected approach would be probably M1; the same happens with Figure 5 More clear differences are shown in Figure 5(d), in which M1 would be selected as the best method, whereas the results obtained in Figure 5 On the other hand, the decision in the case of Figure 5(c) will completely depend on the specific task to be done (M1 behaves more secure; M2 optimizes the trajectories).
Experimental Results
Using these polygraphs (pentagons in the experiments performed, which can be used in a wide range of environments) we have carried out a comparison between the two global navigation algorithms: FM 2 and WaveFront. The idea is to select the best algorithm in general, or the more appropriate one for a given environment.
All Collected Data.
In order to show the obtained results, we present in Figure 6 the pentagon which contains the overall Wilcoxon related results when all the environments, robots, and local navigation systems are considered. As it can be seen, differences appear over the threshold established in four of the five edges; three of the edges indicate a better performance of FM 2 against the only one that favors WaveFront (shorter lengths are obtained), and hence FM 2 would be the selected one. At this point, if the user is not sure about the selection to be made, it would be necessary to look at the failed trajectories-if any-which in our case strengthens the FM 2 quality.
It is interesting to point out that the selection has been made based on the total number of edges that indicate a better performance, giving the same weight to all of them. If the task for which the method is going to be used imposes some requirements, one could consider to give more weight to the features that better represent those requirements. For example, if our main goal is to reach a destination as soon as possible, we would choose WaveFront instead of FM 2 , because it generates shorter trajectories (see edge 1 of the pentagon), at the expense of losing safety (see edges 2, 3, and 5 of the pentagon).
Environments One by One.
As stated before, for each environment an initial position has been fixed, and 10 goal positions have been randomly selected. Figure 7 shows the starting points (with a blue circle) and the goal points (with a red "X") used in each environment. The experimental results obtained with the collected data in each environment are shown in Figure 8. A thorough look at the obtained pentagons shows that length differences appear in all the environments (WaveForm is better from that point of view), but the other differences found are better for the FM 2 approach. In this way, right side differences appear in the Hospital environment (Figure 8(a)), which probably are due to the random trajectories selected (see Figure 2); in Room, TMM, UC3M, and Ulrich environments differences in left and right sides appear (except in the right side 5 minimum mean) which indicates that the distance to obstacles from both sides is larger when using the FM 2 algorithm; in the same way, with respect to Minguez environment, differences appear in the left side readings mean and in the right 5 minimum mean in favor of the FM 2 algorithm.
Conclusions and Future Work
A new approach to perform robot trajectory comparison is presented in this paper; the method could be applied to any kind of trajectory comparisons, both in indoor and outdoor environments and also in simulated and real situations. As an example, the approach is applied to analyse trajectories made by two navigation algorithms (FM 2 and Waveform) in six different simulation environments, with two different robots and using two different local planners as well.
The trajectory comparison method is based on well known statistical tests and thus provides a sound mathematical foundation, and it can help to decide the navigation algorithm to use, the most suitable robot to a particular environment, or to select a combination of methods (for instance, local navigation and global navigation) that are preferred for the goal the robot is programmed for.
It is also important to note that the method offers a visual way to compare different aspects related to the trajectories performed. The polygonal structures obtained give us an image of the relationships of the edges among the selected features. This fact could be used by users to understand better the meaning of the obtained polygons (pentagons in the experiments performed).
In the near future a set of experiments are planned with real robots in real outdoors environments; to deal with the sensors data, a DGPS system with a 2 cm localization error is to be used, combined with a laser sensor and a camera.
As future work, this statistical comparison has to be extended to other environments in which the application is not direct (or, to be more precise, it can be applied but maybe not so well visualized). A set of experiments has to be done with 3D environments (UAV, submarines) in order to improve the way to visualize the 3D comparisons. | 7,046.2 | 2014-11-25T00:00:00.000 | [
"Computer Science"
] |
Modeling the resonance $T_{cs0}^{a}(2900)^{++}$ as a hadronic molecule $D^{\ast +}K^{\ast +}$
The doubly charged scalar resonance $T_{cs0}^{a}(2900)^{++}$ is studied in the context of the hadronic molecule model. We consider $ T_{cs0}^{a}(2900)^{++}$ as a molecule $M=D^{\ast +}K^{\ast +}$ composed of vector mesons, and calculate its mass, current coupling and full width. The spectroscopic parameters of $M$, i.e., its mass and current coupling, are found by means of the QCD two-point sum rule method by taking into account vacuum expectation values of quark, gluon and mixed operators up to dimension $10$. The width of the molecule $M$ is evaluated through the calculations of the partial widths of the decay channels $M \to D_{s}^{+}\pi^{+}$, $M \to D_{s}^{\ast +}\rho^{+}$, and $M \to D^{\ast +}K^{\ast +}$. Partial widths of these processes are determined by strong couplings $g_1$, $g_2$, and $g_3$ of particles at vertices $ MD_{s}^{+}\pi^{+} $, $MD_{s}^{\ast +}\rho^{+}$, and $M D^{\ast +}K^{\ast +}$ , respectively. We calculate the couplings $g_i$ by employing the QCD light-cone sum rule approach and technical tools of the soft-meson approximation. Predictions obtained for the mass $m=(2924 \pm 107)~\mathrm{ MeV}$ and width $\Gamma=(123 \pm 25)~\mathrm{MeV}$ of the hadronic molecule $ M$ allow us to consider it as a possible candidate of the resonance $ T_{cs0}^{a}(2900)^{++}$.
I. INTRODUCTION
Recently, the LHCb collaboration discovered new resonances T a cs0 (2900) 0/++ (in what follows, T a0/++ cs0 ) in the processes B 0 → D 0 D + s π − and B + → D − D + s π + [1, 2], respectively. They were fixed in the D + s π − and D + s π + mass distributions, and are structures with spin-parity J P = 0 + . From the analysis of the decay channels of T a0/++ cs0 it becomes clear that they are fully open flavor four-quark systems of cdsu/cusd. Their resonant parameters are consistent with each other, which means that they are members of an isospin triplet: This is the first observation of an isospin triplet of exotic mesons with four different quark flavors. The resonance T a++ cs0 has an additional attractive feature as the first doubly charged exotic meson discovered experimentally.
It should be emphasized that T a0/++ cs0 are not first fully open flavor resonances seen by the LHCb experiment. Indeed, previously LHCb informed about scalar X 0 (2900) and vector X 1 (2900) structures (hereafter X 0 and X 1 , respectively), which were found in the D − K + invariant mass distribution of the decay B + → D + D − K + [3,4]. In a four-quark picture both X 0 and X 1 have the same contents udsc. New resonances T a0/++ cs0 fill up the list of such particles.
The exotic mesons built of four different quarks have already attracted the interest of researches. Relevant activities started from announcement by the D0 collaboration about the resonance X(5568) [5,6] presumably composed of quarks subd. Despite the fact that LHCb, CMS and ATLAS experiments did not confirm existence of this state, technical tools elaborated during this activity led to some interesting results, and are still in use in numerous research works. One of such results is prediction of a charmed partner X c = [su][cd] of X(5568) in the diquark-antidiquark model [7,8]. In our paper [7] it was investigated in a rather detailed form. Thus, we calculated the mass and full width of this tetraquark in the context of QCD sum rule method using different interpolating currents. In the case of scalar-scalar current we obtained m S = (2634 ± 62) MeV and Γ S = (57.7 ± 11.6) MeV, whereas the axial-axial current led to predictions m A = (2590 ± 60) MeV and Γ A = (63.4 ± 14.2) MeV. It is worth noting that an estimation (2.55 ± 0.09) GeV for the mass of X c was made in Ref. [8], as well.
The doubly charged exotic mesons were also objects of interesting analyses. The −2|e| charged scalar, pseudoscalar and axial-vector diquark-antidiquarks Z cs = [sd] [uc] were explored in Ref. [9]. Another class of tetraquarks Z ++ = [cu] [sd] with the electric charge 2|e| are antiparticles of the states Z cs and have the same masses and decay widths. Parameters of the vector tetraquark Z ++ V from this group of particles were found in Ref. [10].
The discovery of the resonances X 0 and X 1 highly intensified investigations of fully open flavor structures . In these articles different models were suggested to explain the observed parameters of these states and understand their inner organizations. Traditionally they were explored in the diquark-antidiquark and hadronic molecule pictures, which are dominant models to account for similar experimental data. Thus, X 0 was treated as a scalar diquark-antidiquark state [sc] [ud] in Refs. [11,12]. The X 0 was assigned to be the Swave hadronic molecule D * − K * + , whereas X 1 was examined as the P -wave diquark-antidiquark state [ud][cs] in Ref. [13]. There were attempts to consider these structures as rescattering effects. In fact, in Ref. [15] it was asserted that two resonance-like peaks in the process B + → D + D − K + may be generated by rescattering ef-fects and occur in the LHCb experiment as the states X 0 and X 1 .
The structures X 0 and X 1 were studied in our publications as well. The mass and width of the resonance X 0 were calculated in Ref. [34] in the framework of a hadronic molecule model D * 0 K * 0 . Results found in this work for the parameters of X 0 allowed us to confirm its molecule nature. We explored also the resonance X 1 by considering it as a vector diquark-antidiquark state [cs] [35]: It turned out that the diquarkantidiquark structure is an appropriate model to explain the measured parameters of X 1 . The LHCb observed only the vector tetraquark X V = [ud][cs], which was interpreted as X 1 . It is quite possible that, in near future, the diquark-antidiquark structures [ud][cs] with other quantum numbers will be seen in various exclusive processes. Therefore, parameters of these yet hypothetical exotic mesons are necessary to form a theoretical basis for upcoming experimental activities. Motivated by this reason, we computed the masses and full widths of the ground-state and radially excited scalar particles X [36]. The axial-vector and pseudoscalar tetraquarks X AV and X PS were investigated in Ref. [37], in which we evaluated their spectroscopic parameters, i.e., their masses and current couplings, and widths.
The resonances T a0/++ cs0 are last experimentally confirmed members of fully open flavor tetraquark family. In this article we are going to study the doubly charged state T a++ cs0 , therefore, below, write down its parameters measured by LHCb [2]: (1) Observation of new tetraquarks T a0/++ cs0 generated theoretical investigations aimed to bring them under one of existing models of four-quark mesons. In our article [38], we argued that diquark-antidiquark structures are not suitable for these resonances, because parameters of such states were already evaluated and predictions obtained for their masses are well below the LHCb data. One of possible ways to explain T a0/++ cs0 is to treat them as hadronic molecules. Then T a++ cs0 may be interpreted as a hadronic molecule D * + s ρ + or D * + K * + . In Ref. [38], we realized first of these scenarios, and estimated the mass of molecule D * + s ρ + by employing the QCD two-point sum rule approach. Our result m = (2917 ± 135) MeV for the mass of the molecule D * + s ρ + is consistent with Eq. (1). The resonances T a0/++ cs0 were investigated in Refs. [39][40][41][42][43][44][45] as well, in which authors used different models and calculational schemes. The one-boson exchange model was employed in Ref. [39] to study interactions in systems of D ( * ) K ( * ) mesons. Analysis allowed the authors to assign T a++ cs0 to be an isovector D * + K * + molecule state with the spin-parity J P = 0 + and mass 2891 MeV. Interpretation of new tetraquark candidate T a cs0 as the resonance-like structure generated by threshold effects was proposed in Ref. [40]. It was argued that the triangle singularity induced by the χ c1 K * D * loop peaks around the threshold D * K * and may simulate T a cs0 . A multiquark color flux-tube model was used to investigate the resonances T a0/++ cs0 in the context of the diquarkantidiquark model [41]. The authors found that a system [cu][sd] built of color antitriplet diquark and triplet antidiquark with the mass 2923 MeV is a very nice candidate to the resonance T a++ cs0 . Features of the charmedstrange tetraquarks were explored also in Ref. [43] in a nonrelativistic potential quark model. Decays of the neutral state T a0 cs0 in the molecular picture were considered in Ref. [44], whereas production mechanisms of the hiddenand open-charm tetraquarks in B decays were addressed in Ref. [45].
In the present work, we explore the resonance T a++ cs0 in the context of the hadronic molecule model. We implement the second scenario and model T a++ cs0 as the hadronic molecule M = D * + K * + . Our analyses of M include calculations of its mass m, current coupling f and full width Γ. The spectroscopic parameters of M are extracted from the QCD two-point sum rule computations [46,47] by taking into account vacuum expectation values of different quark, gluon and mixed operators up to dimension 10.
To estimate the full width of the molecule M , we consider its decays to pairs of conventional mesons D + s π + , D * + s ρ + , and D * + K * + . Partial widths of these processes depend on parameters of initial and final-state particles, as well as on couplings g i , which determine strong interactions of the molecule M and mesons at the vertices M D + s π + , M D * + s ρ + , and M D * + K * + , respectively. Because masses and decay constants of ordinary mesons are known, and spectroscopic parameters of M are object of present studies, only missed quantities are strong couplings g i . The couplings g i are evaluated in the framework of QCD light-cone sum rule (LCSR) method [48]. Additionally, to treat technical peculiarities of four-quark molecule-two conventional meson vertices, we invoke the technical methods of soft-meson approximation [49,50].
This article is organized in the following way: In Sec. II, we find the sum rules for the mass m and current coupling f of the molecule M = D * + K * + in the framework of QCD sum rule method. Numerical analysis of the quantities m and f is carried out in this section as well, where their values are evaluated. In section III, we investigate the vertices M D + s π + , M D * + s ρ + , and M D * + K * + and calculate the corresponding strong couplings g i , i = 1, 2, 3. Obtained information on g i is used to find partial widths of these decay channels, and estimate full width of the molecule M . The section IV is reserved for our conclusions. The key quantity necessary to investigate the spectroscopic parameters of the molecule M using the QCD twopoint sum rule method, is the interpolating current J(x) for this state. An analytic form of J(x) depends on the structure and constituents of a four-quark exotic meson q 1 q 2 q 3 q 4 . In the molecule picture the color-singlet structures come from [1 c ] q 1 q3 ⊗[1 c ] q 2 q4 and [8 c ] q 1 q3 ⊗[8 c ] q 2 q4 and (q 3 ↔ q 4 ) terms of the color group SU c (3). In the case under discussion, we assume that the hadronic molecule M is composed of two ordinary vector mesons D * + and K * + , and restrict our analysis by singlet-singlet type current. Then, in the [1 c ] dc ⊗[1 c ] su representation J(x) takes the following form where a and b are color indices. This current has the meson-meson structure and is a local product of two vector currents corresponding to the mesons D * + and K * + . It couples well to the molecule state D * + K * + . But, at the same time, J(x) couples also to diquark-antidiquark states, because using Fierz transformation a molecule current can be presented as a weighted sum of different diquark-antidiquark currents [51]. In its turn, a diquark-antidiquark current is expressible via molecule structures (for instance, see Refs. [52,53]). For example, the current J(x) rewritten in the form after Fierz transformation contains the vector-vector component Using the rearrangement of the color indices δ am δ bn = δ an δ bm +ǫ abk ǫ mnk , with ǫ ijk being the Levi-Civita epsilon, it is not difficult to see that The term in Eq. (5) is the −D * + s ρ + /2 meson-meson current, whereas dots indicate the second component which should be further manipulated to become diquark type current(s). In other words, J(x) couples also to a molecule D * + s ρ + and can couple to other meson pairs such as D + s π + with the same contents and quantum numbers. Nevertheless, the current J(x) corresponds mainly to the molecule D * + K * + , which will be demonstrated quantitatively in the next section by comparing its strong couplings g i to different two-meson states.
The sum rules for the mass m and current coupling f of the hadronic molecule M can be obtained from analysis of the correlation function [46,47], with T being the time-ordering operator.
To derive the required sum rules, the correlator Π(p) should be expressed using the physical parameters of the molecule M , as well as calculated in terms of the fundamental parameters of QCD in quark-gluon language. The first expression establishes the physical (phenomenological) side of the sum rules, for which we get To obtain Π Phys (p), we insert a complete set of the intermediate states with the content and quantum numbers of the state M into Eq. (6), and carry out integration over x. In Eq. (7), the contribution of the ground-state particle M is isolated and shown explicitly, whereas dots denote effects due to higher resonances and continuum states in the M channel. For further simplification of Π Phys (p), it is convenient to introduce the physical parameters of M by means of the matrix element 0|J|M = f m.
Then, we get the final formula for the function Π Phys (p): The r.h.s. of Eq. (9) contains only a trivial Lorentz structure, which is the unit matrix I. The function f 2 m 2 /(m 2 −p 2 ) is the invariant amplitude Π Phys (p 2 ) that corresponds to this structure: It will be used in our following analysis. The QCD side of the sum rules, Π OPE (p), has to be calculated in the operator product expansion (OPE) with some fixed accuracy. To derive Π OPE (p), we insert the interpolating current J(x) into Eq. (6), contract the corresponding heavy and light quark fields, and write the obtained expression in terms of the corresponding quark propagators. Having carried out these manipulations, we get for Π OPE (p), where S c (x) and S u(s,d) (x) are the quark propagators. The explicit expressions of the heavy and light quarks propagators can be found in Ref. [54]. The correlator Π OPE (p) has also a simple structure ∼ I and is characterized by an amplitude Π OPE (p 2 ). To find a preliminary sum rule, we equate the amplitudes Π Phys (p 2 ) and Π OPE (p 2 ). This equality contains contributions coming from both the ground-state particle and higher resonances. The latter can be suppressed by applying the Borel transformation to both sides of the sum rule equality. Afterward, using the quark-hadron duality assumption, we subtract the suppressed terms from the obtained expression. These manipulations lead to dependence of the sum rule equality on the Borel and continuum subtraction (threshold) parameters M 2 and s 0 . Obtained by this way, the expression and its derivative over d/d(−1/M 2 ) allow us to find the sum rules for the mass m and coupling f of the molecule M , which read and The function Π(M 2 , s 0 ) in Eqs. (11) and (12) is the invariant amplitude Π OPE (p 2 ) after the Borel transformation and continuum subtraction, and The Borel transform of the amplitude Π Phys (p 2 ) is given by the formula For the correlator Π(M 2 , s 0 ), we find a more complicated expression where M = m c + m s is the mass of constituent quarks in the molecule M . It is worth noting, that we neglect masses of u and d quarks, but take into account terms ∼ m s . At the same time, we do not include into analysis contributions ∼ m 2 s and set m 2 s = 0. The spectral density ρ OPE (s) is computed as an imaginary part of the amplitude Π OPE (p 2 ). Borel transforms some of terms obtained directly from Π OPE (p) are denoted in Eq. (14) by Π(M 2 ). In this paper, calculations are carried out by taking into account vacuum condensates up to dimension 10. Analytical expressions of ρ OPE (s) and Π(M 2 ) are lengthy, therefore we do not write down them here explicitly.
For numerical computations of m and f , one should specify different vacuum condensates, which enter to the sum rules in Eqs. (11) and (12). These condensates are universal parameters, which were extracted from analysis of numerous processes: Their numerical values are listed below: We have also included into Eq. (15) The sum rules in Eqs. (11) and (12) depend also on the Borel and continuum threshold parameters M 2 and s 0 . The choice of working windows for M 2 and s 0 has to satisfy standard constraints imposed on the pole contribution (PC) and convergence of the operator product expansion. To quantify these constraints, it is appropriate to use expressions and where Π DimN (M 2 , s 0 ) = Π Dim(8+9+10) (M 2 , s 0 ). The PC is used to fix maximum of the Borel parameter M 2 max , whereas its minimal value M 2 min is limited by the convergence of OPE. In sum rule analyses of ordinary hadrons PC ≥ 0.5 is a standard requirement. When studying multiquark particles this constraint reduces the region of the allowed M 2 . To be convinced in convergence of the operator product expansion, we demand fulfillment of R(M 2 min ) ≤ 0.05. Our calculations prove that the regions for the parameters M 2 and s 0 , meet all required restrictions. Thus, at M 2 = 2.7 GeV 2 the pole contribution on average in s 0 is 0.53, whereas at M 2 = 2 GeV 2 it equals to 0.72. In Fig. 1 the pole contribution is plotted as a function of M 2 at various fixed s 0 . It is seen that by excluding the small region M 2 ≥ 2.65 GeV 2 at s 0 = 10.7 GeV 2 the pole contribution exceeds 0.5. On average in s 0 , the constraint PC ≥ 0.5 is satisfied in the all working window for the Borel parameter. At the minimum point M 2 = 2 GeV 2 , we find R(2 GeV 2 ) ≈ 0.015 and the sum of dimension-8, 9, 10 contributions is less than 1.5% of the full result. Dominance of the perturbative contribution to Π(M 2 , s 0 ), and convergence of the operator product expansion are another important problems in the sum rule studies. In Fig. 2, we compare the perturbative and nonperturbative components of the correlation function. One sees that the perturbative contribution to Π(M 2 , s 0 ) prevails over nonperturbaative one, and forms more than 53% of Π(M 2 , s 0 ) already at M 2 = 2 GeV 2 growing gradually in the considered range of M 2 . From this figure it is also clear that convergence of OPE is satisfied: Contributions of the nonperturbative terms reduce by increasing the dimensions of the corresponding operators. There is some disordering in these contributions connected with smallness of gluon condensates. The dimension-3, 6, 9 and 10 terms are positive. The Dim3 and Dim6 contributions numerically exceed contributions of other operators, whereas Dim9 and Dim10 terms are very small and not shown in the plot.
Predictions for m and f are obtained by taking the mean values of these parameters calculated at different choices of M 2 and s 0 : The m and f from Eq. (19) effectively correspond to the sum rules' results at M 2 = 2.3 GeV 2 and s 0 = 11.2 GeV 2 noted in Fig. 1 by the red diamond. This point is approximately at the middle of the intervals shown in Eq. (18), where the pole contribution is PC ≈ 0.62. The circumstances discussed above ensure the ground-state nature of M and reliability of the obtained results.
The dependence of the mass m on the parameters M 2 and s 0 is drawn in Fig. 3. In general, a physical quantity should not depend on the auxiliary parameter of computations M 2 . Nevertheless, such residual dependence of m on the Borel parameter, as well as on s 0 exists and generates theoretical ambiguities of the extracted predictions in Eq. (19). It is worth noting that these ambiguities are smaller for m than for f . Indeed, for the mass they are equal only to ±4% of the central value, whereas in the case of f , they amount to ±16%. Such difference is connected by the analytical forms of the sum rules for these quantities: The mass m is given by the ratio of the correlation functions which smooths relevant effect, whereas f depends on Π(M 2 , s 0 ) itself.
Our result for the mass of the molecule D * + K * + agrees very well with the LHCb datum. This is necessary, but not enough to make credible conclusions about the nature of the resonance T a++ cs0 : For more reliable statements, one needs to estimate also the full width of the hadronic molecule D * + K * + suggested in this paper to model T a++ cs0 . the kinematically allowed decay modes of the M . We are going to evaluate the full width of the molecule M using these decay channels. It is noting that, ρ + and K * + mesons decay almost exclusively to π + π 0 and (Kπ) + pairs (see, Ref. [55]), therefore widths of the last two processes can be considered also as widths of the modes M → D * + s π + π 0 and M → D * + (Kπ) + , respectively. Partial widths of aforementioned processes are determined by the strong couplings g i at vertices M D + s π + , and etc. One of the effective ways to evaluate them is the QCD light-cone sum rule method [48]. In this approach, the QCD side of the sum rule, instead of the local vacuum condensates, is expressed in terms of one of the final mesons' distribution amplitudes (DAs). In general, the DAs of a hadron are nonlocal matrix elements of various operators with different twists sandwiched between the hadron and vacuum states. They are specific for each particle and modeled by taking into account the available experimental data. The LCSR method is suitable for analysis of not only the conventional hadrons, but also the multiquark systems such as tetraquarks, pentaquarks, etc. In the case of tetraquark-meson-meson vertices, however, these DAs reduce to the local matrix elements of the meson. For treatment of such vertices, one needs to apply some additional mathematical tools. The LCSR method was adapted for investigation of the tetraquark-meson-meson vertices in Ref. [56] and applied to study numerous decays of four-quark exotic mesons [54].
Here, we consider, in a detailed manner, the decay of the molecule M to pair of pseudoscalar mesons D + s π + . Partial width of this process depends on the spectroscopic parameters of the initial and final-state particles. The spectroscopic parameters of M have been evaluated in the previous section. The masses and decay constants of the mesons D + s and π + are available from other sources. The only unknown quantity required to calculate the M → D + s π + decays's partial width is the strong coupling g 1 of the particles at the vertex M D + s π + . The coupling g 1 is defined in terms of the on-mass-shell matrix element, where the mesons π + and D + s are denoted as π and D s , respectively. In Eq. (20) p ′ , p and q are four-momenta of M , and mesons D s and π.
In the framework of the LCSR method the sum rule for the coupling g 1 can be obtained from the correlation function, where J(x) is the current for the molecule M given by Eq.
(2). The interpolating current J Ds (x) for the meson D + s is defined by the formula with j being the color index. At this stage of our analysis, we express the correlation function Π(p, q) using the physical parameters of the particles involved into the decay process. To this end, we write Π Phys (p, q) in the factorized form [50,57], where m Ds is the mass of the meson D + s . As is seen, the function Π Phys (p, q) contains the matrix elements of the vertex M D + s π + , the molecule M and meson D + s . The matrix element of M is known from Eq.
with f Ds being the decay constant of D + s . After simple manipulations, we get The term in Eq. (25) corresponds to the contribution of ground-state particles in M and D + s channels. Effects of higher resonances and continuum states in these channels are denoted by ellipses. The function Π Phys (p, q) form the physical side of the sum rule for the coupling g 1 . It has the Lorentz structure proportional to the unit matrix I, therefore the expression in r.h.s. of Eq. (25) is the invariant amplitude Π Phys (p 2 , p ′2 ), which depends on two variables p 2 and p ′2 .
The correlation function Π(p, q) calculated in terms of quark propagators and matrix elements of the pion constitutes the QCD side of sum rules and is equal to where α and β are the spinor indices. The correlator Π OPE (p, q), apart from propagators of the c and s quarks, contains also the local matrix elements π|u b α d a β |0 of the pion. In the standard LCSR method, while studying vertices of conventional mesons, the correlator depends on the nonlocal matrix elements of the meson (for instance, π meson), which after some transformations can be expressed in terms of its different DAs. In the case under discussion, the Π OPE (p, q) contains the pion's local matrix elements appearance of which has a simple explanation. Indeed, because the hadronic molecule M is built of four valence quarks located at space-time position x = 0, contractions of two quark operators from the currents J Ds (x) and J(x) leave free the two quark fields from M at the same position x = 0. This feature of the correlation function Π OPE (p, q) connected with differences in the quark contents of tetraquarks and ordinary mesons is unavoidable effect for all tetraquark-meson-meson vertices.
It turns out that the Π OPE (p, q)-type correlators emerge in the limit q → 0 in LCSR calculations [50], which is known as the soft-meson approximation. In this approximation, p = p ′ and invariant amplitudes Π Phys (p 2 ) and Π OPE (p 2 ) depend only on one variable p 2 . It is worth emphasizing that the limit q → 0 is applied to hard parts of the invariant amplitudes, whereas in their soft parts (i.e., in matrix elements) terms ∼ q 2 = m 2 are taken into account. In other words, soft-meson approximation should not be considered as a massless limit of the correlation functions. Technical difficulties generated by this limit in the physical side of sum rules can be cured by means of technical tools elaborated in Refs. [49,50]. It is important that the sum rules for the strong couplings obtained using the full LCSR method, and soft-meson approximation lead to numerically close results [50]. To clarify this last point, we note that in the full version of the LCSR method a sum rule for the strong coupling at a vertex of three conventional mesons depends on numerous twoand three-particle quark-gluon DAs of a final meson. In the limit q → 0 in this expression survive only a few leading terms. Because their contributions are numerically decisive, for the strong coupling the full version and soft-meson limit of the light-cone sum rules give close predictions. Thus, in Ref. [50] the couplings g D * Dπ and g B * Bπ at the vertices D * Dπ and B * Bπ were calculated using both of these methods. In the full LCSR approach these couplings are equal to whereas in the soft-meson approximation, the authors found As is seen, values of the couplings are very close to each other, though uncertainties in the soft-limit are larger than in the full version [50]. These arguments do not imply a necessity of the softmeson approximation to study all of the vertices containing four-quark states. Two tetraquark-meson vertices, for example, can be readily investigated in the context of the conventional LCSR method [58].
The local matrix elements, π|u b α d a β |0 , carry color and spinor indices and are uneasy objects for further operations. We can rewrite them in convenient forms by expanding ud over the full set of Dirac matrices Γ J , and projecting onto the colorless states The operators uΓ J d, sandwiched between the π meson and vacuum, generate local matrix elements of the π meson, which can be implemented into Π OPE (p, q). The expression obtained for the Π OPE (p 2 ) in the soft limit is considerably more simple than the invariant amplitude in the full version of LCSR method. But, at the same time, soft-meson approximation produces problems in the physical side of the sum rule. Below, we will come back to finish calculation of Π OPE (p 2 ), but now it is time to fix sources of complications in Π Phys (p 2 , p ′2 ). To this end, we rewrite this amplitude in the soft limit Π Phys (p 2 ) = g 1 f mf Ds m 2 where m 2 = (m 2 + m 2 Ds )/2 and m π is the mass of the pion. It is seen that the amplitude Π Phys (p 2 ), in the soft approximation, instead of two poles at different points has one double pole at p 2 = m 2 .
The Borel transformation of Π Phys (p 2 ) is given by the expression, Apart from the ground-state contribution, in the soft limit, the amplitude Π Phys (M 2 ) contains additional unsuppressed terms ∼ A [50]. These terms correspond to the transitions from the excited states in M = D * + K * + channel with m * > m, and are not suppressed relative to the ground-state contribution even after the Borel transformation. These circumstances make problematic extraction of the g 1 from Eq. (32). The contributions ∼ A can be removed from the physical side of the sum rule by means of the operator P(M 2 , m 2 ) [49,50], which should be applied to both sides of the sum rule equality. After this operation the remaining suppressed terms in Π Phys (M 2 ), denoted in Eq. (32) by ellipses, can be subtracted by a standard way. As a result, we find the sum rule for the strong coupling g 1 , which reads where Π OPE (M 2 , s 0 ) is the Borel transformed and subtracted invariant amplitude Π OPE (p 2 ).
Recipes to compute the correlation function Π OPE (p, q) in the soft approximation were explained in Ref. [56], therefore we give only principal points of these calculations. Thus, having substituted the expansion (30) into Eq. (26), we perform summations over color indices and fix the local matrix elements of the pion that contribute to the Π OPE (p, q) in the soft-meson limit. It turns out that the contributions to Π OPE (p, q = 0) come from the pion's two-particle twist-3 matrix element, where s , D * , K * , π and ρ, which have been used in numerical computations.
The second equality in Eq. (36) arises from the partial conservation of axial-vector current (PCAC).
The amplitude Π OPE (M 2 , s 0 ) is given by the formula The first term in Eq. (37) is the perturbative component of the Π OPE (M 2 , s 0 ). The nonperturbative term Π NP (M 2 ) is computed with dimension-9 accuracy and has the following form: Besides the vacuum condensates, the sum rule in Eq. (34) contains also the masses and decay constants of the final-state mesons D + s and π + . Numerical values of these parameters, as well as parameters of other mesons, which will be necessary later, are presented in Table I. For the decay constants of the mesons D * + s and D * + , we employ predictions of the QCD lattice method [59]. For all other parameters, we use information of the Particle Data Group, mainly its last edition Ref. [55]. All these input parameters were either measured experimentally or extracted by means of alternative theoretical approaches.
Numerical analysis demonstrates that the working regions shown in Eq. (18) used in calculations of the M molecule's mass meet the required restrictions on the Borel and continuum subtraction parameters M 2 and s 0 imposed in the case of the decay process. Therefore, in computations of Π OPE (M 2 , s 0 ) the parameters M 2 and s 0 have been varied within the limits (18).
For g 1 , the numerical calculations yield The partial width of the decay M → D + s π + is determined by the expression where λ = λ(m, m Ds , m π ) and Then it is not difficult to find that which is large enough to confirm dominant nature of this channel.
B. Processes M → D * + s ρ + and M → D * + K * + These two processes differ from previous decay by a vector nature of produced mesons. This fact modifies matrix elements of the vertices and formulas for decay widths of the processes. We concentrate on analysis of the decay M → D * + s ρ + , and write down only the final predictions for M → D * + K * + .
The correlation function, which should be studied in the case of the decay M → D * + s ρ + , has the following form The correlation function Π µ (p, q) written down in terms of the matrix elements of the particles and the vertex M D * + s ρ + is given by the expression where m D * s and ε µ are the mass and polarization vector of the meson D * + s , and ǫ ν is polarization vector of the ρ meson. The expression in Eq. (45) is the contribution of the ground-state particles to the physical side of the sum rule, whereas ellipses stand for the contributions of higher resonances and continuum states.
We introduce the matrix element of the meson D * + s by the formula We also model the mass-shell matrix element of the vertex M D * + s ρ + in the following way: Then, it is not difficult to calculate the function Π Phys µ (p, q), As is seen, Π Phys µ (p, q) contains two structures proportional to ǫ µ and q µ . We are going to employ the structure ∼ ǫ µ , and corresponding invariant amplitude which in the soft limit has the form with m 2 being equal to (m 2 + m 2 D * s )/2. The QCD side of the sum rule is determined by the correlator This function has the same Lorentz structures as Π Phys µ (p, q). In the soft-meson approximation, it receives contribution from the matrix element where f ρ is the decay constant of the ρ meson.
Having fixed an amplitude which is proportional to ǫ µ and labeled it by Π OPE (p 2 ) it is not difficult to write the sum rule for the strong coupling g 2 Here, Π OPE (M 2 , s 0 ) is the amplitude Π OPE (p 2 ) after the Borel transformation and continuum subtraction procedures. It does not differ considerably from the Π OPE (M 2 , s 0 ) and has the following form The nonperturbative term Π NP (M 2 ) is given by the expression Numerical computations lead to the result |g 2 | = (9.8 ± 1.2) × 10 −1 GeV −1 .
The decay M → D * + K * + can be considered in a similar way. Omitting details, we write down predictions for the strong coupling g 3 and partial width of the process M → D * + K * + : and Γ 3 M → D * + K * + = (37 ± 10) MeV.
Information gained in this section allows us to compare couplings of the current J(x) to different twomeson states. It is seen that g i corresponding to vertices M D * + K * + , M D * + s ρ + and M D + s π + obey the inequalities g 3 > |g 2 | > g 1 . Hence, J(x) describes mainly the hadronic molecule D * + K * + , as it has been asserted in the Sec. II. Differences in the widths of relevant decays are connected not only with g i , but generated also by λfactors and parameters of produced mesons.
Using results obtained for the partial widths of the decays considered in this section, we can estimate the full width of the molecule M which should be confronted with the experimental data Eq.
(1). It is seen that, although Γ and Γ exp do not coincide, they are comparable with each other provided one takes into account errors of the measurements and theoretical analyses.
IV. CONCLUSIONS
In the present article, we have investigated features of the hadronic molecule M = D * + K * + , and calculated its mass and width. The mass of M has been computed using QCD two-point sum rule method. Prediction obtained for the mass m = (2924 ± 107) MeV is in nice agreement with the LHCb datum for the mass of the resonance T a++ cs0 . It also does not differ considerably from the mass (2917 ± 135) MeV of the molecule D * + s ρ + suggested to model T a++ cs0 in our paper [38] . We have evaluated the width of the molecule M by calculating partial widths of the decay channels M → D + s π + , M → D * + s ρ + , and M → D * + K * + . To this end, we have found strong couplings of the particles at vertices M D + s π + , M D * + s ρ + , and M D * + K * + by means of QCD light-cone sum rule approach and soft-meson approximation. The strong coupling of the hadronic molecule M with final-state mesons is large in the case of mesons D * + and K * + , which is understandable because M is composed of these particles. Nevertheless, the partial width of the decay M → D * + K * + is less than that of the decay M → D + s π + . The reason is that the kinematical factor λ in the expression of the decay widths in Eqs. (40) and (56) gets its largest value in the process M → D + s π + . As a result, the dominant channel of M is the decay to a pair of the mesons D + s and π + , which was actually observed by the LHCb collaboration.
The final result Γ = (123 ± 25) MeV for the full width of the molecule M is compatible with the Γ exp within the existing experimental and theoretical errors. The estimate for Γ may be further improved by taking into account another decay channels of the hadronic molecule M . It will be interesting also to compare the Γ and Γ exp with predictions for the full width of the resonance T a++ cs0 obtained in the context of alternative methods. Nevertheless, based on our present results, we may consider the hadronic molecule M = D * + K * + as a possible candidate to the doubly charged resonance T a++ cs0 .
The isoscalar partner of T a++ cs0 , namely the second resonance T a0 cs0 with quark content cdsu may be modeled as a linear superposition of hadronic molecules D * 0 K * 0 and D * + s ρ − . The dominant decay channel of this state is the process T a0 cs0 → D + s π − . The modes T a0 cs0 → D 0 K 0 , D * + s ρ − and D * 0 K * 0 are other possible decay channels of T a0 cs0 . Experimentally measured mass and width differences between T a++ cs0 and T a0 cs0 are equal to ∆m ≈ 28 MeV and ∆Γ ≈ 15 MeV, respectively. To be accepted as a reliable model for T a0 cs0 the molecule picture should be successfully confronted with the available data.
Another problem to be addressed here, is similarities and differences of the resonances T a0/++ cs0 and X 0(1) . It has been noted in Sec. I that X 0(1) are exotic mesons composed of quarks udsc. The scalar structures T a0 cs0 and X 0 differ from each other by quark-exchanges u ↔ u and c ↔ c. They are neutral particles with masses 2892 MeV and 2866 MeV, respectively. It is seen, that a mass gap between these two structures is small. In Ref. [34], we modeled X 0 as a hadronic molecule D * 0 K * 0 and found its mass equal to 2868 MeV, which is in a very nice agree-ment with the LHCb datum. The D * 0 K * 0 and a component D * 0 K * 0 of the molecule model for T a0 cs0 , have almost identical structures, therefore one expects the mass of the isoscalar state T a0 cs0 will be be consistent with experiments.
The mass difference ∼ 55 MeV between T a++ cs0 and X 0 is larger than the gap in the previous case which is connected presumably with doubly charged nature of T a++ cs0 . We explored the vector resonance X 1 in Ref. [35] as a diquark-antidiquark state [ud][cs] and achieved reasonable agreements with the LHCb data. In general, hadronic molecules composed of two mesons may be used to model vector particles as well. Because T a++ cs0 has the spin-parity J P = 0 + , in this article, we have studied only scalar particle D * + K * + . Molecules with the same quark content but different spin-parities are yet hypothetical structures. They are interesting objects for theoretical researches as well, because may be discovered soon in various exclusive processes. Properties of the isoscalar resonance T a0 cs0 , as well as counterparts of T a0/++ cs0 with different spin-parities are issues for future investigations. | 10,598 | 2022-12-22T00:00:00.000 | [
"Physics"
] |
Bilevel Programming for Traffic Signal Coordinated Control considering Pedestrian Crossing
,
Introduction
Taking Nanjing as an example, in recent years, the growth of urban motor vehicles has been obvious.
e main artery roads of many cities are in near-saturated state all the year round.
is has brought great negative impacts on our traveling, which not only affects the efficiency of work, but also causes people emotional dissatisfaction, so it is an important mission of our traffic workers to improve traffic capacity and maximize traffic efficiency within a limited road space [1,2].
rough the coordinated control of traffic signals, we can meet people's traffic needs to the maximum extent while ensuring safety [3][4][5]. e function of an isolated intersection is mainly determined by its control parameters, and of course by other intersections. However, due to the complexity of modern transportation systems, coordinated control of traffic signals has become one of the important traffic management strategies in cities [6,7]. Mapping to reality is even more unimpeded traffic flow, fewer traffic accidents, and more stable driving speed [8].
erefore, it is particularly important to coordinate the signals at the intersections around the subway stations where congestion is increasing and traffic demand is in expansion [9]. e project will use microsimulation as a research tool to analyze the main factors that need to be considered in the coordinated control of traffic signals. e time-space conflict between the vehicle and its influence on the coordinated control of the signals proposes a traffic signal control method that is conducive to subway passengers' travel [10,11].
Here is the literature review of signal coordinated control. In terms of coordinated control of signals, as early as the 1970s, there was a MAXBAND model for coordinated control of artery roads [12]. e concept of a progression band was proposed. e two-way progression bandwidth was taken as the objective function, and the maximum objective function model was used, combining mixed integer linear programming. en there is the MULTIBAND model [13,14], which is based on different traffic requirements on different road sections, and the corresponding bandwidth is calculated to get the best coordination effect. For the regional coordinated control, an off-line optimized network signal timing of TRANSYT proposed by the British Road Traffic Research Institute has been developed to comprehensively consider the comprehensive model of cruise time, bus modeling, peak delay calculation, and fuel consumption estimation [15], as well as inductive regional traffic coordination control systems SCATS, SCOOT, and others, which can effectively improve the traffic conditions of unsaturated and supersaturated road networks [16].
After combining the bus priority strategy, Vasudevan [17], under the framework of bus priority coordination control, with the minimum green time as the constraint and the minimum per capita delay under coordinated control as the optimization goal, established the optimization of trunk coordination control based on bus priority model. Many advanced signal control systems take into account different priority transit strategies and are added to the algorithm to better and more efficiently adapt to multimode control needs. Conversely, some systems are designed to reduce per capita delays, such as the reduction of motor vehicle delays. Some studies [18,19] have added traffic priority based on traffic rules, and, for Lo [20], a series of motor vehicles are selected in advance to implement their priority control methods. In addition, some systems weigh the factors such as pedestrian delays, motor vehicle delays, bus delays [21], or by reducing the transit time of buses and the waiting time of pedestrians on downstream stations and other priority strategies for other transportation systems [22].
Recently, signal coordination control has increasingly favored the use of vehicle-coordinated data, and they have attempted to combine all of the above factors, including weighing the delays of various passers-by, taking into account various priority strategies. In the system operation, real-time traffic information needs to be obtained. Tan realized vehicle information interaction through AVL (Automated Vehicle Location) or APC (Automated Passenger Counter) [23]. However, such systems are limited to two connected main road intersections (not more), and there are more problems with multiple bus lines and multiple priority control strategies [11]. ere are still researches using machine learning methods to deal with the problems within the intersection between vehicles and pedestrians [24][25][26]; however, the results are limited and unexplainable for traffic design and control [27,28].
Although there are some researches focusing on the modeling of pedestrian crossing behavior [29][30][31], to the best of our knowledge, it is rare to combine models of coordinating signal control and pedestrian delay. So, we consider the problems of pedestrian crossing with signal control. In this paper, the situation of green light time and relative offset between two adjacent intersections is analyzed comprehensively. en, according to the average travel time of the motor vehicle, the green wave feasibility analysis is carried out to calculate the corresponding progression bandwidth and the delay of the motor vehicle flowing under the green wave (not considering the delay of the nongreen wave motor vehicle). Finally, the complete intersection green wave analysis is obtained. en, the model of pedestrian delay is analyzed. By collecting a large amount of data, the model of a different motor vehicle and pedestrian flow delays is obtained. en, the vehicle flow and pedestrian flow are simulated by Vissim to test the simulation of each model under different conditions. e degree of integration is obtained to generate a more accurate calculation model of pedestrian delay. Secondly, the algorithm is written in Python, and the above two models are merged together and applied to the actual intersection coordination model, and the optimal coordination scheme is obtained by inputting into the algorithm. Finally, the Vissim is used to simulate the actual situation to judge the rationality of the established model and the edited algorithm and draw conclusions. e remaining part of this paper is as follows: in section 2, we put forward models of progression bandwidth under different situations of cycle length, green time, and offset. Section 3 illustrates the process of establishing models of pedestrian delay. Section 4 proposes the bilevel programming fusing the aforementioned two models and an algorithm to solve it. Furthermore, it also provides a case study to test the reasonableness of them. Finally, we conclude in Section 5.
Model of Progression Bandwidth
Due to the high land utilization rate in large cities, the distance between adjacent intersections is very close. erefore, it is necessary to coordinate the signal scheme to maximize the traffic efficiency of the vehicle. is is called artery traffic coordination control. e so-called green wave means that the vehicle (vehicle flow) continuously passes through a certain main road and encounters less red light as much as possible.
ere are many parameters in the signal coordination control, including signal period, green signal ratio, offset, and so on. e main idea of building a model is obtained [32], which is modeled by drawing a spatiotemporal map.
is paper mainly studies the coordinated control of two adjacent intersections and calculates the delay and progression bandwidth generated by the corresponding green wave traffic by considering the situation of the vehicle queuing at the second intersection. is paper is based on and beyond the content of the former, and at the same time, corrects some errors. rough the comparison of the red and green light phase difference between the two intersections and the first intersection lipstick and green light time, the complete signal set of adjacent intersections is summarized. en, the subclass is divided by the average transit time of the motor vehicle, and then the coordination parameters of each subclass are analyzed in turn, and finally, the complete model is obtained.
Because the coordinated control is affected by multiple factors, the vehicle discretization is serious, resulting in the formation of a fleet; there are a large number of vehicles entering and exiting the road, thus destroying the formation of continuous traffic. e signal lights at the intersection are complex, with more than two phases and coordination difficulties. erefore, before establishing a model, it is necessary to make some reasonable assumptions, both not to deviate from the actual situation and to meet the conditions for establishing the model.
(1) e effects of road traffic conditions, such as weather and road geometry, are not considered. Table 1, and the relationship of some of them is given as follows (specific symbols in models will be given correspondingly): In Figure 1, when Δ r i,i+1 > r i , Δ g i,i+1 < g i , according to the position of the last intersection corresponding to the start time of the red light at the next intersection, it is divided into three parts of four categories. e slope of red lines in Figure 2 is the basis of classification.
Category I (t i,i+1 < Δ r i,i+1 − r i (Figure 1 part ①)): in Figure 2(a), at this moment, some vehicles departing from the green light at the intersection i can pass through the i + 1th intersection, and some of them have to wait for congestion. t 2 denotes the time interval when vehicles meet with congestion at the specified speed, and t 3 denotes the congestion evacuation time (for the evacuation through the parking line, the same below). D denotes traffic delay of vehicles from the progression band, which is represented by the shadowed part in this figure. So we can derive the following equations: Category II (Δ r i,i+1 − r i < t i,i+1 < Δ r i,i+1 (Figure 1 part ②)): in Figure 2(b), the vehicles from ith intersection at red time and the link connecting ith and i + 1th intersection generate queue. So when the progression vehicles come to Offset of red starting time between I i and I i+1 (s) Δ Offset of green starting time between I i and I i+1 (s) q r i Traffic volume at I i+1 when I i is red (pcu/s) q g i Traffic volume at I i+1 when I i is green (pcu/s) S i Saturated flow rate at I i (pcu/s) Average travel time between I i and I i+1 (s) b i Progression bandwidth (s) the i + 1th intersection, the front part of them should wait. We denote t 1 as the max time interval when vehicles leave from ith intersection and wait at the next node. t 2 denotes the waiting time of the foremost vehicle from the progression band, and t 3 denotes the congestion evacuation time. D also denotes the traffic delay of vehicles from the progression band, which is represented by the shadow part in this figure. We then derive the following: Journal of Advanced Transportation Figure 1 part ③)): in Figure 2(c), at this time, the vehicle which reaches at the start time of the next intersection at the specific speed is at the range of green time at ith intersection, and the tail of the traffic flow in the progression band must be congested, and the front of the vehicle should wait or not wait depending on evacuation rate at i + 1th node. At this time, it is divided into two categories. is one discusses that the saturated flow rate is large enough that the congestion has vanished when the head of the progression band passes. We denote t 1 as the max time interval when vehicles leave from ith intersection and wait at the next node. t 2 denotes the waiting time of the end vehicle from the progression band, and t 3 denotes the congestion evacuation time, t′ denotes threshold time between block and unblock. D also denotes the traffic delay of vehicles from the progression band, which is represented by the shadow part in this figure. We then derive the following: In Figure 2(d), when the saturated flow rate is not enough, the head of the progression band from ith intersection should wait. t 1 denotes the green time interval of the tail of traffic flow at ith intersection, t 2 denotes the green time interval of the head of traffic flow at ith intersection, t 3 denotes the congestion evacuation time, and t′ denotes threshold time between block and unblock.
In Figure 3, when Δ r i,i+1 < r i , Δ g i,i+1 < g i , according to the position of the last intersection corresponding to the start time of the red light at the next intersection, it is divided into three parts of four categories. e slope of red lines in Figure 4 is the basis of classification. (Figure 3 part ①)): in Figure 4(a), this situation is the same as category II in the interlaced one ( Figure 2(b)). So the notions are omitted, and equation (3) should be used. Figure 3 part ②)): in Figures 4(b) and 4(c), this situation is the same as category III in the interlaced one (Figures 2(c) and 2(d)), So the notions are omitted, and equation (4) and (5) should be used. Figure 3 part ③)): in Figure 4(d), under the specific speed, the vehicles from the ith intersection of the progression band must wait at the next intersection, so it can generate green wave, which means that this situation is eliminated.
In Figure 5, when Δ r i,i+1 > r i , Δ g i,i+1 > g i , according to the vehicle's position at the last node which reaches at the start Journal of Advanced Transportation time of red at the next intersection, it is divided into three parts of five categories. e slope of red lines in Figure 6 is the basis of classification.
Category Figure 5 part ①)): in Figure 6(a), at this time, the vehicle which reaches at the start time of the next intersection at the specific speed is at the range of green time at ith intersection, and the tail of the traffic flow in the progression band must be congested, and the front of the vehicle should or should not wait depending on evacuation rate at i + 1th node.
At this time, it is divided into two categories. is one discusses that the saturated flow rate is large enough that the congestion has vanished when the head of the progression band passes. We denote t 1 as the max time interval when vehicles leave from ith intersection and wait at the next node. t 2 denotes the waiting time of the end vehicle from progression band, t 3 denotes the congestion evacuation time, and t′ denotes threshold time between block and unblock. D also denotes the traffic delay of vehicles from the progression band, Figure 3: Classification of forward overlapping spatiotemporal figures according to offset. 6 Journal of Advanced Transportation Journal of Advanced Transportation 7 which is represented by the shadow part in this figure.
We then derive the following: In Figure 6(b), when the saturated flow rate is not enough, the head of the progression band from ith intersection should wait. t 1 denotes the green time interval of the tail of traffic flow at ith intersection, t 2 denotes the green time interval of the head of traffic flow at ith intersection, t 3 denotes the congestion evacuation time, and t′ denotes threshold time between block and unblock.
Category Figure 5 part ②)): in Figure 6(c), this situation is the same as category II in the interlaced one (Figure 2(b)). So the notions are omitted, and equation (3) should be used. Figure 5 part ③)): in Figures 6(d) and 6(e), this situation is the same as the category III in the interlaced one (Figures 2(c) and 2(d)), So the notions are omitted, and equations (4) and (5) should be used.
Finally, we have proposed progression bandwidth models considering different offset, green time, and average travel time, which is summarized in Table 2.
Above all, we get the progression bandwidth and motor vehicle delay of adjacent intersections in each case, and finally, there will be multiple progression bandwidths on different road sections. At present, the optimization methods for coordinated control of traffic signals are the maximum progression bandwidth method and the minimum delay method. e maximum progression bandwidth method is to ensure that the vehicle (vehicle flow) can occupy the longest period of one cycle through the intersection in a continuous manner. Since the cycle length of each coordinated intersection is assumed to be the same, the progression band is satisfied here. Of course, this will ensure that the most traffic flow can participate in coordinated control. For the case where the length of the progression band is different in different sections, the minimum value is taken as the inspection index. e minimum delay method is to minimize the sum of the delays of the progression motor vehicle at the intersection (the delay of the nongreen wave vehicle is not considered here), which is another reasonable solution in theory. Delays are not only related to coordinated control but also related to vehicle emissions, parking, fuel consumption, and so forth, thus affecting the corresponding driving costs.
In addition, in the equations of the aforementioned models, some models' bandwidths are negatively correlated with delays, and some models satisfy the quadratic function of the two variables, which is relatively complicated. When the progression bandwidth is the largest, the motor vehicle delay is not necessarily the smallest; otherwise, when the motor vehicle delay is the smallest, the progression bandwidth is not necessarily the largest. In addition to the pedestrian delays to be studied after this article, there are at least three evaluation indicators, as for how to assign weights, how to give comprehensive evaluation indicators reasonably, and then give them in detail in Section 4.
Model of Pedestrian Delay
Since this study not only considers the coordinated control of traffic signals, but also considers a large number of pedestrian flows, it is necessary to consider not only the coordination and optimization of the progression bands at each intersection, but also the minimization of pedestrian crossing delays. In fact, signal control interacts with pedestrians crossing the street. Pedestrians will affect the pedestrian clearing time at the intersection, thus affecting the green time of the opposite vehicle. Too many vehicles will 8 Journal of Advanced Transportation aggravate their conflict with pedestrians, resulting in increasing delays. In addition, there have been many studies on the delays of pedestrians at the intersection of signal timing, so we should consider the degree of adaptation of different models in different specific situations. e specific process of this chapter is as follows: firstly, we introduce several pedestrian delay models, analyze their advantages and disadvantages, applicable conditions, and then use Vissim microsimulation to obtain three cases of motor vehicles through cluster analysis, simulating pedestrian flow from less to more. en the simulation results are compared with the calculation results, and the errors are calculated to determine the adaptability of each model under different flow rates, which lays a theoretical foundation for the actual analysis of pedestrian flow in the following section.
Different Models of Pedestrian Delay
where C denotes cycle length of intersection(s), G denotes green time of a cycle(s). e model is based on the equal pedestrian arrival rate, the same signal period, and there is no conflict between pedestrians and motor vehicles. It is an ideal model which is applicable to intersections where motor vehicles and pedestrian traffic are small, which is not suitable for the background of this project. Nevertheless, a series of improved models based on this model have been promoted even more.
BR Model [33]
where F denotes the proportion of pedestrians obeying traffic rules. is model takes into account pedestrians who do not follow traffic rules and believes they will not be delayed. Especially suitable for the situation in developing areas, people generally have a weak sense of traffic. However, the model does not consider the conflict between pedestrians and motor vehicles, and there is no clear behavioral assumption. e applicable conditions are subject to great constraints. [34].
LI Model
where d G denotes average delays of pedestrians(s), k NU denotes adjustment factor of uneven arrival rate, R E denotes effective red time(s), P w denotes the proportion of violations, and q denotes average arrival rate of vehicles (pcu/s). is model assumes that the pedestrian arrival rate is not fixed throughout a cycle and that pedestrians arriving in the green time and pedestrians who do not obey the traffic rules will still have delays. Furthermore, the average delay of pedestrians varies with the entire cycle, and these changes are certain. At the green time, the average delay of pedestrians is fixed. At the beginning of the red time, the value is the largest, then linearly decreases, and periodically changes. is model is not suitable for areas where pedestrian flow is high, and the calculated value will be small. [35].
Z Model
where s denotes saturated pedestrian flow (ped/h), q denotes average arrival rate of pedestrians (ped/h), λ 1 denotes arrival Table 2: Summary of progression bandwidth models.
Conditions
Analysis position (ith node) Congestion situation Equation Green-green Red-green Green-red-green Mid Head Tail Head and tail Red-green Green-red-green Red-green-red Head Tail Head and tail All flow Green-red-green Red-green Green-red-green Tail Head and tail Head Tail Head and tail rate of left-turn vehicles (pcu/s), λ 2 denotes arrival rate of right-turn vehicles (pcu/s), τ denotes safety gap(s), W denotes width of motorway (m), V p denotes average speed of pedestrians (m/s), R denotes reaction time(s), and l denotes time through vehicle(s). is model considers the delays of pedestrians waiting at the red light and also takes the delays caused by left-or right-turning vehicles as they cross the crosswalk into account. [36].
MV Model
where α 1 denotes adjustment factor of uneven arrival rate, α 2 denotes pedestrian ratio of noncompliance with traffic regulations, Δ t denotes ideal time of crossing(s), c denotes adjustment factor of pedestrian crossing, D VIT denotes conflict delay of pedestrian and vehicle(s). e model actually has three components, including pedestrian waiting time delay, transit time delay, and conflict delay with the motor vehicle. e pedestrian waiting time delay is obtained by correcting HCM delay formula. e transit time delay is obtained by the speed expansion theory. e third part is obtained through a binary logit model, which was obtained by directly looking up the table during the project. e model is suitable for complex intersections and assumes that the pedestrian arrival rate is uneven; pedestrians will violate traffic rules, pedestrian speed changes, and pedestrian-vehicle conflicts.
Adaptive Analysis.
We have obtained five different models from the literature review, and we have two variables: vehicles flow and pedestrian flow. To make it simple, we discrete them, that is, take a value every 50 and 100, respectively, in Vissim simulation. However, we also need a dimensionality reduction. In this study, we use cluster analysis. For more information, please see the appendix. Here we directly show the results. e relationship between pedestrian delay and motor vehicle flow is not significant, while significant in pedestrian flow. According to the flow rate of the motor vehicle, it is divided into three categories, that is, q � 600 pcu/h when the motor flow is small; q � 1500 pcu/h when the motor flow is moderate; q � 2400 pcu/h when the motor flow is large.
Here are the details in Figure 7. ere are six subplots, in the left column are the pedestrian delay(s) as the function of pedestrian flow (ped/h), in the right column are the relative error as the function of pedestrian flow (ped/h). In the first row, the two figures depict the situation under small vehicle flow (q � 600 pcu/h). In the second row, the two figures depict the situation under moderate vehicle flow (q � 1500 pcu/h). In the third row, the two figures depict the situation under large vehicle flow (q � 2400 pcu/h). e gray (only in the left column) lines denote delay in the simulation, the yellow lines denote delay and relative error of HCM model, the red lines denote delay and relative error of BR model, the green lines denote delay and relative error of LI model, the blue lines denote delay and relative error of Z model, and the purple lines denote delay and relative error of MV model. In Figures 7(a) and 7(b), we find that when the arrival rate of pedestrians is less than 600 ped/h; HCM model is more in line with this situation. When the arrival rate of pedestrians is between 600 ped/h and 1200 ped/h, LI model is more accurate because as the pedestrian flow increases, there are more people who do not obey the rules, and these people can also generate delays. When the flow rate exceeds 1200 ped/h, the MV model fits well, because when pedestrians increase, the conflict with the motor vehicle increases gradually (although the motor vehicle flow is small). At this time, both the MV model and the Z model consider the conflict between pedestrians and motor vehicles. However, since the Z model is limited by the maximum flow of pedestrians, the error near the maximum flow is significantly large, and the conflict between pedestrians and motor vehicles in the MV model should be obtained from many curves of surveys, so the fault tolerance rate is higher.
In Figures 7(c) and 7(d), when the pedestrian flow is less than 1200 ped/h, the LI model has a good fitting degree. When the pedestrian flow is greater than 1200 ped/h, the MV model has a high degree of fitting. While other models are not suitable under these conditions, especially unlike before, the HCM model has a low fit at low flow rates. is is because the delay model just only considers cycle length and green time as the vehicle flow increases. ere are also a number of correction factors to consider, including pedestrian behavioral factors, delays caused by pedestrians and motor vehicle conflicts. ese two models take the above effects into account.
In Figures 7(e) and 7(f ), when the pedestrian flow is less than 900 ped/h, the Z model has a higher degree of fitting. When the pedestrian flow is between 900-1600 ped/h, the LI model fits to a higher degree. When the pedestrian flow is greater than 1600 ped/h, only the MV model can be used. is is because when the pedestrian flow is small, the MV model overconsiders the delay caused by the conflict between the motor vehicle and the pedestrians, so the error is relatively large; on the contrary, when the pedestrian flow is large, the collision between the pedestrian and the car is gradually intensified. is should be taken into consideration, and the Z model is nonlinearly increasing due to the limitation of the pedestrian flow, and the growth rate is gradually increasing. erefore, the Z model is no longer applicable when approaching the upper limit of pedestrian flow. At the same time, the LI model takes care of both. 10 Journal of Advanced Transportation Finally, we summarize the equations of calculating pedestrian delay as follows:
Algorithm and Case Study
From Sections 2 and 3, we have established coordinated control progression band models and pedestrian delay models according to different actual situations. e most crucial point of this project is to combine the two models. For example, in the vicinity of the subway station, it is necessary to consider not only the optimization of coordinated control, but also the large number of pedestrian flows periodically entering and leaving the subway station. Firstly, we propose an algorithm to deal with this bilevel problem and then use a case to test the rationality of models and this algorithm.
Bilevel Programming and Algorithm.
From the above analysis, the problem can be transformed into the following: Journal of Advanced Transportation min f C, g 1 , g 2 , . . . , g n , q s.t. G 1 C, g 1 , g 2 , . . . , g n , q ⊂ U, max f 1 C, g 1 , g 2 , . . . , g n , p min f 2 C, g 1 , g 2 , . . . , g n , p Since the study focuses on the delay of pedestrian crossing, the minimization of pedestrian delay is defined as the objective function of the upper planning, where q is the other variable related to pedestrian delay except for the cycle length and the green time, which is represented by a letter and it represents a difference from the lower level planning decision variables; the constraints can be expressed as a general formula, specifically the constraints in the actual problem, including the green light time being less than the signal cycle length and within a certain range such as (C/4, 3C/4). e lower level planning is a multiobjective nonlinear programming. One is that the progression bandwidth is the largest, and the other is that the total delay of the vehicle at the intersection is the smallest. As with the upper plan, a parameter p is used here to represent the decision variables specific to the underlying plan. e constraints of the lower-level planning are more complicated, including not only the limitation of the green time, but also the constraints of various situations in the model.
It is apparent from the equation that correlating the models of the upper and lower layers by the green time and cycle length has several advantages in the analysis of the problem. ere are conflicts and dependencies between the upper and lower layers. Since the road right in the road is certain, the more travel time is given to the pedestrian, the corresponding motor vehicle delay will increase, and the green wave will be difficult to form. Conversely, the smoother the vehicle travels, the less time it takes for pedestrians to cross the street. However, the decision variables in their objective function are repeated and therefore dependent on each other. e decision of the lower layer not only affects the value of its own objective function, but also affects the decision of the upper layer. However, it does not completely unconditionally conform to the upper level plan, and it retains certain autonomy.
ere are many bilevel programming solutions, including fuzzy algorithm, branch and bound method, KT method, and pole algorithm. However, the settings are problem-specific under this scenario, like the cycle length is mainly between 60 and 180's as an integer and the green time is positive.If the range of the specific optimal value is not known in advance, it cannot be obtained by branch and bound. And the n-dimensional model can be established only counting the green time at n intersections, and then the offset of adjacent intersections is calculated. e final model must exceed n-dimensional, so the general gradient algorithm and iterative step size algorithm are very difficult to execute. Considering the particularity of the problem, this study turns the double goal into a single objective function as follows: Comparing the five objective functions [37] of traffic signals and cost-effect function proposed by Dr. Peñabaena-Nibbles [38], we put forward this final objective function, where i denotes ith intersection, j denotes direction of entrance of intersection, b ij denotes width of progression band, d v ij denotes delays of vehicles, d p ij denotes delays of pedestrians, and q ij denotes flow of vehicles. e method needs to list the combination of different green times in the same cycle, calculating the corresponding delay and progression bandwidth and the specific computational structure of each layer is shown in Figure 8. Progression bandwidth and motor vehicle delays require three columns as subsystems for the green time and offset between the two intersections and each intersection requires only green time (and other factors which do not change with cycle length) when calculating pedestrian delays. So, each green light column is listed as a subsystem. We then think of it as solving the shortest path problem in the calculation, using the Dijkstra algorithm here. Each subsystem is regarded as the path in the shortest path problem, and the calculated value of the subsystem is the weight. erefore, the two layers of the problem can be regarded as solving the shortest path problem with n nodes. e pseudocode of the algorithm is in Algorithm 1.
In Algorithm 1, s, i, j denotes node (intersection) and d denotes the total distance of each node. We then suppose an origin and a destination, finding the shortest path between these two nodes. And the corresponding cycle length and offset between the adjacent intersection can be calculated, which means the optimization scheme will be obtained.
Case Study.
is study analyzes the road between Jiming Temple, Fuqiao, and Daxinggong Station of Nanjing Metro Line 3, as shown in Figure 9, namely, Taiping North Road (North-South), Beijing East Road (East-West) from the north and Zhongshan East Road to the south. (Eastwest), with a total length of approximately 1.9 km, with several intersections, including eight signal-controlled intersections. e section is located in the Xuanwu Lake District of Nanjing and is one of the north-south traffic skeleton roads. Judging from the spatial structure of the whole city, Taiping North Road (Beijing East Road-Zhongshan East Road) is an important channel for communication between the north and the south of Xuanwu District, which mitigates the main flow of three subway stations to various functional areas; from the surrounding areas in terms of function, the area of Taiping North Road is an important urban block integrating office, residence, study, shopping, and other functions. ere are Southeast University Sipailou Campus, Huahai 3C Plaza, Sipai Building Business Center and Presidential Palace and major learning, shopping, and office spaces such as libraries. erefore, the traffic design of this main road is not only related to the efficiency of the entire urban transportation system, but also closely related to the work and life of the surrounding residents. It has important practical significance.
In addition, there are many places for students to study and conduct on this main road, including Southeast University and Chengxian Street Primary School. e walking demand is very large, which is in line with the background of pedestrians crossing the street. Furthermore, many intersections, such as Shipopo-Taiping North Road, Wendui Bridge-Taiping North Road, and Sipai Building-Taiping North Road are T-shaped intersections, and Beijing East Road-Taiping North Road is only eastbound. In addition, some north-south roads are forbidden to turn left. All the conditions are similar to our assumption of coordinated control, that is, " e road between intersections does not contain a large number of vehicles that are transferred in or out" is similar. erefore, this study selects this main road as the simulation object.
We collected corresponding data (flow, speed) by field investigation. en according to the aforementioned algorithm, we can finally get the results of traffic signal coordinated control in Table 3. Here we should note that the cycle length among the eight intersections is identical, that is, 120 s, which is one of the assumptions in this study. en we Table 4. We get classification of vehicle and pedestrian service levels to evaluate the traffic situation.
It can be seen that in addition to Zhongshan Road-Taiping North Road and Zhujiang Road-Taiping North Road, the delays of other coordinated intersections have been improved, and some service levels have even improved by one level. e average queue length is 4 to 8 vehicles in accordance with the average headway distance of 6 m, which is acceptable. However, motor vehicle delays at the two complex intersections increased after the improvement, with an average queue of more than 15 vehicles. In terms of pedestrians, the average delay of the 8 intersections is within 30 s, the service level was more in the B and C sections, and the effect on pedestrian control reached expectations.
In short, although the delay of the two separate intersections increased slightly, the control effect of the motor vehicles and pedestrians on the whole road was improved due to the formation of green waves, which basically achieves the purpose of the project, as well as motor vehicle progression band model, pedestrian delay model, and the rationality of the algorithm. To further improve the result, we will analysis and connect findings between branch-and-bound search [39] and algorithm in this paper.
Conclusion and Discussions
In this paper, a progression band model is established for the progression band and delay generated by the motor vehicle passing through adjacent intersections. On the basis of the existing model, the conditions are further refined, so that the model covers different intersection cycle length and green time, and the calculation formulas of progression bandwidth and delay under different conditions are given. In order to obtain a more accurate model for calculating pedestrian crossing delays, different models and formulas established in several documents were integrated, and their advantages and disadvantages and applicable conditions are analyzed. Furthermore, three kinds of motor vehicle flow speed were established with Vissim. In this case, different pedestrian flows are set from small to large, and the simulation delay is compared with the calculation delay. Finally, we get the In order to fuse the above two models, a bilevel programming problem is established. en, we analyze the characteristic of this study to simplify the objective function and use the shortest path searching to get the optimization results. In order to verify the rationality of the algorithm and the corresponding models, we find artery roads in line with the background of the project, conduct research and analysis, and obtain relevant data. After integration, on the one hand, the numerical classification will be carried into the algorithm to obtain the results of coordinated intersection, that is, cycle length, green time and offset, and the progression bandwidth based on the above models; on the other hand, the results are input into Vissim for simulation, in an environment with certain behavioral assumptions. e operation is carried out to obtain the effect and evaluation index after the improvement under the actual situation. Finally, the service level analysis is carried out, and the certain rationality of the project model and algorithm can be guaranteed. e biggest contribution of this paper is to put forward models of progression bandwidth and pedestrian delay and establish a correlation algorithm with intersections as subsystems to solve the corresponding signal coordination parameters.
Here is the future direction of research in my mind. In the establishment of the progression bandwidth model, it is assumed that the upstream vehicles are input with continuous and uniform green wave velocity in the green time. When multiple intersections are considered simultaneously, the situation becomes more and more complicated. For a driver there are two choices at the intersection, waiting or passing. erefore, for a main road with n intersections, there are 2 n− 1 possibilities for a car through the main road. In this paper, only the progression band of two adjacent intersections is simply analyzed, which is deviated from the actual situation. However, direct analysis is very complicated. erefore, in the progression band model, how to efficiently analyze the green wave between multiple intersections becomes a research direction that needs in-depth study.
Cluster Analysis of the Relationship among Variables
To get the dimensionality reduction and better know the relationship between pedestrian flow and two forms of flow, we use K-means clustering. Firstly, k points of clustering number are randomly selected as the starting center, then the remaining points and the points closest to the starting center are classified into one category, and the center of gravity of each category is calculated, then the center of gravity is used as the new center to continue iteration until the convergence conditions are met. In addition, this method needs a given number of clusters and is sensitive to abnormal data and data noise.
System clustering regards each object as an independent class, merges the two closest samples to form a new point, and stops when all the data are combined into a cluster or reaches some convergence rule. We simulate the relationship in Vissim and get the results in Figure 10.
From the figure, we can preliminarily find that the horizontal variation of delay is not obvious; that is, the relationship between pedestrian delay and vehicle flow is not significant. However, the vertical variation is obvious, indicating that the relationship between pedestrian delay and pedestrian flow is significant. In order to better explain the relationship between them, we will use cluster analysis to explain. In addition, according to the figure, we believe that clustering is carried out according to three categories. Table 5 shows the clustering center of vehicle flow and pedestrian delay. Table 6 shows clustering variance of vehicle flow and pedestrian delay. erefore, we can get the result that q � 600 pcu/h when the motor flow is small; q � 1500 pcu/h when the motor flow is moderate; q � 2400 pcu/h when the motor flow is large.
Data Availability
e traffic flow data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
e authors declare that they have no conflicts of interest. | 9,571.8 | 2020-02-13T00:00:00.000 | [
"Computer Science"
] |
Does the sixth wave of COVID‐19 break in Okinawa?
Abstract Background We aimed to forecast possible situations of the COVID‐19 spreading for Okinawa Prefecture in Japan. Methods The VSIIR model is proposed to extend the SIIR model to include vaccine effects where the parameter v denotes the vaccination rate and is treated as a control parameter on which possible situations for Okinawa would depend. Results It is shown that the infection ends without spreading if v>d1+d2 is satisfied where 1/di refers to the antibody duration, i=1 for infection and i=2 for vaccination, respectively. Conclusion It is important to set a vaccination policy that can save lives and maintain daily life at the same time.
| VS IIR MODEL
The SIIR model for COVID-19 spreading has shown to reproduce the observed data of those being positive to the PCR test and clarify that one of the basic features of COVID-19 is asymptomatic individuals who are mostly left unchecked and responsible for the spread of infection. 1,2 In this paper, the VSIIR model is proposed to extend the SIIR model to include vaccine effects, aiming to forecast possible situations for Okinawa Prefecture in Japan at the end of its fifth wave of infection.
Here, variables in VSIIR model at time t are S(t) as susceptible population, I 1 (t) as presymptomatic population (infectious), I 2 (t) as asymptomatic population (infectious), R 1 (t) as symptomatic population (not infectious due to quarantine), R 2 (t) as recovered population (with antibody and not infectious), R 3 (t) as fatalities by COVID-19 (not infectious), and V(t) as vaccinated population (with antibody and not infectious). Then, the interrelationship among the above variables is described by the following coupled differential equations from (1) to (7): In the VSIIR model, the vaccination rate is given as v. Usually, vaccines are supposed to be given to those who are uninfected (non-antibody) and ex-infected (antibody-deficient); however, since it would be realistic to inoculate individuals randomly except those who are symptomatic and quarantined, not only the susceptible population S(t) but also presymptomatic population I 1 (t), asymptomatic population I 2 (t), and recovered population R 2 (t) are treated as subjects in need of vaccination in the model. For this reason, there will be cases where antibody acquisition is duplicated. In fact, the cost of distinguishing uninfected individuals from asymptomatic individuals would be enormous and random vaccination is thought to be more economical and practical in procedure. Here, the antibody duration of the infected and recovered individuals (1 ∕ d 1 ) and that of those who are vaccinated (1 ∕ d 2 ) are set as finite. Note that a conservation law exists as well in the VSIIR model and is given as
| PAR AME TER S AND INITIAL VALUE S
The parameters of the VSIIR model are determined so that the data of the number of new positives of COVID-19 in Okinawa up to the fifth wave match the value of R 1 (t) in the SIIR model: where t 1 and t 2 denote the incubation period and the period of the onset, respectively. [3][4][5] For simplicity, regardless of the antibody acquisition route, the duration of the antibody is assumed to be the same for both the recovery from infection and the vaccine, and is set since there are several findings that the duration of the antibody is about 6 months. 6 In the following section, the parameter v is treated as a control parameter on which the sixth wave of infection in Okinawa would depend.
The initial value of the VSIIR model after the fifth wave is given as with the values shown in Table 1 which are obtained from officially reported data of COVID-19 in Okinawa and the asymptomatic individuals based on the SIIR model. Note that the following constraint condition implies q i cannot be freely chosen.
| S IMUL ATION RE SULTS
In the following simulation, q i is set as uniformly equal probability, namely q 1 = q 2 = q 3 = q 4 = q 5 = w 1 ∕ ∑ 5 i=1 a i ≈ 0.62, so as to satisfy Equation (8). This is because random vaccination is thought to be more economical and practical. At this point, uninfected individuals and recovered asymptomatic individuals who lost antibodies will account for the major targets for vaccination, so the initial susceptible population is small, 22% of the total (≈ S(0) ∕ N), and the effective reproduction number is calculated as 0.939 In case 1 (v = 0.00341 which is equivalent to the actual case in Okinawa so far in which inoculation of 5064 individuals per day is conducted. 2 ), as shown in Figure 1A, the infection remains unchanged for some time. However, during that time, antibody carriers V(t) lose antibodies and its number decreases, and as they are transferred to the susceptible population, S(t) increases.
As S(t) increases, the number of effective reproductions also increases and exceeds unity, the infection spreads, and the sixth wave arrives. After that, the infected population begins to decrease and the infection changes from spreading to shrinking.
However, since v < d 1 + d 2 , V(t) gradually loses their antibody and is transferred to S(t), and then the infection spreads again until it finally converges.
| CON CLUDING REMARK S
It is clear from the above evaluation that vaccination is a key factor in saving lives. In pandemics, it is important to set a vaccination policy that can save lives and maintain daily life at the same time.
However, it has reached a difficult stage to deal with infectious diseases by vaccination alone. In the first place, the causes of infectious diseases are environmental problems such as overuse of wild animals, global warming, and deforestation. In order to prevent the outbreak and spread of infectious diseases, it is required to build a sustainable social system based on harmony with the natural environment.
CO N FLI C T O F I NTE R E S T
The authors have stated explicitly that there are no conflicts of interest in connection with this article.
AUTH O R CO NTR I B UTI O N S
All authors had access to the data and a role in writing the manuscript. | 1,461.6 | 2022-05-02T00:00:00.000 | [
"Geology"
] |
Combination of radiotherapy and targeted therapy for HER2-positive breast cancer brain metastases
Radiotherapy and targeted therapy are essential treatments for patients with brain metastases from human epidermal growth factor receptor 2 (HER2)-positive breast cancer. However, the combination of radiotherapy and targeted therapy still needs to be investigated, and neurotoxicity induced by radiotherapy for brain metastases has also become an important issue of clinical concern. It remained unclear how to achieve the balance of efficacy and toxicity with the application of new radiotherapy techniques and new targeted therapy drugs. This article reviews the benefits and potential risk of combining radiotherapy and targeted therapy for HER2-positive breast cancer with brain metastases.
Background
Breast cancer is one of the most common malignant tumors among women in China. It is one of the tumors with the highest incidence of brain metastases, second only to lung cancer, accounting for 10-16% of brain metastases [1]. Brain metastasis is a significant factor in the decline of overall survival (OS) and degradation of the quality of life in breast cancer patients. Studies have confirmed that 20% of breast cancer patients die of brain metastases [2]. Since most drugs cannot pass through the blood-brain barrier (BBB), chemotherapy alone has a limited effect [3]; additionally, brain metastases are mostly multiple foci, which makes them difficult to be controlled by surgery [4]. Brain radiotherapy is the most commonly used and effective palliative treatment for brain metastases [5]. Brain radiotherapy includes whole-brain radiotherapy (WBRT), WBRT + local supplementation, WBRT + stereotactic radiosurgery (SRS)/ stereotactic radiotherapy (SRT), and SRS/SRT [6]. However, there are not many studies on the evaluation of brain radiotherapy effects, especially the improvement of systemic treatment in recent years. Whether the pattern of radiotherapy has changed is still unclear.
About 20-25% of breast cancer patients have human epidermal growth factor receptor 2 (HER2) gene overexpression [7]. Anti-HER2 therapy is a crucial therapeutic strategy to improve the survival prognosis of this subgroup of patients. Under the background of moleculartyping-guided individualized comprehensive treatment, the incidence of brain metastases has also increased year by year with the prolongation of survival of HER2positive breast cancer patients [8]. HER2-positive breast cancer brain metastases (BCBM) are characterized by multiple small lesions. They are often accompanied by leptomeningeal metastases, and those with meningeal metastases tend to have a poor prognosis [9]. Radiotherapy is the primary strategy for local treatment of patients with BCBM, and the combination of radiotherapy and targeted therapy can bring survival benefits to HER2-positive patients. Recent scientific evidence is demonstrating radiotherapy is capable of improving the quality of life and curative effect of metastases in metastatic prostate cancer [10]. Therefore, objective evaluation of the efficacy and adverse reactions of the combination of radiotherapy and targeted therapy is of great value in optimizing the comprehensive treatment of HER2-positive BCBM patients.
Characteristics of HER2-positive BCBM
In 2000, Perou et al. first proposed the concept of breast cancer molecular typing based on gene chip technology [11]. Then, molecular typing based on immunohistochemistry was further suggested in the St. Gallen International Consensus on Breast Cancer in 2011 [12]. The proposal and refinement of this concept have promoted the development of clinical research on individualized systemic therapy for breast cancer. The guiding value of molecular typing for systemic treatment strategies is now well recognized. The incidence of BCBM is also related to molecular typing, and HER2-positive metastatic breast cancer is the subtype in which brain metastasis occurs with the highest risk [8]. The HERA study followed up early breast cancer patients receiving anti-HER2 therapy for 11 years and found that the rate of central nervous system (CNS) metastases was 2.1% [13]. At the same time, with the progression of the disease course, the incidence of brain metastases in patients with metastatic HER2-positive breast cancer also increased, and the proportion was as high as 37.2% in the registHER study [14].
This finding also led to the reconsideration on the risk of brain metastases under anti-HER2 therapy for HER2positive breast cancer. The use of anti-HER2 therapy drugs such as trastuzumab may contribute to the development of brain metastases. Park et al. [15] analyzed single-center data and found that the occurrence rate of HER2-positive BCBM was 37.8% in the pre-trastuzumab era, and decreased to 25% since the clinical application of trastuzumab (P = 0.028). In addition, the median time to the diagnosis of brain metastases improved from 10 to 15 months in patients receiving trastuzumab treatment [15]. This result suggests that adjuvant anti-HER2 therapy delays the overall development of brain metastases through effective extracranial control.
In addition, the Breast Cancer Brain Metastasis Graded Prognostic Assessment (Breast-GPA) indicated that the median score of patients with scores ranging from 0 to 1.0, 1.5 to 2.0, 2.5 to 3.0, and 3.5 to 4.0 The survival times were 3.4, 7.7, 15.1 and 25.3 months, respectively. The HER2-positive single index score was 1.5 points [16]. This reflects the vital role of HER2 expression in the prognosis of patients with brain metastases, and the prognosis of patients with HER2-positive brain metastases seems to be better. A retrospective study included 112 BCBM patients, of whom the median survival time of the whole group was 14.4 months, and the median survival time of HER2-positive patients was 231 months [17]. A retrospective analysis of 66 HER2-positive BCBM patients by Pessina et al. showed that more than 50% of patients who received anti-HER2 therapy after brain metastases had a 3-year OS of 49%, while those who did not receive anti-HER2 treatment had a 3-year survival rate was only 33% (P = 0.03) [18]. This suggests that under the premise Fig. 1 Evolution of brain radiotherapy: A whole-brain radiotherapy; B hippocampal-avoidance technique; C whole-brain radiotherapy and simultaneous integrated boost technique; D multiple-site stereotactic radiotherapy of effective anti-HER2 therapy, the prognosis of HER2positive BCBM patients is relatively good.
Selection of radiotherapy techniques for brain metastases
Radiation therapy for brain metastases is available in a variety of ways ( Fig. 1): WBRT is the earliest non-surgical treatment for brain metastases, which can relieve neurological symptoms and improve local control. However, studies have shown that whole-brain radiotherapy can impair the cognitive function of patients [6]. For larger brain tumors, increasing the total radiation dose can effectively improve the efficacy of radiotherapy. Compared with whole-brain radiotherapy, WBRT combined with local tumor intensity modulated radiation therapy (IMRT) is currently the primary treatment option for cancer brain metastases [19]. Stereotactic radiotherapy (SRT) uses modern imaging technology to correctly find the target area, accurately delineate the target area through stereotaxic and verification technology, and drive the particular ionizing radiation device through computer control to destroy the target area with high dose. Minimizing radiotherapy's side effects and radiation damage is a modern radiotherapy process characterized [20]. Compared with traditional radiotherapy, SRT has the advantages of a higher degree of precision, a lower radiation dose to organs at risk (OAR), and a higher radiation dose to tumor target areas [21]. SRT adopts multiple fractionation treatment methods, which is more in line with the requirements of radiobiology. The cells with sub-lethal damage to normal tissue after irradiation are almost entirely recovered within the interval between fractionated treatments. Tumor-hypoxic cells reoxidize, and cells in the G0 phase enter the radiosensitive phase. This may lead to better control for malignant tumors without causing serious damage to normal tissues [22]. The characteristics of dose distribution are: the composite dose distribution of multi-line beams is concentrated after spatial beam focusing, and the dose gradient around the target area varies considerably; the dose distribution in and near the target area is uneven; the dose around the target area is low [23]. Therefore, SRT is often used in the treatment of brain tumors. SRT can control the lesion site qualitatively and quantitatively and deliver the dose with precise local control. Therefore, it can improve the OS of patients, and reduce the incidence of adverse reactions. Many scholars believe that it has broad prospects in treating multiple brain metastases. SRS has the advantages of accurate positioning, concentrated dose, relatively minor damage, and short treatment time [24]. SRS has a good effect on isolated brain metastases, and its indications include [25][26][27]: (1) the diameter of single initial metastases was less than 5 cm. (2) The number of metastases for initial treatment should not exceed four. (3) Salvage therapy after WBRT failure. (4) Adjuvant therapy after resection of intracranial metastases. (5) SRS may be reconsidered in patients who have previously received SRS with a duration of response for more than 6 months, and the tumor is considered recurrent rather than necrotic on imaging. (6) Local augmentation of localized meningeal metastases based on WBRT treatment. CyberKnife (CK) is a small linear accelerator installed on a robotic arm with 6 degrees of freedom. There are 160 nodes on spherical surfaces of different radii, which can form 1980 incident directions, thus achieving relatively adequate coverage of the target area and a higher dose gradient at the edge of the target area [28]. The research of Zhou et al. regarded CK as a newly developed SRT technology, using non-isocentric and non-coplanar circular field technology to treat brain tumors [29]. Combining multiple incident directions and the application of reverse planning can achieve high target conformity and minimize the damage to surrounding normal tissues caused by high-dose fractionation.
For early and timely treatment of brain metastases, radiotherapy is a more critical part, and there are various methods to choose from. SRT has the advantages of precise target positioning, concentrated dose, and high target conformity. As a new type of SRT technology, CyberKnife has excellent benefits for isolated lesions. Still, because of its huge expense, it is difficult to be widely promoted. According to the expert group, SRT combined with WBRT is recommended for patients with high-risk intracranial metastases [30].
Selection of targeted drugs
HER2 upregulation enhances the role of growth signals in the extracellular environment, promoting cell survival and proliferation through various downstream effects. Drugs targeting HER2 can block this downstream effect and improve outcomes in patients with HER2positive breast cancer, but also increase the incidence of brain metastases [31]. The main HER2-targeted drugs include monoclonal antibodies, antibody-drug conjugates (ADCs), and tyrosine kinase inhibitors (TKIs) [32].
Macromolecular monoclonal antibodies can bind to the extracellular part of the HER2 molecule, and smallmolecule TKIs can block the signal transduction of the intracellular segment of the HER2 molecule to exert antitumor effects. ADCs can be coupled with cytotoxic drugs based on HER2-targeting monoclonal antibodies, thereby further killing tumor cells [33]. Several clinical trials have explored the efficacy of HER2-targeting mAbs, ADCs, and TKIs in HER2-positive BCBM.
Monoclonal antibodies
Trastuzumab One study demonstrated a 1:420 trastuzumab-to-plasma concentration ratio in the cerebrospinal fluid of patients with BCBM who did not receive radiation therapy. Radiation therapy or surgery can increase this ratio value, but the effect is still limited. In leptomeningeal metastases, intrathecal injection of trastuzumab allows the drug to bypass the BBB and reach therapeutic concentrations in the cerebrospinal fluid, thereby prolonging patient survival [34]. The study by Park et al. found that trastuzumab significantly improved BCBM outcomes. It is mainly related to its ability to control extracranial lesions effectively in the long term [15]. In addition, a preclinical study by Kodack et al. found that the combination of trastuzumab and the small-molecule TKI lapatinib with anti-vascular drugs can delay the progression of intracranial lesions [35]. Phase I NCT00543504 trial further confirmed the effectiveness of the therapy [36]. Among the ten BCBM patients, six had progression-free survival (PFS) of more than 6 months, of which one had a PFS of more than 12 months, and no adverse reactions related to brain metastasis occurred. In the TUXEDO-1 trial, trastuzumab showed a high intracranial response rate in patients with HER2-positive BCBM [37].
Pertuzumab Pertuzumab combining with trastuzumab and taxanes is currently the standard first-line treatment for HER2-positive advanced breast cancer. The phase III CLEOPATRA trial showed that compared with trastuzumab and docetaxel alone, trastuzumab and pertuzumab in combination with docetaxel resulted in prognosis improvement in patients with metastatic breast cancer [38]. Both PFS and OS were significantly prolonged. Swain et al. found that compared with the trastuzumab alone group, the time to occurrence of brain metastases was longer in the trastuzumab plus pertuzumab group (15.0 months VS 11.9 months, P = 0.005) [39]. Given that both trastuzumab and pertuzumab can bring survival benefits to patients with BCBM, it is necessary to dive further into the effect of macromolecular mAbs on BCBM.
ADCs
Trastuzumab emtansine (T-DM1) T-DM1 is the current standard second-line treatment for HER2-positive advanced breast cancer. T-DM1 consists of trastuzumab and the microtubule inhibitor emtansine. The phase III EMILIA trial included 95 treated and asymptomatic BCBM patients, of whom 45 received T-DM1 therapy. Compared with lapatinib combined with capecitabine, T-DM1 significantly prolonged OS in BCBM patients (26.8 months VS 12.9 months, P = 0.008) [40]. A subgroup analysis of the phase IIIb KAMILLA trial showed that among 126 patients with stable brain metastases at baseline, 84 patients had brain metastases shrinking during T-DM1 treatment, indicating that T-DM1 is effective in the treatment of BCBM [41]. The KATE2 trial showed that T-DM1 combined with atezolizumab brought a survival benefit to patients with programmed death-ligand 1 (PD-L1)-positive metastatic breast cancer. Still, BCBM patients were not included, so the role of this therapy in BCBM requires further study [42].
DS-8201 DS-8201 consists of trastuzumab and the topoisomerase I inhibitor deruxtecan. The phase II DES-TINY-Breast01 trial explored its effectiveness as a postline therapy. For 184 patients with metastatic breast cancer who once received T-DM1 in the past, DS-8201 was used for treatment, the median PFS was 16.4 months, and the objective response rate (ORR) assessed by the independent review committee was 60.9%. Of these, 24 were treated patients with BCBM who had no symptoms associated with brain metastasis and had a median PFS of 18.1 months. It is worth noting that the incidence rate of interstitial lung disease is higher after DS-8201 treatment, and pulmonary symptoms should be monitored during treatment [43,44].
SYD985 SYD985, consisting of trastuzumab and the alkylating agent duocarmycin, has been granted by the U.S. Food and Drug Administration (FDA). The phase I NCT02277717 trial dose-expansion cohort enrolled 146 patients with metastatic breast cancer, including 8 patients with BCBM, and the results showed that SYD985 was safe and effective [45]. However, there is no published data on the treatment of brain metastases with SYD985, so the role of SYD985 in BCBM needs further study.
Small molecule TKI drugs
Lapatinib Lapatinib is a small-molecule TKI with two targets epidermal growth factor receptor (EGFR) and HER2. The phase II LANDSCAPE trial showed that lapatinib combined with capecitabine was effective in BCBM who had not received radiation therapy before, and the ORR was 65.9% for the CNS. In patients with HER2-pos- itive BCBM, lapatinib combined with capecitabine can achieve a PFS of 8.3 months, and subsequent radiation therapy can achieve an OS of up to 17 months [46]. In a phase I clinical trial, 35 HER2-positive BCBM patients received lapatinib combined with whole-brain radiotherapy, and the ORR was 79% [47]. Lu et al. developed a dual-targeted micellar delivery system loaded with paclitaxel (PTX) and lapatinib for the combined treatment of BCBM. Prolonged lifespans with brain metastases have been demonstrated in a mouse model [48]. This study provides a promising novel approach for treating BCBM.
Neratinib Neratinib irreversibly inhibits the activity of HER1, HER2, and HER4. The NEfERT-T trial compared neratinib plus paclitaxel with trastuzumab plus paclitaxel in metastatic breast cancer. The results show that the efficacy of the two is similar, but neratinib combined with paclitaxel can delay and reduce the progression of brain metastases [49]. The phase II TBCRC022 trial further demonstrated the efficacy of neratinib in HER2-positive BCBM. Over 90% of patients had CNS progression at enrollment, and the ORR for the CNS was 49% and 33% in lapatinib-naïve and lapatinib-naïve patients, respectively. Median PFS were 5.5 months and 3.1 months, respectively [50]. The phase III NALA study found that neratinib plus capecitabine significantly prolonged PFS compared with lapatinib in patients with metastatic breast cancer. The main reason is the reduction of patients with symptoms of brain metastases requiring intervention [51].
Tucatinib Tucatinib is a reversible TKI that is highly selective for HER2 and has shown promising intracranial activity in both preclinical and clinical studies. Compared with placebo plus trastuzumab and capecitabine, tucatinib plus trastuzumab and capecitabine significantly reduced the risk of disease progression and death. Among the 291 patients with BCBM, 1-year PFS was 24.9% in the tucatinib group and 0 in the placebo group, and the median PFS was 7.6 months and 5.4 months, respectively [52]. Based on the results, tucatinib was granted priority approval by the FDA. This regimen is indicated for treating patients with locally advanced unresectable or metastatic HER2positive breast cancer, including BCBM, which have progressed after undergoing three or more HER2-targeted therapies [53]. In addition, a phase Ib clinical trial found that tucatinib combined with T-DM1 was also influential in BCBM with fewer adverse reactions [54].
Pyrotinib Pyrotinib is a broad-spectrum anti-HER1, HER2, and HER4 intracellular small-molecule TKI independently developed in China [55]. The phase III clinical trial data in HER2-positive metastatic breast cancer showed that PFS was significantly prolonged in the pyrotinib group compared with the placebo group (11.1 months VS 4.1 months). For patients with no brain metastases at baseline, the pyrotinib group had a lower rate of new brain metastases than the placebo group (1.2% VS 3.6%). The time to onset of new brain metastases was longer (397.5 days VS 132.0 days). For patients with untreated brain metastases at baseline, the pyrotinib group had a lower proportion of patients with brain metastases (73.3% VS 87.5%) and a longer time to brain metastases (168.0 d VS 127.0 d) [56]. Tian et al. evaluated the efficacy of pyrotinib in patients with HER2-positive BCBM undergoing WBRT. Twenty patients were divided in a 1:1 ratio into the pyrotinib plus capecitabine group and the capecitabine-only group. Oral pyrotinib combined with radiotherapy significantly improved OS, PFS, and duration of response in patients with HER2-positive BCBM without additional adverse events [57]. Multiple real-world data show that pyrotinib improves outcomes in patients with HER2-positive BCBM [58][59][60].
The possible mechanism of radiotherapy combined with HER2-targeted therapy
Trastuzumab was administered concurrently with radiotherapy and demonstrated HER2 radiosensitization in mouse models [61]. According to Pietras et al., trastuzumab-induced radiosensitization alters cellular DNA repair and cell cycle processes mediated by phosphatidylinositol 3-kinase (PI3K) and Akt [62]. Intracellular signaling cascades mediated by PI3K and Akt are the origin of many biological processes, including cell growth, angiogenesis, long-range migration, and cellular uptake of glucose [63]. Trastuzumab also appears to inhibit Akt and NF-kappaB-induced radioresistance [64]. There is growing evidence that HER2 is involved in breast cancer cells' response to radiation. A related schematic is shown in Fig. 2. By establishing mouse models of cardiac injury with radiotherapy mono-treatment using trastuzumab, and the combination therapy, Yi et al. analyzed whether these two treatments have synergistic effects. They believe that trastuzumab inhibits Akt phosphorylation, thereby promoting intracellular DNA damage. This exacerbates the damaging effects of radiation on cardiomyocytes in vitro [65]. Hou et al. showed that HER2 promotes the phosphorylation of focal adhesion kinase (Fak), thereby upregulating the expression of proteins associated with epithelial-mesenchymal transition (EMT). Inhibition of Fak activity with a Fak inhibitor (PF-562281) restored radiosensitivity in HER2-overexpressing cells. The results suggest that HER2 reduces the radiosensitivity of breast cancer by activating Fak. Fak may be a potential target for radiosensitization of HER2overexpressing breast cancer cells [66]. There are also some preclinical studies of small-molecule TKIs combined with radiotherapy. The study demonstrated that ZD1839 and radiation therapy significantly inhibited tumor growth compared to performing either treatment alone. A quinazoline small-molecule TKI CI1033 in combination with radiation was examined for its effect in a panel of HER-overexpression breast cancer cell lines. Preclinical studies have shown that CI1033 is synergistic with ionizing radiation [67]. EGFR TKIs enhance the radioactivity of bladder cancer cells by synergistically blocking EGFR and HER2 [68]. As to esophageal cancer, pyrotinib sensitized HER2-positive esophageal cancer cells to radiotherapy by inhibiting HER2 phosphorylation, inducing G0/G1 phase arrest, thus reducing EMT and DNA repair [69].
Efficacy of intracranial radiotherapy combined with targeted therapy on intracranial lesions
In the past, it was believed that most chemotherapeutic drugs and targeted therapy drugs are difficult to penetrate the BBB, so the therapeutic effect of systemic therapy on brain metastases is limited [71]. Radiotherapy is the standard treatment for patients with brain metastases. However, HER2-positive brain metastases patients had increased trastuzumab concentrations in the cerebrospinal fluid after WBRT. The blood-cerebrospinal fluid concentration ratio of trastuzumab before and after WBRT was 420:1 and 76:1, respectively. These data theoretically demonstrate that HER2-positive BCBM patients can benefit from subsequent anti-HER2 therapy based on WBRT [72].
Chargari et al. took the lead in analyzing WBRT and concurrent or continuous trastuzumab in 31 HER2positive BCBM patients in 2011. The objective effective rate was 74.2%, the median survival time was 18 months, and the median intracranial disease control time was 10.5 months [73]. Since then, more and more studies have confirmed that WBRT and anti-HER2 therapy can achieve a median OS of 12.8 to 34 months in HER2-positive patients, while the median OS of patients receiving WBRT alone is ≤ 10 months [74][75][76]. Anti-HER2-treated patients with brain metastases have improved outcomes.
In addition, T-DM1 combined with radiation, highenergy focused ultrasound, macitentan, or tucatinib have all achieved good results in BCBM [77]. However, Stumpf et al. found that T-DM1 combined with SRS may increase the incidence of radionecrosis. Given the small number of patients in this study, more extensive prospective studies are needed to evaluate the safety, maximum tolerated dose, and administration time of T-DM1 combined with SRS [70]. Guidelines for treating HER2-positive BCBM were released at the 2018 American Society of Clinical Oncology (ASCO) annual meeting. Although radiotherapy remains the standard option for asymptomatic, lowburden brain metastases that have not been treated with radiotherapy, lapatinib and capecitabine are also considerable options before radiotherapy [78]. Tian et al. showed that pyrotinib could enhance the radiosensitivity of cultured HER2-positive breast cancer cell lines. Pyrotinib is a potent drug that enhances in vivo tumor radiosensitivity with HER2-positive BCBM. Pyrotinib combined with radiotherapy can significantly improve the prognosis of patients with HER2-positive BCBM [57]. Real-world, multicenter data show that radiotherapy and pyrotinib can statistically improve OS in patients with HER2-positive metastatic breast cancer and brain metastases [58].
Curative effect of targeted therapy on extracranial lesions
Why intracranial radiotherapy combined with targeted therapy improves OS compared with radiotherapy alone? The reason is that the use of anti-HER2 therapy cannot only effectively control intracranial lesions but also extracranial metastases. The proportions of HER2-positive BCBM patients who died of extracranial disease progression with or without trastuzumab were 11.9% and 37.1% (P = 0.014), respectively [15]. A retrospective study by Zhang et al. showed that the median OS of patients with HER2-positive brain metastases with and without anti-HER2 therapy after WBRT were 34 months and 8 months, respectively (P = 0.001). Meanwhile, the death rates from extracranial disease progression in patients with and without anti-HER2 therapy were 20.0% and 73.3%, respectively [75]. This shows that intracranial radiotherapy combined with anti-HER2 treatment can effectively control intracranial and extracranial metastases in patients with brain metastases.
Time sequence and selection of targeted therapy and intracranial radiotherapy
Based on the survival benefit of anti-HER2 therapy in BCBM and the cognitive impairment caused by intracranial radiotherapy, more and more scholars are exploring the timing selection of targeted therapy and intracranial radiotherapy after brain metastases. The LANDSCAPE study explores the efficacy of lapatinib combined with capecitabine as first-line treatment in untreated HER2positive BCBM patients [46]. The ORR of the combination therapy was as high as 65.9%. Due to the lack of higher-level data, there is no generally accepted recommendation for a comprehensive treatment strategy for patients with HELL2-positive breast cancer. Still, it suggests that in some patients with low metastatic burden and effective antitumor drug treatment, close follow-up can be performed. Intracranial radiotherapy can be safely delayed under the premise.
Stavrou et al. compiled a schematic diagram to guide us on which treatment method to choose based on the prognosis, tumor size, and the number of BCBM patients [79]. Chan et al. developed an algorithm for the treatment of HER2-positive BCBM [80]. They recommend local therapy with surgery, SRS, or WBRT before systemic therapy. SRS is superior to WBRT in oligometastatic lesions. Anti-HER2 drugs combined with pertuzumab, trastuzumab, or taxane should be used as first-line therapy to control systemic symptoms. Systemic therapy can continue after local CNS therapy if isolated brain metastases worsen without extracranial progression. However, when CNS progression occurs with extracranial progression, anti-HER2 drugs should be switched according to the conventional HER2 treatment pathway. T-DM1 is the next-line treatment option after lapatinib-capecitabine combination therapy. Otherwise, the neratinib-capecitabine combination can be considered. Other treatments include new drugs such as tucatinib, T-DXd, and margetuximab, or other ones participating in clinical trials. The completed clinical trials of targeted drugs combined with radiotherapy in HER2-positive BCBM registered on Clin-icalTrial are listed in Table 1. It is obvious that there are only a few such clinical trials, and the number of patients enrolled is small. We have to notice that although these clinical trials are all displayed as completed, most of the relevant results cannot be retrieved. Prospective clinical trials of BCBM with radiotherapy combined with targeted therapy are listed in Table 2. We look forward to the results of this part of the study. Side effects of radiotherapy combined with targeted therapy
Radiation brain necrosis (RN)
RN is one of the late and irreversible toxic reactions after intracranial radiotherapy, which can cause neurological dysfunction, sometimes even life-threatening. Since RN is a late poisonous reaction secondary to vascular endothelial injury, and its occurrence and development are based on the long-term survival of patients. Therefore, most reports focus on nasopharyngeal carcinoma and glioma after radiotherapy. In the past, the reported overall incidence of RN in BCBM was low, given the poor overall prognosis of patients with brain metastases, the incidence rate of primarily symptomatic brain necrosis was only 6-11% [81][82][83]. Under the background of comprehensive treatment, the survival of HER2-positive breast cancer has been significantly prolonged, and the long-term quality of life of BCBM patients has become a focus of attention.
In addition to trastuzumab, other targeted therapies, including macromolecular monoclonal antibodies, smallmolecule TKIs, and cytotoxic drugs, have gradually clarified their benefits and therapeutic status in HER2positive breast cancer brain metastases, respectively [40,46,84]. The combination of antitumor drugs may have a superimposed or sensitizing effect on radiation damage. With new anti-HER2 therapeutic drugs, reports of related radiation brain necrosis have gradually increased. Geraud et al. reported preliminary results of the combination of SRS and trastuzumab-maytansine conjugate in 12 patients with HER2-positive brain metastases. The ORR was 75%. In this study, the incidence of focal brain necrosis was 50% in the concurrent treatment group and 28.6% in the sequential treatment group [85]. Another case series report also showed that T-DM1 might lead to brain edema after SRS treatment [86]. In a study of 45 patients with HER2-positive BCBM treated with SRS combined with T-DM1 by Stumpf et al., RN was observed in 39.1% of patients treated with T-DM1, compared with 4.5% of patients who did not receive T-DM1, the incidence of RN increased 13.5-fold (P = 0.02) [70]. The strong correlation of SRS with the development of RNs after T-DM1 set the foundation of further prospective studies, in which changes in timing and dose of T-DM1 are controlled, in order to stratify the risk of RNs and mitigate toxicities.
The experiments above are all small sample case studies. Despite this, the studies suggest that the occurrence of RN needs to be re-explored under the circumstances of re-course therapy, multi-line chemotherapy, and combined targeted therapy.
Other side effects
The efficacy of lapatinib combined with WBRT in HER2positive BCBM patients was evaluated in a phase I clinical trial. Dose-limiting toxicities, including grade III rash, diarrhea, hypoxia, and grade IV pulmonary embolism, occurred in 7 of 27 patients when lapatinib was administered at 1250 mg [47]. Other common side effects were diarrhea, fatigue, nausea, neutropenia, stomatitis, and abnormal liver function. Diarrhea is a common side effect, and the exact mechanism of HER1/HER2 TKIinduced diarrhea is still unclear. The complete inhibition of the HER family signaling pathway may cause intestinal complications [87]. No reports are showing that combined radiotherapy will aggravate these symptoms. In terms of radiation-induced toxicity, no expansion of pulmonary fibrosis was observed in a mouse model with concomitant trastuzumab radiotherapy [88].
Outlook
Since the hippocampus plays a vital role in memory preservation, hippocampal-sparing WBRT or IMRT can significantly alleviate radiation-induced neurocognitive and improve patient's quality of life by avoiding dose delivery to the hippocampus in WBRT [89,90]. Memantine is a noncompetitive n-methyl-d-aspartate receptor antagonist for HER2-positive BCBM. It can help improve neurocognitive impairment caused by WBRT. Some studies have proposed using focused ultrasound (FUS), nanotechnology, and radiation-based remote effect therapy for treating HER2-positive BCBM. Among all the possible options, FUS plus microbubbles can temporarily destroy the tight junction of the blood-brain barrier to allow drugs to penetrate. Studies have confirmed that the combination of trastuzumab and FUS has anticancer activity on HER2-positive breast cancer in mouse models [90].
There are also studies showing that pulsed FUS pretreatment of brain tissue can promote multiple enhancements of transgene expression, improving the penetration and efficacy of gene carrier nanoparticles in the central nervous system [91]. These all show the therapeutic potential of this non-invasive technique for targeted drug delivery to the brain. Nanoparticles can be combined with many anticancer agents and have been successfully used as carriers to deliver therapeutics across the blood-brain barrier. Nanoparticles coated with tumor-penetrating peptides could be a promising treatment method for preventing brain metastases [90]. Distant effects of radiation refer to localized irradiation-induced tumor regression at non-irradiated remote tumor sites. This mechanism is believed to be able to fight the tumor by triggering a host immune response by immunogen cell death [89].
Other studies have shown that fatty acid-binding proteins hold promise as potential targets for the treatment of HER2-positive BCBM. It promotes the growth of HER2-positive breast cancer cells in the brain. Elevated expression is associated with lower patient survival and a higher incidence of brain metastases [92]. Sambade et al. reported the prognostic significance of four tissue biomarkers of gliosis, immune infiltration, hemorrhage, and necrosis in BCBM were associated with good prognosis in HER2-positive BCBM [93]. Understanding the brain microenvironment of BCBM can help improve prognosis and may reveal new therapeutic strategies for HER2positive BCBM.
While the systemic treatment of metastatic breast cancer continues to improve, the treatment of brain metastases also requires continuous follow-up. Appropriate local and systemic treatment plans for BCBM patients should be formulated according to the anatomical features, molecular typing, and prognosis of brain metastases. Traditional treatments such as chemotherapy and endocrine therapy have specific effects on BCBM. Some new drugs such as ADCs, TKIs, CDK4/6 inhibitors, PARP inhibitors, and immune checkpoint inhibitors will also bring incredible survival benefits to BCBM patients. Currently, multiple clinical trials on BCBM are ongoing (Table 2), which will continue to bring new hope to BCBM patients.
Conclusions
The combination of targeted therapy and radiotherapy is a new opportunity and challenge in the progress of comprehensive treatment of BCBM. For HER2-positive BCBM, the efficacy of WBRT or SRS combined with trastuzumab or other anti-HER2 therapy has been confirmed. The optimization of the timing of the combination therapy still needs further research and demonstration, and the toxic reactions such as cerebral radiation necrosis cannot be ignored. The safety of the combination therapy should be verified in a larger sample size. It is believed that the combination of radiotherapy and targeted therapy is increasingly safe and standardized based on more effective systemic treatment. Continuous effort is needed to keep this therapy optimized as clinical research progresses. | 7,441 | 2023-01-16T00:00:00.000 | [
"Medicine",
"Biology",
"Psychology"
] |
The Impact of Knowledge Management by Technological Tools and Electronic-means on Academic Staff Performance in Palestinian Universities
This study aims to establish how the management of knowledge through technological and electronic means, impacts the performance of staff within Palestinian universities. Specifically, the study focusses on the West Bank area of Palestine, where 11 universities are located. A total of around 3000 individuals are employed by these universities, and of these, a total of 282 responded to the survey that was used to collect data. Analysis of this data has revealed a positive relationship between the independent and dependent variables that apply. This pattern suggests that the availability of technological and electronic devices does positively affect how staff within universities perform. The study discusses the implications of this and concludes that investment in tools would aid progress within the universities that were considered.
INTRODUCTION
Institutions of higher education are vitally important within any country. Education affects the holistic growth and development of academic students within a country, yet higher education is the final stage of teaching a young person receives before embarking on a career. The knowledge and experience acquired by a student within an educational establishment has a pivotal impact upon his or her career (Eleni, 2003); thus, it follows that the staff within any university have a duty to deliver a high quality of mentoring and instruction, to optimize the learning environment that nurtures the students. One of the most important roles of a university is the purveyance of knowledge. It therefore stands to reason that within a given establishment, the staff's methods of managing knowledge are integral to how well they perform (Monsted, 2006). Increasingly, as technology advances, it comes to play a part in how knowledge is acquired and disseminated. There is an expectation that increased investment in up to date technological and electronic devices could improve how staff manage the knowledge they impart, and thus their overall performance. This study will seek to validate such a hypothesis with quantifiable evidence; it will then look at the implications of knowledge management through technology being demonstrably critical.
For the purposes of this study, Knowledge Management (KM), should be understood as the process by which knowledge and information are obtained, stored, shared, and used to make informed decisions (Sireteanu and Bedrule-Grigoruta, 2007). Knowledge management is a form of active learning, and can entail creation, analysis, storage, and the conveyance of information in such a way as to improve decision making and pave the way for future learning (Chawla and Joshi, 2011 To understand why knowledge management (KM) takes on a unique importance when applied to the context of a university. A university is a learning institution, which means its primary currencies are knowledge, wisdom and information. With this in mind, activities that take place within a university threshold include learning, teaching, research and experimentation. Collectively, for these to be readily achievable, an environment that promotes the wellbeing of staff and students alike becomes a prerequisite (Mikulecká and Mikulecký, 2000). If such an environment is to be created, then regulation and management must come into play, thus knowledge and all practices centered around its acquisition must be coherently managed. Students at a university may attend lectures and tutorials, where they interact with the staff and are able to benefit from knowledge and experience those staff already possess. With these raw materials, students then have to make something more refined, and this is usually achieved by carrying out independent research. This research is yet another aspect of knowledge acquisition that requires managing, to increase its effectiveness. A fundamental aspect of this is the interchange of information between a university's departments (Sarmadi et al., 2017).
This study will explore one particular aspect of how such knowledge is managed; namely, through technological and electronic devices, including computers, tablets, iPads, mobile phones and internet servers. Such devices are significant because they make knowledge and information accessible at the tap of a button, or the typing of a command. It is little wonder that the internet is now recognized as one of the most important tools in the management of knowledge (Trivellaa and Dimitrios, 2015). It is similarly to be expected that there is some recognition worldwide that information technology and modern communication networks render us a human community, or a global village (Bataineh, 2017). Because information and communication technology is proliferating, this study identifies its importance and hones in particularly on how it has influenced the performance of academic staff within Palestine's universities. It also examines the potential implications of Palestinian academic trends for the future of knowledge management.
In Palestine, education falls under the jurisdiction of the Palestinian Ministry of Education and Higher Learning. By comparison with regional and global standards, rates of enrolment in the country are reasonably high. A 2003 survey (UNDP, 2015) indicated that 60% of young people aged 10 -24 prioritized education above other values and measures of success in their lives. By 2007, the enrolment rate within universities reached 46.2% (UNDP, 2015). Within Palestine's universities, there has been widespread recognition of the importance of information and communication devices within knowledge management. This has resulted in much investment in technology, yet public institutions in Palestine, particularly centers for higher education, are confronted with staff who take hours to perform tasks. Queues and administrative delays are consequences of this, and they create environments where it is difficult for employees and students to efficiently perform tasks (EU Commission, 2016). Much recent literature concerning in Arab country region education sector has focused upon quantifiable indicators of successful Knowledge Management, for example, equity, and student: Teacher ratios. Often, these studies omit discussions of the quality of education in terms of processes for knowledge acquisition, and how effective these are for both students and academic staff (Al . This paper will seek to redress that balance. Education in Palestine is a unique subject and a unique issue, because Palestine is one of the countries in the world where development and progress are taking place, despite the daily challenges posed by external forces such as the country's ongoing conflict with Israel.
THEORETICAL BACKGROUND
According to Koenig and Srikantaiah (2000), KM is the practice of creating, replicating information data that is known to be of importance (rich, deep and open communication) within a form and the entire world. This practice involves the creation, acquisition, sharing, organizing, and implementation of information. It can also be seen as the systematic management of an institution's knowledge wealth or asset with the sole intention of value creation and meeting requirements tactically and strategically. The process involves initiatives, strategies, systems as well as methods that enhance the creation, refinement, storage, and assessment of the knowledge asset. Knowledge management is therefore merely getting the right knowledge asses to the intended party promptly.
Acquisition knowledge is the process of obtaining knowledge from external sources like external experts, competitors, partners, customers, and suppliers. It is vital for a organization to view the value chain to appreciate the importance of external knowledge (Gamble and Blackwell 2001), while organization of knowledge is the practice of mapping or indexing knowledge into given categories for storage, retrieval or navigation (Botha et al., 2008). As Chou (2005) the storage of knowledge represents the safekeeping of Organizational knowledge. It can take the forms of an electronic database, physically written documentation, and codified human expertise in expert systems among others.
According to Nonaka's SECI model, (1994) Knowledge creation is the endless process of transfer, the combination as well as the conversion of the various types of knowledge. The process is made possible through the practice, collaboration, interaction and education of the users. Brown and Woodland (1999) a more competitive organization is able to create useful knowledge. While Mills and Smith (2011) Clarify Application of knowledge is the backbone of the knowledge management process. It involves actual use of knowledge effectively in the products, services, production processes, training and motivating the workforce to employ creativity in production and most importantly making user of the workers understanding of the products, services, and company processes. In simple terms application of knowledge is a means of making knowledge more active and relevant for the organization in value creation. Technology tools and electronic means can improve Knowledge management process through a combination of hardware and software (Lucca et al., 2000;Tsui, 2002b).
Most learning institutions have invested heavily in the computerization process (Al- Shobaki et al., 2018). This process includes the utilization of computers, mobile phones, servers, and the internet in conducting daily tasks in the universities. These modern practices are termed to be of more advantageous as compared to traditional methods, as they are cheaper, faster, and more secure when it comes to KM (Al Mudallal et al., 2016). According to Abu-Naser et al. (2016), introduction and adoption of KM by universities contribute positively to the future dynamics of the learning environment, development, and improvement of the efficiency activities of knowledge sharing and improve the overall performance of institutions. The need for consciously managing knowledge in an organization setting is now recognized as an essential issue to enhance innovation, business performance, and client satisfaction (Al Mudallal et al., 2016).
Academic Staff Performance
Academic staff performance can be assessed fundamentally in terms of higher education quality assurance. Many factors relating to staff performance are how rapidly the employees are able to respond to students' requirements, and the frequency with which those requirements are met. Employees' opinions about what constitutes good performance is very consistent. Besides the availability of electronic devices and technological tools, other factors contributing to staff's ability to perform successfully, include their experience, and the availability of library resources (Madi, 2010).
Performance of an organization is measured by its ability to create value. Better performance can be identified through the following indicators; steady Innovations and Growth, Operational excellence, possession of competitive advantages by the organization, and steady value creation. As Terziovski et al. (1999) Technological application, Organizational culture and structure, financial performance and most fundamentally, knowledge management are considered critical for an organization good performance.
Administrative difficulties caused by poor management of knowledge results in long waiting hours for staff to complete their tasks. In many Palestine universities and colleges, it is a norm for students to stand on long queues to receive services (EU-Commission, 2016). Lack of proper knowledge management plan makes it hard for employees in these institutions to perform their tasks.
Building upon the findings of the theoretical and empirical arguments of previous studies, there are links between knowledge management by technological tools and electronic-means and academic staff performance. Thus, to explain the impact of knowledge management by technological tools and electronic-means on academic staff performance, this study hypothesize the following: H 1 : Knowledge management by technological tools and electronicmeans play a significant role in Palestine Universities. H 2 : Academic staff performance plays a significant role in Palestine Universities. H 3 : There is a relationship between knowledge management by technological tools and electronic-means and academic staff performance in Palestine Universities. H 4 : There is impact of knowledge management by technological tools and electronic-means on academic staff performance in Palestine Universities.
Population and Sample Size
The research population consisted of all the staff (3662) from nine Palestine University located in West Bank region. The sample size was determined using population to size sampling methodology (Kothari, 2004).
Where, n = sample size z = the figure of the desired confidence level at 95% (value obtained from the table is 1.96) p = sample proportion (0.5) q = 1-p (0.5) N = size of the population of interest (3662 academic staff distributed on nine universities in West-Bank) ε = precision rate or acceptable error (5.6%) n = required sample size.
Conceptual Model
The conceptual model of this study as shown in Figure 1 consists different types of variables. The independent variables were the implementation of KM (creation, acquisition, sharing, organizing, and application) and the dependent variable was university academic staff performance.
Measurement Scales
Structured questionnaires were developed by researchers and used in collecting data from the (282) academic staffs. The questioner consists of two parts; the first part captured knowledge management by technological tools and electronic means, while the second part focused on academic staff performance. The research questionnaire was administered with a five Likert scale from (5= strongly agree to 1= strongly disagree). Based on previous studies, scholar measures the dependent and independent variables in conceptual model. Implementation of Knowledge Management by Technological Tools and Electronic-means was measured using (24) items scale distributed in four domains: Creation and acquisition, organization and storage, sharing & dissemination and implementation), Also academic staff performance was measured using (22) items scale.
Test for reliability
Cronbach's alpha test method was used to check for internal consistency within the data set as shown in Table 1. According to the results, there is a reasonable range of Cronbach's alpha coefficient across the four domains of KM which ranges between (0.0 and + 1.0) indicating that there is a higher degree of internal consistency in the data, Cronbach's alpha value for the (24) items is (0.908), while the Cronbach's alpha value for the (22) items of academic staff performance is (0.944), suggesting that all the questions have relatively high internal consistency. This finding indicates an excellent validity and reliability of the dataset.
Test for normality
Test for normality for each dimension the study used a Kolmogorov-Smirnov test (K-S) to test the normalcy in the data set as shown in Table 2. The results show that there is a normal distribution in the dataset as the P-values for each domain is higher than the significance level at 5%. The dataset is suitable for carrying out further analysis.
Research Method
In order to examine research hypotheses, this study employs one sample (t-test) to understand the role of knowledge management by technological tools and electronic-means, and role of Academic staff performance in Palestine Universities, in addition Pearson correlation test to understand the relationship between dependent, independent, in the conceptual model. And uses multi-linear regression to test the impact of knowledge management by technological tools and electronic means on academic staff performance.
Testing Hypothesis
H 1 : Knowledge management by technological tools and electronicmeans play a significant role in Palestine Universities.
In order to test this hypothesis, one-sample t test was used with (test value = 3) as shown in Table 2.
As shown in the Table 3, the implementation of KM by technological tools and electronic-means (creation and acquisition, organization and storage, sharing and dissemination, implementation and dissemination) positively. Since the value of calculated (t) was greater than the value of the critical (t) which is equal to (1.96) at the significance level (α≤0.05).
H 2 : Academic staff performance plays a significant role in Palestine Universities.
In order to test this hypothesis, one-sample t test was used with (test value = 3) as shown in Table 3.
As shown in the Table 4, the academic staff performance in Palestine Universities Positively. Since the value of calculated (t) was greater than the value of the critical (t) which is equal to (1.96) at the significance level (α ≤ 0.05).
H 3 : There is a correlations between knowledge management by technological tools and electronic-means and academic staff performance in Palestine Universities.
In order to test this hypothesis, a Pearson correlation was made between knowledge management by technological tools and electronic-means and academic staff performance in Palestine Universities. As shown Table 5.
As shown in Table 5, the results show that all the domains had a positive and significant relationship with staff performance.
H 4 : There is impact of knowledge management by technological tools and electronic-means on academic staff performance in Palestine Universities.
In order to test this Hypothesis, multiple Regression analysis was used, but before start applying regression analysis, the researchers conducted some tests, in order to ensure the suitability of data for regression analysis assumptions, as the following: Assuming that there is no high correlation between the independent variables (multi-collinearity), the researchers used the variance inflation factor (VIF) and (tolerance) test for each independent variable, as shown in Table 6.
As shown in Table 6 the (VIF) values for all dimensions are <10, ranging between (1.376 and 2.798). Tolerance values ranged between (0.357 and 0.726) which is >0.05. It indicates that there is no high correlation between the independent variables which can lead to misleading results for regression analysis.
As in Table 7 beta and t-test values show that knowledge management by technological tools and electronic-means (creation and acquisition, organization and storage, sharing and dissemination, implementation and dissemination) have statistically significant impact on academic staff performance at Palestinian Universities, since P < 0.05, According to adjust R 2 = 0.565 indicates that the independent variables jointly explain 56% variation in the dependent variable (academic staff performance).
Therefore, the p-values of domains; creation and acquisition, organization and storage, sharing and dissemination, implementation and dissemination (P = 0.05, P = 0.00, P = 0.04, P = 0.00) respectively, had a significant and positive impact on the performance of academic staffs. This result indicates that the use of technological and electronic means in creation and acquisition knowledge within a university leads to a general improvement in academic staff performance. Knowledge creation involves the utilization of internal and external resources of an organization to generate new knowledge for achieving the organizational goals, with digital means it is easier for the staffs and managers to manage this process and meet the intended targets. Moodysson (2008) noted that use of this technological and electronic means helps in brainstorming and conducting research so that to better the general performance of an organization. The availability of computerized and electronic means as made it easier for top managers and staffs to efficiently conduct research both online and use of other platforms with the aim of improving their general performance (Calantone and Li, 2008;Pinto, 2012).
While knowledge organization and storage indicate that use of both technological and electronic means has enabled academic teams to organize and retrieve their stored information quickly/ easily, an act that improves their general performance. These results are in line with those of Hadi et al. (2006), where the use of digital (technological and electron means) to store information in a mobile industry lead to improvement in its performance when measured regarding revenue.
But Knowledge sharing and dissemination can be attributed to the advantage that technological and electronic means has when it comes to communication within the universities; as current technologies have made information sharing to be done very fast and accurately with just a tap of a button for example through the use of emails, Skype, telephone among many other digital forms of communication. Bhatt (2001) noted that introduction and adoption of digital ways of discussion and sharing of information have led to the increased performance and general profitability of many business sectors all over the world, as most of the channels used like email are cheaper as compared to the traditional mean like the use of posters to send letters.
Whereas Knowledge implementation suggest that proper use of existing knowledge for decision making as a positive effect on the general staff performance, as it makes it easier for the organization to achieve the intended goals. According to the study done by Chong and Choi (2005), proper utilization of available information to make a decision leads good understanding of issue between the managers and general staffs, hence, resulting to a well-informed decision that leads to the proper performance of the organization. Besides, the use of technological and electronic means it easier to arrange and analyze information (Boulding et al., 2005;Spender, 2009).
CONCLUSION AND RECOMMENDATIONS
The performance of employees is one of the most common variables with an impact of the independent variables on it in the administrative sciences because it plays a vital role in the performance of organizations (Al- Shobaki et al., 2018). In an era where large quantities of data must are processed and information produced in the shortest time possible, the work of university academic staff would be tough without the implementation of proper KM, and this was explicit from the findings. All elements under independent variables appeared to have a positive effect on the performance of the academic staff. The accumulation of individual impact totaled in the conclusion that knowledge management by technological tools and electronic means can significantly improve university academic Therefore, Palestinian Universities stand a great chance of recording improved performance from the team prioritizing KM. It is on this basis the Palestinian universities should continue investing in electronic means and technological tools for knowledge management because it will boost the performance of the staff and help employees collect, store, visualize and share information. These tools help employees to be efficient in their task thus saving time, money, and other resources that could otherwise be wasted. And thus, the overall education quality of the country.
The Palestinian universities should also consider carrying out independent studies to determine how each institution can independently benefit from knowledge management. For future research, the universities are obliged to consider using other variables, that may affect staff academic performance.
LIMITATIONS
Although the findings of the study supported the hypothesis thus leading to the conclusion that KM through electronic means and technological tools had a positive impact on the performance of the university academic staff, one of the significant limitations was to determine the attitude of employees had towards these tools. It was not possible to decide whether or not they felt threatened by technology perhaps because of the way the questionnaires were set up. For future research, this should be included in the survey and accounted for at the end of the study. | 5,054 | 2019-09-01T00:00:00.000 | [
"Education",
"Computer Science"
] |
Financial contagion: The impact of the volatility of global stock exchanges on the Lima-Peru Stock Exchange
Presentado: Aceptado: 04/10/2019, 23/12/2019 DOI: https://doi.org/10.33326/27086062.2019.1.896
INTRODUCTION
From 2002 onward the global financial markets, as can be seen in the figure 1, as were movements of high volatility, until since the year 2007 until 2016, the behaviour of the global markets that have pegged their volatility to the local market, consequently impacting on the volatility of the profitability. The economic context in which frames the present study, is the one that is described in the following lines: For the year 2007, international markets were already several years into a sustained boom, with investors, entrepreneurs, Modelling and measurement of risks is a complicated task. The risk is a slippery concept, that refuses to be enclosed in formal models. The difficulty exists behind both the movements of the prices of financial assets, as the solvency of the economic agents (companies or individuals). The financial risk is associated with factorseconomic, political factors and social factors. In globalized markets, the occurring shock is negative or positive, that cause changes to a greater or lesser volatility, as the case may be, given the behavior of the asymmetric volatility. Studies, such as Engle (1982) and Engle (2003), indicate that the volatility can be captured in models of variance conditioned as well as the models of the family ARCH, with which it is possible to predict the variance of future of an asset is risky. The main objective of this study, it is without doubt, improve the processes of identification and estimation of volatility in International Markets, measurement of the volatility joint and measure how they affect each other the returns of these markets and, in addition, to model the impact of news on the Stock exchange of Peru, and the attitude of the agents who take an active part in the market. governments, and american consumers benefiting from a growth of wealth that seemed to have no end, with companies increasingly large, rich and powerful, this festival of prosperity came to an end in mid-2007, when some banks and financial institutions in the united States and England began to experience serious liquidity problems. In Peru, the Lima Stock exchange, showed a sustained growth and exponential that takes place in the period 2000 until the year 2007, as can be seen in figure 1. For the stock market to fulfill its role successfully, it is necessary that you can know and even to anticipate this information. In this regard, the changes in prices are random and are not predictable to the extent that they incorporate the expectations and information of all market participants. This variation in the performance of the asset is known as volatility.
On the other hand, Enders (2015) on page 155 of his book Applied Econometric Time Series, deals with the TARCH model, citing as the model that best welcomes the impact of the news that have occurrence in the financial markets on the behaviour of the local stock markets. The study of the historical volatility of the stock market of Perú and its relationship with other markets, it is of vital importance for the management of risks in the structuring of investment portfolios by investors. Likewise, knowledge of the historical volatility allows investors to make decisions on entry, stay or departure, and on the other hand, the taking of precautions and assurances that the portfolios required in the process of financial risk management. The volatility that present themselves in the markets of global values has impact on the behavior of the bidders and demanders of financial assets in the stock market. As well as the impact of news on the profitability of the stock markets and the dynamic relationship that manifest. The volatility in the financial markets has been measuring the value of the variance of the asset price. This variable, the variance, becomes explanatory of the evolution of the price itself in terms of information available at t, . At each moment in time, the volatility is known up to the moment immediately before becomes an important mechanism to know the progress of the asset as it is a "stylized" sufficiently proven that the financial markets suffer from "contagion": periods are very volatile, are followed by periods of the same feature, and, once you "calm down", the tendency remains in the observations. Valls (2014), Volatility in financial Markets: The impact of The global financial crisis. doctoral thesis developed in Spain, that deals with the study of the volatility of the global markets using the models of the family ARCH (1) and GARCH (1,1), makes estimates of contagion from the volatility of global markets such as the United States toward smaller Markets as those of Latin America. Serna (2001), a Study of the volatility of the Stock market IBEX 35 in Madrid Spain 1991 -2000, doctoral thesis, developed by Gregorio Serna Calvo, in the Graduate School of the University Carlos III of Madrid -Spain. Study of the determinants of the volatility of the profitability of the Bag under the model of Black and Scholes. Rodriguez (2004), doctoral thesis entitled the Influence of the Impact of the News is not expected on the volatility of the technology stocks in Spain, developed in the Graduate School of the University of Vigo in Spain. The main objective of the work in question focuses on the measurement of the effect of the new information derived from the occurrence of unexpected developments in macroeconomic indicators or internal data from the companies themselves on the volatility through the curves of impact of news. We also verify the influence of the risk premium on the actual return of the shares, based on the postulates of the traditional theory of portfolios, for companies tied to the New Economy. This work is part of the modelling of the conditional variance for the companies in the New Market through the GARCH models, which are used to contrast the existence of a dynamic relationship in the volatility, capturing the effects of asymmetric of the innovations on it. Blanco (2000), a study developed in Bank of Spain by Dr. Robert Blanco, under the title Effects on the volatility of the stock market of Introduction of the Futures Contracts and Options on IBEX 35. The study focuses on the evaluation of the volatility under the model by GARCH. Cargo (2007), doctoral thesis developed by the Esau Cargo Gave in Mexico, under the title Setting of the qualification of the Market Risk of the most active companies listed on the Mexican Stock exchange, with the implementation of an Artificial Neural Network Classifier. This work focuses on the actions more active, that is to say, that is bought and sold on a larger sum each quarter by the economic agents in Mexico, whose sensitivity to the risk of the mexican market is represented by the beta of the Index of Prices and Quotations (IPyC), calculated on statistical methods such as regression analysis and traditional techniques such as fundamental analysis and technical analysis. Engle (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the variance of United Kingdom Inflation, published in the Journal of Econometrics, volume 50, number 4. In this work indroduce the modeling, ARCH and GARCH for the evaluation of the behavior of the inflation at the time. Piffaut & King (2016), in the article Integration, financial contagion and risk on stock markets, examines the problem of financial contagion to global markets by the coefficient of correlation dynamics. Morales (2015), in the study of financial contagion and interdependence in Latin America: analysis of transmission of shocks financial of Brazil to the rest of Latin american countries, is performed by using the correlation coefficient and dynamic conditional. Bejarano (2015), in their study of financial contagion in Latin American markets: an application of correlation dynamics, examines the financial contagion and the transmission of volatility. Medina (2017), in his PhD thesis entitled Financial Contagion international in the emerging countries of Asia and Latin America, models, and analyzes the problem of financial contagion with the model mgarch dcc. Villarino (2016), in financial mathematics volatility is a measure of the frequency and intensity of changes in the price of an asset of a type that is defined as the standard deviation of the change in a specific time frame. It is frequently used to quantify the risk of the instrument. The annualised volatility σ is proportional to the standard deviation of the returns on the instrument divided by the square root of the temporary period of the returns: A first concept in use, is the profitability of the Lima Stock exchange, whose description of the model is presented in the following lines. Return model The variations in the closing price of the index are the cause of profitability that this generates. From the daily prices (closing rates) are calculated by the profitability daily as a random variable to the volatility of the returns.
A first component is formed by the concepts related to the measurement of the descriptive statistics concerning the concept of risk. Chou (1992), Arch Modeling in Finance, published in the Journal of Econometrics, volume 52, number 1-2. In this work we model GARCH for volatility in the options Market. Analysis of GARCH multivariate introduced by Jorge Ludlov and Beatriz Mota in the Autonomous Metropolitan University of Mexico (2006), for the study of the volatility of joint stock markets of NASDAQ and S&P500. Enders (2015), in his text Applied Econometric Times Series, discusses on the use of models of asymmetric TARCH and EGARCH for modeling of the impact of news on the expected volatility of the markets, that is called Leverage effect. He says, that the bad news apparently have a greater effect on stock market volatility than good news, and on the other side, it makes note that there was a strong negative correlation between return and expected volatility (p. 155-156). Chambi (2017), the characterization of the volatility of the exchange of Values of Lima, as a series of time autoregresivo and heteroskedasticity conditioned using the model Garch. Chirinos (2013), in the article Measuring Contagion and Interdependence in Financial by Copulations and extreme events in the countries of Latin America, analyzes the interrelationship and transmission of shocks between financial markets in Latin America.
The problem that now arises is to identify the statistical model that best represents the behavior of prices and profitability. If we define the Return value as the quotient of the difference of prices between period t and period t-
METHODOLOGY
The analytical framework of this study is described below: The hypothesis that delineates the present work is strictly related to the identification of the influence of the volatility in the behavior of the stock exchange of Perú and in the volatility of its profitability, which statement is expressed in the following form: The global financial markets spread volatility to the local market peruvian and consequently impact on the volatility of its profitability Where es a constant and at is a normal random variable with mean zero and variance is the white noise, and that is distributed identically and independently over time. We can then write the Payoff logarithmic as: You use the profitability logarithmic, that for small values of Profitability, Price turns out to be a good approximation of the real yield, and allows the sum of the payoffs.
Where P is the period in years of returns. The volatility generalized for time horizon T is expressed as: it is assumed the assumption that the logarithm of the price verifies the equation: 1, and the price in period t-1 and we have the model:
The risk A second concept is the risk that is developed in the following lines
If we apply the hypothesis that the random variables are independent, we can assume that the profitability of today has no influence on the profitability of tomorrow (Pérez, 2010, p.405).
Stationarity
Montenegro (2010), a stochastic process is strictly stationary if its statistical properties or probabilities do not change with time: that is, if its cumulative distribution function is time-independent (p. 23). A way to perform the test of stationarity of a time series is the test of Dickey-Fuller.
Contrast Augmented Dickey-Fuller (ADF Test).
To perform the test of Dickey-Fuller augmented (ADF) to a time series we run the ordinary least squares OLS , whose model is the following: Where the number of lags of may be chosen by running the model expressed in the lines above, Ԑ_t is the white noise, Montenegro(2010).
Heteroskedasticity
Peña (2010), the heteroskedasticity is the existence of a variance not constant in the random distortions of an econometric model. The basic model of linear regression requires that the conditional variance of the random distortions to the values of the regressors X to be constant: To understand intuitively this restriction we can reason in the following way. Equal variances "or" for the various values of "x" necessarily implies equal dispersion (variances) of "and" for different values of "x", which necessarily implies that the regression line will represent with equal accuracy the relationship between "x" and "y" regardless of the values of "x". This is very important because it must be remembered that the regression analysis is regression analysis conditional "and" on "x" which means, logically, that if you want to obtain a parameter of a stable relationship and useful between the two variables, the values of sample "and" should be equally dispersed with variations of "x". In other words, and in terms of the error, although the error will be greater for higher values of "x" (do not force the error to have a size equal to the travel of "x") the dispersion of the error around the regression line will be the same. This allows to consider also all valid data sample of the regressors "x" to determine the conditional relationship of "and" to the values of "x" without having to ponder a more or less u-values other than "x" in function of the greater or lesser dispersion of "and" in the different cases (p. 435).
A third concept used is: The modeling Garch for the estimation of the volatility of the profitability of the Lima Stock Exchange
Xt-1: resulto of yesterday
The ARCH(1) Model
The process ARCH(1), proposed by Engle(1982) is defined by the following expression quantifies the volatility of an index representative of a stock market in terms of variance.
The autoregressive Model of the time series
ε : noise White Xt= c+αXt-1+ε, Although, usually the hypothesis is formulated without mentioning the conditional nature of the variance, simply as: α : ratio of the result ofmyesterday
The GARCH(1,1) Model
The model GARCH(1,1) was proposed for cases of a series of financial which have excess of kurtosis and the clustering of the volatility around its mean. The model provides an adequate way to forecast the variances and covariances of the returns of the assets. The GARCH has application in the treatment of risk management, in the management of investment portfolio, asset allocation, options, price, exchange rate, interest rate, equity markets. Bollerslev (1986) To carry out the study, through the repositories collects the historical data of the indices of the various countries: the General Index of the Lima Stock exchange (IGBVL), IBEX 35 of Madrid, Spain. S&P500 the United States, Bovespa of Brazil, NIKKEI225 of Japan and Shanghai of China, between the period 2000 to 2016, a period which includes the time of the international financial crisis, as can be seen in the table that follows, which includes each series, the amount of 4412 data of daily exchange rate and the profitability daily Through the indices have data for daily exchange rate at the close of the markets, which makes them a descriptive analysis and it becomes a profitability daily, using the equation of to later submit to statistical evaluation. The series of returns, they perform the test of stationarity with the object of selecting the model to estimate the volatility of the series, and thus to assess the character autoregressive of the same. After the statistical evaluations of the series, you select the model Garch(1,1) for the modeling of the volatility of the profitability. And finally with the model DCC Mgarch evaluates the correlation and dynamic conditional of the series of the indices of the bags in study.
-Secondly: the condition of autoregressive of the series: with the test AR(1).
In summary the methodological process followed is the following:
-Third: select the model, with which to run the modeling, in our case, we select the GARCH(1,1) Model.
-Fourth: test of heteroskedasticity conditional: it is performed by squaring the residual of the Model Garch obtaining, and illustrating in graphical form, the series of the return with the -In the first place, the analysis of stationarity: it is performed with the test of Dickey Fuller.
The descriptive statistics of the bags considered for the study are shown in table 2. Looking at the kurtosis is quite low for each of the entities, except for the BOVESPA, on the other hand, the figure 1, allows us to observe the typical behavior of time series is not stationary, and so effectively, by performing the test of single root is verified that all the series are non-stationary, therefore, it is not possible to submit to modeling stationary. The behavior of the trends of the time series, figure 1, figure 2, it is observed through the curve, the behavior, describing the background of the american stock exchange, japanese and chinese, a fact that already tells us that there is the presence of a phenomenon of transmission and/or contagion from the volatility. (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016).
-The problem of financial contagion is obtained by modeling DCC Mgarch, the correlation and dynamic conditional between the different markets under study. Figure 1 shows the evolution in time of the price of the sotck market of Lima -Peru, noticing a behavior steady between the years 2000 to 2002, but that grows dynamically from 2002 to 2007, then, a depression strong from 2007 to 2008, and 2008 and forward behavior of high and low, circumstances of behavior of high volatility. Figure 2 represents the evolution of the different stock market indices in the period 2000 to 2016, in which we can see a trend almost similar in all the financial markets large and small as the peruvian, as has happened with the historical evolution of IGBVL, we observe an evolution stationary in the periods 2000 to 2002 and for subsequent periods up to 2016 can be guessed that there are a behavior of time series non-stationary, whose Figure background shows the historical behavior of the stock indices that are involved in the study, denoting the behavior of a time series of the type autoregresivo and not stationary, the relationships will be analyzed further on a previous characterization econometric. behavior that describes phenomena of comovimiento and graphically summarized you can visualize the phenomenon of contagion, as can be seen in the figure 3. On the other hand, the figure 4, is the description of the behavior of the profitability of the stock markets under study, in which there is a typical evolution of a time series stationary, with variances very focused towards its mean, kurtosis concentrated, in which it is displayed, periods of high volatility, in the years 2000 to 2002, of low volatility in the years 2004 and 2005, high volatility in the years 2007, 2008, a period that extends until 2016. The boundaries of volatility, in all market ranges between 10% to -10% in most of the markets studied, except in the bag brazilian. The illustrations of the volatility of the profitability of the markets, you can already appreciate the presence of the contagion and transmission of volatility in the larger markets to smaller markets such as peru, that are affected by volatility that occurs in other financial markets, as is described and analyzed, and concludes Valls(2014) in their analysis of stock markets american, european and asian and Bejarano(2014) in the study of market stock american and Latin american markets, occurrence that will confirm this later with the correlation and dynamic conditional, when describing the results of the modeling DCC Mgarch. As can be seen in table 3, the absolute value of the indicator ADF is greater at the three critical levels of Mackinnon and pvalor lower to 0.05, it is inferred that the historic series of profitability of daily Stock market of Lima is stationary. This result is very important for the selection of a model for the estimation of the volatility of the profitability of the Lima Stock exchange. The verification of the character autoregresivo of the historic series of profitability of the Lima Stock exchange is performed with the application of the model Ar(p), table 4, that shows that indeed, the time series of the profitability of the Lima Stock exchange, included in the period 2000 to 2016, has a behavior-stationary, a result that leans to select a model autoregresivo for the measurement of volatility, and use this model to test the prognosis. (1)
series of return daily of the BVL
The information provided by the model Ar(1), table 4, it is inferred that the series in reference to have a behavior autoregresivo, being α the model Ar(1) rather less than 1, and the indicator Inverted Ar Roots = 0.14, widely less than 1, that describes the range of profitability of the Lima Stock exchange as nonexplosive, and that has a variation around the mean, a result that is consistent with the affirmation of Montenegro (2010). The character and behavior heterocedástico of the series of variance or volatility of the profitability of the Lima stock exchange, is illustrated by the following figure, that in a good way illustrates the effect of the news on the volatility of the exchange of Values of Lima. Montenegro (2010), the property statistics of heteroskedasticity is that in the time the volatility is different in each unit of time, is the reading that we confirm with the illustration of the figure 5. As equal as the other descriptive results obtained, it is useful to select the appropriate model to estimate the volatility of profitability. The conditioned behavior of volatility series of return of the Bag of Values of Lima can be seen in the following figure: The evaluation of the conditional nature of the time series is very important in the selection of the model for the estimation of the volatility of the series, Enders (2015), therefore the result of this evaluation is conclusive in rank to the series as one that complies with the feature of conditionality. Finally, making a summary of the statistical evaluation of the time series of the profitability of the Lima Stock exchange, necessary to select the model to estimate the volatility of the series, with the results that are summarized in the table 5. The results presented in table 5, that the indicators are necessary and sufficient to select the model, in which model the volatility of the series of the profitability of the Lima Stock exchange, it is concluded in using the model Garch, with the use of which is obtained the results in table 6 and the model 1 that describes the behavior of the volatility. Convergence achieved after 25 iterations Coefficient covariance computeds using outer product of gradients Presample variance: backcast(parameter = 0.7) GARCH=C(2) +C(3)*RESID(-1)^2+C(4)*GARCH(-1)
Table 6. Model Garch profitability of the Lima Stock Exchange
The model GARCH(1,1) which describes the volatility of the profitability of the Lima Stock exchange, with the data of the table 6 will have the following model for the volatility.
The sum of the coefficients of the model is close to one, which means that the volatility shown by the model, is persistent in time (α + β) =0.975772, Perez (2006). Already finally, with the statistical treatment followed, then you can model the phenomenon of financial contagion from the volatility of the markets globalized, large to the stock market in Perú.
Dynamic conditional correlation MGARCH model
Log likelihood = -91095.19 Prob>chi2 = 0.0000 Table 7 Distribution Gaussian Wald chi2 (16) The results obtained with the modeling DCC Mgarch, shown in table 7, it is inferred that the american market is the one that has the greatest impact on the transmission of volatility to the peruvian market, with a coefficient DCC (0.32705). The Spanish market in the second term with coefficient DCC(0.28388) and with less intensity than the market of Shanghai, with coefficient DCC(0.10339), where it is concluded that stock markets are larger spread and spread volatility to smaller markets such as the peruvian, in the same sense they have finished their studies, Bejarano(2014) and Valls(2014).
CONCLUSIONS
From the indicators obtained and presented in table 6, as a result of the modeling garch time series of the profitability of the Lima stock exchange, it is concluded that the behavior of the time series is autoregresiva and stationary with heteroskedasticity conditional, impacted by the volatility of other financial markets globalized.
The results of the modeling DCC Mgarch are obtained the coefficients of correlation dynamics summarized in table 7, which confirms our hypothesis of the existence of evidence of the phenomenon of the contagion of volatility from stock markets largest to the stock market in Peru, as is the case of the american stock exchange to the peruvian with a correlation dynamics of 0.32, of the spanish stock exchange and the peruvian with the coefficient of 0.28, and in third order of importance the influence of the China market to the stock peruvian with coefficient of 0.10. | 5,944.4 | 2020-06-24T00:00:00.000 | [
"Economics"
] |
DOMINANCE-BASED ROUGH SET APPROACH TO NETWORK BRIDGE MANAGEMENT
. Bridge management is essential for optimizing available resources. Prioritising maintenance and assessing the effectiveness of different maintenance strategies are based on the conventional condition ratings of bridge components. This paper presents the development of a Decision Support System for maintenance management at the Network Bridge Level, based on the theory of the Dominance-Based Rough Set Approach. Dominance-Based Rough Set Approach produces a decision model expressed in terms of easily understandable “if…, then…” decision rules which control the decision process and avoid the “black box” effects of many alternative decision support methods. In the proposed Decision Support System, bridges are described by a set of 16 parameters that describe the state of degradation, structure, territory, traffic and network characteristics. To illustrate this Decision Support System, a case study involving Italian roads is presented. The proposed Decision Support System is a flexible tool because it allows updating parameters periodically as a consequence of practice, expertise and management policies.
Introduction
Bridges are subject to decline due to changes in both physical and mechanical properties of the materials used, but also due to traffic volume and speed, as well as to environmental aggression (e.g. exposure to chlorides, freezing, thawing cycles, etc.) and catastrophic events (floods, earthquakes, landslides, etc.).
In order to optimize the available budget, it is useful for bridge authorities to implement a management system for identifying the structures requiring maintenance and the substantial interventions at an early stage.
It is worth emphasizing the following two aspects: -timely maintenance intervention leads to a longer bridge lifetime; -maintenance costs tend to rise quickly after the deterioration process has started (Rens et al. 2005).
A Bridge Management System (BMS) is a decisionmaking process used to select and prioritize the tasks needed to keep the structure's functional parameters within acceptable limits given its lifetime cycle. The priority-setting process requires considerable attention to minimize costs and disruption of road traffic (Godart, Vassie 2001). An effective management system needs to carry out an individual analysis of the structure (Project Level Bridge Management) and to analyze the level of the network (Network Level Bridge Management). Therefore, decisions need to be considered at two levels: network and project. The one at network level defines when it is necessary to intervene while the one at project level defines the kind of intervention required. Integrating the Project Level with the Network Level is rather complex. This paper proposes a Decision Support System (DSS) for managing the Network Level based on the theory of the Dominance-Based Rough Set Approach (DRSA). This methodology produces a decision model expressed in terms of easily understandable "if….then…" decision rules which reflects the decisionmaker's choices.
The parameters used in the decisional process take into account not only the state assessment of the bridge but also the characteristics of the environment, traffic and road conditions since the network is an integral part of the territory. The goal is not to define any maintenance activities for a bridge, but to determine the priorities on which to base a first approximation of the maintenance program for a bridge network in a way that the available resources are managed optimally.
Maintenance management of bridges
BMS includes all the activities which help maintain a bridge network efficiently, assuring safety and usability through the design, construction and operational phases (Godart et al. 2001). Several procedures have been developed to optimize bridge network maintenance where the funds available are limited. Some are based on inspecting and evaluating bridge condition, whereas more up-to-date procedures use statistical and mathematical tools to completely design maintenance plans at the network and project level (Valenzuela et al. 2010). A complete management system includes: -database; -bridge evaluation; -deterioration prediction and future conditions; -maintenance alternatives evaluation and their cost; -optimized maintenance plans. The database is the sum of information on the bridge network (data, maintenance activities, state of damage, etc). The database is periodically updated as a result of inspections.
The bridge evaluation identifies deterioration processes and the causes of such processes by means of inspections (visual, instrumental, etc). Subsequently, bridges are classified into several categories. These are classified by severity which determines the urgency of the intervention .
The condition data are then used to assess load capacity in terms of structure longevity and towards maximizing the safety and stability over that period (Bevc et al. 1999).
Future conditions are predicted by means of algorithms based either on standard statistical methods or on artificial intelligence techniques (neural networks, genetic algorithms).
Once these bridges are classified, by maintenance alternatives the optimization procedures are formulated.
Optimization means the best maintenance at the minimum cost, while maintaining adequate service levels. Optimization is performed over the period of maintenance interventions; this can vary from a few years to the entire life-time of the bridge. Several optimization procedures are available: classical mathematical formulations (scalar, unconstrained or constrained minimization, linear or quadratic programming, etc.) and artificial intelligence techniques (neural networks, genetic algorithms) .
BMS is a difficult process with different mathematically complex stages. There are many studies on this subject in the literature. For example, Hai (2008) proposes a computer database for maintenance and management for highway bridges in Vietnam. It includes several assessment techniques such as lifespan estimation, deterioration prediction, life cycle cost analysis, cost-benefit analysis and priority maintenance index (PMI). Miyamoto et al. (2001) have proposed a concrete bridge management system based on visual inspection and Concrete Bridge Rating Expert System with machine learning for evaluated bridge performance, and on genetic algorithms for researching optimized maintenance.
Other authors have devoted their attention to the assessment of bridges; for example Valenzuela et al. (2010) proposed an integrated bridge index (IBI) which depends on four factors: the 'BCI Index' which reflects bridge damage levels, the "SI Index" which reflects the importance of the bridge in the road network, the "HV Index" which reflects hydraulic vulnerability and the "SR Index" which reflects seismic risk. The index was calibrated using visual inspection, expert surveys, and regression analysis.
Other authors have devoted their attention to predicting deterioration ratio and optional maintenance plans. Frangopol et al. (2001) showed that bridge management system based on Markovian deterioration modeling has several limitations that overcome using a reliabilitybased approach. Neves et al. (2004) proposed a model for predicting the performance of deteriorating structures by measuring it in terms of condition, safety and maintenance cost. This model considers the interaction between condition and safety by correlating the random variables of the two associated profiles and their relationship. Liu, Frangopol (2004) proposed a multi-objective genetic algorithm for optimal life-cycle maintenance planning of deteriorating bridges where condition index, safety index, and cumulative life-cycle maintenance costs were simultaneously considered in the optimization process. Liu, Frangopol (2005) proposed a multi-objective genetic algorithm in which structure condition, safety, and cumulative lifecycle maintenance costs have been considered as separate objective functions subject to simultaneous optimization.
This study presents an automated procedure with a large pool of alternative maintenance solutions establishing optimized tradeoffs between the competing meritorious objectives. Neves et al. (2006) proposed a probabilistic multi-objective approach to bridge maintenance using genetic algorithms which considers single maintenance types. In this study, the condition index (by visual inspections) and the safety index (by structural analysis) are used as indicators of the deteriorating performance of structures. The decision maker choices are the best possible compromise between available funds, safety and condition parameters and acceptable levels of deterioration, depending on the specific situation, the bridge manager preferences and the on-going maintenance policy. Liu, Frangopol (2006) proposed a comprehensive mathematical model for probability-based bridge network performance evaluation using network theories. Elbehairy et al. (2009) proposed multiple-element bridge management that optimizes repair decisions. In this study, the proposed system uniquely segments the problem into smaller sequential optimizations which are solved using the genetic algorithms technique. Orcesi, Cremona (2011) proposed optimized maintenance strategies for managing bridges across France based on Markov chains fitted to condition data. This study evaluated prediction models for cost analysis and different maintenance strategies.
There is some specific software for managing bridges. Pontis is the most popular, developed by AASHTO in collaboration with the Federal Highway Administration (FHWA). Pontis is currently used in more than 40 agencies in the US and is widely adopted in other countries. Pontis allows both network-and project-level planning where bridges are represented as an assemblage of structural elements each is being classified by visual inspections every two years, in condition-state classes (Estes, Frangopol 2003). Pontis provides optimal maintenance policies for each state and for each type of element and environmental condition. Pontis generates simulated scenarios to determine current and future requirements, predict future performance levels and provide recommendations. The optimized policies at the network-level are selected by the software based on minimizing costs over the life-time of the bridge (Woodward et al. 2001).
Proposed methodology
One of the BMS phases is classifying bridges by assigning an intervention priority level. Accordingly, a first schedule of maintenance interventions is provided which is often based on linear equations that combine all the selected parameters, each having a weight assigned by expertise or literature data.
The aim of this paper is to define maintenance activity priorities by means of a decision-maker support system, taking into account the different roles involved in decision-making, each with its own objective. Thus, a methodology based on decisional rules obtained by the rough-set theory, the DRSA, has been applied. DRSA highlights both the methodological and operational point of view.
Using this methodology it is possible to derive a logical behavior model by observing actions through an inductive learning process (Greco et al. 2002a(Greco et al. , 2002b.
The advantages of this methodology are: -ability to manage vague or inaccurate data; -ability to manage qualitative data; -no need to assign a weight to each criterion; -it is possible to highlight cause-effect relationships between the available data, separating the most relevant and strategic information from the inessential; -construction of a priority model based on decisional rules such as "if … then …"; -identification of rules which support each decision; -facility for the decision-makers to understand how the rules influence their decisions.
The proposed decision-making support system is a flexible tool. In fact, it is possible to evaluate and update it periodically as a consequence of practice, expertise and managing authority's different policies.
In the first part of the paper, the parameters required to describe the phenomenon are defined. In the second part, the form of on-field data gathering is defined. In the third part the proposed decision-making support system is presented. Finally, the proposed methodology is applied to a bridge network.
Bridge characteristics are defined by a set of attributes that describe the state of degradation, the structure, territory, and traffic and network characteristics. The attributes are divided into condition attributes, also called criteria (A 1 to A 15 ) and decision attributes (A 16 ). The value assigned to each criterion increases as conditions worsen. Table 1 describes the attributes and the values in more detail.
Visual inspection and data acquisition
The data required for implementing the DSS are: -project; -thematic maps (hydro-geological risk maps, seismic vulnerability maps, etc); -inspections: a) to identify and classify the various types of structures; b) to identify the damage and its causes; c) to prevent collapse. Each damage depends on several factors: material deterioration, increase in traffic volume, increase in traffic load, lifespan reduction, natural disasters, etc.
There are many kinds of inspections: superficial, general, principal and special. Each country adopts different procedures for such inspections. Usually, general inspections are carried out every 2 or 3 years.
It is possible to do visual inspections or inspections using instruments. Visual inspections are performed in the field by compiling a form that can help identify and classify the damage and the damaged components. Photographs, sketches and notes are useful. The literature reports more evolved data gathering, recording and presentation, such as 3D images and virtual reality.
To investigate the causes and magnitude of the damage in detail, instrument inspections are necessary after visual inspection.
In this study, visual inspections were carried out using 1 st level sheets for the damage state survey. These sheets are classified by bridge type (masonry arch bridges, reinforced concrete girder bridges, reinforced concrete arch bridges, steel girder bridges, pre-stressed r. c. girder bridges). This information facilitates the operator compile the sheets to obtain an objective description.
The damage to each bridge component has been identified by means of these sheets corroborated by photographs.
Dominance-based rough set approach to prioritize maintenance
To prioritise bridge maintenance for a road system, a multi-criterion model based on the DRSA theory (Greco et al. 1999(Greco et al. , 2001(Greco et al. , 2002aSlowinski et al. 2005) has been adopted. This is an upgrade of the Classical Rough Set Approach (CRSA) developed by Pawlak (1991) which is applicable to multi-criterion issues. The DRSA does not only allow the representation and analysis of decision-making but, more generally, of all the phenomena involving monotonicity. DRSA theory grew out of research in the field of multi-criterion decision-making within AI techniques.
Information table and dominance relation
The rough set philosophy assumes that every object in the universe is described by a set of attributes. This requires inputting a set of examples representing preferential information by decision makers, while the analysis output is the model of preferences in terms of decision rules.
For algorithmic reasons, object information is supplied by a "data table" whose rows refer to distinct objects and whose columns refer to different attributes. Each table cell indicates an evaluation (quantitative or qualitative) of the object located in that row by an attribute in the corresponding column.
In this case study the decision support system was collated from a set of 100 bridges whose features represent most of the bridges found on Italian roads.
The row objects are bridges and the columns are the criteria which characterize the bridges, as shown in Table 2.
Formally, a data table in the 4-tuple S = (U, Q, V, f) where U is a finite set of objects (universe), Q = {q 1 , q 2 , ... , q n } is Continued a finite set of attributes, V q is the domain of attribute q, V = U q ∈QV q and f:UxQ → V in a total function such as f(x, q)∈V q for each q∈Q, x∈U, called "information function". The set Q is, in general, divided into set C of condition attributes and a decision attribute d. In multi-criteria classification condition attributes are "criteria". The notion of criterion involves a preference order in its domain while the domains of attributes are not preference-ordered.
In this case, all the condition attributes are criteria because it is possible to order them according to increasing preference of maintenance activity.
Furthermore, decision attribute d makes a partition of U into a finite number of classes Cl = {Cl t , t∈T}, T = {1, ..., n}.
Each x∈U belongs to one and only one class Cl t ∈Cl. The classes from Cl are preference-ordered according to the increasing order of class indices, i.e. for all r, s∈T, such as r > s, the objects from Cl r are preferred to the objects from Cl s .
In the presented case, the set of decision D attributes is a singleton given by the attribute "degree of urgency of the maintenance activity" which divides the set U of 100 bridges into four classes: -Cl 1 : bridges that keep to the inspection schedule; -Cl 2 : bridges requiring prior inspection; -Cl 3 : bridges requiring urgent intervention; -Cl 4 : bridges requiring partial or total closure.
Dominance-based approximation
In multi-criteria classification, due to the preference order in Cl classes the sets requiring approximation are not particular classes but upward unions (1) and downward unions (2) of classes, respectively: , , Union Cl t ≥ is the set of objects belonging to class Cl t or to a more preferred class, while Cl t ≤ is the set of objects belonging to class Cl t or to a less preferred class.
Note, that for t = 2, ..., n , i.e. all the objects not belonging to class Cl t or better, belong to class Cl t -1 or worse.
It the case study the upward union classes are: -the union upward Cl 1 ≥ is formed by bridges with necessity of inspection visual "at least" not advance; -the union upward Cl 2 ≥ is formed by bridges with necessity of inspection visual "at least" advance; -the union upward Cl 3 ≥ is formed by bridges with necessity "at least" of programming for urgent action; -the union upward Cl 4 ≥ is formed by bridges that need "at least" immediate closure or the traffic reduced.
The downward union classes are: -the union upward Cl 1 ≤ is formed by bridges with necessity of inspection visual "at most" not advance; -the union upward Cl 2 ≤ is formed by bridges with necessity of inspection visual "at most" advance; -the union upward Cl 3 ≤ is formed by bridges with necessity "at most" of programming for urgent action.
-the union upward Cl 4 ≤ is formed by bridges that need "at most" immediate closure or the traffic reduced.
In this application, the upward union classes Cl 1 ≥ and the downward union classes Cl 4 ≤ contain all 100 bridges considered: in fact for all these bridges degree of maintenance urgency is always at least scheduled and at most immediate partial or total closure. Usually, classification issues concern data collection for a given class Cl t dividing the universe U into class Cl t (set of positive examples) and its complement U -Cl t (set of negative examples), t = 1, …, n. However, such bipartitions do not take into account the preference order among classes. Thus, multi-criteria classification requires another type of bipartition which divides the universe into upward and downward unions of classes and Cl t ≥ and , t = 1, …, n. Each object from the upward union Cl t ≥ is preferred to each object from the downward union . Data collection for upward union Cl t ≥ considers all objects positive and all objects belonging to as negative. Analogously, data collection for downward union consider all objects belonging to as positive and all objects belonging to Cl t ≥ as negative. In this approach to data collection, the dominance principle is applied as follows.
Let ≥ q be a weak preference relation of U (often called outranking) representing a preference applied to the set of objects associated with criterion q; x ≥ q y means 'x is at 1 3 1 1 1 1 1 1 1 2 1 3 1 3 1 1 2 2 3 1 2 2 1 1 1 2 2 1 2 2 3 2 1 1 3 3 1 3 1 1 1 1 1 2 1 1 1 2 98 2 4 1 1 3 2 3 3 2 3 1 2 2 2 2 4 99 2 4 2 3 3 3 3 2 2 2 2 1 2 1 2 4 100 1 4 2 1 3 1 3 3 1 2 2 2 2 2 1 3 least as good as y with respect to criterion q' . If x ≥ q y for all q∈P, then x dominates y with respect to P⊆C (for short x P-dominates y) denoted by xD P y. Assuming, without loss of generality, that domains of all criteria are ordered such that preference increases with the value, xD P y is equivalent to: f(x, q) ≥ f(y, q) for all q∈P. Observe that for each x∈U, xD P x, that is, P-dominance is reflexive. Given P⊆C and x∈U, the "granules of knowledge" used in DRSA for approximation of the unions Cl t ≥ and Cl t ≤ are: -a set of objects dominating x, called P-dominating set (3): , ( -a set of objects dominated by x, called P-dominated set (4): . (4) In the case study, for example is composed of all bridges with a degree of inspection urgency "at least" equal to x, while is composed of all bridges that have a degree of inspection urgency "more than" equal to x. For example, if the criteria were "type of damage" and "seismic zone", both evaluated on three scales of high, moderate and low, and bridge x is evaluated as moderate regarding "type of damage" as well as "seismic zone", then: is composed of all moderate or low bridges regarding type of damage and seismic zone, and is composed of all moderate or high bridges regarding type of damage and seismic zone.
Given the set of criteria P⊆C, the inclusion of object x∈U in the upward union of classes Cl t ≥ , t = 2, …, n, creates an inconsistency in the dominance principle if one of the following conditions holds: -x belongs to class Cl t or better but it is P-dominated by object y belonging to a class worse than Cl t , -x belongs to a worse class than Cl t but it P-dominates object y belonging to class Cl t or better.
If, given the set of criteria P⊆C, the inclusion of x∈U in Cl t ≥ , t = 2, …, n, creates an inconsistency in the dominance principle, we say that x belongs to Cl t ≥ , with some ambiguity. Thus, x belongs to Clt³ without any ambiguity with respect to P⊆C, if x∈Cl t ≥ , and there is no inconsistency in the dominance principle. This means that all objects P-dominating x belong to Cl t ≥ . It is possible that y∈U belongs to class Cl t ≥ , with eventually some ambiguity, if one object x∈Cl t ≥ exists such as y dominates x with respect to the set P⊆C, or . For example, if "bridge y dominates bridge x", with the latter belonging to the ascending union of classes Cl 3 ≥ of bridges with not less than urgent intervention, it is possible that y belongs to the ascending union of classes Cl 3 ≥ too, if with some ambiguity. In simpler words, if bridge y is no worse than bridge x for all criteria (i.e. y dominates x) then the maintenance urgency of y should be no less than that of x. Some ambiguity is possible if y or some other bridge that dominates x has lower maintenance urgency for specific reasons not taken into account (for example criteria not considered in the general case).
Saying that y∈U belongs to Cl t ≥ does not necessarily mean that it actually belongs to this class. In the previous example, it is possible that y belongs to Cl 3 ≥ but, if its maintenance urgency is 2 (prior inspections), y belongs to class Cl 2 ≥ . This is due to the ambiguity between x and y with respect to criteria set P.
For P⊆C, the set of all objects belonging to Cl t ≥ without any ambiguity constitutes the P-lower approximation (5) of Cl t ≥ , denoted by , and the set of all objects that possibly belong to Cl t ≥ constitutes the P-upper approximation (6) of Cl t ≥ , denoted by : , for t = 1, …, n, (5) , for t = 1, …, n. (6) Analogously, it is possible to define P-lower approximation (7) and P-upper approximation (8) of Cl t ≥ as follows: , for t = 1, …, n, (7) , for t = 1, …, n. (8) All the objects belonging to Cl t ≥ and Cl t ≤ with some ambiguity constitute the P-boundary (9, 10) of Cl t ≥ and Cl t ≤ , denoted by Bn P (Cl t ≥ ) and Bn P (Cl t ≥ ), respectively. It is possible to represent them in terms of upper and lower approximations as follows: , for t = 1, …, n, , for t = 1, …, n. (10) From a data collection point of view, P-lower approximations of unions of classes represent certain knowledge provided by criteria from P⊆C, while P-upper approximations represent possible knowledge and the P-boundaries contain doubtful knowledge (Greco et al. 2002b).
Quality of sorting and reducts
For every P⊆C and t∈T, the quality of approximation of partition Cl by set of attributes P, or in short, quality of sorting was defined (11): .
This quality expresses the ratio of all P-correctly sorted objects in the information table. Note, that enlarging the set of criteria P, the quality of sorting not increase but decrease. In fact, any new criteria that were ambiguous before become non-ambiguous.
In the case study, for example, sorting quality is 0.98; meaning the information table contains "ambiguous objects". In Table 3 the bridge 25 has the same characteristics as bridge 46 but it is made of better material which requires higher maintenance than bridge 46. This means that the conditional criteria alone do not explain the decision maker's choices.
Each minimal subset P⊆C such as γ P (Cl) =γ C (Cl) is called a reduct of Cl and is denoted by RED Cl . Again, it is possible that a data table has more than one reduct. The intersection of all the reducts is known as the core, denoted by CORE Cl (12): .
Is not possible to remove from the data sample set criteria from CORE Cl , without impairing the knowledge to be discovered. This means that in set C there are indispensable criteria included in the core, exchangeable criteria included in some reducts but not in the core, and redundant criteria being neither indispensable nor exchangeable, thus not included in any reduct.
In the case study there are 13 reducts. Table 4 shows the criteria included in the reducts and the core which shows that there are 5 indispensable criteria (material, type of damage, damaged surface, seismic zone, hydrogeological instability), 8 exchangeable criteria and 0 redundant criteria.
Extraction of decision rules
The dominance-based rough approximations of upward and downward unions of classes allow to induce a generalized description of objects contained in the data matrix in terms of "if..., then..." decision rules.
For a given upward or downward union of classes, Cl t ≥ or Cl S ≤ , the decision rules induced under a hypothesis that objects belonging to or are positive and all the others negative, suggest an assignment to "class Cl t or better" , or to "class Cl S or worse", respectively. On the other hand, the decision rules induced under a hypothesis that objects belonging to the intersection are positive and all the others negative are suggesting an assignment to some classes between Cl S and Cl t (s < t).
In multi-criteria classification, it is meaningful to consider the following three types of decision rules: -certain D ≥ -decision rules, providing lower profile descriptions for objects without ambiguity: if f(x, q 1 ) ≥ rq 1 and f(x, q 2 ) ≥ rq 2 and …f(x, q p ) ≥ rq p , then x∈Cl t ≥ , for example: if "Bridge Age" is ≤2, "rate of heavy traffic" is ≤1 and "strategic viability" is ≤1, then the recommended degree maintenance urgency is at least 2 ( prior inspection), i.e. bridge x ∈Cl 2 ≥ ; -certain D ≤ -decision rules providing upper profile descriptions for objects without ambiguity: if f(x, q 1 ) ≤ rq 1 and f(x, q 2 ) ≤ rq 2 and ... f(x, q p ) ≤ rq p , then x∈Cl t ≤ , for example: if "damaged surface" is ≥2, "hydrogeological instability" is ≥2 and "average daily traffic" is ≥2, then the recommended degree of maintenance urgency is at most 2 ( prior inspection), i.e. bridge x ∈Cl 2 ≤ ; -approximate D ≥≤ -decision rules, providing simultaneously lower and upper profile descriptions for objects belonging to Cl s ∪Cl s +1∪…∪Cl t without being able to discern class: if f(x, q 1 ) ≥ rq 1 and f(x, q 2 ) ≥ rq 2 and ... f(x, q k ) ≥ rq k and f(x, q k+1 ) ≤ rq k+1 and ... f(x, q p ) ≤ rq p , then x∈Cl s ∪Cl s+1 ∪…∪Cl t , for example: if "material" is ≤3, "environmental condition" is ≥2, "seismic zone" is ≤2, "static scheme" is ≥3, "hydrogeological instability" is ≥2, then the recommended degree of maintenance urgency must be between 2 (prior inspection) and 1 (scheduled inspection) i.e. bridge x ∈Cl 1 ∪Cl 2 .
On the left side of D ≥≤ -decision rule it is possible to have f(x, q) ≥ rq and f(x, q) ≤ rʹq, where rq ≤ rʹq, for the same q∈C. Moreover, if rq = rʹq the two conditions boil down to 'f(x, q) = rq' .
An object x∈U supports decision rule r if its description matches both the condition and decision part of the rule. Decision rule r covers object x if it matches the condition part of the rule. Each decision rule is characterized by its strength defined as the number of objects supporting the rule. In the case of approximate rules, strength is calculated for each possible decision class separately. If a univocal rule is supported by objects from the lower approximation of the corresponding decision class only, then the rule is called certain or deterministic. If, however, a univocal rule is supported by objects from the upper approximation of the corresponding decision class only, then the rule is called possible or probabilistic. Approximate rules are supported, in turn, only by objects from the boundaries of the corresponding decision classes. Generating decision rules from decision tables is a complex task and a number of procedures have been proposed to simplify it. Existing induction algorithms use one of the following strategies (Stefanowski 1998): -generate a minimal set of rules covering all objects from a decision table, -generate an exhaustive set of rules consisting of all possible rules for a decision table, -generate a set of "strong" decision rules, called a satisfactory set of rules, each of which apply to many objects but not necessarily to all the objects in the decision table.
For the induction of decision rules free software is also available called 4eMka2 [http://idss.cs.put.poznan. pl/site/4emka.html]. This software solves multi-criteria sorting problems using rough set theory and decision rule induction and is freely available on the internet.
For each rule, the number and identity of data table objects supporting that rule are known. They are given in Table 5.
Applying SSDs to the bridges of a secondary suburban road
This study focused on applying current methodology to the bridges of the Italian national road, owned by the National Road Agency (ANAS), to estimate maintenance urgency. There are 14 bridges whose main characteristics are reported in Table 6.
Data acquisition
For each bridge, the data on construction year, static scheme, average daily traffic and heavy traffic ratio were provided by the ANAS database. The foundation soil characteristics and hydrogeological instability data were obtained from thematic maps. The PGA values were obtained by the Italian Technical Code. A GIS was used to locate the bridges on the net and to process alternative routes. Damage typology, damaged surface, damaged components and the presence or not of anti-seismic devices were assessed by visual inspections (section 5.2).
Bridge assessment by visual inspection
In this study, visual inspections were carried out using the First Level Sheets for the Degradation Survey described in section 3.2. For example, for bridge 1 the following phenomena were detected: corrosion of reinforcement and spalling both in the deck and in beam-abutment connection, joint deterioration and intrusive vegetation. Therefore the "type of damage" criterion corresponds to 2, the "damaged surface" criterion is 1 and the "damaged components" criterion is 3.
Determination of the urgency degree of maintenance activities
Once the condition criteria values were known, the following Table 7 was compiled: The decision support system above was used. At this stage of the research, the proposed DSS makes use of simple software to receive the DRSA output. Table data are inputted and the recommended urgency degree for inspections and decisional rules behind them are outputted. For example, let us evaluate the maintenance urgency of bridge No. 1 which has the characteristics described in Table 8.
Obviously, it is unreasonable to give the decision maker a large number of rules (88 for bridge 1), thus, for each class only the most supported rules have been reported. For bridge 1 these are: -if "type of damage" ≤2 then urgency at least 3 (support 80); -if "type of damage" ≤2 and "damaged surface" ≤1 then urgency at least 2 (support 32); -if "seismic zone" ≥3 then urgency at most 2 (support 34); -if "age of the bridge" ≥2 and "damaged elements" ≥3 then urgency at most 2 (support 34).
From these rules, it is clear that the decision criteria are those related to structure damage (type of damage, damaged surface, damaged components), seismic zone (PGA value) and bridge age.
It is possible that the decision maker take into account the suggestion given by the DSS or that he prefers to carry out the maintenance to improve the bridge and reduce urgency.
Proceeding on the same for all other bridge is possible to classify the bridges of the network depending on the degree of urgency of maintenance activities.
Conclusion
1. In this paper a Decision Support System for bridges maintenance management at the network level, based on Dominance Rough Set Approach, is proposed. It allows to set the order of bridges according to their maintenance urgency, on the basis of parameters related to bridge damage, characteristics of the territory, traffic and the network.
2. Using the Dominance Rough Set Approach, a decision model expressed in terms of easily understandable "if…then…" rules has been generated. The decision rules allow to control the decision process and to avoid the "black box" effects of many alternative methods. The starting point of the methodology is represented by the "exemplary decisions" with which the decision maker expresses his preferences.
3. This methodology is like a "glass box", since it is possible to map out from where each rule is derived. The model generated is flexible and could be updated by varying the exemplary decisions set required to calibrate the model. 4. A sample application of the proposed model is also reported. Putting as input the characteristics of some bridges of a rural Italian road, the built Decision Support System gives back the intervention urgency for each bridge and only the more important decision rules that can help decision maker to understand the reasons of the suggestions.
5. This is the first application of the Dominance Rough Set Approach to this type of issue and other new developments will be presented in future. | 8,142.4 | 2014-03-12T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Defects in Quantum Computers
The shift of interest from general purpose quantum computers to adiabatic quantum computing or quantum annealing calls for a broadly applicable and easy to implement test to assess how quantum or adiabatic is a specific hardware. Here we propose such a test based on an exactly solvable many body system–the quantum Ising chain in transverse field–and implement it on the D-Wave machine. An ideal adiabatic quench of the quantum Ising chain should lead to an ordered broken symmetry ground state with all spins aligned in the same direction. An actual quench can be imperfect due to decoherence, noise, flaws in the implemented Hamiltonian, or simply too fast to be adiabatic. Imperfections result in topological defects: Spins change orientation, kinks punctuating ordered sections of the chain. The number of such defects quantifies the extent by which the quantum computer misses the ground state, and is, therefore, imperfect.
I. INTRODUCTION
Adiabatic quantum computing [1][2][3] -an alternative to the quantum Turing machine paradigm -is at its core very simple and very quantum: Evolve a system from the ground state of an "easy" Hamiltonian H 0 to the ground state of H 1 that encodes the solution to the problem of interest by varying the parameter s from 0 to 1 in ( When H(s) varies slowly enough the system will remain in its ground state, and the answer can be "read off" through a suitable measurement of the final state.It has always been appreciated that adiabatic quantum computing will be difficult.For instance, even if the hardware to accurately implement H(s) and measure the final (likely, globally entangled) state were available, how slow is "slow enough" to retain the system in the ground state?This is a difficult question, as H(s) is likely to have -somewhere between H 0 to H 1 -a narrow energy gap ∆ analogous to the critical point of a quantum phase transition in a finite system.The exact size and properties of such a gap are ab initio unknown.Yet, for the computation to succeed, this gap should be traversed slowly, on a timescale longer than /∆.
Here, we put forth a simple test based on the behavior of the exactly solvable quantum Ising chain in transverse field and deploy it on the D-Wave chip.As we shall see, in addition to the issues of adiabaticity and accessibility of global ground states, there are other practical considerations that affect performance of D-Wave computers, and are likely to play a role in similar devices.
There are several efforts that aim at such hardware [4].The D-Wave computer is already available and is the obvious guinea pig that we can test.There are by now several papers that, with varying degrees of success, model the behavior of D-Wave [5].We applaud such efforts, but aim at a rather different goal -a general TAC.
The quantum Ising chain has a Hamiltonian, in the form of Eq. ( 1).It can be implemented on the D-Wave computer, see Fig. the relative energy gap ∆L/J in Eq. ( 4) as a function of the relative transverse field g/J.For long chains the gap has a minimum when g/J = 1.b.The number of kinks in a chain of length L after a quench with a quench time τQ.The dependence crosses over from the power law, Eq. ( 7), to the Landau-Zener formula, Eq. ( 5), at τ AD in Eq. ( 6).
II. TEST OF ADIABATIC COMPUTING
The dynamics of quantum phase transitions was first understood by analyzing the density of kinks in the final post-transition state (g = 0, J at its maximum) as a function of the quench timescale τ Q [6][7][8].Near the critical point, g = J ≡ J c (see Fig. 1b and Fig. 2a), quench is well approximeted by That analysis dealt with the limit of very long chains (L ≫ 1) [6][7][8] where the generation of kinks was a foregone conclusion.However, we are interested in relatively short chains where there is a chance for adiabaticity to survive.This is determined by the gap size, ∆ L , see Fig. 2a.At the critical point, s = s c , where the ground and first excited states (that can accommodate a single pair of kinks) undergo an anti-crossing, where the probability of exciting a pair of kinks is given by the Landau-Zener (LZ) formula [6,7] Thus, when τ Q exceeds we expect exponential suppression of kinks, i.e., quantum annealing should lead to the "correct answer" (in this case, all spins pointing in the same direction).
When the condition for adiabaticity is not met, τ Q ≪ τ AD , the quench timescale also governs the density of excitations according to for sufficiently long closed chains [8].The scaling, Eq. ( 7), conforms with the Kibble-Zurek mechanism (KZM) that relates the density of topological defects (and, more generally, excitations) to the critical exponents of phase transition and the rate of the quench [9,10].
The two regimes -LZ (τ Q ≫ τ AD ) and KZM (τ AD ≪ τ Q ) -switch validity when τ Q ∼ τ AD , see Fig. 2b.A good indication of the "border" between LZ and KZM -i.e., between adiabatic and non-adiabatic -is the expected number of excitations: When it is fractional, LZ is a good approximation; When there are several, then KZM should work.
We expect that, in hardware to implement quantum annealing, one should be able to choose g, J, L, and τ Q to cover the range where the ideal quantum Ising chain undergoes a transition from quantum adiabatic LZ behavior (i.e., a successful computation) to non-adiabatic KZM behavior (i.e., a defective computation).Thus, the quench of the Ising chain gives a simple test of adiabatic computing (TAC) for devices that implement quantum annealing.There are other tests that aim at similar goals (e.g., "quench echo" [11] and the symptoms of entanglement [12]).The physically motivated TAC proposed here will be useful in evaluating quantum annealing hardware.
III. RESULTS
In D-Wave computers, L can vary from L = 2 to L ∼ 10 3 and τ Q by over two orders of magnitude.Moreover, the maximal value of J at the beginning (and the end) of the quench, respectively, can vary by about two orders of magnitude.We have implemented the quench on both the DW2X-SYS4 (based in Burnaby) and the DW2X (based in Los Alamos), as shown in Fig. 1.The number of kinks in long chains as a function of quench time from the Los Alamos D-Wave DW2X are shown in Fig. 3a (see Methods for details and a compilation of results from Burnaby and Los Alamos).
There are several striking and general features of Fig. 3.The plots conform well to a power law with the density of kinks proportional to τ −1 Q .This power law differs from the KZM prediction of τ . Indeed, all of these plots enter the regime where the number of kinks per chain is ∼ 0.1 or less.In this range one expects exponential LZ suppression of excitations, though.We have not found any evidence of such an effect.
Since we do not see the exponential suppression in either open or closed chains of many different lengths from 50 to 500 sites, we search for it in very short closed chains, L = 4, that exhibit LZ crossover for a finite g.Additional a b motivation for this search comes from the scaling ≈ τ −1 Q in Fig. 3a.It is known [13] that decoherence with energy eigenstates as the pointer states [14] results in a τ −1 Q dependence for the LZ regime.
The results for L = 4 closed chains are in Fig. 3d.The scaling with τ −1 Q is still present.This tempts us to regard it as evidence of an anti-crossing in presence of decoherence [13].The number of kinks, though, seems to be larger than the theory can accommodate.Moreover, we found evidence against this "LZ with decoherence" interpretation.For one, quenches with a slightly smaller value of the maximal J max behave differently.The number of kinks can be nearly independent of τ Q , see Fig. 3b.That qualitative change is rather abrupt.Furthermore, quenches with long chains seem to show little dependence on chain length, while one expects the kink number to increase with chain length.
We do not see how these features can be accommodated within any known general theories (e.g., LZ, KZM, LZ with decoherence).Furthermore, we find significant differences between Ising chains of the same length implemented using different "spins" (i.e., Josephson junctions) on the D-Wave chip, as well as differences between the Los Alamos and Burnaby machines.In particular, the number of defects, as well as the scatter, is significantly smaller in the Los Alamos machine compared to the Burnaby machine for similar Ising chains, quench rates, etc. (see Methods).
IV. QUANTUM ISING CHAIN IN A HOSTILE ENVIRONMENT
Many factors can be contributing to this unusual behavior: Heating, randomness in couplings, eigenstate decoherence, local decoherence, self-interactions, non-Markovian effects, noise, etc.Many of these issues will likely be encountered in other settings.We note that, in our case, some of them can be ruled out, while others can not.The following discussion is inspired by our thinking of what can happen to a quantum Ising chain implemented on a D-Wave chip.Essentially, we discuss the behavior of Ising chains that are not completely isolated from their environment.We do not aim to be exhaustive: We have selected models of decoherence that can be described relatively simply (which does not mean that they can be readily solved!).We have also focused on models that can be simply parametrized (thus, for example, we have avoided discussing "mixtures" of models that -like models of noise -have several components).
This selection of what is to be discussed is in accord with the goal we have -understanding of the role of external factors in the dynamics of phase transitions as represented by a quantum Ising chain.This may come handy not just in benchmarking of adiabatic quantum computers, but also in future condensed matter experiments where quantum many-body systems are driven through a symmetry breaking transitions in presence of the inevitable coupling with their environment.Thus, while the D-Wave chip is "on our mind", we feel that many of the problems we shall encounter in the discussion of its physics will be also encountered in other settings.
Thermal excitation.Heating of the Ising chains is an obvious culprit that would add excitations -generate kinks.We do not believe that, in the D-Wave setting, it is dominant.The heating will be most effective near the critical point, as the temperatures of the two D-Wave chips we have worked with exceed the size of the gap only in its vicinity for the chains we studied: Figure 4 shows the minimal energy gap (near the quantum critical point) for different lengths of the quantum Ising chain.Thus, kink generating transitions will be only effective for a period of time that is roughly proportional to τ Q .If this effect was dominant it should result in the number of kinks increasing with τ Q .We observe the opposite trend (e.g., τ −1 Q in the Los Alamos chip).Furthermore, for very short chains (e.g., squares) there is over an order of magnitude difference between the minimal gap and k B T of the chip, suppressing thermal excitations.
For above reasons, we conclude that "heating" is unlikely to be the dominant effect behind the generation of kinks above the Landau-Zener theory predictions.
Coupling to the spins not in the chain.It is a b known that the spins on the D-Wave chip also couple to the spins from which they are nominally decoupled.That is, setting the coupling J kl = 0 between spins k and l does not guarantee that this coupling is indeed negligible.There are also reasons to believe that this coupling is predominantly "Ising" (∼ σ z k σ z l ) rather than, e.g., Heisenberg.
We believe we have seen evidence of such spurious couplings in the behavior of the Ising chains.For instance, the "compact chains" (that cover relatively small area of the chip) yield fewer kinks than "spread out chains" of the same length.This would happen if the spurious coupling with spins that should be decoupled from the chain resulted in the couplings between different fragments of the chain.This would have two related effects: The Hamiltonian of Eq. ( 2) is no longer the whole story (as it will be dressed with the couplings to the spins from which it should be nominally decoupled).We will not model this effect (in part because it requires a detailed account of how these spurious couplings occur and, in part, we believe it may turn out to be too D-Wave-specific).
The second effect that we will model recognizes that such "ghost spins" act as an environment that will decohere fragments of the quantum Ising chain -"ghost spins" monitor the orientation of the spins inside the chain.This is of interest, and is likely to be ubiquitous in other realizations of the quantum Ising systems, both in condensed matter and quantum information processing devices.
We model this effect in Methods for both open chains of varying length, see Fig. 5(a), and closed "squares", see Fig. 5(b).There is a generic pattern that emerges: When decoherence due to "ghost spins" acts for sufficiently long time, the number of kinks begins to increase with τ Q until it saturates at ≃ L/2.A similar effect was studied before in Ref. [15] where it was described as anti-Kibble-Zurek behaviour.
Randomness in the Hamiltonian.
It is now known that the implementation of the Ising Hamiltonian, Eq. ( 2), suffers from errors both in the value of the couplings between spins [i.e., J(t)] and the bias field g(t).These errors are difficult to characterize in detail especially in the critical region where g(t) ≈ J(t).They tend to be several percent of the maximal values of g and J 1 .The relative error, though, in g−J near the critical point, however, could be large.
Such randomness has a profound effect on the dynamics and kink generation that to some extent has been analyzed [16][17][18].Random couplings and transverse fields, which we allow for in the Hamiltonian of Eq. ( 18), alters the universality class for a long enough chain.We note that we take the randomness in g i (t) and J i (t) to include static random fluctuations around uniform g(t) and J(t), respectively.The number of kinks after a quench is no longer a power law ∼ τ predicted by KZM for a homogeneous chain but a logarithmic decay ∼ (ln τ Q ) −2 [16][17][18].
This slow decay might possibly explain the absence of the exponential LZ decay for long enough chains: In the presence of disorder, the adiabaticity estimate in Eq. ( 6) is no longer valid and much longer quench times are required.However, the longer chains seem to conform to a power law rather than the logarithmic decay and, what is more important, the power law persists even in short chains like the L = 4 squares.As seen in Fig. 4(a), the square has a relatively large gap even at the anti-crossing so the disorder could only have a weak perturbative effect on the outcome of the quench, see Fig. 4(b).Thus, we conclude that disorder is not the main culprit for the observed discrepancies with respect to the pure Ising chain.
Decoherence in energy eigenstates.A model of an anti-crossing with decoherence via Lindblad superoperators that are diagonal in the instantaneous energy eigenstates turns out to be exactly solvable [13].Moreover, for short chains (i.e., squares), decoherence that favors energy eigenstates can be relevant (as it tends to set in whenever the separation of energy levels is large compared to the other relevant energy scales [14]).
In this regime, the probability of a transition to the excited state is given by the equation where γ and ε ∼ τ −1 Q are the decoherence and transition rates, respectively, and Q is a simple function with a maximum value of ∼ 0.65 [13].Our results with squares yield values of Q that are close to Q ∼ 1 and that sometimes "dip" to within the region below 0.65 consistent with the equation above.We note that our estimates of the parameters in Eq. ( 8) can be significantly affected by the caveats listed above, so we cannot rule out significance of this model for squares. 1 Private communication with D-Wave Inc.
In particular, the probability of kink formation for both ferro and anti-ferro cases exhibits the same quenchrate dependence (τ −1 Q ) consistent with Eq. ( 8) only in the Los Alamos machine and when the scale of J is set to its maximal range, see Fig. 6(b).However, even a relatively modest change of that scale from the maximum leads to a fairly dramatic change in the behavior undermining hope in the utility of Eq. ( 8) for the problem at hand, see Fig. 3(b).
V. DISCUSSION
Complex behavior of quantum annealers demands global tests of adiabaticity and quantumness, as even when components of the device work, their integration raises questions of decoherence, control, and what "slow enough" is.We propose a global test based on a quench in the quantum Ising chain.It can assess reliability of the whole device.Such general tests will prove valuable in establishing adiabaticity and benchmarking/comparing different implementations of adiabatic quantum computers expected in the future.
In spite of the outcome of the TAC, D-Wave may, in some cases, find the right or at least approximate, solutions to problems.Obviously, a more precise implementation would result in a more successful adiabatic quantum computation/quantum anneal.Indeed, the noticeable decrease in the number of defects between the tests of Burnaby and Los Alamos machines is likely due to the improvements in hardware.One can hope that the next generation of quantum annealers will be even better.
Methods
Numerical simulations.To obtain the results in Fig. 2b, we first brought the Hamiltonian (2) into its fermionic representation [8], using the Jordan-Wigner transformation [19] σ where c n (c † n ) is the fermionic annihilation (creation) operator for site n.For the quadratic correlation functions x pq := c † p c q and y pq := c † p c † q , this gives the closed system of equations i ẋp,q = −J p x p+1,q − J p−1 x p−1,q + J q x p,q+1 + J q−1 x p,q−1 + J q y p,q+1 − J q−1 y p,q−1 + J p y * p+1,q − J p−1 y * p−1,q + 2 (g p − g q ) x p,q , q ≥ p; (12) and i ẏp,q = −J p y p+1,q − J p−1 y p−1,q − J q y p,q+1 − J q−1 y p,q−1 − J q x p,q+1 + J q−1 x p,q−1 + J p x * p+1,q − J p−1 x * p−1,q − J p δ p+1,q + 2(g p + g q )y p,q , q > p, (13) with y pp = 0.The above equations are solved with the initial condition corresponding to the system's ground state when J > 0 and with the boundary conditions c 0 = c L+1 = 0. To carry out numerical computations, we used an adaptive Adams method from LSODA.Finally, the number of kinks was obtained from Here ℜ means real part.Both the ground state and the gap depicted in Fig. 2(a) where calculated using techniques described in Ref. [20].Thus, to compute the number of kinks we used the following formula N is the numbers of couplings in the chain.The final energy E can be read in directly from the D-Wave solver.Burnaby versus Los Alamos chip.One would expect different chips of the same generation of annealers to generate roughly the same number of kinks for ferro and anti-ferro cases.However, the DW2X based in Los Alamos seems to perform better (i.e., generates less kinks) when J < 0, see Fig. 6(a).The Burnaby machine, though, has the same behavior for ferro and anti-ferro cases, see Fig. 6(b).
Thus, chips that belong to different architectures may behave differently.For instance, Fig. 7 compares the DW2X based in Los Alamos and a previous generation DW2X-SYS4 in Burnaby.Not only do the number of kinks differ between these two systems but it also exhibits different quench-time dependence (τ −1 ). Decoherence by "ghost spins".
Numerical results presented in Fig. 5 are obtained using the following Linbdlad master equation [19]: where the superoperator is The number of kinks is different for ferro and anti-ferro cases.Smaller number of defects when J < 0 suggest that the Los Alamos chips performs better in this regime.b.DW2X system based in Burnaby.As one would expect, the number of kinks is roughly the same for both ferro and anti-ferro cases.
and H(t) takes the form
where we allow for time and spatial dependence in both J n and g n .Expectation values, O = Tr(Oρ), of an operator O evolve according to This equation is solved using the Jordan-Wigner transformation [20] where c n (c † n ) is a fermionic annihilation (creation) operator.For an open chain, the above transformation brings
1 .FIG. 1 .FIG. 2 .
FIG. 1.The quantum Ising chain implemented in a D-Wave computer.a.An example of an Ising chain on the D-Wave "chimera graph".The red lines are active couplings between "spins".b.A typical annealing protocol for a D-Wave annealer.Here J(s) = Jmax • j(s), where j(s) is a predetermined function increasing from j(0) = 0 to its maximal value j(1) and Jmax ∈ [−1, 1] is a free parameter that can be turned at will.
10 - 8 10 - 6 10 - 4 kinksQFIG. 3 .
FIG. 3. Defect generation in a quench of the quantum Ising chain on a D-Wave computer.a.The number of defects versus quench time for two different length chains (Jmax = −1 for all) on the Los Alamos machine.Solid line shows the best fit to the function A • τ −x Q .b.The number of defects versus quench time for a short chain (L = 4) for different values of Jmax.Solid line shows the best fit to the function A • τ −1Q .These results were obtained by averaging over different runs and realizations of the same chain on the chimera graph.Errors are the standard errors of the mean.Note the dramatic change in the behavior between the quenches that start with maximum initial coupling strength (upper right corner) and only 8% smaller initial coupling strength (lower right corner).
1 kinksFIG. 5 .
FIG. 5. Ghost spins -defects with decoherence.a.The number of kinks as a function of quench rate J/τQ for different decoherence strengths γ and L = 100.Here, g(t) = J(1 − t/τQ) and γ = γ/J.b.The same as in a. but for a periodic chain of length L = 4 (i.e., a "square").
AFIG. 6 .
FIG. 6.Comparison between the same D-Wave architectures (L = 300).a. DW2X system based in Los Alamos.The number of kinks is different for ferro and anti-ferro cases.Smaller number of defects when J < 0 suggest that the Los Alamos chips performs better in this regime.b.DW2X system based in Burnaby.As one would expect, the number of kinks is roughly the same for both ferro and anti-ferro cases. | 5,383 | 2017-07-29T00:00:00.000 | [
"Physics"
] |
Image Semantic Description Based on Deep Learning with Multi-attention Mechanisms
. In the era of big data, cross-media and multi-modal data are expanding, and data processing methods fail to meet corresponding functional requirements. Aiming at the characteristic of large expression gap of multi-model data, This paper proposes a multimodal data fusion method based on deep learning, which combines the advantages of deep learning in the field of image detection, text sequence prediction, and the multi-attention mechanism. The BLEU algorithm is used to calculate the similarity of four levels of description statements of model output and image. Training and testing were conducted in the Flickr8K data set. Comparing with the traditional single mode state image description method, the experiments show that under the BLEU index, the multi-AM model can achieve better results.
Introduction
With the emergence of various high-tech electronic products, the carrier of important information is no longer a traditional single text, video or audio, but a variety of media.Cross-media and multi-modal data mainly showed the underlying data the characteristics of heterogeneous and high-level semantic expression similar to the "semantic gap" problem, in recent years, more and more scholars and researchers have been involved the study of multi-modal data [1,2].Image scene description is a important research direction in the field of image understanding, its object of study is by the color, texture, shape representation of image information, such as the target task is to get a accurate description of image content text sequences, across the two modal images and text information expression.Traditional image description task mainly has two key issues -image content representation and classification judgment, namely to find the most representative image scene, and then to learning and training of scene, scene category classification model.Image content description often requires human visual feature extracting, design visual dictionary, such as complex work, and need additional researchers' prior knowledge, this part of the work has a great influence for the classification effect.The main sources of problems or image and text data in the underlying data expression differences, how to eliminate the differences, and for a variety of modal data fusion is the core content of this paper.
Hinton since 2006, put forward the concept of deep learning, a large number of papers published about deep learning, in-depth study has been successfully applied to computer vision, speech recognition, natural language processing, and other fields.In multiple modal data fusion, image and text, for example, the depth of the neural network can use different models of two kinds of modal data feature extraction, and image and text are similar characteristics of space vector modeling method, therefore, for the fusion of images and text on the feature space, image semantic expression based on deep learning can be realized.
Related Work
The study of semantic description of traditional image scenes is mainly based on single-modality images.To reduce the "semantic gap", an image analysis layer such as a visual dictionary is constructed between the low-level visual features and high-level semantic information.Image semantic information description must establish the mapping relationship between low-level visual features and high-level semantics.In recent years, more and more scholars have begun to pay attention to the research field of multimodal data fusion.Sawant Neela,et al(2011) thinks it needs to capture events, locations, and personalities in addition to the visual features of the human beings in the traditional object monitoring and scene interpretation [3].The abstract concept of a reference, Ma, Hao, et al(2011) carried out related research on image and text fusion methods, and proposed a data fusion framework based on image content and tags-a new random walk model that uses fusion parameters to balance content and labels between the impact [4].Hollink L, et al. (2005) describes a semi-automatic image annotation algorithm in specific fields, the goal is to identify domain features to increase semantic understanding [5].
In recent years, the intensified research on deep neural networks has remained high and breakthroughs have also been made.This has benefited from convolutional neural networks and recurrent neural networks [6], and most researchers are based on these two types of deep neural network models and have done a lot of optimization work.Karpathy, Andrej, and F. F. Li (2015) and Xu, Kelvin, et al(2015) did a lot of work in the field of image understanding [7,8].F. F. Li et al. propose an image semantic alignment model, extract the key information in the image and align it with the keywords in the sentence description.However, they all use the RNN structure in the language model, and there is a lack of semantic relevance.
Deep neural network model based on multi-attention mechanism
In this paper，we propose a deep neural network based on Convolution Neural Network(CNN) and Long Short Term Memory Network Network(LSTM) to describe the image in sentences, and introduce multi-attention mechanism on this basis.When we describe an image, we need to pay attention to the content of the image as well as the language foundation.When we get the word "cat," we focus on the cat part of the image and ignore the rest.The prediction of a word requires not only the introduction of attention mechanism in the language model, but also in the image.
CNN for Feature Extraction
Russakovsky, Olga, et al (2015) summarized the competition results of each team in the ImageNet competition and the brief description of the algorithm in the last five years [9].Among them VGG network performance is particularly outstanding.Simonyan, Karen, and A. Zisserman(2014) believed that the filter of 7x7 could be decomposed into a number of 3x3 filters, the smaller filter means more flexible channel [10].Fig. 1 shows the convolution structure of vgg-16 network, We used his convolutional layer to extract image features as input to the image part.
LSTM for Sequences' Predict
DNN may be able to extract excellent characteristic expression, but LSTM is better than DNN in word prediction.LSTM is an improved recurrent neural network [11], general RNN cannot save too much information, there is only one state in the hidden layer, it is very sensitive to short-term input, if we add another state C to save longterm information, the problem will be solved.LSTM uses gate to control long-term status C. The gate can be expressed as: W is the weight vector of the gate and b is the bias term. is the sigmoid function and the range is (0,1), so the state of the gate is half open and half closed.The structure of a single node in the LSTM network is shown in Fig. 1.The final output of the LSTM is jointly controlled by the output gate and cell state:
Multi-attention mechanism
The AM model is one of the most important developments in the NLP field in the past few years, which appear in most of the current papers are attached to the Encoder-Decoder framework.But the AM model can be used as a general idea, When a general RNN model generates a language sequence, the predicted next word is only related to its first n words, and n is generally less than 5.
= ( − , − , − ⋅⋅⋅, ) The above formula C represents the semantic encoding, Obviously the semantic semantics of each word is C is unreasonable, and a word will not only be related to the most recent words, So we give each word a probability distribution that expresses its relevance to other words, and Replace C with .
indicates the number of other words associated with , represents the probability of interest between two words. is the information of the word itself.The question now is how to calculate the probability distribution.It is usually to calculate the similarity between the current input information and the previous information .In the word2vec model, it is the distance between two vectors.After going through a multi-layer convolutional structure, the image information is compressed into a vector I.When predicting each word, you need to associate some information in the vector.The attention parameter W for the image is what we need to train to get.
Finally, the functional relationship of each predicted word is as follows and The model is shown in Fig. 2.
Experiments
In order to compare with the prior art, we conducted a large number of experiments using the BLEU metrics to evaluate the effectiveness of our model.Experiments used the Flickr 8K data set, contrast traditional image scene expression method.
Experimental environment and parameter deployment
Experiments using the current popular TensorFlow framework, and VGG-16 model to extract image features, In the whole model, set the batch-size to 8 to relieve the pressure of GPU memory.Fully connected layer functions as a "classifier" throughout the convolutional neural network, while the convolutional layer, the pooled layer, and the activation function layer can be viewed as mapping the image to the feature space.Deeper layers will inevitably bring better results.The experiment uses the Flickr8k dataset, which includes Flickr8k_Dataset and Flickr8k_text.We compressed the image to a size of 300x300 pixels so that we could train more samples; In Flickr8k_text, each image corresponds to 4 different types of descriptions.We use Word2vec to vectorize the words.In terms of semantically similar words, the Euclidean distances of their vectors are often very close.Then we only select the first 200 words of frequency, and the rest are replaced by [UNK], which makes the load of the model smaller.
evaluating indicator
The popular automatic evaluation method is the BLEU algorithm proposed by IBM [12]，The BLEU method first calculates the number of matching n-grams in the reference sentence and the generated sentence, and then calculates the ratio of the number of n-grams in the generated sentence as an evaluation index.It focuses on the accuracy of generating the word or phrase in the sentence.The accuracy of each order N-gram can be calculated by the following formula: The upper limit of N is 4, which means that only the accuracy of 4-gram can be calculated.
Results and discussion
There are two comparisons in the experiment.One is to compare the traditional basic model, and the other is to compare the current mainstream model.As can be seen from Table 1, the accuracy of the Multi-AM model in the keyword is better than the traditional model.
Conclusions
Semantic description of images is a complex task, and the framework based on deep learning has become the current mainstream method.This paper proposes a multiattention mechanism based on deep neural network, we need to understand the grammar of the sentence generation, as well as the content in the image.Words have different levels of attention to image content and different levels of attention from context.Experimental results show that the multi-attention mechanism can achieve higher scores under the BLEU evaluation criteria, which shows that the method can extract more keywords.Future research should attempt to lack the sentence description data set and improve the semantic matching of sentences.We need to accurately position the predicted word in the image, which is very difficult.
Table 1 .
Comparison with other methods on the flicker8K datasetFrom the results of Table2, the accuracy of one and two keywords is better than other mainstream algorithms, but the effect of obtaining more keywords is not good.but the effect of obtaining more keywords is not good.
Table 2 .
Comparison with other mainstream model on the flicker8K dataset | 2,595.6 | 2018-10-19T00:00:00.000 | [
"Computer Science"
] |
Rapid and Low-Cost Quantification of Adulteration Content in Camellia Oil Utilizing UV-Vis-NIR Spectroscopy Combined with Feature Selection Methods
This study aims to explore the potential use of low-cost ultraviolet-visible-near infrared (UV-Vis-NIR) spectroscopy to quantify adulteration content of soybean, rapeseed, corn and peanut oils in Camellia oil. To attain this aim, test oil samples were firstly prepared with different adulterant ratios ranging from 1% to 90% at varying intervals, and their spectra were collected by an in-house built experimental platform. Next, the spectra were preprocessed using Savitzky–Golay (SG)–Continuous Wavelet Transform (CWT) and the feature wavelengths were extracted using four different algorithms. Finally, Support Vector Regression (SVR) and Random Forest (RF) models were developed to rapidly predict adulteration content. The results indicated that SG–CWT with decomposition scale of 25 and the Iterative Variable Subset Optimization (IVSO) algorithm can effectively improve the accuracy of the models. Furthermore, the SVR model performed best for predicting adulteration of camellia oil with soybean oil, while the RF models were optimal for camellia oil adulterated with rapeseed, corn, or peanut oil. Additionally, we verified the models’ robustness by examining the correlation between the absorbance and adulteration content at certain feature wavelengths screened by IVSO. This study demonstrates the feasibility of using low-cost UV-Vis-NIR spectroscopy for the authentication of Camellia oil.
Introduction
Camellia oil, as one of the most valuable edible oils [1,2], is highly sought after by consumers because of its great potential in the health care, medical, beauty, and chemical fields [3,4]. The superior physicochemical properties possessed by Camellia oil result in its price being significantly higher (5-10 times) than that of common edible oils (such as soybean and rapeseed oils) [5]. Due to the high demand, several fraudulent practices have emerged in the Camellia oil industry. These involve illegal traders who blend low-priced oils, such as soybean, corn, and rapeseed oils, into the genuine Camellia oil, as well as falsely label their product to make illicit profits [6]. Such practices are serious violations of regulations such as Chinese standard GB 2716-2018. It is therefore critical to develop a rapid, effective and robust method for quantifying adulteration content in Camellia oil.
Traditional methods for detecting adulteration in Camellia oil based on visual or odor assessments are often subjective, leading to unreliable results [7]. Recently, primary methods for detecting edible oil adulteration have included chromatography [8], nuclear magnetic resonance [9], electronic nose [10], and spectroscopy [11]. Among them, chromatography, nuclear magnetic resonance, and the electronic nose method have certain drawbacks. For example, gas chromatography and liquid chromatography require complex
Spectrum of the Oil Samples
The raw spectrum profiles of the prepared samples were presented in Figure 1. As shown in Figure 1a, there were five absorption peaks in the 244 spectrum curves at around 250 nm (UV band), 430 and 660 nm (Vis band), and 930 and 1050 nm (NIR band), respectively. Figure 1b illustrated that there were differences between the spectrum curves of the five pure oils, particularly in some bands where Camellia oil differed from the four lower-priced oils. Specifically, at the characteristic peak band near 430 nm, the largest magnitude differences between Camellia oil and rapeseed, corn, and soybean oils were observed. Additionally, a significant magnitude difference existed between Camellia oil and peanut oil at the characteristic peak band around 660 nm. The observed differences between the collected pure oil spectrum provided evidence of utilizing UV-Vis-NIR transmission spectroscopy (200-1100 nm) as a feasible method to estimate adulterated content. However, due to the similarity between spectra curves, it is necessary to employ chemometrics and machine learning techniques to further analyze the data.
Spectrum Preprocessing Results
The raw spectra were preprocessed with SG, SG-1st, SG-2nd, and SG-CWT with 9 decomposition scales (i.e., L1-L9), respectively ( Figure 2). To determine the optimal preprocessing method, the SVR models were developed using the full preprocessed spectral dataset, and then R 2 and RMSE were evaluated. As shown in Table 1, the optimal method was SG-CWT (L5) with an R 2 of 0.9998 and RMSE of 0.0059. Moreover, compared to SG-2nd that was the second-best method, SG-CWT (L5) To determine the optimal preprocessing method, the SVR models were developed using the full preprocessed spectral dataset, and then R 2 and RMSE were evaluated. As shown in Table 1, the optimal method was SG-CWT (L5) with an R 2 of 0.9998 and RMSE of 0.0059. Moreover, compared to SG-2nd that was the second-best method, SG-CWT (L5) can improve RMSE by 21.33% and R 2 by 0.02%. In addition, the results verified that SG-CWT (L1−L9) was able to gradually amplify the insignificant characteristic peaks and valleys in the spectral curves at low decomposition scales, thus highlighting the local differences ( Figure 2). However, increasing decomposition scale led to too smooth spectral curves, and hence, some inconspicuous feature peaks and valleys were gradually removed, which increased the difficulty of capturing spectral feature information. It was demonstrated that CWT can effectively smooth the data and reduce noise at low decomposition scales. Therefore, SG-CWT (L5) was adopted to preprocess spectra for the following parts.
Feature Wavelength Screening Results
Four kinds of wavelength screening methods, including CARS, SPA, BOSS, and IVSO, were used to select the feature wavelengths from the full spectrum with SG-CWT (L5) preprocessing. As a result, CARS, SPA, BOSS, and IVSO screened 27, 28, 30, and 48 feature wavelengths, respectively, effectively reducing the number of wavelengths to 1.31%, 1.35%, 1.45%, and 2.32% of the full spectrum (2068 wavelengths).
To determine the optimal feature wavelength screening method, the SVR and RF-based models were established using full spectrum (FS) and the feature wavelengths screened by CARS, SPA, BOSS and IVSO, respectively. Then, the evaluation criteria of different models were compared in Figure 3. The results demonstrated that the IVSO method was the most appropriate for feature wavelength screening, trailed by BOSS and CARS, while SPA was the least suitable. Furthermore, the results indicated that the use of IVSO-RF provided the optimal performance for quantifying the percentage of adulterant in Camellia oil adulterated with corn, peanut, or rapeseed oils. However, for Camellia oil adulterated with soybean oil, the best performance was achieved using the IVSO-SVR combination.
To further clarify the advantages of IVSO compared to other methods, the distribution characteristics of the screened wavelengths were analyzed ( Figure 4). The wavelengths extracted by CARS, BOSS, and IVSO were predominantly in the Vis band, while SPA had comparable numbers of wavelengths among the UV, Vis and NIR bands. Specifically, CARS, BOSS, and IVSO concentrated the feature wavelengths on two characteristic peak and valley positions at approximately 510 nm and 660 nm. In contrast, the feature wavelengths generated by SPA were primarily concentrated at both ends of the spectrum, where excessive noise interference could render SPA a distinct disadvantage over the other methods. In addition, IVSO showed better clustering characteristics than CARS and BOSS in the Vis band. screened by CARS, SPA, BOSS and IVSO, respectively. Then, the evaluation criteria of different models were compared in Figure 3. The results demonstrated that the IVSO method was the most appropriate for feature wavelength screening, trailed by BOSS and CARS, while SPA was the least suitable. Furthermore, the results indicated that the use of IVSO-RF provided the optimal performance for quantifying the percentage of adulterant in Camellia oil adulterated with corn, peanut, or rapeseed oils. However, for Camellia oil adulterated with soybean oil, the best performance was achieved using the IVSO-SVR combination. To further clarify the advantages of IVSO compared to other methods, the distribution characteristics of the screened wavelengths were analyzed ( Figure 4). The wavelengths extracted by CARS, BOSS, and IVSO were predominantly in the Vis band, while SPA had comparable numbers of wavelengths among the UV, Vis and NIR bands. Specifically, CARS, BOSS, and IVSO concentrated the feature wavelengths on two characteristic peak and valley positions at approximately 510 nm and 660 nm. In contrast, the feature wavelengths generated by SPA were primarily concentrated at both ends of the spectrum, where excessive noise interference could render SPA a distinct disadvantage over the other methods. In addition, IVSO showed better clustering characteristics than CARS and BOSS in the Vis band.
Model Development
In this study, we developed an SVR model to predict the adulteration content of soybean oil mixed with Camellia oil, and three RF models to measure adulteration with corn, peanut, and rapeseed oils, respectively, according to the results shown in Figure 3.
Moreover, to further enhance the prediction ability of the proposed models, the main
Model Development
In this study, we developed an SVR model to predict the adulteration content of soybean oil mixed with Camellia oil, and three RF models to measure adulteration with corn, peanut, and rapeseed oils, respectively, according to the results shown in Figure 3.
Moreover, to further enhance the prediction ability of the proposed models, the main parameters in SVR and RF models, as presented in Table 2, were optimized. Specifically, the SVR model determined the optimal penalty factor c and the kernel function γ by the grid search method that minimized 10-fold cross-validation error. Moreover, the RF models attained the optimal number of decision trees n by using the particle swarm optimization algorithm, which was run with a particle dimension of 2, population size of 30, and maximum 100 iterations. The performance of both SVR and RF models were also shown in Table 2. As presented in Table 2, it was apparent that the parameter-optimized models significantly outperformed their unoptimized counterparts ( Figure 3). Additionally, the SVR and RF models demonstrated no signs of underfitting or overfitting.
Next, a detailed analysis of each of the four models was presented. The analysis utilized the evaluation criteria for prediction sets and provided insight into each model's performance. The R 2 P values indicated that the parameter-optimized models performed better in each of the four types of adulterated oils. Specifically, in the case of Camellia oil adulterated with soybean oil, the parameter-optimized IVSO-SVR model achieved a higher R 2 P of 0.9925 (an improvement of 0.13%), and a lower RMSE P of 0.0325 (a decrease of 8.96%) compared to the unoptimized IVSO-SVR model (0.9912 and 0.0357, respectively). The same trend held true for the parameter-optimized IVSO-RF model in the other three types of adulterated oils, exhibiting an increase in R 2 P of 0.92% to 0.19% and a decrease in RMSE P of 10.14% to 18.94% when compared to unoptimized models. Figure 5 illustrates that the predicted adulteration content of soybean, corn, peanut and rapeseed oils all agreed well with actual ones in terms of prediction sets. Therefore, these results strongly indicated that the developed models can greatly assist in quantifying the adulteration content in Camellia oil with high precision and reliability. Furthermore, the performance of the developed models was compared with that of other spectroscopic quantitative techniques including Vis-NIR [19], Fourier transform infrared (FTIR) [22] and UV-Vis [15] (Table 3). It was observed that our models demonstrated comparable predictive capabilities, while providing a broader range for adulteration ratios.
Wavelength Characteristics Study
In order to further emphasize the applicability of the models established in this study and the rationality of the selected feature wavelengths, three representative wavelengths among the feature wavelengths proposed by IVSO were analyzed by significance test and Pearson correlation coefficient. They were 313.759 nm in the UV band, 486.401 nm in the Vis band, and 929.144 nm in the NIR band. The significance coefficients ρ for these three wavelengths were all less than 0.05, and therefore, possessed the significance of Pearson correlation analysis for the study [23]. soybean, canola, sunflower and sesame oil UV-Vis 1-20% 0.94-0.99 [15] Camellia oil adulterated with soybean oil
Wavelength Characteristics Study
In order to further emphasize the applicability of the models established in this study and the rationality of the selected feature wavelengths, three representative wavelengths among the feature wavelengths proposed by IVSO were analyzed by significance test and Pearson correlation coefficient. They were 313.759 nm in the UV band, 486.401 nm in the Vis band, and 929.144 nm in the NIR band. The significance coefficients ρ for these three wavelengths were all less than 0.05, and therefore, possessed the significance of Pearson correlation analysis for the study [23].
We compared the Pearson correlation coefficients across three bands for Camellia oil adulterated with four oils (Figure 6). It was found that the absolute values of coefficients |R| were all greater than 0.5. This suggested there were some correlations between the absorbance and adulteration content. Furthermore, Figure 6 displays the Pearson correlation coefficient of absorbance and adulteration content in decreasing order of strength from Vis, NIR, and UV. This supports the possibility that the inadequate number of Vis wavelengths may have an adverse effect on the predictive capability of the SPA algorithm. We compared the Pearson correlation coefficients across three bands for Camellia oil adulterated with four oils (Figure 6). It was found that the absolute values of coefficients |R| were all greater than 0.5. This suggested there were some correlations between the absorbance and adulteration content. Furthermore, Figure 6 displays the Pearson correlation coefficient of absorbance and adulteration content in decreasing order of strength from Vis, NIR, and UV. This supports the possibility that the inadequate number of Vis wavelengths may have an adverse effect on the predictive capability of the SPA algorithm.
We compared the Pearson correlation coefficients across three bands for Camellia oil adulterated with four oils (Figure 6). It was found that the absolute values of coefficients |R| were all greater than 0.5. This suggested there were some correlations between the absorbance and adulteration content. Furthermore, Figure 6 displays the Pearson correlation coefficient of absorbance and adulteration content in decreasing order of strength from Vis, NIR, and UV. This supports the possibility that the inadequate number of Vis wavelengths may have an adverse effect on the predictive capability of the SPA algorithm. Specifically, Camellia oil that is adulterated with soybean oil (Figure 6a-c) exhibited negative correlation across all three wavelengths with an R value less than −0.94. This implied that accurate prediction of the adulteration content of soybean oil can be made in the wavelength bands of 200-1100 nm. Next, the Camellia oil adulterated with corn oil (Figure 6d-f) displayed negative correlation in all three bands. The Vis and NIR bands showed a high level of correlation (with R value less than −0.90), whereas the UV band demonstrated a moderate correlation with an R value of −0.671. This indicated that the Vis and NIR bands contained more feature information than the UV band. In addition, the adulteration of Camellia oil with peanut oil (Figure 6g-i) displayed positive correlation for the UV and Vis wavelengths, but showed negative correlation in the NIR band. R values Specifically, Camellia oil that is adulterated with soybean oil (Figure 6a-c) exhibited negative correlation across all three wavelengths with an R value less than −0.94. This implied that accurate prediction of the adulteration content of soybean oil can be made in the wavelength bands of 200-1100 nm. Next, the Camellia oil adulterated with corn oil (Figure 6d-f) displayed negative correlation in all three bands. The Vis and NIR bands showed a high level of correlation (with R value less than −0.90), whereas the UV band demonstrated a moderate correlation with an R value of −0.671. This indicated that the Vis and NIR bands contained more feature information than the UV band. In addition, the adulteration of Camellia oil with peanut oil (Figure 6g-i) displayed positive correlation for the UV and Vis wavelengths, but showed negative correlation in the NIR band. R values of 0.989 (very strong correlation), −0.759 (strong correlation), and 0.535 (moderate correlation) were obtained for the Vis, NIR, and UV bands, respectively. This indicated that the Vis wavelength contained more sensitive information in the adulteration of peanut oil. Last, in the instance of Camellia oil that is adulterated with rapeseed oil (Figure 6j-l), negative correlation was observed across all three bands, with Vis and NIR bands exhibiting very strong correlation (R values less than −0.82), while a strong correlation (R value of 0.754) was exhibited by the UV band. This demonstrated that the prediction ability of the Vis and NIR bands was stronger than that of the UV band in the case of rapeseed oil adulteration. In summary, the IVSO-based feature extraction method was demonstrated to be robust.
Materials and Methods
The overall research process diagram is shown in Figure S1 of Supplementary Material.
Samples Preparation
Five different types of oils were purchased from the local supermarkets in Changsha, China, including Camellia, soybean, rapeseed, corn, and peanut oils. All oils used during the test were within the shelf life.
Soybean, rapeseed, corn and peanut oils were blended into Camellia oil at different blend ratios to prepare adulterated samples. The proportion of blend was 1%, 3%, 5%, 7%, 10%, 15%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% respectively. Four samples were prepared for both each blend ratio of the adulterated samples and five kinds of pure oils. Consequently, the number of test samples in each set of adulterated oil samples reached 64, while the total number of samples in this study was 256. For preparation, the mixed oil samples were placed in a magnetic mixer and stirred at 35 • C for 1 h, followed by a low temperature resting period of 24 h.
Experimental Platform
An experimental platform (Figure 7) for collecting transmission spectra was composed of a dark box, a cuvette holder, two probe holders, two optical fibers, a spectrometer (OceanView Maya2000 pro, OceanView Company of the United States, Phoenix, AZ, USA), and a light source (HL1000 tungsten halogen lamp, Wen Yi Optoelectronics Technology Co., Shanghai, China). The spectra were collected by OceanView spectroscopy software. Soybean, rapeseed, corn and peanut oils were blended into Camellia oil at different blend ratios to prepare adulterated samples. The proportion of blend was 1%, 3%, 5%, 7%, 10%, 15%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% respectively. Four samples were prepared for both each blend ratio of the adulterated samples and five kinds of pure oils. Consequently, the number of test samples in each set of adulterated oil samples reached 64, while the total number of samples in this study was 256. For preparation, the mixed oil samples were placed in a magnetic mixer and stirred at 35 °C for 1 h, followed by a low temperature resting period of 24 h.
Experimental Platform
An experimental platform (Figure 7) for collecting transmission spectra was composed of a dark box, a cuvette holder, two probe holders, two optical fibers, a spectrometer (OceanView Maya2000 pro, OceanView Company of the United States, Phoenix, AZ, USA), and a light source (HL1000 tungsten halogen lamp, Wen Yi Optoelectronics Technology Co., Shanghai, China). The spectra were collected by OceanView spectroscopy software. The spectrometer has a spectrum scan range of 200-1100 nm, and was configured to the spectrum integration time of 32 ms and a number of scans of 100. Prior to the experiment, the spectrometer was preheated for 40 min. The mean value was obtained by measuring the same sample three times and calculating the average. The absorbance of the The spectrometer has a spectrum scan range of 200-1100 nm, and was configured to the spectrum integration time of 32 ms and a number of scans of 100. Prior to the experiment, the spectrometer was preheated for 40 min. The mean value was obtained by measuring the same sample three times and calculating the average. The absorbance of the samples was calculated by Equation (1).
where A λ is the absorbance, S λ is the intensity of the collected sample spectrum, D λ is the background intensity of the dark spectrum, and R λ is the intensity of the empty cuvette reference spectrum.
Spectrum Preprocessing
The spectrum acquisition process is highly susceptible to interference from the external environment or its own internal instability, thus causing confusion and loss of valid information in the spectrum data. To improve the model accuracy, Savitzky-Golay (SG), SG-1st, SG-2nd, and SG-multi-decomposition scale Continuous Wavelet Transform (CWT) were used to preprocess the raw spectra in this study. SG smoothing can effectively improve the signal-to-noise ratio and also has a significant effect on reducing random noise. In this study, the window size for the SG was set to 15 and the polynomial degree was set to 2. Setting the window size too large would lead to excessive smoothing of the spectrum curve, while setting it too small would result in ineffective noise removal [24]. First-order and second-order derivative processing are effective methods for resolving overlapping peaks and eliminating background noise [24]. CWT has the property of refining weak information to highlight localization and can effectively enhance spectrum feature information, and has been applied in noise reduction, de-contextualization, and compression of spectrum data [25,26]. The decomposition scales in CWT were set to 2, 2 2 , 2 3 , 2 4 , 2 5 , 2 6 , 2 7 , 2 8 , and 2 9 , which were chosen as the mother wavelet functions for the identification of the dopant content spectra. For simplification, the nine decomposition scales were designated as L1-L9, respectively [25,26].
The preprocessed spectra were brought into the SVR prediction model, and then the optimal preprocessing method was selected by comparing the evaluation criteria of coefficient of determination (R 2 ) and root mean square error (RMSE).
Feature Wavelength Selection Method
The full spectrum has 2068 wavelengths, and the number of redundant wavelengths affects the accuracy and speed of model predictions. To simplify the prediction model, the feature wavelengths of the preprocessed data were selected by Competitive Adaptive Reweighted Sampling (CARS), Successive Projections Algorithm (SPA), Bootstrapping Soft Shrinkage (BOSS), and Iteratively Variable Subset Optimization (IVSO), respectively.
CARS screens the subset of wavelengths with the smallest root mean square error of cross-validation (RMSECV) as the feature wavelength set with a 10-fold interaction validation cycle [27]. The number of Monte Carlo runs was set to 100 in this study, and 80% of the samples were taken each time as the calibration set.
SPA minimizes the spectrum data dimensionality by reducing the number of input features [28]. The range of the number of wavelengths after setting the SPA downscaling in this study was from 1 to 40.
BOSS continuously adjusts the weights of each wavelength by weighted autonomous sampling (WBS), which can achieve optimal shrinkage of wavelength space [29]. The number of bootstrap samples was set to 1000 in this study.
IVSO simulates the competitive process by weighted binary matrix sampling (WBMS) and sequential addition to progressively reduce the number of useless and interfering information wavelengths [30]. The number of WBMS samples was set to 1000 in this study.
Models
Support Vector Regression (SVR) and Random Forest (RF) algorithms were utilized to develop the rapid quantitative model of adulterated Camellia oil based on extracted feature wavelengths. Before constructing models, the Kennard-Stone (K-S) algorithm [31] was used to divide the datasets into two segments in a 2:1 ratio, resulting in 43 samples in calibration set and 21 samples in prediction set for each type of adulterated oil samples. Furthermore, the model's performance was improved through the use of a parameter search method.
SVR constructs the optimal hyperplane to solve the optimal solution by selecting different kernel functions so that the features are mapped to the high-dimensional space. The radial basis function in the kernel function is a nonlinear projection that can cope better with the nonlinear relationship between the label and the predictor variables [32]. In this study, the radial basis function was chosen as the kernel function to develop the SVR model for the fast prediction of adulteration content within Camellia oil. The penalty factor c and kernel function γ within the SVR model were optimized using the grid search method [33] to improve its ability to predict adulteration content within Camellia oil.
RF is an ensemble learning method that utilizes decision trees to make a collective decision, where the majority vote determines the final results [34]. The number of decision trees is a crucial parameter that influences the accuracy of RF. To improve the performance of RF model in predicting the adulterated content of Camellia oil, a particle swarm optimization algorithm [35] was utilized to determine the optimal number of decision trees.
Model Evaluation
This study evaluated the performance of the developed models by using the coefficient of determination (R 2 ), mean absolute error (MAE), and root mean square error (RMSE) [36], which were defined as Equations (2)-(4), respectively. The accuracy of the models was measured by R 2 , which ranges from 0 to 1. A lower value of RMSE indicates a better agreement between the predicted and actual adulteration content. Moreover, MAE is a better measure than RMSE for evaluating model accuracy in the presence of outliers. In addition, the calibration set results in the evaluation criteria are expressed as R 2 C , RMSE C , MAE C , respectively, while the prediction set results are expressed as R 2 P , RMSE P , MAE P , respectively.
where, y andŷ denote real and predicted adulteration content, respectively; y denotes the corresponding average value. In addition, to investigate the robustness of the extracted feature wavelengths, Pearson correlation coefficient (R), defined as Equation (5) [37], was adopted to analyze the relationships between the absorbance and adulteration content under certain feature wavelengths. Herein, Pearson correlation coefficients ranging from −1 to 0 indicate a negative correlation between adulteration content and absorbance, while the values from 0 to 1 denote a positive correlation. Moreover, the coefficients closer to 1 or −1 demonstrate a strong correlation.
where x and y are the absorbance and adulteration content, respectively; x and y are the corresponding average values. | 5,987.8 | 2023-08-01T00:00:00.000 | [
"Environmental Science",
"Chemistry"
] |
Anomalies detection for smart-home energy forecasting using moving average
ABSTRACT
INTRODUCTION
SMART Homes is one of the areas which first involves internet of things (IoT).A large number of data is collected from the home energy management system (HEMS), which also involves different challenges in different data analysis stages.Not only in the smart home field, accurate forecasting is required in different fields, such as Weather forecasting [1], patients number forecasting [2], marketing researches forecasting [3], mortality rates forecasting [4], rainfall forecasting [5], and more.The data can be collected, pre-processed, analyzed, and monitored using predictive analysis (PA), and advance intelligent technologies can help convert these data into reports, charts, and graphs.In 2019, it was reported by [6], that Malaysia Tenaga Nasional Berhad (TNB) raided many properties that were assumed of snooping on electricity supply in a bitcoin mining operation, which resulted in $25 million loss for the utility company.These problems are Int J Elec & Comp Eng ISSN: 2088-8708 Anomalies detection for smart-home energy forecasting using … (Jesmeen Mohd Zebaral Hoque) 5809 limited to Malaysia and conquered in different other countries, such as Iran, Argentina, Brazil, Venezuela, Turkey and few other European countries, and eastern powerhouse Russia.As stated by [7], "data quality (DQ) is generally described as the capability of data to satisfy stated and implied needs when used under specified conditions".To maintain DQ, it is essential to initiate the most common dimensions of DQ (i.e.Accurate date, complete data, consistent data) [8], [9], for further there are other dimensions such as consistent representation, accessibility, timeliness, and relevancy [10].It was proved by different resources about the loss of billions of dollars due to poor DQ [11], [12].Low-level DQ can cause due to wrong or missing data and is very essential to handle this type of dataset [13].It may lead to incorrect or misleading decisions, predictions, or instructions.As stated by [14], dirty data can slow down any processing depending on data analysis (DA) and even affect the total cost for the organization; the cost can be over billions of dollars per year.It was also mentioned that around 60% of data in an organization contain data issues; hence, organizations are now worried about those dirty data.
Leonardi et al. [15] states that 'PeerEnergyCloud' covered the use cases related to the application of smart home technology in different fields.It indicates various applications are responding differently to different DQ phases besides to variable grades.It addressed the most common DQ aspects faced in smart home energy monitoring systems.They are data accuracy, data completeness, and data delay.However, they did not propose any real solutions to the issues.It is also essential to overcome the issues.Moreover, the study [16] has stated the importance of anomaly detection system requirement in a residential community for electrical load dataset.Detecting real-time abnormal behaviors are essential for smart home system users and TNB.Anomalies detection can help to point out outlier data and examine details and can avoid keeping attention on anomalous meters.Accurate load forecasting has become a significant part of planning and operation for all active participants in the electricity market; it will enable effective outcomes in HEMS and provide precise prediction and healthy real-time power control [17], [18].With the new market structure in place, the penalty costs for under or over contracting electricity have significantly increased, minimizing costs and revenue losses more critical than ever [19].To achieve the goal of an efficient system anomaly detection models by using technical analysis tool is proposed.These detection models will be implemented and adapt to the ever-growing usage of IoT devices involved in time series forecasting cases.The output is detected based on past energy usage, it is known as a trend-following or lagging indicator.
The first contribution is creating an application programming interface (API) for handling duplicate features and data deployed in a smart home environment.The main contribution is modelling the unusual behaviors of this smart home environment using moving average (MA) models; it can be utilized for detecting abnormal behaviors.The previous studies detected anomalies in energy usage in a household or a building apartment.However, they did not validate the system for time series forecasting energy usage.In response, a system was developed for time series data anomalies detection that will perform other pre-processing steps, eliminate anomalies without being liable on a specific monitoring system/tool, and modularize detecting anomalies method in a certain amount of evidently best definite modules.Here, an anomaly in energy consumption is detected and removed for the predictive model.Finally, the system was evaluated using the time series forecasting model auto regressive integrated moving average (ARIMA) to the specified scenario of HEMS; the model-assisted the reduction of forecasting error mean squared error (MSE) from 0.179 to 0.066.
LITERATURE REVIEW
Most researchers focused on anomaly detection to find the abnormal data which can threaten the management system.Vikhorev et al. [20] had developed an anomaly detection model for building management that caused extreme energy usage and probable growth in carbon taxes.Sial et al. [21] had presented four heuristics to identify abnormal energy consumption using a contextual grouping of smart meters.They grouped the meters containing the similar context of energy usage within the neighborhood of the meters by using distance from K-nearest neighbor days.However, using K-nearest neighbor model labelled datasets is required, which is challenging to obtain from different households for the study presented in this paper.Another system had proposed an anomaly detector for smart home security systems using hidden Markov model (HMM).They had achieved good accuracy while classifying potential anomalies that indicate attacks [22].HMM can be implemented as both supervised and unsupervised learning.However, this author also implemented it for supervised learning.
Anomaly detection process can be beneficial for different aspects; for example, [23] had identified the anomalies in consumers' behaviors over streaming data study, since anomaly can occur due to customer profile changing (known as concept drift) in the circumstances relatively theft, scam, or damages.Andrysiak et al. [24] had focused on detecting anomalies in the last-mile radio frequency (RF) smart grid communication network to find out the energy theft, and customers using energy deliberately or unconsciously, which cause disturbance in the system.A similar work [25] proposes an anomaly detection ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 6, December 2022: 5808-5820 5810 system for thefts detection in communication in a simple process rather than using central point or electricity meters.Cui and Wang [26] had studied electricity consumption data of school and tested five models to detect anomalies.They had projected a hybrid model that connects polynomial regression and Gaussian distribution to identify anomalies in facilities management company datasets.They had concluded that the proposed prototype could also be implemented for different types of time series datasets.However, a good training dataset will be required to train the model manually before the actual detection process.Moreover, a MA is a statistical model which does not require any training.Most of the researchers indicated data anomaly caused due to energy theft in low-voltage networks.The old technique to detect these types of anomalies is by going through irregularities in the customer billing information.This centralized method requires time to detect as it requires scanning over manually historical long-term usage data.Zidi et al. [27] indicates the use of different sophisticated methods for theft detection.Another research work was held for daily real-time usage prediction using a hybrid neural network integration with ARIMA model for daily energy usage.They also detected anomalies by finding the differences between actual and predicted usage using the two-sigma rule [28].Yu et al. [29] had applied -nearest-neighbor with a sliding window and found that it is a valuable tool for identifying anomalies in hydrological time series cases and it improves DQ and helps to make better [29].It also concludes that it is crucial to select the best combination of sliding window size and confidence coefficient for the specific use case and time series input.Hence, it is essential to select the best parameters to overcome the fitting issue.
Since time-series data may contain abnormal data, it is essential to remove these data for better forecasting.MA with a sliding window is the most straightforward technique used for anomaly detection.However, it is essential to get the tune parameters for the optimal detection system.As concluded by the researcher cited above, many had detected anomalies, but they had not evaluated after eliminating the anomalies improving the time-series forecasting.In this study, ARIMA was selected for testing the enhancement of time-series forecasting, as ARIMA is a powerful technique in which an own series history is used as an explanatory variable.Due to uni-variate modeling capability, ARIMA cannot exploit the leading indicators or descriptive variables.
METHOD: DATA ANALYTICS PROCESS WITH DATA QUALITY
Depending on HEMS, a DA model is designed and developed to analyze a smart home energy monitor system.The DA process was implemented in steps presented in Figure 1.Data issues are usually involved in different stages of DA.For instance, in the DA stages of collection, pre-processing and cleaning, and analysis, the issues that can handle are integrity, incomplete and duplicate data, and inaccurate data, respectively.Hence, it is required to maintain the primary cases for data issues in every stage of DA.
Data collection
One of the significant roles to obtain result accuracy is the data collection stage.Collecting data from a reliable source is very important to make sure data is in real-world data.Typically, collected data contains data issues.It is essential to examine the data set to help to obtain accurate results clearly.The data is collected from UMass Trace Repository, which contains network, storage, and other traces.The Electrical dataset (aggregated and individual circuits) was used as input from 'HomeC' in this research.This data set will be helpful to validate the proposed approach for detecting and eliminating anomalies in time series.
Data pre-processing and cleaning
Data combined from heterogeneous sources can contain data inconsistencies and missing values.It is very important to clean the data before data analyzing [30].Before data cleaning, a few steps of data
Data analysis and modelling
Predictive modelling will be executed by using a fully scripted Python Language.Here, in the time series in Figure 2, the output of the total cost data for a particular sure on a daily basis (Month on the horizontal axis and cost on the vertical axis) is presented.In this time series, the anomalies were detected for one month after 2nd January 2016 till 1st February 2016.
However, for forecasting 70/30 training to testing ratio will be selected, as it is one of the ideal ratios for training and testing dataset [31].According to [32], 50% to 70% of the training set will more likely help get a good model, where a total of 70% of data will be used for the training purpose of the ARIMA method and the rest 30% for testing purpose.Present-day data is calculated with the help of past data using a moving average technique.MA is categorized into simple moving average (SMA) and exponential moving average (EMA).EMA outcome is contributed from the latest data, unlike SMA.In this experiment, MA is executed on a weekday basis for SMA and EMA.The records from the last weekdays are taken into the system for current value estimation.For example, to estimate the present Monday's value, records from last Monday are used.Here, MA can identify and filter out the abnormal short-term fluctuations and smooth out the outcome.By calculating the values, it will be easy to detect and monitor the anomalies.These anomalies are one of the DQ issues [30], which occurred due to unusual behaviors such as incorrect data from the meter or energy theft.These will enable minimizing the outcomes of a variety of attacks from inside and outside structures.The processing of handling anomalies is presented in algorithm 2. Here, mean absolute error (MAE) function can calculate the mean absolute error (output presented in section 4.2), it is used to calculate the upper bound and lower bound from the rolling mean.
Next, ARIMA model is trained in such a way that it will be able to predict based on historical observations.In this case of the energy monitoring system, the prediction will have the capacity to better forecast electricity use.This can result in decreased costs by reducing the usage of electricity.This is the domain of machine learning (ML), with a detailed group of approaches and procedures mainly suitable for value prediction of a dependent class to time perspective.This prediction model is a combination of autoregression (AR) and MA.AR is calculated using lagged values for y and MA is calculated using lagged errors, as presented in (1).
The ̂ contains predicted values using AR and MA terms.Where, AR:n is order of the autoregression of the model and MA:m = order of the MA aspect of the model.According to the calculation, the ARIMA function is specified by three order parameters: (n, i, m).Here, i is Integration; it uses observation differences to produce the time series stationary, i.e. degree of difference.
Detected anomaly data
From the outcome of anomaly detection, it was found that there are several data anomalies in one month.These anomalies were detected by using the mean rolling trend (green line) and calculate upper bond and lower bond of usage (red line), as indicated in graphs in Figure 3, for various window sizes such as 6 in Figure 3(a), 12 in Figure 3(b), 24 in Figure 3(c), 48 in Figure 3(d) and 96 in Figure 3(e) (using SMA) and Figure 4, for various values of alpha such as 0 in Figure 4(a), 0.05 in Figure 4(b), 0.10 in Figure 4(c), 0.20 in Figure 4(d), 0.40 in Figure 4(e) and 0.80 in Figure 4(f) (using EMA).The red dot indicates anomaly detected.Data plotted outside the red line are considered anomalies.Here the detection proceeds with 24 hours window.Here, the advantage of smaller window size had increased sensitivity to the usage changes in the primary process of generating the data as required, i.e. predicted data.However, a larger window size helped to reduce data noise due to the size of the data.Therefore, the task is to select the best window size, which will provide maximum predictive accuracy and minimum predictive error.It will maximize predictive accuracy by reducing error, which is the predictive value minus the predictive error as shown in Table 1.Here, all MA output is a substantial downside due to the lagging indicators.As MA is dependent on past facts of usage before there are changes in trend, it undergoes a time lag.Electricity usage may change quickly before a MA can exhibit a new trend transformation.In this case, a shorted MA faces issue from this lagging than in a longer MA.The output of SMA was found to be the most straightforward calculation, as the average usage obtains it over a chosen time period.With the use of SMA as a rolling mean, the identification of anomaly in the time was made easily using upper bond and lower bond line.However, EMA provided higher weighting to recent usage changes, its responses more rapidly to the values changes than the SMA.EMA was not proven effective for anomaly detection in forecasting time series (comparison in Tables 2 and 3).
Error measurement
Error measurement is a statistical calculation used to obtain the model error.Here, the mean absolute error, MAE is calculated using (2).It is used to analyze the amount of error in the model sure to different MA window sizes.
The concept of MAE is used here to find the degree of closeness.It is obtained from the new estimated outcome (i.e.predicted values, ̂) and the exact value (i.e.observed values, ).Here, is the number of observations.The calculated output of different window sizes is presented in Table 1 and plotted in Figure 5.
The MAE shown in Figure 5 is the absolute difference between the estimated value and exact value.Here the rolling mean line is the estimated line.The window 12 MAE was considered to plot the upper and lower bound because after 12; the value seems stable.It is better to take a small window for faster processing.
System evaluation
The proposed system was evaluated by using the time series forecasting model ARIMA.The output obtained from ARIMA is evaluated by different parameters.By using forecast() function from 'statsmodels.tsa.arima_model.ARIMA'(ARIMA) class for making forecasting.Initially, the data set is splatted into a training and testing set.The training set is used to fit the model by using fit() function.It will ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 6, December 2022: 5808-5820 5816 help to produce predicted outcomes for every element of the test set.Rolling forecasting is performed by re-creating the ARIMA model once each new observation is provided.This rolling forecasting is important for dependence on elements in earlier time steps for differencing and AR models.Using variable 'history', all elements were kept on track.This variable was seeded with the training dataset, and next, in each iteration, new elements were appended.
Figure 5. Mean absolute error
The time series forecasting graph is presented for ARIMA in Figure 6, for various window sizes such as original in Figure 6(a), 6 in Figure 6(b), 12 in Figure 6(c), 24 in Figure 6(d), 48 in Figure 6(e), and 96 in Figure 6(f) (see in appendix).Here, a blue straight line is plotted to present the expected outcome and then the dotted green line after the red horizontal line is plotted to compare with the rolling forecast predictions.It can be clearly understood, the forecasted elements illustrate trends close to the expected one, and they are on the correct scale too.The reason the proposed model outperformed the common statistical method, because the detected anomaly is based on current trend rather than fixing a threshold value.
Comparison using mean squared error
mean squared error (MSE) is the average of the squared errors used to calculate the forecasting error.Errors of opposite signs will not cancel each other out in either measure.MSE the values are all positive due to the squaring; this makes it easier to use in an optimization technique.The output for ARIMA for SMA and EMA is presented in Tables 2 and 3, respectively.Here, in the tables term "Window" indicates window size in an hour, term "Anomaly" and "Not Anomaly" is the number of usage anomalies detected and the number of usages not anomalies, term "MSE" output of error in the ARIMA model after removing the anomalies, term "Predicted" is predicted forecasting outcome removing the anomalies, and term "Expected" actual forecasting outcome in the time series forecasting after removing the anomalies.The first row of the table is the output of the training of the forecasting model without removing anomalies.Hence, the expected outcome should be close to 0.935902 to get an effective forecasting outcome.
CONCLUSION
This paper shows an effective proposal and algorithms, which will help detect anomalies in electricity use for the especially for smart home energy monitoring system.This will solve the issue of inaccurate data in data analysis stage.To achieve better anomaly detection outcome for time series smart HEMS, a practical model is presented a combination of MA and rolling mean.Besides, it also contains the implementation of cleaning data, such as the removal of duplicate or unwanted data.Handling duplicate and unwanted data will overcome the issue in the data pre-proposing stage.Next, ARIMA is implemented for forecasting time series data of smart home energy usage with detection and removal of anomalies.ARIMA is executed in the data analysis stage.Hence it was used to evaluate the proposed system.Before the evaluation process after detection and removal, the ARIMA model was tested and found that the forecasted elements illustrated closely to the expected outcome.Finally, it was proved that on detecting and removing anomalies by using SMA provides better forecasting than with anomalies.SMA helped to reduce the forecasting error MSE from 0.179 to 0.066.Moreover, EMA is not adequate for detecting anomalies compared to SMA as it reduces the expected outcome than the original one.
Figure 2 .
Figure 2. Time series plot of energy usage data
ISSN: 2088- 8708 Figure 3 .
Figure 3. SMA for different windows with upper bond/lower bond line: (a) output for window size=6, (b) output for window size=12, (c) output for window size=24, (d) output for window size=48, and (e) output for window size=96
Figure 6 .Figure 6 .
Figure 6.Time series forecasting using ARIMA: (a) original, (b) window:6, (c) window:12, (d) window:24, (e) window:48, and (f) window:96 (continue) 5811processing are held as follows presented in algorithm 1.Here, the first API, 'getDuplicateColumns' will be able to receive the dataset and find the columns name containing duplicate data by iteration process.The following API, 'dropDuplicateColumns' will receive the dataset too, and by using 'getDuplicateColumns' will find the duplicate columns and drop those columns.Algorithm 1. Handle duplicate data (rows and columns) ISSN: 2088-8708 Anomalies detection for smart-home energy forecasting using … (Jesmeen Mohd Zebaral Hoque)
Table 1 .
Mean absolute error respected to hours of window Anomalies detection for smart-home energy forecasting using … (Jesmeen Mohd Zebaral Hoque) 5815
Table 2 .
MSE with respect to Hours of Window for SMA
Table 3 .
MSE with respect to Alpha for EMA | 4,834.2 | 2022-12-01T00:00:00.000 | [
"Medicine",
"Computer Science",
"Engineering"
] |
Bohr-type inequalities for bounded analytic functions of Schwarz functions
: In this paper, some new versions of Bohr-type inequalities for bounded analytic functions of Schwarz functions are established. Most of these inequalities are sharp. Some previous inequalities are generalized.
Introduction
Let B denote the class of analytic functions f (z) = ∞ k=0 a k z k defined in the unit disk D := {z ∈ C : We call the Bohr sum of f (z).The well known Bohr radius problem is to find r 0 , such that holds for |z| ≤ r 0 .The constant r 0 = 1/3 is sharp, which is called the Bohr radius.The radius was originally obtained in 1914 by Bohr [13] with 1/6.Later, Wiener, Riesz and Schur established the inequality (1.1) for r = |z| ≤ 1/3 and showed that the constant 1/3 cannot be improved [22,25,26].
There are lots of works about the classical Bohr inequality and its generalized forms.Ali et al., [8] and Kayumov and Ponnusamy [15] considered the problem of Bohr radius for the classes of even and odd analytic functions and for alternating series, respectively.In [19], the authors generalized and improved several Bohr inequalities.In [21], several Bohr-type inequalities were obtained when the Taylor coefficients of classical Bohr inequality are partly replaced by higher order derivatives of f .It is worth pointing out that Bohr's radius problem deal with analytic functions from unit disk D into D initially, but later it was generalized to mappings from D to punctured disk [4] or other domains [2].For more discussion on the Bohr radius for analytic functions [3,7,9,27].
The Bohr-Rogosinski sum R f N (z) of f ∈ B is defined by Observe that if N = 1 and f (z) is replaced by f (0), then the Bohr-Rogosinski sum is the Bohr sum.The corresponding Bohr-Rogosinski radius problem is to find R N , such that Recently, Kayumov and Ponnusamy [16] have given the Bohr-Rogosinski radius of f .In [21], the author also solved some problem of the Bohr-Rogosinski radius.Let S N (z) = N−1 k=0 a k z k denotes the partial sums of f .The corresponding Rogosinski radius is [18,23,24].It is obvious that Hence, the Rogosinski radius is related to the Bohr-Rogosinski radius. Let m) (0) 0} be the classes of Schwarz functions, where m ∈ N = {1, 2, • • • }.Our aim of this article is to generalize or improve many versions of Bohr-type inequalities for bounded analytic functions of Schwarz functions.
The paper is organized as follows.In Section 2, we state some lemmas.In Section 3, we present many theorems which improve several versions of Bohr-Rogosinski inequalities and Bohr's type inequalities for bounded analytic functions.There are some corollaries and an open problem in Section 4.
Some Lemmas
In order to establish our main results, we need the following some lemmas which will play the key role in proving the main results of this paper.
and equality holds for distinct z 1 , z 2 ∈ D if and only if φ is a Möbius transformation.In particular, and equality holds for some z ∈ D if and only if φ is a Möbius transformation.
The proof is simple, we omit it.
Lemma 2.4.There is a unique root ξ m of the equation and a unique root α m,n of the equation for r ∈ (0, 1) and m, n ∈ N, respectively.Furthermore, α m,n ≤ ξ m for m ≥ n.
Then we have Observe that k(0)k(1) < 0. Thus the monotonicity of k(r) implies that there is an α m,n that is the unique root of (2.2).
Main results
Theorem 3.1.Suppose that f where R m,n,N is the unique root in (0, 1) of the equation and the radius R m,n,N cannot be improved.
By using inequality (3.3) and Lemma 2.2, we have Obviously, it is enough to show that 2r nN (1 Then it is easy to verify that g(0)g(1) < 0 and g(r) is a continuous and increasing function of r ∈ [0, 1].Thus R m,n,N is the unique root of g(r) and g(r) ≤ 0 holds for r ≤ R m,n,N .
Next we show the radius R m,n,N is sharp.For a ∈ [0, 1), let Taking z = r, substituting (3.4) into the left side of inequality (3.1), then we have Now we just need to show that if r > R m,n,N , then there exists an a, such that the right side of (3.5) is greater than 1.That is Therefore, if r > R m,n,N , then there exists an a, such that inequality (3.6) holds.
where α m,n is the unique root in (0, 1) of the equation The radius α m,n cannot be improved. where and ξ m is the unique root in (0, 1) of the equation It is obvious that Φ m,n (1, r) is monotonically increasing function of r ∈ [0, 1).By the hypothesis or Lemma 2.4, we have Furthermore, observe that Φ m,n (a, r) is a monotonically increasing function of a ∈ [0, 1] for each fixed r ∈ [0, 1).Thus Therefore, by inequalities (3.8) and (3.9), we obtain inequality (3.7).
where s ∈ N, β m,n,s is the unique root in (0, 1) of the equation The radius β m,n,s cannot be improved.Proof.Using inequality (3.3) and Lemma 2.2, we have It is sufficient for us to prove that the right side of (3.14) is less than or equals to 1 for r ≤ β m,n,s .Actually, we just need to prove φ(r) ≤ 0 for r ≤ β m,n,s , where Let h(r) = r m + 3r sn + r m+sn − 1.Then it is easy to verify that h(0)h(1) < 0, h(r) is a continuous and increasing function of r ∈ [0, 1].Thus β m,n,s is unique root of h(r) and h(r) ≤ 0 holds for r ≤ β m,n,s .Thus φ(r) ≤ 0 for r ≤ β m,n,s .
To show the radius β m,n,s is sharp, we consider the functions ω m (z), ω n (z) and f (z) is the same as (3.4).Taking z = r, the left side of inequality (3.12) reduces to Next, we need to show that if r > β m,n,s , then there exists an a, such that the right side of (3.15) is bigger than 1.That is r m+ns a s+1 + 2r ns a s + r ns a s−1 + r m − 1 > 0. (3.16) Let A 3 (a, r) = r m+ns a s+1 + 2r ns a s + r ns a s−1 + r m − 1.
Observe that A 3 (a, r) is a continuous and increasing function for a ∈ [0, 1).It follows that A 3 (a, r) ≤ A 3 (1, r) = r m+ns + 3r ns + r m − 1 = h(r) holds for r ∈ (0, 1).Furthermore, the monotonicity of h(r) leads to that if r > β m,n,s , then A 3 (1, r) > 0. Hence, by the continuity of A 3 (a, r), if r > β m,n,s , we have Therefore, if r > β m,n,s , then there exists an a, such that inequality (3.16) holds.
Proof.On the one hand, by the assumption, we have r 2n 1 − r 2n .Now we need to show that above inequality is smaller than or equal to 1.It is sufficient for us to prove ψ(r) ≤ 0, where Furthermore, it is easy to verify that r m + 3r 2n + r m+2n − 1 is increasing on r ∈ [0, 1) and have a unique zero γ m,n .Therefore, we have ψ(r) ≤ 0 for r ≤ γ m,n .
On the other hand, we have It is obvious that the last item of above is greater than or equals −1 for all r ≤ γ m,n .We complete the proof.
where R m,1,N is the unique root in (0, 1) of the equation and the radius R m,1,N cannot be improved.
where R 1,n,N is the unique root in (0, 1) of the equation and the radius R 1,n,N cannot be improved.
where α m,1 is the unique root in (0, 1) of the equation The radius α m,1 cannot be improved.
where α m,m is the unique root in (0, 1) of the equation The radius α m,m cannot be improved.
where β m,m,s is the unique root in (0, 1) of the equation The radius β m,m,s cannot be improved.
Conclusions
We obtain some new versions of Bohr-type inequalities for bounded analytic functions of Schwarz functions by replacing the variable z by Schwarz functions in function's power series expansions.we conclude that most of the corresponding Bohr radii are exact.These inequalities generalize the classical Bohr inequality and some earlier results on the Bohr inequality.
Theorem 3 . 2 .
Suppose that f (z) = ∞ k=0 a k z k ∈ B, a := |a 0 | and ω m ∈ B m , ω n ∈ B n with m, n ∈ N and m ≥ n.Then we have
Corollary 4 . 1 .
Suppose that f (z) = ∞ k=0 a k z k ∈ B, a := |a 0 | and ω ∈ B m for m ∈ N. Then we have
Corollary 4 . 2 .
Suppose that f (z) = ∞ k=0 a k z k ∈ B, a := |a 0 | and ω ∈ B n for n ∈ N. Then we have
Corollary 4 . 5 .
Suppose that f (z) = ∞ k=0 a k z k ∈ B, a := |a 0 | and ω ∈ B m for m ∈ N. Then we have | 2,270.8 | 2021-01-01T00:00:00.000 | [
"Mathematics"
] |
Coupled Modal Analysis and Aerodynamics of Rotating Composite Beam
This study primarily focuses on conducting, both experimentally and numerically, a modal analysis of a cantilever composite beam. Through extended numerical simulations, we investigate Campbell diagrams, which, depending on the rotation speed of the structure, comprise natural frequencies and their corresponding modal shapes. Our results are categorized into two main aspects: the classical single-mode behavior and an innovative extension involving linearly coupled modal analysis. One key novelty of our research lies in the introduction of an analytical description for coupled mode shapes, which encompass various deformations, including bending, longitudinal deformations, and twisting. The most pronounced activation of dynamic couplings within the linear regime for a 45∘ preset angle is observed, though the same is not true of the 0∘ and 90∘ preset angles, for which these couplings are not visible. In addition to the modal analysis, our secondary goal is to assess the lift, drag forces, and moment characteristics of a rectangular profile in uniform flow. We provide insights into both the static and dynamic aerodynamic responses experienced by the beam within an operational frequency spectrum. This study contributes to a deeper understanding of the dynamics of composite rotating beams and their aerodynamic characteristics.
Introduction
Beams are among the most popular construction elements in engineering.Therefore, it is crucial to have a solid understanding of both the basic and advanced theories related to beam modeling.This knowledge is not only applied but also enhanced in the case of rotating beams, which find widespread use in various industrial applications.Some of the most common applications include wind turbines, helicopter rotors, and airplane propellers.
In their work [1], the authors provided a comprehensive review of the most common theories pertaining to beams, which have been utilized by scientists over the past few decades.They examined classical approaches, such as those by Da Vinci, Euler-Bernoulli, and Timoshenko, in addition to the Generalized Beam Theory.Special emphasis was placed on the Carrera Unified Formulation (CUF) in one dimension, and the authors presented numerical examples illustrating its application in static, dynamic, and aeroelastic problems.Furthermore, they conducted an overview of two recently developed methods: axiomatic/asymptotic and component-wise approaches.The primary conclusion drawn from this critical review is that beam theories are still in need of further development and improvement.In another study by Wang et al. [2], a reduced model for vortex-induced vibrations (VIVs) in turbine blades is derived.In this study, the authors modeled the blades as uniform cantilever beams and employed the multiple scale method to investigate nonlinear dynamics.Subsequently, they calculated frequency-response curves and identified two types of bifurcation.The results presented underscored the necessity of employing coupled models to analyze the rich dynamics of VIVs.
The asymptotic development method is employed in [3] to investigate the free nonlinear oscillations of initially straight Timoshenko beams.The authors focused on two different definitions of curvature: one with respect to the deformed length and the other with respect to the undeformed length.The comparison of these two methods was the primary objective of their study, and the authors demonstrated that the results for slender beams are very similar when using both approaches.Furthermore, in [4], the authors analyzed the model of a geometrically exact nonlinear Timoshenko beam.They derived the equations of motion for the structure but primarily concentrated on one-dimensional constitutive equations.The paper presents basic numerical results.A similar approach is applied in [5] to analyze the dynamics of an elastic isotropic rotating beam.The eigenvalues and mode shapes are obtained for the linear problem, and the coupling between flapping, lagging, axial, and torsional components is studied.In the second part of the paper [6], the authors focused on analytical calculations.They applied the multiscale method directly to the partial differential equations of motion and drew backbone curves.Additionally, they analyzed three flapping modes as the angular speed varied from low to high.The scientists demonstrated that the nonlinearities of the flapping modes are strongly correlated with angular speed and can transition from hardening to softening and vice versa.In addition, Thomas et al. [7] conducted a study on the influence of rotation speed on the nonlinear vibrations of a cantilever beam.They focused on the phenomena of hardening/softening and jump effects, particularly when dealing with large amplitudes.To analyze these phenomena precisely, they employed three different models: two analytical models and one original model based on finite-element discretization.On a related note, the nonlinear vibrations of a rotating Timoshenko beam were investigated using the p-version finite element (FE) method in [8].This study considered two types of nonlinearities: the strain-displacement relationship and the inertia force resulting from the rotation speed.Nonlinear forced vibrations were analyzed in the time domain, with consideration for both constant and non-constant rotation speeds.Carrera et al. [9] examined the free vibrations of a rotating composite blade.They employed the Carrera Unified Formulation (CUF) and the FE method to solve the governing equations.The authors placed their focus on both flapwise and lagwise motion, and they also accounted for the Coriolis force in their analysis.In a related study, presented in [10], the authors delved into the nonlinear vibration of a rotating beam with variable angular velocity.They concentrated on the coupling between longitudinal and bending vibrations.The authors derived the governing equations of motion using Hamilton's principle and the Galerkin method.They then applied the multiscale method to obtain a first-order approximate solution.Their results were compared to those obtained through numerical integration, demonstrating a very good agreement.In the work of [11], the same methods were applied to derive the equations of motion for a rotating composite Timoshenko beam with both open and closed box-beam cross-sections.The authors stated that the change in pitch angle significantly influences the coupling between flapwise bending and chordwise bending motions, which is associated with the centrifugal force.The presented results take into account nonconstant angular speed as well as a nonzero pitch angle.Given the practical applications of rotating beams and structures, it is of paramount importance to consider the significant impact of aerodynamic loads on their dynamics.In the paper by DiNino et al. [12], an in-depth analysis of a homogeneous viscoelastic beam was conducted under the influence of uniformly distributed turbulent wind flow.This study encompasses an examination of both the steady and turbulent components of the wind, with a particular focus on their roles in Hopf bifurcation and parametric excitation.The authors also emphasized the interaction between bifurcation phenomena and the critical and post-critical behavior of the beam.Meanwhile, in [13], Elmiligui et al. present results obtained from numerical simulations of flow past a circular cylinder.Two distinct approaches are employed to prepare the model for simulations, and the resulting data are compared with previously published experimental findings.Nonlinear vibrations of the blade under high-temperature supersonic gas flow and varying angular speed are presented in [14].The authors assume that the blade is pre-twisted, presetting, and a thin-walled rotating cantilever beam is used.The equations of motion are derived using Hamilton's principle and the Galerkin method, revealing the presence of 1:1 internal resonance as well as primary resonance.The numerical results presented in the paper show that not only periodic motions but also chaotic motions can occur in the nonlinear vibrations of the rotating blade when the angular speed varies.Furthermore, in [15], a bifurcation analysis of a rotating pre-twisted beam is presented, taking into account varying speed and aerodynamic forces.The model is analyzed in both the chordwise and flapwise directions, revealing phenomena such as jumps, saturation, and double jumps.Additionally, in [16], a model of an Euler-Bernoulli beam with nonlinear curvature and coupled transversal-longitudinal deformation is introduced.The authors applied Hamilton's principle to derive the equations of motion, with a focus on time delay control as the primary task.They presented the influence of linear and cubic control methods on vibration reduction for different rotating speeds.Meanwhile, nonlinear vibrations of a slowly rotating beam with a tip mass are studied in [17].The authors applied the extended Euler-Bernoulli theory to analyze longitudinal-bending-twisting vibrations.They utilized the multiple time-scale method to solve partial differential equations and demonstrate the influence of angular speed, tip mass, and hub on nonlinear vibrations.Furthermore, the free vibrations of the beam model with a tip mass are explored in [18].The authors focused on cross-sectional rotations, lateral bending, and transverse bending.The numerical simulations illustrate the effects of tip mass, rotary inertia, viscoelastic damping, and the beam inertia ratio on the stability of the system, as well as on natural frequencies.In their work, Huang et al. [19] presented fascinating results from experimental studies on slowly rotating cantilever beams.They employed Digital Image Correlation, the Phase Mapping Method, and direct measurements under operational conditions to analyze three beams, subjecting them to twenty different angular velocities.Their findings revealed centrifugal hardening behaviors in the flap-wise direction, confirming the accuracy of their chosen model.Notably, they achieved excellent agreement between experimental data and numerical calculations for hardening frequency.Another study of rotating composite beams is discussed in the paper by Gawryluk et al. [20].In this research, the authors assumed a constant angular velocity for the rotating beam and utilized a Macro Fiber Composite TM (MFC) actuator for excitation.They employed numerical solutions via the FE method, which were subsequently validated through experimental testing.Additionally, Rafiee et al. [21] provided a critical review of scientific papers focused on rotating beams.The authors examined various approaches to calculations, including analytical, semi-analytical, and numerical methods, and discussed different beam theories.This paper offers a comprehensive overview of research on beam vibrations that has been conducted in recent years.
In a study by Teter et al. [22], modal analysis of a rotor composed of three active composite beams is presented.They compare experimental results obtained from a laser vibrometer and a LMS Test.Lab analyzer ® with modal hammer to numerical simulations performed using Abaqus ® software.The authors achieved excellent agreement among all methods, not only for natural frequencies but also for mode shapes.In the subsequent paper authored by Mitura et al. [23], the dynamics analysis of the rotor operating at a constant angular velocity is presented.The authors employed a Digital Signal Processing (DSP) system to excite vibrations in the beams and control angular speed.The authors investigated the influence of the piezoelectric effect and the hub's speed on the rotor's dynamic behavior.An analysis of force vibrations in a mistuned three-bladed rotor is presented in Warminski et al. work [24].They assumed that beam mistuning in the rotor results from manufacturing processes in composite production.The rotor was excited by harmonic torque, or by chaotic oscillations.This study revealed the localization phenomenon.Furthermore, the localization and synchronization in a rotor with three beams were studied by Szmit in [25].The model was analyzed numerically based on equations of motion and through numerical simulations using Abaqus ® software.Additionally, the paper presented results from experimental studies, including natural and force vibrations.Finally, Szmit et al. [26] conducted fully experimental studies on a three-bladed rotor.They used high-speed cameras during constant angular speed rotation to analyze the aerodynamic loads at different preset angles.The results include polynomials describing aerodynamic loads based on camera images.
Despite the extensive literature on rotating beams' vibrations, in which the singlemode linear behaviour of the eigenvalue problem is corrected through nonlinear effects, the mechanical coupling, which already occurs in the linear problem between two distinct orthogonal modes, appears to be overlooked in the analytical/numerical models.This provided motivation for conducting a numerical modal analysis within detailed inspection of interactions already in the the linear scope.Furthermore, the linear dynamics of beams is supplemented with aerodynamic characteristics that are closely dependent on the beam's geometry.Research on this aspect is lacking in the majority of studies on rotating beams.
The paper is organized as follows.In Section 2 linear modal analysis of the rotating structure are presented.Graphs illustrating the change in natural frequencies and associated linear mode shapes with rotor rotational speed are discussed, and linear mode couplings of bending, longitudinal motion and torsion in the spatial coordinate system are explored.The aerodynamic characteristics of static and dynamic lift/drag forces, together with aerodynamic momentum, are investigated in Section 3. The article concludes with final remarks and a description of future scientific research directions in Section 4.
Dynamic Response of Composite Structure
Let us consider a composite beam attached to a rigid hub with a radius R; see Figure 1.The beam is made of highly elastic ThinPregTM 120EP-513/CF resin and M4JB-12000-50B (TORAY) carbon fibers.Moreover, a specific stacking sequence [0/−60/60/0/−60/60 3 / −60 2 /0 2 /−60/0 2 /60 2 /−60] ensures isotropic properties of material in the linear elastic regime, as defined by Hook's law [27].Uniform distribution of the material along the specimen's length L = 595 mm and cross-sectional area b × h = 35 mm × 0.9 mm is assumed [25].The effective mechanical properties of the composite structure are gathered in Table 1.In Figure 1a, only one coordinate system exists that rotates with the rotating beam-hub structure.The x-axis aligns with the longitudinal axis of the undeformed beam, the z-axis coincides with the hubs' rotation axis and the y-axis completes the right-handed Cartesian coordinate system.Additionally, in Figure 1b, an angle Θ is measured from xy-plane positively defined in accordance with the right-hand rule about the x-axis.A preset angle Θ can be varied from 0 • to 90 • , and describes the orientation of the blade attached to the hub.The system rotates with a constant speed φ.The hub's mass moment of inertia is infinite; hence, the rotating imbalance and inertial coupling between successive beams are not taken into account.The target of this assumption is to eliminate additional interactions between consecutive beams.The attention is devoted only to the beam as a 3D continuous structure, which can be deformed out of plane (outplane bending i), in-plane (inplane bending j), along the main of the beams' axis (longitudinal k) as well as twist (torsion l).Note that, since the xyz coordinate system is embedded in the rotating hub, the directions of introduced deformations i and j are not aligned with the xy and yz planes.Only longitudinal k and twisting l motions can be referenced relative to the x-axis.
Table 1.Effective mechanical properties of the composite beam: density, mass per unit length, Young's modulus, shear modulus, Poisson's ratio [16].Commercial Ansys ® software was used for all numerical simulations presented in the paper.In the first step, the natural frequencies and associated mode shapes were validated in accordance with analytical calculations, simulations of competitive commercial software [17,28], as well as experimental studies performed in the absence of rotation ( φ = 0) e.g., by neglecting the centrifugal force [16].Nevertheless, the experimental investigations were restricted solely to the first two modes of natural vibrations.This prompted the authors to explore higher frequencies of the system's natural vibrations within the frequency range that aligns with forthcoming numerical analyses.
Experimental measurements were conducted in the laboratory of the Department of Applied Mechanics at the Lublin University of Technology.An advanced PSV 500 laser scanning vibrometer and an electromechanical exciter SmartShaker K2007E01 were used for the measurements [22].The measurement system setup is illustrated in Figure 2. The experiment was conducted based on a periodic chirp excitation in the frequency range of 0-25,132.7 rad/s (0-4 kHz), with the excitation applied at the base of the beam using the head of the electromechanical shaker.The calibrated scanning head performed three measurements for each of the 385 predefined points.Fast Fourier Transform (FFT) was then applied to the recorded time-domain signals for each point to identify resonant peaks and their associated vibration modes.The results of the vibration tests are presented as the first twenty detected modes of vibrations shown in Figure 3, and the corresponding magnitude-frequency plots are presented in Figure 4.It is worth noting at this stage that in the absence of angular velocity, despite the use of a composite structure and a very broad frequency spectrum, no dynamic couplings were observed in the linear range of the dynamic response.The detected natural frequencies align with the numerical calculations reported in the Section 2.1.The authors regret that, due to technical constraints, they were unable to perform modal analysis considering a rotating structure.Consequently, experimental measurements were complemented only with numerical simulations using the finite element method.
Campbell Diagram
In this Section, the rotating system is axially pre-stressed due to centrifugal forces and then subjected to linear modal analysis.The distribution of centrifugal forces depends on angular velocity φ as well as the dimensions of the beam and the radius of the hub.It interferes with inertia and stiffness matrices and has a significant impact on eigenvalue problems such as linear eigenfrequencies and associated modes shapes.Natural frequencies as a function of rotational speed, e.g., Campbell diagrams, for five preset angles are presented in Figure 5.The linear natural frequencies up to 3000 rad/s are reported, and extended analysis for higher-order modes with logarithmic scale on ordinate are gathered in Appendix A. In the angular velocity absence φ = 0, the natural frequencies are the same regardless of the radius of the hub and the preset angle of the blade.When rotation is activated, the two boundary angles Θ = 0 • and Θ = 90 • represent the dynamics of clear single-modes of vibration.In Figure 5a,b, despite numerous intersections of natural frequencies, no couplings occur.It is very interesting that for a rotational speed of 260 rad/s, three curves intersect at 650 rad/s.In general, values of natural frequencies increase with increasing rotational speed, but the slope trends are different.In contrast to the other curves, only the first torsion mode at Θ = 0 • has a constant value of natural frequency.In the scenario in which linear modal couplings occur, indications on Campbell charts are not reported because they cannot be assigned to the conventional vibration modes included in the legend of the graphic.The individual interpretation will be performed in Section 2.3.Therefore, for preset angle Θ = 30 • , Θ = 45 • and Θ = 60 • strong linear modal interactions are observed in Figure 5b-d.In the first and third cases, the 1st inplane bending mode is lacking only for 300 rad/s and 400 rad/s, respectively.The preset angle Θ = 45 • seems to be the critical one, for the sake of only torsion modes, and the 1st outplane modes were matched in the studied angular speed interval.This means that in the linear range, there is already a strong coupling or multiple instabilities in simulations on the beam.
Linear Mode Shapes
Campbell diagrams display only natural frequencies and lack information about the deformation of the shape.Based on three selected angular speeds, the change in linear mode shapes necessitates a proper discussion on deflection half-waves and the modal nodes location.To facilitate the observed changes, selected higher-order modes are presented in Figure 6.The third out-of-plane bending mode is very susceptible to angular velocity in the range of up to 1000 rad/s.Firstly, the natural frequency varies from 295.591 rad/s to 3917.31 rad/s.Secondly, the two modal nodes shift at approximately 1.5% and 0.84% at 100 rad/s.The changes become more prominent at approximately 3.7% and 3.5% at 100 rad/s.The mentioned shifts in % refer to nodals' displacements over the length of the beam in the free rest configuration.Standardization of the results to the maximum beam deflection also shows that with the increase in rotational speed, the amplitude of the first two half-waves decays with respect to the free end.Moreover, the deflection arrows of the half-waves are inclined to the right.The second flexural in-plane mode shape remains constant for increasing rotational speed, while its natural frequency changes from 3968.35 rad/s to 4569.89 rad/s, which provides an increase of about 15% (see Figure A1).Analogously to the bending mode in the susceptible direction, torsional vibrations display a shift in the modal node by approximately 0.5% and 5.9% for 100 rad/s and 1000 rad/s, respectively.The second analogy is the reduction in the maximum twist in the first halfwave.We note that standard linear mode shape projections (Φ i , Φ j , Φ k and Φ l ) consisting of amplitudes (A 1 -A 4 , B 1 -B 4 , C 1 -C 2 and D 1 -D 2 ) and characteristic coefficients (λ 1 , λ 2 , λ 3 and λ 4 ) can be described in the form (1) for outplane/inplate bedning, and for longitudinal and twisting are sufficient.Hoverer, the indicated amplitudes and characteristic coefficients must satisfy the sclerotic boundary conditions at x = 0 and rheonomic constraints x = L by balancing internal forces, centrifugal forces, Coriolis forces and inertia terms.To date, finding an analytical solution to such a complex problem remains challenging.
Linear Mode Couplings
In this section, we devote attention to more sophisticated mode shapes, which involves combining at least two linear unidirectional mode shapes [29].The introduced i, j, k, l notations can be extended to combined mode shapes Φ(i, j, k, l) in the linear regime, e.g., the third inplane bending mode interacting with the first longitudinal mode and second twist mode can be classified as Φ(0, 3, 1, 2).In proposed notation, the frequency dependence is omitted for simplicity.Referring to Campbell charts of Figure 5c, a set of the most interesting solutions of numerical simulations for preset angle Θ = 45 • and φ = 800 rad/s is presented in Figure 7.This is a particularly complicated case, in which twin modes of vibrations Φ(4, 2, 0, 0) for ω 7 = 4164.62rad/s and Φ(4, 2, 0, 0) * for ω 9 = 4662.44rad/s are obtained.Despite the fact that both consist of the fourth flexible mode and the second flexible mode with greater stiffness, their natural frequencies differ.Moreover, in Figure 7a the i-type mode is dominant, while in Figure 7b, the j-type mode is more exposed.Since the notation counts only the dominant modes, it is conventional to implement weights ( Ā, B, C and D) for each mode of vibration where ω n corresponds to the nth natural frequency of a given φ, while t is the time.
Other detected modal couplings include the combination of the 9th outplane bending with the 3rd in plane bending and 1st longitudinal with 10th torsion, which are presented in Figure 7c and Figure 7d, respectively.We have observed that neither the first in-plane bending singular mode nor any coupled modes are detectable; therefore, this mode can be subtly incorporated into other coupled modes of vibration.Extended results for fixed preset angle Θ = 45 • and gradually varied rotational speed φ for 200 rad/s, 300 rad/s, 400 rad/s, 500 rad/s, 600 rad/s, 700 rad/s, 900 rad/s and 1000 rad/s are reported in Figures A2-A8.These results provide a solid basis for further analyses using analytical methods, indicating the level of complexity of the issue in 4D space and in the time/frequency domain.
Lift/Drag Forces and Momentum
In this section, we focus on the aerodynamic aspects of the 2D blade in the flow of uniform air.The rectangular cross-section of the beam is placed at a given preset angle, Θ.In the studied case of a non-deformable structure, the preset angle is consistent with the angle of attack.Geometric details of the Computational Fluid Dynamics (CFD) simulations are presented in Figure 8.During the simulations, aerodynamic forces were recorded over time.In post-processing, the maximum and minimum magnitudes, as well as the mean values, of steady-state motion time histories were grouped according to the angle of attack Θ and varying airflow conditions.The translational airflow to rotation of the beam-hub structure is converted as follows where v corresponds to the air flow velocity at the tip of the blade and R + L describe the distance between the main axis of rotation and the beam tip in a free and undeformed configuration, with dynamic and centrifugal forces disabled.This assumption will be utilized to simplify our analysis.Figure 9 presents lift drag forces in the function of preset angle Θ and angular speed φ.At zero angle of attack, no lift force was detected, and the drag forces were at their minimum compared to the entire chart.Moreover, in the steady-state flow of the considered velocities, oscillations did not occur.Increasing the angle of attack to 5 • resulted in a significant increase in lift force with only a slight increase in drag force.Further increasing the angle of attack to 15 • and 30 • led to significant air resistance with only a minor rise in lift force.Karman vortices and the associated oscillations of forces in time histories appeared at an angle of attack of 45 • .For this angle of attack, the values of lift and drag forces were nearly equal to each other.Subsequent changes in the angle of attack to 75 • and 90 • resulted in a significant increase in oscillations with increased drag and decreased lift forces.Furthermore, at a preset angle of 90 • , the lift force oscillated around zero while drag reached its maximum values.The analogous chart depicting the values of the aerodynamic moment acting on the beam is presented in Figure 10.For high airflow velocities, negative values of the aerodynamic moment for angles of attack at 5 • , 15 • , 30 • , and 45 • draw attention.The remaining three angles of attack either exhibit zero moment values for 0 • or symmetric oscillations around zero for 75 • and 90 • .It is worth noting that slight oscillations also occur at Θ = 45 • and v = 100 m/s, but they diminish with increasing velocity.The above-mentioned aerodynamic loads can induce quasi-static deformations of mechanical system or excite its vibrations near resonance frequencies.This provides the foundation for examining another crucial aspect; namely, the frequency windows that impact the sample, along with the measurement of their magnitudes.In essence, we are establishing the groundwork for a comprehensive analysis of how specific frequency ranges may affect the sample and the extent of their influence.
Frequency Spectra
The time histories were subjected to a Fast Fourier Transform (FFT) to determine the airflow frequencies.In many cases, the frequency-magnitude plots exhibited one or two peaks.In order to consolidate the results, Figure 11 depicts a bubble chart on the rotational speed vs. response frequency plane.The bubble sizes are normalized to the dominant value, corresponding to the highest indication, while the remaining values (if present) are proportionally smaller.
For rotational speeds below 5 rad/s, oscillations occur only at 30 • , 45 • , and 75 • .Additionally, two harmonics are excited only for preset angle 30 • and 45 • .For angular speeds between 5 rad/s and 15 rad/s, a zero-degree angle of attack are inactive.However, for rotational speeds exceeding 20 rad/s, the first indication is observed at 150 rad/s, and the second at 300 rad/s.The arrangement of bubbles can be divided into two groups: the first group includes angles of attack of 30 • and 45 • with a nonlinear trend of decreasing frequency indication values, while the second group includes 75 • and 90 • degrees with a trend of increasing frequency with the rotational speed φ.The angle of attack 5 • has only three data points and appears to exhibit a linear trend.All time histories containing two distinct indications show that the lower harmonic has a greater value.However, it is essential to consider both frequencies to excite or avoid vibrations when their values coincide with the natural vibration frequencies, as depicted in the Campbell diagrams in Figures 5 and A1 as well as coupled vibration mode shapes presented in Figures 7 and A2-A8.
Final Remarks and Further Developments
The numerical tools presented in the paper for the FE method and CFD simulations depict the issues related to rotating composite laminates, in which, in addition to the specimen fabrication processes, rotational speed play an important role.After presenting the linear single modes of vibrations and their corresponding natural frequencies, the focus shifted towards linear modal interactions and their deformation field description using an analytical method, considering a combination of two bending directions, i and j; longitudinal motion k; and torsional l mode shapes.The mechanical system can be subjected to external loads arising from aerodynamic flow and centrifugal forces.Depending on whether we want to avoid vibrations or excite them, the natural frequencies must be either isolated from the excitation frequencies or targeted.Beyond the excitation frequency, the amplitude and the force/momentum distribution represent critical factors that have a direct impact on the efficiency of motion excitation.It is worth mentioning the possibility of indirectly exciting vibrations, for instance, by stimulating torsional modes and utilizing mechanical couplings to induce significant longitudinal motion.One should consider various types of internal resonances, external subharmonics, and superharmonics, which may arise from both linear and nonlinear mechanical couplings.
In the future research development of rotating composite structures, three main topics will be explored: (i) analytical modelling of vortex-induced vibrations, (ii) the utilization of an electromechanical system for energy harvesting from mechanical vibrations, and (iii) control of coupled vibrations via MFC patches.The first topic involves the expansion of an analytical model presented in the [17].Besides the nonlinear beam model and aerodynamic flow, there is a plan to incorporate nonlinear Van der Pol equations based on the aerodynamic characteristics of the rectangular cross-section beam and its associated frequency spectra.The second research area includes experimental measurements on the prototype presented in [26].Based on the vibration modes, it is possible to estimate the optimal location for a harvester that operates proportionally not to the maximum displacement amplitude, but to the maximum curvature.Furthermore, linearly coupled modes of vibrations appear to be a choice of higher efficiency.The final issue pertains to the vibration suppression during rotor operation, which involves avoiding resonant frequencies associated with aerodynamic flow or an vibration reduction active control by piezoelectric transducers.
Conclusions
The primary objective of this study was to perform experimental and numerical modal analysis of a composite cantilever beam.In the laboratory investigations with specialized measurement equipment, detailed maps of beam deformations (mode shapes) and magnitude-frequency curves were executed.Additionally, in the absence of rotation, the study conclusively affirmed the absence of linear modal interactions in the composite beam.Through numerical simulations, we delved into the intricacies of Campbell diagrams, determining the natural frequencies and their corresponding modal shapes.Our findings were classified into two distinct categories: the classical single-mode behavior and the pioneering extension of linearly coupled modal analysis.The two fundamental preset angles of Θ = 0 • and Θ = 90 • did not have dynamic couplings within the linear range.However, when the preset angle was adjusted to Θ = 30 • and Θ = 60 • , couplings between linear mode shapes in the plane emerged.Rotational speeds exceeding φ = 300 rad/s and a preset angle of Θ = 45 • proved to be the most linearly coupled, with flexural-flexural and longitudinal-torsion modes strongly interfering with each other, respectively.The results for the preset angle were categorized based on the coupling type and presented graphically.
Notably, we introduced an analytical description of coupled mode shapes, encompassing various deformations such as bending, longitudinal deformations, and twisting.This contribution is a noteworthy advancement in understanding the behavior of rotating structures.
In addition to the modal analysis, our secondary objective was to assess the lift, drag forces, and moment characteristics of a rectangular profile in uniform flow.The preset angle variation between Θ = 0 • and Θ = 90 • demonstrated lift/drag force transmission, in which, for the preset angle of Θ = 45 • , these forces were almost equal over the entire range of rotational speeds.Comprehensive insights into both the static and dynamic aerodynamic responses acting upon the beam within its operational frequency spectrum were provided.For preset angles 30 • and 45 • , the vortex-induced vibrations occurred at very small angular speed φ = 1 rad/s, exhibiting two prominent harmonics.
This study represents a substantial step forward in the field of composite rotating beams, offering a deeper understanding of their dynamic characteristics and their interaction with aerodynamic forces.These findings hold significant promise for various engineering applications and contribute to the broader knowledge of dynamic systems.
Figure 1 .
Figure 1.The beam-hub structure: (a) an isometric top view, and (b) a viewpoint orthogonal to the primary axis of the beam.
Figure 2 .
Figure 2. The scheme of the experimental setup.
Figure 4 .
Figure 4. Frequency magnitude curves of dynamic tests for measured signals: velocity multiplied by force sensors' voltage, displacement, velocity, and acceleration (from top to bottom).
Figure 8 .
Figure 8. Geometry of CFD simulation domain 60D × 40D (upstream 20D and wake 40D), the near-field cylinder 10D and the blade 1D corresponding to the width of the beam b.
Figure 9 .
Figure 9. Aerodynamic lift (red) and drag (black) forces acting on the beam for the constant flow rate; see Equation (7).
Figure 10 .
Figure 10.Aerodynamic momentum acting on the beam for the constant flow rate, see Equation (7).
Figure
Figure Frequency spectra of aerodynamic loads. | 7,541.8 | 2023-11-26T00:00:00.000 | [
"Engineering",
"Physics"
] |
Towards a dynamic compression facility at the ESRF
The results of the 2018 commissioning and experimental campaigns of the new High Power Laser Facility on the Energy-dispersive X-ray Absorption Spectroscopy (ED-XAS) beamline ID24 at the ESRF are presented.
Introduction
Dynamic compression induced by powerful lasers offers a route to extreme conditions of pressure and temperature that go beyond what is achievable today by static compression with the laser-heated diamond anvil cell. The capability of reproducing and probing such extreme conditions in matter is relevant for planetary and exoplanetary science (Remington et al., 2006b;Kraus et al., 2017;Noack & Lasbleis, 2020), fundamental studies of condensed matter (Grochala et al., 2007), industrial applications such as new materials synthesis (He et al., 2001) and energy science for Inertial Confinement Fusion (ICF) (Dittrich et al., 1999). (Exo)planetary science is witnessing a revolution with the discovery of thousands of extrasolar planets orbiting nearby stars (Batalha, 2014). Characterizing such planetary bodies requires knowledge of the physical properties (structural and electronic) of the key constituents at pressures of multi-Mbar and temperatures of a few thousands of Kelvin. In the interior of the Earth and planets, matter can be found in the Warm Dense Matter (WDM) state, somewhere between the solid and plasma state. Such an intriguing regime (Riley, 2017) is still challenging to describe by theoretical models, as conventional approximations, that apply to solids or ideal plasmas, break down and since experimental data are scarce. WDM states are also encountered in ICF during laser-induced target compression.
Under more moderate conditions, dynamic compression can be used to study the behaviour of materials under high strain rates (Rusty & George, 2012). Phase diagrams obtained under dynamic compression can differ greatly from the static case and there is a need to understand the strain rate and temperature dependence of kinetics, phase nucleation, metastability, elasticity and plasticity effects (Mulliken & Boyce, 2006;Gleason et al., 2015;Briggs et al., 2019;Gorman et al., 2018;Pé pin et al., 2019). This area of research also encompasses industrial processes such as laser machining or the synthesis of new materials. Under dynamic conditions, new chemistry can occur (i.e. Celliers et al., 2018;Millot et al., 2019;Brygoo et al., 2021) or new phases can be formed .
Historically, such science has been predominantly developed at large laser facilities, such as the OMEGA laser (Hoose, 1977;Boehly et al., 1997) and the National Ignition Facility (NIF) (Miller et al., 2004) in the USA or the LULI2000 (Koenig et al., 2006) in France, where most extreme states can be induced up to the TPa range. Secondary X-ray probes may be produced in situ at the expense of a large part of the laser energy to drive plasma excitation or capsule implosion (Harmand et al., 2009;Benuzzi-Mounaix et al., 2011;Ping et al., 2013;Denoeud et al., 2014;Coppari et al., 2017;Krygier et al., 2018). A notable example is the development of X-ray absorption spectroscopy (XAS) measurements at NIF and OMEGA, where good-quality EXAFS (extended X-ray absorption fine structure) could be obtained under ambient conditions (Coppari et al., 2017;Krygier et al., 2018) and rampcompressed Fe (Ping et al., 2013). Moreover, recently, much effort has been devoted to the improvement of the energy resolution so as to be able to observe XANES features (Chin, 2020). However, user access to these facilities remains very limited due to the low shot rate.
In recent years, a new strategy has emerged: coupling more compact lasers to brilliant X-ray sources such as synchrotrons or XFELs to ensure high-quality X-ray measurements (Glenzer et al., 2016;Wang et al., 2019;Inubushi et al., 2020), thus exploiting the long-standing expertise of the synchrotron community.
In this context, the ESRF has developed the opportunity of coupling dynamic compression experiments to time-resolved single-pulse XAS at beamline ID24. Laser-shocked Fe and Ta (Pé pin et al., 2020) were investigated up to a pressure of several Mbar using a 35 J portable laser, delivering for the first time high-quality data in both the XANES and the EXAFS range for materials under dynamic compression.
At the ESRF, dynamic compression was also coupled to X-ray Imaging (XRI) (Rutherford et al., 2017;Olbinado et al., 2018;Yanuka et al., 2019;Miller et al., 2019;Derrick et al., 2019;Cohen et al., 2019;Escauriza et al., 2020;Farbaniec et al., 2021) and X-ray Diffraction (XRD) Pé pin et al., 2019) on the ID19 and ID09 beamlines, respectively. The success of these first experiments led to the launch of the High Power Laser Facility (HPLF-I) project, that foresees the coupling of a 100 J laser to the ID24 beamline to perform laser shock and ramp-compression experiments probed by timeresolved XAS.
Among other facilities of this kind, i.e. MEC at LCLS (Glenzer et al., 2016), BL3-EH5 at SACLA (Inubushi et al., 2020), DCS at APS (Wang et al., 2019) and HED at EuXFEL (Descamps et al., 2020), HPLF-I is the only one dedicated to and optimized for XAS in both the XANES and the EXAFS range. However, XANES of laser-shocked Fe has also been measured at MEC (Harmand et al., 2015), but with limited data quality, mostly due to intrinsic intensity fluctuations of the X-ray beam, leading to the need for averaging over multiple acquisitions. High-quality single-pulse EXAFS, under laser-shock compression, has also been demonstrated recently at APS (Das et al., 2020), but with insufficient energy resolution for the XANES region.
Extension to other X-ray techniques, such as XRI, XRD and XES (X-ray Emission Spectroscopy), is foreseen at HPLF in a second phase (HPLF-II after 2023). In this article, we present the first phase of HPLF-I where the front-end of the Amplitude laser, delivering 15 J, was coupled to beamline ID24, together with related technical details and initial experimental results.
Energy-dispersive beamline ID24
The ED-XAS beamline ID24 of the ESRF is optimized to couple the time-resolved ED-XAS technique under extreme conditions (pressure, temperature and magnetic field). Taking advantage of the dispersive scheme, dynamic compression is one of the main emerging applications Mathon et al., 2016).
A divergent X-ray beam is focused and energy dispersed by a bent crystal polychromator. The X-ray beam is focused on the target and the transmitted X-rays diverge onto a positionsensitive detector. As a result, the whole X-ray absorption spectrum is acquired at once, with no moving components during the acquisition. The XH detector (Borri et al., 2021a,b), developed for pump-probe single-pulse measurements (see x2.2, X-ray detector), is capable of isolating a single X-ray bunch in different filling modes of the ESRF, namely, 4-bunch mode, 16-bunch mode and 7/8+1 mode (see Table 1). Therefore, the ultimate time resolution is given by the X-ray pulse length [100 ps FWHM (full width at half-maximum) at the ESRF] convoluted with the temporal jitter between the drive laser and the X-ray bunch itself. The jitter is measured to be less than 50 ps RMS (root mean square) and the convolution with the X-ray bunch length gives 65 ps RMS (or 155 ps at FWHM). This is well suited to laser-shock-induced dynamic compression, as typical shock-time scales and most of the related processes are in the several hundreds of picosecond and nanosecond ranges. ID24 provides X-rays in the energy range 5-28 keV using a combination of U27 and U32 undulators. So far, single-pulse measurements up to 20 keV have been performed under ambient conditions and up to 11 keV under shock compression (L 3 -edge of Bi; see x4.3, Bismuth). Depending on the working energy and the beamline setup, the X-ray focal spot ranges from 3 to 50 mm FWHM horizontally and from 3 to 100 mm FWHM vertically. A small beam size is an important aspect in laser-shock experiments. Indeed, in order to probe a spatially homogeneous shock state, the X-ray beam must be much smaller than the laser spot and the shock front at the target position. A small X-ray spot will thus allow the use of smaller phase plates for the laser, increasing the available deposited power density and therefore extending the achievable pressure and temperature domains. However, when using a small phase plate, the target design, and especially the target thickness, has to be carefully considered to limit border effects and keep a homogeneous shock at the sample position (Remington et al., 2006a).
ID24 provides a 10 13 -10 14 photons per second flux on the sample, depending on the energy , in multibunch mode (ring current 200 mA). At the Fe K-edge, this translates into an average of 1.5  10 4 photons/bunch/ strip in the 4-bunch mode (ring current 40 mA) , which is confirmed by our measurements after XH detector calibration via a calibrated Si diode. Fig. 1 reports the single-pulse reference measurements performed on Fe targets at beamline ID24 (L branch) in different configurations (left panel) and the corresponding direct beams (right panel). The photon distribution of the direct beam at the Fe K-edge is not flat but increases with energy. Therefore, different choices can be made in the beamline alignment to favour a higher signalto-noise ratio (S/N) in the edge range (black spectrum) or a larger energy range at the expense of higher noise in the XANES (red spectrum). The average noise levels in the preedge range are 0.0056 and 0.0065 for the black and red spectra, respectively [same a.u. as in Fig. 1(a)]. For the black and red spectra, the beam was only focused horizontally by the polychromator (the beam size was around 5 mm  90 mm, H  V FWHM).
Vertical focusing is achieved using an additional vertically refocusing mirror (VRM). This mirror cannot be placed under vacuum, but is fluxed with N 2 , which explains the slight increase of the average noise level to 0.012 in the pre-edge range (green spectrum).
Black, red and green spectra were acquired during the 4-bunch mode, the most favourable for single-pulse acquisition, as the current in one bunch reaches 10 mA and bunches are separated by more than 700 ns, allowing for a longer charge-collection time with the XH detector.
We show a single bunch acquisition during the 16-bunch mode again with VRM in place (blue spectrum). The current in a single bunch in this mode is around 5 mA and bunches are separated by only 176 ns, which accounts for the higher noise (0.16 on average in the pre-edge range).
Despite this, single-bunch spectra in 16-bunch mode are exploitable at least in one energy region at a time, i.e. by setting the beamline alignment to optimize XANES or EXAFS. Data quality for single-pulse spectra acquired in 7/8+1 mode is expected to be closer to that of the 4-bunch mode as the current in the single bunch reaches 8 mA. Singlepulse measurements in the 7/8+1 mode were performed on Fe alloy targets which were showing radiation damage and were thus protected by attenuating the beam with thick kapton foils (see x4.2, Fe x O y , Fe-10 wt%Ni and Fe-3.5 wt%Si). A direct comparison of the S/N ratio is therefore not possible here.
The energy resolution of an energy-dispersive spectrometer depends on the central energy, E 0 , the crystal diffracting Figure 1 (a) Single-pulse XAS measurement of Fe (3.5 mm deposition on a diamond substrate) under ambient conditions in different configurations. Black, red and green lines are spectra acquired during the 4-bunch mode, while the blue spectrum was acquired in the 16-bunch mode. In the black spectrum, the spectrometer is aligned so that the Fe K-edge is in the middle of the energy range; in the red spectrum, the edge is moved towards low energies to increase the energy range; the green spectrum is the same as the red spectrum, but with the beam focused vertically using an additional mirror (VRM); and the blue spectrum is the same as the green spectrum but in the 16-bunch mode. (b) The corresponding direct beams (colours matching). planes (h, k and l), and the geometry, i.e. the focusing distance and detector distance.
The contributions to the effective angular spread are: (i) the spatial resolution of the detector, (ii) the Darwin width of the curved polychromator crystal, (iii) the size of the X-ray source and (iv) the spread of the monochromatic beam on the detector due to the Borrmann fan (only in the case of Laue geometry) . In the case of dynamic compression experiments, the focusing distance is 1.1 m and the XH detector can be placed at up to 3 m from the sample (4.1 m from the polychromator). In Bragg geometry, Fig. 2 (left panel) shows that our calculated energy resolution dE/E is better than the core hole lifetime broadening for the K-edges (dE/E < 2 Â 10 À4 ) up to E = 10 keV, and increases up to 5 Â 10 À4 at E = 25 keV. However, above 15 keV, the Laue geometry becomes preferable to avoid the effect of the asymmetrical reflectivity profile of the highly curved Braggtype crystal, degrading energy resolution and creating an asymmetrical focal spot. In Fig. 2(b), we show two example spectra at the Fe K-edge, acquired in Bragg geometry with Si(111), with different sample-to-XH-detector distances in comparison with a reference spectrum from a standard XAS beamline (BM23 at ESRF). The energy resolution improves at larger detector distances (purple curve). Depending on the scientific case, i.e. the XAS features that need to be resolved, one can choose to optimize the energy resolution or the flux (S/N ratio) by choosing a larger or smaller detector distance, respectively.
X-ray detector
One of the most critical elements in the setting up of singlebunch XAS measurements to probe laser-shocked matter has been the development of the XH detector. This detector is devoted to fast time-resolved applications, such as singlebunch pump/probe mode and film mode experiments. The critical part is linked to the Ge sensor technology, which is far less developed than Si technology. Si sensors are not usable due to strong radiation damage when exposed to the direct beam. The development of the Ge strip detector is the result of a long-standing collaboration between the ESRF and the Science & Technology Facility Council (STFC, Daresbury Laboratory, UK) (Borri et al., 2021a,b). The acquisition electronics features a readout time of 2.8 ms, allowing one acquisition per ESRF ring revolution to be performed. The minimum integration time of around 100 ns allows the isolation of a single bunch in 4-bunch and 16-bunch modes, and the main intense bunch in the 7/8+1 mode (see Table 1). The XH detector has 1024 strips (rectangular pixels) of 25 mm width, 50 mm pitch and 5 mm height, leading to a total active area of 51.2 mm  5 mm.
The original system was delivered to the ESRF and used successfully for laser shock dynamic compression experiments (Headspith et al., 2007;Torchio et al., 2016;Pé pin et al., 2020). Since 2017, an upgraded design was manufactured, with improved thermal performances and new germanium sensors from Mirion Technologies (Borri et al., 2021a,b).
Laser
The laser is a custom-made Intrepid system from the Amplitude Laser Group (Continuum division in San Jose, CA, USA). It contains the generation of the laser pulses, spatial and temporal shaping, and amplification up to 15 J. Fig. 3 presents the optical layout of the laser used as the shock driver for the experiments reported here.
The seed source laser is inside a Front-End ModBox from iXBlue (Besançon, Fr). A Distributed FeedBack laser generates a continuous wave at 1053 nm. Within the same ModBox and using only fiber components, electro-optic modulators perform the temporal pulse shaping of this continuous wave. The temporal pulse shaping pre-compensates for the non- linear pulse distortion that occurs in the amplifier chain and allows nanosecond pulses to be delivered with the required duration and shape on target. Before leaving the ModBox and entering free-space propagation, another electro-optic modulator spectrally broadens the pulses for the Smoothing by Spectral Dispersion (SSD) system. The energy per pulse reaches the nJ level at the end of this all-fibre section. The laser pulses are then coupled to free-space propagation and injected into a linear regenerative amplifier (Regen or RGA). There, a 5 mm diameter rod amplifies the energy up to the mJ range in a few passes. At the output of the RGA, a Pockels cell (PC) acts as an isolation stage, while also improving the temporal contrast of the single pulse. It is then further amplified in a single-pass 5 mm diameter rod, enlarged through an afocal telescope up to its final diameter of 23 mm. The final amplification is performed by two 25 mm diameter rod amplifiers in a double-pass scheme with birefringent compensation through a quartz rotator plate, isolated on both sides by large-diameter Faraday isolators. A final in-vacuum telescope relays the image plane close to the output port of the laser enclosure.
All amplifiers are pumped by flash lamps. In order to keep the bandwidth induced by the SSD system and to avoid FM-to-AM modulations (Rothenberg et al., 1999;Hocquet et al., 2008), all amplifiers use Nd:glass rods. Given the limited thermal conductivity of the laser glass and the significant thermal load due to flash pumping, the repetition rate of the laser is limited to 0.1 Hz. To keep the thermal load as constant as possible, all the flash lamps are always triggered at 0.1 Hz and the overall alignment of the laser takes into account the induced thermal lensing. For easier alignment, it is possible to drive both 5 mm diameter amplifiers at 0.5 Hz without significant changes in alignment. To prevent maximum amplification during the alignment process while keeping the thermal lensing of the 25 mm diameter amplifiers constant, their flash lamps, still running at 0.1 Hz, can be time delayed by a few milliseconds. We also used this capability to define four different delays for the 25 mm diameter amplifier flashlamp trigger resulting in four different energy output levels of 15, 10, 5 and 0.08 J, with the last corresponding to no amplification at all using a delay significantly larger than the fluorescence lifetime of the Nd:glass rods. These energy levels are selectable from the beamline control interface.
Synchronization
The synchronization of all instruments was achieved through ESRF-developed electronics, namely, the Bunch Clock Delay Unit (BCDU8) and Octal Programmable I/O Module (OPIOM) cards (Fig. 4).
The BCDU8 takes as its only input the radiofrequency clock of the storage ring (RF master clock) and outputs synchronous pulses of adjustable delays and widths. Two of its output channels are capable of fine delays (11 ps steps). One of these channels is used for the laser timings. While providing fine delays on two channels, the total delays are limited to approximately half of the output period (i.e. %1.4 ms in our case). As our laser and detector require longer delays, the BCDU8 outputs are then fed to the OPIOM card.
This second electronic device provides combinational logic between its inputs through a programmable logic device (PLD) and a microcontroller. The OPIOM works using its inputs as its time base, both for delays and pulse durations. In our case, we have two input clocks running at 355 kHz (i.e. 2.82 ms ticks, corresponding to the ESRF storage ring revolution or bunch orbit). According to a precompiled firmware, the OPIOM then generates the following output signals, each with its own coarse delay, repetition rate and duration: a single pulse trigger for the XH detector; a clock for the 5 mm amplifiers either at 0.1 or 0.5 Hz, with a fixed delay of 520 ms; a clock for the 25 mm amplifiers always at 0.1 Hz, with a default delay of 0 ms which can be increased by nearly 1.5 ms to Schematic view of the synchronization system. The synchrotron RF is distributed to all instruments through a set of two cascaded in-house electronics (BCDU8 and OPIOM). The frequency and corresponding period are shown for each clock, while only the repetition rate is shown for trigger events.
Figure 3
Optical layout of the laser front-end; see text for details. PC is the Pockels cell, Amp are the rod amplifiers with their diameter for indication, SA are the apodizing apertures, L are the lenses, FI are the Faraday Isolators, Pol is the thin-film polarizer and QR is the quartz rotator. prevent amplification while keeping the thermal load constant; a trigger for the internal delay generator of the laser driving the ModBox and the Pockels cells; a trigger for the shocks diagnostics. The OPIOM outputs drive the subsequent devices: the laser, and both X-rays and visible diagnostics. The overall timing scheme is depicted in Fig. 4, which shows the signal distribution from the synchrotron RF to the final instruments. As the synchronization is partly based on the bunch clock (RF/992), all acquisitions are performed following always the same single bunch within the storage ring. The synchronization setup then remains identical for all filling modes of the storage ring (see Table 1 for details), apart for the fine delay to superimpose the laser on the X-ray pulse.
This setup allows a complete synchronization of the facility based on the storage ring radiofrequency and also provides control for both the operating mode of the laser and the detector from the beamline control session.
Laser pulse/X-ray pulse fine synchronization is observed through a single ultrafast avalanche photodiode (APD) placed at the sample position. The laser delay is then adjusted with the fine delay output of the BCDU8 card in order to superimpose the rising edges of both X-rays and laser pulses.
The final High Power Laser Facility will benefit from a modern in-house-developed delay generator using the recently deployed RF over a White Rabbit network of the ESRF (Goujon et al., 2018).
Target chamber
The interaction geometry was kept similar to previous experiments Pé pin et al., 2020). The X-rays are normal to the sample surface, while the drive laser arrives at 30 . Fig. 5 details the beam configuration.
Two in-vacuum microscopes offer sample visualization from upstream and downstream. In order to observe perpendicular to the sample surface, a flip mirror folds the beam path for each microscope. These flip mirrors are then retracted to free the X-ray beam path.
A Point VISAR (Velocity Interferometer System for Any Reflector) -model Valyn VISAR with a Verdi CW laser from Coherent -was used to characterize the loading conditions using aluminium samples. Given the interaction geometry, as depicted in Fig. 5, the X-rays and the VISAR cannot be operated at the same time. Hence, the VISAR was used offline by inserting a small mirror close to the target rear face. This is a clear limitation of the current interaction geometry. In order to perform XAS and loading conditions measurements simultaneously, the future interaction geometry for HPLF will be modified. The same relative angle between the X-rays and laser drive will be kept but the sample normal will sit in between both beams (i.e. X-rays incident at +15 and laser drive at À15 ). This opens up the rear side enough to install a normal-incidence optical access for visible diagnostics of the shock conditions. A line VISAR and a SOP (Streaked Optical Pirometry) system will be implemented in HPLF.
The vessel was evacuated down to 10 À4 mbar with a turbomolecular pump backed up by a dry pump. Additional under-vacuum tubes were used between the polychromator and the target chamber and in front of the detector in order to minimize X-ray absorption in air. The configuration of the beams (not to scale). The beamline pink beam is diffracted and focused normal to the sample surface (pink then sketched as a few rainbow rays). The laser, in red, arrives at 30 . Downstream is the X-ray detector. A flip mirror can be inserted in the X-ray beam path for VISAR analysis (green). A direct line-of-sight camera can be used to record the laser focal spot in the absence of samples (dashed red). The vacuum vessel, its windows and the two in-vacuum microscopes for sample observation are not shown for clarity.
Figure 6
A photograph of the experimental hutch in November 2018. Beams are shown as solid arrows, whereas instruments are shown as dashed lines. X-rays are shown in pink, the drive laser in red and the shock diagnostics in green. For scale, the laser is 2 m long.
Laser characterization
The laser breadboard (2 m  1 m) was installed inside the experimental hutch. All the electronics, power supplies and cooling group were installed inside the control cabin providing easy access.
The laser beam cross section at 15 J is shown in Fig. 7. Beam inhomogeneities are limited to, respectively, 8 and 10% RMS over the central parts (defined as 90% of the diameter) of the horizontal and vertical profiles, and there are no sharp spots. The cross section of the beam is only slightly elliptical (minor/major = 93%) and is missing small amounts of energy in the lower part, as can be seen in the unbalanced vertical profile. The edges are sharp (super-Gaussian order >10 along both axes).
Repeatability of the laser parameters (delivered energy, temporal shape and beam pointing) is of paramount importance to be able to duplicate shots or compare successive shots with different time delays with respect to the X-ray probe. Hence, the qualification runs were performed over 50 shots at a default repetition rate of 1 shot every 4 min (maximum shot rate for the future 100 J laser).
The energy output was 14.5 J on average with an energy stability of 1.2% RMS (8.8% peak-to-peak).
The beam-pointing stability was measured with a 1 m focal length lens at 14 mrad RMS (45 mrad peak-to-peak horizontally and 34 mrad peak-to-peak vertically).
In 2018, the temporal pulse shape was fixed to a 9 ns square, with a rise time of 300 ps (20-80%) and a contrast better than 10 4 (detection limit with the present setup) on the nanosecond timescale before the main pulse, as shown in Fig. 8. This pulse shape can be improved, especially with respect to the rise time between 10 and 90% (1.4 ns), and the plateau fluctuations. Concerning reproducibility, the qualification tests (50 shots) showed that the amplitude of the plateau was reproducible within AE10% peak-to-peak and the width was stable at 8.7 ns (40 ps RMS).
The future facility will offer square pulses from 2 to 15 ns and also provide the possibility of pulse shaping for rampcompression experiments.
Laser beam transport, focusing and alignment
From the laser output port, a set of mirrors steers the laser beam up to the interaction chamber. In order to match the size of the phase plates used in previous experiments , the beam diameter at the laser front-end output is enlarged by a Keplerian telescope from 23 to 40 mm approximately midway between the laser output port and the sample (for a total of about 4 m of free propagation). The focusing lens (f = 350 mm) is placed before the laser input port of the vacuum chamber, the phase plate being in between the focusing lens and the vacuum window. An imaging system (microscope objective and a camera) is placed on the axis of the laser beam and monitors the focal spot shape and the size at the target position at low energy. Fig. 9 shows a typical focal spot when using a 250 mm Hybrid Phase Plate. The obtained profile is quite inhomogeneous, with intensity variation up to 50% over the micrometric scale. However, recent studies at LCLS (Smith, 2016) have shown that in laser-driven dynamic compression experiments, the laser spatial profile inhomogeneity can be smoothed by a sufficiently thick target ablator thanks to thermal conductivity. Moreover, the future facility will feature a larger input beam size which will increase the density of smaller speckles. It will also feature Smoothing by Spectral Dispersion (SSD) which will smear out the speckles along one axis.
The X-ray focal spot is materialized by scanning a 50 mm pinhole in the X-ray beam and visualizing the pinhole position on the on-axis image. The laser focal spot of Fig. 9 is then moved to the same position using the translations of its focusing lens. Fine spatial overlap is finally checked through direct observation of low-energy laser shots on plastic samples placed at the sample position.
The laser parameters and overall alignments were found to be reproducible and stable over several days, with some minor adjustments to the regenerative cavity due to the temperature increase inside the hutch and fine alignments on the target. A photograph of the beam on burnpaper at the laser output (not focused and without a phase plate, left). Horizontal and vertical profiles recorded with a beamviewer (Gentec Beamage) and the corresponding super-Gaussian fits (right) with profile / expðÀr N Þ.
Figure 8
Laser temporal profile recorded with a fast photodiode (EOT ET-3500) connected to a fast oscilloscope (LeCroy WaveMaster 20 GHz). Orange dotted lines represent the rise time between 20 and 80% of the maximum, i.e. 300 ps.
This allowed the successful collection of XAS spectra and the summation of successive identical shots as described in x4.3 (Bismuth).
Targets
The iron, iron alloy and iron oxide targets were designed, fabricated and assembled at the IMPMC laboratory. Three major target designs were used to ensure both homogeneous and well-controlled thermodynamic conditions at the time of the X-ray probe, a few ns after the laser impinges on the target front face. They are shown in Fig. 10.
The first design, labelled A in Fig. 10, was used in a previous ID24 laser shock experiment . It consists in a 4 mm plastic parylene-N ablator, a 40 mm diamond and a deposited Fe or Fe 2 O 3 layer on a second 40 mm diamond.
The shock Hugoniot conditions were determined by hydrodynamic simulations with the MULTI code (Ramis et al., 1988) using the SESAME EOS Table 2150 for Fe, 7440 for Fe 2 O 3 , 7411 for sapphire and 7592 for CH (initial density of 1.044 g cm À2 ). The input laser pulse is a square pulse of 9 ns with an intensity of 1.8 Â 10 12 W cm À2 . This laser intensity was calibrated using CH-Al targets with the same ablator thickness, by adjusting the simulated free surface velocity and shock arrival time to those obtained from off-line VISAR Capture of the laser spot at the sample position using a hybrid phase plate designed to generate a 250 mm focal spot. The profiles shown at the top and to the right are 40 mm thick lineouts through the focal spot at Y = 0 and X = 0, respectively. Full width at half-maximum (FWHM) is close to 200 mm along both axes. Enclosed energy measurements on this figure show 50% of the energy inside a 180 mm diameter, 70% inside a 226 mm diameter and 80% inside a 290 mm diameter.
measurements. Examples of simulations are shown in Fig. 10. Unfortunately, it has not been possible to perform VISAR measurements of the targets directly because of radiation damage from the continuous VERDI laser.
For target design A, the simulations show that the thermodynamic conditions remain stable in the range 7-8 ns and correspond to a pressure of about 40-50 GPa for both Fe and the alloys. The two other target designs, labelled B and C in Fig. 10, allow us to reach a higher pressure using the impedance mismatching between the plastic ablator and the investigated samples.
The B target design consists of a multilayer of a deposited parylene-N (60 mm) and a deposited Fe 2 O 3 (5.9 mm) on a 40 mm sapphire window. This design allows us to keep the thermodynamic conditions in the range 2-3 ns thanks to the similar impedance between our samples and the sapphire window. The C target design corresponds to a 60 mm parylene-N, that was either directly deposited on Fe-Si and Fe-Ni alloys or used as a substrate for Fe and Fe 2 O 3 depositions. For this target design, the thermodynamic conditions release rapidly due to the fast expansion of the rear side of the target. For both the B and C designs, the achieved pressures under the conditions of the experiment are around 110-120 GPa (for both Fe and alloys), which go far beyond the bcc-hcp phase transitions of Fe and Fe alloys and beyond the Mott phase transition of Fe 2 O 3 at about 50 GPa (Sanson et al., 2016). Polycrystalline Fe, Fe-Si and Fe 2 O 3 samples were obtained by physical vapour deposition at IMPMC and their thicknesses were optimized to enhance the X-ray absorption signal. The Fe-Ni alloys were polycrystalline commercial foils from HMW Hauner GmbH & Co. KG.
The Bi targets were a multilayer made of a sapphire window (200 mm thickness) glued on to 10 mm thick Bi foils from Goodfellow which are provided on a support layer of polyimide on the back side (125 mm). This target design allows us to work in a confined plasma-driven shock scheme, where the laser ablation does not occur at the target front face, but at the target/sapphire interface (Fabbro et al., 1990). This scheme provides a reproducible pressure time evolution in the Bi sample, allowing the shock states to be maintained for several nanoseconds, but reaching limited pressures (5-10 GPa). More details about the expected conditions for the results shown here are reported in x4.3 (Bismuth).
Fe
x O y , Fe-10 wt%Ni and Fe-3.5 wt%Si The investigation of Fe-rich alloys, such as FeNi, FeSi and Fe oxides, under extreme conditions of pressure and temperature is of crucial interest for the understanding of the composition and evolution of the mantle and core of the Earth and Super-Earth exoplanets (Wicks et al., 2018;Boulard et al., 2019;Miozzi et al., 2020;Torchio et al., 2020;Boccato et al., 2020). The influence of lighter or minor elements on the Fe phase diagram is still not fully understood.
In the case of Fe-10 wt%Ni, we observe an unambiguous laser-induced bcc-to-hcp transition, similar to pure Fe (Torchio et al., 2016) [Fig. 11(a)]. On the contrary, mixed bcchcp phases are observed in Fe-Si alloys: the bcc feature at around 7.195 keV (indicated with dashed lines in the figure) is visible in the normalized XAS spectra up to an 8 ns time delay between the optical laser and the X-ray pulses [ Fig. 11(b)]. The addition of a small percentage of Si (3.5 wt%) to Fe thus seems to kinetically hinder the complete bcc-hcp phase transformation similar to recent X-ray diffraction measurements under laser compression that have shown no hcp phase transitions for Fe-16 wt%Si (Fischer & Campbell, 2015;Wicks et al., 2018;Edmund et al., 2019;Krygier et al., 2021). It should be noted that the S/N ratio in the FeSi alloy data is lower than in the FeNi alloy. During the alignment, the sample was showing X-ray beam damage due to the high flux of the 7/8+1 mode, and was therefore protected by four kapton foils of 75 mm, thus reducing the photon flux by 30%. The same problem occurred for Fe 2 O 3 described below. In the future HPLF, the installation of motorized attenuation will be implemented to protect the sample during alignment and only expose it during the shot.
In the case of Fe 2 O 3 , we show XANES measurements under shock and release conditions in Fig. 12 Normalized single-shot XAS spectra of (a) Fe-10 wt%Ni (4-bunch mode) and (b) Fe-3.5 wt%Si (7/8+1 bunch mode) recorded at various time delays between the optical laser and X-ray pulses. The spectra under ambient conditions, representing the bcc structure, are shown in black. taken with target design B which includes a sapphire window for maintaining the pressure and temperature conditions for several ns and that allows pressures of $120 GPa to be reached thanks to the impedance mismatching between the plastic ablator and the Fe 2 O 3 deposited layer.
In Fig. 12(a), we show Laser-Heated Diamond-Anvil-Cell (LH-DAC) data obtained at 80 GPa and 1500-2000 K for comparison . In the LH-DAC data, we observe (i) a change of the pre-edge feature, (ii) a decrease of the absorption signal, (iii) a slight modification of the XANES shoulder at 7150 eV and (iv) a shift of the first XANES oscillation toward high energies. This behaviour was also observed in the recent article by Sanson et al. (2016) and was attributed to the High Spin-Low Spin (HS-LS) phase transition at $53 GPa and was followed by the formation of the orthorhombic structure with the space group Aba2 (Bykova et al., 2016). Similar observations were made in the Fe 2 O 3 shock data obtained during this experimental campaign [see Fig. 12(b)]. The feature labelled 'iv' shifts to higher energies, indicating the compression of the lattice parameters while the intensity of feature 'ii' decreases and a slight modification of pre-edge 'i' is observed. This indicates that the HS-LS transition was crossed and that most probably the orthorhombic Aba2 structure of Fe 2 O 3 was formed within the duration of our experiment, i.e. less than 1 ns after the arrival of the shock in the Fe 2 O 3 sample.
Further studies under optimized experimental conditions and at a higher laser energy would allow higher pressure ranges to be reached and high-pressure phases and the electronic local order of Fe 2 O 3 to be disentangled. It should be noted that the increased resolution in the pre-edge range of the static data is mainly due to the use of the Si(311) Bragg polychromator.
Bismuth
Bismuth is a prototype example of a material whose PT phase diagram changes as a function of the strain rate. Despite recent advances on its phase diagram under dynamic solicitation (Gorman et al., 2018;Pé pin et al., 2019), questions remain about high-pressure phase stability as a function of kinetics (Fig. 13). Here we investigate Bi under laser-induced dynamic compression probed by time-resolved XAS, in particular looking for the signature of the Bi I (rhombohedral) to Bi V (body-centredcubic) transition that occurs around 8 GPa in static compression and already from 4 GPa in dynamic compression Pé pin et al., 2019).
The laser was focused down to 500 mm at the sample position. Singlebunch XAS measurements were performed at the Bi L 3 -edge (13.4 keV) using the XH detector with the 7/8+1 filling mode. XANES features of the Bi L 3 absorption edge are quite small [A, B, C and D in Fig. 14(a)]; the sum of 8-10 single X-ray bunch acquisitions was needed to discern them.
Compression conditions were estimated by hydrodynamic simulations using the ESTHER code (Colombier et al., 2005). However, because of the polyimide backing (Bi foils from Goodfellow are not stand alone), measurements could not be performed directly on the Bi targets. Therefore, the simulation parameters were preliminarily calibrated by comparison with VISAR measurements on Al targets with the same front sapphire window, following a procedure previously used for Bi (Pé pin et al., 2019) (see Fig. 13). According to hydrodynamic simulations, at 8 ns Bi is in a uniform pressure state of around 5 GPa, and a full conversion into Bi V is expected.
The pressure-induced Bi I to Bi V transition shows up in tiny changes in the XANES region, as is visible from static compression (DAC) data in Fig. 14(c) .
Our XANES spectrum obtained under dynamic compression shows changes at 13.432 and 13.437 keV [indicated by arrows in Fig. 14(b)], similar to that obtained in static compression, and is thus compatible with the observation of the transition. Starting from 13.45 keV, the shocked spectrum shows a flat shape as a consequence of thermal disorder [red spectrum in Fig. 14(a)]. At 25 ns, the Bi state reverts to ambient-pressure conditions. The spectrum acquired at 25 ns is noisier since it was only averaged over five accumulations. However, its edge shape looks like that of the ambient reference, which is compatible with the recovery of the Bi I (a) X-ray absorption spectra of Fe 2 O 3 at pressures of 5, 35 and 59 GPa and ambient temperatures, and at 81 GPa and 2100 K, using the LH-DAC apparatus at ESRF ID-24 . (b) X-ray absorption spectra of Fe 2 O 3 under shock at an estimated pressure and temperature of 120 GPa and 1500 K, and under adiabatic release at ambient pressure and 1000 K (SESAME EOS 7440). The black dotted spectrum is the ambient reference. structure. The detection and phase diagram location of the other expected phases (Bi, Bi II and Bi III ) might be the subject of future work.
Conclusions and perspectives
We presented here the commissioning results of the laser front-end of the future High Power Laser Facility at ESRF. The laser was characterized and coupled to the dispersive XAS beamline ID24. First-user experiments were performed and new X-ray Absorption data of iron compounds and bismuth were collected under laser-induced dynamic compression. Several aspects of the preliminary setup described here will be improved for the final version of HPLF. The final interaction geometry will allow simultaneous XAS and loading condition measurements (both line VISAR and SOP), minimizing the number of targets needed and improving the reliability of the pressure/temperature conditions associated with the XAS spectra, not having to rely on the reproducibility of the target and laser conditions.
The synchronization scheme will also be refined to be more versatile and easier to operate.
During the ESRF shut down for the major Extremely Brilliant Source (EBS) upgrade of the storage ring (2019), the laser was shipped back to Amplitude Technologies for further improvements and to build the amplification stage up to 100 J. The pressure map of a Bi target (sapphire/Bi/polyimide) when the same simulation parameters are applied. The used EOS in the simulations are: SESAME 3720 for Al, SESAME 7411 for sapphire and BLF for Bi. source and beamline upgrades, an increase of flux by a factor 2-5 (depending on the energy) is expected. In the longer term, the HPLF laser is planned to be shared with a second adjacent beamline to implement further time-resolved X-rays probes, such as X-ray diffraction, X-ray imaging and X-ray emission, for laser shock and ramp experiments. | 9,779 | 2022-01-01T00:00:00.000 | [
"Physics",
"Engineering"
] |
DeepGreen: deep learning of Green’s functions for nonlinear boundary value problems
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem domains including fluid mechanics, electromagnetics, quantum mechanics, and elasticity. The fundamental solution, or Green’s function, is a leading method for solving linear BVPs that enables facile computation of new solutions to systems under any external forcing. However, fundamental Green’s function solutions for nonlinear BVPs are not feasible since linear superposition no longer holds. In this work, we propose a flexible deep learning approach to solve nonlinear BVPs using a dual-autoencoder architecture. The autoencoders discover an invertible coordinate transform that linearizes the nonlinear BVP and identifies both a linear operator L and Green’s function G which can be used to solve new nonlinear BVPs. We find that the method succeeds on a variety of nonlinear systems including nonlinear Helmholtz and Sturm–Liouville problems, nonlinear elasticity, and a 2D nonlinear Poisson equation and can solve nonlinear BVPs at orders of magnitude faster than traditional methods without the need for an initial guess. The method merges the strengths of the universal approximation capabilities of deep learning with the physics knowledge of Green’s functions to yield a flexible tool for identifying fundamental solutions to a variety of nonlinear systems.
1D Problems
The data for all of the one-dimensional systems are created using the same method and forcing functions. Each solution is computed on an evenly-spaced 128-point grid using MATLAB's bvp5c solver with a relative error tolerance of 10 −8 and an absolute error tolerance of 10 −10 . The forcing functions F k (x) are designed to yield a variety of solutions u k such that ||u k || 2 1.
The training data consists of two types of systems: Gaussian-forced and cosine-forced systems. The Gaussian-forced systems have forcing functions of the form However, there were 97 solutions of the nonlinear biharmonic equation that did not meet the error tolerance and were therefore discarded. Of the remaining data, 10% are randomly chosen and withheld as test data, 80% are used as training data, and 20% are used as validation data. In order to test the ability of the network to generalize, we also have another test data set that consists of solutions with cubic forcing functions of the form where γ ∈ {0.01, 0.03, 0.05, . . . , 0.29}, and cubic forcing functions of the form where γ ∈ {0.01, 0.03, 0.05, . . . , 0.29}, ζ ∈ {0.01, 0.03, 0.05, . . . , 0.49}, and ψ ∈ {−5, −4, −3, . . . , 5}. There are a total of 4140 solutions with cubic forcing functions.
2D Problem
The two-dimensional data satisfies the nonlinear Poisson equation in the manuscript. The solutions are computed with a finite element method using the DOLFIN library 1 Figure S2. Decoder network architecture for the two-dimensional data. All transposed convolutional layers use 4 × 4 kernels with stride size 2, zero-padding, and ReLU activation functions except for the last layer which has stride size 1. data in that there are Gaussian and cosine forcing functions along with a separate data set of cubic polynomial forcing functions used to test the ability of the network to generalize. The Gaussian forcing functions are of the form where γ x , γ y ∈ {0.01 + 0.28k/3|k = 0, 1, 2, 3}, and cubic forcing functions of the form
Neural Network Implementation Details
The model training procedure is kept constant for all of the examples in this work. The networks are optimized with an Adam optimizer (β 1 = 0.9, β 2 = 0.999). Every numerical experiment starts by training a set of 20 models for a 'small' number of epochs. Each of the 20 models has a randomly selected learning rate for the Adam optimizer, uniformly selected between 10 −2 2/6 Supplementary Figure S3. Layer-by-layer autoencoder architecture for 1D problems.
and 10 −5 . The initial training period consists of two phases: autoencoder-only (75 epochs) and full model (250 epochs). The autoencoder-only phase only enforces the autoencoder losses L 1 and L 2 during backpropagation. A checkpoint algorithm is used to keep track of the model with the lowest overall loss throughout the training procedure. At the end of the initial period, the best model is selected and the others are eliminated. The best model is trained for an additional 2500 epochs. There are two network architectures in this work. The architectures depicted in Figs. S1 and S2 are applied to the two-dimensional nonlinear Poisson BVP. The architecture depicted in Fig. S3 is applied to one-dimensional problems.
The two architectures have a few training variables in common. Both models use variance scaling initialization, 2 regularization (λ = 10 −6 ), and ReLu activation functions for fully connected (1D architecture) and convolutional (2D architecture) layers. Notably, the two layers immediately before and after the latent space do not have activation functions. A normalized mean squared error loss function is used for all of the loss functions, as described in the manuscript. The models are trained in batches of 64 samples.
The 2D architecture utilizes convolutional layers and pooling layers, as shown in Figs. S1 and S2. All convolutional layers use a kernel size of 4 × 4. There are differences between the convolutional layers in the encoder and the convolutional layers in the decoder. The encoder convolutional layers use a stride size of 1 × 1 and an increasing number of filters (8, 16, 32, 64). The deconvolutional layers use a stride size of 2 × 2 with decreasing filter size (32, 16, 8). Pooling layers are similar for both the encoder and decoder with a stride size of 2 × 2 and a pool size of 2 × 2.
Additional Results
The repeatability of the results and models learned by the DeepGreen architecture are interesting to study from the perspective of operator convergence and latent space representations. In both cases, we aim to investigate the convergence of the model parameters to determine if the learned latent spaces and operators are unique or non-unique.
Operator Initialization
We repeat the training procedure for DeepGreen with three different initialization approaches for the operator L. Again, we train with data from the example nonlinear cubic Helmholtz model. This experiment focuses on comparing the initial values of the operator L with the final values of the operator at the end of training to determine if the DeepGreen approach tends to converge to a specific operator construction. The results in Fig. S4 show the initial and final operator for identity-initialized, randomly initialized, and Toeplitz-initialized operator matrices. Impressively, the result shows that the network tends to learn operators with diagonal dominance for all of the tested initialization strategies. This approach, which DeepGreen appears to prefer, draws strong parallels to the coordinate diagonalization approach commonly used in physics.
3/6
Supplementary Figure S4. Initial vs learned operators for an operator matrix L for different initial conditions. The top row shows identity matrix initialization, the middle row shows random initialization (He normal), and the bottom row shows a Toeplitz gradient initialization.
Latent Space Analysis
We repeat the training procedure for the example system, the nonlinear cubic Helmholtz model, a total of one hundred times. A single sample was selected from the training data and the latent space representation, v i and f i , of the input vectors u i and F i are computed. Statistics for the latent space representations are presented in Fig. S5. It is evident that the latent space vectors are not identical between runs, and that the values in the vector do not follow any particular statistical distribution. This information implies that the learned weights in the model and the learned latent space representations vary for each training instance and do not appear to converge to a single representation.
Residual network architecture
All of the autoencoders used in this work use a residual network (ResNet) architecture. In order to demonstrate the advantage of the ResNet architecture, we trained six models using the DeepGreen architecture for each of the four systems. Three of the models use the ResNet skip connections, while three do not use the ResNet architecture.
For the two simplest systems, the nonlinear cubic Helmholtz equation and the nonlinear Sturm-Liouville equation, the difference between the models with and without the ResNet skip connections was negligible. For the nonlinear cubic Helmholtz equation, the mean validation loss for the non-ResNet models was 2.7 × 10 −3 and the median validation loss was 2.4 × 10 −3 . Using the ResNet architecture resulted in a mean validation loss of 3.5 × 10 −3 and a median validation loss of 8.8 × 10 −4 . The ResNet architecture resulted in a lower median validation loss but a higher mean due to one of the three models performing much more poorly than the other two. The results for the nonlinear Sturm-Liouville system are analogous. With a non-ResNet architecture, the mean validation loss was 4.5 × 10 −3 and the median validation loss was 4.0 × 10 −3 . With a ResNet architecture, the mean validation loss was 5.7 × 10 −3 and the median validation loss was 3.1 × 10 −3 . Therefore, the use of the ResNet architecture produced similar results to a non-ResNet architecture for these two simple systems.
For the two systems that had larger losses -the nonlinear biharmonic equation in 1D and the 2D nonlinear Poisson
Comparison to baseline solvers
The DeepGreen architecture has several advantages over traditional BVP solvers with speed being one of the most striking. In order to demonstrate this, we performed speed tests of DeepGreen versus the numerical solvers that we used to generate the training and test data: MATLAB's bvp5c for the one-dimensional data and the finite element method of the DOLFIN library for the two-dimensional data. All speed tests were performed on a MacBook Pro with a 2.3 GHz Quad-Core Intel Core i7 processor and 32 GB of RAM. We recorded the time it took to solve the BVPs for each of the four model systems using the cubic polynomial forcing functions described above. The times in seconds are given in Supplementary Table S1. The last column gives the time using the traditional solver divided by the time using DeepGreen (labeled as "Speed up"). In all cases, the DeepGreen method is orders of magnitude faster than the traditional solver with the difference being most extreme for the one-dimensional systems. One thing to note is that the times given for DeepGreen are conservative. As it is currently implemented, the predict method of the DeepGreen architecture takes a forcing function as input and outputs a prediction of the solution to the BVP, but it also takes a solution as input and outputs a prediction of the forcing function corresponding to that solution. Additionally, it runs both the forcing function and solution through their respective autoencoders. The times given in Supplementary Table S1 include all four of those evaluations and not just the time needed to produce a solution given a forcing function.
For several of the cubic polynomial forcing functions, MATLAB's bvp5c did not converge for the nonlinear biharmonic equation due to an initial guess that was outside the radius of convergence. This cannot happen for DeepGreen since no initial guess is required. In order to circumvent the issue of a poor initial guess, the BVP can be solved using a continuation method. However, this would require many nonlinear equation solves and the speed difference would be even more stark. | 2,707.6 | 2020-12-31T00:00:00.000 | [
"Computer Science"
] |
Study on the Impact of Collaborative Agglomeration of Manufacturing and Producer Services on PM2.5 Pollution: Evidence from Urban Agglomerations in the Middle Reaches of the Yangtze River in China
In this paper, using panel data of 28 cities in the middle reaches of the Yangtze River from 2003 to 2020 as the research sample, we built a dynamic spatial Durbin model based on the STIRPAT (stochastic impacts by regression on population, affluence, and technology) model and conducted an empirical study on the impact of the coordinated agglomeration of manufacturing and producer services on particulate matter (PM) 2.5 pollution. The results show a significant positive spatial spillover effect of PM2.5 pollution in the middle reaches of the Yangtze River. The coordinated agglomeration of manufacturing and producer services in the urban agglomerations there is conducive to reducing PM2.5 pollution. Similar to the inverted-U curve of the classic environmental Kuznets curve hypothesis, there is a significant inverted-U curve relationship between PM2.5 pollution and economic growth in urban agglomerations in the middle reaches of the Yangtze River. The proportion of coal consumption, the proportion of secondary industry, and the urbanization level are significantly and positively correlated with PM2.5 pollution in urban agglomerations in this area. Technological innovation, environmental regulation, and annual average humidity play an important role in addressing the PM2.5 pollution and spatial spillover effect. Industrial structure and technological innovation are the main ways for the coordinated agglomeration of manufacturing and producer services to affect PM2.5. The research conclusion can be of great practical significance to optimize the regional industrial layout, control PM2.5 pollution, and establish a sustainable development policy system in the middle reaches of the Yangtze River in China.
Introduction
With the rapid development of industrialization and urbanization, the urban air pollution problem is becoming increasingly serious, posing challenges to the human living environment and the sustainable development of society [1]. Particulate matter (PM) 2.5 is one of the most common air pollutants. PM 2.5 has had profound effects on socioeconomics, the ecological environment, and human health [2]. Studies have shown that PM 2.5 is toxic, causing respiratory diseases and even cancer [3,4]. The urban agglomeration in the middle reaches of the Yangtze River is the largest urban agglomeration in China and also one of the areas with a particularly serious haze pollution problem. According to the air quality index from 2015 to 2018 released by the Ministry of Environmental Protection in China, the average number of days in the middle reaches of the Yangtze River clusters was 247 days [5]. Therefore, research on PM 2.5 pollution in the middle reaches of the Yangtze River is needed. This study will have a positive significance for promoting regional ecological environmental protection and realizing economic, societal, and ecological environment sustainability. The environmental Kuznets curve (EKC) reveals that there is an inverted-U curve relationship between economic growth and environmental pollution in developed countries. This theory holds that after economic development reaches a certain extent, the role of economic growth on environmental quality will shift from inhibition to promotion [6]. From the perspective of economic development, the aggravation of environmental pollution is closely related to the extensive development mode, excessive proportion of coal consumption, lagging industrial structure, low environmental governance, and other factors [7]. The manufacturing industry is the core part of the industrial system that is dominated by the real economy, which effectively promotes the development of regional industrialization and urbanization [8]. The rapid development of the manufacturing industry is often accompanied by serious environmental pollution [9]. At present, China's traditional manufacturing industry still has problems such as ecological environmental pollution, high resource energy consumption, and a lack of scientific and technological innovation capacity [10][11][12].
In recent years, with the transformation from the industrial economy to the service economy and knowledge economy as well as the refinement of the industrial division of labor, production services are gradually becoming separated from the manufacturing industry and have formed a phenomenon of synergistic agglomeration with the manufacturing industry. The coordinated agglomeration of the manufacturing industry and producer services is also considered an important factor affecting regional industrial upgrading, technological progress, energy conservation, and emissions reduction [13][14][15]. Industrial collaborative agglomeration refers to the spatial interdependence phenomenon among heterogeneous industries with a high correlation degree. This concept was first proposed by Ellison [16]. The generation mechanism of the collaborative agglomeration effect is mainly centered around the idea of Marshall space externalities, that is, the connection between intermediate inputs and end-product suppliers, sharing the labor market, increases information exchange and innovation opportunities [17,18]. Although scholars have carried out a lot of studies on the environmental effects of collaborative agglomeration, their conclusions are not consistent. On the one hand, industrial collaborative agglomeration may improve production efficiency and energy utilization efficiency through benign interaction between the external economy and industries [19,20], which can reduce regional economic growth while promoting environmental pollution [21][22][23]. On the other hand, industrial collaborative agglomeration may also further aggravate regional environmental pollution due to the crowding effect [24,25]. An industrial collaborative agglomeration is a special form in the process of the dynamic development of industrial agglomeration. With capital, talent, technology, and information as the carriers, it is the expression of the collaborative division of labor [26]. The existing research mainly measures the spatial co-agglomeration relationship between the manufacturing industry and producer services from the perspective of industrial agglomeration. The methods of industrial agglomeration measurement mainly include industry concentration [27], location entropy [28], the Huffender-Herschmann index [29], and the geographic concentration index [16]. Then, as the largest urban agglomeration in China, the coordinated agglomeration of manufacturing and producer services in the middle reaches of the Yangtze River has promoted local PM 2.5 pollution or alleviated local PM 2.5 pollution through its technical spillover effect. How to address local PM 2.5 pollution in the Yangtze River Delta urban area needs to be explored in depth, and existing studies have not provided clear empirical evidence.
The air pollution of urban agglomerations is characterized by seasonality, location, and industrial correlation [30,31]. Studies have shown that the emission, meteorological conditions, and topographic factors of pollution sources will have an important impact on air pollution in urban agglomerations [32,33]. At the same time, urbanization not only promotes regional economic development but also brings about environmental pollution problems [34]. The impact of industrial development on the environment will be affected by economic scale, environmental regulation, industrial structure, and production technology [35][36][37]. Therefore, after controlling for economic and natural factors, it is important to explore the impact of the collaborative agglomeration of manufacturing and producer services on PM 2.5 pollution, which is of great practical significance in optimizing the regional industrial layout, controlling PM 2.5 pollution, and establishing a policy system for sustainable development of the urban agglomerations in the middle reaches of the Yangtze River.
Based on this, this paper used panel data of 28 cities in the middle reaches of the Yangtze River from 2003 to 2020 as the research sample, constructed a dynamic spatial Durbin model based on the STIRPAT (stochastic impacts by regression on population, affluence, and technology) model, and conducted an empirical study on the impact of the collaborative agglomeration of manufacturing and producer services on PM 2.5 pollution. There are three main innovations in this paper: (1) In terms of the research area, the urban agglomeration was taken as the research object, especially the urban agglomerations in the middle reaches of the Yangtze River, and the data of prefecture-level cities were used to capture the spatial effect of PM 2.5 pollution in detail. (2) The joint inclusion of natural factors and economic factors as control variables in the model made the empirical results more reliable compared to traditional studies that focus only on economic variables. (3) Based on the lighting composite index, the urban agglomerations in the middle reaches of the Yangtze River can measure the urbanization level based on global nighttime light data to avoid the possible statistical error of the urbanization rate that only considers the representation of the urban population proportion.
The rest of this paper is organized as follows: Section 2 presents the theoretical analysis and research hypotheses; Section 3 presents the study area, theoretical models, and data sources; Section 5 presents the empirical results; Section 4 presents the discussion; and Section 6 presents the conclusions and policy implications. The collaborative agglomeration effect among industries is mainly realized through externalities [16,17]. The collaborative agglomeration of the manufacturing industry and producer services can affect environmental pollution by deepening the division of labor, technological innovation, and spatial externalities [38]. Collaborative agglomeration makes the spillover effect of internal technologies more obvious, which can accelerate the research and development of clean energy technologies and promote the application of advanced technologies such as energy conservation and emission reduction in the manufacturing industry under the influence of technology. Collaborative agglomeration can enhance the effect of economies of scale, reduce the energy consumption per unit output through increasing the income from scale, and promote the centralized consumption of resources and the centralized treatment of pollutants so as to improve the efficiency of resource allocation. Collaborative agglomeration can improve the agglomeration level and professional capacity of producer services, while the agglomeration of producer services can provide more perfect production supporting services for local manufacturing enterprises, improve the service level of the manufacturing industry, and thus reduce the emission of air pollutants [39]. Based on this, we propose Hypothesis 1 (H1).
H1:
The coordinated agglomeration of manufacturing industry and producer services can reduce the degree of PM 2.5 pollution.
The Collaborative Agglomeration of Manufacturing Industry and Producer Services and the Transmission Mechanism of PM 2.5 Pollution
The coordinated agglomeration of the manufacturing industry and producer services can accelerate the interaction and integration between the two industries [19,20]. By increasing the input of human capital, technical capital, and other service factors, the structure of factor input and factor allocation are optimized, promoting the innovation of the production paradigm and then the green development of the industrial chain [36]. At the same time, the knowledge production and knowledge service functions of producer services make high-tech industries focus more on their core production links, and promote the traditional manufacturing industries associated with upstream and downstream industries to accelerate product upgrading and process improvement, and thus reduce the emission of air pollutants. Based on this, we propose Hypothesis 2 (H2).
H2:
The coordinated agglomeration of manufacturing industry and producer services will reduce the degree of PM 2.5 pollution by affecting the regional industrial structure.
The collaborative agglomeration of industries enables the manufacturing industry to enjoy the intermediate input of high-added value and high-technology content provided by productive services more conveniently and improves the overall technological innovation level of the manufacturing industry through knowledge and technology spillover [40]. At the same time, the collaborative agglomeration of industries reduces the innovation cost of high-tech industries through face-to-face service, stimulates the innovation power of enterprises, and promotes innovative development [41]. Technological innovation can catalyze the scale effect and substitution effect of the agglomeration area, improve energy efficiency, and reduce pollution emissions [42]. Based on this, we propose Hypothesis 3 (H3).
H3:
The coordinated agglomeration of manufacturing and producer services will reduce the degree of PM2.5 pollution by affecting the technology level.
Study Area
The urban agglomeration in the middle reaches of the Yangtze River is the first superlarge national urban agglomeration recognized by the Chinese government. From the perspective of spatial location, the urban agglomeration in the middle reaches of the Yangtze River connects the east to the west and the south to the north (Figure 1). Urban agglomerations in the middle reaches of the Yangtze River plays an important role in China's regional development pattern. Recent years have seen remarkable economic and social development in the urban agglomerations in the middle reaches of the Yangtze River, but environmental problems have become increasingly prominent [43,44]. The natural conditions and economic and social differences between the urban agglomeration in the middle reaches of the Yangtze River and that in the Beijing-Tianjin-Hebei region, the Yangtze River Delta, and the Pearl River Delta are mainly reflected in four aspects: (1) The urban agglomeration in the middle reaches of the Yangtze River is the largest urban agglomeration in China. It covers an area of 326,000 square kilometers, 1.5 times that of the Beijing-Tianjin-Hebei region and the Yangtze River Delta urban agglomeration, and six times that of the Pearl River Delta. (2) The urban agglomeration in the middle reaches of the Yangtze River has a developed water system, and its river distribution density is 0.557 km/km 2 , second only to the Yangtze River Delta urban agglomeration (0.78 km/km 2 ) [45]. (3) The per capita GDP of the urban agglomeration in the middle reaches of the Yangtze River is relatively low. In 2021, the per capita GDP of the urban agglomeration in the middle reaches of the Yangtze River was CNY 73,800, much lower than that of the Beijing-Tianjin-Hebei urban agglomeration (CNY 117,300), the Yangtze River Delta urban agglomeration (CNY 123,500), and the Pearl River Delta urban agglomeration (CNY 153,000). (4) The urban agglomeration in the middle reaches of the Yangtze River is still in the middle stage of urbanization. In 2021, the urbanization rate of the urban agglomeration in the middle reaches of the Yangtze River was 61.75%, which lags behind the Beijing-Tianjin-Hebei urban agglomeration (65.8%), the Yangtze River Delta urban agglomeration (73.83%), and the Pearl River Delta urban agglomeration (80%).
Tianjin-Hebei urban agglomeration (CNY 117,300), the Yangtze River Delta urban agglomeration (CNY 123,500), and the Pearl River Delta urban agglomeration (CNY 153,000). (4) The urban agglomeration in the middle reaches of the Yangtze River is still in the middle stage of urbanization. In 2021, the urbanization rate of the urban agglomeration in the middle reaches of the Yangtze River was 61.75%, which lags behind the Beijing-Tianjin-Hebei urban agglomeration (65.8%), the Yangtze River Delta urban agglomeration (73.83%), and the Pearl River Delta urban agglomeration (80%).
Model
The STIRPAT (stochastic impacts by regression on population, affluence, and technology) model originates from the IPAT (Impact = Population × Affluence × Technology) equation [46,47]. The expression for the IPAT equation is: where I represents environmental load; P represents population size; A represents affluence; and T represents the technical level. York et al. constructed a STIRPAT model based on the IPAT equation [48], which is expressed as follows: where a is a constant; b, c, and d are the index terms of P, A, and T, respectively; and is an error term. In Equation (2), I, P, A, and T have the same meaning as in Equation (1). To eliminate possible heteroscedastic effects in model (2), all variables were extended [49]. The logarithmic-extended STIRPAT model is as follows (3): The advantage of the STIRPAT model is its scalability, and the explanatory variables allow it to add more relevant influencing factors to explore its impact on the environment [50]. To explore the effect of the collaborative agglomeration of manufacturing and producer services on PM2.5 pollution emission in the middle reaches of the Yangtze River in
Model
The STIRPAT (stochastic impacts by regression on population, affluence, and technology) model originates from the IPAT (Impact = Population × Affluence × Technology) equation [46,47]. The expression for the IPAT equation is: (1) where I represents environmental load; P represents population size; A represents affluence; and T represents the technical level. York et al. constructed a STIRPAT model based on the IPAT equation [48], which is expressed as follows: where a is a constant; b, c, and d are the index terms of P, A, and T, respectively; and ε is an error term. In Equation (2), I, P, A, and T have the same meaning as in Equation (1). To eliminate possible heteroscedastic effects in model (2), all variables were extended [49]. The logarithmic-extended STIRPAT model is as follows (3): The advantage of the STIRPAT model is its scalability, and the explanatory variables allow it to add more relevant influencing factors to explore its impact on the environment [50]. To explore the effect of the collaborative agglomeration of manufacturing and producer services on PM 2.5 pollution emission in the middle reaches of the Yangtze River in China, an extended STIRPAT model was constructed after logarithmic based on the study of Zhu [51], which is expressed as follows: where PM 2.5 represents PM 2.5 pollution; ICA represents the coordination and agglomeration of the manufacturing industry and producer services; P represents population density; A represents economic development level; T represents technical level; X represents the control variable group; a represents a constant and b, c, d, e, f, g, and h are index items; i represents the city; t represents the year; u i represents the fixed effect of city i that controls for features that do not change over time; v t represents the annual fixed effect, used to control the time-varying omitted variables and random shocks common to all cities; and ε it represents the error term.
This study comprehensively considers the spatial spillover (Appendix A provides a spatial autocorrelation test) and lag effects [52] in the presence of PM 2.5 pollution. We constructed a dynamic space measurement model based on Equation (4). The specific model is as follows: where w represents the spatial weight matrix; ρ represents the spatial factor of the dependent variable; τ represents the dynamic factor of the dependent variable. In Equation (5), PM 2.5 , P, A, T, ICA, and X have the same meaning as in Equation (4). This study considers the endogenous problem of the economic distance matrix [53], so we adopted the inverse distance matrix as the spatial weight matrix.
Variables Selection
In this study, PM 2.5 concentration was used to measure PM 2.5 pollution in urban agglomerations in the middle reaches of the Yangtze River. The core explanatory variable of this study is the co-agglomeration of the manufacturing industry and producer services, as measured by the industrial co-agglomeration index. Considering the research purpose and the availability of data in this paper, we should make reference to the idea of collaborative agglomeration among industries proposed by Ellison [16] and refer to the practice of Liu [54]. This paper first used the location entropy index to measure the agglomeration index of the manufacturing industry and producer service industry. Then, the cooperative agglomeration situation of the manufacturing industry and producer service industry was calculated based on the difference in the economic activity agglomeration index. The calculation formula is as follows: where ICA ij represents the j year collaborative agglomeration index of the manufacturing industry and producer services in region i; MAG ij represents the location entropy index of the j year manufacturing industry in region i; PAG ij represents the location entropy index of the j year producer services industry in region i; Q mij and Q pij respectively indicate the number of employees in the manufacturing industry and producer service industry in i region in j year; Q mj and Q pj respectively indicate the employment figure in manufacturing and producer services in the j year; Q ij is the sum of the employment figure of manufacturing and producer services in i region in year j; and Q j is the sum of employment in manufacturing and producer services in China. The greater the value of ICA ij , the higher the agglomeration degree of the two industries, and the more significant the synergism.
The control variables in this study included two parts: economic factors and natural factors. The economic factors were as follows: (1) Population density, characterized by the population per unit area [7], was expected to have a positive sign. (2) The economic development level was characterized by per capita GDP. According to the EKC hypothesis, both the primary and quadratic terms of per capita GDP were introduced into the model [55].
(3) Technical level, measured by the number of patents applied for in the current year, had a negative overdue limit. (4) Industrial structure, using the proportion of the added value of the secondary industry (including total industry and the construction industry), was measured by GDP. The process of industrialization leads to a large amount of fossil energy consumption and pollution emissions. At the same time, the rapid development of the construction industry has also increased the demand for highly energy-intensive products such as steel and cement [56,57]. The symbol was expected to be positive. (5) Energy structure was characterized by the proportion of coal consumption in the total energy consumption measurement [58]. The combustion of coal is an important source of PM 2.5 pollution and was expected to be positive. (6) The level of opening up was measured by the total amount of foreign direct investment (FDI). Concerning the impact of FDI on environmental pollution, the academic community has formed two hypotheses: the pollution haven hypothesis and the pollution halo hypothesis. The former argues that FDI, through introducing a high-pollution industry in the host country, deteriorates the host country's environmental quality, and the latter argues that FDI can introduce environmentally friendly products and technology to improve environmental quality [59]. Thus, the impact of FDI on PM 2.5 pollution is uncertain. (7) To measure environmental regulation, the word frequency method was used to calculate environmental protection-related words in government reports to obtain the intensity coefficient of environmental regulation [60], and the expected symbol was negative. (8) The level of urbanization was characterized by the stable nighttime light data released by NOAA (National Oceanic and Atmospheric Administration) [61]. The urbanization process was accompanied by the agglomeration of population and factors, and the impact of the agglomeration process on environmental pollution is uncertain [62]. (9) Natural factors include average annual temperature, average annual relative humidity, and average annual wind speed [63,64].
Data Sources
Based on the availability and completeness of the data, we built a complete panel dataset using data from 28 cities in the middle reaches of the Yangtze River during the period 2003-2020. Concentration data for PM 2.5 were obtained from Washington University, St. Louis, MI, USA [65]. Stable light data were from the NOAA [66,67]. The data for the other variables in this paper were obtained from the China Urban Statistical Yearbook (2004-2021) [68], the Statistical Yearbook of Jiangxi Province (2004-2021) [69], the Statistical Yearbook of Hubei Province (2004-2021) [70], and the Statistical Yearbook of Hunan Province (2004-2021) [71]. The manufacturing industry studied in this paper mainly includes 13-43 categories classified in the Industry Classification of the National Economy (GB/T4754-2017) [72]. According to the Statistical Classification of Producer Services (2019), there are seven categories of producer services [73]. Table 1 shows the descriptive statistics of the variables. GDP is based on 2002 data adjusted using the GDP deflator, which is actual GDP excluding price changes.
Inspection of the Spatial Measurement Models
According to the model setting, we used the spatial autoregressive model (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM) as alternative models and analyzed them with Stata/SE16.0 (StataCorp, Lakeway, TX, USA). First, the appropriate spatial measurement model was selected via the Wald test and the likelihood-ratio test ( Table 2). The results showed that the explanatory variable had a significant spatial spillover effect, indicating that the results rejected the null hypothesis, which showed that the SDM model cannot be simplified to the SAR model or the SEM model (Table 3). Therefore, the fixed-effect SDM model was used as the main tool for the empirical analysis.
Estimation Results for the Spatial Panel Durbin Model
The regression results in Table 4 show that the coordinated agglomeration of the manufacturing industry and producer services has a negative impact on PM 2.5 pollution, which shows that the coordinated agglomeration of the manufacturing industry and producer services is conducive to alleviating PM 2.5 pollution in the urban agglomerations in the middle reaches of the Yangtze River. The collaborative agglomeration of manufacturing industries and producer services may improve the local level of pollution by improving local production efficiency or environmental protection technology, or by spreading environmental awareness and sharing green management experience. With the classical EKC hypothesis that there is an inverted-U curve, the coefficient of the economic development index is positive and negative, and all data points are significant at the level of 1%, indicating that there is a significant inverted-U curve relationship between PM 2.5 pollution and economic growth, namely that the degree of PM 2.5 pollution increases with the economic growth level. Both industrial structure and energy structure have a significant positive impact on PM 2.5 pollution, which is consistent with the conclusion of most studies on the relationship between industrial structure and environmental pollution [7]. This paper also found that the increased proportion of secondary industry will aggravate PM 2.5 pollution. The increase in coal consumption has a significant effect on PM 2.5 pollution, which is consistent with our expectations. The level of urbanization has a significant positive effect on PM 2.5 pollution. It shows that the influence of urbanization levels on PM 2.5 pollution is mainly reflected in the scale effect. This is because the urban agglomerations in the middle reaches of the Yangtze River are at a relatively early stage of urbanization. Urbanization has generated a large amount of demand for infrastructure construction, which has driven the excessive growth of the heavy chemical industry with high energy consumption and high emissions characteristics, such as cement and steel, and caused a large amount of energy consumption and environmental pollution [62]. FDI has a significant positive effect on PM 2.5 pollution. It shows that the technology spillover effect brought by FDI to the middle reaches of the Yangtze River is not obvious. The coefficient of environmental regulation intensity and technical innovation is significantly negative, indicating that government environmental regulation effectively suppresses PM 2.5 pollution. Among the natural factor control variables, annual mean humidity has a significant negative effect on PM 2.5 pollution, probably because increased air humidity helps inhibit aerosol formation and thus reduces PM 2.5 pollution; population density and other natural indicators were not significant.
Decomposition of Direct and Indirect Effects
Referring to the study of LeSage and Pace, we further decomposed the effects of each factor on PM 2.5 pollution into direct effects and indirect effects [74]. Because this paper uses a dynamic spatial panel data model, we discuss empirical results for the long-term effects of time lag effects.
Observation Table 5 shows that the direct effect of the control variables on PM 2.5 contamination in this region is in line with the aforementioned analysis of the regression estimation results. Both the direct and indirect effects of the collaborative agglomeration of the manufacturing industry and producer services are significantly negative, indicating that the coordinated agglomeration of the manufacturing industry and producer services in the urban agglomerations in the middle reaches of the Yangtze River has an effect on reducing the PM 2.5 pollution in the surrounding areas. This result proves that Hypothesis 1 is correct. The possible explanation is that, on the one hand, the employment opportunities brought by the coordinated agglomeration of the manufacturing industry and producer services contribute to population migration from the surrounding underdeveloped areas to the developed areas, and the environmental pollution scale effect of population agglomeration in these areas is weakened. On the other hand, under the pressure of performance assessment or promotion, local governments have the imitation effect of industrial green development. The direct and indirect effects of economic development have an inverted-U curve relationship, and they are significant at the 1% level. This result shows that in the early stage of economic development, the difficulty of PM 2.5 pollution control in the middle reaches of the Yangtze River and its surrounding areas will intensify. However, as the level of economic development continues to rise, the PM 2.5 pollution in this region and its surrounding areas will decrease. The reason for this situation may be that economic improvement will drive improvements in energy-saving technology and pollution control technology. Both the direct and indirect effects of energy structure and industrial structure are significantly positive. This shows that the increase in the proportion of coal consumption in the urban agglomeration of the middle reaches of the Yangtze River is not conducive to the improvement in PM 2.5 pollution in the surrounding areas. The positive relationship between the degree of urbanization and PM 2.5 concentration indicates that the current urbanization pattern will still increase the pollution level of PM 2.5 in the middle reaches of the Yangtze River in the long term. Both the direct and indirect effects of FDI were significantly positive, consistent with the pollution haven hypothesis. Finally, both the direct and indirect effects of technological innovation and environmental regulation are significantly negative, which is conducive to PM 2.5 pollution control in the surrounding cities. In the natural factor control variables, the direct and indirect effects of annual average humidity were negative and significant. The results prove that the climatic characteristics of urban agglomerations in the middle reaches of the Yangtze River play an important role in the diffusion of PM 2.5 pollution. However, the direct and indirect effects of population density and other natural factors were not significant.
Robustness Test
Considering the possible extreme values of the variables in this paper, this study used the robustness test of the model by shrinking the data. Tail reduction for all variables at the 5% and 95% levels was re-estimated using an SDM model with spatial fixed effects. According to Tables 6 and 7, the overall estimation results of the model tended to be the same as the aforementioned benchmark regression results. Although the estimation coefficient of individual variables was slightly different, the fundamental change in direction and significance and the fitting degree of significance were good, which shows that the empirical estimation results of the selected model have good robustness.
Analysis of the Influence Path of the Manufacturing and Producer Services Collaborative Agglomeration on PM 2.5 Pollution
According to the analysis above, the coordinated agglomeration of the manufacturing industry and producer services in the middle reaches of the Yangtze River is conducive to alleviating PM 2.5 pollution. To further understand the transmission path of the coordinated agglomeration of manufacturing and producer services, we referred to the method of Baron and Kenny [75], selected the industrial structure and technological innovation as the intermediary variables, and identified the above conduction pathway with the help of the intermediary effect model.
According to Table 8, industrial structure and technological innovation play a partial intermediary role in the influence mechanism of the coordinated agglomeration of manufacturing and producer services on PM 2.5 , which shows that industrial structure and technological innovation are the main ways for the coordinated agglomeration of manufacturing and producer services in the middle reaches of the Yangtze River to affect PM 2.5 pollution. Specifically, when the industrial structure is regarded as an intermediary variable, the estimated coefficient of collaborative agglomeration of manufacturing and producer services is significant at the level of 1%, indicating that the industrial structure of urban agglomerations in the middle reaches of the Yangtze River has some intermediary effect on the influence mechanism of the coordinated agglomeration of manufacturing and producer services on PM 2.5 . This also means that the coordinated agglomeration of manufacturing and producer services can significantly optimize the local industrial structure, thus reducing the PM 2.5 pollution level. Similarly, when technological innovation is regarded as an intermediary variable, the estimated coefficient of collaborative agglomeration of manufacturing and producer services is significant at the level of 10%, indicating that technological innovation in urban agglomerations in the middle reaches of the Yangtze River has some intermediary effect on the influence mechanism of collaborative agglomeration of manufacturing and producer services on PM 2.5 . It can be seen that the impact of the coordinated agglomeration of manufacturing and producer services in the middle reaches of the Yangtze River on PM 2.5 pollution is realized through the industrial structure and technological innovation. The above results prove that Hypotheses 2 and 3 are correct.
Discussion
The urban cluster in the middle reaches of the Yangtze River, one of the first superlarge national urban clusters approved by the Chinese government, is one of the most polluted areas with PM 2.5 in China. Therefore, in the context of high-quality economic and ecological development, it is necessary to explore the impact of the synergistic agglomeration of manufacturing and producer services on PM 2.5 pollution, while considering both economic and natural factors. The empirical results of this study show that there is a significant positive spatial spillover effect of PM 2.5 pollution in the urban agglomerations in the middle reaches of the Yangtze River, and the coordinated agglomeration of manufacturing and producer services is conducive to alleviating PM 2.5 pollution there. The above results support Ellison, Tang, and Wu, who state that industrial collaborative agglomeration may improve production efficiency and energy utilization efficiency through the external economy and benign interaction between industries [17][18][19][20]. Clusters can also be understood as the middle reaches of the Yangtze River urban agglomeration manufacturing, and producer services can enhance the local effect of economies of scale by increasing scale income to reduce energy consumption per unit output, promoting the concentration of resource consumption and centralized management of pollutants, building a circular economic system, improving the efficiency of resource allocation, and manufacturing green development.
In addition to the above results, we also demonstrated the inverted-U curve relationship between PM 2.5 pollution and economic growth in the middle reaches of the Yangtze River, which is consistent with the EKC hypothesis [6,76]. In addition, urbanization, the proportion of secondary industry, and the coal consumption structure will all have a significant positive impact on PM 2.5 pollution in urban agglomerations in the middle reaches of the Yangtze River. Compared with social and economic factors, natural factors play a more stable role in the influence of the manufacturing industry and producer service industry in the urban agglomerations in the middle reaches of the Yangtze River.
Conclusions
In this paper, taking panel data of 28 cities in the middle reaches of the Yangtze River from 2003 to 2020 as the research sample, we built a dynamic spatial Durbin model based on the STIRPAT model and conducted an empirical study on the impact of the coordinated agglomeration of manufacturing and producer services on PM 2.5 pollution. The results show that there is a significant positive spatial spillover effect of PM 2.5 pollution in the middle reaches of the Yangtze River. The coordinated agglomeration of manufacturing and producer services in the urban agglomerations in the middle reaches of the Yangtze River is conducive to reducing PM 2.5 pollution. Following the classic EKC hypothesis, there is a significant inverted-U curve relationship between PM 2.5 pollution and economic growth in urban agglomerations in the middle reaches of the Yangtze River. The proportion of coal consumption, the proportion of secondary industry, and the degree of urbanization are significantly and positively correlated with PM 2.5 pollution in urban agglomerations in the middle reaches of the Yangtze River. Technological innovation, environmental regulation, and annual average humidity play an important role in suppressing PM 2.5 pollution and the spatial spillover effect in the urban agglomerations in the middle reaches of the Yangtze River. Industrial structure and technological innovation are the main ways for the coordinated agglomeration of manufacturing and producer services in the middle reaches of the Yangtze River to have an impact on PM 2.5 pollution. This conclusion can be of great practical significance in optimizing the regional industrial layout, controlling PM 2.5 pollution, and establishing a sustainable development policy system in the middle reaches of the Yangtze River. Based on the above conclusions, the recommendations of this paper mainly focus on the following three aspects.
(1) Based on the advantageous industries of the urban agglomerations in the middle reaches of the Yangtze River, the layout of the manufacturing industry and producer service industry is scientifically coordinated. We will continue to optimize the internal structure of industries and appropriately control the development scale of resource-dependent industries to narrow the gap between the industrial collaborative agglomeration level within urban agglomerations, give full play to the knowledge of the spillover effect between manufacturing and producer services in different cities, and reduce the PM 2.5 pollution degree in urban agglomerations in the middle reaches of the Yangtze River. (2) We will adjust the energy consumption structure of urban agglomerations in the middle reaches of the Yangtze River and reduce the proportion of coal in the energy consumption structure. The proportion of clean energy used should be increased by adjusting the energy structure. At the same time, we will further strengthen the implementation of a series of policies, such as setting emission reduction targets and lowering emissions limits, giving full play to the guiding role of government funds, and encouraging highly polluting enterprises to adopt technological transformation. We will strengthen the rectification and management of industries with high emissions and high pollution and eliminate the illegal discharge of pollutants. We will change the economic development mode and force the green upgrading of industrial structure and energy structure through market environmental regulation.
(3) We will establish a joint PM 2.5 pollution prevention and control mechanism in urban agglomerations in the middle reaches of the Yangtze River. While strengthening the economic and cultural cooperation within urban agglomerations, the cooperation between local governments in air pollution control should also be strengthened. Cross-regional air pollution prevention and control requires cooperation between governments, and only joint governance can achieve real results.
The limitations of this study are as follows: PM 2.5 contamination is the result of the interaction between human activities and natural factors. The degree of PM 2.5 pollution is not only related to the energy structure, FDI, urbanization level, industrial structure characteristics, and other factors; the structure of industrial collaborative agglomeration, industrial distribution, and residents' lifestyles also affect regional PM 2.5 pollution. Our future research will combine the data of subdivided industries, monthly meteorological data, and animal and plant data in the middle reaches of the Yangtze River to discuss the role of the above factors in the coordinated agglomeration of manufacturing and producer services on PM 2.5 pollution and build a more reasonable index system. In addition, we will carry out a study on the differentiation between provinces and cities within the urban agglomeration in the middle reaches of the Yangtze River from the perspective of regional heterogeneity.
Conflicts of Interest:
The authors declare no conflict of interest.
Appendix A
This paper uses the Moran's I index [77] to test whether PM 2.5 pollution exists in the urban agglomeration in the middle reaches of the Yangtze River. The calculation formula is as follows: where I represents the Moran's I index; n represents the 28 prefecture-level cities within the urban agglomeration in the middle reaches of the Yangtze River; x i and x j represent the concentration values of PM 2.5 contamination in cities i and j, respectively; x represents the mean value of the PM 2.5 concentration across all cities; and w ij represents the spatial weight matrix. The Moran's I statistic is valued at [-1, 1], and when the Moran's I symbol is positive (negative), it indicates that the data has a spatial positive (negative) correlation. The value of the Moran's I dataset used for the analysis is directly proportional (inversely proportional) to the spatial aggregation degree, and the greater the absolute value of this value, the more obvious the spatial correlation is. The results of the spatial correlation test (Table A1) showed that the Moran's I index was positive under the inverse distance matrix, and they all passed the significance level test of 1%. The above results indicate a significant positive spatial spillover effect of PM 2.5 pollution in the urban agglomeration in the middle reaches of the Yangtze River. In other words, the local PM 2.5 pollution is affected by the neighboring areas, which is specifically characterized by the spatial distribution of "high-high" and "low-low". Table A1. Moran's I of PM 2.5 pollution in the urban agglomerations in the middle reaches of the Yangtze River based on geographical distance weight matrix.
Year
Moran's I E(I) sd(I) z p-Value | 9,353.4 | 2023-02-01T00:00:00.000 | [
"Economics"
] |
Search for $W' \rightarrow tb$ decays in the hadronic final state using pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
A search for $W'$-boson production in the $W' \rightarrow t\bar{b} \rightarrow q\bar{q}' b\bar{b}$ decay channel is presented using 36.1 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector at the Large Hadron Collider in 2015 and 2016. The search is interpreted in terms of both a left-handed and a right-handed chiral $W'$ boson within the mass range 1-5 TeV. Identification of the hadronically decaying top quark is performed using jet substructure tagging techniques based on a shower deconstruction algorithm. No significant deviation from the Standard Model prediction is observed and the results are expressed as upper limits on the $W' \rightarrow t\bar{b}$ production cross-section times branching ratio as a function of the $W'$-boson mass. These limits exclude $W'$ bosons with right-handed couplings with masses below 3.0 TeV and $W'$ bosons with left-handed couplings with masses below 2.9 TeV, at the 95% confidence level.
Introduction
Several theories beyond the Standard Model (SM) involve enhanced symmetries that predict new gauge bosons, usually called W or Z bosons.The W boson is the mediator of a new charged vector current that can be massive enough to decay into a top quark and a b-quark (as in Figure 1).Many models such as those with extra dimensions [1], strong dynamics [2][3][4][5], composite Higgs [6], or the Little Higgs [7,8] predict new vector charged-current interactions, some with preferential couplings to quarks or third-generation particles [6,[9][10][11][12].Due to the large mass of the top quark, its interactions decouple from the rest of the phenomenology in many theories beyond the SM.An effective Lagrangian is used to capture the relevant phenomenology of the Sequential Standard Model (SSM) [13] W → t b signal [14,15], which has the same coupling strength to fermions as the SM W boson but higher mass.Searches for a W boson decaying into t b,1 classified as either leptonic or hadronic according to the decay products of the W boson originating from the top quark, were performed at the Tevatron [16,17] and the Large Hadron Collider (LHC) in final states that include leptons [18][19][20][21] or that are fully hadronic [22].The specific search for a W boson decaying into t b allows for a right-handed W boson (W R ) in models in which the right-handed neutrino's mass is assumed to be much higher than that of the W boson (m ν R > m W ), which the leptonic decay mode cannot access.In such a model, the branching ratio for a W R boson decaying into t b is O(10%) higher relative to that for a W L boson decaying into t b since a W L boson can also decay to a lepton and neutrino.Limits on a SSM left-handed W boson (W L ) decaying into a lepton and a neutrino have been set previously [23,24].Previous searches in the all-hadronic final state exclude W R bosons with masses up to 2 TeV, set at the 95% confidence level (CL) using 20.3 f b −1 of pp collision data at a centre-of-mass energy ( √ s) of 8 TeV [22].A recent search by the CMS Collaboration in the lepton+jets final state excludes W R -boson masses up to 3.6 TeV using 35.9 f b −1 of pp collision data collected at √ s = 13 TeV [18].
This analysis searches for a W boson decaying into t b with a mass in the range of 1-5 TeV, in the invariant mass spectrum of the top quark and bottom quark (m tb ) reconstructed in the fully hadronic channel.This includes a W R boson that is not kinematically allowed to decay into a lepton and neutrino and a W L boson that can decay into quarks or leptons.The large W mass results in a top quark and a b-quark that have high transverse momentum (p T ). 2 The decay products of the top quark become more collimated as the top-quark p T increases, and their showers partially overlap [25].This high-p T topology is referred to as boosted.The boosted top-quark decay is reconstructed as a single jet.The shower deconstruction (SD) algorithm [26,27] is employed to select, or tag, jets from boosted top-quark decays.A signal would be reconstructed as a localised excess in the m tb distribution rising above the smoothly falling background originating mostly from jets created by the strong interaction described by quantum chromodynamics (QCD).This analysis represents an improvement on the previous ATLAS analysis in this channel [22] due to a higher centre-of-mass energy, higher integrated luminosity, and better top-tagging techniques, understanding of systematic uncertainties, and statistical treatment.
ATLAS detector
The ATLAS detector [28] at the LHC covers almost the entire solid angle around the collision point.Charged particles in the pseudorapidity range |η| < 2.5 are reconstructed with the inner detector (ID), which consists of several layers of semiconductor detectors (pixel and strip) and a straw-tube transition-radiation tracker, the latter covering |η| < 2.0.The high-granularity silicon pixel detector provides four measurements per track; the closest layer to the interaction point is known as the insertable B-layer (IBL) [29].The IBL was added in 2014 and provides high-resolution hits at small radius to improve the tracking performance.
The ID is immersed in a 2 T magnetic field provided by a superconducting solenoid.The solenoid is surrounded by electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroid magnet systems.The calorimeter system covers the pseudorapidity range |η| < 4.9.Electromagnetic calorimetry is performed with barrel and endcap high-granularity lead/liquidargon (LAr) electromagnetic calorimeters, within the region |η| < 3.2.There is an additional thin LAr presampler covering |η| < 1.8, to correct for energy loss in material upstream of the calorimeters.For |η| < 2.5, the LAr calorimeters are divided into three layers in depth.Hadronic calorimetry is performed with a steel/scintillator-tile calorimeter, segmented into three barrel structures within |η| < 1.7, and two copper/LAr hadronic endcap calorimeters, which cover the region 1.5 < |η| < 3.2.The forward solid angle up to |η| = 4.9 is covered by copper/LAr and tungsten/LAr calorimeter modules, which are optimised for energy measurements of electrons/photons and hadrons, respectively.The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers that measure the deflection of muons in a magnetic field generated by superconducting air-core toroids.The ATLAS detector uses a tiered trigger system to select interesting events.The first level is implemented in custom electronics and reduces the event rate from the LHC crossing frequency of 40 MHz to a design value of 100 kHz.The second level is implemented in software running on a general-purpose processor farm which processes the events and reduces the rate of recorded events to ∼1 kHz [30].
Monte Carlo (MC) event generators were used to simulate signal and background events.Signal events were generated at leading order (LO) in QCD by M G 5_ MC@NLO 2.2.3 [31], using a chiral W -boson model in which the coupling strength of the W boson to the right-and left-handed fermions are the same as those of the SM W boson to left-handed fermions.The W L boson can decay into all lefthanded fermions, but the W R boson can decay only into right-handed quarks as the right-handed neutrino is assumed to be more massive than the W R boson.M G was used to simulate the top-quark and W-boson decays, taking spin correlations into account.P 8.186 [32] was used for the modelling of the parton shower, fragmentation and the underlying event.The NNPDF23LO parton distributions function (PDF) set [33] and the A14 set of tuned parameters [34] were used for the event generation.All simulated samples were rescaled to next-to-leading-order (NLO) calculations using NLO/LO K-factors ranging from 1.3 to 1.4, depending on the mass and handedness of the W boson, calculated with Z [15].The width of the M G simulated W boson is set to the NLO Z width calculation, O(3%) of its mass.Signal samples with gauge-boson masses between 1 and 3 TeV were generated in 250 GeV steps, and between 3 and 5 TeV in 500 GeV steps.
The dominant SM background process is multi-jet production.In order to reduce the dependence on the modelling of the simulation a data-driven method is implemented as described in Section 5. Corrections in this method are estimated using QCD dijet simulation produced at LO by P 8.186.Uncertainties in this method are obtained using simulated QCD dijet events produced at LO by H ++ 2.7.1 [35] and S 2.1.1 [36], and at NLO by P -B 2 [37,38] with either P 8 or H +J [39] for the parton shower, fragmentation and the underlying event simulation (referred to as P +P and P +H , respectively).Vector bosons (W/Z) produced in association with jets are included in the data-driven approach.These processes are expected to contribute less than 1% of the multi-jet background.This W/Z+jets prediction is checked using events simulated with the S 2.2.1 [36] generator and the CT10 PDF set [40].
Top-quark pair production is an important background with an inclusive cross-section of σ t t = 832 +46 −51 pb for a top-quark mass of 172.5 GeV as obtained from calculations accurate to next-to-next-to-leading order and next-to-next-to-leading logarithms (NNLO+NNLL) in QCD with T ++2.0 [41][42][43][44][45][46][47].Simulated top-quark pair processes were produced using the NLO P -B 2 generator with the CT10 PDF.The parton shower, fragmentation and the underlying event were added using P v6.42 [48] with the Perugia 2012 set of tuned parameters [49].To increase the number of simulated events at high mass, samples were produced binned in t t mass.Interference and background contributions from the SM s-channel single-top process are found to be negligible and are not considered further in this analysis.
The generation of the simulated event samples includes the effect of multiple pp interactions per bunch crossing, as well as the effect on the detector response due to interactions from bunch crossings before or after the one containing the hard interaction.For all M G , P , P and H samples, the EvtGen v1.2.0 program [50] was used for the bottom and charm hadron decays.The simulated samples were passed through the G 4-based ATLAS detector simulation [51,52] and were reconstructed with the same algorithms as the data events.
Event reconstruction and shower deconstruction 4.1 Event reconstruction
This analysis relies on the reconstruction and identification of jets initiated by the top-and bottom-quark daughters of the W boson. Jets are built from topologically related energy depositions in the calorimeters with the anti-k t algorithm [53] using the FastJet package [54].Two radius parameters are used for jet reconstruction: a small radius (small-R) of 0.4 and a large radius (large-R) of 1.0.The momenta of both the small-R and large-R jets are corrected for energy losses in passive material and for the non-compensating response of the calorimeter [55].Small-R jets are also corrected for the average additional energy due to pile-up interactions [56].Energy depositions from pile-up are removed from large-R jets using the trimming algorithm [57]: the constituents of the large-R jet are reclustered using the k t jet algorithm [58,59] with R = 0.2.Constituent jets contributing less than 5% of the large-R jet's p T are removed.The remaining energy depositions are used to calculate the trimmed-jet kinematics and substructure properties.In order to improve on the angular resolution of the calorimeter, the mass of a large-R jet is computed using a combination of calorimeter and tracking information [60].
Small-R jets are used to identify the jets compatible with originating from a b-quark created either directly from the W boson or from the top-quark decay.Only small-R jets with p T > 25 GeV and |η| < 2.5 (in order to be within the coverage of the ID) are considered in this analysis.Additional p T requirements are applied to enhance the sensitivity of the search (see Section 5).To reduce the number of small-R jets originating from pile-up interactions, a likelihood discriminant, based on track and vertex information, is used to determine whether the primary vertex3 is the origin of the charged-particle tracks associated with a jet candidate and rejects jets originating from pile-up interactions [61].This is done only for small-R jets with p T < 60 GeV and |η| < 2.4.Small-R jets which originate from b-quarks are identified using a multivariate b-tagging algorithm [62,63].Several observables, such as those based on the long lifetime of b-hadrons and the bto c-hadron decay topology, are used as algorithm inputs to discriminate between b-jets, c-jets and other jets.The b-tagging requirement corresponding to an efficiency of 77% to identify b-jets with p T > 20 GeV, as determined from a sample of simulated t t events, is found to be optimal for the statistical significance of this search.This 77% working point (WP) provides rejection factors against light-flavour/gluon jets and c-jets of 134 and 6 respectively [63,64].Jets identified this way are referred to as b-tagged jets.Since the b-tagging factors are measured in a different p T region, an uncertainty is assigned to the extrapolation of the measurement to the high p T region of interest.
Events with reconstructed electrons [65] or muons [66] are vetoed in order to ensure statistical independence of this analysis from analyses using the leptonic decay of the W boson from the top quark [19].Electrons and muons with transverse momenta above 25 GeV and selected with criteria similar to those used in Ref. [67] are considered for this veto.
Boosted-top identification using shower deconstruction
The SD algorithm can be used to identify the jets compatible with the hadronic decay of a W/Z boson, Higgs boson, or a top quark as well as to discriminate between quark-and gluon-initiated jets.In this analysis, an SD-algorithm-based tagger (SD tagger) is used to identify jets originating from the top quark.
The SD tagger calculates likelihoods that a given large-R jet originates from a hadronic top-quark decay or from a high-momentum light quark or gluon.The constituents of the trimmed large-R jet are used to build exclusive subjets [54], and the four-momenta of these subjets serve as inputs to the SD algorithm.These subjets are used as substitutes for individual quarks and gluons originating from the hard scatter.A likelihood weight is calculated for each possible shower history that can lead to the observed subjet configuration.This step is analogous to running a parton shower MC generator in reverse, where emission and decay probabilities at each vertex, colour connections, and kinematic requirements are considered.For each shower history, the assigned weight is proportional to the probability that the assumed initial particle generates the final configuration, taking into account the SM amplitude for the underlying hard process and the Sudakov form factors for the parton shower.A variable called χ SD is defined as the ratio of the sum of the signal-hypothesis weights to the sum of the background-hypothesis weights.For a set {p k i } of N observed subjet four-momenta, where i ∈ [1, N], the value of χ SD is given by: , where P({p k i }|top-quark jet) is built using the weights for the hypothesis that a signal process leads to the observed subjet configuration {p k i } and P({p k i }|gluon/light-quark jet) is built using the weights for the hypothesis that a background process leads to the observed subjet configuration.The perm notation represents the sum over all the shower histories in which signal processes lead to the subjet configuration.The large-R jet is tagged as a top-quark jet if χ SD is larger than a given value, which is adjusted to achieve the desired tagging efficiency.There is an internal mechanism in the SD algorithm to suppress pile-up contributions to the jets, through the application of additional weights in the likelihood ratio, which contain the probability that a subset of the subjets did not originate from the hard interaction but from pile-up [68].
The SD algorithm selects events that are kinematically compatible with a hadronic top-quark decay.The following requirements are made to optimise the algorithm to achieve a balance between good top-quark jet signal selection efficiency and rejection of gluon/light-quark jet backgrounds: the large-R jet has at least three subjets; two or more subjets must have a combined invariant mass in a 60.3-100.3GeV window centred on the W-boson mass; and at least one more subjet can be added to obtain a total mass in a 132-212 GeV window centred on the top-quark mass.
The SD tagger was optimised for this analysis so that it is more efficient for top-quark jet signal selection and gluon/light-quark jet background rejection for p T > 800 GeV compared to the version of the SD tagger first studied by the ATLAS Collaboration [25].This is done by building subjets obtained by using an exclusive k t algorithm [54].First, the k t algorithm with R = 1.0 is run over the large-R jet constituents and the k t reclustering is stopped if the splitting scale [69] is larger than 15 GeV.Once the k t reclustering is stopped the reclustered protojets are used as subjets.The choice of a 15 GeV requirement is based on the expected discrimination between signal and background events.The six highest p T subjets are used as inputs to the SD algorithm.This reduces the computation time needed for the calculation of χ SD , which grows exponentially with the subjet multiplicity, without loss of background rejection power.
The signal efficiency WP of the SD tagger is set by applying a selection on the logarithm of χ SD .The 50% and 80% signal efficiency WPs are used in this analysis (see Section 5).The background rejection for the 50% (80%) signal efficiency WP is 80 (25) for a jet p T of 0.45 TeV and 30 (10) for a p T of 1.3 TeV.The log( χ SD ) variable is studied using samples enriched in hadronically decaying top quarks by selecting t t events where one top quark decays hadronically and the other into lepton+jets for events with large-R jet p T (p J T ) > 420 GeV and |η| (|η J |) < 2.0.To obtain a top-quark-enriched sample, events are selected with two b-tagged jets and either an electron or muon using criteria similar to those used in Ref. [25].The data are found to be consistent with simulation in the log( χ SD ) distribution within the SD tagger uncertainty, described in Section 6, as shown in Figure 2.
Event selection and background estimation
An initial selection of events is made at the trigger level by requiring at least one small-R jet [30] with p T larger than 380 GeV.To ensure that the analysis is performed in the fully efficient regime of the trigger, the p T values of the large-R and small-R jets, used to identify the top-and b-quark daughters from the W -boson decay, are required to be larger than 420 GeV.Candidate events must have at least one primary vertex.
Table 1: Summary of the top-quark jet candidate and b-quark jet candidate selections before categorisation of events into signal and control regions.The selections are defined in Sections 4 and 5.The events satisfying these criteria are grouped into the categories and regions described in Figure 3.
Event reconstruction and selection
Large-R jet (J) p J T > 420 GeV, |η| < 2.0 Small-R jet ( j) p The top-quark jet candidate is selected from the large-R jets satisfying the requirements defined in Section 4. The large-R jet with the largest value of m j + 0.15 × m J , where m j is the mass of the highest-p T small-R jet with minimum p T > 25 GeV with ∆R < 1.0 of the large-R jet and m J is the mass of the large-R jet, is selected as the top-quark jet candidate.This combination enhances the fraction of events where the selected large-R jet is associated with the top quark, since m j is less affected by final-state radiation effects, which are important at high p T [70].The highest-p T small-R jet with p T > 420 GeV and ∆R > 2.0 from the top-quark jet candidate is chosen as the b-quark jet candidate in the event.The top-and b-tagging criteria are applied to the selected top-and b-quark jet candidates after rejecting events in which the b-quark jet candidate has |η| > 1.2.This improves the signal sensitivity at high m tb since the high-p T b-quark jets from the W -boson decay tend to be more central (smaller |η|) than the jets from the multi-jet background.A summary of the top-and b-quark jet candidate selection is shown in Table 1.
Events are divided into two categories: the "1 b-tag in" category and the "0 b-tag in" category.For the "1 b-tag in" category, exactly one b-tagged small-R jet with p T > 25 GeV with ∆R < 1.0 from the top-quark jet candidate is required, while for the "0 b-tag in" category, it is required that there be zero b-tagged small-R jets with p T > 25 GeV within the large-R jet.
The binning of the m tb distribution is chosen to balance the sensitivity coming from the different signal and background distribution shapes against the diminishing statistical sensitivity of the data at high m tb .
Requirements are imposed on the expected number of background events per bin and the bin width is adapted to a resolution function that represents the width of the reconstructed mass peak for each studied W -boson signal sample.For each m tb bin and in each of the "b-tag in" categories, the data sample is divided into six regions by using top-tagging and b-tagging criteria, which are described in Figure 3.The "not loose top-tagged" regions consist of events where the selected top-quark jet candidate fails to meet the loose top-tagged (80% WP) identification criteria, the "loose-but-not-tight top-tagged" regions consist of events where the selected top-quark jet candidate satisfies the loose top-tagged identification criteria but not the tight top-tagged criteria (50% WP) and the "tight top-tagged" regions consist of events where the selected top-quark jet candidate satisfies the tight top-tagged criteria.The signal regions are constructed from events in which the selected small-R jet b-candidate is b-tagged: signal region SR1 consists of events classified as "tight top-tagged, 0 b-tag in", signal region SR2 consists of events classified as "loose-but-nottight top-tagged, 1 b-tag in" and signal region SR3 consists of events classified as "tight top-tagged, 1 b-tag in".A validation region (VR), with negligible signal contamination, is defined to test the performance of the data-driven method of estimating the multi-jet + W/Z+jets background.This region consists of events where the b-candidate is b-tagged, and classified as "loose-but-not-tight top-tagged, 0 b-tag in".The prediction is found to be in agreement with data within uncertainties.
The W -boson signal selection efficiency, for masses below 2.5 TeV, is higher in SR2 and SR3 than in SR1, due to the requirement of zero b-tagged jets with ∆R < 1.0 of the large-R jet ("0 b-tag in" category) in SR1, making the topology less like the signal in SR1.For masses above 2.5 TeV, the signal efficiency is higher in SR1 than in SR2 and SR3 for the same reason: the b-tagging efficiency, decreasing with p T , affects SR2 and SR3 more due to the requirement of the additional b-tagged jet.Thus, the addition of the "0 b-tag in" category improves the signal sensitivity at large W -boson masses.The dominant background from multi-jet production is estimated directly from data using a six-region "2D sideband" method that predicts both the shape and normalisation of the m tb distribution.These regions are shown in Figure 3.The amount of multi-jet + W/Z+jets background in the signal regions and in the VR is estimated bin-bybin in the m tb distribution using the observed number of events in the control regions after subtracting the contribution from t t events: where "bkg" stands for multi-jet background and W/Z+jets background, N bkg A and N bkg B are the numbers of multi-jet + W/Z+jet background events in regions A and B estimated using this method; N data k and N t t k (k = C, D, E, F) are the numbers of observed events and the expected number of t t events in each region, respectively.The correlation between the top-and b-tagging variables (R corr ) is evaluated using five simulated QCD dijet samples as: where N dijet MC is the number of events predicted by QCD dijet simulation in a given region.The prediction by P is used to correct for this correlation, while the difference between the predictions of the correlation by other QCD dijet simulations (see Section 3) is used to determine the systematic uncertainty of this 2D sideband method.Experimental systematic uncertainties (see Section 6) are found to have a negligible impact on R corr .The value of R corr is found to depend on the signal region and varies between 0.6 at low m tb and 1.3 at high m tb .
The event yields in the different regions considered are shown in Table 2.The multi-jet background makes up more than 90% of the total background in SR1, SR2 and VR, and 75% of the total background in SR3.The contribution of t t events is 4%, 9% and 25% of the total background in SR1, SR2 and SR3.The data are well described by the background model.For regions C, D, E and F, the number of multi-jet + W/Z+jets is equal to the number of data events after subtracting the t t contribution.
Table 2: Event yields in the different regions including the signal regions, SR1, SR2 and SR3.Also shown are the total systematic uncertainties in the estimate of the multi-jet + W/Z+jets and t t backgrounds in the different regions.The numbers in parentheses are the percentage fractions of the total background.For regions C, D, E and F, the number of multi-jet + W/Z+jets is equal to the number of data events after subtracting the t t contribution.
Systematic uncertainties
The sources of systematic uncertainty can be broadly divided into three groups: those of experimental nature, those related to the modelling in simulation, and those related to the data-driven multi-jet background estimation.
The simulated samples are affected by uncertainties related to the description of the detector response.The dominant detector-related systematic effects are due to the uncertainties in the jet energy scale (JES) and resolution (JER) [71], in the b-tagging efficiency and mistag rate [63] and in the top tagging.The main contributions to the uncertainties in the small-R JES, derived as a function of jet p T and η, are related to in situ calibration, the dependence on the pile-up activity and on the flavour composition of jets [55,72].The uncertainty in the scale and resolution of large-R jet energy and mass is evaluated by comparing the ratio of calorimeter-based to track-based measurements in multi-jet data and simulation [25,60].The flavour-tagging efficiency and its uncertainty for b-jets [62] is estimated in t t events, while the misidentification rate for c-jets and other jets and their corresponding uncertainties are determined using a t t-enriched region and multi-jet events, respectively.The SD top-tagging uncertainty is estimated by varying the p T of the subjets used as inputs to the SD algorithm by 2.5%.This value is derived using a procedure described in Ref.
[25] and is found to cover any data/simulation differences in the log χ SD distribution (see Figure 2).Systematic uncertainties in the lepton veto are found to have a negligible effect.
Flavour-tagging simulation-to-data efficiency correction factors [62] depend on the jet p T and η.These correction factors have several sources of uncertainty.They are split into uncorrelated components that are then treated independently.Additional uncertainties are considered in the extrapolation of the b-quark jet and c-jet efficiency calibration from low p T , where there is enough data to make a measurement, to high p T .
The average number of interactions per bunch crossing is rescaled in simulation by 9% to improve agreement with data, and an uncertainty, as large as the correction, is assigned.Finally, a global normalisation uncertainty of 2.1% is assigned due to the uncertainty in the luminosity measurement.It is derived, following a methodology similar to that detailed in Ref. [73], from a calibration of the luminosity scale using x-y beam-separation scans performed in August 2015 and May 2016.
The multi-jet background uncertainties pertain primarily to the estimation method itself.Simulation predictions for the correlation between top-and b-tagging criteria in the multi-jet background estimation are one source of uncertainty; different event generators are compared to account for differences in modelling of the matrix element and parton showering.The uncertainty in the total background yield arising from the contribution of multi-jets is 15% in SR1, 22% in SR2 and 22% in SR3.
The second largest background, from t t events, is assigned a 6% normalisation uncertainty corresponding to the uncertainty in the production cross-section.An additional uncertainty in the modelling of this background is derived from data/simulation differences observed in the top-quark p T spectrum in t t differential cross-section measurements [67].This uncertainty has an approximately linear dependence on m tb .It is 13% at m tb = 1 TeV, 31% at m tb = 2 TeV, 48% at m tb = 3 TeV and 65% at m tb = 4 TeV.
The total systematic uncertainty in the background yield is dominated by uncertainties in the 2D sideband method and in the flavour-tagging efficiencies.The dominant systematic uncertainty in the signal yield is due to uncertainties in flavor tagging and top tagging efficiencies.The impact of theoretical uncertainties in the signal acceptance on the results of the analysis is negligible.The statistical uncertainty of the data dominates for m tb > 2 TeV.
Statistical analysis and results
In order to test for the presence of a massive resonance, templates in the variable m tb obtained from the simulated signal event samples and the background events estimated using data-driven methods and simulation, are fit to data, using a binned maximum-likelihood approach based on the RooStats framework [74,75].The fits are performed simultaneously in the three signal regions (see Section 5).The background processes considered in the maximum-likelihood fit are the dominant multi-jet background and W/Z+jets, estimated together using the 2D sideband method (see Section 5), and t t events (see Table 2 for event yields).
The systematic uncertainties described in Section 6 may change the acceptance and shape of the m tb distribution of both a potential W -boson signal and the background processes, and are incorporated into the fit as nuisance parameters with log-normal constraints, with correlations across signal regions and signal and background processes taken into account.Some systematic uncertainties, such as those in the JES, affect the shapes of the histogram templates.These systematic uncertainties in the shapes are accounted for by introducing nuisance parameters α k that describe the possible variation in the shapes of the histograms for each process k.A log-normal constraint with mean 0 and width 1 is applied to each of the parameters α k .When performing the maximum-likelihood fit, all of the parameters α k are allowed to vary.
The signal (s) and background (b) expectations are functions of the nuisance parameters ì θ.These functions are built such that the response of s and b to each θ is factorised from the nominal value (s 0 ) of the expected rate: where ν( ì θ) describe the effect of variations in the nuisance parameters ì θ and similarly for b.
The p-value p b , representing the probability that the data is compatible with the background-only hypothesis, is estimated using the log-likelihood ratio (LLR) test statistic and evaluated using the asymptotic approximation [76].In the absence of any significant excess above the expected background, upper limits at the 95% CL on the signal production cross-section times branching ratio are derived using the CL s method [77].Limits derived using the asymptotic approximation were cross-checked using pseudo-experiments and found to have a difference of less than 10% for all W signal masses.
Figure 4 shows the m tb distributions in the three signal regions and the validation region after the fit to data.The fit in VR is done independently to test the post-fit agreement of the prediction with data.The maximum value of m tb observed in data is 5.8 TeV.The hatched band in the bottom panel includes the systematic uncertainties described in Section 6 after the fit to data.The most discrepant region, at 2.25 TeV, has a local significance of 2.0 σ for the combined fit in the three SRs, consistent with the backgroundonly hypothesis.In the absence of any significant excess over the background-only hypothesis, 95% CL limits are derived on the cross-section times branching ratio of W to t b decay, as shown in Figure 5, for the right-handed and left-handed couplings.The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses.They translate to observed (expected) lower limits on the mass of a W boson, with the same coupling to fermions as the SM W boson, of 3.0 (3.0) TeV and 2.9 (2.8) TeV in the right-and left-handed models, respectively.These mass limit values are obtained from the intersection of the theory curve and the observed and expected limit curves using a linear interpolation between the 2.75 TeV and 3 TeV W -boson signal mass points.The narrow dotted curve in Figure 5 shows the cross-section times branching ratio of W to t b decay calculated with Z [15].The band around this curve shows the uncertainty in the theoretical cross-section obtained by summing in quadrature the uncertainties in the estimation of the parton distribution function, strong coupling
Summary
A search for W → t b → q q b b is presented using 36.1 fb −1 of √ s = 13 TeV proton-proton collision data collected with the ATLAS detector at the LHC.The analysis makes use of jet substructure tagging optimised to select large-R jets originating from hadronically decaying top quarks using the shower deconstruction algorithm and b-tagging of small-R jets.The observed m tb spectrum is consistent with the background-only prediction and exclusion limits at 95% CL are set on the W -boson production crosssection times branching ratio to t b for right-handed and left-handed couplings as a function of the W mass in the range 1-5 TeV.Cross-section limits are set at high W -boson masses, excluding W bosons with right-handed couplings with masses below 3.0 TeV and excluding W bosons with left-handed couplings with masses below 2.9 TeV(at 95% CL). [
Figure 1 :
Figure 1: Feynman diagram for W -boson production with decay into t b and a hadronically decaying top quark.
Figure 2 :
Figure2: Comparison of the log( χ SD ) distribution between data (dots), t t MC events (line histogram) and background MC events (solid histogram) in samples with an enriched contribution from hadronically decaying top quarks using selection criteria similar to those in Ref.[25].The hatched band shows the effect of the SD uncertainty described in Section 6.
Figure 3 :
Figure 3: Illustration of the 2D sideband method showing the two-dimensional plane of the large-R jet substructure variables vs the small-R jet b-tagging information used to estimate the background yield in regions A (B), from the observed yield in the three control regions C, F, D (C, F, E) for the (left) "0 b-tag in" and (right) "1 b-tag in" categories.The top-and b-tagging criteria are applied after rejecting events in which the b-quark jet candidate has |η| > 1.2.
Figure 4 :
Figure 4: Reconstructed m tb distributions in data and for the background after the fit to data in the three signal regions and in the multi-jet validation region: (a) SR1, (b) SR2, (c) SR3, and (d) VR.The top panel shows the total-background m tb distribution before the fit to data as the narrow dotted line and the 3 TeV W R -boson signal m tb distribution as the dashed line.The "non all-had t t " label refers to t t events in which the W boson from one or both top quarks decays leptonically.The bottom panel of the plot shows the ratio of data to prediction and the hatched band includes the systematic uncertainties after the fit to data.
Figure 5 :
Figure 5: Observed and expected 95% CL limits on the W R -boson (top) and W L -boson (bottom) cross-sections times branching ratio of W to t b decay as a function of the corresponding W -boson mass.The expected 95% CL limits are shown with ±1 and ±2 standard deviation (s.d.) bands.The narrow dotted curves show the theoretical cross-section predictions and the bands around them show the uncertainties in the predictions for the corresponding W -boson signal.The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses.
The W -boson signal event selection efficiency is about 10% at low mass, decreasing to about 7% at high mass.The difference between the W R -boson and W L -boson signal selection efficiencies depends on the signal region and the efficiency is on average ∼10% higher for W R -boson signal samples.The difference in efficiency between W R -boson and W L -boson signals comes from a difference in angular separation between the W boson and the b-quark from the top-quark decay due to the different W -boson handedness, leading to a difference in the overall top-tagging efficiency.For instance, the 3 TeV W R -boson signal sample has a selection efficiency of 2.9% in SR1, 2.5% in SR2 and 2.4% in SR3, while the 3 TeV W L -boson signal sample has a selection efficiency of 2.7% in SR1, 2.3% in SR2 and 2.3% in SR3.
21] CMS Collaboration, Search for W → tb decays in the lepton + jets final state in pp collisions at √ s = 8 TeV, JHEP 05 (2014) 108, arXiv: 1402.2176[hep-ex].[22] ATLAS Collaboration, Search for W → tb → qqbb decays in pp collisions at √ s = 8 TeV with the ATLAS detector, Eur.Phys.J. C 75 (2015) 165, arXiv: 1408.0886[hep-ex].Identification of high transverse momentum top quarks in pp collisions at √ s = 8 TeV with the ATLAS detector, JHEP 06 (2016) 093, arXiv: 1603.03127[hep-ex].Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain j Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia k Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China l Also at Universita di Napoli Parthenope, Napoli, Italy m Also at Institute of Particle Physics (IPP), Canada n Also at Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy o Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Romania p Also at CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France q Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia r Also at Borough of Manhattan Community College, City University of New York, New York City, United States of America s Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece t Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South Africa u Also at Louisiana Tech University, Ruston LA, United States of America v Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain w Also at Department of Physics, The University of Michigan, Ann Arbor MI, United States of America x Also at LAL, Univ.Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France y Also at Graduate School of Science, Osaka University, Osaka, Japan z Also at Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität, Freiburg, Germany aa Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands ab Also at Near East University, Nicosia, North Cyprus, Mersin 10, Turkey ac Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ad Also at CERN, Geneva, Switzerland ae Also at Georgian Technical University (GTU),Tbilisi, Georgia a f Also at Manhattan College, New York NY, United States of America ag Also at Hellenic Open University, Patras, Greece ah Also at The City College of New York, New York NY, United States of America ai Also at Departamento de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain), Spain a j Also at Department of Physics, California State University, Sacramento CA, United States of America ak Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia al Also at Ochadai Academic Production, Ochanomizu University, Tokyo, Japan am Also at Departement de Physique Nucleaire et Corpusculaire, Université de Genève, Geneva, Switzerland an Also at Department of Physics, The University of Texas at Austin, Austin TX, United States of America ao Also at Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain ap Also at School of Physics, Sun Yat-sen University, Guangzhou, China aq Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria ar Also at Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, Russia as Also at National Research Nuclear University MEPhI, Moscow, Russia at Also at Department of Physics, Stanford University, Stanford CA, United States of America au Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary av Also at Giresun University, Faculty of Engineering, Turkey aw Also at Department of Physics, Nanjing University, Jiangsu, China ax Also at Institute of Physics, Academia Sinica, Taipei, Taiwan ay Also at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia az Also at Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia f Also at Department of Physics, California State University, Fresno CA, United States of America g Also at Department of Physics, University of Fribourg, Fribourg, Switzerland h Also at II Physikalisches Institut, Georg-August-Universität, Göttingen, Germany i * Deceased | 9,661.4 | 2018-01-24T00:00:00.000 | [
"Physics"
] |
DEVELOPMENT OF A METADATA MANAGEMENT SYSTEM FOR AN INTERDISCIPLINARY RESEARCH PROJECT
In every interdisciplinary, long-term research project it is essential to manage and archive all heterogeneous research data, produced by the project participants during the project funding. This has to include sustainable storage, description with metadata, easy and secure provision, back up, and visualisation of all data. To ensure the accurate description of all project data with corresponding metadata, the design and implementation of a metadata management system is a significant duty. Thus, the sustainable use and search of all research results during and after the end of the project is particularly dependent on the implementation of a metadata management system. Therefore, this paper will describe the practical experiences gained during the development of a scientific research data management system (called the TR32DB) including the corresponding metadata management system for the multidisciplinary research project Transregional Collaborative Research Centre 32 (CRC/TR32) ‘Patterns in Soil-VegetationAtmosphere Systems’. The entire system was developed according to the requirements of the funding agency, the user and project requirements, as well as according to recent standards and principles. The TR32DB is basically a combination of data storage, database, and web-interface. The metadata management system was designed, realized, and implemented to describe and access all project data via accurate metadata. Since the quantity and sort of descriptive metadata depends on the kind of data, a user-friendly multi-level approach was chosen to cover these requirements. Thus, the self-developed CRC/TR32 metadata framework is designed. It is a combination of general, CRC/TR32 specific, as well as data type specific properties. * Corresponding author.
INTRODUCTION
An important task in every interdisciplinary, long-term research project is the management and archiving of research data, including sustainable storage, description with metadata, easy and secure provision/exchange, back up, and visualisation of all collected or created project data.In particular, projects that focus on environmental field studies and regional modelling in a spatial context have to consider this issue (Mückschel and Nieschulze, 2004).The overall success of such projects depends, besides the scientific research, on a well organized management of all scientific research data.Jensen et al. (2011) notice that standardised metadata are a necessary requirement for the documentation and persistent safeguarding of research data.Consequently, metadata are supporting access and reuse of data-based research results.Moreover, funding organisations like the German Research Foundation (DFG) accentuate the description of scientific data with metadata.All data should be at least described using the Dublin Core metadata standard.In addition, all primary data should be described with metadata referring to the content of the dataset to reuse them in the context of other research questions (DFG, 2009b).
Therefore, a main priority within scientific research data management should be the establishment of a corresponding metadata management system to guarantee the accurate description of all project data.Jensen et al. (2011) emphasize the significance of a management system or software to create extensive metadata documentations.These applications should support input, management, and versioning of metadata.Furthermore, Jensen et al. (2011) point out that most applications are adapted to the needs of a special discipline.Thus, the sustainable use and search of all research results during and after the end of the project particularly depend on the implementation of a metadata management system with focus on the scientific background of the project.
Unfortunately, many data managers gain the experience of 'empty archives' after setting up their systems (Nelson, 2009) and notice the unwillingness of scientists to share their data (Borgman, 2010;Piwowar, 2011) including metadata.There are several approaches to solve these problems.With focus on metadata, data managers should generate tools that automatically store data and their metadata in one system (Rajabifard et al., 2009).Data and corresponding metadata should be captured at the same time, when submitted to a repository (Downs and Chen, 2010).
In the context of metadata management, some scientific research projects focus their work on Digital Object Identifiers (DOI, http://www.doi.org).In general, the aim of a DOI is to cite and link to electronic resources, which is widely used for scientific articles.The usage of DOIs for scientific primary data is getting more and more popular.A DOI offers a persistent and stable reference to scientific data and is therefore an easy way to link an article with the underlying scientific data (Brase and Farquhar, 2011).
In this contribution, we present the development of a metadata management system, which is an important part of the entire scientific research data management of the Transregional Collaborative Research Centre 32 (CRC/TR32) 'Patterns in Soil-Vegetation-Atmosphere Systems: Monitoring, Modelling, and Data Assimilation' funded by the DFG.First of all, we will give an overview about the research project and the corresponding project data.Then, we will focus on the development of the metadata management system, which includes an outline on the entire research data management.Finally, the paper ends with a discussion and conclusion.
PROJECT BACKGROUND AND DATA
The CRC/TR32 (www.tr32.de) is an interdisciplinary, joint research project between the German Universities of Aachen, Bonn, Cologne, and the Research Centre Jülich.The project funding started in 2007 and is expected to expire at the end of 2018.The involved research partners cover several scientific disciplines like hydrology, soil and plant science, geography, meteorology, and geophysics.They work in different project sections on exchange processes between the soil, vegetation, and the adjacent atmospheric boundary layer (SVA).The overall research goal of the CRC/TR32 is to yield improved numerical SVA models to predict CO 2 -, water-and energy transfer by calculating the patterns at various spatial and temporal scales.The hypothesis of the CRC/TR32 covers the explicit consideration of structures and patterns, which lead to a common methodological framework.The project participants focus their study on the catchment area of the river Rur, situated in western Germany, parts of Belgium and the Netherlands (CRC/TR32, 2011).
The overall CRC/TR32 is subdivided into different project areas, the so-called clusters.These are four scientific clusters and a central, coordination cluster.The scientific clusters differ by the sub-system (Soil-Vegetation-Atmosphere) and by the spatial scale range (local, sub-basin, regional/basin), on which they concentrate.Each cluster is split up into project sections (SP).Currently, the DFG is funding 23SPs for research.Within each SP around 1-2 PostDocs and 1-2 PhDs plus Master/Bachelor students are working on the research goal of the CRC/TR32.As a result, the numerous project members create a lot of different data in various spatial and temporal scales.In particular, a huge amount of data is collected during several field measurement campaigns, from various sensor networks, hydrological or meteorological monitoring or airborne measurement campaigns.Results from field observations or flight campaigns are for example, wind temperature, air CO 2 concentration , soil water content, soil CO 2 concentration, leave characteristics, root growth, land use analyses, crop surface or volume models (Hoffmeister et al., 2009;Waldhoff and Bareth, 2009;Korres et al., 2009).In addition, some research partners produce results from laboratory measurement methods or model simulations.As a consequence of the various results from field measurements and airborne campaigns, corresponding analyses and model simulations, all project participants create a great number of publications, pictures, presentations, and reports.
Within the framework of the CRC/TR32, adequate geodata of different scales were purchased to support and cover the needs of the project participants concerning their modelling and estimation purposes.For example, geodata (e.g.soil, elevation, climate, topographic, land use, or remote sensing data) was ordered from different local and national institutions like the National Survey Agency of North-Rhine Westphalia, Germany's National Meteorological Service, and the National Agency of Geology.
Format and size of the project data varies due to the different research background of the project participants.Therefore, the project participants provide data files for example in MS Excel, ASCII, NetCDF, binary format, PDF JPEG, TIF, or geodata format.In addition, the size of a single file varies from only few kilobytes to several gigabytes.
DEVELOPMENT OF A METADATA MANAGEMENT SYSTEM
The developed metadata management system is a basic component of the scientific research data management or the so-called project database of the CRC/TR32 (TR32DB).Therefore, in this section at first it is essential to describe the TR32DB and then the focus will be on the metadata management system.
Demands and design of the TR32DB
The entire CRC/TR32 scientific research data management (Curdt et al., 2010), which includes the metadata management system, is physically located at and implemented in cooperation with the Regional Computing Centre of the University of Cologne (RRZK).The TR32DB is accessible online (www.tr32db.de).It is developed following specific DFG guidelines, like the 'Proposals for Safeguarding Good Scientific Practice' (DFG, 1998) and a specific bulletin concerning 'Service-projects for information management and information infrastructure in CRC -INF' (DFG, 2009a).
Moreover, the TR32DB has to consider the demands and needs of the interdisciplinary background of the project.Therefore, data from different research fields (SVA) and various spatial scales (local/point to regional/basin) have to be handled.
Besides collected or created research data, research results like publications, presentation, reports, or pictures need to be observed.Additionally, a multitude of purchased geodata has to be managed.
In detail, the TR32DB design (Figure 1) comprises a file system, a database, and a web-interface with integrated web mapping application.The next section will give a short overview about the three components.
The file system is the physical storage of the CRC/TR32 project data.It is implemented by the Andrew File System (AFS), which is a distributed networked file system.The AFS was chosen in cooperation and discussion with the RRZK.Reasons for the AFS are for example security and scalability, cross platform access, and location independence.Furthermore, it is simple to archive and backup data.As a result of the cooperation with the RRZK, all project data are available during and beyond the end of the project.
The AFS is connected to a database.This is put into practice by storing the path of the datasets in a MySQL database.The main task of the database is the physically storage and management of the entire metadata, which belong to the project data.In addition, the MySQL database has to handle administrative data like user details or user rights.The self-developed TR32DB web-interface (www.tr32db.de) is the connecting component between AFS and MySQL database.
Management and visualisation of all project data and purchased data (e.g.climate data or geodata) via metadata are the main duty of the web-interface.In other words, the web-interface is the user-interface to the metadata management system.
The web-interface is implemented in a simple layout.The user can access general information on the top menu.The side menu enables just access to the project data, for example via a search tool or according to data topic, data type, research region/location or in order by the project structure.Besides the functions, which are connected to the metadata management system, authorized users can also use specific tools to access geodata, search for climate data, and share their project data.
By means of the implemented internal Web-GIS, authorized users can visually search and explore existing geodata and their attributes.For example, users can match various geodata together like land use and soil data of a specific region.Moreover, they can search for climate data stations in the Rur catchment and display corresponding attributes (e.g.station name, measuring period, parameters or measurement gaps).
A specific climate data tool, also implemented in the internal area of the web-interface, enables users to quick and easy access the purchased climate data (e.g. from German Weather Service or Meteomedia Group).Via a search form, users can query climate data attributes by selecting multiple stations in combination with a specific time extent.Finally, they can export the result.In addition, authorized users can generate a diagram of a climate data query by selecting multiple stations, climate data parameters, and a temporal extent.
Project members can temporary share their data via a special exchange area in the AFS.Data in the share area are available for all authorized users via the web-interface.
The TR32DB metadata management systems
The metadata management system was designed, realized, and implemented according to different requirements, to describe all project data with accurate metadata.First of all, the needs of the project background and participants have to be considered.It is important to arrange a simple and user-friendly metadata management system, which does not overburden the users.Furthermore, it has to cover all demands on the interdisciplinary data.All data types, collected/created by the project participants have to be included.Finally, recent metadata standards have to be noticed.Since quantity and sort of descriptive metadata depend on the kind of data, a user-friendly multi-level approach was chosen to cover all requirements.
Thus, the self-developed multi-level CRC/TR32 metadata framework is designed (Figure 2).It is a combination of general, CRC/TR32 specific, and data type specific properties.
Figure 2. CRC/TR32 metadata framework The qualified Dublin Core Metadata Element Set (DCMES, http://www.dublincore.org/)was chosen as a 'basic' level for the metadata model.The DCMES is a simple and widely accepted standard, which covers all general requirements and information to describe a dataset.This assures, that all types of data can be at least described with the 'basic information'.These are (mandatory elements are marked with an asterisk): - In addition, CRC/TR32 specific metadata properties with focus on SVA can be added to reach the specific needs and demands of the project.For example, the datasets can be described with specific keywords with focus on SVA or project special CRC/TR32 data topics (e.g.Soil, Vegetation, Atmosphere, Land Use, Remote Sensing or Topography).
Furthermore, to fulfil the requirements of the six data types (publications, presentations, pictures, reports, measured/ modelled data, and geodata), specific data properties can be added.For example, a 'report' can be described with additional attributes like: the report date, the report type, the report city, the report institution, the report volume or the report pages.A 'picture' can be described with: the recorded date (begin/end), location, region, event, orientation (landscape, portrait), size, camera, and copyright information.A 'presentation' can be completed with information like: presenter, presentation date, presentation type (e.g.keynote, poster, talk, other), presentation event (e.g.conference, cross group meeting, project meeting, other), the event title, event location, and event period (begin/end).
The supplementary attributes of the data type 'publication' make an exception, because different publication types require various attributes, which has to be considered.Therefore, the additional properties of the data type 'publication' are initially: year, status (e.g. in print, in review, published, submitted, and unpublished), review (e.g.yes, no), and publication type (e.g.article, event paper, book section).Further attributes for a 'publication' are now dependent on the choice of the publication type.For example, an 'article' can be described with article type (e.g.electronic, journal, magazine, newspaper), publication source, publication source URL, publisher, volume, issue, pages, and page range.
The data types 'measured/modelled data' and 'geodata' also represent a particular case.To fulfil the requirements of spatial related datasets, demands and requirements of geographic metadata standards like ISO 19115 or the INSPIRE directive have to be considered.Therefore, both spatial related dataset can be described with attributes like: temporal extent (begin/end), lineage, reference system name and system identifier, or a geographic bounding box (north, east, south, west coordinates).Moreover, to 'measured/modelled data' properties like measurement/model region, measurement/model location, as well as the used instrument (e.g.equipment group/method, model, manufacturer, registered office, URL) and resolution distance, temporal frequency and measured/modelled parameter can be added.To enable, that the dataset can be understood without contacting the data creator, it is possible to add an extra description file in PDF format.Thus, a user can provide complete information about the content or creation of a dataset, which are not covered by the metadata elements.This are for example background information about the measurement or a detailed description of measurement parameters and units.
The so-called 'metadata on metadata' of a dataset are stored automatically.These are for example: data file storage path, metadata creator (e.g.name, institution, email, phone), metadata changing date, as well as funding phase and project section, where the dataset was created.
As already described in section 3.1, to realize the metadata management system, a MySQL database was implemented to store the entire metadata of the project.This database is connected to the CRC/TR32 web-page to provide a userfriendly interface.Via the web-interface, authorized users are able to link their project data with adequate and specific metadata.Users, who are logged in, are requested to add metadata to a specific dataset, which they have just uploaded to the data storage (AFS).The input of the corresponding metadata is carried out by a simple structured metadata input form, which is adjusted according to the multi-level CRC/TR32 metadata framework.In the current online version (Figure 3), users at first choose the dataset, whom they want to add metadata to.The input form will be automatically arranged according to the chosen data type.Now, the user has to enter and submit the metadata to the system.To make the input form more userfriendly, a template function was implemented.Here, the user can reuse metadata of an older dataset and modify the details for the new dataset.Hence, the users are saving time and avoiding mistakes.After submitting the metadata, the dataset details are immediately available online and searchable via the webinterface.In addition, authorized users can view and edit their uploaded metadata in their 'user home'.
Another function of the metadata management system is the application of CRC/TR32 DOIs.Users, who have already submitted their data to the TR32DB, can apply for a CRC/TR32 DOI to make the scientific dataset citable as a publication.The user has to follow and accept some conditions, for example he has to describe the dataset with specific metadata.Both, the CRC/TR32 metadata framework and the DOI system (Brase, 2004), are based on the Dublin Core metadata standard.Thus, the already connected metadata to a dataset can be reused and just have to be completed according to further DOI requirements.Consequently, the application of a CRC/TR32 DOI is designed very comfortable and user-friendly.As a result, a primary scientific dataset, stored in the TR32DB, can now be cited in a publication using the following citation: For example, Waldhoff (2010) is the underlying scientific dataset to describe the study in Bolten and Waldhoff (2010).
Every visitor of the web-interface is able to search for project data via metadata by the left menu according to the topic and type of data or project phases and clusters.In addition, a search tool can be used.Via the search form the user can combine various queries with each other like for example a full-text search, data type, funding phase, temporal extent, CRC/TR32 keywords, creator, and regions/sites.As result of all searches by the web-interface, a list of datasets will be displayed (Figure 4).By clicking on the info button, the metadata details of the data file will be shown in a pop-up window.The metadata are again arranged in a list according to the multi-level approach.First, the 'basic' metadata details are displayed, followed by the specific metadata of each data type.Every user is able to view the additional description file of the dataset, but only authorized users have permission to download the data file.By downloading the file, the user is encouraged to obey the CRC/TR32 data policy, for example concerning the use and adequate citation of the dataset.
DISCUSSION AND CONCLUSION
The centralised management of scientific research data of an interdisciplinary research project involves several problems, due to various demands on the system.Mückschel et al. (2007) point out that all heterogeneous data should be stored in an explicit structure including the corresponding metadata.Büttner et al. (2010) complete the importance of metadata.Scientific data should be described with sufficient information to enable the reconstruction and verifiability of the dataset.As a consequence, the dataset can be used as a basis to answer further scientific questions.
We have implemented a running system (TR32DB) to manage all scientific research data of the CRC/TR32, including an accurate metadata management system.This was developed according to the funders requirements (DFG, 1998;DFG, 2009a;DFG, 2009b).In addition, all project data and metadata are captured at the same time and in one system according to Rajabifard et al. (2009) and Downs and Chen (2010).
The TR32DB was designed according to the needs and demands of the users.The system can handle huge amounts of heterogeneous data files from various disciplines in different data file sizes (kb to GB).All collected or created project data can be described with accurate metadata via the user-friendly metadata input form, which is integrated in the TR32DB webinterface.This enables users to enter metadata and edit their metadata wherever they have internet access, as well as access and download their data.For example, project participants who started their work in the second funding phase are able to access project data including accurate metadata, which was collected during the first funding phase via the TR32DB.
By implementing a multilevel metadata framework, we have considered the needs of the project participants.Every metadata provider can choose for his specific dataset, how much extra metadata he wants to enter in addition to the mandatory fields.Therefore, users are not overburden by the multiplicity of metadata input fields.Furthermore, the demands on the data types are considered, as well as recent geographic standards and principles (e.g.ISO19115 or INSPIRE directive).In particular for spatial related data, metadata are vital, because they will provide the user with information about its purpose, accuracy, quality, and actuality (Rajabifard et al., 2009).
To solve the problem of 'empty archives' described by Nelson (2009) and to create an additional value to the TR32DB, all users can apply for a persistent CRC/TR32 DOI for their data, e.g.Waldhoff (2010).This corresponds to other interdisciplinary projects like 'Scientific Drilling Database' (www.scientificdrilling.org) or 'PANGAEA' (www.pangaea.de).
However, the TR32DB posses disadvantages concerning data connection.Although, all data files can be linked to other data files using a relation, which is a voluntary element from the DCMES, the TR32DB data are not connected like in a semantic web (e.g.Heimann et al., 2010;Willmes et al., 2012).The interdisciplinary background of the CRC/TR32, the produced heterogeneous data files, and the time-consuming development are the main reason against the semantic web approach.For future developments, the design of an ontology for selected frequent data (e.g.Eddy covariance stations) is possible, particularly with regard to Sensor Networks.
Currently, all project data are just stored in the TR32DB and are not represented in an open data repository, data library, or a data centre, yet, like PANGAEA (Data Publisher for Earth & Environmental Science) or the WDCC (World Data Center for Climate).This is another task for the future work.At the moment, the metadata management system is in rearrangement.A more user-friendly wizard to enter metadata according to the CRC/TR32 metadata framework is in development, as well as an improved representation and search of all metadata on the web-interface.Currently, the TR32DB design including metadata framework is transmitted to another interdisciplinary research project with focus on resilience, collapse and reorganisation in social-ecological system of African Savannas.Due to the developed multi-level metadata approach, it was very easy to adapt the metadata management system to another discipline.
Figure 1 .
Figure1.TR32DB design (modified afterCurdt et al., 2011) Title: Main title of the dataset (*) -Creator: Person who created the dataset (*) -Subject: TR32 specific topic of the dataset (*) -Description: Abstract describing the dataset (*) -Publisher: Organization responsible for making dataset available -Contributor: Person and/or institution responsible for making contributions to dataset content -Date: Date of publication/creation of dataset (*) -Type: Type of dataset.Recommended setting is dataset.Dataset collection is recommended for dataset series (*) -Format: Format of the dataset (*) -Identifier (incl.Identifier-Type): Identifier of the dataset, e.g.URN, DOI -Language: Primary language of the dataset (*) -Relation (incl.relation-type): A reference to a related resource including type of relation -Coverage (temporal): Time (period) covered by the content of the dataset, depending on the data type (*) -Rights: Access-permission of the dataset (*)
Figure 4 .
Figure 4. Request on type 'data' with metadata info window | 5,432 | 2012-07-16T00:00:00.000 | [
"Computer Science"
] |
Machine Learning Profiling of Alzheimer's Disease Patients Based on Current Cerebrospinal Fluid Markers and Iron Content in Biofluids
Alzheimer's disease (AD) is the most common form of dementia, characterized by a complex etiology that makes therapeutic strategies still not effective. A true understanding of key pathological mechanisms and new biomarkers are needed, to identify alternative disease-modifying therapies counteracting the disease progression. Iron is an essential element for brain metabolism and its imbalance is implicated in neurodegeneration, due to its potential neurotoxic effect. However, the role of iron in different stages of dementia is not clearly established. This study aimed to investigate the potential impact of iron both in cerebrospinal fluid (CSF) and in serum to improve early diagnosis and the related therapeutic possibility. In addition to standard clinical method to detect iron in serum, a precise quantification of total iron in CSF was performed using graphite-furnace atomic absorption spectrometry in patients affected by AD, mild cognitive impairment, frontotemporal dementia, and non-demented neurological controls. The application of machine learning techniques, such as clustering analysis and multiclassification algorithms, showed a new potential stratification of patients exploiting iron-related data. The results support the involvement of iron dysregulation and its potential interaction with biomarkers (Tau protein and Amyloid-beta) in the pathophysiology and progression of dementia.
INTRODUCTION
Alzheimer's disease (AD) is the most common cause of dementia (International, 2019), characterized by a complex etiology and unsatisfactory therapeutic approaches (Long and Holtzman, 2019). The duration of the preclinical and prodromal phase of AD varies from 10 to 20 years before clinical symptoms emerge (Vermunt et al., 2019). Mild Cognitive Impairment (MCI), which identifies a clinical condition that includes impairment in memory and/or non-memory cognitive domains, is assumed as a prodromal stage of AD, also referred to as MCI due to AD (Albert et al., 2011).
The presence of extracellular amyloid-beta (Aβ) deposition as neuritic plaques and of intracellular accumulation of hyperphosphorylated tau (p-Tau) as neurofibrillary tangles are the two hallmark lesions that histopathologically characterize the brains of AD patients (Ittner and Götz, 2011). However, there is evidence that significant accumulation of these pathological features can occur in non-demented individuals (Fagan et al., 2007;Aizenstein et al., 2008;Villemagne et al., 2008;Price et al., 2009) and also a high neuropathological heterogeneity is observed in patients with clinical diagnosis of AD (Rabinovici et al., 2016;Di Fede et al., 2018;Robinson et al., 2018). The abnormal concentration in the Cerebrospinal Fluid (CSF) of the proteins responsible for the plaque formation, i.e., Aβ42, p-Tau, and total-Tau (t-Tau), is assumed to be a measurable fingerprint of their brain deposition, reflecting neurochemical changes arising from AD pathology (Henry et al., 2013).
Although diagnostic criteria for AD and MCI are currently used (Dubois et al., 2007(Dubois et al., , 2010Albert et al., 2011;McKhann et al., 2011;Sperling et al., 2011), defining the preclinical state of MCI/AD aiming at discovering therapies preventing the irreversible progression of AD (Fiandaca et al., 2014) remains a challenge.
New biomarkers and a deeper comprehension of the neuropathological processes involved in AD are urgently needed, with the aim to identify alternative disease-modifying therapies counteracting the disease progression. Actually, additional fluid biomarkers measured in CSF or in blood (Palmqvist et al., 2020) unraveled promising candidates, reflecting several inter-related mechanisms of AD pathophysiology (Molinuevo et al., 2018).
In this regard, a growing amount of evidence suggests the involvement of brain iron metabolism in the onset of several neurodegenerative diseases, in particular its accumulation in brain regions (Hare et al., 2013;Ward et al., 2014) and its potential key role in the pathogenesis of AD (Silvestri and Camaschella, 2008;Kozlov et al., 2017). Iron is an essential element for our body but, in spite of its ubiquity, it requires very careful managing (Gozzelino and Arosio, 2016). Free iron is a potentially toxic element that may generate Reactive Oxygen Species (ROS) triggering oxidative stress, lipid peroxidation, and DNA damage, also promoting cell death in the novel form of "ferroptosis" (Dixon et al., 2012;Hao et al., 2018). Therefore, most of the circulating and stored iron is linked to proteins and other transporters, such as transferrin (s-Tf) and ferritin (Pantopoulos et al., 2012;Eid et al., 2017). The systemic organs and the brain share the same iron regulatory mechanisms and pathways based on iron-modulating proteins, providing a link to the maintenance of iron homeostasis within the brain (Singh et al., 2014).
The imbalance in iron homeostasis in AD and its interaction with the more consolidated biomarkers Aβ and Tau have been described (Ndayisaba et al., 2019;Spotorno et al., 2020), supporting the conjecture of new therapeutic strategies based on iron chelators or other iron-toxicity counteracting drugs as a valuable approach for AD treatment (Liu et al., 2018;Ashraf and So, 2020). Several studies supported the notion that brain iron elevation (Lane et al., 2018;Ayton et al., 2019) or even the levels of iron-related proteins, e.g., plasma transferrin, are associated with AD and cognitive decline (Hare et al., 2015;Guan et al., 2020). Furthermore, the concentration of several elements included iron in biological fluids (Duce and Bush, 2010;Schrag et al., 2011;Cicero et al., 2017) has been evaluated with different techniques but highlighting difficulties to compare results. However, a direct evaluation of iron concentration in the brain remains a difficult task and conclusive results about the combined role of iron and iron-protein levels on biological fluids (i.e., CSF and serum) with the preclinical stage of dementia are not still clearly established.
Recently, the application of machine learning techniques gave strong support to AD diagnosis, in particular for classification tasks (Tanveer et al., 2020) and clustering analysis (Alashwal et al., 2019), aiming at identifying which features are involved in the conversion from early-stage AD to dementia. In particular, clustering analysis is a potentially strategic tool able to establish subsets of individuals sharing similar patterns and has been applied to investigate disease-related profiles of different AD and dementia stages (Racine et al., 2016;Alashwal et al., 2019).
This study aimed to investigate potential patterns of iron imbalances both in CSF and in serum, to improve early diagnosis and the related therapeutic possibility. While the content of iron in serum was assessed using standard clinical methods to detect transferrin (s-Tf), an accurate quantification of total iron in CSF was obtained using atomic absorption spectrometry, not currently used in clinical practice, leading to a potential added value to the clinical information about the status of the patients.
Firstly, to discriminate iron profiles between different forms of dementia, iron concentration in CSF of AD patients was compared with patients affected by Frontotemporal Dementia (FTD), a heterogeneous disorder with distinct pathological features and clinical phenotypes, encompassing changes in behavior, language, executive control, and often motor symptoms (Olney et al., 2017). Secondly, we compared patients affected by AD, MCI, and non-demented controls, to evaluate shared patterns and the ability to discriminate these conditions.
To check whether the new iron-related biomarkers could add significant improvements to AD early diagnosis, a stepby-step procedure was adopted, iteratively adding to the wellconsolidated features (Aβ42, p-Tau, and t-Tau) also the results from s-Tf and iron content in CSF.
Cluster analysis was performed, to unravel subgroups within heterogeneous data such that individual clusters classify similar profiles, having better homogeneity than the whole. In particular, the hierarchical agglomerative clustering (HAC) algorithm was applied, a suitable technique for partitioning patients based on their similarity.
Since clustering analysis can reveal similar (pathological) profiles and identify potential altered biological mechanisms, we investigated how such clusters are influenced by the addition of the iron-related parameters and whether MCI can be better discriminated from controls and AD. Multiclassification algorithms with different features sets are used to compare diagnostic power and to rank the relevance of features for the prediction of the model.
Participants
We retrospectively included 69 patients (35 males and 34 females, mean age: 70.5 years ± SD: 7.2), evaluated and followed at the Department of Neurosciences of University Hospital "Città della Salute e della Scienza, " Torino and at Fondazione IRCCS Istituto Neurologico Carlo Besta, Milano, Italy. CSF samples from all 69 patients, including 14 non-demented neurological control (CT) patients, 17 patients affected by MCI, 16 AD, and 22 FTD (behavioral variant) were collected.
Diagnosis of FTD was made according to Rascovsky Criteria (Rascovsky et al., 2011).
Diagnosis of AD has been made according to NIA-AA (National Institute of Aging-Alzheimer Association) criteria (McKhann et al., 2011).
For the classification of MCI, the Petersen criteria were used: cognitive complaint, decline or impairment; objective evidence of impairment in cognitive domains; essentially normal functional activities; not demented (Petersen, 2004;Petersen et al., 2009).
MCI group included a mix of amnestic, non-amnestic, and multidomain subjects, with disease onset before (N = 3) and after (N = 13) 65 years.
As control group, CSF of 14 patients with neurological conditions (see Supplementary Material) without dementia was analyzed.
Cognitive functions were assessed by Mini Mental State Examination (MMSE).
A complete description of data is available in Table 1. The experiments conformed to the principles of the Declaration of Helsinki and were approved by the local ethics committee. Informed consent for liquor collection and storage relative to the retrospective study was given by all subjects or by their caregivers.
Details of procedure for the collection of CSF and serum samples, also with determination of CSF levels of Aβ42, p-Tau, and t-Tau and of serum transferrin, are reported in Supplementary Material.
Iron Determination in CSF by GF-AAS
Frozen aliquots of CSF samples were transported on dry ice until the shipment to the analytical chemistry laboratory, were kept frozen during storage and unfrozen 1 h before the analysis.
The determination of iron in CSF samples was carried out by means of Graphite Furnace Atomic Absorption Spectrometer (GF-AAS) as detailed in Supplementary Material.
Statistical and Machine Learning Analysis
The assumption of equality of variance and normal distribution were assessed through Levene's test and Shapiro-Wilk's test, respectively. One-way analysis of variance (ANOVA) for normally distributed variables, Kruskal-Wallis test for variables not following a normal distribution, and chi-squared test (for categorical variables) were conducted to determine group differences. Post-hoc tests (t-test and Dunn's test adjusted for multiple comparisons errors according to Bonferroni) were performed, respectively, after significant results of ANOVA and Kruskal-Wallis test. The same procedures were applied to compare clusters in the cluster analysis, described below.
Bivariate correlations between clinical data, biomarkers, and the iron concentration levels were tested both using Spearman's test and Pearson's test for non-parametric and parametric relationships (r s = Spearman's rank correlation coefficient, r = Pearson's correlation coefficient), respectively. We assumed as correlated only the variables simultaneously satisfying the two correlation criteria, with both |r| and |r s |>0.5. Results from statistical analysis were evaluated against a threshold of p < 0.05.
Before the cluster analysis, Hopkins's test was applied to assess the clustering tendency of the datasets. For the hierarchical clustering, the clustering variables were selected based on the results of bivariate correlations, avoiding to include features with a high degree of collinearity (a threshold of r > 0.7 was set Dormann et al., 2013). For the variables presenting some association with age, additional analysis was performed including the age correction in the clustering analysis (Supplementary Material).
HAC was applied, a bottom-up approach in which each data point starts in a separate cluster, and pairs of clusters are merged at the bottom going up the hierarchy. After data standardization (Z-score unit), patients were grouped using HAC with Ward's method of minimum variance and Euclidean distance metric and visualized in dendrograms. Ward's method joins two clusters to make the smallest increases in the pooled within-cluster variation (Ward, 1963).
The number of resulting clusters was set finding clustering step where the acceleration of distance growth is the largest, stopping the process and selecting a distance cut-off in the dendrogram to determine the correct number of clusters (>2 clusters). Different sets of features in two datasets were considered for clustering, and a heatmap was used to visualize the median value of the features in each cluster. The values of features within each cluster are reported for the different feature sets used (Supplementary Material).
The clusters obtained for each feature set were compared based on the following clustering scores: Adjusted Rand Index (ARI) and Adjusted Mutual Information (AMI), measuring the similarity and agreement of the two assignments; V-measure, evaluating the homogeneity, and completeness of the clusters. In the subpopulation in which all features considered are available, the ratio (Fe CSF/s-Tf) was calculated for each cluster and the dataset was divided into quartiles to observe where the values of variables in each cluster fall with respect to the whole population (Supplementary Material).
The dataset was used to train two machine learning models based on Support Vector Machine (SVM) and Logistic Regression (LR) adapted for multiclass classification, using two different sets of features, comparing the performance of the classifiers and ranking the relevance of features. The SVM algorithm is very popular for discrimination tasks because it is able to reach good generalization ability and accurately combines features, finding the maximal margin hyperplane, and minimizing the classification error to divide data belonging to different classes (Cortes and Vapnik, 1995).
Two feature sets used for the cluster analysis have been included in the model. After standardization of the datasets, an exhaustive search over parameter values for the estimators has been carried out by cross-validated grid search to optimally tune parameters of the classifiers.
For the present study, the OnevsRest (OVR) classifiers based on SVM with linear kernel and LR were used for the classification of the three groups (CT, AD, MCI) and to evaluate the importance assigned to the features. The classification performance of the constructed models, varying the input features presented to it, was computed using the macro-averaged Area Under the Receiving Operating Curve (AUROC). The performance of the classifiers was assessed via 100 times stratified shuffle split cross-validation method (proportion of train:test size = 60:40). This cross-validation method returns stratified randomized folds that preserve the percentage of samples for each class.
The values of the importance for each feature were obtained applying the model inspection technique based on repeated permutations of features on test datasets. The permutation feature importance is defined to be the change in a model score when a single feature value is randomly shuffled. This procedure indicates how much the model depends on the feature, breaking the relationship between the feature and the target, correcting possible bias of the model.
Statistical and machine learning analysis was carried out under the programming language Python, also using library Scikit-Learn (Pedregosa et al., 2011).
Demographic and Clinical Data
Demographic and clinical data of the patients classified by clinical diagnosis as described in section Materials and Methods 2.1 are reported in Table 1 (see also Supplementary Figure 1). Values of MMSE and s-Tf are available for different subgroups of the population composed of 69 patients.
In addition, the four groups were not significantly different for values of glucose and protein dosed in CSF (data not shown) and there were not significant differences in iron variables (s-Tf and iron in CSF) between men and women.
Iron Concentration in CSF
Total iron concentration in CSF samples of patients is shown in Figure 1. Significant differences have been reported between AD and all the other groups, but not between CT and MCI. No difference was found between FTD and CT groups.
Clustering Analysis
Clustering analysis was performed including CT, MCI and AD groups on two different populations: total dataset comprising 47 patients, and the subset composed of 29 patients for which the FIGURE 1 | Distribution of iron concentration in CSF samples of AD (56.3 ± 15.6 µg/L), MCI (38.6 ± 21.2 µg/L), CT (26.5 ± 9.9 µg/L), and FTD (35.2 ± 16.8 µg/L) patients by means of GF-AAS. Iron levels were significantly different between AD and CT (p < 0.001), AD and FTD (p = 0.003), and AD and MCI (p = 0.02). Statistical differences have been evaluated by means of Kruskal-Wallis test and Dunn's post-hoc test using Bonferroni correction for p-value (*p < 0.05; **p < 0.01; ***p < 0.001). measurement of s-Tf is available. The sets of features used to compare the results are the following: a Standard Biomarkers dosed in CSF (SBs) (p-Tau, Aβ42); b SBs + Iron in CSF c SBs + s-Tf d SBs + s-Tf + Iron in CSF For the application of hierarchical clustering we dropped t-Tau, due to its high correlation with p-Tau.
SBs + Iron in CSF
The addition of iron dosage in CSF unraveled four clusters (sizes: N = 9, N = 19, N = 7, N = 12) after the application of HAC, reported in Figure 3. The clusters composed of AD and MCI patients (cluster 3 and cluster 4) significantly differed among them for iron (p = 0.038) and p-Tau (p < 0.001) profiles and from cluster 2 (mainly composed of CT patients) for all variables with high significance (p < 0.001), except for p-Tau between cluster 2 and 4 (p = 0.018). Cluster 3 differed from cluster 1 for CSF iron content (p = 0.006).
The addition of CSF iron improved V-measure (0.25), ARI (0.16), and AMI (0.20) with respect to the same scores obtained with the biomarkers set, described in the previous section.
SBs + s-Tf
Considering the subpopulation including data of s-Tf (N = 29 patients), the results for HAC using same feature sets as in sections SBs and SBs + Iron in CSF are reported in Supplementary Figures 2, 3. In this subpopulation, the application of HAC using the feature set comprising biomarkers and s-Tf revealed four clusters (sizes: N = 7, N = 6, N = 9, N = 7), reported in Figure 4. Significant differences among clusters were found for all the features values between cluster 1 and 2 (for Aβ42, p-Tau p < 0.001; for s-Tf p = 0.02), for the p-Tau values (p < 0.001) when comparing clusters 1 and 3 and 1 and 4; s-Tf differed between clusters 2 and 4 (p = 0.001) and 3 and 4 (p < 0.001); Aβ42 was significantly different when comparing clusters 2 and 3 (p < 0.001) while the difference in Aβ42 between clusters 3 and 4 is borderline (p = 0.05).
SBs + s-Tf + Iron in CSF Considering all the above features four clusters emerged (sizes: N = 7, N = 7, N = 8, N = 7). The application of HAC in the subpopulation for which s-Tf is available (Figure 5) reported an increase of clustering scores (V-measure = 0.43; ARI = 0.28; AMI = 0.37). Cluster 1 and cluster 2 are composed only by AD and MCI patients. One of these clusters (cluster 1) presented significant difference in the levels of s-Tf (p = 0.002), Iron CSF (p = 0.004), and p-Tau (p = 0.007) with respect to cluster 3 (mainly CT patients). Cluster 2 differed from cluster 4 (composed only by MCI and CT patients) in the biomarkers (for Aβ42 p = 0.004; for p-Tau p < 0.001) and s-Tf (p = 0.008) profiles. Clusters 1 and 2, as well as clusters 2 and 3, significantly differed only for p-Tau (p < 0.001). Finally, cluster 4 differed from cluster 3 only for the s-Tf values (p <0.001).
We performed additional HAC analysis considering age correction for the variable s-Tf, showing a sharper separation on s-Tf profiles albeit without substantial differences in the cluster composition (Supplementary Figures 4-6).
Classification Models
We finally used a Linear SVM and LR model to evaluate the classification performance based on the same feature sets used for the clustering analysis in the population (N = 47). For SVM, the classification performance (AUROC) using SBs (Aβ42, p-Tau) and SBs + Iron in CSF was (0.74 ± 0.14) and (0.73 ± 0.12), respectively. In the first case, the values of feature importance for the biomarkers set showed a higher weight for Aβ42 (0.21 ± 0.18) respect to p-Tau (0.15 ± 0.11). In the second case, CSF iron reported a higher value (0.07 ± 0.09) respect to p-Tau (0.06 ± 0.09) and Aβ42 (0.03 ± 0.12). For LR model, AUROC using SBs and SBs + Iron in CSF was (0.77 ± 0.12) and (0.75 ± 0.12), respectively. The values of feature importance for the biomarkers set showed a higher weight for Aβ42 (0.20 ± 0.14) respect to p-Tau (0.11 ± 0.13). Even in LR model, CSF iron reported a higher value (0.10 ± 0.02) respect to p-Tau (0.06 ± 0.13) and Aβ42 (0.09 ± 0.08). In our dataset, for both models the addition of age as feature did not improve the AUROC, and the value of feature importance for age was not relevant (around zero).
DISCUSSION
The present results support the hypothesis that iron accumulation is involved in AD neurodegeneration. In clinical practice, the pathological changes occurring in AD can be detected by the use of biomarkers in different modalities, among which the evaluation on CSF (i.e., Tau and Aβ biomarkers) is less accessible but presents lower intrinsic protease activity than blood and reflects brain changes, helping to diagnose AD pathology in both the prodromal and the dementia stages (Lashley et al., 2018).
In our study, both the "standard" biomarkers significantly differed between AD and CT groups (only CSF Aβ42 between AD and MCI), but this result requires confirmation in a larger cohort of patients also due to the large dispersion of biomarker values in our MCI population ( Table 1). In fact, core-AD hallmarks are present also in elder healthy people with good cognitive function (Driscoll and Troncoso, 2011), probably showing different patterns only with respect to the AD brain. We added the information on iron content in CSF, intending to discover shared profiles and potentially improve early diagnosis. The analytical measurements of total iron in CSF by means of GF-AAS is expected to provide an accurate quantification, reflecting the iron status in brain patients more directly than brain imaging techniques. Indeed, biochemical changes in the brain, occurring in preclinical phases produce corresponding alterations in the CSF (Jack et al., 2010). Iron concentration in CSF is minimal and therefore very difficult to measure, requiring accurate and highly sensitive techniques such as atomic absorption spectrometry, providing reproducible and reliable results, without the need for hard pre-treatment of CSF samples. Moreover, this measurement is not currently used in clinical practice, leading an added value for the standard information on iron status in the brain.
Several studies evaluated iron levels in biological fluids, and meta-analysis conducted by Tao et al. showed lower iron in serum and an iron overload in several specific brain regions of AD patients, however highlighting the need for further studies to evaluate iron in CSF (Tao et al., 2014).
In the present work, CSF iron concentration in 69 patients was analyzed, finding a statistically significant increase in the total iron concentration in AD with respect to CT patients, and between AD and MCI (Figure 1), showing a potential discriminating power of our analysis. Iron dysregulation could generate a progressively toxic environment during the different stages of dementia. In fact, a well-known consequence of increased iron concentration is the production of ROS, leading to DNA damage and cell death (Zecca et al., 2004), that feature AD.
The concentration of iron in CSF is very low, and it has been suggested that Tf saturation in the CSF is much higher than in the periphery and that a larger proportion of free iron circulates the CNS (Leitner and Connor, 2012). An imbalance of free iron can be responsible for toxic damage taking part in Fenton reaction and consequently to the onset of neurodegeneration.
Interestingly, it is reported that different stages of cognitive and functional impairment are associated with changes in CSF reactive iron, possibly in relation to the development of cognitive and functional decline (Lavados et al., 2008).
The importance of iron in AD and aging has been shown also from the evaluation of altered local levels of proteins regulating iron levels, such as transferrin (Loeffler et al., 1995;Lu et al., 2018).
Then, it has been assessed that CSF ferritin, the iron storage protein of the body, plays a role in AD. It has been demonstrated that CSF ferritin, assumed to be an index of brain iron load, is strongly associated with CSF apolipoprotein E levels and was elevated by the Alzheimer's risk allele, APOE-ε4 (Ayton et al., 2015). Also, CSF ferritin levels have been associated with longitudinal changes in CSF Aβ and Tau, showing that iron might facilitate Aβ deposition in AD and accelerate the disease process . These evidences provide proofs that a disturbance in iron metabolism can be involved in neurodegenerative processes.
To check whether our technique was accurate enough to detect small differences in the iron concentration in CSF and to evaluate the possibility to discriminate between AD and other dementias, in the first part of our study we compared AD and FTD patients. The results (Figure 1) showed a marked difference in iron concentrations in FTD patients with respect to AD, suggesting a possible different role for this metal in these two types of dementia. This result should be confirmed in larger cohorts, however, different levels of biological metals in CSF have been showed in different neurodegenerative diseases (Hozumi et al., 2011), in particular AD, Amyotrophic Lateral Sclerosis, and Parkinson disease, so it is plausible that a difference exists also in FTD (Ashraf and So, 2020).
AD is a complex disease (Devi and Scheltens, 2018), requiring advanced computational algorithms to discover deep relationships in the data and their relative patterns. In this work we applied clustering analysis, a powerful technique suitable to discover patterns and similar subgroups, which has been successfully applied in recent studies on AD (Racine et al., 2016;Alashwal et al., 2019;Toschi et al., 2019). We tested how considering different sets of features can better diagnose the progression of AD and point out new potential pathological mechanisms involved in neurodegeneration. Results from hierarchical clustering analysis revealed that using the standard AD biomarkers Aβ42 and p-Tau, two groups of patients presented alternative signatures (clusters 1 and 2, Figure 2). One of these (cluster 1, Figure 2) could be associated with the AD profile showing low levels of Aβ42 and high levels of p-Tau, reflecting the accumulation of amyloid plaques and neurofibrillary tangles. However, a third subgroup emerged (cluster 3, Figure 2) with a heterogeneous composition of AD, MCI, and CT, underlining that the two standard biomarkers alone are unable of a sharp discrimination of the patient status. Probably, the sparse presence of MCI patients in all the clusters is due to the wide spectrum of cognitive and functional impairment that is captured by the MCI designation, impacting the heterogeneity of outcomes (Roberts and Knopman, 2013).
Interestingly, the information on iron concentration in CSF added one more cluster, generating two separated groups composed of patients classified with diagnosis of AD and MCI (clusters 3 and 4, Figure 3), both presenting low values of MMSE. These clusters differed for p-Tau and CSF iron levels, albeit presenting similar Aβ42 profile. Cluster 3 could be considered as a typical AD profile, with low levels of Aβ42 and high values for p-Tau, and in addition higher values of iron with respect to the two clusters containing mainly CT patients (clusters 1 and 2, Figure 3). Cluster 4 presents low levels of Aβ42, lower levels of p-Tau with respect to cluster 3, and the highest levels of CSF iron. The improvement of clustering scores assessed a better discrimination of patients by adding the iron content in CSF to the standard biomarkers. One possible interpretation of these results is that cluster 4 could be associated to patients in stages of dementia in which p-Tau starts to aggregate but deposition of Aβ plaques is already present.
In fact, according to the current models describing the timing of pathophysiological brain events in relation to the clinical course, preclinical phases of AD are characterized by plaques deposition, followed by later spread of neurofibrillary tangles (Jack et al., 2010;Long and Holtzman, 2019). Furthermore, the higher iron concentration combined with lower levels of p-Tau could suggest a harmful interaction between iron and p-Tau accumulation at early stages, inducing or worsening neurodegenerative events. This hypothesis is consistent with several studies, supporting the evidence that iron can promote the aggregation and pathogenicity of Tau (Smith et al., 1997;Yamamoto et al., 2002;Lovell et al., 2004;Ahmadi et al., 2017;Spotorno et al., 2020). Chelation therapies, based on intranasal deferoxamine treatment, may exert suppressive effects on the iron-induced tau phosphorylation, providing a valuable approach in preventing AD progression (Guo et al., 2013). In addition, further studies on patients reported an investigation of novel treatment strategy based on a metal-protein-attenuating compound to reduce toxic properties of Aβ mediated by copper and zinc (Ritchie et al., 2003;Lannfelt et al., 2008).
According to our results, the clusters containing patients affected by AD showed an increased level of iron with low levels of Aβ42, hallmark for senile plaques deposition, which confirms the link between iron and Aβ plaques. There are evidences for a variety of interactions between iron and Aβ: iron accumulates and co-localizes with Aβ plaques (Connor et al., 1992;Meadowcroft et al., 2009;Ndayisaba et al., 2019), their binding can form redox reactive and toxic species (Nakamura et al., 2007;Bousejra-ElGarah et al., 2011), with evidence for the formation of an iron-amyloid complex (Telling et al., 2017), and also iron levels can increase prior to plaques formation in an animal model of AD (Leskovjan et al., 2011). Increased iron levels are believed to enhance Aβ production via the downregulation of furin (Silvestri and Camaschella, 2008) and the iron regulatory pathways are also involved in proteostasis of Amyloid Precursor Protein (APP) (Rogers et al., 2008;. It has been hypothesized that brain oxidative damage concurs to AD pathogenesis before Aβ accumulation (Praticò et al., 2001), therefore iron accumulation might precede and cause the formation of plaques. Recently it has been proposed that an increase in the intracellular labile iron levels, due to mitochondria dysfunction, enhances the rate of APP synthesis and the activity of APP cleavage by beta-secretase resulting in Aβ formation (Kozlov et al., 2017). In addition, a recent study confirmed the link between iron retention in cells and mislocalization of APP, due to alteration of ferroportin activity in the modulation of iron efflux: this effect causes a change in endocytic trafficking with consequent neuronal iron elevation and oxidative damage that feature AD pathology (Tsatsanis et al., 2020).
Further connections between iron and lipoprotein metabolism have been detected, highlighting causative interaction and synergies between genes of iron homeostasis and established genetic risk factors of AD, such as APOE4, suggesting the iron metabolism as a possible therapeutic target (Tisato et al., 2018).
Emerging evidence suggested that blood iron homeostasis is altered in AD and already in MCI (Faux et al., 2014;Guan et al., 2020), including systemic variation of markers of iron metabolism, such as transferrin saturation and ceruloplasmin/transferrin ratio in serum (Squitti et al., 2010). Interestingly, in our case, we found a negative correlation between t-Tau and Tf in serum in AD that can support a role of Tf in neurodegeneration. Despite our observations require further confirmation in a larger cohort of patients, cluster analysis also found different concentrations of Tf in serum and iron levels in CSF for patients with MCI and dementia.
Using features set including standard biomarkers and s-Tf, four clusters emerged, with different profiles of s-Tf. Cluster 1 (Figure 4) containing mainly AD patients, associated typical AD profile with a lower level of s-Tf compared to two of three remaining clusters. This result might support that serum iron is lower in AD than in healthy controls (Tao et al., 2014), and that decreased plasmatic iron in AD could be due to transferrin desaturation (Hare et al., 2015), pointing out a role for systemic variations of iron metabolism in neurodegeneration. However, the other cluster comprising AD and MCI patients (cluster 3, Figure 4) reported a higher level of s-Tf with respect to the cluster 4 (Figure 4) composed of MCI and CT patients, requiring a further investigation on the s-Tf profiles in a larger population. Using a step-by-step approach, we finally used the full set of features, including also information on iron concentration in CSF, which largely improved the discrimination of patients according to their clinical diagnosis. Clustering analysis unraveled four clusters, visualized in the dendrogram (Figure 5), in which AD and CT patients are well-separated, supported by a good improvement of clustering scores. As previously discussed, the presence of MCI patients in all clusters reflected their wide spectrum in the current MCI diagnosis. Interestingly, a recent study reported that postmortem MRI and histology demonstrated differential iron accumulation in earlyand late-onset AD (Bulk et al., 2018), showing the presence of various distribution patterns for iron accumulation in subtypes of AD patients.
Two subgroups containing AD and MCI patients (clusters 1 and 2, Figure 5) differed in p-Tau levels and showed CSF iron levels higher with respect to the clusters composed of CT and MCI (clusters 3 and 4, Figure 5). This result sustains our previous hypothesis that iron concentration and p-Tau levels in CSF could play a crucial role in differentiating the actual stage of dementia.
The interpretation of clusters 3 and 4 ( Figure 5) is less simple. The different profiles of s-Tf for these clusters, containing CT and MCI patients, could be due both to the small size of samples requiring further investigation in a larger cohort.
Significant differences in s-Tf profiles have been detected in the clusters containing mainly AD and CT, respectively, showing also an increased ratio between the iron content in CSF and s-Tf in clusters only formed by patients affected by dementia and for the AD with respect to CT group. It is increasingly recognized that AD is a clinically heterogeneous disease with multiple causes, with an important role for brain vasculature (Montagne et al., 2017;Sweeney et al., 2018a). Our approach could be considered an indirect evaluation of the potential connection between iron homeostasis and blood-brain barrier (BBB) dysfunction. BBB dysfunction is a mechanism involved in the neurodegeneration and subsequently in cognitive impairment (Nation et al., 2019), and recently included in a hypothetical model of AD biomarkers (Sweeney et al., 2018b). Interestingly, the export mechanisms at the BBB level are altered in dementia, leading to potential targets for treatment (Pahnke et al., 2014). AD is characterized by altered BBB permeability and a link between iron-overload and BBB breakdown and brain mitochondrial dysfunction has been demonstrated (Sripetchwandee et al., 2016).
In fact, BBB prevents the diffusion of Tf from blood into CNS, as well as the migration of non-transferrin bound iron (NTBI), potentially toxic from the brain. Tf is transported across brain capillary endothelial cells following an endocytic mechanism mediated by Tf-receptors (Moos et al., 2007). The breakdown or alteration of this system could be part of the cause for pathological accumulation of iron into the brain and consequently in the CSF. In fact, CSF can be produced both via the choroid plexus or by the interstitial fluid of the brain (Nakada and Kwee, 2019).
Moreover, various studies proposed that iron trafficking across the blood-brain capillaries is involved in the aggregation of Aβ peptides leading to the potential onset of AD (McCarthy and Kosman, 2015), and also that iron accumulation may be associated with the age-induced changes in the expression of iron metabolism proteins in the brain (Lu et al., 2017).
To extract further information on the data, useful for future clinical studies, machine learning models have been trained to evaluate the impact of the inclusion of iron-related data in the diagnostic power of dementia. We selected LR model and linear SVM, one of the most used techniques for AD classification problem (Tanveer et al., 2020), giving good generalization performances also for small samples. In particular, the present results for both models were comparable, underlining a potential relevance of the iron-related feature (CSF iron) for the classification of AD, CT, MCI patients. Although AUROC did not detect a significant increase, in ranking the relevance of features the addition of CSF iron could suggest a potential role in the improvement of the diagnostic power of AD, MCI, and CT patients, provided further investigation on larger samples are performed. Moreover, the cross-sectional nature of our study is a limitation of the present investigation and longitudinal studies will be necessary to clarify the involvement of abnormal iron homeostasis in different stages of the disease process, i.e., including iron-related data from blood or MRI. Additionally, further studies with larger samples will be useful to quantitatively parse out our results and to confirm the stratification of patients turned out in the cluster analysis.
Finally, the use of cluster analysis proved its potential utility for identifying patterns of variables that might characterize disease progression. The addition of iron-related data to the corebiomarkers can help to capture the multifaceted nature of AD, co-characterized by Aβ plaques deposition and neurofibrillary tangles aggregation as well as other related processes. Future works should focus on the evaluation of abnormal iron concentrations in different stages of dementia, which can generate deposition in CSF or changes in circulating iron (protein-bound or free) arising from possible imbalances of the blood-brain exchange of iron. The evaluation of iron in the CSF can improve the tuning of personalized therapeutic strategies based on systemic or intrathecal administration of chelating agents acting directly into the brain.
In conclusion, our results support the evidence of iron overload in AD, and consequently the hypothesis that different clinical conditions with specific backgrounds involve the actual iron brain levels. Cluster analysis revealed a new potential stratification of patients when new parameters, related to the iron concentration in serum and CSF, are accounted for, advancing our understanding of the role of iron dysregulation in AD pathophysiology. Tight regulation of iron metabolism is pivotal to warrant neuronal homeostasis and its investigation can prompt avenues for both research on new pathological mechanisms involved in neurodegeneration and development of new treatments. The potential addition of iron-related data in clinical evaluation of dementia could improve the early diagnostic power and support new personalized disease-modifying therapies based on iron chelation able to slow the progression and worsening of the neurodegenerative processes.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by Comitato Etico Interaziendale A.O.U. Città della Salute e della Scienza di Torino -A.S.L. Città di Torino. The patients/participants provided their written informed consent to participate in this study.
AUTHOR CONTRIBUTIONS
EF, SB, FD'A, CG, OA, and IR: conceptualization and design. EF, SA, and OA: methodology. PC, GDF, AI, and IR: patient enrollment and clinical data managing. EF: computational design and manuscript preparation. SB, FD'A, CG, OA, PC, GDF, and IR: writing-review and supervision. All authors: contributed to the article and approved the submitted version.
FUNDING
This study was supported by Ministero dell'Istruzione, dell'Università e della Ricerca e MIUR project Dipartimenti di Eccellenza 2018 e 2022 to Department of Neurosciences Rita Levi Montalcini, University of Torino and the AIRAlzh Onlus-ANCCCOOP (SB). | 9,100 | 2021-02-22T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
Comparative Study of Two Processes to Improve the Bioavailability of an Active Pharmaceutical Ingredient : Kneading and Supercritical Technology †
Two processes have been developed for the enhancement of bioavailability of a poorly-soluble active substance, Eflucimibe by associating it with γ-CD (γ-cyclodextrin). In the first process (process a), Eflucimibe was added to an aqueous slurry of CD, in a kneading device. The evolution of the transformation was followed by DSC, FTIR, Eflucimibe dissolution kinetics, as well as semi-solid state change of the mixture. An optimization of the process was performed and a prevision of the scaling-up was made using dimensionless numbers. This process is simple and robust. It can be compatible at the industrial scale with a good economy and appropriate control. In the second process (process b), Eflucimibe and CD are co-crystallized using an anti-solvent process, dimethylsulfoxide being the solvent and supercritical carbon dioxide being the anti-solvent. Then, the co-crystallized powder is held in a static mode under supercritical conditions for several hours. A final stripping step, is used to extract the residual solvent. The coupling of the first two steps brings about a significant synergistic effect to improve the dissolution rate of the drug. Both processes resulted in a strong acceleration of the in vitro dissolution rate of the drug. Finally, in an in vivo test, these two processes appeared to be very effective, process (a) and (b) giving respectively an 8-fold and 11-fold increase in bioavailability.
Introduction
An important parameter in pharmaceutical formulations is the bioavailability of the active substance.Many new Active Pharmaceutical Ingredients (API) are ver y poorly water soluble.Their absorption by the human organism is therefore extremely low and difficult to control.In case of very low solubility, one of the first rule of the formulation process is to increase this bioavailability by enhancement of the dissolution rate and apparent solubility.A way to reach this goal is to associate these low-solubility active molecules with cyclodextrins (CDs) by forming inclusion complexes.
Although many articles describe the interactions between active molecules and CD only few papers deal with the processes used for such complexes production.Four classes of processes can be distinguished: liquid (co-precipitation, co-evaporation, spray-dr ying, freeze-dr ying, neutralisation), using supercritical CO2, semi-solid (kneading), and solid (sealed-heating, high energy co-grinding).Anyhow, the success of a drug deliver y technology and of the process used to produce it, are highly dependent on whether it can be scaled-up, is reproducible and allows for cost-ef fective manufacturing.This paper is focused on the comparison of two of them: kneading (a) and supercritical fluid processing (b), in the case of the complexation of Eflucimibe with γ-cyclodextrins (γ-CDs).
A first description of the kneading process has been presented by Gil １) and Hutin ２) .The use of supercritical carbon dioxide (SC-CO2) for particle generation of pharmaceuticals and for improving their bioavailability is well documented ３) .
These processes (a) and (b) will be described in the case of Eflucimibe, a highly potent acyl-coenzyme A O-acyltransferase (ACAT) inhibitor with the molecular formula C29H43NO2S (Fig. 1), treating hypercholesterolemia.Its structure and extreme hydrophobicity confers to this molecule a very poor solubility in water.
In terms of solubility and permeability, according to the Biopharmaceutics Classification System BCS ４) , it can be considered as a Class Ⅳ compound (Table 1), with low solubility in aqueous media and low permeability through the intestinal mucosa.The result is a high variability in blood level when formulated in lactose capsules １) and a poor bioavailability.
γ-CD is a cyclic octasaccharide (Fig. 2) obtained by enzymatic degradation of starch, consisting of 8 D-Glucose units, and presenting an hydrophilic external wall and an hydrophobic internal cavity that can receive organic molecules.This configuration allows to perform the dissolu-tion of the drug substance in aqueous solutions and to liberate it by dissociation of the complex, followed by the absorption of the drug in the circulatory system (Fig. 3) Eflucimibe was provided by Pierre Fabre Laboratories (Castres, France).γ-CD was purchased from Wacker-Chemie GmbH (München, Germany).
The Kneading Process
The kneading process can be considered as a mechanochemical process carried out in the presence of a small amount of solvent (water or other) that acts as lubricant for the molecular diffusion.This catalyst behaviour of the solid sate process, results in a smooth transformation of the reactants into the final products avoiding the contamination of the active ingredient by secondary transformation not suitable in the production of pharmaceutical products ５) .
We applied this process to the complexation of Eflucimibe with γ-CD.
Kneading equipment
The kneading equipment was a 316 L stainless steel Aoustin ® kneader with dual Z blades (Fig. 4).Those dual blades take up an important relative volume and the space between the wall of the kneader and the side of the blades is ver y small, initiating large shearing effects.Two scales of this apparatus were used : MX1 with a nominal capacity of 1.5 L and MX2 with a nominal capacity of 3 L.
Kneading process
The blade speed of the kneader was fixed at 50 rpm.γ-CD was introduced in the kneader bowl kept at 305 K (optimized temperature 2) ); Purified water (1 ml.min -1 ) is added to a mixture of Eflucimibe/CD at a (1:2) molar ratio and the blend is kneaded thoroughly while following simultaneously the tempera-ture and torque measurement until the increasing of the viscosity of the mixture which is a characteristic of the complexation (Fig. 5) 1) .The final mass quantity of purified water in the mixture was 27.5 %.The evolution of the transformation was followed by DSC (Differential Scanning Calorimetry), FTIR (Fourier Transform Infrared Spectroscopy), Eflucimibe dissolution kinetics, as well as semi-solid state change of the mixture (Fig. 6).For each sample taken, the paste obtained was dried at 313 K for 12h using a vacuum oven.The dried product was sieved below 50μm.The area called "ENERGY" under the curve is a characteristic of the process.The interaction between Eflucimibe and CD occurs if this area is sufficient.
Several approaches are available for controlling the process at one scale and for scaling-up to another scale.The experimental design approach can be a powerful tool to model processes.Three input variables that are water extent, blade speed and temperature have already been selected.Two output variables are also selected : dessolution rate of the product and the extent of inclusion determined by DSC.The principle is to determine for each output variables a model involving each input variables and their interactions.By comparison of the models it is possible to optimise the different input variables to obtain a compromise between them and achieve the desired results of the output variables.The effect of the following process parameters on the extent of inclusion and solubility enhancement (Fig. 7) has been investigated by means of an experimental design analysed at MX1 scale which allows the definition of an optimised experiment with those operating conditions.
DSC and thermoanalytical procedure for the determination of the percentage of transformed Eflucimibe (Y) Thermal analysis by DSC was carried out using a Perkin Elmer DSC 7 apparatus.Samples of 3 mg were introduced into sealed aluminium pans.
DSC scans were per formed in triplicate under nitrogen, at a heating rate of 5 K.min -1 in the temperature range of 303 K to 378 K. Heats of fusion were automatically determined by the software following calibration with Indium (28.4 J.g -1 ), using integration of the areas under the DSC endothermic peaks of melting.A thermoanalytical procedure can be applied to quantify the interaction yield 6) .F is the fraction by weight of Eflucimibe in the starting mixture and N, the fraction by weight of Eflucimibe in the initial state after the kneading step.The percentage of transformed Eflucimibe after interaction, Y, is calculated according to equation ( 1) where N is calculated according to DSC results and equation (2) (2)
FTIR spectroscopy and spectroscopic procedure to follow Eflucimibe interaction
The infrared spectra were recorded on a Nicolet FTIR spectrometer.The analysed component was dispersed in KBr medium in solid state before acquisition.
The Eflucimibe interaction with CD led to a decrease of Eflucimibe band intensity.In order to quantify this modification, the Beer-Lambert law was applied by the determination of Log I0/I with I0 corresponding to the absorbance at 1572 cm -1 (spectral region where Eflucimibe and CD do not present spectral band) and I corresponding to absorbance at 1537 cm -1 (spectral region where only Eflucimibe presents spectral band).
Determination of Eflucimibe solubilisation kinetics
The Eflucimibe solubilisation kinetics were determined with samples corresponding to 50 mg of Eflucimibe.These samples were added to 100 ml of the solubilisation medium corresponding to an aqueous solution containing 5 % (w/V) of sodium lauryl sulfate.The samples were continously stirred while remaining in a water bath at 310 K (normalized temperature for pharmaceutical test).At various time intervals, samples were withdrawn and filtered through 0.45μm membrane.The amount of Eflucimibe dissolved was determined by HPLC using UV detection at 220 nm.Acetonitrile and purified water at 82 : 18 V/V was run at 1ml.min -1 flow rate through a reverse phase C8 column.
Use of dimensionless numbers to study the scaling-up
The principle of the methodology is to solve the relationship on one scale and then to use it to calculate the power required on another scale to obtain a same finished product quality.We applied the Buckingham theorem 7) ; the main physical variables are found to be: The power number : Np = The Reynolds number : Re = The Froude number : Fr = The fill ratio of the kneader : H/R The blade size : (R)/L Where g is the gravitational constant, R, L respectively the blade, length and radius, N the blade rotational speed, h the height of powder, ρ the bulk density of the powder, η the viscosity and ΔP the net blade power consumption that is to say total power less power required to stir the dry powder.
Results and discussion
The process is fast and evolves as shown on Fig. 6 The complexation induced a dramatic increase of Eflucimibe dissolution rate (Fig. 7) An optimization of the process was performed and a prevision of the scaling-up was made using dimensionless numbers.
As the viscosity is unknown, it was replaced by the mean torque before complexation and the dimensionless Re becomes a pseudo-Reynolds ψRe 8) .
The relationship between the power number and the other dimensionless group is established by Fig. 8 and equation 4: Where the correlation coefficient is 0.99 for 17 experiments.
One experiments has been repeated three times under the same conditions to test the reproducibility of the process.The resulting points on the scale-up relationship (Fig. 8 and 9) were ver y close to another.
Three experiments carried out under the optimised conditions give good results in agreement with the dimensionless relationship.
Those equations are applicable for a series of geometrically similar kneader of different sizes.It was possible to check those predictions at a twice scale, with an MX2 kneader.Plot of Np versus the combination of the four remaining dimensionless numbers are presented in Fig. 9 with those last experiments.The relationship between the power number and the other dimensionless group stay the same as equation 4 where the correlation coefficient is 0.99 for 17 experiments at MX1 scale and 6 experiments at MX2 scale.
The results show that the process is fast, simple and robust.Using dimensionless numbers it can be conducted at the industrial scale with a good economy and appropriately monitored using technologies recommended by FDA's Process Analytical Technology (PAT).
The Supercritical Process
SC-CO2 has recently emerged as a new medium for complexation with CD due to its properties of improved mass transfer and increased solvating power 9), 10) .
We have implemented a new process by combining a co-crystallisation anti-solvent process SAS 11) with a maturing step 9) and adding finally a stripping step to extract residual solvent.
Experimental set-up and procedures
All experiments were performed in a flexible supercritical machine (Separex, France) shown on Fig. 10.
Dimethylsulfoxide (DMSO) as the solvent and SC-CO2 as the antisolvent were used in the SAS experiments.CD and Eflucimibe were both dissolved in DMSO.This solution was injected into the CO2 stream in the mixing chamber of a nozzle (Spraying System, France), and sprayed into an expansion vessel.The powder formed was collected in a porous bag placed in the expansion vessel after depressurisation.
For the maturing step, 7 g of Eflucimibe/CD powder (with a molar ratio of 1/2) were wetted by 2.33 g of water (corresponding to 25 mass% of total powder) and placed in a 2 l autoclave.This vessel was filled with SC-CO2 at the desired pressure and temperature and left for several hours without any agitation.The powder was recovered after gentle depressurisation.
In the final stripping step, the powder was submitted to a continuous flow of SC-CO2 for two hours in a stainless steel basket.
Powder characterisations
After each step, composition of the powder obtained was determined.Eflucimibe content was measured by HPLC, residual DMSO content by GPC and water content with a Karl Fisher titrator.γ-CDcontent was then calculated from all these results.Eflucimibe, DMSO and water contents are given in mass percentage of the total powder mixture.
The DSC thermograms were performed on a Perkin-Elmer, DSC-7 calorimeter equipped with a thermal flux cell device.The DSC patterns of the samples (2-3 mg) were obtained between 313 K and 413 K at a heating rate of 5K/min under a N2 gas stream.They are shown in Fig. 11, for the initial powder mixture (Fig. 11a) and after each processing step (Fig. 11 b, c and d).By integrating the melting peak of drug in DSC thermograms, which is generated by the crystalline form of the powder, and knowing independently the total drug content, it is possible to calculate the amount of non-crystalline Eflucimibe.This last one corresponds to the drug not visible on DSC thermogram, hence drug molecule likely implied in interactions with CD and microcrystalline aggregates dispersed among CD matrix.It acts as an indicator of the level of drug/CD complexation.
To estimate the dissolution rate improvement, in vitro dissolution studies were performed at 310 K as described elsewhere 12) .The dissolution rate is defined as the Eflucimibe content dissolved in the medium after a fixed time, expressed in μg of Eflucimibe per ml of solution.The dissolution curves are
Co-cr ystallisation step
This step has been conducted according to previously published procedure by Rodier et al. 13) .On ESEM microphotographs (not shown) an intimate mixture of both components can be seen: large CD particles with drug fibres deposited on them.
The Eflucimibe melting temperature (Fig. 11a) of the physical mixture with γ-CD was found to be 402 K.For the co-crystallised powder, we observed a melting temperature of 399.1 ± 0.6 K (mean of 29 experiments).In addition, a part of Eflucimibe contained in the mixture after co-cr ystallisation is not visible by DSC.
After this step, the dissolution rate was higher than that of the physical mixture with the same profile (Fig. 12b).It was no longer correlated to the specific surface of the powder, which can be tuned by the operating conditions with Eflucimibe alone 14) but not in the presence of CD.For instance, the mass ratio CO2 /DMSO, had no effect on the composition and dissolution rate of the resulting powder.On the contrary, decreasing the mole ratio of Eflucimibe to CD in the initial mixture from 1/1 to 1/3 increased the drug crystallisation yield from 40 % to 70 % (w/w).This yield is defined as the ratio between the mass of powder formed and the mass of powder initially dis-solved in DMSO.
Maturing step
This process, first described by Van Hees et al 9) is very effective for complexation.Several drugs have been processed successfully with this method 15,16) .After this step, drug fibres are not so clearly distinguishable from CD particles on microphotographs (not shown).Furthermore, only a ver y small Eflucimibe melting peak can be seen on DSC thermogram (Fig. 11c).A strong increase in the drug dissolution profile is noticed with a peak at 500mg/ml (Fig. 12c).
The influence of CO2 density and viscosity was evaluated on the dissolution rate.Both the noncr ystalline drug content and the dissolution rate increase when CO2 density and viscosity decrease as shown on Table 2. Besides, the non-crystalline drug content is not linked to the solubility of the active substance in CO2.This suggests that mass transfer would limit the maturing step and that CO2 solvent power is not a crucial point.
In addition, the influence of the operating time of this static step has been studied.A classical saturation-shape evolution was noticed: up to 6 hours, the powder composition is modified and dissolution kinetics increases, while both remain constant beyond 6 hours.
We have also studied the effect of the initial mixture composition.Three mixtures having the same mass composition were wetted, placed in the autoclave and submitted to the same conditions (30 MPa, 373 K, 16 hours).The first mixture was composed of the initial drug and CD, the second of drug and CD cr ystallised separately by SAS process and the third of drug and CD co-crystallised by SAS.Table 3 shows the dissolution rate after 2 hours for each mixture at different stages: just after mixing, just after adding water and after the static maturing step.
This table provides also the specific surface area of the mixtures.Comparison of the first and the second mixtures before the static step confirms that the amount of dissolved drug increases with the specific surface area.Comparing the second and the third mixtures, it appears that the amount of dissolved drug is no longer correlated to the specific surface area.Therefore, the static step may enhance the dispersion of the drug into the CD matrix and thus it may increase the dissolved drug concentration in all cases.However, the improvement of the compound dissolution is significantly higher for the before hand co-crystallised powder.In conclusion, a strong synergistic effect is obtained by coupling the co-crystallisation and the static steps.
Stripping step
After the stripping step, a homogeneous aspect of the powder was observed (not shown).This can be linked with the complete disappearance of the Eflucimibe melting peak (Fig. 11d) and in a sharper and higher dissolution peak (Fig. 12d).The aim of the stripping step was to decrease the solvent content below 5000 ppm, which is the pharmaceutical standard for a class III solvent.Decreasing the solvent below this threshold is possible, but some drug extraction will be unavoidable, which is the main drawback of this step.In addition, the stripping step has dehydrated the CD: roughly, water content drops from 13%mass to 2-3%mass.Some of the adsorbed water onto CD was dissolved into the SC-CO2 flowing through the bed of powder, thus dehydrating it.This explains the fast initial dissolution rate due to its enhanced hygroscopicity.
Dissolution kinetics
The dissolution kinetics evolves in the following way.First, the dissolving medium diffuses into the CD matrix containing Eflucimibe.Then, Eflucimibe is dispersed into the dissolving medium and is temporarily stabilized into SDS micelles corresponding to the maximum dissolved drug concentration on Fig. 12. Then follows a recr ystallization of Eflucimibe leading back, after a sufficient period of time (at least 20 h), to the solubility of pure Eflucimibe in this dissolving medium, (that is around 100 μg/ml).According to this scenario, the increase in dissolved drug concentration does not correspond to a true dissolution of the active substance, but to the generation of a metastable colloidal dispersion of SDS micelles including drug.Finally, the acceleration of the dissolution kinetics after the stripping step may be due to the acceleration and amplification of the first dissolution step, which is the diffusion of the aqueous medium through the dehydrated CD matrix Finally, this new process using supercritical CO2 and γ-CD leads to a dramatic increase in the drug dissolution rate.This process includes three steps: (1) a semi-continuous co-cr ystallization by a supercritical anti-solvent process generating a solid dispersion, (2) a batch maturing step during which the powder mixture evolves towards a more intimate mixture, and (3) a final semicontinuous stripping step where residual solvent is extracted with some Eflucimibe and water.
The main novelty of this process lies in the coupling of these three steps, exhibiting a strong synergistic effect in the improvement of the dissolved drug concentration of the drug.
Comments on both processes
A new innovative and promising supercritical process but not yet fully understood and controlled; a more classical, usual one but better controlled and more advanced in terms of scaling up.
Concerning the supercritical process, the main limiting point is the use of organic solvent in the SAS step.It has to be pointed out that the co-crystallization step leads to an intimate mixing of the API and CD; this can be an advantage when the API is a voluminous molecule that may present difficulties to be efficiently mixed.But this step is not needed in many others cases to improve the efficiency of the maturing step and therefore physical mixtures can be sufficient.This has been confirmed for instance for the binary Ketoprofen-β-CD 10) .In addition, the stripping step is needed only when SAS step is performed; it is a typical extraction process where enhanced transfer properties of the supercritical CO2 are determining parameters.Besides, to be industrially conceivable, SAS and stripping steps imply that supercritical CO2 is regenerated (a solvent/antisolvent separation is needed) to be recycled.The key-step that is the maturing step is a very simple one, easy to handle, and a "green" one, low energy-consuming (the main energy requirement is when pressurizing the CO2).In addition, it delivers a ready-to-use product without any further processing: it has been observed with the Ketoprofen-β-CD mixture that no additional water remained in the produced association complex, not needing then a subsequent stripping or drying step 10) .On a scaling-up point of view, in the SAS step, the ratio Solvent/Antisolvent has to be kept constant together with the API concentration in the solvent: these are the predominant invariant parameters and the scaling up could be performed as "scaling out" by setting lab-scale autoclaves with their nozzles in parallel.As for the maturation step, the main invariant parameter that has to be kept constant when changing scale is the mixture (API/CD/Water) composition and duration, with mixing conditions unchanged.Yet, in spite of its already proved efficiency, this step has to be further investigated in order to fully understand the phenomena implied.On a process point of view, the handling of the produced powders could also be improved.The longest step is the maturing one, which is 6 hours.In any case, this newly set-up process has proved to be highly effective concerning the in vivo bioavailability of the Eflucimibe, which was multiplied by 11 (AUC, Area Under the time con-centration Curve ) in dog studies (unpublished data).
As for the kneading process, the device used is more conventional and simple.Scaling-up is relatively easy to perform with the existing commercial devices using traditional approaches of chemical engineering like dimensional analysis and experimental design.This process performed with water avoids the use of organic solvent and works at low temperature level.The produced powder allows a significant enhancement of the API bioavailability.However, it has to be noticed that the operating parameters, in terms of formulation, have to be previously optimized in order to allow the scaling-up based on the capacities of commercial devices: a wrong formulation may induce a very high increase of the required torque, that is not acceptable on the mechanical point of view, by commercial devices.
Conclusion
Both processes resulted in a strong acceleration of the in vitro dissolution rate of the drug.Finally, in an in vivo test, different Eflucimibe processed formulations have been compared.In comparison with other technologies used (data not published) these two processes appeared to be the most effective, process (a) and (b) giving respectively a 8-fold and 11-fold increase in bioavailability.
Process (a) can be anticipated as a "green process", as it does not use any organic solvent, but only a small amount of water, eliminated by final drying.It is fast, easily scalable and easy to monitor with Process Analytical Technology (PAT) tools; it can be continuously monitored, evaluated and adjusted using validated inprocess measurements, tests, controls, and process end-point.In addition, it needs fewer investments, the material is easy to clean, and it allows the treatment of large quantities.
Process (b) appears to be the most efficient.It uses SC-CO2 as antisolvent that can be recycled in the process and only a small amount of DMSO as solvent eliminated during the final stripping step.A drawback may lie in the fact that it requires highpressure equipment.
Depending on the physical-chemical properties (solubility...) of the active ingredient and on the context of drug development and production (NDA-New Drug Application, generics) depending on economics, rationality and efficiency, and depending on how easy it is to obtain a good complexation percentage, energy needs, it can be better to use one or the other technique.
Fig. 5
Fig. 5 Torque and temperature versus time during complexation of Eflucimibe and cyclodextrin.
Table 1
Biopharmaceutics Classification System
Table 2
Effect of the maturing step on Eflucimibe-crystalline content and dissolution rate as a function of CO 2 density and viscosity
Table 3
Maturing step, dissolution rates and specific surface areas as a function of the initial mixture | 5,838 | 2007-01-01T00:00:00.000 | [
"Chemistry",
"Medicine"
] |
The software structure for agent-oriented simulation with distributed dispatching
This paper deals with the problem of the implementation of the agent-oriented simulation on high-dimensional models in the social science domain. It was shown that high dimensionality of models and the complexity of their development using the existing tools were the main constraint factors. The analysis of existing agent-oriented simulation systems was held. Some special aspects of platforms, on which such systems were performed, were considered. The influence of clustering on the simulation rate was shown. The structure of the software for the agent-oriented simulation using the existing agent-oriented simulation systems on the basis of the distributed scheduler, which provides clustering optimization of a model problem, was proposed.
Introduction
At the present time there are a great number of investigations in the social science domain due to the growth of adversarial social phenomenа [1,2]. Nowadays the most advanced analysis tool, which is applyed in the social science domain, is simulation on the basis of an agent-oriented approach [3]. In works [4][5][6] the results of the above mentioned method for analysis of large social groups were shown.
The successful application of the agent-oriented simulation in the social science domain takes place due to the fact that the method closely corresponds to the domain field.
It should be emphasized that there are some peculiarities for the agent-based simulation in the social science domain: -large agent population (hundreds of thousands of agents), -complex agent behavior, -dividing the agent by groups/types, -using the high-efficiency cluster solution.
The analysis of agent-oriented simulation software
There are some key problems of the agent-oriented simulation application for real tasks: -inadequate agent models due to the lack of domain data; -inadequate tools [8][9][10], which requair some special user's knowledge, which does not link with a domain.
In [9] the latest agent-oriented simulation, systems (AOSS) were presented. The results of We note that the majority of AOSS, which are oriented to performe scaled models, in order to achieve a required efficiency, keep an operation on clusters and have optimized implementations (for example, Flame-HPC, Repast-HPC).
Due to enhancement of the efficiency of graphics processors as compared to general-purpose processors [11] the problem of AOSS implementation on GPU has become currently important.
AOSSs based on FLAME-GPU, which are aimed at using the NVidia made graphics accelerator, was developed in [12]. The above mentioned AOSS performs modeling of scaled systems without an accessibility to clusters.
However, in the context of GPU modeling, it should be taken into account that, since a particular limit, GPU efficiency begins to reduce the population growth much faster than in cases when clusters are used. Though, FLAME-GPU can be considered as the necessary alternative to cluster solutions in case of the out-of-the-box solution, when the population size is not extrimal and GPU has certain efficiency.
To sum up, it can be said that FLAME, FLAME-HPC, Repast-HPC, FLAM-GPU are optimal solutions among the open AOSSs in the social science domain, which can be described in terms of large models and complex agent behavior.
The analysis of implementation platforms for AOSSs
On the basis of AOSS analysis, it can be concluded that AOSS efficiency depends on the agent model which is used. As a result, the choice between the cluster and GPU solutions is rather problematic, particularly, at the initial stages.
The AOSS comparison on the basis of the implementation platform is presented in Table 2. 3 We can observe in Table 2 that GPU-based solutions are much better in terms of the cost/performance ratio. At the same time, model size restrictions do not allow us to use GPU-based solutions for extremely large size models. To some extent it can be negated by means of several GPUs in a workstation computer. However, it requires buying specialised GPUs and a mother card. But this approach does not solve a scaling problem. It just increases a limit when AOSS simulation performance begins to reduce. It follows that a combined solution, which involves clusters of workstations and GPU, can be considered as an optimal. Herewith, the number of workstations can be increased according to scaling demands. In this case, the problem of communication between GPUs both intra-cluster and intra-workstations, is meant to be solved. To deal with this problem NVIDIA company developed NCCL -NVIDIA Collective Communications Library, which provides parallel computation primitives on multi-GPU and multi-node environment [13].
Cluster solutions use the powerful interfaces of date transmission both between cluster nodes and cluster interconnects. For example, NCCL provides date transmission between nodes by means of InfiniBand verbs, libfabric, RoCE and IP Socket.
Another way to solve a scaling problem involves middleware using. It provides model code crosscompilation. This approach allows us to use some AOSSs of various types with various implementation platforms. The similar approach using of OpenABL is presented in [14].
It must be mentioned that the foregoing approach allows us to solve the problem of high complexity model development. As it shown in [9], highly-efficient AOSSs are characterized by high complexity model development (Table 1). Herewith, for this purpose a general-purpose programming language is used. If model often changes during the modeling process, it is necessary to attract programmers to solve some current problems. As a result, the bottle neck of modeling is the rate of model change by the programmers for needs of domain experts instead of the execution speed of a model. There is some information about the cost of model development in eLOC for various AOSSs in [14]. We can see that FLAME GPU demonstrates the cost of development, which can be compared with ABL cost. It comes from the fact, that a pattern system is used for model development [11,15].
Another way to simplify the process of model development is middleware usage. It represents a graphical interface for model development. In this case, original model code is generated automatically on the basis of input data. This approach can be easily implemented for AOSS, which uses the various configuration files for model description (for instance, FLAME, FLAME GPU). The step of code generation should perform on a separate module, as in [14], in order to increase its functionality (for example, various AOSS supporting) regardless of middleware.
Secondly, factors, which have an impact on model execution speed, should also be considered. A scheduler, which executes an agent replacement, should be put in the cluster system. The scheduler is responsible for monitoring of the state of the cluster and carries out agent replacement when computational node workload exceeds the threshold or heavy network load takes place. In order to provide performance and scalability of the system, the scheduler should be distributed. In [16,17] the description of distributed scheduler usage in the context of failover problem solving in distributed computing environment was presented.
The assessment of factors having an impact on the simulation rate
It must be mentioned that there are some factors having an impact on the simulation rate: -cluster node performance, -speed of data transmission interface between the cluster nodes, -intensity of communications between the cluster nodes, -complex agent behavior. There are some methods to speed up the simulation rate: -cluster node performance enhancement, -high-speed network interface, -effective agent distribution. The first two methods can be used if there is an opportunity to choose a cluster or to change its configuration. In the context of a given cluster these methods cannot be used.
In this work we will dwell upon the last method. For this purpose, we should assess in what way the ineffective distribution of agent groups influences the simulation rate.
Let the intensity of communications be from agents, which are split into M groups: (2) Let us assess the volume of a single node transmission considering the following assumptions: -an agent participates only in one group, -each group is fully located on one node. Let agents be involved in groups of equal size i N , which are equally distributed on computational nodes (k groups per node).
Let l be all nodes, and then the total number of agents is described by the following equation: We assume that agents communicate with each other with intensity in S within a cluster and out S between clusters. Considering the fact that each cluster is located on one computational node, information exchange within a cluster does not lead to occurrence of traffic in the network. From among out S communications a part of them ( 1) i kN is transmitted to agents of a cluster, which are located on the same node as an agent-transmitter is. It also does not lead to occurrence of traffic in the network. The number of communications which are transmitted by each agent of any node to agents of other nodes is equal to And for all agents it is equal to ( ) / out ii kN S N kN N . Herewith, the agents of a node will receive communications from agents of each other nodes: Consequently, a generic traffic of a node is calculated using the following formula: From the given expression we can see that the volume of data transmission grows in a linear direction when: -increasing the group size, -increasing the number of clusters on the node, -increasing the transmitted communications. It must be mentioned that: -increasing the number of nodes increases the traffic limitedly ( -synchronization of agent performance within a simulation cycle in case of different computation and data transmission time leads to reduction in the computation system effectiveness and the simulation time increases respectively.
The obrained expressions allow evaluating the possibility of simulation, depending of model parameters and communication interface.
In figure 1 a "node trafficnumber of agents per node" diagram is presented. It allows evaluating the possibility of simulation, depending of model size and equipment configurationnumber of nodes and communication interface parameters. It is worth noting that, in case when an agent can be involved in more than one group simultaneously, these groups should be located on one computational node. If it is impossible to implement such distribution, then it is necessary to reduce the number of agents included in groups, which are located on different computational nodes.
The software structure for agent-oriented simulation
To provide clustering controlling during the simulation, the software structure for agent-oriented simulation is presented in figure 3. The system involves a control node and execution nodes. The control node is a coordinator of the whole system. AOSS is not performed on it. A scheduler on the control node executes only communication between schedulers from other nodes.
The following components are deployed on the control node: -model development module, which provides domain-specific tools for model development and setting; -visualization and analysis module, which provides simulation result representation and analysis tools; -control module, which provides simulation control (launch, stop and so forth); -model generator, which creates configuration files on the basis of data from model development module that are necessary for AOSS performance; -scheduler, which provides monitoring of the state of the model implementation platform using data exchange with other schedulers and performs AOSS configuration data transmission to other nodes.
AOSS is launched on the execution nodes. The scheduler provides the AOSS configuration and control, and is performed on the same node.
The system operates in the following manner (we assume that a model has been developed and the initial distribution has been prepared): 1.
Schedulers are launched on each node.
2.
Schedulers exchange data about their own nodes condition, coordinating the approval of their conceptualization about the system.
3. When synchronizing is reached, a scheduler of control node transfers data, which needed for simulation (configuration files, initial distribution files, etc)
4.
After having received needed data, schedulers perform a resynching. When the resynching is successfully completed, schedulers run simulation. 5.
During the simulation, schedulers monitor the state of the environment: nodes operability, nodes processor utilization, data transmission channel loading, etc). 6.
In case of abnormal situations (node failure, loading threshold exceeding of a computing resource) schedulers break simulation. 7.
On the basis of the last completed iteration schedulers create a new initial distribution and perform a synchronizing of a new system state. 8.
After system synchronizing the simulation is run. 9.
If it is necessary, 7-8 steps are repeated until simulation is completed. In the event that there is no need to use a cluster, the system can be deployed on a single node. In this case the scheduler also provides control functions.
It must be mentioned that when we use a single node configuration, the scheduler is not necessary. A software structure can be simplified. In this case AOSS access to configuration data should be provided and control functions should be put in the control module.
Conclusion
The problem of agent-oriented simulation in social science domain was examined in this work. It was shown that the main difficulties in this field are high dimensionality of models and high complexity of model development due to shortcomings of existing modeling tools.
The analysis of existing AOSSs was held and some peculiarities of platforms, on which AOSS is launched, were examined. Some approaches to model scaling and simplification of model development were considered. | 3,052 | 2020-11-01T00:00:00.000 | [
"Computer Science"
] |
White Matter Tissue Quantification at Low b-Values Within Constrained Spherical Deconvolution Framework
In the last decades, a number of Diffusion Weighted Imaging (DWI) based techniques have been developed to study non-invasively human brain tissues, especially white matter (WM). In this context, Constrained Spherical Deconvolution (CSD) is recognized as being able to accurately characterize water molecules displacement, as they emerge from the observation of MR diffusion weighted (MR-DW) images. CSD is suggested to be applied on MR-DW datasets consisting of b-values around 3,000 s/mm2 and at least 45 unique diffusion weighting directions. Below such technical requirements, Diffusion Tensor Imaging (DT) remains the most widely accepted model. Unlike CSD, DTI is unable to resolve complex fiber geometries within the brain, thus affecting related tissues quantification. In addition, thanks to CSD, an index called Apparent Fiber Density (AFD) can be measured to estimate intra-axonal volume fraction within WM. In standard clinical settings, diffusion based acquisitions are well below such technical requirements. Therefore, in this study we wanted to extensively compare CSD and DTI model outcomes on really low demanding MR-DW datasets, i.e., consisting of a single shell (b-value = 1,000 s/mm2) and only 30 unique diffusion encoding directions. To this end, we performed deterministic and probabilistic tractographic reconstruction of two major WM pathways, namely the Corticospinal Tract and the Arcuate Fasciculus. We estimated and analyzed tensor based features as well as, for the first time, AFD interpretability in our data. By performing multivariate statistics and tract-based ROI analysis, we demonstrate that WM quantification is affected by both the diffusion model and threshold applied to noisy tractographic maps. Consistently with existing literature, we showed that CSD outperforms DTI even in our scenario. Most importantly, for the first time we address the problem of accuracy and interpretation of AFD in a low-demanding DW setup, and show that it is still a biological meaningful measure for the analysis of intra-axonal volume even in clinical settings.
In the last decades, a number of Diffusion Weighted Imaging (DWI) based techniques have been developed to study non-invasively human brain tissues, especially white matter (WM). In this context, Constrained Spherical Deconvolution (CSD) is recognized as being able to accurately characterize water molecules displacement, as they emerge from the observation of MR diffusion weighted (MR-DW) images. CSD is suggested to be applied on MR-DW datasets consisting of b-values around 3,000 s/mm 2 and at least 45 unique diffusion weighting directions. Below such technical requirements, Diffusion Tensor Imaging (DT) remains the most widely accepted model. Unlike CSD, DTI is unable to resolve complex fiber geometries within the brain, thus affecting related tissues quantification. In addition, thanks to CSD, an index called Apparent Fiber Density (AFD) can be measured to estimate intra-axonal volume fraction within WM. In standard clinical settings, diffusion based acquisitions are well below such technical requirements. Therefore, in this study we wanted to extensively compare CSD and DTI model outcomes on really low demanding MR-DW datasets, i.e., consisting of a single shell (b-value = 1,000 s/mm 2 ) and only 30 unique diffusion encoding directions. To this end, we performed deterministic and probabilistic tractographic reconstruction of two major WM pathways, namely the Corticospinal Tract and the Arcuate Fasciculus. We estimated and analyzed tensor based features as well as, for the first time, AFD interpretability in our data. By performing multivariate statistics and tract-based ROI analysis, we demonstrate that WM quantification is affected by both the diffusion model and threshold applied to noisy tractographic maps. Consistently with existing literature, we showed that CSD outperforms DTI even in our scenario. Most importantly, for the first time we address the problem of accuracy and interpretation of AFD in a low-demanding DW setup, and show that it is still a biological meaningful measure for the analysis of intra-axonal volume even in clinical settings.
Keywords: diffusion MRI, DTI, CSD, AFD, tractography, white matter quantification, corticospinal tract, arcuate fasciculus INTRODUCTION In the last decades diffusion MRI allowed to study non-invasively white matter (WM) by analyzing water molecules diffusion process in vivo (1). Diffusion Tensor imaging (DTI) was the first model historically developed to describe tridimensional water anisotropic motion in the brain (2). DTI is based on the estimation of diffusion tensors, i.e., order 3 positive definite matrices: tensor eigensystem describes water apparent diffusivity (the eigenvalues) in three main orthogonal directions (the eigenvectors) (3). Taking into account tensor model, tissues quantification has been characterized over the years by means of several scalar indices, such as fractional anisotropy (FA) and mean diffusivity (MD) (4). These values have been shown to correlate with WM integrity in normal vs. pathological conditions (5,6).
CSD is a modified high angular resolution diffusion imaging (HARDI) based model (18, 23) that investigates water motion by fitting a set of rotational and spherical harmonics to determine the so-called fiber Orientation Distribution Function (fODF) (21,22). CSD attempts to individuate all fiber populations insisting over WM voxels based on a representative one-fiber population signal, the so-called response function. From CSD framework it is possible to derive indices to quantify at voxel-wise level WM fiber bundles (24,25); compared to DTI based features, these indices are unbiased with respect to the presence of multiple fiber bundles insisting inside the same voxel. In particular, in Raffelt's paper (25) apparent fiber density (AFD) has been introduced: based on the properties of diffusion signal, AFD attempts to estimate intra-axonal volume fraction (26) of each distinct fiber bundle insisting over WM voxels. AFD has been recently successfully applied in normal as well as pathological conditions (27,28).
In current literature, like other HARDI based methods, CSD and AFD are recommended to be employed in diffusion datasets with relatively high b-values (3,000 s/mm 2 ) and a minimum of 45 distinct encoding diffusion directions (19). At the same time, other tissue quantifications techniques, e.g., NODDI (29) or CHARMED (30), involve schemes with multiple shells (i.e., multiple b-values).
Currently, especially in clinical environments, a huge number of acquisition protocols make use of datasets with lower b-values (1,000-1,200 s/mm 2 ), and fewer unique directions (∼30). This happens because of the old machine used, or mainly because they require less time to be accomplished. Time factor is indeed of huge importance when dealing with patients, who are usually less tolerant and collaborative due to their particular conditions. In such scenarios, the common approach is to stick with tensor model and related analyses. Despite that, in the last years an emerging number of studies applied CSD on datasets derived from a setup that is below the recommended standards, see for instance (31)(32)(33).
In this study we aim at systematically investigating the amount of information achievable within the CSD framework on real data with a very low-demanding setting, i.e., when employing a single shell (b-value = 1,000 s/mm 2 ) and 30 unique diffusion gradient directions. To this end, we compared CSD outcomes with DTI model ones, which is the gold standard with those settings. We performed tractographic reconstruction and related tract-based ROI analysis (TB-RA) of two well-known pathways, namely the Corticospinal Tract (CST) and the Arcuate Fasciculus (AF). Deterministic as well as probabilistic tractography were implemented and compared based both on DTI and CSD models (21,(34)(35)(36)(37). By means of multivariate statistics we subsequently analyzed tissue quantification dependence on the diffusion model adopted as well as on the threshold levels applied to noisy tractographic maps. Most importantly, for the first time with the abovementioned hardware settings, we focus on the biological meaningfulness of AFD to understand whether it can be still considered a valid surrogate of intraaxonal volume fraction. Eventually, based on the TB-RA, we investigate the nature of the relationship between AFD and FA.
MRI Protocol and Pre-processing
Thirteen right-handed healthy subjects (6 women and 7 males, mean age 32.4 years, age range 25-42 years) without any history of neurological disease were recruited for this study. Before MRI acquisitions, each participant signed a written informed consent. The entire study was approved by the Ethical Committee of IRCCS Centro Studi Neurolesi "Bonino-Pulejo"; investigation has been conducted in accordance with the Declaration of Helsinki. MRI acquisition protocol was performed on a 3T Achieva Philips scanner (Philips healthcare, Best, The Netherlands) mounting a 32-channel SENSE head coil. Following datasets were collected: For each subject, motion and eddy current distortions artifacts occurring on DW volumes were corrected by means of eddy FSL tool (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/). Rotational part of transformations originating from correction process was subsequently applied to gradient directions. To obtain an estimation of AFD that could be comparable across subjects, the same preprocessing pipeline suggested in Raffelt et al. (25) was adopted. Therefore, b0 volume was used to estimate a multiplicative bias field by means of fast FSL routine. After applying bias field to b0 and DW images, all volumes were normalized by dividing by the median b0 intensity measured on an WM mask. T1w image was later on co-registered to preprocessed DWs following a scheme previously reported (38): in brief, CSF probability maps were estimated separately for b0 and T1 images by means of New Segment option of SPM8 (https://www.fil.ion.ucl.ac.uk/spm/). B0-based CSF probability map was then up-sampled to the same resolution of T1; flirt and fnirt FSL commands were subsequently employed to warp T1-based CSF probability map to the b0 based one. Estimated warping field was eventually applied to structural scan.
Tractography
Tensor estimation and DT based tractography were accomplished using CAMINO package (39) (http://cmic.cs. ucl.ac.uk/camino/). In this context, tensors fitting was computed by means of a non-linear constrained procedure (7,8). After terminating DT fitting procedures, WM voxels were inspected in order to detect possible unreal eigenvalues; any implausible eigenvalue was found in the datasets. CSD based computations were performed by means of MRtrix software package (40), version 3 (www.mrtrix.org). Subjectspecific response functions were firstly estimated for each DW dataset (41), and then averaged to produce a study-specific averaged response function. This latter was subsequently used to estimate fODF in each diffusion dataset; for those computations, maximal harmonic order was set to 6.
Deterministic and probabilistic tractographic reconstructions were performed using track CAMINO command and tckgen MRtrix command for DTI and CSD, respectively.
For AF tracking, a single seed ROI (s-ROI) was placed following a procedure previously suggested (42,43). For CST tracking, medial (med-CST) and lateral (lat-CST) CST portions were separately reconstructed. To this end, two cortical s-ROIs related to the pathways of interest were manually defined by an expert radiologist (M.G.). When seeding for either the medial or lateral portion of CST, the other s-ROI was included as Region of Avoidance (ROA); in addition, another ROA was placed to impede reaching of the contralateral hemisphere. All tractographic reconstructions were allowed to propagate within a mask comprising WM voxels: for each subject, this mask was created based on segmentation of coregistered T1 as provided by New Segment SPM8 tool. Prior running tractography, WM mask was moderately dilated (npass = 3 option of maskfilter MRtrix command) to permit to the streamlines to reach GM. For deterministic DTI and CSD tracking, a single seed was initialized for each voxel of related s-ROI, whereas 100 streamlines were generated from each voxel being part of seed ROI for probabilistic tracking. For deterministic DTI (d-DTI), directional clues were provided by eigenvector coupled to highest eigenvalue using FACT algorithm (44). For probabilistic DTI tracking (p-DTI), uncertainty in principal diffusion direction (PDD) was determined using the probabilistic index of connectivity (PICo) (35); Bingham distribution was used to estimate PDDs distribution. For both reconstruction methods, Runge-Kutta 4th order for streamline direction interpolation step was used, as well as an overall FA threshold of 0.2 together with an angular threshold of 60 • to avoid unrealistic trajectories for streamlines. For deterministic CSD (d-CSD), direction corresponding to highest fODF peak was used; for probabilistic CSD (p-CSD) tractography we used an algorithm described in Jeurissen et al. (37). Ifod2 interpolation scheme (45) was employed to interpolated fODF peak directions at each reconstruction step, whose length was set to 0.2 mm. Minimal fODF amplitude and angular threshold were set to 0.15 and 60 • , respectively.
Analysis of Tractographic Maps and DTI Parameters
As first part of our experiment, we aimed at measuring performances of different tractographic methods in reconstructing WM fiber bundles under examination. To this end, we estimated Overlap Fraction (OF) (46,47). OF was measured via the following formula: in which V reference represents a tract-based volume defined on the basis of p-CSD tractographic outcome, whereas V target is the tract-based volume estimated for all the other methods (d-DT, p-DTI, and d-CSD). Those tract-based volumes were created by generating corresponding track density images (TDIs) (48). TDI is a map in which each voxel is assigned a value corresponding to the number of streamlines passing through it. To address the issue of false positive artifacts in streamlines output, OFs calculation were repeated after thresholding TDIs at different density levels. For each reconstructed pathway and method used, maximal density was calculated; then, only voxels whose density was above a given percentage of that maximal value were retained. Since streamlines trajectories are known to be prone to false positive artifacts, we thresholded TDIs at the following percentages: 0% (raw TDIs), 1, 5, 10% of the maximal density for that reconstruction. OF analyses were performed in normalized MNI space: for each subject, FA maps were warped to match FMRIB58_FA template by using flirt and fnirt commands. Estimated warping fields were later on applied to TDIs to obtain those maps in normalized space. Tensor features were computed by means of in-house algorithms written with MATLAB software package (www. mathworks.com/products/matlab/), release 2015. Thresholded TDIs were used as masks from which gathering and averaging following measures: FA, MD, Linear Coefficient (CL), Planar Coefficient (CP), Spherical Coefficient (CS), Axial (AD), and Radial (RD) diffusivity. Tensor based maps were created in native spaces and later on warped using the same warping field previously estimated to project TDIs into the MNI space.
Impact of tractographic techniques and cutoff levels on tensor features was investigated by means of multivariate Wilks' Lambda tests using cutoff (levels: 0, 1, 5, 10%) and method (levels: d-DTI, p-DTI, d-CSD, p-CSD) as within-subjects factors; all analyses were conducted using SPSS statistical package (http://www-01. ibm.com/software/), release 22. Where necessary, Bonferroni correction was applied in post-hoc analyses to correct for multiple comparisons in order to get a global significance type-I error of 0.05.
Estimation of Intra-Axonal Volume Fraction and Comparison With FA
In the second part of our experiment, we estimated and analyzed intra-axonal volume fractions in our datasets. This task has been accomplished in four steps: (i) voxels having a relatively high FA were isolated; (ii) for each voxel, the highest fODF lobe amplitude (the peak) and the corresponding peak direction were detected. (iii) Assuming that fiber population is pointing along direction provided by highest fODF peak, intensity of DW volume whose gradient direction was the more perpendicular to highest peak direction was extracted for each voxel. This intensity should correspond to DW signal radial to the fiber population. (iv) Eventually, intensity was normalized by the intensity of the b0 signal acquired in the same voxel. Consistently with (25), such normalized value has been interpreted as an estimate of intra-axonal volume fraction for that given voxel. Steps i-iv were repeated for four different FA cutoff levels: 0.7, 0.75, 0.8, 0.85. Selection of voxels based on FA level, fODF estimation and peak detection were done by using MRtrix. Final data were gathered and visualized by means of Matlab.
A deeper investigation of AFD has been accomplished by performing comparison with one of the mostly known DTI parameters, namely FA. At this stage the focus was placed on p-CSD based reconstructions. Of note, we worked in the native space of our subjects to avoid biases in normalization process of fODF lobes (28). Firstly, AFD was calculated in all voxels from which at least one streamline was passing through. To this end afdconnectivity MRtrix command was adopted. Subsequently, for each subject and WM pathway analyzed, both linear and cubic polynomial fits were applied to see how FA was related to AFD. Fitting results were later on compared each other by estimating the following F-statistic: where SS smal and SS big are the residual sum of squares of linear and cubic models having df smal and df big degrees of freedom, respectively. With the goal to individuate the most plausible pattern between the two measures, the value above described was observed on an F distribution with df big −df small and df big degrees of freedom, respectively. A linear fit would of course indicate a linear relationship; if a cubic "S-shape" fit would instead better represent FA vs. ADF profiles, a non-linear relationship should be inferred between AFD and FA, in particular when analyzing lowest and highest FA values. Curve fitting (robust estimation) and F-tests were carried out by means of tools available within Matlab.
The pipelines of both experiments are shown for visualization purposes at the end of the manuscript (see Figure 5).
Tractographic Reconstruction Accuracy and Robustness
Results of OF analysis are reported in Table 1 and shown in Figures 1B-G for visualization purposes: in Table 1, OFs were averaged over subjects and between hemispheres. For all WM fasciculi investigated, probabilistic CSD tractography determined the densest and widest reconstructions in all subjects. As expected, raw count of voxels traversed by streamlines decreased as density cutoff increased (Figures 1B-D).
When investigating AF results, differences between probabilistic CSD based reconstruction and other methods tended to decrease as density increased; however, all OFs resulted below 60% ( Figure 1E). A different behavior was instead observed for medial and lateral CST reconstructions if compared to AF results (Figures 1F,G): in those situations, differences between p-CSD and OFs measured with other techniques tended to slightly increase as density cutoff increased. Analysis of lateral and medial CST portions determined similar results.
Tractographic results obtained by thresholding at 5% of maximal density are shown for visualization purposes in Figure 2. TDIs maps obtained from all subjects were warped and averaged into the MNI space and overlaid onto a reference T1w template; maps were intensity scaled to maximize visibility. p-CSD related TDI (in red) provided the best result for AF, either in terms of tract definition (cyan arrows) as well as in the depiction of its curvature (black circles appearing in Sagittal views of Figure 2). Huge differences between p-CSD with respect to d-DTI (green maps), p-DTI (purple maps) related density images were observed when comparing reconstruction of medial (green ellipses) as well as lateral (blue ellipses) CST portions. All these maps showed how CSTs were well described by p-CSD, whereas poor results were obtained by the other methods. Deterministic CSD (orange map) resulted inadequate for providing robust reconstructions.
TB-RA
In this section we investigated impact of tractographic algorithms on TB-RAs. In Figure 3 we show FA and MD variation for AF, medial and lateral CST portions for all density cutoff levels and reconstruction algorithms. Details of multivariate statistical analyses results are reported in Table 2 For each density cutoff levels and pathway investigated. Overlap Fraction measures the amount of tract preserved with respect to reference p-CSD tractographic reconstructions. which no significant differences were observed after Bonferroni correction. A similar trend was found when investigating MD variation. Like for FA, cutoff factor resulted always significant, and post-hoc analyses confirmed a significant negative trend either for AF (F = 124.023, uncorrected p = 1.11E-07), medial CST (F = 30.866, uncorrected p = 1.25E-04), and lateral CST (F = 23.556, uncorrected p = 3.96E-04) portions. Method factor resulted always significant, except when inspecting reconstructions of lateral CST. In a symmetric fashion with respect to FA, post-hoc analyses showed that MD averaged from voxels traversed by p-CSD led to systematically higher values if compared to other techniques.
Analyses of Westin indices as well as of AD and RD yielded similar results (see Table 2).
AFD Estimation Results and Comparison With FA
Results of estimated intra-axonal volume fraction in our datasets were shown in Figure 1A. Estimated fraction was below both the theoretical intra-cellular volume fraction (26) (80%) as well as the intra-axonal volume fraction reported in Raffelt et al. (25), where an average value of 75% was found based on b = 3,000 s/mm 2 . In our data, we observed a clear volume fraction dependence on FA cutoff level for voxels selection: indeed, based on FA cutoff of 0.7 we estimated an average FIGURE 2 | Tractographic results. TDIs maps (thresholded at 5% of the maximal density) obtained from all subjects were warped and averaged in the MNI space for each method: p-CSD (red) related TDIs show the best results for AF, either in terms of tract definition (cyan arrows) as well as in the depiction of its curvature (black circles). p-CSD clearly outperforms DTI, shown with green and purple maps for deterministic and probabilistic results, in reconstructing medial (green circles) and lateral (blue circles) CST portions. Deterministic CSD (orange) is inadequate as well to produce robust reconstructions. AF, Arcuate Fasciculus; CST, Corticospinal Tract.
volume fraction of 55.16% (SD = 2.90%); for 0.75 FA cutoff, average volume fraction was 56.45% (SD = 3.34%). For voxels having FA ≥ 0.8, the estimated intra-axonal volume fraction was 58.97% (SD = 3.00%). Eventually, we estimated an average intra-axonal volume fraction of 60.51% (SD = 4.95%) based on voxels having FA equal or above 0.85. These results are shown in Table 3 together with the percentages of voxels involved in the calculation.
The relationship between AFD and FA in the investigated pathways are shown in Figure 4. In Figure 4A we reported histograms of AFDs gathered from all subjects separately for AF, medial and lateral CST portions. Despite the lack of a nominal limit, AFD values ranged primarily between 0 and 2. Similar distributions were observed for all pathways, with a moderate smaller mode for AF (around 0.7); modes for medial and lateral CST based AFDs were instead around 0.9.
In Figure 4B statistical results of model selection tests were shown for all subjects and pathways; to help visualization, p-values were reported on a log scale. For most of the comparisons, the polynomial cubic fit was the one that better represented the data, thus underlying the non-linear nature of the relationship. A few exceptions were observed in three subjects when reconstruction the lateral portion of CST, and in one subject (S5) in which the linear fit over-performed the cubic one. All p-values are reported in Table 4.
First of all, as expected, as long as cutoff increases FA tends to increase and its variance to decrease. The lower prevalence of orange clouds for AF over the panels reporting data collected from medial and lateral CST portions is likely due to the substantial overlap of 0 and 1% clouds in the latter two situations. This latter is a sign of the higher variability when reconstructing AF.
Overall, a clear positive trend was observed; importantly, in the bottom right part of all the panels, we could see a huge number of points for which FA was relatively low (between 0.1 and 0.4), whereas AFD substantially increased. This secondary trend corresponded to voxels over which crossing or branching multiple fibers insisted.
Black colored curves showed results of the cubic fit averaged over all subjects (Figure 4). Shadow represents standard deviation. It is clear how at the borders a strictly linear relationship between FA and AFD did not hold. This phenomenon was especially evident for AF and medial portion of CST, and confirmed that AFD was able to span a higher range of fiber geometries configurations; such geometries could not in turn be exhaustively represented by FA because of its known limitations. Since for three subjects a linear fit betted represented the data, by averaging data obtained from lateral CST, a more flat curve was estimated (Figure 4). For each FA cutoff level (0.7, 0.75, 0.8, 0.85), average intra-axonal volume fraction has been estimated from all subjects; standard deviations are reported between brackets. In the bottom part, percentage of voxels involved in calculations at each cutoff level is reported; such percentage is related to foreground voxels of a whole brain mask obtained on b0 volumes. Even in this case, standard deviation is reported between brackets.
DISCUSSION
In this study we compared CSD and DTI model ability in reconstructing and quantifying two well-known fiber pathways, the Corticospinal Tract and the Arcuate Fasciculus.
While other pathways could have been investigated, we preferred to focus on CST and AF for two reasons. First of all their anatomical configurations, i.e. their width as well as the smooth changes of direction along their courses, should in principle ease reconstructions provided by the simpler DTI model, thus rendering a comparison with CSD consistent and robust. Secondly, those pathways have been historically widely investigated by means of DTI model to probe motor and associative brain networks, both in healthy and pathological conditions.
CSD and DTI Models
It is known that DTI is unable to resolve multiple fibers configurations such as bending, kissing, and crossing fibers (3,5); more complex models are therefore needed (18, 19,22). Within the CSD framework, the estimation of the fODF (19,21) allows to properly model diffusion signal; successful applications were obtained in healthy cohorts as well as in pathological populations (27,30,48). AFD (25) is a parameter developed with the aim to provide an estimate of intra-axonal volume fraction; it was shown to be in close correspondence with intra-axonal volume fraction as measured in Syková and Nicholson (26).
CSD framework, along with AFD, is recommended to be applied by using a b-value of at least 3,000 s/mm 2 and a minimum of 45 unique diffusion encoding gradient directions (19). Other tissue quantification parameters, like those coming from CHARMED (30) or NODDI (29), require multi-shell acquisitions as well.
In this study we investigated CSD based performances in comparison to the standard DTI model when very minimal technical requirements are used (b-value = 1,000 s/mm 2 , 30 unique diffusion encoding directions). In this scenario, particular importance was given to the applicability and biological meaningfulness of AFD.
Tractographic Reconstruction and Tensor Features Analysis
OF analysis confirmed that, if compared to other approaches tested here, probabilistic CSD based tractography determined the densest and widest reconstructions in all subjects investigated. Differences between p-CSD and other techniques (d-CSD, d-DTI, and p-DTI) slightly decreased as density increased when analyzing AF reconstructions in all subjects (Figure 1).
Furthermore, when investigating tractographic reconstruction of CST, we observed that DTI model markedly underestimated CST if compared to p-CSD (Figure 1). Unlike for AF, differences between p-CSD based TDIs and OFs measured with other techniques tended to increase as density cutoff increases. This is a sign of the fact that p-CSD depicts CST in a more homogeneous way if compared to other techniques, in which a denser kernel pathway is likely reconstructed. It is worth to remark that the reconstruction of lateral and medial CST portions led to similar results.
The improvement achieved by probabilistic CSD can be visually appreciated in Figure 2, in which the warped TDI maps coming from all subjects were averaged and over-imposed onto a T1w template in MNI space.
Altogether those results are consistent with previous literature (13,52,53), and confirm that probabilistic CSD is a useful instrument for a more consistent tractographic reconstruction in contexts like pre-surgical planning (13,54), in case-control studies or in longitudinal analyses.
We furthermore demonstrated that both the tractographic method adopted and the cutoff chosen to threshold TDIs strongly influence reconstructions outcomes used to perform TB-RA of diffusion tensor indices. This statement was confirmed by multivariate statistical analysis ( Table 2).
Regardless to the pathway reconstructed, FA smoothly increased as density cutoff increased, whereas MD decreased. These results are not unexpected: an increasing cutoff is indeed likely going to preserve voxels containing a major dominant fiber population insists, thus explaining both FA and MD behaviors (24).
Post-hoc analyses showed that FA was lower when estimated from voxels detected via p-CSD; this situation was expected, since p-CSD involves voxels in which multiple fiber populations insists over, subsequently causing a decrease of FA average. Symmetrically to what it was observed for FA, post-hoc analyses showed that MD averaged from voxels traversed by p-CSD was significantly higher when compared to MD estimated on the basis of all other techniques. Variation of Westin indices as well as AD and RD led to similar conclusions.
As already abovementioned, p-CSD involves in TB-RA a higher number of voxels with multiple fiber bundles insisting over them. As we have shown, this situation impacts tensor indices estimation, and therefore might induce to carefully consider p-CSD applicability in pathological conditions where well-established variations (e.g., FA decrease) are traditionally considered linked to WM damages. A possible scenario is the following: if two distinct fiber populations were to insist over the same voxel, and only one of them were damaged by a given disease, we might detect overall FA increase in the patient if compared to a control. In TB-RA context, by summing over all possible voxels, the likelihood of not detecting differences in case-control studies might lead to erroneous results. One might think that the use of tensor based tractography may prevent such circumstances to happen. However, this is not the case because the same situation would apply even if DTI model were adopted: it is indeed known that more than 90% of WM voxels contain complex geometries (14). As a consequence, the same potential wrong conclusions may be taken.
The above example puts the emphasis for the need of quantitative indices that should be able to take into account complex fiber geometries at the voxel level, and that be unbiased against such potential troubles. Different indices were considered in the past to overcome these issues, e.g., the Q-ball based generalized fraction anisotropy (18), or those based on Diffusion Kurtosis Imaging (55). As an alternative, multi-compartmental models were found to better describe non-gaussian water motion of in presence of complex geometries, like ball and stick (56), CHARMED (30), or NODDI (29). Those models however require high signal to noise ratios, a big number of diffusion directions, or multi-shell acquisitions.
AFD Interpretability at Low b-Values
AFD (25) was introduced to infer about intra-axonal volume fraction. Authors showed that radial DW signal is strictly linked to AFD which in turn is roughly proportional to intra-axonal volume fraction. In that way they found an average value of 75%, thus highlighting a close correspondence with an estimation of 80% for intra-cellular volume reported in Syková and Nicholson (26). However, such high correlation was reported to hold at high b-values (b = 3,000 s/mm 2 ).
In this study we estimated, based on similar assumptions, an average value of 60% when considering voxels with high FA values (≥0.85) ( Table 3). The reasons for such divergence may be manifolds and can be placed in two categories, namely biological and technical. From the technical point of view, a number of confounds may contribute to the underestimation intra-axonal volume fraction. First of all, in this study the estimation of the radial signal was based on DW volume whose diffusion gradient was the more transverse with respect to measured fODF peak. Due to the limited number of DW directions acquired, signal intensities could be chosen from a limited set of directions. It might be possible, therefore, that a slightly different spherical distribution could have contributed to ameliorate estimation of intra-axonal volume fraction. Moreover, the use of a single peak to detect underlying fiber direction is more error-prone in presence of noisy data, whereas an analogous search performed by integrating over fODF lobes may have led to better results. Eventually, due to partial volume effect, CSF component might influence our estimation by causing fictitious increasing of b0 signal and, consequently, a decrease of DW signal (26).
Another set of explanations is more inherently biological: it has been indeed recently found that the corpus callosum, a structure traditionally considered highly coherent in terms of fiber directionality, shows instead a rather elevated dispersion ranging from 10 to 35 • (57). Therefore, the fiber dispersion might cause intra-axonal volume fraction underestimation. It is known that extra-cellular component decreases its contribute to diffusion weighted signal when high b-value are used (58); for lower b-values, like the one we used in the present study, extra-cellular compartment augments its influence on DW signal (59) and could potentially contribute to the observed underestimation.
Other micro-structures might further influence water fraction estimation due to water exchange between membrane barriers (60). It should be noted that in Syková and Nicholson (26) myelin component was considered part of the intra-cellular compartment. It has been shown that myelin water fraction ranges around 20% (61), and that the possible contemporary presence of both myelinated and unmyelinated axons might decrease the accuracy in myelin estimation (60).
Interestingly, if we were to add to myelin water component percentage the intra-axonal volume fraction as it was estimated in this study, we would almost equal the limit that Sykova and Nicholson measured for intra-cellular volume fraction (26). It could be however argued that myelin has a minor influence on our measure due to the short T2 decay of water trapped between myelin layers (61).
It is worth to mention that our results at b = 1,000 s/mm 2 are in contraposition with numerical Monte-Carlo simulations provided in Raffelt et al. (25): there, it was reported that both restricted and permeable derived radial signals show a higher ratio between DW and unweighted signal (close to 90%) at low bvalues. Such discrepancy could be likely due to some limitations in their model assumptions: as it was indeed reported there, possible relationships between diffusion phenomenon and other microbiological structures, e.g., myelin layers, may not have been properly modeled (25).
Pooling together all those considerations, we may conclude that, even when using a b-value of 1,000 s/mm 2 , and some limitations, we were still able to obtain a biologically meaningful estimation of intra-axonal volume fraction. As a consequence, we may be able to infer fiber population density even at such relatively low b-value. To the best of our knowledge, this is the first study exploring such implication.
AFD and FA
We were particularly interested in showing the relationship between AFD and FA; it was already demonstrated (25,27) that AFD provides richer insights on WM integrity when dealing with high demanding datasets.
Our aim was to show if the similar results could be confirmed with a low b-value (1,000 s/mm 2 ) and a limited number of directions. Statistical analyses (Figure 4B) demonstrated that in almost all the cases, for all pathways of interest, a non-linear cubic S-shape relationship was detected ( Figure 4C). As expected, for FA between 0.3 and 0.6, a linear relationship was observed; almost the same trend was found, for instance, when comparing FA with intra-axonal volume fraction provided by NODDI scheme (29). While a primary linear trend was evident, several points for which FA is relatively low (between 0.1 and 0.4) resulted to be coupled to AFD data increase. Such patterns were consistent for almost all subjects and correspond to voxels over which crossing or branching multiple fibers insist.
When investigating lower AFD values, we observed a relative high FA variability. Those points may likely correspond to situations in which multiple fibers have an angular distance so small to cause the tensor model to wrongly detect a single pathway pointing in a unique direction, therefore giving biased FA values. Such patterns caused the cubic S-shape fits we showed to better predict data in our subjects.
Angular resolution tends to overall decrease when fewer directions are used, and that could in turn cause inaccuracies in the correct estimation of complex fiber patterns even for fODF lobes. However, angular accuracy is by the way inherently more accurate when measured via CSD over DTI based estimation (19); therefore we can again conclude that AFD provides a more meaningful biological information.
CONCLUSIONS
In accordance with existing literature, in this article we confirmed that CSD outperforms DTI one even in datasets with low demanding hardware settings (b-value = 1,000 s/mm 2 and 30 diffusion encoding directions). Such setup needs to be preferred over more demanding ones especially when dealing with patients who are usually less collaborative due to their conditions.
Moreover, we showed that TB-RA of diffusion tensor parameters strongly depends on the cutoff chosen for voxels selection and on the method adopted for tractography, thus highlighting the importance of a careful check for principled data handling and analysis. Those considerations both apply to probabilistic DTI and CSD based tractographic analyses.
For the first time to our knowledge, we demonstrated that, with some limitations, AFD is a meaningful estimate of intra-axonal volume fraction when measured on diffusion acquisitions which can easily performed in clinical settings. Therefore, even with b = 1,000 s/mm 2 and only 30 diffusion encoding directions, AFD can provide richer information than solely tensor features to investigate WM integrity in clinical studies.
To conclude, it is worth to notice that in this study a relatively small sample size has been adopted. In the future similar analyses on bigger populations will be therefore necessary to further confirm our results.
AUTHOR CONTRIBUTIONS
ACal and AA contributed conception and design of the study, performed statistical analysis, interpreted data, and wrote the manuscript. EM contributed conception of the study and interpreted data. DM, ACac, SM, and GC revised the manuscript. MG and AQ contributed conception and design of the study and revised the manuscript. All authors read and approved the final manuscript. | 8,719.2 | 2018-08-28T00:00:00.000 | [
"Medicine",
"Engineering",
"Computer Science"
] |
Non-Abelian black holes in string theory
We study a family of 5-dimensional non-Abelian black holes that can be obtained by adding an instanton field to the well-known D1D5W Abelian black holes. Naively, the non-Abelian fields seem to contribute to the black-hole entropy but not to the mass due to their rapid fall-off at spatial infinity. By uplifting the 5-dimensional supergravity solution to 10-dimensional Heterotic Supergravity first and then dualizing it into a Type-I Supergravity solution, we show that the non-Abelian fields are associated to D5-branes dissolved into the D9-branes (dual to the Heterotic"gauge 5-branes") and that their associated RR charge does not, in fact, contribute to the entropy, which only depends on the number16 pages of D-strings and D5 branes and the momentum along the D-strings, as in the Abelian case. These"dissolved"or"gauge"D5-branes do contribute to the mass in the expected form. The correct interpretation of the 5-dimensional charges in terms of the string-theory objects solves the non-Abelian hair puzzle, allowing for the microscopic accounting of the entropy. We discuss the validity of the solution when alpha prime corrections are taken into account.
Introduction
One of the common features of black holes or black rings with genuinely non-Abelian fields 1 in Einstein-Yang-Mills (EYM) theory, where they are only known numerically [7,8], or in N = 2, d = 4, 5 Super-EYM (SEYM) theories [9,10,11,12], where they are known analytically, is that their non-Abelian fields fall off at spatial infinity so fast that they cannot be characterized by a conserved charge. For this reason they are sometimes called "colored" black holes, as opposed to "charged" black holes. As a consequence, the parameters that characterize the black holes must be understood as pure non-Abelian hair.
In the SEYM case it has also been observed that the non-Abelian fields seem to contribute in a non-trivial way to the BH entropy because their near-horizon behavior is similar to that of their Abelian counterparts [9,10,11,12]. Thus, apparently, the entropy of these non-Abelian black holes and rings depends on non-Abelian hair! If the BH entropy admits a microscopic interpretation, this conclusion is clearly unacceptable.
In this paper we are going to solve this puzzle for a family of particularly simple non-Abelian 5-dimensional black holes that can be embedded in String Theory [11] and which can be seen as the well-known 3-charge D1D5W black-hole solutions discussed in Ref. [13] 2 with the addition of a BPST instanton [15], which is genuinely non-Abelian in the sense discussed above. 3 The embedding is realized via Heterotic Supergravity (that is: N = 1, d = 10 supergravity coupled to vector supermultiplets) without the terms of higher order in the curvature of the torsionful spin connection which corresponds to the low-energy effective field theory of the Heterotic Superstring. Our solution is an exact supergravity solution but, clearly, the issue of α corrections needs to be addressed. As we show in Appendix A, the supergravity solution we are studying is also good to order α in Heterotic Superstring theory, but only in the near-horizon region and needs to be α -corrected elsewhere. Finding these corrections is a problem that we will tackle in a forthcoming publication [17] and, in the meantime, one can work with the supergravity solution within the limits we just mentioned. In particular, the supergravity solution should be enough to characterize the different branes the black hole is "made of". 1 That is: non-Abelian fields that cannot be related to an Abelian embedding via a (possibly singular) gauge transformation [1]. Gauge transformations, whether regular or singular, have no effect whatsoever on the spacetime metric and, therefore, if the non-Abelian fields can be related to an Abelian embedding, the metric is effectively that of a solution with an Abelian field. This was the only kind of regular solutions thought to exist in the Einstein-Yang-Mills theory, basically because the non-Abelian fields were expected to behave at infinity like the Abelian ones [2,3,4]. See also See Refs. [5,6] and references therein. 2 More information on these black holes and the String Theory computation of their BH entropy can be found in Ref. [14] and references therein. 3 Technically, this family of black holes is a solution of the SU(2)-gauged ST [2,6] model of N = 1, d = 5 supergravity. This model and the solution-generating technique used to obtain the black-hole family is described in full detail in an Appendix of Ref. [16].
Back to the non-Abelian hair puzzle, in this case at least, the solution lies in the correct interpretation of the different charges that characterize the black hole. As we have shown in Ref. [16], the charges that count the underlying String Theory objects are combinations of the naive ones. The correctly identified charges can be switched off one by one and, switching off those that count the objects that give rise to the Abelian charges (that is, setting to zero the number of D1s, D5s and the momentum) one is left with the object that produces the net non-Abelian field. In 5 dimensions, this object is a globally regular, horizonless gravitating instanton [16] which, when uplifted to 10-dimensional Heterotic Supergravity (the effective field theory of the Heterotic Superstring), is nothing but Strominger's gauge 5-brane [18]. 4 In terms of these charges, as we will see, there is a non-Abelian contribution to the mass and the non-Abelian contribution to the entropy disappears, solving the puzzle. This is a very important clue that we are going to apply to these solutions. In Section 1 we are going to introduce them and rewrite them in terms of the charges that describe the underlying String-Theory objects. In Section 2 we are going to uplift them to 10-dimensional Heterotic Supergravity, a theory that has non-Abelian vector fields in 10 dimensions, and, in Section 3 we will reinterpret the solution in terms of intersections of fundamental strings, solitonic 5-branes and gauge 5-branes, plus momentum along the strings, and we will dualize it into a solution of Type-I Supergravity (the effective field theory of Type-I Superstring Theory) [20,21,22] with D-strings, momentum, D5-branes and "gauge D5-branes", the duals of the gauge 5-branes, also referred to as D5-branes dissolved into the D9 branes. Then, in Section 4 we discuss how this brane configuration leads to the same entropy as the Abelian one, pointing to directions for future work. Finally, in Appendix A we discuss the validity of our solution of 10-dimensional Heterotic Supergravity as a solution of the Heterotic Superstring taking into account α corrections.
5-dimensional non-Abelian black holes
We consider the SU(2)-gauged ST [2,6] model of N = 1, d = 5 supergravity, which can be obtained from d = 10 Heterotic Supergravity by compactification on T 5 followed by a truncation. This is most conveniently done in two stages: first, compactification on T 4 followed by a truncation to N = (2, 0), d = 6 supergravity coupled to a tensor multiplet and a triplet of SU(2) vectors and, second, further compactification on S 1 . The first stage is almost trivial: all the 6-dimensional fields are identical (up to rescalings) to the first 6 components of the 10-dimensional ones. The second stage is described in detail in Ref. [23]. This model is determined by the symmetric tensor C 0xy = 1 6 η xy , with x, y = 1, 2, A, A, B, . . . = 3, 4, 5 and η xy = (+, −, −, −, −). 5 The A, B, . . . are adjoint SU(2) indices.
The bosonic content of this model consists of the metric g µν , 3 Abelian vectors, A 0 , A 1 and A 2 a triplet of SU(2) vectors A A , and 5 scalars which we choose as φ, k and A where φ can be directly identified with the 10-dimensional heterotic dilaton and k is the Kaluza-Klein scalar of the last compactification from d = 6 to d = 5.
A particularly simple family of non-Abelian black-hole solutions of N = 1, d = 5 supergravity can be constructed by adding a BPST instanton to the standard 3-charge solution [24,11,16]. The family of solutions is determined by 3 harmonic functions L 0,± which depend on three constants B 0,± satisfying 27 2 B 0 B + B − = 1 and three independent charges q 0,± L 0,± = B 0,± + q 0,± /ρ 2 , (1.1) and a non-Abelian contribution that depends on the 5-dimensional gauge coupling constant g and on the instanton scale κ (1. 2) The non-Abelian contribution appears combined with the harmonic function L 0 as follows:L and, since it goes like 1/ρ 6 at spatial infinity while L 0 goes like B 0 + q 0 /ρ 2 , it is not expected to contribute to the mass. However, both the Abelian and non-Abelian contributions diverge like 1/ρ 2 near the horizon at ρ = 0, and, naively, one expects both of them to contribute to the entropy. This can be manifest by rewritingL 0 as where we have combined Abelian and non-Abelian 1/ρ 2 terms inL 0 , leaving a purely non-Abelian contribution which is finite at ρ = 0. As in Ref. [16], we will callq 0 ≡ q 0 − 2 9g 2 the coefficient of the 1/ρ 2 term. The constants B 0,± are related to the moduli i.e. the values of the 2 scalars at infinity 6 as follows Is is convenient to use the functionsZ 0 ≡L 0 /B 0 and Z ± ≡ L ± /B ± and the charges Q 0 ≡q 0 /B 0 = (q 0 − 2 9g 2 )/B 0 and Q ± ≡ q ± /B ± .
It is also convenient to transform the BPST instanton field from the gauge used in Refs. [11,12] to one in which the 10-dimensional solution will be easier to recognize: 7,8 The vector field strength is, evidently, the same, but the Chern-Simons term is not and this difference will also affect the 10-dimensional 2-form. After all these transformations, the active fields of the solutions are 9 where the metric function f is given by 8) and the Z functions take the form (1.9) The mass and entropy of this family of black-hole solutions take the form 7 The reason why this gauge was not used in Refs. [11,12] is that, in it, the gauge field cannot be consistently reduced following Kronheimer. 8 Our conventions for the SU(2) gauge fields are slightly different from the ones used in Refs. [11,12]. Here the generators satisfy the algebra [T A , T B ] = + ABC T C , the left-invariant Maurer-Cartan 1-forms are defined by v L ≡ −U −1 dU and the right-invariant ones by v R ≡ −dUU −1 . The gauge field strength is defined by F = dA + gA ∧ A. 9 Since we are going to use hats to denote 10-dimensional fields, we have removed the hats that we use in our notation for the metric function f .
Using the chargeQ 0 instead of Q 0 ≡ q 0 /B 0 , and assuming thatQ 0 is not related to the non-Abelian fields, the mass contains a net O(1/g 2 ) contribution from the instanton while the entropy does not, against the naive expectations exposed above. We are going to argue that, indeed,Q 0 is a charge completely unrelated to the non-Abelian vector fields, showing that it counts the number of neutral 5-branes (also known as solitonic or NSNS 5-branes) while Q − and Q + count, respectively, the number of fundamental strings and the momentum along them. Setting these three charges to zero we are left with the only non-Abelian component of this solution which is the globally regular and horizonless gravitating Yang-Mills instanton that we have found in Ref. [16], showing that it is is nothing but the dimensional reduction of Strominger's gauge 5-brane [18].
In Ref. [16] we have argued that the gravitating Yang-mills instanton (or the gauge 5-branes) should not contribute to the entropy while, obviously, it must contribute to the total mass of black-hole solutions, just as the global monopole does in 4 dimensions [25,26]. The above mass and entropy formulae reflect this fact.
Embedding in d = 10 Heterotic Supergravity
As a first step towards embedding the 5-dimensional supergravity black hole solution into Heterotic Superstring theory, we are going to embed it in 10-dimensional Heterotic Supergravity (N = 1, d = 10 supergravity coupled to vector supermultiplets), with just an SU(2) triplet of gauge fields. Since the 5-dimensional theory we start from does not have any terms of higher order in curvatures, we do not consider this kind of terms in the 10-dimensional theory. Observe, however, that the gauge fields occur at first order in α and, since our non-Abelian solution has non-trivial vector fields, in order to be consistent we are forced to study its validity as solution of Heterotic Superstring theory to first order in α . At this order there are other terms in the action and we are going to study their relevance for this solution in Appendix A.
First of all, we are going to show how the reduction and truncation of the bosonic sector of the 10-dimensional Heterotic Supergravity with a SU(2) triplet of gauge fields leads to the SU(2)-gauged ST [2,6] model of N = 1, d = 5 supergravity we are working with.
The action of Heterotic Supergravity in the string frame, including only a SU(2) triplet of vector fields, is where the field strengths are defined aŝ and ω YM is the Chern-Simons 3-form In the above expressions, α , the Regge slope, is related to the string length s by α = 2 s , and g s , the string coupling constant, is the value of the exponential of the dilaton at infinity: g s = e φ ∞ in asymptotically-flat configurations. The somewhat unconventional factor of g 2 s in front of the action ensures that, after a rescaling from the string frame to the modified Einstein frame defined in Ref. [27] with powers of e φ−φ ∞ , the action has the standard normalization factor (16πG (10) N ) −1 . The 10-dimensional Newton constant is given by If we compactify this theory on T 4 , it is not difficult to see that truncating all the components of the fields with indices in the internal coordinates y i , i = 1, · · · , 4, is a consistent truncation. The resulting 6-dimensional action and field strengths have exactly the same form as the 10-dimensional ones, although the action carries an extra factor (2π s ) 4 which is the volume of the T 4 : The 6-dimensional modified Einstein metricĝ Eμν is related to the 6-dimensional string metricĝμν byĝμν and, in this frame, the action takes the form which coincides exactly with the action of the theory of gauged N = (2, 0), d = 6 supergravity that we called N = 2A in Ref. [23] upon the redefinitionŝ which lead to the introduction of the 6-dimensional Yang-Mills coupling constant g 6 = (g s α ) −1/2 . Further compactification of this theory on a circle leads to the SU(2)-gauged ST [2,6] model of N = 1, d = 5 supergravity we are working with, with Newton and Yang-Mills constants given by (2.10) This reduction was carried out in detail in Ref. [23] and we can use its results, but we have to take into account that we have to rescale the 5-dimensional metric with the Kaluza-Klein scalar k divided by its asymptotic value, k ∞ in order to preserve the normalization of asymptotically-flat metrics. This introduces an additional factor of k 1/3 ∞ in the relations between higher-dimensional fields and 5-dimensional vector fields and an additional factor of k 2/3 ∞ in the relations between higher-dimensional fields and 5-dimensional 2-form fields.
Combining the k ∞ -corrected rules given in Ref. [23] to uplift 5-dimensional configurations to d = 6 and the relations given above between 6-and 10-dimensional fields in the string frame, we arrive to the following rules that allow us to uplift any solution of the SU(2)-gauged ST [2,6] model of N = 1, d = 5 supergravity to a solution of 10-dimensional Heterotic Supergravity preserving the normalization of the fields at spatial infinity: where we have introduced the auxiliary fields (2.12) Notice that the map gives us the 3-form field strengthĤ, but not the 2-form poten-tialB because the process involves a dualization. ThereforeB must be obtained from (2.3) once the field strengthsĤ andF A have been computed.
String Theory interpretation
Using the uplifting formulae of the previous section, and defining the coordinate u = k ∞ z (whose period is 2πR z ) we get the following solution of d = 10 Heterotic Supergravity 1) whereZ 0 and Z ± are given in Eqs. (1.9). In terms of the stringy constants,Z 0 is given byZ As shown in Appendix A, forQ 0 >> κ 2 this is a good solution of the Heterotic Superstring effective action to order α in the near-horizon (ρ →) region. This is enough for our purposes. Eq. (3.2) shows that the chargeQ 0 which is the coefficient of the 1/ρ 2 term is probably associated to neutral (or solitonic or NSNS ) 5-branes [28] while the last term should be associated to gauge 5-branes. We are first going to discuss this point in more detail.
We start by noticing that, in absence of the Yang-Mills instanton, this supergravity solution is the one found in Refs. [29,30] which describes solitonic 5-branes wrapped on T 5 , and fundamental strings wrapped around one cycle of the T 5 with momentum along the same direction.
Let us consider the coupling of N S5 solitonic 5-branes lying in the directions 1 2 (u + v), y 1 , · · · , y 4 , to the Heterotic Supergravity action given in Eq. (2.1). Since the effective action of the solitonic 5-branes is written in terms of the NSNS 6-formB, we must first rewrite the action in terms of that field. It is convenient to use the language of differential forms, so the action Eq. (2.1) takes the form and, after dualization e −2φĤ =Ĥ ≡ dB (3.4) The 6-form will couple to the Wess-Zumino term in the effective action of N S5 coincident solitonic 5-branes via its pullback over the worldvolume (3.5) and the 6-form equation of motion is where (4) δ (4) (ρ) is a 4-form in the 5-branes' transverse space whose integral gives 1.
Integrating both sides of this equation over the transverse space 10 we get which confirms thatQ 0 = Q 0 − 8α n, where n would the instanton number in more general configurations counts solitonic (neutral) 5-branes. The number of gauge 5branes N G5 coincides with the instanton number n. Thus, we conclude that the parameter Q 0 of the solution is (3.9) 10 We replace e 2φĤ byĤ for simplicity and use Stokes' theorem in the first term. For the second term we have 1 the instanton number.
The function Z − is clearly associated to 10-dimensional fundamental strings wrapped around the coordinate 1 2 (u − v). If we couple N F1 fundamental strings lying in the direction 1 2 , (3.10) where V 8 is the space transverse to worldsheet parametrized by u and v, whose boundary is the product T 4 × S 3 ∞ . Using Stokes' theorem and the value of volume of T 4 (2π S ) 4 , we get Finally, the function Z + is associated to a gravitational wave moving in the compact direction 1 2 (u − v) at the speed of light. The simplest way to compute its momentum is to T-dualize the solution along that direction. This operation interchanges winding number (N F1 ) and momentum (N W ) and, at the level of the solution, it interchanges the functions Z − and Z + or, equivalently, the constants Q − and Q + . Thus, where we have taken into account the transformation of the string coupling constant under T-duality. We conclude that the fields that give rise to the 5-dimensional non-Abelian black hole in Eq. (1.7),(1.8) and (1.9) correspond to those sourced by N F1 fundamental strings wrapped around the 6th dimension with N W units of momentum moving in the same direction and N S5 solitonic (neutral) and N G5 = 1 gauge 5-branes wrapped around the 6th direction and a T 4 . In terms of these numbers, the black hole's mass and the entropy in Eqs. (1.10) and (1.11) take the form Unfortunately, the dynamics of String Theory in the background of non-perturbative objects such as solitonic and gauge 5-branes is not as well understood as its dynamics in the background of D-branes. Therefore, it is convenient to perform a string-weak coupling Heterotic-Type-I duality transformation [20,21,22] which acts on the fields as follows: 11,12 where g I ≡ eφ ∞ is the Type-I string coupling constant. These transformations lead to the Type-I supergravity action (3.18) and our solution takes the form 11 These are the transformations that preserve the normalization of the string metric at spatial infinity and lead to the correct normalization of the action of the Type-I theory. In particular, the rescaling of the gauge fields is required in order to reproduce correctly the term that appears in the expansion of the Born-Infeld action of the O9-D9-brane system (in the Abelian case). The effective worldvolume action of the D9-brane (Born-Infeld plus Wess-Zumino (WZ) terms) iŝ where g I is the Type I string coupling constant. In the physical gauge, ignoring the cosmological constant-type term because it will be cancelled by the O9-planes, and using T D9 = [(2π s ) 9 s g I ] −1 we getŜ where, now, 16πG (10) N,I = (2π s ) 7 s g 2 I . If we rewrite the Type-I supergravity action in terms of the RR 6-formĈ (6) , just as in the Heterotic case, we get a termĈ (6) ∧F A ∧F A . This term originates in the WZ term of the D9 effective action as well. 12 The same procedure (a strong-weak coupling duality transformation within Type-IIB supergravity) was followed in Ref. [13] to derive the D5D1W solution without non-Abelian fields from the solution in [29,29,30] which can be embedded directly in the Type-IIB NSNS sector. The presence of non-Abelian vector fields suggests the route we have taken.
(3.19) In agreement with the fact that under Heterotic/Type-I duality fundamental strings and solitonic 5-branes transform into D1-and D5-branes, respectively, gravitational waves remain gravitational waves with the same momentum, this solution describes the fields produced by a D5-brane intersecting a D1-brane in the z direction with a wave propagating along that direction. The Yang-Mills instanton is a non-perturbative configuration of the non-Abelian Born-Infeld field that occurs in the worldvolume of the parallel D9-branes that give rise to the Type-I theory from the Type-IIB and sources D5-branes. Thus N D1 = N F1 , N D5 = N S5 , N GD5 = N G5 and, in Type-I variables, the mass and entropy formulae take the form In absence of the instanton (N GD5 = 0) this solution is identical to the one originally considered in Ref. [13], which is itself very closely related to Strominger and Vafa's original model [31]. 13 The same conditions (namely, that all the Ns are large and N W >> N D1,D5 ) ensure that this solution describes at leading order in α (low curvature) and in g s (perturbative string theory) a good background for Type-IIB string theory.
Discussion
In the previous sections we have shown that the 5-dimensional supergravity black holes with 3 quantized Abelian charges N D1 , N D5 , N W and a non-Abelian instanton can be 13 See also Refs. [27,32,14]. seen, up to dualities, as the fields associated to a 10-dimensional Type-IIB configuration with 1. An orientifold O9 + -plane and 16 D9-branes and their mirror images, that give rise to the Type-I superstring theory with gauge group SO(32) (see, e.g. [33] and references therein).
2. N D5 D5-branes wrapped around the 5th-9th directions and N D1 D-strings wrapped around the 5th direction with N W units of momentum along the 5th direction.
Open strings can end on these D-strings and D5-branes.
3. N GD5 = 1 "gauge D5-brane", sourced by an instanton field located in the 1st-4th dimensions, which are not compact. This brane, which is the dual of the heterotic gauge 5-brane is often referred to as a D5-brane "dissolved" into the spacetime-filling D9-branes and differs essentially from standard D5-branes because no strings can end on them.
Since the entropy of the D1D5W black holes can be understood as associated to the massless states associated to strings with one endpoint on a D1 and the other on a D5 (1-5 states) and this fact, as discussed in Ref. [13] is unchanged by the presence of the D9-branes and O9 + -plane that defines the Type-I theory 14 the microscopic interpretation of the entropy of these non-Abelian black holes must be the same as in the Abelian case and should give the same result at leading order. Observe that, as an intermediate step in the uplift of the solution to 10 dimensions one obtains a non-Abelian string solution in 6 dimensions with an AdS 3 ×S 3 near-horizon geometry where the AdS 3 radius only depends on 3 quantized Abelian charges N D1 , N D5 , N W .
It is important to stress that the correct identification of the charges and their meaning in terms of branes plays a crucial rôle to reach this conclusion as well as in solving the apparent non-Abelian hair problem explained in the Introduction. A more detailed study is, however, necessary to find corrections to the entropy. In particular, the α corrections to this solution in the asymptotic limit need to be determined (see the Appendix).
In the last few years we have constructed non-Abelian static and rotating black-hole solutions in 4 and 5 dimensions [35,9,25,26,10,11], as well as black-ring solutions [12] and microstate geometries [36] in 5 dimensions. All those constructed with "colored monopoles" in 4 dimensions and many of the 5-dimensional solutions exhibit non-Abelian hair which seems to contribute to the entropy or the angular momentum on the horizon but cannot be seen at infinity. Many of them can be uplifted to 10-dimensional Heterotic Supergravity and then dualized into Type-I Supergravity solutions and it is likely that the correct interpretation of the charges of those solutions is enough to understand the non-Abelian hair problem. Work in this direction is in progress.
Acknowledgments
TO would like to thank Ángel Uranga for very useful conversations. This work has been supported in part by the Spanish Government grants FPA2012-35043-C02-01 and FPA2015-66793-P (MINECO/FEDER, UE), the Centro de Excelencia Severo Ochoa Program grant SEV-2012-0249 and the Spanish Consolider-Ingenio 2010 program CPAN CSD2007-00042. The work of PAC was supported by a "la Caixa-Severo Ochoa" International pre-doctoral grant. The work of PFR was supported by the Severo Ochoa pre-doctoral grant SVP-2013-067903. TO wishes to thank M.M. Fernández for her permanent support.
A The issue of α corrections
As we have mentioned in the main body of the paper, the solution of 10-dimensional Heterotic Supergravity that we have obtained by uplifting the 5-dimensional non-Abelian supersymmetric black hole solution has non-trivial SU(2) gauge fields. These occur at first order in α in the low-energy Heterotic Superstring effective action together with other terms that we are going to describe following Ref. [37], and which we have ignored. The purpose of this appendix is to study the relevance of the omitted terms for the solution at hands. Only if these are negligible with respect to those we have considered can the solution be considered a good solution of the Heterotic Superstring effective action to first order in α .
At lowest order (zeroth) in α , the Heterotic Superstring effective action is nothing but the action of pure N = 1, d = 10 supergravity [38,39]. The coupling to super-Yang-Mills multiplets [39,40] leads to the exactly supersymmetric Heterotic Supergravity theory described in Section 2. From the point of view of the Heterotic Superstring effective action, the terms associated to the Yang-Mills fields are of higher order in α : their kinetic term occurs in the action Eq. (2.1) at first order and their Chern-Simons 3-form ω YM occurs in the Kalb-Ramond 3-form field strengthĤ at first order as well, Eq. (2.3), modifying its Bianchi identity so that it takes the form This correction inĤ introduces terms of second order in α in the action and in the Einstein equations but it is precisely this mixture of terms of different orders in α that is exactly supersymmetric and gauge invariant.
The existence of additional terms at first order in α in the Heterotic Superstring effective action is both a blessing, because it makes possible the Green-Schwarz anomalycancellation mechanism [41], and a curse because, once they are included, the action will only be supersymmetric and gauge-invariant to second order in α [42]. The addition of further α corrections only makes the action supersymmetric and gaugeinvariant to higher order in α [37] and will not be considered here.
With the addition of the aforementioned missing terms, the Heterotic Superstring effective action takes the form HereΩ (−)âb is one of the two torsionful spin connection 1-forms that can be constructed by adding to the Levi-Civita spin connectionωâˆb 1-form a torsion piecê whose curvature 2-forms are defined bŷ The Kalb-Ramond field strength 3-form is now given bŷ whereω L (±) is the Chern-Simons 3-form of the torsionful spin connectionΩ (±) ω L (±) = dΩ (±)âb ∧Ω (±)bâ − 2 3Ω (±)âb ∧Ω (±)bĉ ∧Ω (±)ĉâ , (A.7) and, correspondingly, its Bianchi identity becomes Written in this way, and besides the explicit ones, the action contains an infinite number of implicit α corrections which arise due to the recursive way in whichĤ is defined, since it depends on the Chern-Simons form ofΩ (−) , which is defined in terms ofĤ. At the order at which we are working, it is enough to keep in the definitions of Ω (±) only the terms of zeroth order in α , that iŝ and we will ignore all the α 2 terms in the action Eq. (A.2). Now, by plugging the solution Eq. (3.1) into the equations of motion that follow from the action Eq. (A.2) with the torsionful spin connection defined in the previous equation, we can study if they are satisfied to first order in α .
Following the scheme explained in Ref. [43] the variations of the action with respect to the each field can be separated into variations with respect to explicit occurrence of the field in the action and variations with respect to the implicit occurrence via the torsionful spin connection. The former are the zeroth order equations plus terms proportional to the so-called "T-tensors," which we will define shortly and are of order α . According to the lemma proved in Section 3 of Ref. [37], the latter are of order α and proportional to the zeroth order equations of motion. Since the solution Eq. (3.1) satisfies the zeroth order equations of motion up to terms of first order in α , the implicit variations are of order α 2 and can be ignored.
The conclusion is that it is enough to study theT-tensor-corrected zeroth-order equations of motion. The 3T-tensors that appear in the corrections are defined aŝ The 4-formT-tensor is the r.h.s. of the Bianchi identity ofĤ, the symmetric 2-index T-tensor is the term that occurs in the Einstein equations and its trace occurs in the dilaton equation.
Let us start by analyzingT (4) : in the near-horizon region ρ → 0 the leading term iŝ (A. 15) In this limit, the α corrections of our solution will be small if κ −4 >>Q −2 0 , that is, if Q 0 >> κ 2 so the number of S5-branes is very large.
Asymptotically (ρ → ∞), the leading term iŝ 16) and the absence of α corrections in this limit requires exactly the opposite to happen: Q 0 << κ 2 and the number of S5-branes should be very small. The analysis of the other tensors sheds identical results, indicating that we can only consider our solution a good solution of the Heterotic Superstring effective action in either the near-horizon ρ → 0 region forQ 0 >> κ 2 or in the asymptotic ρ → 0 region forQ 0 << κ 2 . In either case, the solution will have to be α corrected in the other region.
For the purpose of computing the entropy it is more convenient to takeQ 0 >> κ 2 so that the near-horizon region is well described to order α in Heterotic Superstring effective action. The α corrections which are needed in the asymptotic limit will be determined and studied in a forthcoming publication [17]. | 7,735 | 2017-04-04T00:00:00.000 | [
"Physics"
] |
N-glycoproteomic Proling Revealing New Coronavirus Therapeutic Targets That Maybe Involved in Cepharanthine’s Intervention
N-glycosylation is an important post-translational modication involved in protein folding, signal transduction, extracellular matrix organization and immune response. Evidence showed that glycosylated SARS-CoV-2 Spike protein may be a potential target in viral pathogenesis and drug/vaccine design. To investigate the mechanism of coronavirus infestation and drug targets from glycosylation perspective, we constructed a SARS-CoV-2 cellular model using GX_P2V-infected VeroE6 cells to study the effects of GX_P2V on glycoproteins in presence or absence of Cepharanthine (CEP) through N-glycoproteomics proling. The results showed that coronavirus GX_P2V could cause aberrant protein glycosylation, whereas CEP can partially maintain GX_P2V-induced aberrant glycoproteins at homeostasis. Further study revealed that proteins LAMB1 and FN1 were pivotal in counteracting coronavirus-induced aberrant protein glycosylation by CEP. Furthermore, CEP can dramatically regulate the glycosylation of viral proteins S, M and N. Our results suggest that despite the strong anti-coronavirus effects of CEP, drug combinations need be considered to achieve optimal therapeutic strategies.
Introduction
The current global pandemic of COVID-19 caused by the highly contagious coronavirus SARS-CoV-2 has had a huge impact on international community. Currently, no anti-SARS-CoV-2 drugs or vaccines have been o cially and clinically approved due to the absence of adequate evidence for exact mechanism of SARS-COV-2 infestation. Therefore, it is of great urgent need to deeply understand its mechanism to screen potential drug targets 1 .
Glycosylation is the most abundant and complex post-translational modi cation which can have profound structural and functional effects on the conjugate 2 . The oligosaccharide fraction is considered to be related with multiple biological processes and affects the physical properties of proteins. It has been known that protein glycosylation is de nitely stable among the normal people, although it is different from person to person. Only when a person's homeostasis changes due to lifestyle or pathological conditions, will glycosylation changes signi cantly 3,4 . The glycosylation has been labeled an important quality attribute of biopharmaceuticals 5 . The S1 N-terminal domain of the spike protein (S1-NTD) may "hide" sites for recognition and binding of sialic acid-containing glycans, which may provide possibilities for ACE2 alternative receptors 6 . Therefore, it is reasonable to take the glycosylation in consideration in the treatment of coronavirus infestation.
GX_P2V is a SARS-CoV-2 related coronavirus isolated from pangolin. Its spike protein shares 92.2% amino acid identity with the spike protein of SARS-CoV-2 7 . Besides, GX_P2V also has the shared receptor with SARS-CoV-2 but has no pathogenicity to human. Based on the above characteristics, it has been reported that GX_P2X can be used as an accessible in vitro model for developing therapies or for mechanism investigation against SARS-CoV-2 7 . Here we adopted this well-established coronavirus SARS-CoV-2 cellular model by using GX_P2V infestation with Vero E6 to investigate the mechanisms of coronavirus SARS-CoV-2 infestation with respect to the dysregulation of glycoprotein and screening for potential targets for therapeutic intervention.
We have reported that cepharanthine (CEP), a clinically approved drug to increase immune function after chemotherapy, has anti-coronavirus properties that prevent the infected host cells from further damage 7 .
But the mechanism of CEP on glycosylation targets remains unclear. In this paper, we carried out Nglycosylation modi cation proteomics analysis to study the mechanisms of SARS-CoV-2 infection and the anti-coronavirus effects of CEP. Using the advanced technique 4D label-free quanti cation technology, we constructed the N-glycoproteomic pro ling, which revealed new therapeutic targets against coronavirus infestation and CEP's intervention. Our results provide important insights into the mechanism of coronaviruses infection and the identi cation of drug targets for anti-coronavirus of multi-target drug combination usage.
Results And Discussion
N-glycoproteomic pro ling highlights the differentially expressed glycoproteins in SARS-CoV-2 infection cellular model and CEP intervention.
N-Glycosylation is one of the most important post-translational modi cations of proteins 8 . Although there are only a few hundreds of glycoproteins in total, their highly complex glycosylation increases the number of theoretical protein morphology by several orders of magnitude 9 . Many cell surface and extracellular matrix-related proteins become glycosylated through secretory pathways, thereby regulating their adhesion interactions, physical and chemical properties, and diversifying their functions 10 .
To systematically study the differentially expressed glycoproteins during SARS-CoV-2 infestation, we adopted our well-established SARS-CoV-2 cellular model 7 with GX_P2V-treated Vero E6 cells, and performed the N-glycoproteomic pro ling via the 4D label-free LC-MS/MS analysis in presence or absence of GX_P2V and/or CEP. The work ow for the experiment was outlined in supplementary Figure S1. First, the cell samples were harvested and enzymatically digested and then analyzed by 4D label-free LC-MS/MS and bioinformatics. A total of 737,202 secondary spectrograms were obtained by mass spectrometry (supplementary Figure S1B). A total of 1770.0 N-glycosylation modi cation sites on 828.0 proteins were identi ed with database searching, of which 1298.0 sites on 624.0 proteins have quantitative information. The detected N-glycosylation tends to obey N-X-T, N-C-S, N-G-S, N-X-S, N-X-C, N-N rules (supplementary Figure S1C).
We then performed the analyses of global proteomics and respective of glycosylation occupancy ( Figure 1A), and took the fold changes (Fc= expression levels of glycosylated peptide in Group2 (or 3 or 4)/Group 1 ratios) at Fc ≥ 2 folds (up-regulated) or Fc≤0.5 folds (down-regulated) as differentially expressed protein, where group 1 was the mock control (Vero), group 2 was treated with CEP only (Vero_C) , group 3 was treated by coronavirus GX_P2V only (Vero_P) and group 4 was treated by CEP and GX_P2V (Vero_C_P). In comparison with the mock control group, GX_P2V treatment can up-regulate 26 glycosylation sites in 23 proteins and down-regulate 58 glycosylation sites in 47 proteins, whereas in presence of CEP, GX_P2V treatment can induce 26 glycosylation sites up-regulated in 22 proteins and 110 glycosylation sites down-regulated in 75 proteins in host Vero E6 cells ( Figure 1B).
To investigate the protein-protein interaction (PPI) networks and the interaction modules of these differentially expressed proteins in Vero E6 cells in response to GX_P2V treatment, we conducted STRING and Cytoscape analysis ( Figure 1C). We found that the key interaction module obtained from PPI network with MCODE plugin involved in 9 aberrant glycoproteins including 4 up-regulated glycoproteins namely Integrin Subunit Alpha 1(ITGA1), Integrin Subunit Beta 3(ITGB3), Laminin Subunit Gamma 1 (LAMC1) and Heparan Sulfate Proteoglycan 2(HSPG2), and 4 down-regulated glycoproteins namely Integrin Subunit Beta 1 (ITGB1), Laminin Subunit Beta 1(LAMB1), Integrin Subunit Alpha 5(ITGA5) and Fibronectin 1 (FN1). The protein (ITGA3) contains both up-and down-regulated glycosylation sites ( Figure 1D). LAMC1 was reported to be involved in cell proliferation, angiogenesis, growth, migration and invasion 11,12 . Remarkably, majority of the 9 aberrant glycoproteins in the key interaction module were enriched in ECM-receptor interaction pathways ( Figure 1D Coronavirus GX_P2V-induced alteration in protein glycosylation are prevalent in infected cells N-linked glycosylation was involved in multiple biological processes, such as receptor interactions, immune responses, protein secretion and transport, cell adhesion, signal transduction, etc. As described above, we detected 84 sites of aberrant glycosylation sites present in 69 glycoproteins from coronavirus GX_P2V-treated Vero E6 cells. To study these sites holistically, we performed functional enrichment clustering analysis of these differential glycoproteins using Metascape (Figure 2A), and the results were graphically presented using the Sangerbox mapping toolbox ( Figures 2B and 2C).
Upon the treatment of GX_P2V, the involved functions alteration related to differentially expressed proteins were present in Figure 2A and 2B. The most involved top 20 functions were listed in Figure 2A, and corresponding glycosylation counts of each function presented in Figure 2B. The circle diagram of protein function enrichment analysis demonstrated that ITGB1 was involved in the most relevant function and the extracellular matrix organization was enriched for the most genes. Besides, in response to coronavirus GX_P2V infection, the top 5 aberrant glycoproteins most involved relevant functions include ITGB1, TGFB2, ITGB3, ITGB5 and FN1, and the top 5 most aberrant functions involved most genes were those related to extracellular matrix organization, response to wounding, regulation of cell adhesion, signaling pathway regulated exocytosis and transmembrane receptor protein tyrosine kinase. Other important functions such as protein maturation, viral entry into host cell and a platelet degranulation are also affected.
To have an overview about the effects of coronavirus GX_P2V treatment on host cells, we summarized the subcellular localization of differentially expressed glycosylated proteins and PPI networks by UniProt database 13 and STRING software ( Figure 3).
Aberrant alteration of protein glycosylation can be seen in cytoplasm, endoplasmic reticulum, Golgi apparatus, lysosome, nucleus, cell membrane and extracellular matrix. The PPI networks of differentially expressed glycoproteins in each subcellular distribution were also highlighted ( Figure 3). These results suggest that coronavirus-induced alterations in glycosylation of host cell proteins are widespread in infected cells and have multiple subcellular localizations. The most involved glycoproteins locate in cell membrane, extracellular matrix, lysosomes, and endoplasmic reticulum system and cytosol.
Effects of CEP on GX_P2V-induced aberrant glycosylation of proteins in Vero E6 cells.
We have reported that CEP could effectively inhibit coronavirus infestation 7 . To identify the potential targets of CEP in coronavirus-infected cells in response to GX_P2V treatment, we compared the aberrant glycosylation sites and glycoproteins with and without coronavirus treatment in presence or absence of CEP and perform Reactome Pathway Analysis ( Figure 4).
We then carried out Reactome Pathway Analysis on the CEP-affected 12 glycoproteins to understand intervention mechanism of CEP ( Figure 4B). The results showed that CEP can exert its antiviral and cellprotective effects by targeting multiple pathways such as ECM proteoglycans, extracellular matrix organization, platelet degranulation, response to elevated platelet, neutrophil degranulation, and etc.
Among these 12 proteins, LAMB1 and FN1 are also the pivotal proteins in the key interaction module which consists of 9 aberrant glycoproteins in response to coronavirus GX_P2V infestation ( Figure 1D), indicating that proteins LAMB1 and FN1 might be the key targets of CEP against GX_P2V infestation ( Figure 3).
In addition, several proteins can be over-regulated by CEP against GX_P2V (Supplementary Table S1). There are two aberrant glycosylation sites on MRC2 induced by GX_P2V infection. In presence of CEP, the site N69 on MRC2 protein can remain normally glycosylation state, while the other site N1134 is shifted from virus-induced up-regulation to down-regulation. MRC2 may contribute to cellular uptake, remodeling and degradation of extracellular collagen matrices. Like the glycosylation regulation at N1134 site on MRC2 regulated by CEP against GX_P2V, the glycosylation of N83 site on plasminogen activator urokinase receptor (PLAUR) can be over-regulated by CEP, but it is shifted from down-regulation to upregulation, by which CEP might regulate plasminogen activation system controlling the extracellular level of PLAUR/PLAU, and thus may regulate protease activity at the cell surface 14,15 . Over-regulated glycosylation by CEP can also be seen at the site N277 of granulin precursor (GRN), which is a secreted glycoprotein that acts as a key regulator of lysosomal function and as a growth factor involved in in ammation, wound healing and cell proliferation 16 . It involves in regulating protein tra cking to lysosomes and, also the activity of lysosomal enzymes 16,17 . Alteration of glycosylation GRN may contribute to lysosome-related functions. Therefore, CEP might also perform its anti-viral effect via regulation of glycosylation of MRC2, PLAUR, and GRN.
Effect of CEP on the N-glycosylation of GX_P2V viral proteins.
Coronavirus viral proteins are normally extensively glycosylated, especially coronavirus spike proteins where it encodes around 66-87 N-linked glycosylation sites per trimeric spike. It has been known that the extensive glycosylation of viral protein plays a role in protein folding and shielding immunogenic epitopes, resulting in immune evasion 18,19,20 . Remarkably, SARS-CoV and SARS-CoV-2 recognize the human angiotensin converting enzyme-2 (ACE-2) receptor via their glycosylated spike proteins 21 .
From the dataset for N-glycoproteomic pro ling, we observed that the identi ed viral proteins include M, N and Spike were highly glycosylated ( Figure 5A), which might offer the viral proteins a glycan shield 18,19 . Interestingly, we found that the glycosylation of viral proteins M, N and S was affected by CEP treatment. In particular, CEP can up-regulate the glycosylation of the N5 site of M protein, the N-terminal sites of the viral S protein (including the N30, N122, N331 and N343 sites) and the sites N1070 and N1094 sites in the S2 region (N1070 and N1094, the corresponding positions on SARS-CoV-2 spike protein are N1074 and N1098, respectively). However, CEP can dramatically decrease N25-site glycosylation of viral N protein, but no obvious effect can be seen in the glycosylation of the C-terminal sites N1154, N1169, and N1190 of S proteins under CEP treatment.
To observe and analyze the location of these affected glycosylation sites on S proteins and their possible roles, we compared the sequences of spike protein of SARS-CoV-2 and GX_P2V viruses. Due to the structure of GX_P2V viral S protein is not available by far, and considering the high sequence similarity between SARS-CoV-2 and GX_P2V, we adopted the 3D structure of SARS-CoV-2 (6VXX, closed state; 6VYB, closed state) to label the affected glycosylation sites (Fig. 5B-G). Among the sites affected by CEP on Spike protein, N30 and N122 are located at NTD region, N331 and N343 are in CTD/RBD region, and N1070 and N1094 are in S2 region 22 . As can be seen from the cartoon image ( Figure 5G), the CEPaffected Spike protein glycosylation sites are located at both ends of the S protein. Four of the sites (including those located in the NTD and CTD/RBD regions) are at one end away from the virion, while the sites affected by the two sites affected locate in the S2 region at one end close to the virion. This suggests that one of the effects of CEP on viral S proteins might be to interfere with viral assembly and viral recognition or binding to the S protein receptors to exert its antiviral effects.
Multi-target drug combination is essential for the treatment of coronavirus infestation
Through the analysis of coronavirus GX_P2V-induced host cell glycoproteomics, we found that the viral effect on infected host cells is multifaceted. It involved in dysfunction of multiple proteins and pathways, including ECM-receptor interaction, extracellular matrix organization, response to wounding, platelet degranulation, and etc. (Figure 1 and Figure 2). Our data uncovered coronavirus GX_P2V-induced aberrant glycosylation of a variety of proteins on membrane ( Figure 3). There are more than 75% of aberrant glycosylation of proteins after GX_P2V infection in correspondence to membrane-related subcellular structures, involving cell membrane, endoplasmic reticulum membrane, lysosomal membrane, Golgi apparatus membrane and nuclear membrane (Figure 3). These abnormal changes in glycoproteins caused by coronaviruses may play an important role in viral invasion of host cells, resulting in cellular dysfunction.
We found that the antiviral mechanism of CEP is also diverse, as it exerts its antiviral function by regulating the glycosylation of about 12 proteins which locate in endoplasmic reticulum, lysosomal, nucleus, cell membrane and ECM ( Figure 3). However, at least 57 aberrant glycoproteins caused by coronavirus were not signi cantly improved by CEP treatment. Therefore, multi-target drug use in combination with CEP is essential for the treatment of coronavirus infection.
Taken together, the results highlight the differentially expressed glycoproteins targets and related pathways in coronavirus infection and CEP intervention. Generally, coronavirus GX_P2V-induced aberrant N-glycosylation alteration in infected cells are prevalent. CEP can reduce the N-glycosylation of proteins located on cell membrane surface, indicating that CEP may achieve the protective effect against virus invasion by interfering potential N-glycoprotein targets in the affected cells. Besides, CEP can regulate the glycosylation of viral proteins S, M, and N, revealing targets or pathways relevant for viral pathogenicity. The enhancement of glycan shield on the viral proteins S and M might weaken coronavirus' binding to its recognition targets. Nevertheless, the dramatic down-regulation of N-glycosylation witnessed at the N25 site in viral N protein caused need further study.
This study provides a landscape of N-glycoproteomic pro ling using the established SARS-CoV-2 cellular model, suggesting that it is of great importance in therapeutic target screening for drug discovery. The results indicated that coronavirus can cause alterations in the glycosylation of proteins at multiple levels in infected cells, whereas CEP can partially maintain GX_P2V-induced aberrant N-glycoprotein targets as well as partially regulate the glycosylation of viral proteins, suggesting that multi-target drug combination is essential for the treatment of coronavirus infestation so as to achieve optimal therapeutic results. These aberrant N-glycosylation of GX_P2V infestation might be potential targets for combination therapy.
Protein extraction and trypsin digestion
Samples stored in -80°C refrigerator were thawed on ice and centrifuged at 12,000 g at 4°C for 10 min to remove cell debris. The supernatant was transferred to a new centrifuge tube for protein concentration determination using BCA kit.
Equal amount of each protein sample was enzymatically lysed with same volume of lysis buffer containing the appropriate amount of reference protein. The protein samples were mixed with ve times of the sample volume and precipitated with pre-cooled acetone at -20℃ for 2 h, followed by centrifugation at 4500 g for 5 min, the precipitate was collected and washed twice with pre-cooled acetone. The protein precipitate from each sample was dried, and then sonicated in buffer containing 200 mM Triethylammonium bicarbonate (TEAB). The digestion was performed by incubation with trypsin at a ratio of 1: 50 (enzyme: protein, m/m) with protein samples for overnight. Finally, the samples were desalted according to the C18 ZipTips instructions, and vacuum freeze-dried for HPLC analysis.
The enrichment of glycosylation modi cation of peptides The peptide fragments were dissolved in 40 μL of enrichment buffer (80% acetonitrile/1% tri uoroacetic acid) and transferred to a hydrophilic micro-column. The enrichment was completed by centrifugation at 4000 g for approximately 15 min in HILIC. The hydrophilic micro-column was washed for 3 times with enrichment buffer. The glycopeptides were eluted with 10% acetonitrile, then the eluate was collected and vacuum dried. After drying, the eluate was reconstituted in 50 μL of 50 mM ammonium bicarbonate buffer dissolved in 50 μL of hydrogen peroxide with 2 μL of water. The glycopeptides were incubated with PNGase F glycosidase overnight at 37 °C. Finally, salt was removed according to the C18 ZipTips instructions and vacuum freeze-dried for liquid-liquid analysis.
Liquid Chromatography-Mass Spectrometry (LC-MS)
The peptides were dissolved in liquid chromatography mobile phase A (0.1% (v/v) formic acid aqueous solution) and then separated using NanoElute ultra-e cient liquid phase system. Mobile phase A is an aqueous solution containing 0.1% formic acid; mobile phase B is an acetonitrile solution containing 0.1% formic acid. Liquid phase gradient setting: 0-50 min, 2%~22%B; 50-52 min, 22%~35%B; 52-55 min, 35%~90%B; 55-60 min, 90%B, the ow rate is maintained at 450 nL/min. The peptides were separated by an ultra-high-performance liquid phase system and injected into a capillary ion source. Then the peptide segments are analyzed by a TIMS-TOF Pro mass spectrometer. The ion source voltage was set to 1.6 kV and both the peptide parent ion and its secondary fragments were detected and analyzed using TOF. The secondary mass spectrometry scan range was set to 100-1700 m/z. The data acquisition mode used parallel cumulative serial fragmentation (PASEF) mode. One primary mass spectrometry acquisition followed by 10 PASEF mode acquisitions of secondary spectra with parent ion charge numbers in the range 0-5. The dynamic exclusion time of the tandem mass spectrometry scan was set to 30 seconds to avoid repeated scans of the parent ion.
Database Search
Retrieval parameter settings: the database was FA105LPNg_ Chlorocebus_sabaeus_60711_Ensembl_GX_P2V_protein_TX_combine_20200413 (19267 sequences), an anti-library was added to calculate the false positive rate (FDR) caused by random matching, and a common pollution library was added to the database to eliminate the contamination protein in the identi cation results Impact; the digestion method was set to Trypsin/P; the number of missed cleavage sites was set to 2; the minimum length of the peptide was set to 7 amino acid residues; the maximum modi cation number of the peptide was set to 5.
The mass error tolerance of the primary precursor ions in First search and Main search was respectively set to 20 ppm and 20 ppm, and the mass error tolerance of the secondary fragment ions was 0.02 Da. The cysteine alkylation was set as a xed modi cation, and the variable modi cation was the oxidation of methionine, the acetylation of the N-terminus of the protein, and the deamination of asparagine (18O). The FDR for protein identi cation and PSM identi cation was set to 1%.
Bioinformatics analyses
Glycoproteomic data of GX_P2V infection group and 14 glycosylation sites in 12 glycoprotein targets of CEP treatment in presence of GX_P2V l was analyzed by Metascape web-based platform 24 . Pathway and process enrichment analysis were carried out with the following ontology sources: KEGG Pathway, GO Biological Processes, Reactome Gene Sets, Canonical Pathways and CORUM. PPI networks were constructed by string (STRING; http://string-db.org. version 11.0) 25 Schematic diagram of subcellular location and PPI of differentially expressed glycoproteins in GX_P2V treated Vero E6 cells as well as the intervention targets of CEP. The subcellular location of aberrant glycoproteins was determined using UniProt. The PPI network maps of these dysregulated glycoproteins were generated using STRING. The red color highlights CEP-regulated proteins. Upon GX_P2V treatment in presence of CEP, 12 out of 69 glycoproteins dysregulated by coronavirus GX_P2V remains in normal glycosylation state, suggesting that these proteins and glycosylation sites might be the targets of CEP. Note: Since the 3D structure of GX_P2V viral S proteins is not available, considering the high sequence | 4,971.4 | 2020-09-24T00:00:00.000 | [
"Biology"
] |
An Evaluation Survey of Score Normalization in Multibiometric Systems
Multibiometric fusion is an active research area for many years. Score normalization is to transform the scores from different matchers to a common domain. In this paper, we give a survey of classical score normalization techniques and recent advances of this research area. The performance of different normalization functions, such as MinMax, Tanh, Zscore, PL, LTL, RHE and FF are evaluated in XM2VTS Benchmark. We evaluated the performance with four different measures of biometric systems such as EER, AUC, GAR(FAR=0.001) and the threshold of EER. The experimental results show that there is no single normalization technique that would perform the best for all multibiometric recognition systems. PL and FF normalization outperform other methods in many applications.
Introduction
Biometric recognition refers to the use of distinctive physiological or behavioral characteristics for automatically confirming the identity of a person. Multibiometrics which combines more information is expected to improve the performance of biometric system efficiently. Depending on the level of information that is fused, the fusion scheme can be classified as sensor level, feature level, score level and decision level fusion [1]. Apart from the raw data and feature sets, the match scores contain the richest information about the input pattern. Also, it is relatively easy to get and combine the scores generated by biometric matchers. Consequently, score level fusion is the most commonly used approach in Multibiometric systems. Scores generated by different matchers are not homogeneous often. For example, scores of different matchers may not be on the same numerical range and may follow different probability distributions. Therefore score normalization which transforms these scores into a common domain before fusion is needed. This paper will give an overview and comparison of score normalization methods in multimodal fusion.
The remainder of this paper is organized as follows. Section 2 introduces the Fusion in multimodal biometrics include the ideal normalization function, the performance measure and the combination rules. In Section 3, several score normalization techniques are introduced include classical and the advances of normalization methods. To study the effectiveness of different normalization techniques, section 4 gives the experimental results. The last section summarizes the results of this work.
Fusion in multimodal biometrics
The Ideal Normalization Function. In this paper, matching score coming from samples of the same individual is noted as genuine score while that coming from samples of different individuals noted as imposter score. Since scores from different recognition systems are not comparable, the normalization step tries to find the function which can transform the scores into the common domain and make the the scores of different matchers comparable. The ideal normalization function is the posteriori probability functions which is given by ( | ) / ( ( | ) ( | )) ideal s p genuine s p impostor s p genuine s = + (1) ( | ) p genuine s and ( | ) p impostor x refer to conditional density of the matching score being that of a genuine user or impostor user. It is difficult to estimate the density of matching scores in that they may not obey a certain distribution model. Therefore the ideal normalization function is not easy to implement. And different normalization techniques have been proposed in literature to solve this problem. A good normalization method should be robust and insensitive [1]. Robustness refers to insensitivity to the presence of outliers and Efficiency refers to the proximity of the obtained estimate to the optimal estimate when the distribution of data is known.
Performance Measures. Let us denote with t an acceptance threshold so that users whose score is larger than t are assigned to the genuine class, while users whose score is smaller than t are assigned to the impostor class. The two errors, respectively the False Rejection Rate (FRR), and the False Acceptance Rate (FAR) are defined as follows.
The Genuine Accept Rate (GAR) is the fraction of genuine scores exceeding the threshold t. Therefore GAR=1-FRR. The most widely accepted method used to evaluate the performance of a biometric system is the Receiver Operating Characteristic (ROC) curve. The ROC curve plots the GAR (or FRR) against the FAR. The Equal Error Rate (EER) is the point of the ROC curve where the two errors, i.e. the FAR and the FRR, are equal. EER is widely used in the biometric field to assess the performance of biometric systems. GAR(FAR=0.001 or else) is another performance measure which is also widely used in biometric performance evaluation [1]. In ROC analysis the Area Under the Curve (AUC) [2] is the also used evaluate the performance of a two-class system because it is a more discriminating measure than the accuracy. In biometric recognition systems, we always try to make EER smaller and GAR(FAR=0.001) as well as AUC larger. Combination Rules. After normalizing the matching scores and then we need to acquire a new score through a certain combination fusion rule to make final decision. Kittler [3] et al. proposed a general fusion theory framework and deduced five basic fusion rules: Sum, Product, Max, Min and Median. Since Sum rule works better in most applications [4], we use Sum rule to get the final mark in our experiments to evaluate the performance of the normalization techniques.
Score normalization schemes
Several classical score normalization techniques such as MinMax, Tanh, Z-score, Median, Median/MAD and Decimal Scaling have been described in Ref. [1]. Among the classical normalization techniques, Median/MAD and decimal scaling are not robust and Efficiency, therefore, we choose MinMax, Tanh and Z-score in the experiments in Section 4. Then we describe the progress of normalization techniques in recent years. In this section, let X, X G and X I denote the set of raw matching scores, genuine scores and imposter scores of training data. And let s denotes the new score which associated with the same matcher. The normalized score of s is then denoted by s′ . , , , Max Min Median and µ σ are the maximum, minimum, median, mean and standard deviation values. Piecewise linear (PL) [5] normalization technique transforms the scores in the range of [0, 1]. The normalization function of PL maps the raw scores using piecewise linear function as, 0 min( ) Four Segment Piecewise-Linear(FSPL) [6] technique divides the regions of impostor and genuine scores into four segments and map each segment using piecewise linear functions. The scores between two extremities of the overlap region are mapped using two linear functions separately in range of [0, 1] and of [1,2] towards left and right of t, respectively as equation (4). min( ) 0 ( min( )) / ( min( )) where (max(X )<t<min(X )) 1 ( Linear Tanh Linear(LTL) [6] normalization technique takes the advantage of the tanh estimator and the PL normalization. Normalization function of LTL maps the non overlap region of impostor scores to a constant value 0 and non overlap region of genuine scores to a constant value 1. The overlapped region between max(X I ) and min(X G ) is mapped to a nonlinear function using tanh estimator as, [7] is derived from min-max normalization scheme. The idea behind RHE is based on following observations: Any kind of normalization always causes loss of information content. Multimodal biometric systems suffer mainly from the 'low' genuine scores instead of 'high' impostor scores. So the RHE normalization method is given by
Experimental Results
Database. The XM2VTS-Benchmark [9] database consists of five face matchers and three speech matchers and was partitioned into training and evaluation sets according to the Lausanne Protocol-1(LPI). The benchmark of LPI includes two files, one is dev.label and the other is eva.label. We use dev.label as training data and eva.label as test data. Our experiments are conducted based on this match score benchmark. We sign the face matcher as face-1, face-2, face-3, face-4 and face-5 and the speech matcher as speech-1, speech-2 and speech-3 respectively.
Experimental Results. We conducted experiments to measure the benefits between the 7 normalization methods: MinMax(MM), Tanh, Zscore, PL, LTL, RHE and FF. The EER of all the matchers can be found in Table 1. As shown in Table 1, among face matchers, matcher face-3 and face-5 gain the best and worst performance respectively. And among speech matchers, the performance order is speech-1, speech-3 and speech-2. The experiments are conducted with 15 kind multimodal combinations. In each combination, the scores of different matchers are normalized first and Sum rule is used to get the final score. Then different thresholds are set to compute the FRRs and FARs. Table 2 shows the EER of multi-modal fusion among the 7 normalization methods. In order to evaluate the performance precisely, for each fusion, we give each matcher the performance mark. The performance mark for the best matcher is 7 and followed by 6, 5, 4, 3, 2 and 1. If the performance of two matchers are the same, for example, both are the second best, then the two matchers get the same mark (6+5)/2=5.5. Table 3 is the performance mark of different fusion techniques which is measured by EER. From Table 3, we can easily find that the proposed fusion method FF shows the best performance because the total mark is the largest one. And we observe that the PL and Zscore methods also perform well. To show the comparison of all the algorithms in multimodal biometric systems, Fig 1 shows the EERs of the 7 normalization algorithms. From the last column of Table 3, the sum of performance mark summaries the performance from EER aspects. It is easy to find that FF, PL and Zscore methods give better performance than other normalization methods. Fig 2 and
170
Emerging Engineering Approaches and Applications Table 4 shows the sum of performance mark of different normalization techniques based on EER, AUC and GAR (FAR=0.001). From AUC aspects, PL, RHE and Zscore techniques outperforms other normalization methods. From the GAR (FRR=0.001), PL, LTL and FF normalization algorithms give better performance than other algorithms.In order to verify the stabilization of different normalization techniques, Fig 4 shows the Thresholds of EERs(TE). From Figure 4, we observe that the TE of FF normalization varies slowly and is about 0.5. Also, the TE of Tanh and LTL normalization techniques vary slowly also. FF, LTL and Tanh show better performance than other normalization methods from the change of TE. In section 3, we have introduced that LTL and FSPL are the improvement of PL. In Ref. [6], LTL showed better performance than LTL normlization method, and LTL and FSPL outperformed PL nomalization method. However, our experimental results show that PL works better than LTL nomalizaiton method with EER, AUC and GAR(FAR=0.001).
Conclusions
The experimental results suggest that there is no single normalization technique that would perform the best for all multibiometric recognition systems. Four measures: EER, AUC, GAR(FAR=0.001) and the threshold of EER, are selected to evaluation of different normalization techniques. Different normalization functions should be choosing according to different applications. FF, PL and Zscore should be chosen if EER is the performance measure; PL, LTL and FF should be chosen if GAR(fixed FRR) is the performance measure; PL, Tanh and RHE should be chosen if AUC is the performance measure; FF, LTL and Tanh should be chosen if we want threshold of EER to be fixed. We can conclude that PL and FF normalization work better than other methods in many applications. | 2,653 | 2011-09-01T00:00:00.000 | [
"Computer Science"
] |
Positive metric entropy arises in some nondegenerate nearly integrable systems
The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. In this paper we present a Lagrangian perturbation of the geodesic flow on a flat 3-torus. The perturbation is $C^\infty$ small but the flow has a positive measure of trajectories with positive Lyapunov exponent, namely, the flow has positive metric entropy. From this result we get positive metric entropy outside some KAM tori.
Introduction
Already in the early 50's the study of nearly integrable Hamiltonian systems has drawn the attention of many outstanding mathematicians such as Arnol'd, Kolmogorov and Moser. Indeed, for any integrable Hamiltonian system the whole phase space is foliated by invariant Lagrangian submanifolds that are diffeomorphic to tori, generally called KAM tori, and on which the dynamics is conjugated to a rigid rotation. Therefore, it is natural to ask what happens to such a foliation and to these stable motions once the system is slightly perturbed. In 1954 Kolmogorov [10] -and later Arnol'd [1] and Moser [11] in different contexts -proved that, for small perturbations of an integrable system it is still possible to find a big measure set of KAM tori. This result, commonly referred to as KAM theorem, contributed to raise new interesting questions, for instance about the destiny of the stable motions that are destroyed by effect of the perturbation (in other words, about the dynamics outside KAM tori). In this context, Arnol'd [2] constructed an example of a perturbed integrable system, in which some orbits outside KAM tori have a wide range in action variables (even though the rate of change of action variables is exponentially small [12]). This striking phenomenon, known as Arnol'd diffusion and still quite far from being fully understood, shows the presence of some randomness in the dynamics outside KAM tori. The question we address in the present paper is therefore the following: how much random can the motion outside KAM tori be?" It is well-known that, C 2 -generically the Hamiltonian flow has positive topological entropy (cf. [13], see also [6] for an analogous statement for Riemannian geodesic flows). Once we turn our attention to metric entropy, the problem becomes more challenging and one cannot simply derive positive metric entropy from positive topological entropy. In fact, Bolsinov and Taimanov [3] built an example of a Riemannian manifold on which the geodesic flow has positive topological entropy but zero metric entropy.
Recently Burago and Ivanov [4] used dual lens map to construct a reversible Finsler metric C ∞ -close to the standard metric on S n , n ≥ 4, such that its geodesic flow has positive metric entropy. However the geodesic flow on the sphere is degenerate, hence it does not lie in the realm of KAM theory.
Unlike the case of spheres, the geodesic flow on flat tori are nondegenrate. In this paper we therefore provide an example analogous to Burago-Ivanov's one on T 3 . More precisely, we prove the following: Main Theorem. For every ǫ > 0 there exists a reversible Finsler metric on T 3 which is ǫ-close to the Euclidean metric in the C ∞ -sense and such that the associated geodesic flow has positive metric entropy.
Our theorem shows that in the complement of KAM tori, the behavior of nearly integrable Hamiltonian flows can be quite stochastic. However our example does not possess Arnold diffusion. For details, see Remark 4. In order to prove the main theorem we start with perturbing the return map associated with the standard geodesic flow on a specific section to get positive metric entropy. To prove positiveness of metric entropy we use Maupertuis principle and Donnay-Burns-Gerber cap [5][7] to perturb the kinetic Hamiltonian. This method was also used by Donnay and Liverani [8]. By pulling back via the standard projection, we can perturb the return map to get positive metric entropy. Now, using Burago-Ivanov dual lens map theory [4], from the perturbed return map we get a (reversible) Finsler metric on T 3 satisfying all the requirements of the main theorem. We shall however notice that, by upper semicontinuity (see [14]), the metric entropy we get is microscopic.
Preliminaries
Let M be a smooth n-dimensional manifold, T * M its cotangent bundle, and ω the standard symplectic form on T * M. To the pair (H, ω) we can associate a unique vector field X H by ω(X H , V ) = dH(V ) for any smooth vector field V on T * M, which is called the Hamiltonian vector field. The flow Φ t H on T * M defined by X H is called the Hamiltonian flow of H.
A typical example of a Hamiltonian flow is the geodesic flow on a Finsler manifold. Let ϕ be a Finsler metric on M, i.e. a smooth family of quadratically convex norms ϕ(x, ·) on each tangent space T Denote with UT M its unit tangent bundle; the Finsler metric ϕ defines a dual norm on the cotangent bundle T * M by The geodesic flow g t on (M, ϕ) is defined to be the Hamiltonian flow on T * M with Hamiltonian (ϕ * ) 2 /2. Recall that the geodesic flow can also be viewed as the Euler-Lagrange flow on T M associated with the 2-homogeneous Lagrangian ϕ 2 /2. One can easily see that Φ t H is a symplectomorphism (i.e. preserves ω) and hence volume-preserving. Once we fix a level set H −1 (c), we can define a conditional measure on this level set from the volume form. Such conditional measure is invariant under Φ t H and it is called the Liouville measure. For any point x in (M, ϕ), the unit ball B x in T x M is a convex body. By F. John [9], among all ellipsoids contained in B x , there exists a unique ellipsoid E x with maximum volume. E x is the unit sphere of some quadratic form on T x M. In this way we can define quadratic forms on each tangent spaces and these forms are close to Finsler norms. In this way we can associate with the Finsler metric ϕ a Riemannian metric g ϕ , from which UT M inherits a Riemannian structure (see [16] for details). This metric is called the Sasaki metric. For each vector ζ ∈ T v UT M we define the Lyapunov exponent by For our purpose, there is no need to recall the precise definition of the metric entropy h µ for the Liouville measure µ on UT M. Indeed, it is enough to know that Pesin's inequality [15] provides a lower bound of metric entropy. Indeed, this formula tells us that the metric entropy is no less than the mean of upper Lyapunov exponent.
The Gaussian curvature is positive on {r ≤ r 0 }, negative at C r 1 , and strictly decreasing from center to boundary.
If a torus contains a non-ergodic DBG cap and outside the cap the Gaussian curvature is nonpositive, then we call it a non-ergodic DBG torus. Sketch of proof. The proof is similar to the proof of Theorem 1.1 in [5]. By virtue of Clairaut's integral, any geodesic entering the cap C will go out of the cap. Let c : [−T 1 , T 1 ] → C be an arc-length parametrized geodesic with endpoints in C r 1 such that c(0) is the point of c closest to the origin; suppose furthermore that c(±T 2 ) lie in C r 0 , for some 0 < T 2 < T 1 . Let J S , J C be two Jacobi fields on c with be the Gaussian curvature at c(t). Then both u S and u C satisfy the Riccati equation: By imitating the proofs of Lemma 2.5 and Lemma 2.6 in [5], we get This means the graph of u must lie above that of u S . By (A) and (B) we have u(T 1 ) ≥ 0. So the cone J ′ J ≥ 0 is preserved by the cap. Figure 2. Graphs of u S , u C and u By Poincaré recurrence theorem, almost every vector in UT C will come back infinitely many times. For any geodesic c entering the cap C at time t 0 , when it returns to the cap again, say at time t 1 > t 0 , the image of the cone {J ′ (t 0 )J(t 0 ) ≥ 0} under the translation will lie strictly in the interior of {J ′ (t 1 )J(t 1 ) ≥ 0}. By Wojkowski's cone field theory [17], the vectors with non-zero Lyapunov exponents form a set with positive Liouville measure. By Pesin's inequality (1) the geodesic flow has positive metric entropy.
Construction of a Non-ergodic DBG torus
In this section we construct a conformal metric on [−1, 1] × [−1, 1] which is flat outside a disc and centrally symmetric inside the disc. More precisely we want to build a function g : [0, 2] → (0, 1] such that the torus with conformal metric is a non-ergodic DBG torus.
In order to get such a function g we change our coordinate system to geodesic polar coordinates. However before doing this we need some preliminary.
Proof. Since Both sides of ( * ) have singularity at 0. Since ρ is odd at 0, ρ ′ (0) = 1, for small l we whereρ is a smooth function that is even at 0. We integrate both sides of ( * ) regarding r as a function of l with r(0) = 0. Then we get Therefore lim l→0 ln(r/l) = 0 and ln(r/l) is even at 0. By direct computation, it is now easy to see that r/l is even at 0. This implies that r is odd at 0. From ( * ) we have Therefore ln r(l) is strictly increasing and smooth, so is r(l). By the Inverse Function Theorem there exists a smooth l : R ≥0 → R ≥0 which is the inverse function of r(l). (v) There exists l 2 > l 1 such that K(l) is negative on [l 1 , l 2 ) and ρ ′ (l) = 1 for l ≥ l 2 .
Indeed once we have such a function ρ, by Lemma 4.2 we have smooth functions g, l : R ≥0 → R ≥0 with ρ(l(r)) = rg(r) and l(r) = r 0 g(t)dt. Consider the metric defined by (2). By changing the coordinate system to geodesic polar coordinates, the metric becomes ds 2 = dl 2 + ρ(l) 2 dθ 2 .
(v) guarantees the metric is negatively curved on the annulus {r 1 < r < r 2 } and is flat outside {r = r 2 }. So once ρ satisfies (i)-(v), the torus with metric (3) will be a non-ergodic DBG torus.
Here is the construction of ρ(l): For any a > 0, let λ 1 : R ≥0 → [0, 1] be a C ∞ function with the properties that a . The last part to be verified is (iv). Since we only need to verify that ρρ ′′′ − ρ ′ ρ ′′ = 100a 2 l 3 (1 + 12al 2 − 40a 2 l 4 ) is positive on (0, 1 √ 5a ]. This can be done by direct calculation. This finishes the construction. Remark 1. The function g constructed in this way is strictly decreasing on [0, r 2 ] and constant for r ≥ r 2 since dρ dl = dρ dr a . So the supremum of g is g(0) = 1. From Lemma 4.2 we know that the lower bound is positive. Figure 3. Graph of ρ Remark 2. If g satisfies the condition that a torus with metric g(r) 2 (dx 2 + dy 2 ) is non-ergodic DBG, we can find a constant δ 0 such that for all δ ∈ (−δ 0 , δ 0 ), a torus with metric (g(r) 2 + δ)(dx 2 + dy 2 ) is also non-ergodic DBG. This follows from the fact that being a non-ergodic DBG torus is an open condition.
Perturbation of the Hamiltonian H 0
Suppose the fundamental domain of the deck group on the universal cover of our torus T 2 ∼ = R 2 /Z 2 is {−1 < x, y < 1}. We use α, β to denote the coordinates in the cotangent space and denote B * T 2 := {(x, y, α, β) ∈ T * T 2 : α 2 + β 2 < 1}. In this section we want to perturb the kinetic Hamiltonian Since g is positive and 0 ≤ 1 − g 2 < 1 (by Remark 1), we have Notice that if H ǫ < 1/6 then α 2 + β 2 < 1/3, therefore ξ ≡ 1 whenever the total energy is small. By the Maupertuis principle, the Hamiltonian flow Φ t Hǫ on the level set {H ǫ = ǫ} is a time change of the geodesic flow on T 2 with metric This metric has positive metric entropy since, by Lemma 3.2, the metric ds 2 = g(r) 2 (dx 2 + dy 2 ) does.
Perturbation ofH 0
In this section we prove that a smooth perturbation of can be derived from a suitable perturbation of H 0 . Since this result holds for all degrees of freedom, we use (q, p) to denote the coordinates instead of (x, y, α, β).
Suppose T n = R n /Z n has coordinates q = (q 1 , ..., q n ) and let p = (p 1 , ..., p n ) be the coordinates in the cotangent bundle. Denote B * T n = {(q, p) : Let V (q, p) be a C 2 -smooth function on B * T n . We perturb H 0 andH 0 by V in the following way: Then we have Lemma 6.1. If suppV ⊆ { p 2 i ≤ C < 1} for some C ∈ R + , then for every δ, m, T > 0, there exists ǫ = ǫ(V, δ, m, T ) > 0 such that for each 0 ≤ T ≤ T we have (q, p) by (∆q, ∆p) as they usually do this in calculus books. Put (q(t), p(t)) := Φ tH ǫ (q, p). Suppose that H ǫ (q, p) = E. Theṅ If p 2 i > C, thenṗ(t) ≡ 0, hence ∆p = 0. Consider the trajectory (q(t), p(t)), V p vanishes along it, hence ∆q = 0. Therefore we only need to consider the case p 2 i ≤ C. Since V is compactly supported we may assume that ǫ is small enough so that p 2 i + 2ǫV < (1 + C)/2 < 1. In this case
POSITIVE METRIC ENTROPY ARISES IN SOME NONDEGENERATE NEARLY INTEGRABLE SYSTEMS 11
We can see from the above calculation that since p 2 i + 2ǫV < (1 + C)/2 < 1, (∆q, ∆p) converges to 0 uniformly in C m as ǫ → 0.
The Burago-Ivanov Theorem
Here we use the notions and definitions from [4]. A Finsler metric ϕ on an n-dimensional disc D is called simple if it satisfies the following three conditions: (S1) Every pair of points in D is connected by a unique geodesic.
(S2) Geodesics depend smoothly on their endpoints. (S3) The boundary is strictly convex, that is, geodesics never touch it at their interior points.
Once (D, ϕ) is simple, denote by U in , U out the set of inward, outward pointing unit tangent vectors with base points in ∂D respectively. With any vector ν ∈ U in , we can associate a unique vector β(ν) ∈ U out , namely the tangent vector of the (unique) geodesic with initial velocity ν at its next intersection point with ∂D. This defines a map β : U in → U out , which is called the lens map of ϕ. If ϕ is reversible, then the lens map is reversible in the following sense: −β(−β(ν)) = ν for every ν ∈ U in .
We denote by UT * D the unit sphere bundle with respect to the dual norm ϕ * . Let L : T D → T * D be the Legendre transform of the Lagrangian ϕ 2 /2. It maps UT D to UT * D. For a tangent vector ν ∈ UT x D, its Legendre transform L (ν) is the unique covector χ ∈ U * x D such that χ(ν) = 1. Then consider subsets U * in = L (U in ) and U * out = L (U out ) of UT * D. The dual lens map of ϕ is the map σ : U * in → U * out given by σ := L • β • L −1 where β is the lens map of ϕ. If ϕ is reversible then σ is symmetric in the sense that −σ(−σ(χ)) = χ for all χ ∈ U * in . Note that U * in and U * out are (2n − 2)-dimensional submanifolds of T * D. The restriction of the canonical symplectic 2-form of T * D to U * in and U * out determines the symplectic structure. And the dual lens map σ is symplectic. In [4], Burago and Ivanov proved the following theorem: Theorem 7.1 (Burago-Ivanov [4]). Assume that n ≥ 3. Let ϕ be a simple metric on D = D n and σ its dual lens map. Let W be the complement of a compact set in U * in .
Then every sufficiently small symplectic perturbationσ of σ such thatσ| W = σ| W is realized by the dual lens map of a simple metricφ which coincides with ϕ in some neighborhood of ∂D.
The choice ofφ can be made in such a way thatφ converges to ϕ wheneverσ converges to σ (in C ∞ ). In addition, if ϕ is a reversible Finsler metric andσ is symmetric thenφ can be chosen reversible as well.
Perturbation of flat metric
Let ϕ 0 be the Euclidean metric on T 3 . We regard T 3 as the cube [−1, 1] 3 with sides identified. Let T 0 := [−1, 1] 2 × {−1} be the 2-torus on T 3 given by the "bottom face" of T 3 , and we use x, y, α, β to denote the coordinates in its cotangent bundle. Let z be the vertical coordinate of T 3 and γ the corresponding coordinate in the cotangent space.
Observe that Π is a symplectic bijection between Γ 0 and B * T 0 . Let By a simple calculation we know that the map R : B * R 3 → B * R 3 defined by R(x, y, α, β) := x + α is a lift of R 1 to the universal cover. Define a functionH 0 on B * T 0 bỹ It is not hard to see that R 1 = Φ 1H 0 .
Let R ǫ be a lift of R ǫ 1 to the universal cover. Define a dual lens map σ ǫ : U * in → U * out by σ ǫ (χ) = otherwise.
It is clear that σ ǫ is symmetric and coincides with σ outside a compact set. Moreover σ ǫ → σ in C ∞ as R ǫ → R in C ∞ . The map σ ǫ is a symplectic perturbation of σ 0 and σ ǫ = σ 0 outside a compact set in U * in . By Theorem 7.1, there exists a reversible Finsler metric ϕ ǫ in D 3 that agrees with ϕ 0 in a neighborhood of the boundary ∂D 3 and such that the dual lens map for (D 3 , ϕ ǫ ) is σ ǫ . Now extend ϕ ǫ to the whole T T 3 by setting it equal to ϕ 0 outside D 3 . It has positive metric entropy since the return map does. As ǫ → 0, we have ϕ ǫ → ϕ 0 in C ∞ . Remark 4. The example we construct in the main theorem does not have Arnold diffusion. In fact, since ϕ is close to the flat metric, we have only to prove that the return map on Γ 0 cannot have large range in action variables α, β. This is clear, since for ǫ > 0 small enough and for α 2 + β 2 ≥ 1 the return map coincides withF hence the ranges of action variables are uniformly bounded.
Acknowledgments
The author thanks Dmitri Burago for numerous helpful conversations. In particular he suggested this topic and offered help on this problem. The author is grateful to Moisey Guysinsky, Sergei Ivanov, Anatole Katok, Mark Levi, Federico Rodriguez Hertz and Yakov Sinai for useful discussions. The author thanks the anonymous referee for the helpful comments in revising this paper. | 5,009.2 | 2016-04-26T00:00:00.000 | [
"Mathematics",
"Physics"
] |
Evolution of industrial diversification and its determinants in West Germany: Evidence from population data of enterprises
Germany is among the largest countries in the world in terms of total GDP, owing largely to rapid industrialization and expansion of economic activities into several sectors. This paper contributes to the literature on German economic development by investigating the evolution of industry diversification in Germany; particularly focusing on the recent concepts of related (RV) and unrelated variety (UV) in West German regions. It also identifies the statistical and economic determinants of variation in variety over time. Among several industry structure measures; RV is the only measure that reveals a pronounced increasing trend. Since RV is composed of two parts: 1) entropy at five-digit within a two-digit classification, and 2) shares of two-digit sectors in total output, we examined which of the two components dominate. Our findings suggest that the entropy component within two-digit sectoral shares of the RV index is more dominant than the two-digit sectoral shares themselves. We further examined entries and exits of the firms among regions with top and bottom rankings in RV. Findings suggest that both the top and bottom regions experienced an increase in the total number of industries, however, exits were much less pronounced in the bottom regions. It suggests that an increase in variety among top regions is the result of the creative destruction type effect where new industries force inefficient old industries to leave the region. Finally, analysis shows support for the inverse u-shaped relationship between development and diversification.
Introduction
Regional growth literature identifies the industrial composition of regions as one of the key determinants of growth. Some studies argue that specialization is beneficial for growth while other studies show that diversification allows regions to follow a sustainable growth trajectory [1][2][3]. Recent evidence also suggests that diversification and specialization strategies vary at different stages of development [4]. Despite contradictory evidence, stylized facts seem to favor diversification rather than specialization for economic development as diversified economic structure provides resistance against external shocks and results in radical innovation through recombination of knowledge across sectors [5][6][7]. The importance of regional industrial structure for recombination of knowledge arises from the fact that that some knowledge spillovers are sticky to their locations due to the tacit nature of knowledge. Therefore, the most efficient way to transfer tacit knowledge is through face-to-face contact [8].
There are two contradictory theories on how knowledge spillovers take place in a region, namely, Marshall-Arrow-Romer (MAR) externalities and Jacobs externalities. MAR externalities suggest that knowledge is sector-specific; hence, specialization accelerates knowledge spillovers within industries which accelerates economic growth. On the contrary [6], argued that a diversified industrial structure allows the recombination of knowledge across industries. Such knowledge transfers are more likely to result in radical types of innovations as compared to incremental innovations in the case of specialization [9]. Alternatively, diversity can also be viewed in terms of the portfolio theory in which an increase in diversity reduces the vulnerability of regions to external shocks [10].
Diversification can be disentangled into related and unrelated variety as proposed by [9]. Authors propose that knowledge spillovers are more frequent among related industries as compared to unrelated ones as cognitive proximity of related industries facilitates knowledge spillovers. While the impact of related and unrelated variety on regional growth has been widely empirically examined in recent years, much less is known about how the patterns of diversification evolve and what determines a certain evolution pattern.
According to the World Development indicators, Germany is one of the most industrialized countries in the G7 in terms of industrial value-added as a percentage of GDP. It is the largest economy in the EU with its GDP standing at 3.85 trillion USD in 2019 (World Development Indicators (WDI)). Despite the global significance of the German economy, the literature on the evolution of sectoral composition in Germany especially approached from the related and unrelated variety perspective, is scarce. Therefore, this study investigates long-term development patterns of regional industrial diversity, related variety (RV), and unrelated variety (UV). The unique feature of this study is that it uses the data for entire population of enterprises in West German regions over more than thirty years from 1976 until 2010. The data is accessed through special permission from IAB-Institut für Arbeitsmarkt-und Berufsforschung der Bundesagentur für Arbeit in Nurnberg, Germany. The paper deals with the following main research questions: • How has industrial structure emerged in West Germany over time? Has there been any difference in the evolution of diversification patterns in related and unrelated sectors?
• What is the driving force behind strong increasing trends of related variety in West Germany over time? Two sources are addressed: First, is it driven by sectoral shares of two-digit industries or entropy within two-digit industries? Second, the role of sectoral entries and exits on the increase in RV is investigated.
• Do diversification patterns vary at different stages of regional development and depending on proximity to highly diversified regions?
The paper is organized as follows. Section 2 provides an overview of the main theoretical concepts related to industrial composition and their associated different types of externalities. Data, spatial framework, and construction of indices are outlined in Section 3. Section 4 provides an overview of the long-term development patterns of industry structure in West Germany and further differentiates between related and unrelated diversification. Section 5 analyzes statistical and economic drivers of the strong increasing trend in RV in West Germany. Section 6 concludes by indicating some future research directions on this topic.
Literature review
The role of industrial composition in the diffusion of knowledge across sectors has been recognized and debated since [11]. One strand of the literature proposes that specialization in few industries ensures learning-by-doing effects, and knowledge transfers are relatively frequent under such a structure. Externalities arising from similar sectors are termed as "localization externalities", or MAR externalities, named after decades of reformulation of ideas by [11][12][13]. Specialized industrial composition benefits from specialized labor, specialized suppliers, and large markets. On the contrary [6], argued that externalities associated with diversified industry structures are stronger determinants of long-run regional growth as compared to localization externalities. According to this point of view, diversity provides opportunities to interact and recombine practices and thus could foster the generation of new ideas and innovations [14]. The recombination of knowledge across sectors under a diversified industrial structure is expected to lead to radical types of innovations [9]. Such positive externalities are generally termed as "Jacobs externalities".
However, there may be significant differences in the types of innovations generated by spillovers between related and unrelated sectors. Jacobs externalities are criticized in literature due to the oversimplification of the concept. This question has been elaborated by [9] by introducing the concept of related and unrelated variety. The concepts of related and unrelated variety, proposed by [9], disentangles diversification based on the degree of relatedness among sectors to differentiate between knowledge spillovers and portfolio effects of diversification. In particular, [9] claimed that knowledge spillovers are relatively frequent among related sectors as compared to unrelated sectors. Moreover, diversification in unrelated sectors helps to protect regions from sector-specific shocks due to limited reliance on a few industries. Therefore, economic effects associated with different types of variety are expected to be different and, in the analysis of regional performance, they should be empirically separated from each other. The terms 'diversity' and 'variety' are used interchangeably in this study, although, variety is more attributed to the concept that distinguishes between related and unrelated variety. Frenken [15] point to their preference for the term 'variety' since 'diversity', according to their view, is more attributable to the biology. Similarly, 'sectors' and 'industry' are used interchangeably in this study. Spillovers between similar industries, according to [16], are more likely to lead to incremental innovation, but spillovers between unrelated industries are more likely to lead to radical innovation, such as entirely new products. If radical innovation generates more positive regional development impulses than incremental innovation, then it is unclear which form of diversity will be more significant for growth: radical or incremental. Spillovers between similar industries may be more common but have a minor impact, whereas spillovers between unrelated industries should be less common but have a larger impact [17]. Table 1 summarizes the types of externalities and innovations generally associated with specialized and diversified economic structures as explained above.
Data description
This study is based on a comprehensive dataset on German firms. The case of Germany is interesting because is the most industrialized country in G7 with industrial value-added as a percentage of GDP standing at 26.8% in 2019 (WDI). It is the 4 th most developed country according to the Human Development Index 2018 and it has the highest trade to GDP ratio in G7. It has the 3 rd highest GDP in PPP terms among G7 countries. Finally, it is the 8 th most diversified country in the EU according to the report by the European Union entitled "Competing in Global Value Chains: EU Industrial Structure Report 2013". This section describes the data and construction of industry representative diversification indices. The spatial framework of the analysis is the 71 planning regions of West Germany. Planning regions are functional spatial units that consist of at least one core city and the surrounding area and are comparable to the labor market areas in the United States. The choice of planning regions over districts is justified by the fact that various effects (e.g., knowledge spillovers that are of the particular importance in the concept of RV and UV) which might be relevant for larger units of an observation than districts and therefore could decrease the potential presence of spatial autocorrelation in the empirical estimations. Furthermore, labor market regions are the most appropriate spatial unit of analysis for agglomeration research [15].
The analysis is restricted to West Germany because many empirical studies indicate that the East German economy in the 1990s was a special case with very specific conditions that cannot be directly compared to those of West Germany [19]. Besides, long term data (before the 1990s) is not available for East Germany. Data on industry composition is obtained from the German Social Insurance Statistics (IAB-Institut für Arbeitsmarkt-und Berufsforschung der Bundesagentur für Arbeit). This dataset contains every establishment in Germany that employs at least one person obliged to make social insurance contributions [20]. Each establishment can be assigned to a 3-digit-level industry classification over the period covered in the analysis. All industry related measures account for changes in the industry classification over time (for details see [21]). The public sector, agriculture, and mining industries are excluded from the analysis.
Measuring diversification
The literature on economic diversification provides a wide range of indices to capture industry structure. Depending on the assumptions behind each measure, the interpretation of diversification can be different. For discussions on diversification and specialization indices with their advantages and disadvantages see [22] or [23]. Broadly, diversification indices can be divided into absolute and relative measures depending on the benchmark used. In the context of this study, for absolute measures, the reference level is an equal distribution of employment across all industries, whereas, for relative measures, it is the average economic structure of the reference level, e.g., a country under study. Hence, relative measures reveal how dissimilar the sectoral composition of a region is compared to the reference level (which is generally a country if the unit of analysis is a region). An advantage of relative measures is that they compute a measure for a region relative to the country which minimizes the chances of over or underrepresentation of the regional industry composition if measured in isolation. Another important aspect of industry assessment is the choice of the industry aggregation level that can produce diverse empirical evidence [23]. Absolute diversification can be measured by the Theil [24] index which, in principle, is an entropy measure. Diversification measured by entropy index measures the degree to which the employment is equally distributed across sectors. When one or a few dominant industry sectors are present, the diversification index takes a low value indicating the specialization of a region in a few sectors. On the contrary, if employment is equally spread across all sectors, then the index takes its highest value indicating a high level of diversification. Being based on entropy measures, the Theil index can be decomposed at different levels of industrial classification, a property that is applied to construct the measures of related and unrelated variety below.
Relative diversification, on the other hand, is measured by the inverse of a Hirshman-Herfindahl index [25,26] as applied by [5,27]. The index increases with the increase in regional sectoral diversity which mirrors sectoral diversity at a national level. Relative diversification indices are not directly decomposable into the related and unrelated variety.
In what follows, the study focuses on absolute diversity measure (denoted as 'Overall variety') which is also decomposed into RV and UV. Overall variety (OV) is calculated using the entropy measure at the three-digit industry classification level in the following way: where p i is employment in a three-digit industry share. The values of OV can vary from 0, when all employment is concentrated in only one three-digit sector, up to log 2 (n) when all sectors employ an equal number of employees. Data used in this study contains a total of 174 three-digit private sectors which means that the theoretical upper bound of the OV index is 7.44. Further, we distinguish between UV and RV following the methodology used by [9] who apply the decomposable nature of an entropy measure to distinguish between the related and unrelated variety. Unrelated variety measures entropy across two-digit industries and thus assumes that industries at this level of aggregation are unrelated to each other because they are not cognitively proximate. A common belief is that knowledge spillovers are less frequent among unrelated sectors, however, recombination of knowledge among unrelated sectors is expected to result in radical innovations [17]. UV is calculated using the following formula: where P g is the share of employment in the two-digit sector S g (where g = 1,. . .,G) over the total employment in a region. The UV measures the degree to which employment shares are evenly distributed across unrelated (in this case two-digit) sectors. The values of UV can vary from 0, when all employment is concentrated in only one two-digit sector, up to log 2 (G) when all sectors employ an equal number of employees. In this study, there are a total of 41 two-digit private sectors that correspond to the theoretical upper bound of 5.36. Related variety is measured as the weighted sum of entropy at the three-digit level within each two-digit sector assuming that industries within this level of aggregation are related based on cognitive proximity and thus can effectively learn from each other [9]. RV is calculated using the following formula: where P g is the share of employment in the two-digit sector S g over the total employment in a region; p i is the share of employment in the three-digit sector S i (where i = 1,. . .,I) belonging to the same two-digit sector S g . The RV indicates the degree to which employment at the twodigit level is evenly spread across its three-digit subsectors. The values of RV can differ from 0 when, within each two-digit sector, employment is concentrated in only one of its three-digit subsectors up to log2(I)-log2(G) when all subsectors employ an equal number of employees (based on entropy decomposition theorem by [24], as applied by [17]). The higher the RV value is, the more evenly employment is spread across the subsectors indicating to the higher number of technologically related industries in a region. According to the underlying concept of the RV, such industry structure is conducive to inter-sectoral knowledge spillovers. In this study, there are a total of 174 three-digit subsectors (I) under 41 two-digit sectors (G) which means that the theoretical upper bound of the index is 2.09.
Results
This section presents the findings of the study in two parts. The first part presents the trends of diversification over time and the second part presents the determinants of diversification.
Trends of overall, related and unrelated diversification over time
Evolution of overall industrial structure over time. The evolution of absolute industry diversification measured by Theil index and relative diversification measured by the inverse HH index are presented in Fig 1. For each year, the dashed line represents the region with the lowest diversification whereas the dotted line shows the region with the maximum diversification. The black solid line represents the mean value whereas the grey solid line represents the median value of diversification. The absolute diversification index shows relatively less variation as compared to the relative one. The solid lines for the mean and median of the diversification indices show that there has been a slight increase in diversification over 34 years. In particular, mean absolute diversification has increased by 5% (0.1% annual growth on average) whereas mean relative diversification has increased by 15% (0.4% annual growth on average). Overall, Fig 1 shows that industrial diversification in West Germany has increased but quite slowly over 34 years. However, it should be noted that these indices are measured at a high level of aggregation due to which, some inter-sectoral dynamics might be suppressed within the indices. For this reason, the overall variety measure is decomposed into its related and unrelated components which are further analyzed in the Sections 0-0.
Evolution trends of related and unrelated variety over time. This section disentangles overall variety into the related and unrelated variety and compares these variety measures with general evolution in industry structure. Long term patterns of industry structure shown in Section 0, in line with other studies on developed economies, reveal slow growth in diversification. On the evolution of RV and UV [14], based on findings of [28,29], conclude that expansion in unrelated sectors is likely to be persistent over time because it is more likely for regions to diversify in activities that are related to existing fields. Also [30], note that existing evidence shows that new industries do not appear out of the blue, rather they evolve from existing industries and competencies that are available in regions.
Long term development patterns of OV and its decomposition into RV and UV is shown in Fig 2. The average values of UV over the years of observation lie between 4.35-4.42. Considering the theoretical upper bound of UV being 5.39, this indicates a rather diverse yet stable unrelated industry composition of West German regions. Such high stability might be explained by difficulties to attract new industries if they are not technologically proximate to current regional activities (as shown by [31]). While UV remains largely unchanged over time, RV reveals a continuous increase for West German regions. The average values of RV have increased over the years of observation from 1.34 up to 1.61. Fig 3 indicates that the RV component of the OV is the driving force behind the slightly increasing trend of the OV. An increase in RV means that the employment distribution across three-digit sectors within each two-digit class is becoming more evenly spread. Theoretically, there can be three possible technical reasons for changes in RV: 1) changes in sectoral shares with no change in total sectors, 2) entry of new sector(s) and 3) exits of the old sector(s). A brief analysis of these possible dynamics is presented in Section 0.
Regarding the evolution of RV over time, there is almost no evidence for long term RV trends in the literature to make a reasonable comparison between West Germany and other economies. The study by [32] is an exception which, for the period between 1993 and 2006, reveals a similar trend of the continuous increase in RV for Finnish regions. Reasons for such a trend, however, are unclear and have not been analyzed in detail. Nevertheless, the particular period in Finland is described as the one during which the Finnish economy experienced a shift to a high tech economy, and the relevance of intra-industry knowledge spillovers for high tech sectors is emphasized [32]. From the theoretical perspective, it might mean that the development of the high-tech sectors has primarily taken place via incremental type innovation.
Continuous increase in RV might be viewed in the context of those few studies that show evidence that regions tend to expand and diversify in activities that are related to those of existing ones. By exploring long term development patterns of Swedish regions from 1969 to 2002 [31], showed that regions are more likely to expand in industries that are related to their existing industry portfolio. Furthermore, even if the newly introduced industries are conceptually related to each other, they might still be different from the existing portfolio of industries present in the region and may result in increasing related variety. Boschma [30] investigated a similar question for Spanish regions from 1988 to 2007 and concluded that new industries that emerged in Spanish regions tended to use similar capabilities of existing industries. It is important to note that these studies apply different relatedness indicators to measure regional related diversification. Neffke [31] measured relatedness based on co-occurrence of products from diverse industries within portfolios of manufacturing plants, whereas [31] used a product proximity indicator developed by [30] to determine to what extent two products share similar capabilities.
Looking at the evolution of related and unrelated variety from a different lens, the analysis of the probability density function over time (Fig 3) reveals another interesting trend for RV. In addition to the shift of the RV distribution to the right side, which reflects an increase in absolute values, there is also a pronounced change in the shape of the distribution. Distribution of the RV gets steeper over time indicating that regions converged around a mean variety in related activities. Distribution of UV confirms long term persistence in absolute values relative to related variety. There is also a change in the shape of the distribution, however, it is less pronounced and consistent compared to RV.
Persistence of related and unrelated variety over time. Fig 4 illustrates the range of variation and the level of persistence of variety indices relative to its state ten and thirty years ago. In these graphs, the 45-degree line indicates no change in variety over time. Fig 4 show that regional related variety increases over time as most of the regions lie above the 45-degree line. This is especially pronounced when the current variety is compared with its level thirty years ago. Changes over time confirm previously described an increase in the overall RV for planning regions. Contrary to RV, the evolution of UV is less pronounced as most of the regions are spread around the 45-degree line showing low or no change over ten and thirty years.
Munich is among the top 5 regions with the most unrelated industrial structure in all years covered in this study and it is known for its vibrant entrepreneurial spirit. Other regions include Unterer Neckar and Mittlerer Oberrhein, which share borders with Munich, and Aachen and Göttingen are among regions with high unrelated variety. In nearly all years of analysis, the lowest UV is observed for Ingolstadt which is a host of the giant automobile producer Audi (other regions with the lowest UV in all years of the analysis are Main-Rhön, Braunschweig, Landshut, and Siegen). Among the top 5 regions with the most related industrial structure are Düsseldorf; Bochum/Hagen; Duisburg/Essen; Hamburg and Siegen. It is
Statistical and economic determinants of variation in variety indices
This section analyzes the driving forces behind the continuous increasing trend of one type of variety, namely related variety, in West Germany over time. First, it studies the extent to which such an increase in RV is driven by sectoral shares of two-digit industries or entropy within two-digit industries (Section 0). Second, it studies the role of entries and exits of sectors in the industrial composition on the increase in RV (Section 0). Finally, Section 0 estimates the general relationship between both types of varieties and regional development as well as the distance to variety frontiers.
The effect of changes in sectoral shares (Pg) and entropy within these sectors (Hg) on the evolution of the related variety. As shown in Section 0, Related Variety is a weighted sum of entropy at the three-digit level within each two-digit sector. Entropy within each twodigit sector (Hg) is weighted by the share of the two-digit sector (Pg) in total employment of the region. The intuition behind assigning weights is that the measure of entropy is unaffected by the magnitude of employment. As a result, even though sectors with significantly different levels of employment are likely to have very different effects on the overall economy, they still can have the same entropy levels. Therefore, entropy within two-digit sectors is weighted by sectoral shares to give more weight to the sectors with larger shares in total employment.
The interpretation of the increase in RV is generally attributed to the increase in sectoral shares of industries related to each other. This interpretation implies that the increase in RV is driven by entropy within two-digit sectors (Hg). However, since measurement of RV involves Pg and Hg, the variation in the index can be amplified by either two-digit sectoral shares (Pg), entropy within these sectors (Hg), or both. If the effect of Pg is dominant, then the interpretation of the increase in RV becomes less trivial as one can no longer associate the increase in RV with the increase in entropy in related sectors.
To analyze whether the strong increasing trend in RV in West Germany is driven by Pg or Hg, two additional RV indices are introduced in the analysis. In the first index (RV1), Pg is held constant at its level in 1976, while Hg can vary. In practice, such transformation would imply that, while sectoral shares can vary at the three-digit level, they do not affect the broad industry structure at two-digit levels. Likewise, in the second index (RV2), Hg is held constant at its level in 1976, while Pg can vary. In this case. industry distribution at its lowest (threedigit) level is held constant, while aggregated industry structure at the two-digit level can vary over time. Fig 7 compares the trend of the original RV index with two artificially generated indices RV1 and RV2. The indices are calculated for West Germany by using mean (black lines) and median (grey lines) across regions. Fig 7 shows that RV and RV1 are overlapping from 1976 to 1989, and RV1 shows a strong increasing trend in the later years. On the contrary, the line plot for RV2 shows, on average, a relatively weaker positive trend especially until 1990. Fig 7 shows that the trend in RV is mostly driven by an increase in Hg. Therefore, it can be concluded that the increase in RV in West German regions has taken place via the increase in variety in related sectors rather than the increase in shares at a broader (two-digit) sectoral level. In other words, the driving force behind the increase in RV is a change in the distribution of sectoral shares within two-digit sectors rather than the magnitude of employment at the two-digit level.
The average flows reported in Fig 7 show the overall evolution of RV in Germany. Fig 7, however, does not capture the variation of trends across regions. Since each region has its own economic structure, the evolution of industrial structure is likely to differ across regions. Moreover, the effects of Pg and Hg on the behavior of the RV index could also differ for where Pg has no long term effect on RV. Put differently, for 'top-performing' regions there has been an important role for the increase in diversity at the two-digit level that is generally more difficult to achieve since regions tend to diversify in sectors that require capabilities similar to the existing ones in the region. For 'bottom performing' regions, until 1995, RV followed a positive trend. During this period, RV and RV1 lines are approximately parallel to each other showing that Hg is the driving force behind the increase in RV. This can also be confirmed by the relatively flat curve of RV2 for the same period which shows that there was no significant effect of Pg on the evolution of RV before 1995 in the bottom 5 regions. After 1995, RV shows a U-shaped relationship which is mostly driven by Hg, as RV1 also shows a similar trend. During this period, RV2 shows a slightly increasing trend, however, the overall effect of Pg from 1976 to 2010 in the evolution of RV, as shown by the RV2 plot, is insignificant as the initial and final positions in the graph are almost identical. From the analysis in this section, we can conclude that the driving force behind a strong increasing trend in RV is variation in industrial distribution or entropy at the three-digit level and not the overall magnitude of employment at the two-digit level which is used as a weighting variable in the calculation of RV.
The role of sectoral entries and exits on the increase in related variety. Related variety can increase due to a change in the number of related industries in the region or due to change in the distribution of employment across related industries. Increase in variety achieved through an increase in the shares of existing industries in the regional industry portfolio is termed as variety in intensive margins, while an increase in variety due to the entry of new sectors in the industrial portfolio is termed as variety in extensive margins [33]. An absolute increase in the number of industries in a region can be the result of entries or the net positive difference between entries and exits. If entries are approximately equal to exits, provided that the shares of new industries match the distribution of exiting industries, industrial variety will be unaffected.
The dynamics of industry entries and exits could be different for regions with the highest increase in RV as compared to the regions with the lowest increase in RV, as low RV implies that regional employment is dominated by a few industries and theoretically opportunities to enter into new industries are higher in those regions. On the contrary, if employment is relatively equally shared by existing industries, then the resulting RV will be high and it implies that there is some level of competition in each industry, therefore exits are expected to be This section aims to explore whether an increase in RV via the change in the number of industries is purely because of entries or if it is because of the net positive difference between entries and exits. The task is performed only for the top 3 and bottom 3 regions in terms of changes in RV because of the expected difference in sectoral dynamics: especially between low and high performing regions in terms of the industrial variety.
The comparison in Fig 10 and Table 2 shows that although the number of industries has increased over time for both high and low variety regions, the number of exits is different for the regions in the top and bottom group. A large number of exits in the top-performing regions could be an indication of the creative-destruction type effect where new industries take over the inefficient old ones. If new sectors replace old ones, the distribution of industries is likely to change significantly as the employment shares in existing industries may also change due to competition effects which may result in the movement towards the equalization of employment shares. A technical explanation of the difference is that entries and exits at the same time create a larger distortion than pure entries. Therefore, due to the uneven evolution of sectoral shares, diversification measures increase. Analysis of the top and bottom regions, in terms of the increase in RV, shows that sector exits in the bottom 3 regions are quite low even though sector entries are, on average, like the ones for the top 3. It appears as if new industries did not alter the previous industrial structure in the bottom group regions which might be due to an increase in the number of industries in sectors unrelated to the existing industrial portfolio, therefore, not leaving an impact of related variety measures. Unless the shares of employment absorbed by the new entering industries are large enough to change the industrial structure significantly (i.e. technically via the sectoral shares Pg, see the discussion in Section 0), it will not change the related variety noticeably. However, detailed analysis to confirm or reject these propositions is outside the scope of this study and requires further research. Relation of variety with the stage of development and spatial dependence to frontiers. The natural question that arises after analysis of the evolution of variety in regions is why some regions can diversify while others are not. The question does not necessarily concern itself with the issue of causation but also implies the co-evolution of variety with other economic factors such as the level of development [4] or geographical factors such as the distance from the most diversified regions [34]. It is particularly important to study the determinants of unrelated variety as it involves riskier investments and requires a locally unavailable skill-set, as compared to related variety, which can also take place automatically through an evolutionary process due to the relatedness of required skills with the existing skill-set of a region.
Intuitively, developed regions are better able to invest in the diversified product basket, as compared to less developed regions, due to the riskiness of new investments. The non-linear relationship between development and diversification was identified by [4] who found that countries diversify at the early stages of development; however, they re-specialize after reaching a threshold level of per capita income. Moreover, also geographical proximity with highly diversified regions is expected to increase diversification in other regions as a result of knowledge spillovers and skill transfers through increased mobility of labor, trade, and entrepreneurship across borders due to reduced transportation and transaction costs [34]. Geographical proximity can also reinforce MAR, or Jacobs externalities, and reach beyond the boundaries of the region itself. Studies on knowledge spillovers highlight the importance of face-to-face contact for transfer of uncodified (tacit) knowledge, the possibility of which increases when geographic proximity is high. Moreover, entrepreneurs in the highly diversified regions are expected to make use of nearby regions for their business especially if the nearby regions are providing a favorable policy mix for the investors. As a result, nearby regions may attract locally unavailable capabilities from highly diversified regions to increase the diversification at home. One can, therefore, expect the diversification levels of regions to be high if they are in proximity to the most diversified regions.
To empirically assess the role of the stage of development and geographical proximity on the level of variety, this section uses the following empirical model: Where the dependent variable is either related or unrelated variety and Emp Areai;t is employment in a region per square meter. Employment levels are divided by the area of the regions to minimize the scale effects. Employment levels are used to proxy the stage of regional development.
The squared term of the employment level is added to test the non-linear relationship between the stage of development and diversification as identified by [4]. Following the results of [4] one would expect a positive sign for the main effect of the employment level and a negative sign for the squared employment level. Taking inspiration from [35,36], the Distance variable is the distance of the region in question with the closest of the top 10 regions in terms of variety. In other words, each year regions are ranked in descending order according to their related and unrelated variety levels. In the next step, distance is calculated between each region in the sample and the top 10 regions in terms of variety. In the last step, the shortest of the distances calculated in the second step is taken as a value for the Distance variable for that region. Following the construction, interpretation of the variable is an inverse to the proximity variable i.e. the larger the value of the Distance variable is, the less likely a region is to have a high level of variety. Therefore, one would expect the sign of the Distance variable to be negative.
The results of the estimation are presented in Table 3. The results show strong support for the [4] results i.e. regions seem to diversify at early stages of development (measured by employment levels) and re-specialize at later stages. The result holds for both related and unrelated variety. The distance variable is found to have a negative relationship with variety, both for related and unrelated variety, confirming the expectation that regions that are distant from highly diversified regions find it difficult to diversify their product portfolio. The effect is particularly strong for unrelated variety showing that distance matters more for unrelated variety as compared to related variety as the import of locally unavailable capabilities from other regions is easier when a region is geographically proximate to highly diversified region(s).
Conclusion
This paper investigated the long-term evolution of industrial structure in West German regions with attention to the industry diversity, which was distinguished between the overall, related, and unrelated variety. Among several industry structure measures; analysis reveals a strong and continuous increase in RV. This confirms findings in the literature [30,31] that regions tend to diversify in related sectors. Moreover, a relatively weaker positive trend was found for overall variety while unrelated variety did not change significantly throughout. Regarding the question of the driving force behind the continuous increase in RV, several causes for the continuous increasing trend were investigated. First, an increase in RV was investigated with the help of statistical analysis to see if the increase was dominated by the effect of changes in sectoral shares (Pg) or entropy within these sectors (Hg). Findings suggest that the entropy component (Hg) measuring variety at the three-digit industrial classification within the two-digit level is more dominant than the twodigit sectoral shares (Pg) in the overall evolution of RV. This shows that the interpretation of the RV increase in the context of an increase in variety in related sectors is viable in the case of West Germany. The dominance of Hg holds for the top 5 and bottom 5 regions in terms of increased RV as well.
To approach the question of the driving force behind the continuous increase in RV from another perspective, analysis of top and bottom regions with the most and least increase in RV was performed to explore the role of sectoral entries and exits in the dynamics of RV evolution. Findings suggest that while both the top and bottom regions experienced an increase in the total number of industries, exits were much less pronounced in the bottom regions. It suggests that an increase in variety among top regions is the result of the creative destruction type effect where new industries force inefficient old industries to leave the region. The relatively frequent entry and exit of industries ensured that the shares of industries remained relatively even and, therefore, an increase in variety for these regions was observed.
Finally, the question of the relation of variety with the stage of regional development and spatial dependence to frontiers was investigated. Concerning the relationship between development and diversification depending on the stage of regional development, the study at the regional level confirms findings by [4] who show that countries diversify at the initial stages of development, however, after a certain threshold, re-specialize by quitting inefficient sectors. Apart from that, closeness to the most diversified regions is also related to the level of diversity of a region.
While providing several new insights to the RV and UV concept, the following limitations apply to this research. First, the effect of sectoral entries and exits in shaping the variety was performed on the bases of a few top and bottom performing regions in terms of the increase in RV. In principle, this approach approximates the study of the diversification via intensive and extensive margins. Application of such a study at the aggregate level of regional industry diversification patterns could be a promising way to increase our understanding of how regional diversification takes place. Another important question for analysis of diversification would be to identify the role of start-ups and exits in the process of diversification. Are they more of related or unrelated sectors and what type of variety do they increase? Also, some macro studies have found a relationship between variety and human development such as [37,38] and found that variety has a positive relationship with human development. Similar relationship can be analyzed at regional level. Finally, the determinants of regional diversification into related and unrelated sectors are hardly ever analyzed in the literature. Analysis in final section of results slightly touches only two dimensions of variety determinants. Nevertheless, estimations presented in that section do not aim to provide a model explaining variety types. Instead, they aim to test the relationship between the stage of development and the distance to the frontier in terms of variety. This also explains the rather low explanatory power of the models. Further work on the identification of the possible determinants of different variety types and time required for these determinants to influence variety is certainly a further avenue of research. Likewise, case studies of regions that experienced the most pronounced increase in either RV or UV might help to reveal some insights behind the structural change. | 9,724.4 | 2021-11-03T00:00:00.000 | [
"Economics"
] |
Polo-like kinase 1 (Plk1) overexpression enhances ionizing radiation-induced cancer formation in mice
Polo-like kinase 1 (Plk1), a serine/threonine protein kinase normally expressed in mitosis, is frequently up-regulated in multiple types of human tumors regardless of the cell cycle stage. However, the causal relationship between Plk1 up-regulation and tumorigenesis is incompletely investigated. To this end, using a conditional expression system, here we generated Plk1 transgenic mouse lines to examine the role of Plk1 in tumorigenesis. Plk1 overexpression in mouse embryonic fibroblasts prepared from the transgenic mice led to aberrant mitosis followed by aneuploidy and apoptosis. Surprisingly, Plk1 overexpression had no apparent phenotypes in the mice. Given that no malignant tumor formation was observed even after a long period of Plk1 overexpression, we reasoned that additional factors are required for tumorigenesis in Plk1-overexpressing mice. Because Plk1 can directly participate in the regulation of the DNA damage response (DDR) pathway, we challenged Plk1-overexpressing mice with ionizing radiation (IR) and found that Plk1-overexpressing mice are much more sensitive to IR than their wild-type littermates. Analysis of tumor development in the Plk1-overexpressing mice indicated a marked decrease in the time required for tumor emergence after IR. At the molecular level, Plk1 overexpression led to reduced phosphorylation of the serine/threonine kinases ATM and Chk2 and of histone H2AX after IR treatment both in vivo and in vitro. Furthermore, RNA-Seq analysis suggested that Plk1 elevation decreases the expression of several DDR genes. We conclude that Plk1 overexpression may contribute to tumor formation by both inducing chromosomal instability and suppressing the DDR pathway.
Chromosome instability and aneuploidy are hallmarks of human cancers (1). Most human cancers contain aneuploid cells, and a significant number of studies have pointed to failure in various critical mitotic events as a cause of aneuploidy in tumors (2)(3)(4). Defects in mitotic events, including centrosome maturation, microtubule-kinetochore attachment, chromosome alignment, and completion of cytokinesis, are the causes of aberrant cell division, eventually resulting in aneuploidy in daughter cells (5,6). The regulation of proper mitotic progression that is important to genomic integrity is predominantly controlled by protein phosphorylation driven by several evolutionarily conserved serine/threonine kinases, known as mitotic kinases. The most prominent mitotic kinases include Polo-like kinase 1 (Plk1), cyclin-dependent kinase 1 (Cdk1), aurora family, and NIMA (never in mitosis A) family kinases (7).
The Polo gene was first cloned from Drosophila melanogaster, with the observation that mutations in Polo induced abnormal spindle poles during mitosis (8). Five mammalian homologues for Polo, named Plk1 to Plk15, were soon identified (9). Among them, the best characterized member of human Plk family is Plk1. It has been well-documented that Plk1 is involved in almost every step of mitosis (10). Thus, it is probably not surprising that Plk1 is overexpressed in many cancer types, including melanoma, breast, non-small cell lung, colorectal, prostate, pancreatic, ovarian, and head and neck cancers, as well as non-Hodgkin's lymphomas and acute myeloid leukemia (9,11). More importantly, recent studies have also linked Plk1 with other cancer-associated pathways (12). For example, cross-talk between Plk1 and the p53 tumor suppressor has been described, because Plk1 negatively regulates both p53 protein stability and nuclear localization (13,14). In another study, Plk1 elevation was shown to cause PTEN inactivation, resulting in a tumor-promoting metabolic state in prostate cancer cells (15). In line with this observation, Plk1-associated kinase activity was demonstrated to contribute to the low-dose arsenic-mediated metabolic shift from oxidative phosphorylation to glycolysis via activation of the PI3K/AKT/mTOR pathway (16). In addition, elevation of Plk1 leads to acquisition of resistance to various therapies, including radiotherapy (17), taxol (18), metformin (19), gemcitabine (20,21), and androgen signaling inhibitors (22). All these studies strongly suggest that Plk1 likely plays a critical role during carcinogenesis.
Inhibition of cell proliferation and induction of apoptosis are two basic principles of anticancer therapy. Antimitotic therapy is a standard of care for many cancer types. Overexpression of Plk1, observed in a broad spectrum of cancers, has often been correlated with disease stage, histologic grade, poor prognosis, metastatic potential, and survival (9). The key role of Plk1 in oncogenic events gave impetus to the development of potent and specific small molecule Plk1 inhibitors (10). Consequently, several Plk1 inhibitors have been developed, with some agents showing encouraging results in various cancer cell lines and xenograft models of human cancer (23,24). Preclinical studies have demonstrated a particular sensitivity to Plk1 inhibition in human cancer cells harboring specific genetic abnormalities, including mutations in p53, Ras, and PTEN (10). In contrast to marked antitumor activity in leukemia, overall antitumor activity of Plk1 inhibitors in patients with solid tumor has been modest in trials (23). Thus, there is a critical need for understanding the physiological functions of Plk1 in vivo. Lack of Plk1 transgenic mice is one major hurdle to achieve that.
Herein, we generated a transgenic mouse model to investigate the involvement of Plk1 in tumorigenesis. Using a Cre-loxP system, we achieved the conditional expression of Plk1. Elevated Plk1 expression resulted in mitotic failure, leading to apoptosis and aneuploidy in mouse embryonic fibroblasts (MEFs). 2 In addition, Plk1 overexpression caused a defective DNA damage response (DDR) pathway. Our findings indicated that this mouse model is a useful system to study the physiological roles of Plk1 in cancer etiology and therapeutics.
Strategy and design for the conditional Plk1 transgenic mouse
Considering that overexpression of Plk1 induces abnormalities in cell division in vitro, we selected a conditional transgenic system to prevent the possible embryonic lethality of founder animals (Fig. 1A). The configuration of this transgenic cassette was chosen so that Plk1 would be overexpressed in the transgenic mice after expression of Cre recombinase. To prevent the chromosomal positional effects associated with the random nature of transgenic integration, we inserted the cassette into the well-characterized euchromatic locus Rosa26 (Fig. 1A). The standard transfection procedures using this exchange vector were followed by the recombinase-mediated integration, which resulted in more than 90% positive embryonic stem (ES) cell clones ( Fig. 1, B-H). Plk1-KI mice were subsequently obtained from the recombinant ES cells.
Establishment and characterization of transgenic mouse founders for Plk1 expression
We successfully obtained four conditional transgenic founders by pronuclear injection to mouse embryos. Female conditional Plk1-KI mice were mated with male CMV-Cre transgenic mice that have a wide tissue distribution for expression of Cre recombinase (25). Expression of Plk1 in CMV-Cre/Plk1-KI double transgenic mice was detected in several organs with quantitative RT-PCR (qRT-PCR) ( Fig. 2A), immunoblotting (IB) analysis (Fig. 2B), and immunohistochemistry (IHC) staining (Fig. 2C). Increase of Plk1 expression was also confirmed in CMV-Cre/Plk1-KI MEFs (Fig. 2D). To further validate the Plk1 overexpression system, Plk1-KI mice were crossed with Myod-Cre mice, which express Cre in a muscle-specific manner. As indicated, Plk1 expression was detected only in muscle in Myod-Cre/Plk1-KI mice (Fig. 2, E and F). These data indicate that the Plk1 conditional transgenic system works properly in vivo.
Elevated Plk1 expression leads to mitotic abnormalities and apoptosis in late-passage mouse embryonic fibroblasts
Considering that Plk1 has multiple functions during the cell cycle, we next examined the effects of Plk1 overexpression on the proliferation and cell-cycle progression of MEFs. Overexpression of Plk1 was confirmed in MEFs isolated from two different CMV-Cre/Plk1-KI mouse lines (supplemental Fig. S1A). Surprisingly, massive Plk1 overexpression had no apparent impact on the proliferative activity of early-passage MEF lines compared with control MEFs (supplemental Fig. S1B). Furthermore, we assessed the potential correlation between Plk1 overexpression and cell cycle distribution. Despite much higher levels of the Plk1 expression in CMV-Cre/Plk1-KI lines, FACS analyses showed no apparent increase in G 2 /M populations compared with control MEF cells (supplemental Fig. S1iC). Given that MEFs undergo abnormal mitosis and senescence at late passages, we tested whether Plk1 overexpression affects this process. Interestingly, induction of Plk1 overexpression resulted in significantly increased abnormal mitotic figures in late-passage MEFs (Fig. 3A). Staining by propidium iodide showed various mitotic defects, including chromosome misalignment, chromosome missegregation, and chromosome bridges, observed at higher rates in late-passage Plk1-overexpressing MEFs (Fig. 3A). To further assess the chromosome instability induced by Plk1 overexpression, we analyzed chromosome spreads generated from serial passages of MEFs according to the 3T3 protocol (Fig. 3B). The total number of chromosomes in each cell was determined, and cells were scored as diploid (2n ϭ 40) or aneuploid. Primary control MEFs, under normal culture conditions, spontaneously become aneuploidy. However, we found that Plk1-overexpressing MEFs were significantly more aneuploidy than control MEFs at later passages (Fig. 3B). Examination of the absolute number of chromosomes per cell revealed a highly significant increase in the frequency of di-and multinucleated cells compared with control MEFs.
The proliferation of control and Plk1-overexpressing MEFs at later passages was investigated using MTT assay. Control MEF cells was observed to proliferate significantly faster than the Plk1-KI cells at passage 5 (Fig. 3C). To determine whether the growth arrest in the Plk1-KI MEFs was associated with cell cycle defects, DNA content was analyzed. We found that Plk1-KI cells at passage 5 caused a significant increase in the cell number of cells in G 2 /M phase, concomitant with a significant decrease in the percentage of cells in G 0 /G 1 phase (Fig. 3D). Furthermore, MEFs with overexpression of Plk1 exhibited a substantial increase in the sub-G 1 population, suggesting that a large number of cells at G 2 /M phase underwent cell death (Fig. 3D). Using senescence-associated -galactosidase assay, we found that Plk1-overexpressing MEFs displayed an increased senescence phenotype (Fig. 3E). 2
Plk1 contributes to cancer formation Phenotypic analysis of Plk1-KI mice
The CMV-Cre/Plk1-KI double transgenic mice displayed no apparent developmental abnormalities during mouse development. They grew and gained weight normally during the first 9 months of their life. However, by 18 months of age CMV-Cre/ Plk1-KI mice exhibited slightly reduced weight compared with WT littermates (Fig. 4A). Litter sizes were similar for CMV-Cre/Plk1-KI and WT mice, ranging from 7 to 9 pups per litter. The pups were born healthy and developed normally at a normal growth rate, maturing at the age of 3-4 weeks. Further, we did not observe any obvious behavioral difference between CMV-Cre/Plk1-KI and WT animals. However, a minor reduced survival rate in Plk1-KI mice was observed, when the mice were monitored up to 25 months of age (Fig. 4B). The complete morphological analyses did not reveal significant histological differences between the organs of CMV-Cre/Plk1-KI mice and WT animals at the ages of both 1 and 11 months (Fig. 4, C and D). To determine the consequences of Plk1 overexpression on whole-body energy balance, we performed indirect calorimetry analyses. On a chow diet, CMV-Cre/Plk1-KI mice showed a slightly higher energy expenditure than control mice, as indicated by both slightly increased O 2 consumption (Fig. 4E) and slightly increased CO 2 production (Fig. 4F). Considering that Plk1 is critical for energy metabolism in cultured cells (16), we examined the glucose uptake in a glucose tolerance test (GTT). Glucose uptake from CMV-Cre/Plk1-KI mice was slightly increased in comparison to WT littermates (Fig. 4G). Given that Plk1 is essential for many mitotic events, we exam- A, relative Plk1 mRNA levels in the tissues of CMV-Cre/Plk1-KI animals were compared with the levels in Plk1-KI but without Cre expression (Control, Ctrl) animals (mean Ϯ S.D., n ϭ 3 for each tissue). B, total cellular protein was prepared from the indicated tissues of adult CMV-Cre/Plk1-KI or control mice and subjected to IB. C, animals were sacrificed at the age of 1 month, followed by anti-Plk1 IHC staining of indicated tissues. Sections representing the organs of control (Plk1-KI only) and CMV-Cre/Plk1-KI mice. Bar, 200 m. D, top panel, whole cell extracts from MEFs isolated from CMV-Cre/Plk1-KI and control animals were subjected to IB. Bottom panel, PCR of mouse genomic DNA (tail clips) are presented. E, relative Plk1 mRNA levels in the tissues of Myod-Cre/Plk1-KI animals were compared with the levels in control animals (mean Ϯ S.D., n ϭ 3 for each tissue). F, total cellular protein was prepared from the indicated tissues of Myod-Cre/Plk1-KI and control mice. **, p Ͻ 0.05; ***, p Ͻ 0.01.
Plk1 contributes to cancer formation
ined the proliferative activity in CMV-Cre/Plk1-KI mice by staining Ki67 of various tissues. The proliferation index was moderately increased only in the liver (see Fig. 6A).
Plk1-KI mice and MEFs are hypersensitive to DNA damage
Because no malignant tumor formation was detected in the Plk1-overexpressing mice after a long latency, we then challenged Plk1-overexpressing mice with carcinogens to see whether Plk1 overexpression affects carcinogenesis under stimulation condition. Mounting evidence suggests that Plk1 directly participates in the regulation of DNA double-strand break repair (26,27). We therefore explored whether Plk1 overexpression affects cellular response to DNA damage in vivo.
Cohorts of CMV-Cre/Plk1-KI and WT mice were irradiated with 10 Gy of ionizing radiation (IR) and closely monitored for radiation toxicity. Although ϳ60% of WT littermates (n ϭ 14) survived beyond 50 days, over 80% of CMV-Cre/Plk1-KI ani-mals (n ϭ 15) died within 50 days (Fig. 5A), indicating that CMV-Cre/Plk1-KI mice were more sensitive to IR) than WT littermates. To confirm this observation, we plated MEFs (WT or CMV-Cre/Plk1-KI) at clonal density and exposed to increasing doses of IR, followed by colony formation assay. In agreement with the in vivo results, the viability of CMV-Cre/Plk1-KI MEFs after IR was significantly impaired compared with WT MEFs, indicating that Plk1-overexpressing MEFs are more sensitive to DNA damage induced by IR (Fig. 5B). In a separate experiment, CMV-Cre/Plk1-KI and WT mice at the age of 10 weeks were exposed to a single dose of 5 Gy whole body ␥-ray irradiation and monitored for additional 4 months. CMV-Cre/ Plk1-KI, but not WT, mice showed severe dermatitis, scratching bloody areas in head, neck, and ears (Fig. 5C). Although none of WT mice had tumors after 4 months, 10.3% of CMV-Cre/Plk1-KI developed life-threatening spleen lymphomas, a difference that was statistically significant (p ϭ 0.0386; Fig. 5D,
Plk1 contributes to cancer formation
bottom panel). Upon IR, CMV-Cre/Plk1-KI mice showed apparent splenic enlargement and disruption of normal splenic architecture, forming diffused lymphoma (Fig. 5D, top panel). Increased radiation sensitivity is one of the hallmarks of defective DDR. The results described above suggested that Plk1 elevation leads to inhibition of DDR. To directly test this hypothesis, we analyzed DDR of mice. Spleens were prepared from three different mice that were exposed to IR and subjected to IB to follow the DDR pathway. IR led to activation of DDR, indicated by elevated phosphorylation of ATM, Chk2, and H2AX in WT, but not in CMV-Cre/Plk1-KI mice (Fig. 5E). Finally, IR also led to activation of the ATM/Chk2 pathway in WT but not in CMV-Cre/Plk1-KI MEFs (Fig. 5F).
Overexpression of Plk1 leads to increased proliferation and hypersensitivity to DNA damage in liver
Because liver is the only tissue that showed increased proliferation upon Plk1 overexpression in the absence of IR (Fig. 6A), we further analyzed liver-associated phenotypes after IR. A 4-fold increase in liver tumors in CMV-Cre/Plk1-KI versus normal littermates was observed (p ϭ 0.0472; Fig. 5D, bottom panel). Upon IR, the livers of CMV-Cre/Plk1-KI mice were apparently enlarged and carrying small tumors compared with WT controls (Fig. 6B). IR of WT mice led to multifocal lymphoid hyperplasia, seen in a perivascular location (Fig. 6C, top panel). For IR-treated CMV-Cre/Plk1-KI mice, we observed multiple lymphocytic overgrowth in the parenchyma and mitotic figures, suggesting the formation of mild lymphoma (Fig. 6C, middle panel) or severe lymphoma (Fig. 6C, bottom panel). To determine whether lymphoma in IR-treated CMV-Cre/Plk1-KI mice is of T-cell or B-cell origin, we stained a T cell marker with CD3. Approximately 80 -90% of the neoplastic round cells demonstrated moderate to strong positive staining with CD3 antibody, indicative of T lymphocyte origin (Fig. 6D). Further, Ki67 IHC staining was performed to the same samples. Ki67 signal was virtually undetectable in WT samples but significantly increased in lymphoma areas of CMV-Cre/Plk1-KI mice (Fig. 6E). Finally, we also observed apparent diffuse and sever fatty change in the parenchyma of liver of one CMV-Cre/ Plk1-KI mouse (Fig. 6F).
To understand how Plk1 overexpression accelerates IR-induced cancer formation, we performed an RNA-Seq analysis of MEFs under different conditions (Ϯ Plk1-KI Ϯ IR irradiation). Expression levels of 648 genes were affected upon Plk1 overex-
Plk1 contributes to cancer formation
pression, whereas most of the affected genes were down-regulated. In the presence of IR irradiation, Plk1 overexpression led to modulation of 227 genes (Fig. 7, A and B). This observation is expected because it has been documented that Plk1 is a target of DNA damage. Plk1 KI affects the expression of 97 genes in both the presence and the absence of IR irradiation. Detailed description and analysis of RNA-Seq data will be reported separately. Herein, we only focus on genes related to DNA damage repair pathways. As indicated in Fig. 7C, Plk1 overexpression clearly affects the expression of a series of DNA damage repair genes. In addition, RT-PCR was performed to confirm this observation (Fig. 7D). Thus, deregulation of DNA damage repair pathways upon Plk1 overexpression is the likely reason to explain the enhanced IR-induced cancer formation.
Discussion
Mitotic kinases are critical regulators of cell cycle progression, and the timing of expression and activities of those kinases are tightly regulated during the cell cycle. Plk1 is associated with mitotic spindle poles and centromere/kinetochore regions and the expression and activity of Plk1 peak during late G 2 to M phase (9, 10). Although the majority of studies highlights the
Plk1 contributes to cancer formation
essential role of Plk1 for mitosis, overexpression of Plk1 is often observed in interphase of many cancer cell lines and tumor samples. In addition to these pathological observations, evidence that Plk1 overexpression in NIH3T3 cells induces tumor formation in nude mice suggests that dysregulation of Plk1 expression is a potential cause of sporadic malignant tumors (28). These observations have prompted research into the potential therapeutic application of Plk1 inhibition in cancer. Mitotic catastrophe and tumor growth inhibition have been observed in preclinical studies using Plk1 inhibitors or siRNAs (12,29). However, with all the evidence pointing to Plk1 as a worthwhile cancer target, it should be noted that the molecular evidence of Plk1 being a bona fide oncogene is still lacking. Accordingly, we have established a Plk1 transgenic mouse line to achieve overexpression of Plk1 with a new conditional trans-genic system. In this system, the expression of Plk1 is regulated by the recombination with the transgene mediated with Cre protein and its target sequences.
Previous cellular studies indicate that sustained overexpression of Plk1 increases the oncogenic potential of cultured cells (28). Herein, we have taken advantage of a conditional expression model to modulate the expression of Plk1. Our data based on MEFs confirmed the effect of Plk1 overexpression on the generation of misaligned chromosome and aneuploidy. We have also observed that Plk1 overexpression induces apoptosis in cultured MEFs at later passages. Several studies have indicated that expression of activated oncogenes, such as Aurora-A or Myc, generally induces apoptotic cell death in MEFs. Further, apoptotic cell death induced by Aurora-A or Myc has been demonstrated to be p53-dependent (30 -32). Because studies
Plk1 contributes to cancer formation
have also revealed a connection between Plk1 and p53, it is possible that p53 might be involved in apoptosis of MEFs with deregulated Plk1. It was shown that Aurora-A overexpression in mammary epithelial cells results in increased apoptosis, with a low frequency of tumor formation that is accelerated in a p53-null background (32). It should be interesting to test whether Plk1 overexpression accelerates tumor formation in a p53-null background.
To our surprise, Plk1 overexpression alone is not enough to drive cancer initiation, indicating that additional genetic modifications are required for tumor formation. Of note, inducible Plk1 knockdown mice described previously did not show any significant phenotype either (33). Increasing evidence suggests that Plk1 is directly involved in overall DNA damage response, including DNA damage checkpoint activation, checkpoint maintenance, damage recovery, and DNA repair (34). Accordingly, we challenged Plk1-overexpressing mice with IR to ask whether Plk1 overexpression affects DDR pathway. Indeed, Plk1 overexpression clearly showed increased radiation sensitivity and accelerated IR-induced carcinogenesis in mice. Based on our observation, we postulate that Plk1 is a critical regulator of IR-induced carcinogenesis, likely because of premature
Plk1 contributes to cancer formation
checkpoint termination and reduced DNA repair in Plk1-KI mice.
We understand that most of previous studies suggested that Plk1 plays an important role in turning off the later stages of DDR. Interestingly, we recently found that Plk1 also phosphorylates key factors upstream of ATM/ATR and regulates their DDR-related functions in human cells. Specifically, Plk1 directly phosphorylates Mre11, a component of the Mre11-Rad50 -Nbs1 complex, at serine 649 during DDR. Phosphorylation of Mre11 inhibited loading of the Mre11-Rad50 -Nbs1 complex to damaged DNA, leading to checkpoint termination and inhibition of DNA repair (35). This is one likely mechanism to explain why Plk1 KI mice are hypersensitive to ionizing radiation, because Plk1-overexpressed cells will continue to cycle even in the presence of DNA damage, eventually resulting in a much higher chance for tumorigenesis. In addition, Plk1-KI leads to inactivation of p53 and PTEN, two most important tumor suppressors. This statement has been supported by many of our previous publications. For example, we once showed that Plk1 depletion leads to p53 stabilization (36). Mechanistically, we later showed that Plk1 phosphorylation of GTSE1 and Topors, two negative regulators of p53, results in p53 inactivation (13,14). Directly related to Plk1-KI mouse work, we recently showed that Plk1 KI causes p53 inactivation in MEFs (37). Finally, our RNA-Seq analysis provided in Fig. 7 of this manuscript clearly showed that additional DNA damage repair genes are down-regulated upon Plk1 overexpression. Thus, Plk1-KI-associated increased cancer formation upon IR is likely due to multiple factors.
Animal experiments
All procedures involving mice were guided by Purdue University Animal Care and Use Committee (Protocol no. 1111000133E001). Mice housed in the animal facility with free access to standard rodent chow and water were under pathogen-free conditions and maintained in a 12-h light/12-h dark cycle.
Isolation of total RNA from murine tissues
After Plk1-KI and WT mice were quickly killed, different organs were prepared and stored in RNAlater stabilization reagent (Qiagen). For the RNA preparation, tissue pieces of 20 mg were dispersed with a PCR tissue homogenizing kit, followed by total RNA isolation using an RNeasy mini kit (Qiagen).
Establishment of MEFs derived from WT and Plk1-KI embryos
After removing the head and organs of embryos at day 13.5, the tissue was minced and rinsed with PBS, followed by incubation with 0.5 ml of 0.1% trypsin for 20 min at 37°C. Trypsin was inactivated by addition of 5 ml of DMEM supplemented with 10% FBS. After centrifugation, the cell pellets were resuspended with DMEM and plated onto a 10-cm dish. Medium was changed to remove the large clumps after 24 h. For Plk1-KI MEFs, 5 ϫ 10 6 cells were treated with 1 mM 4-hydroxytamoxifen for 48 h to induce Plk1 expression. The genotypes of embryos were detected by PCR with primers that are specific to the Plk1 sequence. The cells were cultured at 37°C with 8% CO 2 in DMEM supplemented with 10% (v/v) fetal calf serum, penicillin, streptomycin, and 50 M 2-mercaptoethanol. The MEFs were frozen as stocks at the second passage and used for subsequent studies.
Plk1 expression analysis
Real-time RT-PCR was carried out using the primer pairs 5Ј-TAATGACTCAACACGCCTGATT-3Ј and 5Ј-AGCTCA-GCAGCTTGTCTACCAT-3Ј. The -actin-specific primers were used as controls: 5Ј-GAGGAGCACCCCGTGCTGC-3Ј and 5Ј-CCTGCTTGCTGCTGATCCACA-3Ј. To quantify Plk1 transcripts, 1 g of RNA was subjected to qRT-PCR. The qRT-PCR was conducted using a TaqMan gene expression assay for murine Plk1. As an internal control in the TaqMan assay, murine -actin was used (Applied Biosystems). In brief, the 10-l PCR included 1 l of RT product, 1 ϫ TaqMan Universal PCR Master Mix, 0.2 l of TaqMan probe, 1 l of forward primer, and 1 l of reverse primer. The reactions were incubated in a 96-well plate at 95°C (10 min), followed by 40 cycles of 95°C (15 s) and 60°C (1 min). All reactions were run in triplicate.
Analysis of mouse genotypes
To test the genotype of WT or Plk1-KI mice, genomic DNA was prepared from tail clips 0.5-0.8 mm in length with Viagen Direct PCR-Tail reagent (Peqlab Biotechnologie, Erlangen, Germany) according to the manufacturer's protocol. For the standard PCR, 10 ng of genomic DNA was amplified using the sense primer 5Ј-ACTTCGTATAGCATACATTATACGAAG-TTATC-3Ј and the antisense primer 5Ј-TCCTTTACCC-AGAAAGCGC-3Ј.
FACS analysis
The cells in culture dishes were trypsinized, washed with PBS, and fixed in 95% ice-cold ethanol overnight. After centrifugation, the cells were resuspended in PBS and incubated with 50 mg/ml propidium iodide in the presence of 100 units/ml RNase A, followed by FACS analysis.
Measurement of energy expenditure
Oxygen consumption (VO 2 ) and carbon dioxide production (VCO 2 ) were measured under a consistent environmental temperature and light cycle using an indirect calorimetry system (Oxymax; Columbus Instruments). After the male mice were acclimated to the metabolic chamber for 2 days, VO 2 and VCO 2 were measured in each individual mouse at 15-min intervals during a 48-h period.
Glucose tolerance test
GTT was performed by intraperitoneal injection of D-glucose (Sigma) at a dose of 2 mg/g body weight with an Onetouch Ultra glucometer (Lifescan) into male mice after an overnight fast. Blood glucose levels were then measured at different times (15,30,45,60,75, and 90 min).
Chromosome aneuploidy
After cells were treated with 50 ng/ml colchicine for 4 h, the cells were collected and hypotonically swollen in 75 nM KCl for 30 min at 37°C. The cells were fixed in freshly made Carnoys fixative solution (75% methanol, 25% acetic acid) with three changes of fixative. The cells were then dropped onto glass slides and dried at room temperature. Chromosomes were stained with DAPI for 30 m, rinsed with PBS three times, and mounted.
Tumor analysis and histopathology
Aged mice were sacrificed by cervical dislocation following anesthetization with isofluorine. Necropsies were performed, and tissues as well as tumors observed by gross inspection were fixed in 10% formalin 2 days and then embedded in paraffin. For IHC analysis, representative sections were deparaffinized, rehydrated in graded alcohols, and processed using the avidinbiotin immunoperoxidase method. Sections were subjected to antigen retrieval by microwave oven treatment using standard procedures.
RNA-Seq analysis
MEFs were irradiated with 2 Gy ␥-ray, incubated for 12 h, and harvested for RNA extraction. Total RNA was extracted from 1 ϫ 10 7 cells using TRIzol reagent (Life Technologies), followed by purification with the RNeasy mini kit (Qiagen) based on the manufacturer's instructions. Quality of input total RNA was assessed using an Agilent Bioanalyzer RNA nano chip. Libraries were constructed largely as directed by the Illumina TruSeq Stranded mRNA sample preparation guide (catalog no. RS-122-9004DOC), using reagents from the Illumina TruSeq RNA library preparation kit (catalog nos. RS-122-2001 and RS-122-2002). Briefly, poly(A) ϩ RNA was isolated by annealing biotinylated oligo(dT) to total RNA, followed by capture with streptavidin-conjugated magnetic beads. Non-bound RNAs were then largely removed by discarding the supernatant after magnetic pelleting of Ampure beads. More binding buffer was added followed by an 80°C incubation to strand denature all RNA from the oligo(dT) captured poly(A) ϩ RNA, followed by another cycle of binding and supernatant removal. The poly(A) ϩ RNA was eluted in a divalent cation and hexamer first-strand synthesis primer containing buffer and fragmented with a 4-min incubation at 95°C. Reverse transcriptase in the presence of actinomycin D to repress any DNA-templated polymerization was used to synthesize first-strand synthesis of cDNA. Second-strand synthesis was performed, replacing dTTP with dUTP, which largely eliminates second-strand amplicons during subsequent amplification. cDNA ends were repaired, 3Ј-adenylated, and ligated to Illumina adapters. Products were subjected to a 0.8:1 Ampure:sample purification to reduce lower molecular weight amplicons, and the resulting libraries were assessed with an Agilent DNA high sensitivity chip for yield. Based on the overall yields, it was surmised that 8 cycles of amplification, rather than the 15 cycles recommended by the Illumina protocol, would be used. Amplified final libraries were titered for clustering using a KAPA library quantification kit Illumina (KAPA catalog no. KR045), pooled, and clustered in a single HiSeq 2500 v2 Rapid Chemistry lane to generate 60 base single reads. To analyze the data, all sequenced libraries were mapped to the mouse genome (UCSC mm10) using STAR RNA-Seq aligner (37). The uniquely mapped reads were assigned to mm10 refGene genes using featureCounts (from subread) (38). The data were normalized using TMM (trimmed mean of M values) method. The gene expression was finally summarized on base-2 logarithmic scale. We excluded genes with average expression level lower than 1 for all phenotypes. Differential expression analysis was performed using edgeR with paired samples setting (39,40). The false discovery rate was computed from p values using the Benjamini-Hochberg procedure. Genes with false discovery rates of Ͻ0.05 and absolute values of fold change (FC) larger than 1.5 were considered as differentially expressed genes (DEGs).
Statistical analysis
All data are presented as means Ϯ S.D. Statistical calculations were performed with Microsoft Excel analysis tools. Although a two-tailed, unpaired Student's t test was used to assess the difference between the effects of treatment in cell lines, one-way analysis of variance was used to determine statistically significant differences from the means in the animal study. p values of Ͻ0.05 were considered statistically significant. *, p Ͻ 0.05; **, p Ͻ 0.01.
Author contributions-Z. L. conducted most of the experiments, analyzed the results, and wrote most of the paper. J. Liu, J. Li, Y. K., and G. S. also conducted some of the experiments. X. R., Y. L., and J. W. analyzed RNA-Seq data. X. L. analyzed the data and wrote the paper with Z. L. | 6,889.4 | 2017-09-12T00:00:00.000 | [
"Biology",
"Medicine"
] |
COVID-19: Structural Changes in the Relationship Between Investor Sentiment and Crude Oil Futures Price
The recent outbreak of the coronavirus (COVID-19) pandemic is not only threatening public health but also carries significant repercussions for the sustainability of the financial market (Ali et al., 2020). Crude oil futures is one of those financial products severely impacted by COVID-19. The volatility of investor sentiment, combined with a sharp decrease in the demand for crude oil, resulted in a negative West Texas Intermediate (WTI) crude oil futures price on April 20, 2020. The existing literature focuses mainly on the interrelationship between investor sentiment and oil prices; see also Narayan (2019). Qadan & Nama (2018) find that investor sentiment has significant effects on oil prices, especially when oil-based financial products become a popular asset class for investors. The study by He & Casey (2015) shows substantial forecasting ability of sentiment on crude oil price changes, especially the WTI prices. Narayan (2020) shows the relative importance of negative and positive oil price news in influencing oil prices. In addition, some studies discuss the relationship between investor sentiment and futures price. The empirical results in Simon & Wiggins (2001), for instance, reveal that investor sentiment has both statistical and economic forecasting power when Standard & Poor’s 500 futures returns are modelled. Maslyuk-Escobedo et al. (2017) demonstrate that energy futures prices have a high degree of co-movement with any sentiment proxies. However, there is little work done on understanding how investor sentiment influences crude oil futures price. By focusing on sentiment and oil price volatility over the COVID-19 period, our paper joins several studies that evaluate the impact of COVID-19 on the crude oil market. Most of them explore the direct influence that COVID-19 has had on the oil price (Gil-Alana & Monge, 2020; Liu et al., 2020; Narayan, 2020; Qin et al., 2020). However, few studies focus on any possible change in the relationship between investor sentiment and futures price. This focus is important because after any major shock, the influencing mechanism or the influence level of the factors that drive futures prices, are likely to be different. The inspiration for this comes from the work of Kollias et al. (2013), who find that the covariance between stock and oil returns is affected by war. In a similar vein, Wang et al. (2020) demonstrate that the effect of oil price changes on the stock market is stronger under extreme shocks than under normal circumstances. Given this background, we empirically examine the relationship between investor sentiment (which we proxy using the OVX index) and crude oil futures price. We use the Engle & Granger (1987) two-variable cointegration approach to examine whether the relationship between investor sentiment and crude oil futures price remains stable when the COVID-19 shock took place. Then, we employ the GregoryHansen (1996) test for cointegration with regime shifts in order to find the structural change point. Consistent with our hypothesis, we find a breakpoint when the COVID-19 epidemic turned into a pandemic.
Introduction Introduction
The recent outbreak of the coronavirus (COVID-19) pandemic is not only threatening public health but also carries significant repercussions for the sustainability of the financial market (Ali et al., 2020). Crude oil futures is one of those financial products severely impacted by COVID-19. The volatility of investor sentiment, combined with a sharp decrease in the demand for crude oil, resulted in a negative West Texas Intermediate (WTI) crude oil futures price on April 20, 2020.
The existing literature focuses mainly on the interrelationship between investor sentiment and oil prices; see also Narayan (2019). Qadan & Nama (2018) find that investor sentiment has significant effects on oil prices, especially when oil-based financial products become a popular asset class for investors. The study by He & Casey (2015) shows substantial forecasting ability of sentiment on crude oil price changes, especially the WTI prices. Narayan (2020) shows the relative importance of negative and positive oil price news in influencing oil prices. In addition, some studies discuss the relationship between investor sentiment and futures price. The empirical results in Simon & Wiggins (2001), for instance, reveal that investor sentiment has both statistical and economic forecasting power when Standard & Poor's 500 futures returns are modelled. Maslyuk-Escobedo et al. (2017) demonstrate that energy futures prices have a high degree of co-movement with any sentiment proxies. However, there is little work done on understanding how investor sentiment influences crude oil futures price.
By focusing on sentiment and oil price volatility over the COVID-19 period, our paper joins several studies that evaluate the impact of COVID-19 on the crude oil market. Most of them explore the direct influence that COVID-19 has had on the oil price (Gil-Alana & Monge, 2020;Liu et al., 2020;Narayan, 2020;Qin et al., 2020). However, few studies focus on any possible change in the relationship between investor sentiment and futures price. This focus is important because after any major shock, the influencing mechanism or the influence level of the factors that drive futures prices, are likely to be different. The inspiration for this comes from the work of Kollias et al. (2013), who find that the covariance between stock and oil returns is affected by war. In a similar vein, Wang et al. (2020) demonstrate that the effect of oil price changes on the stock market is stronger un-der extreme shocks than under normal circumstances.
Given this background, we empirically examine the relationship between investor sentiment (which we proxy using the OVX index) and crude oil futures price. We use the Engle & Granger (1987) two-variable cointegration approach to examine whether the relationship between investor sentiment and crude oil futures price remains stable when the COVID-19 shock took place. Then, we employ the Gregory-Hansen (1996) test for cointegration with regime shifts in order to find the structural change point. Consistent with our hypothesis, we find a breakpoint when the COVID-19 epidemic turned into a pandemic.
Data Data
Panic resulting from COVID-19 is associated with heightened volatility in financial markets and this association is stronger for industries that are hardest hit by the pandemic (Haroon & Rizvi, 2020). According to and Qadan & Nama (2018), OVX is a reasonable gauge of investor fear. These studies find causality from OVX changes to WTI returns is significant. In addition, Simon & Wiggins (2001) used the volatility index (VIX) to forecast S&P 500 futures returns. From these discussions, it is clear that one can use OVX from the CBOE, (perceived as WTI's panic index) to represent investor sentiment. The WTI crude oil futures price is chosen as the dependent variable. In order to get valid log of the WTI crude oil futures price, is treated as zero when the price is negative. The sample period covers January 2, 2019 to May 11, 2020, consisting of 340 observations.
Methodology Methodology
To study structural changes in the relationship between the WTI crude oil futures price and the OVX, we follow and employ the Engle & Granger (1987) two-variable cointegration method. This allows us to evaluate any possible long-term cointegration relationship between the two variables. The regression form can be expressed as: Where and , respectively, represent the WTI crude oil futures price and the OVX. If both variables are unit root processes and the error term ( is stationary, this will indicate a cointegration relationship between crude oil futures price and investor sentiment. However, the Engle-Granger cointegration approach cannot be effectively utilized to identify any structural changes in the cointegrating relationship. The residualbased cointegration test assumes that the cointegration vector ( , ) does not change with time. This is a very strict assumption which is unlikely to hold. We, therefore, address this limitation by using the Gregory & Hansen (1996) test, which endogenously identifies the breakpoint.
Gregory-Hansen propose the following models of regime shift which we employ: Model C is called the level shift model, which implies that the intercept, , changes while the slope coefficient, , is held constant. In the expression above, is the intercept before the shift and represents the change in the intercept at the time of shift. This model is based on a level shift with a time trend.
Model C/S is a regime shift model which permits the equilibrium relation to rotate as well as shift. In this case, denotes the cointegrating slope coefficient before the regime shift and denotes the change in the slope coefficient.
Model C/S/T is based on the regime shift model with a time trend.
In this model, represents the location of the structural breakpoint, which is endogenously determined by the model. When , or, We follow Gregory and Hansen to use test statistic to judge if has a unit root process.
Where T is the length of sequence, represents the ADF unit root test statistic at the structural breakpoint . When is higher than the critical value, it indicates existence of a cointegration relationship.
Empirical Analysis Empirical Analysis
We first use the Engle and Granger two-step cointegration test to analyze the possibility of a long-term cointegration relationship amongst the two variables. The results are: Where t-statistics are reported in parentheses. We find that over the sample period, , which is significant at the 1% level. The result is in line with .
Second, we choose the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root test (Kwiatkowski et al., 1992) to exam whether follows a stationary process. The null hypothesis is that the time series is stationary. According to the test results, the relationship between the crude oil futures price and OVX is not a long-term cointegration relationship.
We use four models of Gregory and Hansen and find that after considering the endogenous breakpoint, there exists a 1. Model C specifies a shift in the constant term as: 2. Model C/T specifies a shift in the constant and the trend as: 3. Model C/S specifies a shift in the constant and the slope as: 4. Model C/S/T specifies a shift in the constant, the slope and the trend as: This table reports results of the four models proposed by Gregory-Hansen. When is higher than the critical value, it indicates a cointegration relationship. Breakpoint represents the time when structural change took place. Finally, *** indicates statistical significance at the 1% level. cointegration relationship. The null hypothesis for the four models is that there is no cointegration relationship. The results in Table 1 show test statistics in those four models all reject the null hypothesis, indicating the presence of a cointegration relationship between investor sentiment and crude oil futures price. There are two structural change break periods: between April 25, 2019 to April 29, 2019 and December 31, 2019 to February 25, 2020. The first period corresponds to the time when the U.S. crude oil inventories continued to exceed expectations, leading to the volatility of crude oil supply and its futures price. The second period corresponds to the outbreak of COVID-19 during which the demand for crude oil declined. We can see in Figure 1 that an obvious deviation occurred around the end of February when the pandemic spread worldwide.
We further explore what structural changes took place. Table 2 demonstrates the estimated results of the cointegration equation under the four model settings. In all cases, investor sentiment statistically significantly influences crude oil futures price; however, the impact of sentiment in the second period is significantly strengthened. For example, under the C/S model, on 31 Dec. 2019 the elasticity of crude oil futures price to investor sentiment was -0.295, meaning that when investor sentiment increased by 1% the crude oil futures price decreased by 0.295%. However, after the breakpoint, the coefficient turns out to be -0.678 (= -0.295-0.383). This means that when investor sentiment increases by 1%, the crude oil futures price falls by 0.678%. This implies that the influence of the sentiment to crude oil futures market grew significantly.
Conclusion Conclusion
In this paper, we examine the long-run relationship between investor sentiment as proxied by the crude oil volatility index and the WTI oil futures price index. Using the Gregory-Hansen regime shift cointegration test, we document that there was a structural change in this relationship due to COVID-19. This finding will be of help for future research in this area. One future research area in this regard is crude oil price forecasting. Our results show that in this quest, COVID-19 will need to be specifically modelled. | 2,872.8 | 2020-07-09T00:00:00.000 | [
"Economics"
] |
Depth with Nonlinearity Creates No Bad Local Minima in ResNets
In this paper, we prove that depth with nonlinearity creates no bad local minima in a type of arbitrarily deep ResNets studied in previous work, in the sense that the values of all local minima are no worse than the global minima values of corresponding shallow linear predictors with arbitrary fixed features, and are guaranteed to further improve via residual representations. As a result, this paper provides an affirmative answer to an open question stated in a paper in the conference on Neural Information Processing Systems (NIPS) 2018. We note that even though our paper advances the theoretical foundation of deep learning and non-convex optimization, there is still a gap between theory and many practical deep learning applications.
Introduction
Deep learning has seen practical success with a significant impact on the fields of computer vision, machine learning and artificial intelligence. In addition to its practical success, deep learning has been theoretically studied and shown to have strong expressive powers. For example, neural networks with one hidden layer can approximate any continuous functions (Leshno et al., 1993;Barron, 1993), and deeper neural networks can approximate functions of certain classes in more compact manners (Montufar et al., 2014;Livni et al., 2014;Telgarsky, 2016).
However, one of the major concerns in both theory and practice is that training a deep learning model requires us to deal with highly non-convex and high-dimensional optimization. Optimization problems with a general non-convex function and with a certain nonconvex function induced by some specific neural networks are both known to be NP-hard (Murty and Kabadi, 1987;Blum and Rivest, 1992), which would pose no serious challenge if only it were not high-dimensional (Kawaguchi et al., 2015(Kawaguchi et al., , 2016. Therefore, a hope is that non-convex high-dimensional optimization in deep learning allows some additional structure or assumption to make the optimization tractable. Under several simplification assumptions, recent studies have proven the existence of novel loss landscape structures that may play a role in making the optimization tractable in deep learning (Dauphin et al., 2014;Choromanska et al., 2015;Kawaguchi, 2016). More recently, Shamir (2018) has shown that a specific type of neural network, namely residual network (ResNet) with a single output unit (a scalar-valued output), has no local minimum with a value higher than the global minimum value of scalar-valued linear predictors (or equivalently, one-layer networks with a single output unit). However, Shamir (2018) remarks that while it is natural to ask whether this result can be extended to networks with multiple output units (vector-valued outputs) as they are commonly used in practice, it is currently unclear how to prove such a result and the question is left to future research.
As a step towards establishing the optimization theory in deep learning, this paper presents theoretical results that provide an answer to the open question remarked in (Shamir, 2018). Moreover, this paper proves a quantitative upper bound on the local minimum value, which shows that not only the local minimum values of deep ResNets are always no worse than the global minimum value of vector-valued linear predictors (or one-layer networks with multiple output units), but also further improvements on the quality of local minima are guaranteed via non-negligible residual representations.
Preliminaries
The Residual Network (ResNet) is a class of neural networks that is commonly used in practice with state-of-the-art performances in many applications (He et al., 2016a,b;Kim et al., 2016;Xie et al., 2017;Xiong et al., 2018). When compared to standard feedforward neural networks, ResNets introduce skip connections, which adds the output of some previous layer directly to the output of some following layer. A main idea of ResNet is that these skip connections allow each layer to focus on fitting the residual of the target output that is not covered by the previous layer's output. Accordingly, we may expect that a trained ResNet is no worse than a trained shallower network consisting of fewer layers only up to the previous layer. However, because of the non-convexity, it is unclear whether ResNets exhibit this behavior, instead of getting stuck around some arbitrarily poor local minimum.
Model
To study the non-convex optimization problems of ResNets, both the previous study (Shamir, 2018) and this paper considers a type of arbitrarily deep ResNets, for which the preactivation output h(x, W, V, θ) ∈ R dy of the last layer can be written as h(x, W, V, θ) = W (x + V z(x, θ)). (1) Here, W ∈ R dy×dx , V ∈ R dx×dz and θ consist of trainable parameters, x ∈ R dx is the input vector in any fixed feature space embedded in R dx , and z(x, θ) ∈ R dz represents the outputs of arbitrarily deep residual functions parameterized by θ. Also, d y is the number of output units, d x is the number of input units, and d z represents the dimension of the outputs of the residual functions.
There is no assumption on the structure of z(x, θ), and z(x, θ) is allowed to represent some possibly complicated deep residual functions that arise in ResNets. For example, the model in Equation (1) can represent arbitrarily deep pre-activation ResNets (He et al., 2016b), which are widely used in practice. To facilitate and simplify theoretical study, Shamir (2018) assumed that every entry of the matrix V is unconstrained and fully trainable (e.g., instead of V representing convolutions). This paper adopts this assumption, following the previous study.
Remark 1. (On arbitrary hand-crafted features) All of our results hold true with x in any fixed feature space embedded in R dx . Indeed, an input x to neural networks represents an input in any such feature space (instead of only in a raw input space); e.g., given raw input x raw and any feature map φ : Remark 2. (On bias terms) All of our results hold true for the model with or without bias terms; i.e., given original x original and z original (x, θ), we can always set x = [(x original ) ⊤ , 1] ⊤ ∈ R dx and z(x, θ) = [(z original (x, θ)) ⊤ , 1] ⊤ ∈ R dz to account for bias terms if desired.
Optimization problem
The previous study (Shamir, 2018) and this paper consider the following optimization problem: minimize where W, V, θ are unconstrained, ℓ is some loss function to be specified, and y ∈ R dy is the target vector. Here, µ is an arbitrary probability measure on the space of the pair (x, y) such that whenever the partial derivative exists, the identity, holds at every local minimum (W, V, θ) (of L); 1 for example, an empirical measure µ with a training dataset {(x i , y i )} m i=1 of finite size m always satisfies this condition. Therefore, all the results in this paper always hold true for the standard training error objective, δ (x i ,y i ) with the Dirac measures δ (x i ,y i ) . In general, the objective function L(W, V, θ) in Equations (2) and (4) is non-convex even in (W, V ) with a convex map h → ℓ(h, y).
This paper analyzes the quality of the local minima in Equation (2) in terms of the global minimum value L * {x} of the linear predictors Rx with an arbitrary fixed basis x (e.g., x = φ(x raw ) with some feature map φ) that is defined as Similarly, define L * {x,z(x,θ)} to be the global minimum values of the linear predictors ( 1. A simple sufficient condition to satisfy Equation (3) is for ∂ (W,V ) ℓ(h(x, W, V, θ), y) to be bounded in the neighborhood of every local minimum (W, V, θ) of L. Different sufficient conditions to satisfy Equation (3) can be easily obtained by applying various convergence theorems (e.g., the dominated convergence theorem) to the limit (in the definition of derivative) and the integral (in the definition of expectation).
Background
Given any fixed θ, let L θ (W, V ) := L(W, V, θ) be a function of (W, V ). The main additional assumptions in the previous study (Shamir, 2018) are the following: PA1. The output dimension is one as d y = 1.
PA2. For any y, the map h → ℓ(h, y) is convex and twice differentiable.
PA3. On any bounded subset of the domain of L, the function L θ (W, V ), its gradient ∇L θ (W, V ), and its Hessian The previous work (Shamir, 2018) also implicitly requires for Equation (3) to hold at all relevant points for optimization, including every local minimum (see the proof in the previous paper for more detail), which is not required in this paper. Under these assumptions, along with an analysis for a simpler decoupled model (W x+V z(x, θ)), the previous study (Shamir, 2018) provided a quantitative analysis of approximate stationary points, and proved the following main result for the optimization problem in Equation (2).
The previous paper (Shamir, 2018) remarked that it is an open question whether Proposition 1, along with quantitative analysis of approximate stationary points, can be obtained for the networks with d y > 1 multiple output units.
Main results
Our main results are presented in Section 3.1 for a general case with arbitrary loss and arbitrary measure, and in Section 3.2 for a concrete case with the squared loss and the empirical measure.
Result for arbitrary loss and arbitrary measure
This paper discards the above assumptions from the previous literature, and adopts the following assumptions instead: Assumption A2. For any y, the map h → ℓ(h, y) is convex and differentiable.
Assumptions A1 and A2 can be easily satisfied in many practical applications in deep learning. For example, we usually have that d y = 10 << d x , d z in multi-class classification with MNIST, CIFAR-10 and SVHN, which satisfies Assumption A1. Assumption A2 is usually satisfied in practice as well, because it is satisfied by simply using a common ℓ such as squared loss, cross-entropy loss, logistic loss and smoothed hinge loss among others.
Using these mild assumptions, we now state our main result in Theorem 1 for arbitrary loss and arbitrary measure (including the empirical measure).
Theorem 1. If Assumptions A1 and A2 hold, every local minimum (W, V, θ) of L satisfies . (5) Remark 3. From Theorem 1, one can see that if Assumptions A1 and A2 hold, the objective function L(W, V, θ) has the following properties: (i) Every local minimum value is at most the global minimum value of linear predictors with the arbitrary fixed basis x as Here, the set of our assumptions are strictly weaker than the set of assumptions used to prove Proposition 1 in the previous work (Shamir, 2018) (including all assumptions implicitly made in the description of the model, optimization problem, and probability measure), in that the latter implies the former but not vice versa. For example, one can compare Assumptions A1 and A2 against the previous paper's assumptions PA1, PA2 and PA3 in Section 2.3. We note that along with Proposition 1, the previous work (Shamir, 2018) also provided an analysis of approximate stationary points, for which some additional continuity assumption such as such PA2 and PA3 would be indispensable (i.e., one can consider the properties around a point based on those at the point via some continuity).
In addition to responding to the open question, Theorem 1 further states that the guarantee on the local minimum value of ResNets can be much better than the global minimum value of linear predictors, depending on the quality of the residual representation z(x, θ). In Theorem 1, we always have that (L * {x} − L * {x,z(x,θ)} ) ≥ 0. This is because a linear predictor with the basis φ θ (x) = [x ⊤ z(x, θ) ⊤ ] ⊤ achieves L * {x} by restricting the coefficients of z(x, θ) to be zero and minimizing only the rest. Accordingly, if z(x, θ) is non-negligible (L * {x} − L * {x,z(x,θ)} = 0), the local minimum value of ResNet is guaranteed to be strictly better than the global minimum value of linear predictors, the degree of which is abstractly quantified in Theorem 1 and concretely quantified in the next subsection.
Result for squared loss and empirical measure
To provide a concrete example of Theorem 1, this subsection sets ℓ to be the squared loss and µ to be the empirical measure. That is, this subsection discards Assumption A2 and uses the following assumptions instead: Assumption B1. The map h → ℓ(h, y) represents the squared loss as ℓ(h, y) = h − y 2 2 .
Assumption B2. The µ is the empirical measure as µ = 1 m m i=1 δ (x i ,y i ) .
Assumptions B1 and B2 imply that Let us define the matrix notation of relevant terms as X := x 1 x 2 · · · x m ⊤ ∈ R m×dx , Y := y 1 y 2 · · · y m ⊤ ∈ R m×dy , and Z(X, θ) := z(x 1 , θ) z(x 2 , θ) · · · z(x m , θ) ⊤ ∈ R m×dz . Let P [M ] be the orthogonal projection matrix onto the column space (or range space) of a matrix M . Let P N [M ] be the orthogonal projection matrix onto the null space (or kernel space) of a matrix M . Let · F be the Frobenius norm. We now state a concrete example of Theorem 1 for the case of the squared loss and the empirical measure.
As in Theorem 1, one can see in Theorem 2 that every local minimum value is at most the global minimum value of linear predictors. When compared with Theorem 1, each term in the upper bound in Theorem 2 is more concrete. The global minimum value of linear predictors is L * {x} = 1 m P N [X]Y 2 F , which is the (averaged) norm of the target data matrix Y projected on to the null space of X. The further improvement term via the residual representation is This is the (averaged) norm of the residual P N [X]Y projected on to the column space of P N [X]Z(X, θ). Therefore, a local minimum can get the further improvement, if the residual P N [X]Y is captured in the residual representation Z(X, θ) that differs from X, as intended in the residual architecture. More concretely, as the column space of Z(X, θ) differs more from the column space of X, the further improvement term P [P N [X]Z(X, θ)]P N [X]Y 2 F becomes closer to P [Z(X, θ)]P N [X]Y 2 F , which gets larger as the residual P N [X]Y gets more captured by the column space of Z(X, θ).
Proof idea and additional results
This section provides overviews of the proofs of the theoretical results. The complete proofs are provided in the Appendix at the end of this paper. In contrast to the previous work (Shamir, 2018), this paper proves the quality of the local minima with the additional further improvement term and without assuming the scalar output (PA1), twice differentiability (PA2) and Lipschitz continuity (PA3). Accordingly, our proofs largely differ from those of the previous study (Shamir, 2018).
Along with the proofs of the main results, this paper proves the following lemmas.
Lemma 1. (derivatives of predictor)
The function h(x, W, V, θ) is differentiable with respect to (W, V ) and the partial derivatives have the following forms:
Proof overview of lemmas
Lemma 1 follows a standard observation and a common derivation. Lemma 2 is proven with a case analysis separately for the case of rank(W ) ≥ d y and the case of rank(W ) < d y .
In the case of rank(W ) ≥ d y , the statement of Lemma 2 follows from the first order necessary condition of local minimum, ∂ (W,V ) L(W, V, θ) = 0, along with the observation that the derivative of L with respect to (W, V ) exits.
In the case of rank(W ) < d y , instead of solely relying on the first order conditions, our proof directly utilizes the definition of local minimum as follows. We first consider a family of sufficiently small perturbationsṼ of V such that L(W,Ṽ , θ) = L(W, V, θ), and observe that if (W, V, θ) is a local minimum, then (W,Ṽ , θ) must be a local minimum via the definition of local minimum and the triangle inequality. Then, by checking the first order necessary conditions of local minimum for both (W,Ṽ , θ) and (W, V, θ), we obtain the statement of Lemma 2.
Proof overview of theorems
Theorem 1 is proven by showing that from Lemma 2, every local minimum (W, V, θ) induces a globally optimal linear predictor of the form, In the proof of Theorem 2, we derive the specific forms of L * {x z(x,θ)} for the case of the squared loss and the empirical measure, obtaining the statement of Theorem 2.
Conclusion
In this paper, we partially addressed an open problem on a type of deep ResNets by showing that instead of having arbitrarily poor local minima, all local minimum values are no worse than the global minimum value of linear predictors, and are guaranteed to further improve via the residual representation. This paper considered the exact same (and more general) optimization problem of ResNets as in the previous literature. However, the optimization problem in this paper and the literature does not yet directly apply to many practical applications, because the parameters in the matrix V are considered to be unconstrained. To improve the applicability, future work would consider the problem with constrained V .
Mathematically, we can consider a map that takes a classical machine learning model with linear predictors (with arbitrary fixed features) as an input and outputs a deep version of the classical model. We can then ask what structure this "deepening" map preserves. In terms of this context, this paper proved that in a type of ResNets, depth with nonlinearity (a certain "deepening" map) does not create local minima with loss values worse than the global minimum value of the original model.
Appendix
This appendix presents complete proofs.
Appendix A. Proofs of lemmas
A.1 Proof of Lemma 1 Proof. The differentiability follows the fact that h(x, W, V, θ) is linear in W and affine in V given other variables being fixed; i.e., with g(W, Taking derivatives of h(x, W, V, θ) in these forms with respect to vec(W ) and vec(V ) respectively yields the desired statement.
A.2 Proof of Lemma 2
Proof. This proof considers two cases in terms of rank(W ), and proves that the desired statement holds in both cases. Note that from Lemma 1 and Assumption A2, ℓ(h(x, W, V, θ), y) is differentiable with respect to (W, V ), because a composition of differentiable functions is differentiable. From the condition on µ, this implies that L(W, V, θ) is differentiable with respect to (W, V ) at every local minimum (W, V, θ). Also, note that since a W (or a V ) in our analysis is either an arbitrary point or a point depending on the µ (as well as ℓ and h), we can write E x,y∼µ [g(x, y)W (µ)] = g(x, y)W (µ)dµ(x, y) = E x,y∼µ [g(x, y)]W (µ) where g is some function of (x, y) and W (µ) = W with the possible dependence being explicit (the same statement holds for V ). Let z = z(x, θ) and E x,y = E x,y∼µ for notational simplicity.
Case of rank(W ) ≥ d y : From the first order condition of local minimum with respect to V , Similarly, from the first order condition of local minimum with respect to W , where the second line follows Lemma 1. This implies that where the last equality follows from that E x,y [zD] = 0. Therefore, if (W, V, θ) is a local minimum and if rank(W ) ≥ d y , we have that E x,y [zD] = 0 and E x,y [xD] = 0.
If (W, V, θ) is a local minimum, (W, V ) must be a local minimum with respect to (W, V ) (given the fixed θ). If (W, V ) is a local minimum with respect to (W, V ) (given the fixed θ), by the definition of a local minimum, there exists ǫ > 0 such that is an open ball of radius ǫ with the center at (W, V ). For any sufficiently small ν ∈ R d L such that (W,Ṽ (ν)) ∈ B ǫ/2 (W, V ), if (W, V ) is a local minimum, every (W,Ṽ (ν)) is also a local minimum, because there exists ǫ ′ = ǫ/2 > 0 such that for all (W ′ , V ′ ) ∈ B ǫ ′ (W,Ṽ (ν)) ⊆ B ǫ (W, V ) (the inclusion follows the triangle inequality), which satisfies the definition of local minimum for (W,Ṽ (ν)). Thus, for any such sufficiently small v ∈ R dz , we have that ∂L(W,Ṽ (ν), θ) ∂ vec(W ) = 0 since otherwise, (W,Ṽ (ν)) does not satisfy the first order necessary condition of local minima (i.e., W can be moved to the direction of the nonzero partial derivative with a sufficiently small magnitude ǫ ′ ∈ (0, ǫ/2) and decrease the loss value, which contradicts with (W,Ṽ (ν)) being a local minimum). Hence, for any such sufficiently small v ∈ R dz , where the last line follows from the fact that 0 = ∂L(W,V,θ) ∂ vec(W ) = ∂L(W,Ṽ (0),θ) ∂ vec(W ) = E x,y [vec((x + V z)D)] and hence E x,y [(x + V z)D] = 0. Since u 2 = 1, by multiplying u ⊤ both sides from the left, we have that for any sufficiently small ν ∈ R dz such that (W,Ṽ (ν)) ∈ B ǫ/2 (W, V ), Then, from ∂L(W,V,θ) ∂ vec(W ) = 0, Since the map h → ℓ(h, y) is convex and an expectation of convex functions is convex, E x,y [ℓ(h, y)] is convex in h. Since a composition of a convex function with an affine function is convex, L R (R, θ) is convex in R = R(W, V ). Therefore, from the convexity, if then R is a global minimum of L R (R, θ). We now show that if (W, V, θ) is a local minimum, then ∂L R (R,θ) ∂ vec(R) R=R(W,V ) = 0, and hence R = R(W, V ) is a global minimum of L R (R, θ). On the one hand, with the same calculations as in the proofs of Lemmas 1 and 2, we have that On the other hand, Lemma 2 states that if (W, V, θ) is a local minimum of L, we have that Proof. From Theorem 1, we have that L(W, V, θ) ≤ L * {x z(x,θ)} . In this proof, we derive the specific forms of L * {x z(x,θ)} for the case of the squared loss and the empirical measure. Let Z = Z(X, θ) for notational simplicity. Since the map h → ℓ(h, y) is assumed to represent the squared loss in this theorem, the global minimum value L * {x z(x,θ)} of linear predictors is the global minimum value of where R ∈ R (dx+dz)×dy . From convexity and differentiability of g(R), R is a global minimum if and only if ∂g(R) ∂ vec(R) = 0. Since solving ∂g(R) ∂ vec(R) = 0 for all solutions of R yields that and hence X Z R = P X Z Y.
Also, the same proof step obtains the fact that P F is the global minimum value of g ′ (R) = 1 m XR − Y 2 F , which is the objective function with linear predictors R ⊤ x.
On the other hand, since the span of the columns of X Z is the same as the span of the columns of X P N [X]Z , we have that P X Z = P X P N [X]Z , and | 5,692.4 | 2018-10-21T00:00:00.000 | [
"Computer Science"
] |
Clean Environment-Clean Technologies , Hydrogen Peroxide for Clean Environment
If any substance is interesting, it’s hydrogen peroxide. By now everyone’s aware of the ozone layer that surrounds the earth. Ozone consists of three atoms of oxygen (03). This protective layer of ozone is created when ultraviolet light from the sun splits an atmospheric oxygen molecule (02) into two single, unstable oxygen atoms. These single molecules combine with others to form ozone (03). Ozone isn’t very stable. In fact, it will quickly give up that extra atom of oxygen to falling rainwater to form hydrogen peroxide (H202). It is this hydrogen peroxide in rainwater that makes it so much more effective than tap water when given to plants. With the increased levels of atmospheric pollution, however, greater amounts of H202 react with air-borne toxins and never reach the ground. To compensate for this, many farmers have been increasing crop yields by spraying them with diluted hydrogen peroxide. We can achieve the same beneficial effect with house plants. If you’ve never used Hydrogen Peroxide you are overlooking one of the most powerful healing tools ever discovered. Most of us started on hydrogen peroxide shortly after birth. Not only does mother’s milk contain high amounts of H202, the amount contained in the first milk (colostrum) is even higher. This seems only reasonable now that we know one of its main functions is to activate and stimulate the immune system. Hydrogen peroxide is safe, readily available and dirt cheap. And best of all, it works! We do know that it is loaded with oxygen. (Half a liter of the food-grade 35% solution contains the equivalent of 65 lits of oxygen under normal conditions. We also know that when H202 is taken into the body (orally or intravenously) the oxygen content of the blood and body tissues increases dramatically. Hydrogen Peroxide is most versatile chemical used in various industries as bleaching agent, reagent in chemical synthesis, environmental control / effluent treatment, sterilization etc. The important constituent being active oxygen which is obtained by the controlled decomposition of H2O2 and water as a by-product. In this paper, the usage of H2O2 to provide ‘clean’ processes, without the production of any harmful or environmentally unsafe product is presented.
are anaerobic and cannot survive in the presence of oxygen or H 2 0 2 .We can agree that hydrogen peroxide produced within individual body cells is essential for life.And no one doubts its effectiveness when it comes to even treating infections topically.
In BOD/COD removal as an oxygen supplemental source
Hydrogen peroxide has been used to reduce the BOD and COD of industrial wastewaters for many years.While the cost of removing BOD/ COD through chemical oxidation is typically greater than that through physical or biological means, there are nonetheless situations which justify its use.H 2 O 2 can be used as a stand alone treatment or as an enhancement to existing physical or biological treatment processes, depending on the situation.H 2 O 2 can be used alone or with catalysts such as iron, UV light, ozone (O 3 ) and alkali to oxidize BOD/ COD contributing compounds in wastewaters.
If a large fraction of the BOD/COD is contributed by inorganic reduced sulfur compounds such as sulfides or thiosulfate, then H 2 O 2 alone is typically effective.Depending on the wastewater pH, the oxidation of these compounds by H 2 O 2 yield sulfate or colloidal sulfur, neither of which contribute to BOD/COD.If the primary contributors to BOD/ COD are dissolved organics, then a more reactive oxidation system is needed.A generalized reaction for reducing BOD/COD with Fe +2 as catalyst can be expressed as follows: is metered directly into the aeration basin of a biological treatment system to provide an immediate source of DO.The conversion of H 2 O 2 to DO in an activated sludge mixed liquor proceeds according to the following reaction: Theoretical H 2 O 2 requirement: 0.48 lbs H 2 O 2 (100%) per mg/L DO.The above reaction shows that two parts of H 2 O 2 will yield one part of DO.Therefore, the amount of H 2 O 2 required to oxygenate the wastewater is surprisingly small.
Aquaculture in india
India is making rapid strides with its Blue revolution and today, ranks third in the world in aquaculture.Prawns and shrimps rank as the highest foreign exchange earner among our marine product exports, with framed shrimps accounting for close to half of the total shrimp exports in volumes and fetching over 70 per cent in value.
India is a major supplier of shrimp to Japan, Europe, USA and still has tremendous untapped potential in this segment.Improved yields and adherence to stringent environmental regulations like HACCP (Hazard Analysis Critical Control Point), International Food Quality Standards etc., imposed by international bodies like the European Union and US FDA play a pivotal role in enhancing business prospects for export of Indian aquaculture products.In order to meet these standards, it is necessary that we have to grow Contamination and Disease free Aquaculture products.Pond parameters such as water hardness, acidity/ alkalinity, dissolved oxygen levels play an important role in development of a good culture harvest.Marine products produced in culture ponds are also prone to infections by microorganisms, including fungal, bacterial and viral infections.
Hydrogen peroxide in aquaculture
Oxygen is one of the critical factors for the aquatic life, especially for shrimps and scampi.Though some amount of Dissolved Oxygen (DO) is always there in the ponds, under semi-intensive shrimp farming the rate of depletion of DO is quite high, but such drops make the culture weak, susceptible to diseases and reduce their growth rate.On the other hand, such conditions favor the growth of harmful bacteria and promote the anaerobic decomposition of feed and other organic matter including culture excreta and wastes leading to production of toxic materials, besides sludge formation.This further affects the health, productivity and survivability of the culture.
Hydrogen Peroxide brings the assurance of a new life for farms and ponds.Hydrogen Peroxide generates and releases the lifesaving oxygen and helps maintain the Dissolved Oxygen levels of the pond.Reduce the sludge formation and reduce the chances of Bacterial and viral diseases.Also used to lower the organic load in ponds and helps in inducing moulting in prawns.Hydrogen Peroxide will be very useful in increasing the Dissolved Oxygen levels, especially during like rainy days, cloudy weather, high bacterial count in water and summer when oxygen levels decrease in the ponds.This is mainly used for prawn culture as the prawns crawl at the lower surface of pond unlike fishes that move on the top layer of water and consume oxygen from air.
Hydrogen peroxide as dechlorinating agent
Hydrogen peroxide (H 2 O 2 ) is a safe, convenient alternative for many dechlorination needs, especially those involving "free available chlorine" as opposed to "combined available chlorine."The chlorine as HOCl and OCl -is referred to as free available chlorine.This is the form of chlorine typically found in cooling water circuits, industrial bleaching systems, and many chemical processing operations.Nitrogen containing compounds such as ammonia, amines and proteins are usually present in municipal wastewater.Free available chlorine reacts readily with these materials to form chloramines in which the chlorine is described as combined available chlorine.The available chlorine remaining after disinfection of municipal wastewaters is usually present in the combined form.
Dechlorination can be accomplished by several means, the most widely used being sulfur dioxide -either as a gas (SO 2 ) or as a salt (e.g., sodium metabisulfite).However, this method has several short comings.Hydrogen peroxide reacts with free available chlorine in solutions with pH > 7.While there is no upper limit to the pH (e.g., H 2 O 2 can be used to dechlorinate effluent from caustic/chlorine odor scrubbers), as a practical matter, pH 8.5 is preferred in order to provide an instantaneous reaction.
About 200 gms of hydrogen peroxide is required to destroy 500 gms of free available chlorine.In most cases the oxygen produced by the reaction will remain dissolved in the solution (saturation is about 10 ppm D.O.).Where higher concentrations of chlorine are involved, the solutions may effervesce and provision must be made to accommodate the O 2 evolved.The reaction is mildly exothermic, liberating 37 kcal/mole as opposed to 199 kcal/mole when using SO 2 .Significantly, hydrogen peroxide reacts very slowly with combined available chlorine.Consequently, solutions which contain ammonia (e.g., most municipal wastewater effluents) cannot be dechlorinated with H 2 O 2 .
Hydrogen peroxide should be investigated as a dechlorination agent in industrial waters characterized by free available chlorine.These include: Cooling water blowdown where chlorination is used for microbiological control.Municipal wastewater effluent that has been denitrified prior to chlorination.Tests show 100% fish survival after 96 hours in the undiluted hydrogen peroxide-treated effluent.In fact, the dissolved oxygen from the hydrogen peroxide reaction with chlorine may improve the quality of the receiving water.
As a disinfectant
Among other applications, hydrogen peroxide is used as a disinfectant.It is used to treat inflammation of the gums and to disinfect (drinking) water.
In the United States, hydrogen peroxide is used more and more frequently to treat individual water supplies.It is used to prevent the formation of colors, tastes, corrosion and scaling by pollution degradation (iron, manganese, sulphates) and micro-organism degradation.Hydrogen peroxide reacts very fast.It disintegrate into oxygen and water, without the formation of byproducts.This increases the amount of oxygen in water.The disinfection mechanism of hydrogen peroxide is based on the release of free oxygen radicals.
The legislation for hydrogen peroxide
In the USA, hydrogen peroxide is registered as a pesticide by the EPA in 1977.Hydrogen Peroxide is immediately dangerous to life or health at higher concentration (75 ppm)
Therapeutic uses of H 2 O 2
When it comes to hydrogen peroxide therapy there seems to be only two points of view.Supporters consider it one of the greatest healing miracles of all time.
When exposed to other compounds hydrogen peroxide dismutates readily.The extra oxygen atom is released leaving H 2 0 (water).In nature oxygen (0 2 ) consists of two atoms a very stable combination.A single atom of oxygen, however, is very reactive and is referred to as a free radical.Over the past several years, we've continually read that these free radicals are responsible for all types of ailments and even premature aging.What many seem to forget, however, is that our bodies create and use free radicals to destroy harmful bacteria, viruses, and fungi.In fact, the cells responsible for fighting infection and foreign invaders in the body (your white blood cells) make hydrogen peroxide and use it to oxidize any offending culprits.The intense bubbling you see when hydrogen peroxide comes in contact with a bacteria-laden cut or wound is the oxygen being released and bacteria being destroyed.The ability of our cells to produce hydrogen peroxide is essential for life.H 2 0 2 is not some undesirable byproduct or toxin, but instead a basic requirement for good health.
Newer research indicates we need hydrogen peroxide for a multitude of other chemical reactions that take place throughout the body.For example, we now know that vitamin C helps fight infections by producing hydrogen peroxide, which in turn stimulates the production of prostaglandins.
There are references indicating use of hydrogen peroxide release during mouth rinsings on the composition of the microbiota of developing plaque in humans and the amount and pathogenecity of the plaque formed.The mouthwash which is used as the only oral hygiene significantly retarded gingivitis development.
Using hydrogen peroxide for cleaning
Clear liquid, non volatile, non explosive, non inflammable and non toxic product that looks like water but with a great amount of oxygen, that´s why in many languages it´s name is "oxygenated water", this product has a slight biting odor and a little bit irritating for the eyes, at the contact with the skin and the eyes it produces oxidation burns, so you must always wear rubber gloves.First off, it is anti-bacterial, anti-fungal, anti-mold and anti-mildew.Whew! so it makes sense to use it as a household cleaner.Using hydrogen peroxide for cleaning is practical, non-toxic and cheap!Hydrogen Peroxide can be used for cleaning tiles, stained toilets, stained plastic, carpet stains for using sodium percarbonate a powdered form of hydrogen peroxide.Just put some 3% hydrogen peroxide into a spray bottle.Spray it on and wipe it off as you would with other household cleaners.It can be bought in concentrated form and in bulk, using hydrogen peroxide for cleaning is very inexpensive.And, finally, using hydrogen peroxide for cleaning tends to keep your sponges, mops, and scrubie pads a whole lot cleaner.(They'll all get a bit of disinfecting every time you use them.)
90% hydrogen peroxide: for rocket fuel
Believe it or not is used as an oxygen source for rocket fuel.The hydrogen peroxide rocket engines are, in fact steam rockets, but this steam is produced by a violent exothermic reaction of the peroxide.When passed through a catalyst pack, the peroxide decomposes into superheated steam and oxygen.This high pressure steam is expelled supersonically through a DeLaval nozzle, which produces thrust.For each volume of liquid injected at the catalyst, after the reaction you get 5000 times that volume in gas expelled at the nozzle.The Hydrogen Peroxide is the only product used in the reaction, this places it in the monopropellant liquid rocket fuel classification.This kind of rocket, whether using steam or hot water, is the safest of all the rocket engines.Sometimes considered a "cool rocket," it does not produce flame, and therefore can be made of stainless steel.(Juan Manuel Lozano G. June 2008, Motociclismopanamericano)
Hydrogen peroxide for plants
Many farmers have been increasing crop yields by spraying them with diluted hydrogen peroxide (300 gms of 35% H 2 0 2 mixed with 500 lit of water per acre).You can achieve the same beneficial effect with your house plants by adding 30 gm of 3% hydrogen peroxide (or 16 drops of 35% solution) to a liter of water you give your plants.
(It can also be made into an excellent safe insecticide.Simply spray your plants with 225 gm of 3% peroxide mixed with 225 gm of white sugar and 5 lit of water.)Slow releasing forms of Hydrogen peroxide wherever liquid hydrogen peroxide cannot be used, H 2 O 2 is available in paste, honey, slow releasing solid forms.
Honey
Hydrogen peroxide is formed in a slowrelease manner by the enzyme glucose oxidase present in honey.It becomes active only when honey is diluted, requires oxygen to be available for the reaction (thus it may not work under wound dressings, in wound cavities or in the gut), is active only when the acidity of honey is neutralised by body fluids, can be destroyed by the protein-digesting enzymes present in wound fluids, and is destroyed when honey is exposed to heat and light.Also, the antioxidant constituents in honey help clean up oxygen free radicals present.
When honey is used topically (as, for example, a wound dressing), hydrogen peroxide is produced by dilution of the honey with body fluids.As a result, hydrogen peroxide is released slowly and acts as an antiseptic.
Sodium percarbonate
The name "sodium percarbonate" (SPC) does not reflect the structure of this oxidizing agent, which is in fact a carbonate perhydrate: 2 Na 2 CO 3 • 3 H 2 O 2 .Although SPC is very storage-stable if dry, the solid material has a slight vapour pressure of hydrogen peroxide leading to exchange with water or to violent reactions with oxidizable substrates, even in the solid state.
Sodium perborate
Unlike sodium percarbonate and perphosphate, the sodium perborate is not simply an adduct with hydrogen peroxide, but contains a cyclic anion (B 2 O 4 (OH) 4 2-) with two peroxo bridges and does not contain the BO 3 " ion.This makes the substance more stable, and safer for handling and storage.The formulae of the mono and tetra hydrates can therefore be wr itten as Na 2 H 4 B 2 O 8 (anhydrous) and Na 2 H 4 B 2 O 8 •6H 2 O respectively.Sodium perborate undergoes hydrolysis in contact with water, producing hydrogen peroxide and borate.It serves as a source of active oxygen in many detergents, laundr y detergents, cleaning products, and laundr y bleaches.It is also present in some tooth bleaching formulas.
Manufacturers information
The cost of 30 % Aq.H2O2 in bulk is available for approx.Rs. 40 per Kg (Ref.National Peroxide Ltd., Mumbai, India.)
CONCLUSION
Hydrogen Peroxide is non-toxic for people, plants, household animals, and the earth.Don't forget that whatever we use do end up going back through the sewage system or otherwise to the ear th, rivers, oceans and environment eventually.This chemical though a strong oxidizing agent has no harmful products except useful products like pure oxygen and water.Though one has to be careful in using this wonder chemical in appropriate dilutions.
The challenge is how to achieve the goals of conservation, sustainable development, and access and benefit shar ing for biological resources and traditional knowledge.Thirteenth Finance Commission of India, states that in making its recommendations, the Commission shall have regard, among other considerations, to the need to manage ecology, environment and climate change consistent with sustainable development, and the need to improve the quality of public expenditure to obtain better outputs and outcomes. | 3,987.2 | 2006-06-25T00:00:00.000 | [
"Environmental Science",
"Chemistry"
] |
Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem
: This paper introduces an efficient and robust sliding algorithm for the creation of no-fit polygons. The improved algorithm can cope with complex cases and is given an implementation in detail. The proposed concept of a touching group can simplify the judging process when recognizing the potential translation vector for an orbital polygon. In addition, the generation of the no-fit polygon only involves three main steps based on the proposed concept. The proposed algorithm has a mechanism that searches other start positions to generate a complete no-fit polygon for handling complex cases. To improve the efficiency, many acceleration strategies have been proposed, such as point exclusion strategy and point inclusion test. The robust and efficient performance of the algorithm is tested by well-known benchmark instances and degenerate and complex cases, such as holes, interlocking concavities and jigsaw-type pieces. Experimental results show that the proposed algorithm can produce complete no-fit polygons for complex cases, and acceleration strategies can reduce the creation time of no-fit polygon on benchmark instances by more than sixteen percent on average.
Introduction
In the field of cutting and packing problems, there is a kind of problem known as the two-dimensional (2D) irregular packing problem or the nesting problem.It is commonly encountered in many industries and applications, such as metal sheet cutting [1,2], leather [3], clothing [4], paper [5] and spatial arrangement [6].Through excellent algorithms to optimize the packing, even a one percent increase in the material utilization rate will save lots of resource costs for enterprises and generate huge economic benefits for the whole society.Despite the many practical applications and benefits, the problem has received relatively little attention in the literature when compared to the regular packing problem [7][8][9].One of the main reasons is that researchers have to deal with the geometry problem, which is the first obstacle they encounter.This means that satisfying the constraint of having all irregular pieces without overlapping is much harder than regular pieces.
Direct trigonometry involving line intersection and point inclusion testing is the classic method to identify the positional relationship between two polygons.However, the optimization algorithms will become inefficient when it adopts this method, which results in the slightly poor performance of the algorithms.The alternative used in irregular packing problems is the no-fit polygon (NFP), which is also used in the field of engineering and robot motion planning and the aircraft parking stand allocation problem [10].The no-fit polygon facilitates the research of irregular packing problems [11][12][13][14].It is an increasingly popular option since it is more efficient than direct trigonometry, particularly when using an iterative search.Determining whether polygons overlap, touch, or are separated only needs to conduct a simple test to identify whether the reference point is inside the NFP.Essentially, the no-fit polygon describes the region in which two polygons intersect.The computational efficiency gained by utilizing this method is very attractive.Hence, it is important to develop an algorithm for creating NFP for the research of irregular packing problems.The algorithm can enrich the application in 2D geometrical computer software.
However, there are few published works on algorithms for generating NFP.Note the fact that developing a robust geometry library is still needed, and this task is very timeconsuming and difficult.Furthermore, it is difficult to develop a robust NFP generator because of the complexity of irregular piece shapes.Thus, we propose an improved sliding algorithm for the generation of NFP and give an implementation in detail of our algorithm.Such an algorithm can become good preparation for applying more strategies to solve the irregular packing problem.For instance, in the work published by Costa et al. [15], if the NFP algorithm is efficient, it can directly calculate the new merged piece instead of approximating by one already computed because of this time-consuming operation.In other words, the more efficient the algorithm is, the better.
The proposed algorithm only involves two simple geometric stages.The first is generating the external NFP between two polygons, which includes three main steps: finding the touching group, determining the translation vector from all touching groups and computing the translation distance.The second stage is searching on the unvisited edges to determine whether there is a feasible starting point that can be found.If the starting point is available, then return to the first stage to generate the NFP.
The contributions of this study are:
•
To address the problem of the efficient and robust creation of the no-fit polygon;
•
To propose an improved sliding algorithm and provide a detailed implementation;
•
To present the concept of touching group, resulting in the number of cases to consider being reduced by half when determining the feasible translation vector;
•
To develop many acceleration strategies to improve the algorithm's efficiency, such as the point exclusion strategy, the right side test, and the point inclusion test;
•
To assess the performance of the proposed algorithm using the benchmark instances, degenerate and complex cases;
•
To help the further dissemination of using the no-fit polygon within both the industrial and academic communities.
The remainder of this paper is organized as follows.Section 2 provides an overview of NFP, including the definition and approaches.The proposed algorithm is exhaustively introduced in Section 3. The results obtained by our approach are presented and compared in Section 4. The final section discusses the conclusions.
Overview for No-Fit Polygon
In this section, we describe the definition and properties of the NFP in detail and briefly introduce some approaches that have been used to produce NFP within the previous literature.
Definition and Properties
Considering that the position of polygon A is fixed, the no-fit polygon between polygons A and B is the polygon described by the locus of points, where, if the reference point of polygon B is placed, then the polygons are in contact.We denote the no-fit polygon between two polygons A and B by NFPAB. Figure 1a
Approaches for Generating NFP
Here, the main techniques that have previously been used for the creation of no-fit polygons in the literature are briefly reviewed; please see the literature [16] for more details.Note that it is easy to generate a no-fit polygon when both polygons are convex.Given two convex shapes, A and B, the no-fit polygon is generated by the following steps: (i) shape A is anticlockwise, and shape B is clockwise (see Figure 2a); (ii) all edges from A and B are translated to a single point (see Figure 2b); these edges are connected in anticlockwise order to yield the no-fit polygon (see Figure 2c).It is very simple and extremely quick to use a standard sorting algorithm in combination with edge reordering through translation.However, no-fit polygons cannot be generated for non-convex shapes when using this method.Thus, other approaches are needed.
Decomposition and Phi-Function
Given the complexity of obtaining the NFP when a polygon is non-convex, one of the alternative methods is decomposition.Fast no-fit polygon creation methods can be applied if a polygon with concavities can be decomposed into convex sub-polygons.Seidal [17] suggested a fast polygon triangulation algorithm that has an O(nlogn) complexity.Watson and Tobias [18] proposed decomposing a simple polygon into a set of convex polygons by cutting between pairs of concave vertices, while Li and Milenkovic [19] decomposed a polygon into star-shaped polygons.When an irregular polygon has been decomposed into manageable shapes, the NFPs are generated by passing each subpolygons of shape B around each sub-polygons of shape A, and finally combining the NFPs of the sub-polygons to generate the NFP of the two original polygons.
Although the decomposition method can tackle non-convex polygons, it also creates two further issues: efficient decomposition and robust recombination of the sub-NFPs.Agarwal et al. [20] conducted an extensive investigation into different decomposition and recombination operations with respect to constructing Minkowski sums of non-convex polygons.There are further challenges in the recombination operations.If edges from two sub-NFPs coincide or cross in and out of each other, careful analysis must be performed to identify whether these edges are part of the boundary of the NFP.Particular difficulty occurs if the original shapes contain holes, as it is unclear whether intersecting no-fit polygon subsections define holes or regions that can be discarded.
The Phi-function was conceived and applied by Stoyan et al. [21,22].It is a series of mathematical expressions that represent the positional relationships of two objects.Specifically, if the value of the phi-function is greater than zero, then the objects are separated; equal to zero, then their boundaries touch; and less than zero, then they overlap, and the value should represent the Euclidean distance between the two objects.Stoyan et al. [21] analytically construct phi-functions for all primary objects (rectangles, circles and other convex polygons) and define mathematical intersection relationships for non-convex polygons through the union, intersection and complement of primary objects.Later, the authors [22] further develop phi-functions for all 2D objects that are formed by linear segments and circular arcs.This approach appears to have great potential for contributing to the field of nesting problems.However, the lack of an algorithmic process of obtaining the phi-function becomes a barrier to a wider adoption of this approach.
Minkowski Sums and Sliding Algorithm
The concept of Minkowski sums is as follows: given two arbitrary point sets, A and B, the Minkowski sum of A and B is defined by the following: To produce no-fit polygons, we must use the Minkowski difference, A ⊕ −B.In addition, it requires a non-mathematical implementation of this methodology.
Ghosh developed a set of boundary addition theorems for both the convex case and non-convex case.See Ghosh [23] for a detailed explanation of these theorems.Later, Bennell et al. [24] proposed an approach that extracts key elements of Ghosh's method and develops a set of algorithmic steps that produce the NFP.However, their approach cannot deal with internal holes, as it is difficult to detect which of the internal no-fit polygon edges can be discarded and which form the internal no-fit regions.Therefore, Bennell et al. [25] presented some modifications to provide a more robust approach.Dean [26] also presented an extension of Ghosh's NFP algorithm.
The Minkowski sums methodology is an effective approach to produce the NFP of two polygons.However, many exceptional cases need to be considered, making this method slightly complex and hard to understand.
The first discussion and implementation of a sliding algorithm is detailed in Mahadevan's Ph.D. thesis [27].The key points of Mahadevan's approach include three main steps: calculation of touching vertices and edges, determination of the translation vector and calculation of the translation length.Later, Whitwell et al. [28] proposed some improvements for Mahadevan's approach, and the robustness of the previous algorithm was enhanced.Based on the previously published literature, we propose a more efficient and robust sliding algorithm for the generation of NFP.All known degenerate cases can be successfully addressed, and many benchmark instances are tested.In addition, inspired by the interaction of the two polygons and the definition of the no-fit polygon, Liu et al. [29] proposed a different approach for no-fit polygon calculation.
Improved Sliding Algorithm
The sliding algorithm derives from the definition of a no-fit polygon, which is the tracing movement.The core of this methodology is selecting the correct direction of translation according to the touching case of two polygons and then calculating the translation distance.This is an iterative procedure, and each iteration will create an edge of the no-fit polygon.
The Concept of Touching Group
In this paper, we assume that A is the fixed polygon, B is the orbital polygon and both polygons are anti-clockwise.Based on the observation, there are three possibilities of a touching case: Each case results in one type of touching group (see Figure 4).It consists of three or four oriented edges from polygons A and B. The adjacent edges that form the vertex of the polygon will be recorded, and the oriented edge touched in the middle by a vertex from another polygon is also recorded.Thus, the touching group has four edges (d, c, e, f), three edges (d, c, f) and three edges (f, g, d) in case (a), case (b) and case (c), respectively.It is very easy to recognize the potential translation vector for each touching group when using this concept of a touching group, resulting in simplification of the judging process compared with Whitwell's method.For instance, we can easily identify the oriented edge d as the translation vector for polygon B in Figure 4c.
Creation of No-Fit Polygon
The process of creating NFP in the improved sliding algorithm can be broken down into the three subparts, which will be discussed in turn: finding touching groups, determining the translation vector from all touching groups and computing the translation distance.
Find the Touching Group
The creation of a no-fit polygon starts with the operation of finding the touching group between two polygons.The ability to correctly find touching edges is vital to the sliding approach because the remaining two subparts are based on this.This is achieved by testing each edge of fixed polygon A against each edge of orbital polygon B. Note that it only needs to test whether the starting point of the edge touches the starting point or the middle of the edge from another polygon.For example, in Figure 3a, the starting point of edge d touches the starting point of edge f.In Figure 3b, the starting point of edge d touches in the middle of edge f.The touching groups found in this step will be stored in a list, referred to here as the T list.
Determine Translation Vector (i) Recognize the potential translation vector
The first step is to recognize the potential translation vector from each touching group in the T list.For the first type of touching group, as shown in Figure 4a, only the edge pair in which the starting point coincides is considered.If the ending point of edge f from the orbital polygon is on the left side of another edge d from the fixed polygon, edge f is the potential translation vector.Otherwise, edge d is the potential translation vector.As shown in Figure 5a, the ending point of edge f is on the left side of edge d, so the potential translation vector is edge f.As shown in Figure 5b, the potential translation vector is edge d because the ending point of edge g is on the right side of edge d or these two edges are parallel.Note that the oriented edge needs to be reversed if it derives from the orbital polygon.For example, edge f should reverse in Figure 5a.For the second and third types of touching groups, the potential translation vector is the edge where the vertex touches (see Figure 4b,c (ii) Determine the feasible translation vector Each touching group in the T list produces a potential translation vector, but not all of them are feasible.In other words, the orbital polygon translating along the vector may intersect with the fixed polygon.For instance, assuming that the touching case of two polygons is as shown in Figure 6, there are two touching groups, and we can identify that the potential translation vectors are edges e and d.If we translate polygon B along vector d, this would result in an intersection between edges i and e or g and e.Thus, vector d is infeasible, while vector e is feasible.Hence, we propose a test to determine whether the potential translation vector is feasible.First, we calculate the angular direction at the touch point for which the edge of the orbital polygon can move without intersecting with the edge of the fixed polygon.Then, we identify whether the potential translation vector from other touching groups is within the angular direction.Note that a potential translation vector is feasible only if it is within the angular direction of all other touching groups.Based on the observation, the feasibility test only considers four types, as shown in Figure 7.For the second and third types of touching groups shown in Figure 7a,b, the angular direction (given by the circular arcs) is easy to calculate, and we only need to test the potential translation vector v on the right side of (or parallel to) the potential translation vector produced by this touching group.Obviously, the vector v is feasible for this touching group, as shown in Figure 7a, and not for the touching group, as shown in Figure 7b.
For the first type of touching group, i.e., touching at a vertex, it needs to determine the boundaries before calculating the angular direction.As shown in Figure 7c, if edge g′ (produced by reversing edge g) is on the right side of edge d, the boundary is g′.Otherwise, the boundary is edge d.In the same way, we can recognize that the second boundary is edge c.Thus, the angular direction is produced by edges c and g′.In Figure 7d, the boundary edges are edges a1 and a2.Note that the potential translation vector is feasible for this touching group if it is on the right side of (or parallel to) one of the boundary edges for the case of Figure 7c, while it is feasible for this touching group only if it is on the right side of both boundary edges for the case of Figure 7d.
(iii) Select a feasible translation vector According to the observation, there is only one feasible translation vector in most cases in the process of creating a no-fit polygon.However, when degenerate cases such as holes, interlocking concavities and jigsaw-type pieces occur, many feasible translation vectors exist.A good method is needed to select a vector for producing the correct NFP.The method chooses the edge that is nearest (in edge order of fixed polygon) to the previous move.As shown in Figure 8b, the edge order of the previous move is 2 in this situation, and the nearest translation vector is edge a3, so the orbital polygon translates along the vector a3.In conclusion, there are three subparts of this step: finding the potential translation vector from the touching group, judging whether it is feasible and selecting a suitable vector if there are more than one.The Pseudo code of this step is shown in Algorithm 1.
Algorithm 1: Determine Translation Vector.Input: T list // T list,; Input: t1; // last touching group; Output: t2; // the selected touching group t = the number of touching groups in T; for each touching group in T do Get the potential translation vector of Ti; Calculate angular direction of Ti; end for if t is equal to 1 t2 = T0; return; i = 0; for i < t do for j < t do if j is not equal to i // do feasible test Get the potential vector vi in Ti; if vi is not suitable for Tj Flag vi is infeasible; break; j = j+1; end for i = i +1; end for if only one feasible translation vector in T t2 = feasible translation vector in T; return; t2 = Select a feasible vector from T based on t1; return;
Compute Translation Distance
The translation vector only provides the direction of movement of the orbital polygon because the translation distance is not always the full length of the vector from the touching group.As shown in Figure 9a, when polygons A and B touch at a vertex, there is only one touching group, and the translation vector is oriented edge d.Polygon B will intersect with polygon A if applying the entire translation vector d, as shown in Figure 9b.Therefore, we compute the feasible translation distance to avoid overlap.The task is trivial to the human eye.The maximal translation distance is the vector v, as shown in Figure 9c.However, for the computer, there needs to be a set of algorithmic steps.
(i) Computation method
The method projects the translation vector at each of the vertices of polygon B and tests it for intersection with all edges of polygon A, as shown in Figure 10a.The projection is also executed in the opposite direction for the vertices of polygon A, as shown in Figure 10b.Once the vertex of polygon B that will cross into polygon A is found and the length of the new translation vector is smaller than the current translation vector, the current translation vector is replaced by the new one.This method ensures that the correct nonintersecting translation is found.(ii) Acceleration strategy This is the most time-consuming operation for the sliding algorithm, and the time complexity is O(mn) in theory, where m and n are the numbers of vertices of polygons A and B, respectively.This paper proposes a point exclusion strategy to accelerate this operation.The strategy identifies the vertex that will not cross into the polygon when translating along the selected vector, and then does not test these vertices.It can take less time than we thought if many ineffective tests are excluded.
First, we calculate the upper boundary and lower boundary of the fixed polygon and orbital polygon based on the translation vector.Then, a simple test for the vertex of the polygon is performed before testing it for intersection with all edges of another polygon.Specifically, if the vertex is out of the range of the boundary, there is no need to test it for intersection with other polygon edges.Figures 10c,d show in detail an example of this strategy.In Figure 10c, three vertices of polygon A are out of the range of the boundary, and the two endpoints of edge d can also be excluded.Theoretically, the operation of projecting and intersection test needs to be executed 6 × 3 times, while practically, it only needs 1 × 3 times by using the point exclusion strategy.The effect of reducing the computation time is significant and will be further verified in Section 4. The Pseudo code of this step is shown in Algorithm 2.
Up to now, the direction and distance of translation have been determined, and the final step is to translate polygon B by the shortened translation vector.Then, we perform a test to detect if the reference point of polygon B has returned to its initial starting position.If not, the process of creating a no-fit polygon is restarted from the finding touching group.The starting point of v = ; The ending point of v = ; end for end for
Searching Oher Start Positions
The creation of NFP in the sliding algorithm starts with selecting a touching but nonintersecting position for two polygons.This is an easy task, and usually, the largest ycoordinate of orbital polygon B is placed touching the smallest y-coordinate of fixed polygon A. Then, the three steps described in Section 3.1 are iteratively performed to create the no-fit polygon.An example is shown in Figure 11b.However, the produced nofit polygon may be incomplete if only these steps are performed.As shown in Figure 11b, polygon A has concavity, and its entrance is so narrow that polygon B is not able to slide into the concavity.Thus, another method is needed to determine this possibility.
Method of Searching Feasible Starting Position
If the position of orbital polygon B shown in Figure 11c can be found, then the creation of a no-fit polygon can start with this position.Whitwell et al. [28] proposed an approach to identify such possibilities.The basic principle is that if an edge of a fixed polygon has not been traversed when creating a no-fit polygon, then these edges will be searched for feasible start positions.Specifically, given an edge u of fixed polygon the first step is to translate polygon B such that the first vertex of it is aligned to the start point of u; then, performing an overlap test [30], if the polygons do not intersect in this position then this is a feasible start position; if they intersect, then performing a sliding operation including calculating the translation distance and translating polygon B along edge u, this operation is similar to the steps described in Section 3.2.3.After sliding, the overlap test is executed again.This is an iterative process until a non-intersecting position is found or the end of edge u is reached.If the first vertex of polygon B cannot find a feasible starting point, then try the rest of its vertices.Note that the edge of the fixed polygon is flagged as "visited" whether the feasible start position is found or not.The Pseudo code of searching for other starting points is shown in Algorithm 3. The method can fully search for feasible starting positions, but it is time-consuming due to three main aspects.First, for an unvisited edge of a fixed polygon, all vertices of the orbital polygon need to be tested.Second, the test contains the operation of computing translation distance, which takes a lot of time in the sliding algorithm.Third, the overlap test is also time-consuming and must be performed after each translation.Hence, some strategies are applied to improve the efficiency of this method.
The first acceleration strategy is to examine whether the two connected edges of polygon B are both on the right of or parallel to edge u of polygon A [28], called the "right side" test.The D-function [31] is used to recognize the relative position of a point with respect to an oriented edge.If either of the edges are left of u, then overlapping between polygons A and B occur and never yield a feasible starting position when sliding along vector u.Hence, we can abandon this vertex and test the next one, which results in reducing the number of operations of computing translation distance and overlap test, thereby improving efficiency.Figure 12a,b show examples of this strategy.In Figure 12a, edge b2 is on the left side of edge a4, which dissatisfies the requirement.However, in Figure 12b, both edges b2 and b3 are on the right side of edge a4.The second strategy is a "point inclusion".In the operation of computing the translation distance, if the minimal distance corresponding to a certain vertex of polygon B is larger than or equal to the length of edge u and this vertex is inside of polygon A, then this vertex of polygon B is abandoned because the two polygons always overlap when sliding along edge u.This is the same for the vertex of polygon A. As shown in Figure 12c, when projecting translation vector a5 at vertex P1 and only intersecting with a9, the translation distance is obviously larger than the length of a5 and P1 is inside polygon A, so the vertex can be abandoned, and there is no need to take a sliding operation.
The third acceleration strategy is the improved "point exclusion" strategy.The improvement is keeping all translation vectors in the operation of computing translation distance instead of adopting a replacement strategy.This method avoids recalculating after translating polygon B and only needs to shorten all stored vectors.See an example shown in Figure 12d.There is only one vertex of polygon A (the starting point of a7) that needs to be calculated when applying the point exclusion strategy.This vertex will intersect with edges b1 and b4, resulting in two translation vectors being stored.After iteratively performing the overlap test and sliding operation, the feasible start position is found, as shown in Figure 12f.The Pseudo code of the improved operation of computing the translation distance is shown in Algorithm 4. To further test the robustness and efficiency of ISA, we also use it to generate the NFP for all polygons from the benchmark datasets.Each dataset contains many simple polygons and is used as a common test set in the cutting and packing community.The computation times for benchmark datasets are provided in Table 1.The procedure of the proposed algorithm was coded in Visual Studio C++, and the instances were run on a PC with 8 GB, Core i7 1.8 GHz processer.It is difficult to create no-fit polygons involving holes.However, the no-fit polygon can be generated easily and completely using the operation of searching other start positions.In Figure 13, the no-fit polygon contains holes for Figure 13a,d,f,i-k; in particular, there are multiple holes for a, d, j and k.Furthermore, the fixed polygon has concavities within the concavities in Figure 13j,k.There also exist cases involving sliding through exactly fitting ''passageways'' that are hard to handle.Figure 13b shows such a case, and another example of this case is previously discussed in Figure 8.
Figure 13c shows the problem case involving jigsaw pieces that fit together with no movement.Thus, the no-fit polygon is a singular feasible point rather than an internal loop.After obtaining a feasible start position, our algorithm will perform a simple test to determine whether there is a feasible translation vector to identify this case.Most of the previous approaches including the Minkowski sun and convex decomposition, have difficulty handling this case [28].The no-fit polygons shown in Figure 13e,g are from the "Swim" benchmark datasets.
Efficiency Performance of ISA
Table 1 shows the creation times for benchmark datasets by the improved sliding algorithm (ISA).To evaluate the effect of the point exclusion strategy (PES) and the point inclusion test (PIT) on the algorithm's efficiency, we also test the creation time of the nofit polygon for the ISA without the PES and PIT.The meaning of the capital letters in the header of Table 1 is illustrated by notes below the table.The column of "In." represents the percent of increased time when compared to the ISA.
All experiments evaluating the performance of Whitwell's approach were conducted on a Pentium 4 2 GHz processor with 256 MB RAM.The experimental results in Table 1 show that the ISA creates no-fit polygons quicker than Whitwell's approach for all of the datasets, especially for the poly5b, poly4b, Jakobs1, Jakobs2 and swim datasets.Although this comparison is unfair due to the difference in hardware, it shows that the method proposed in this paper is able to quickly generate no-fit polygons and that all the improvements contribute to the computing efficiency.The strategy of PIT is effective in terms of improving efficiency for many datasets, especially for the swim dataset, for which the average number of edges is larger than others.However, there is a possibility that the creation time will increase because it takes time to perform the test.
Computational results show that the proposed PES can largely increase computational efficiency, and the more edges the polygon has, the better.This is further verified by the instance named Arc1, in which all edges of the polygons are arcs.The results are shown in Table 2.The arcs are discretized with different precisions, resulting in different numbers of edges.The creation time is reduced by 20 percent when the average number of edges is 76.0.It is able to be reduced by 51.2 percent when the average number of edges is 652.0.
Conclusions and Future Works
In this paper, an efficient and robust sliding algorithm for generating a no-fit polygon is proposed.Creating a no-fit polygon only contains three steps based on the proposed concept of touching group, i.e., finding the touching group, determining the translation vector and computing the translation distance.The first feasible start position is easy to identify, but other starting positions are likely to exist when the polygon is non-convex.Hence, the searching other start positions procedure is adopted to produce a complete nofit polygons.Many strategies are proposed to improve the algorithm's efficiency.Experimental results show that the algorithm is highly efficient for the creation of a no-fit polygon.The calculation time in benchmark instances is increased by 21.0% and 3.20% on average if there is no PES and PIT, respectively.The proposed algorithm is a computational geometric algorithm used for generating no-fit polygons of 2D graphics.It cannot handle curves, so the discretization operation is needed.In other words, the input graphic is a simple polygon without self-intersecting edges.To the best of our knowledge, the algorithm has many applications, such as irregular packing problems, engineering and robot motion planning and the aircraft parking stand allocation problem.
Future works need to further investigate how to reduce the time of the second phase, i.e., searching other feasible start positions to generate a complete NFP, and propose strategies to further improve the efficiency.
Figure 1 .
Figure 1.(a) Polygons A, B and construction of NFPAB and (b) The properties of the no-fit polygon.
Figure 2 .
Figure 2. Method of generating a no-fit polygon with convex polygons.(a) Polygons A and B; (b) All edges are moved to a single point; (c) Generation of NFPAB
Figure 3 .
Figure 3. Three touching cases of two polygons.(a) First touching case; (b) Second touching case; (c) Third touching case.
Figure 4 .
Figure 4. Three types of touching groups.(a) First type of touching group; (b) Second type of touching group; (c) Third type of touching group.
, edges f and d).
Figure 5 .
Figure 5. Method of recognizing the potential translation vector; (a) Derived from edge f; (b) Derived from edge d.
Figure 6 .
Figure 6.Method of identifying the feasible translation vector.
Figure 7 .
Figure 7.The feasible boundary for all types of touching groups.(a) The second type; (b) The third type; (c) The first type; (d) The first type.
Figure 8 .
Figure 8. Examples of two polygons involving fitting passageways.(a) An example from literature; (b) An example from "Jakobs1" benchmark instance
Figure 9 .
Figure 9. Illustration of shortening a translation vector to avoid overlap.(a) The translation vector is edge d; (b) Overlap between A and B; (c) The translation distance is the length of vector v.
Figure 10 .
Figure 10.Illustration of shortening the translation vector and the "point exclusion" strategy.(a) Projection of the vertices of polygon B; (b) Projection of the vertices of polygon A; (c) Boundary of polygon A; (d) Boundary of polygon B.
Figure 11 .
Figure 11.An example of interlocking concavities: (a) Polygons A and B; (b) NFP produced by first stage; (c) complete NFP.
Figure 12 .
Figure 12.Improvements on searching start position and the generation process.(a) Failure to right side test; (b) Right sided test is passed; (c) Illustration of point inclusion strategy; (d) Illustration of point exclusion strategy; (e) Translation along edge a4; (f) The feasible start position.
Figure 13 .
Figure 13.NFPs of degenerate cases and complex instances from published literature.(a) NFP with holes; (b) An example of exact sliding; (c) The jigsaw-type; (d)NFP with holes; (e) An example from "swim" instance; (f) Polygon with narrow entrance; (g) An example from "swim" instance; (h) An example from literature; (i) Instance from literature; (j) Instance f from literature; (k) Instance from literature; (l) Instance from literature
Algorithm 2 :
Compute translation distance.Input: PA, PB //two polygons; t2 // the selected touching group Get the translation vector v in t2; Initialize ub, lb; // the upper and lower bound Get the boundary ub and lb about PA based on v; i = 0; for each vertex point of PA do if is not in ub and lb bound continue; // point exclusion test for each edge of PB do Calculate the cross point of the along v with edge e; if exists // intersection happened Get distance d between and ; if d less than the current length of v; The starting point of v = ; The ending point of v = ;
end for end for Get
the boundary ub and lb about PB based on v; i = 0; for each vertex point of PB do if is not in ub and lb bound do continue; // point exclusion test for each edge of PA do Calculate the cross point of the along v with edge e;; if exists // intersection happened Get distance d between and ; if d less than the current length of v;
Algorithm 3 :
Search other Start Point.Input: PA, PB //two polygons, Input: Ptnfp; // the starting point of new NFP Initialize V = ∅;// the list of storing all translation vectors for each edge of PA do if is visited do continue; Set is visited; for each edge of PA Move PB by making starting point of and coincidence; if both −1 and are not on the right side of do continue; // "right side" test V = ∅;// clear stored vectors If the result of getting translation vectors (PA, PB, ) is false do continue; // Algorithm 4 while the starting point of does not on the ending point of do if PA does not overlap with PB at this position Ptnfp = PBrf;; // the reference point PBrf of PB return true; Shorten all vectors in V and get the translation vector v;
Algorithm 4 :
Get translation vectors.Input: PA, PB; // two polygons Input: v; // the oriented edge of PA Output: V; //the list of storing all vectors Initialize ub, lb; // the upper and lower bound Initialize Vt = ∅; // temporarily store the translation vectors Get the boundary ub and lb about PA based on v; for each vertex point of PA do if is not in ub and lb bound do continue; // point exclusion test for each edge of PB do Calculate the cross point of the along v with edge e;; if exists do Add new vector u = − to Vt; Get the boundary ub and lb about PB based on v; for each vertex point of PB do if is not in ub and lb bound do continue; // point exclusion test for each edge of PA do Calculate the cross point of the along v with edge e; if exists Add new vector u = − to Vt;
Table 1 .
No-fit polygon creation times for 19 datasets from the literature.The meaning of the letter in the header of Table: E: Average number of edges; N: Number of different shapes; R: Rotational constraints; L: Logical total number of shapes; O: Total number of NFPs; T: Total creation time(seconds); P: NFPs per second.
Table 2 .
The creation time for the Arc1 instance. | 8,730.4 | 2022-08-15T00:00:00.000 | [
"Computer Science"
] |
Ab initio three-loop calculation of the W-exchange contribution to nonleptonic decays of double charm baryons
We have made an ab initio three-loop quark model calculation of the $W$-exchange contribution to the nonleptonic two-body decays of the doubly charmed baryons $\Xi_{cc}^{++}$ and $\Omega_{cc}^{+}$. The $W$-exchange contributions appear in addition to the factorizable tree graph contributions and are not suppressed in general. We make use of the covariant confined quark model previously developed by us to calculate the tree graph as well as the $W$-exchange contribution. We calculate helicity amplitudes and quantitatively compare the tree graph and $W$-exchange contributions. Finally, we compare the calculated decay widths with those from other theoretical approaches when they are available.
I Introduction
The discovery of the double charm baryon state Ξ ++ cc by the LHCb Collaboration [1] in the multibody decay mode (Λ c K − π + π + ) has provided a strong incentive for further theoretical analysis of the weak decays of double charm baryons. The lifetime of the Ξ ++ cc has been measured to be (0.256 +0.024 −0.022 (stat) ± 0.014(syst)) ps [2]. The existence of the Ξ ++ cc was confirmed in Ref. [3], again by the LHCb Collaboration, who reported on the first observation of a two-body nonleptonic decay of the doubly charmed baryon Ξ ++ cc → Ξ + c + π + . In the same report the mass of the Ξ ++ cc measured in [1] was confirmed. The nonleptonic two-body decays of baryons have five different color-flavor quark topologies. The set of contributing topological quark diagrams divides into two groups: (i) the reducible tree-diagrams, and (ii) the irreducible Wexchange diagrams. The tree-diagrams are factorized into the lepton decay of the emitted meson and the baryonbaryon transition matrix elements of the weak currents. The W -exchange diagrams are more difficult to evaluate from first principles. First attempts to estimate the W -exchange contributions have been made in [4,5] using a pole model approach and in [6] using final state interactions based on triangle diagrams describing one-particle exchanges. The authors of [4,5] and [6] emphasize that their results provide only first estimates of the W -exchange contributions, in particular since their calculations involve generous approximations the errors of which are hard to quantify.
From the work of [4,5] one knows that the W -exchange contributions to nonleptonic double charm baryon decays are sizeable and cannot be neglected. The W -exchange contributions can interfere destructively or constructively with the tree diagram contributions. It is therefore of utmost importance to get the W -exchange contributions right. In this paper we set out to calculate the W -exchange contributions to the Cabibbo favored nonleptonic two-body decays of double charm baryons. We use the framework of our previously developed covariant constituent quark model to calculate the contributing three-loop quark Feynman diagrams. In a precursor of our present model some of us have calculated nonleptonic charm and bottom baryons including W -exchange contributions [7]. We used a structureless static approximation for the light quark (u, d, s) propagators and the leading-order contribution for the heavy quark (c, b) propagators in the 1/m c/b expansion. In the present calculation we use full quark propagators for the light and heavy quarks. We also now include quark confinement in an effective way.
II Decay topologies of Cabibbo favored doubly charmed baryon nonleptonic decays
We begin by a discussion of the different color-flavor topologies that contribute to the nonleptonic two-body transitions of the double heavy Ξ cc and Ω cc states. The relevant topologies are displayed in Fig. 1. We refer to the topologies of Ia and Ib as tree diagrams. They are also sometimes called external (Ia) and internal W -emission (Ib) diagrams. The topologies IIa, IIb, and III are referred to as W -exchange diagrams. The labeling of the topologies follows the labeling introduced in [8,9]. In [10] the W -exchange diagrams are denoted as the exchange (IIa), color-commensurate (IIb) and bow tie (III) diagram. The contribution of the various topological diagrams to a particular decay is determined by the quark flavor composition of the particles involved in the decay. For example, the decay Ξ ++ cc → Σ ++ c +K * 0 proceeds solely via the tree diagram Ib. In [11,12] this decay has been interpreted as making up a large part of the discovery final state channel (Λ + c K − π + π + ) via the decay chain Ξ ++ cc → Σ ++ c (→ Λ + c + π + ) +K * 0 (→ K − + π + ). As shown in Fig. 1, the color-flavor factor of the tree diagrams Ia and Ib depend on whether the emitted meson is charged or neutral. For charged emission the color-flavor factor is given by the combination of the Wilson coefficients (C 2 + ξC 1 ), where ξ = 1/N c and N c is the number of colors, while for neutral emission the color-flavor factor reads (C 1 + ξC 2 ). We take C 1 = −0.51 and C 2 = 1.20 at µ = m c = 1.3 GeV from Ref. [13]. We use the large N c limit for the color-flavor factors. For the W -exchange diagrams the color-flavor factor is given by (C 2 − C 1 ).
Ib
IIa The decay of present interest Ξ ++ cc → Ξ + c + π + [3] is fed by the tree diagram Ia and the W -exchange diagram IIb. We treat this decay as well as the seven remaining 1/2 + → 1/2 + + P (V ) decays that belong to the same topology class, namely The W -exchange contributions to these decays fall into two classes. The first class of these decays involves a Ξ ′+ cbaryon containing a symmetric {us} diquark described by the interpolating current ε abc (u b Cγ µ s c ), where C = γ 0 γ 2 is the charge conjugation matrix defined in terms of the Dirac matrices. The W -exchange contribution is strongly suppressed due to the Körner, Pati, Woo (KPW) theorem [14,15]. This theorem states that the contraction of the flavor antisymmetric current-current operator with a flavor symmetric final state configuration is zero in the SU (3) limit. The antisymmetric [us] diquark emerging from the weak vertex is in the 3 * representation and cannot evolve into the 6 representation of the symmetric final state {us} diquark. In the following we will calculate SU (3) breaking effects for the W -exchange contributions to this class of decays. The second class involves a Ξ + c -baryon containing a antisymmetric [us] diquark described by the interpolating current ε abc (u b Cγ 5 s c ). In this case the W -exchange contribution is not a priori suppressed. In Table I we display the quantum numbers, mass values, and interpolating currents of double and single charmed baryons needed in this paper.
III Matrix elements and decay widths
The effective Hamiltonian describing thesc →ūd transition is given by where we use the notation for the weak matrices with left/right chirality. The nonlocal version of the interpolating currents shown in Table I reads m j ) and m i is the quark mass at the space-time point x i , and Γ 1 , Γ 2 are the Dirac strings of the initial and final baryon states as specified in Table I. Here F B and Φ B are the Bethe-Salpeter kernel specifying the coupling of baryon with constituent quarks and correlation function, describing the distribution of quarks in baryon, respectively. The tree diagram and the IIb W -exchange contributions to the matrix element of the nonleptonic decays of the Ξ ++ cc and Ω + cc read The tree diagram color factor for the neutral Ω + cc decays is given by C T = −(C 1 + ξC 2 ) and by C T = +(C 2 + ξC 1 ) for the charged Ξ + cc decays. The factor of ξ = 1/N c is set to zero in our numerical calculations. The overall factor of 12 in Eq. (4) has its origin in a combinatorial factor of 2 and a factor of 6 from the contraction of two Levi-Civita color tensors. The Feynman diagrams describing these processes are depicted in Fig. 2.
The coupling constants g M , g B1 and g B2 are determined as described in our previous papers (for details see, e.g. [11,16]). The Dirac matrix Γ M in M (1) T reads γ 5 and ǫ V · γ for the pseudoscalar meson P and for the vector meson V . The connection of M (1) T with the leptonic decay constants f M = f P , f V is given by M The minus sign in front of f P appears because the momentum q flows in the opposite direction from the decay of P -meson. The Fourier-transforms of the vertex functions described by the nonlocal interpolating currents are denoted by Φ H . We use for them the Gaussian functional form: Φ H (−k 2 ) = exp(k 2 /Λ 2 H ), where Λ H is the hadron size parameter. Here and in the following the arguments of the baryonic vertex functions are expressed through the Jacobi momenta (q 1 , q 2 ) and (r 1 , r 2 ) by Ω 2 1 = 1 2 (q 1 + q 2 ) 2 + 1 6 (q 1 − q 2 ) 2 , Ω 2 2 = 1 2 (r 1 + r 2 ) 2 + 1 6 (r 1 − r 2 ) 2 . The momenta q i and r i are defined from momenta conservation in each vertex of the diagrams (see details in Ref. [11,16]).
The calculation of the three-loop W -exchange contribution is much more involved because the matrix element does not factorize. By using the Fierz transformation O α1α2 where Γ 1 ⊗ Γ 2 = I ⊗ γ 5 for B 2 = Ξ + c and −γ ν γ 5 ⊗ γ ν for B 2 = Ξ ′ + c . Here P = k 2 − k 1 + w d p 1 + w u p 2 is the Jacobi momentum in the meson vertex function.
We are now in the position to verify the KPW theorem in our three-loop calculation. To do this, we change the order of Dirac matrices in the trace by using the properties of the charge conjugation matrix. Keeping in mind that γ 5 does not contribute to the trace, we have We insert Eq. (7) into Eq. (6) and shift the integration variable k 3 → −k 3 + k 1 − p 2 . One can check that Ω 2 2 goes into itself under this transformation accompanied by an interchange of the u− and s− quark masses. Thus, if m u = m s then M W is identical zero which directly confirms the KPW-theorem. We have checked numerically that the three-loop integral vanishes in this limit. Details of the calculation of the loop integrals and the subsequent reduction of the integration over Fock-Schwinger variables to an integration over a hypercube may be found in our previous papers (see e.g. the most recent papers [11,16]). Compared to the two-loop calculation of [11,16]) we are now dealing with a three-loop calculation involving six quark propagators instead of the four propagators in the two-loop case. The calculation is quite time-consuming both analytically and numerically.
Next one expands the transition amplitudes in terms of invariant amplitudes. One has < B 2 P |H eff |B 1 >= g effū (p 2 ) (A + γ 5 B) u(p 1 ) , The invariant amplitudes are converted to a set of helicity amplitudes H λ1 λM as described in [8]. One has where m ± = m 1 ± m 2 , Q ± = m 2 ± − q 2 and |p 2 | = λ 1/2 (m 2 1 , m 2 2 , q 2 )/(2m 1 ). The helicities of the three particles are related by λ 1 = λ 2 − λ M . We use the notation λ P = λ t = 0 for the scalar (J = 0) contribution in order to set the helicity label apart from The two-body decay widths read where we denote the sum of the squared moduli of the helicity amplitudes H = H V − H A by H S and H V [16].
IV Numerical results
All model parameters have been fixed in our previous studies except for the size parameter Λ cc of the double charmed baryons. As a first approximation we equate the size parameter of double charm baryons with that of single charm baryons, i.e. we take Λ cc = Λ c = 0.8675 GeV where we adopt the value of Λ c from [17]. Numerical results for the helicity amplitudes and decay widths are displayed in the Tables II-V. In this paper we concentrate on our predictions for rate values. On top of the rate predictions, Tables II-V contain a wealth of spin polarization information. For example, for the decay Ξ ++ cc → Ξ + c + π + one finds an asymmetry parameter of α [4] predict a value in the range α = [−0.86, −1.00] depending on their model assumptions. Note that the W -exchange contribution in [4] is purely p-wave, i.e. proportional to H A 1/2 0 , due to the nonrelativistic approximations that they employ. This is in stark contrast to our relativistic result where the s-wave amplitude dominates in this process, i.e. H V 1/2 0 /H A 1/2 0 = 3.3. Both model calculations agree on a very substantial destructive interference of the tree and W -exchange contributions.
Our results highlight the importance of the KPW theorem for the nonleptonic decays when the final state involves a Ξ ′+ baryon containing a symmetric {su} diquark. Tables II-V show that the relevant W -exchange contributions are strongly suppressed. Nonzero values result from SU (3) breaking effects which are accounted for in our approach. Take for example the decay Ξ ++ cc → Ξ ′ + c + π + . When compared to the tree contribution the SU (3) breaking effects amount to ∼ (2 − 4) %. While the consequences of the KPW theorem for the W -exchange contribution are incorporated in the pole model approach of [4] they are not included in the final-state interaction approach of [6].
In Table VI we compare our rate results with the results of some other approaches [4-6, 12, 18, 19]. Note that the rates calculated in [18] include tree graph contributions only. There is a wide spread in the rate values predicted by the various model calculations. All calculations approximately agree on the rate of the decay Ξ ++ cc → Ξ ′ + c + ρ + which is predicted to have a large branching ratio of ∼ 16 %. In our calculation this mode is predicted to have by far the largest branching ratio of the decays analyzed in this paper. As concerns the decay Ξ ++ cc → Ξ + c + π + discovered by the LHCb Collaboration [3] we find a branching ratio of B(Ξ ++ cc → Ξ + c π + ) = 0.70 % using the central value of the life time measurement in [2]. The small value of the branching ratio results from a substantial cancellation of the tree and W -exchange contributions. The branching ratio is somewhat smaller than the branching ratio B(Ξ ++ cc → Σ ++ c +K 0 ) = 1.28 % calculated in [11]. We predict a branching ratio considerably smaller than the range of branching fractions (6.66 − 15.79) % calculated in [4].
An important issue is the accuracy of our results. The only free parameter in our approach is the size parameter Λ cc of the double heavy baryons for which we have chosen Λ cc = 0.8675 GeV in Tables II-V. In order to estimate the uncertainty caused by the choice of the size parameter we allow the size parameter to vary from 0.6 to 1.135 GeV. We evaluate the meanΓ = Γ i /N and the mean square deviation σ 2 = (Γ i −Γ) 2 /N . The results for N = 5 are shown in Table VII. The rate errors amount to 6 − 15%. Since the dependence of the rates on Λ cc is nonlinear the central values of the rates in Table VII do not agree with the rate values in Tables II-V.
V Outlook
We now have the tools at hand to calculate all Cabibbo favored and Cabibbo suppressed nonleptonic two-body decays of the double charm ground state baryons Ξ ++ cc , Ξ + cc , and Ω + cc . These would also include the 1/2 + → 3/2 + +P (V ) nonleptonic decays not treated in this paper. Of particular interest are the modes Ξ + cc → Σ ( * )+ + D ( * )0 (III), Ξ + cc → Ξ ( * )0 + D ( * )+ s (III), and Ω + cc → Ξ ( * )0 + D ( * )+ (IIb) which are only fed by a single W-exchange contribution as indicated in apprentices. Of these the three modes involving the final state 3/2 + baryons Σ * + and Ξ * 0 would be forbidden due to the KPW theorem. It would be interesting to check on this prediction of the quark model. | 4,146.8 | 2018-12-21T00:00:00.000 | [
"Physics"
] |
Ship Detection Using Deep Convolutional Neural Networks for PolSAR Images
Ship detection plays an important role in many remote sensing applications. However, the performance of the PolSAR ship detection may be degraded by the complicated scattering mechanism, multi-scale size of targets, and random speckle noise, etc. In this paper, we propose a ship detection method for PolSAR images based on modified faster region-based convolutional neural network (Faster R-CNN). The main improvements include proposal generation by adopting multi-level features produced by the convolution layers, which fits ships with different sizes, and the addition of a Deep Convolutional Neural Network (DCNN)-based classifier for training sample generation and coast mitigation. The proposed method has been validated by four measured datasets of NASA/JPL airborne synthetic aperture radar (AIRSAR) and uninhabited aerial vehicle synthetic aperture radar (UAVSAR). Performance comparison with the modified constant false alarm rate (CFAR) detector and the Faster R-CNN has demonstrated that the proposed method can improve the detection probability while reducing the false alarm rate and missed detections.
Introduction
As one of the most important applications in remote sensing, ship detection has played significant roles in commercial, fishery, vessel traffic services, and military applications, etc. [1][2][3]. Particularly, polarimetric synthetic aperture radar (PolSAR) is vital in ship detection because it permits good target characterization and guarantees effective detection regardless of illumination and weather conditions by capturing massive structural and textural information. Therefore, ship detection from PolSAR images has drawn increasing attention in recent years. Featured by adaptive detection threshold, CFAR has become one of the most popular ship detectors [1][2][3][4][5][6]. However, its performance strongly depends on statistical modeling of the local background clutter and empirical sliding window size (i.e., the target window, protect window, and background window). As we all know, heterogeneous clutter and interfering targets often lead to inaccurate estimations and biased modeling in practice. To deal with the intrinsic drawbacks of the CFAR detector, modified CFAR detectors have been proposed, where the heterogeneous clutter is reduced by advanced background estimation method [7] and the problem of statistical contamination, i.e., the sliding window contains one or more interfering targets, is solved by truncated statistics [8,9]. Additionally, other ship detectors have been developed by exploiting polarimetric scattering characteristics; e.g., polarization entropy, cross entropy, the degree The major contributions include that the modified Faster R-CNN is proposed to achieve fast and accurate ship detection for ships with differing size. Meanwhile, the proposed ship detector can mitigate the influence of azimuth ambiguities on ship detection, and has exhibited superior detection performance for the heterogeneous PolSAR images.
The organization of this paper is listed as follows: Section 2 provides detailed description of the ship detection method and gives an introduction of the overall architecture, as well as the components of the proposed method. Section 3 presents experimental results on measured AIRSAR and USVSAR datasets, and Section 4 concludes the paper.
Theory and Methodology
The workflow of the proposed ship detector is shown in Figure 1. There are four core processes involved: preprocessing, DCNN based sea-coast-ship classifier, modified Faster R-CNN ship detector, and the target fusion. Firstly, in the preprocessing stage, we convert the covariance matrix of the PolSAR data to real vector by Pauli decomposition. To enrich the training dataset and suppress overfitting for DCNN, we segment the PolSAR image with sliding windows and do multi-scale rotation to segmented samples. Meanwhile, we apply the box-car multi-look processing for speckle noise reduction. Secondly, we designed a sea-coast-ship classifier based on deep convolutional neural network to extract samples containing ships. Thirdly, we use the modified Faster R-CNN detector to detect ships of the selected samples by using sea-coast-ship classifier. Finally, we merge the detection results according to the geometrical relationship of samples and output the final detection results. Below, we will discuss them sequentially.
Detection Results
PolSAR MLC Images
Preprocessing
To feed PolSAR data into real-valued DCNN, the Pauli decomposition are utilized to generate color-coded images. The Pauli decomposition can express the Sinclair scattering as elementary scattering mechanisms, and they are given by Specifically, a represents single scattering from a plane surface, b and c represent dihedral scattering with relative orientations of 0 • and 45 • , respectively, and the final elements are all the antisymmetric components of the scattering S matrix. The corresponding color-coded image of the Pauli decomposition with Red = |a| 2 , Green = |b| 2 , and Blue = |c| 2 . Then, the input can be expressed as Input = |a| 2 , |b| 2 , |c| 2 (2) In the UAVSAR and AIRSAR datasets, the number of PolSAR images containing ships are usually limited. Meanwhile, the image resolution is low and most of the ships are small in size. To avoid severe overfitting and improve detection performance, it is required to generate sufficient samples by segmenting the PolSAR image with sliding windows. According to the prior knowledge of ship size in the UAVSAR and AIRSAR datasets, we set the segmentation size and stride size at 64 × 64 and 8 pixels, respectively, in the training stage. The stride is set to 64 or 32 pixels in the testing stage. To further enrich the training data and suppress overfitting for DCNN, we do multi-scale rotation to segmented samples, and the multi-scale rotation mainly refers to rotating the samples 180 degrees and flipping the sample from left to right.
Illustratively, Figure 2 shows some Pauli images of the three types of targets, each image at 1090 × 5111 pixels. Figure 2a shows Pauli images of coast, Figure 2b shows Pauli images of sea, and Figure 2c shows Pauli images containing ships and sea. Meanwhile, some rotated Pauli images of sub-samples are presented in Figure 3 and them are extracted from Figure 2, where the top row corresponds to ship samples, the middle row corresponds to sea samples, and the bottom row corresponds to coast samples. It is worth noting that the first image in Figure 2a and the second image in Figure 2b are collected by AIRSAR in L band, while other images are collected by UAVSAR in L band. Meanwhile, the training dataset consists of different sea states, resolution, and azimuth ambiguities samples to make the sea-coast-ship classifier and the modified Faster R-CNN more robust. Additionally, severe speckle noise will appear in the PolSAR imagery and affect ships with weak scattering due to the unique scattering and imaging mechanism for SAR. Therefore, multi-look processing should be utilized to suppress speckle noise before image segmentation. In this paper, we apply the simple box-car multi-look processing for speckle noise reduction, which will be proven necessary for detection from heterogeneous PolSAR data in Section 3.
Sea-Coast-Ship Segmentation
Compared to sea surface, ships usually exhibit stronger backscattering due to their unique double-bounce structures and large radar cross sections. On the contrary, ships and coast have similar backscattering intensity in PolSAR images, which would prevent effective detection. Therefore, coast samples should be removed firstly from the dataset before implementing the modified Faster R-CNN. Common approaches to coast masking include manual operation or designing classifiers with domain knowledge, which usually have poor performance with large computational burden. In this paper, we propose a DCNN-based sea-coast-ship classifier to distinguish ships, coast, and sea, which extracts ship samples automatically.
The network architecture is shown in Figure 4, which consists of 8 convolutional layers, 3 max-pooling layers, and 2 fully connected layers. The network architecture is designed by the best performance of the classification for sea, coast, and ship [24,25]. The sea-coast-ship classifier based on CNN is trained on the NVIDIA Titan-X GPU using caffe [26]. All the weights and biases are learned via the mini-batch stochastic gradient descent algorithm [26], where the mini-batch size is 64, the momentum parameter is 0.9, the weight decay parameter is 0.0005, and the learning rate is 0.001. Meanwhile, we randomly initialize the layers by drawing weights from Gaussian distributions with zero mean and standard deviation of 0.01, and initialize the bias by small constants; e.g., 0.1 [13].
Modified Faster-RCNN
With sufficient samples, we perform ship detection by modified Faster R-CNN, which is an improved version of Faster-RCNN specifically designed for ship detection. Originally, the Faster R-CNN is a DCNN-based detection algorithm, and the core is the region proposal network (RPN) that shares full-image convolutional features with the detection network. Figure 5 shows a typical architecture of the Faster R-CNN, which mainly includes two modules: (1) a fully DCNN that generates region proposal; and (2) the Fast R-CNN detector [15] that detects target based on region proposal generated by the first module. Such architecture enables a unified and deep-learning-based object detection system, which runs at near real-time frame rates and achieves satisfying performance with object detection. The performance of the state-of-the-art ship detection networks depends heavily on region proposal algorithms; e.g., the RPN in the Faster R-CNN. The RPN simultaneously predicts a set of rectangular object bounds with object scores. To generate a region proposal, a small network with a spatial window of 3 × 3 slides over feature maps produced by the last shared convolutional layer. Each sub-feature included in the sliding window is then mapped to lower-dimension features, which is fed into two sibling fully connected layers: the proposal-regression layer (termed "Proposal_bbox_pred" in Figure 7) and the proposal-classification layer (termed "Proposal_cls_score" in Figure 7). At each position, the small network simultaneously predicts multiple region proposals and the number of maximum possible proposals; i.e., k. Therefore, the proposal-regression layer has 4k outputs encoding coordinates of k boxes, and the proposal-classification layer outputs 2k scores to give the probability of being a ship or not a ship for each proposal. The k proposals are parameterized relative to k reference boxes; namely, anchors. By default, the "proposals" are dense sliding windows of 4 scales (2,4,8,16) and 3 aspect ratios (1:1, 1:2, 2:1).
The detection network takes the entire image and the set of object proposals as input, and processes the whole image with several convolutional and max pooling layers to generate feature maps. It shares convolutional layers with RPN, where the fully connected layer demand fixed-length vectors as inputs. Therefore, the region of interest (ROI) pooling layer utilizes max-pooling to convert features inside a valid region of interest into a small feature map with fixed spatial extent. Figure 6 shows the structure of an ROI pooling layer, where each valid ROI feature map is converted into a vector with fixed length. Then, each feature vector is fed into a sequence of fully connected layers, which are finally branched into two sibling output layers; i.e., the box-regression layer (termed "Bbox_pred" in Figure 7) and the box-classification layer (termed "Cls_score" in Figure 7). The box-classification layer produces softmax probability of the ships plus a catch-all "background", and the box-regression layer outputs four real-valued numbers to calibrate the coordinates of the boxes.
Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 14 Figure 6. Structure of the region of interest (ROI) pooling layer, the proposal in the last feature map must be converted into the same size to fit the input of the fully connected layer. According to the translation-invariant property, the base proposal size defined in (3) depends on the total stride of the last convolutional layer, where NumP is the total stride. Meanwhile, the architecture of the Faster R-CNN should be determined by the ship size; i.e., a large ship needs a large receptive filed to learn instinct features and generate large proposals, while a small ship needs a relatively small receptive filed to create small proposals. Additionally, the detection resolution, also known as the minimum detectable distance between two ships, should be equal to the base proposal size. Obviously, the conventional Faster R-CNN fails to simultaneously detect large and small ships in the PolSAR images. Therefore, we propose the modified Faster R-CNN, which is capable of detecting ships of varying size. The new architecture is shown in Figure 7, where we add an additional proposal-classification layer and proposal-regression layer after the lower-level feature map (conv2) to generate small proposals. Meanwhile, we add an additional box-regression layer and box-classification layer to improve the detection accuracy for small ships. It is observed that the RPN and the detection network share the first two convolutional layers, and the modified architecture could predict proposals with differing size from the last two shared convolutional layers. As shown in Figure 7, we apply a small feature extraction network instead of a classical network architectures (e.g., VGG-16 [13], ResNet-101 [27] and DenseNet [28]) to capture the low-level visual features of the ships in the PolSAR images. These classical network architectures are designed for optical images which have the characteristics of high resolution, large target size, and refined features. Compared with the targets in the optical images, the targets in the PolSAR images just have some rough features (e.g., brightness and edge). Meanwhile, due to the low resolution of the PolSAR images of the AIRSAR and UAVSAR, the sizes of ships usually do not match with the total stride of the classical network architectures. For example, the total stride of VGG-16 is 16, while the ship size in the PolSAR images is generally less than 16 × 16 pixel units. It is worth noting that the proposals generated from the Conv2 and Conv3 are conveyed to the Conv2-based and Conv3-based detection networks, respectively. Then, the Conv2-based and Conv3-based detection networks produce softmax probability of the ships and the coordinates of the boxes. Sharing Features To improve the quality of region proposals, we first segmented the PolSAR image into sub-samples with the size of 64 × 64 pixels, and set the smallest ship size at 2 × 2 pixels. In the training stage of RPN, we randomly sample 64 anchors in an image to compute the loss function of a mini-batch, where the momentum parameter is set to 0.9, the decay parameter is set to 0.0005, and the learning rate is set to 0.01. Meanwhile, the weights are initialized from Gaussian distributions with a zero mean and standard deviation of 0.01, and the biases are initialized with a small constant of 0.1 [16]. The parameter values for setting up RPN network is determined by the best performance of the ship detection according to the references [24,25]. The modified Faster R-CNN is trained on the NVIDIA Titan-X GPU using caffe [26]. It takes advantage the GPUs, which makes for efficient prediction of object bounds and objectness scores at each position. The detection network shares the convolutional layer with RPN, and detailed architecture can be found in Figure 7. We train the detection network by backpropagation and stochastic gradient descent. Similarly, the detection network adapts the same parameter values as the RPN.
Target Fusion and Localization
As has been discussed previously, we segment the PolSAR image into sub-samples by the sliding window technique to fit the input size of DCNN and improve the ship detection performance. The stepping window structure of the segmented PolSAR image is shown in Figure 8, where the dashed Remote Sens. 2019, 11, 2862 9 of 27 rectangle indicates the edge of the PolSAR image, and the solid rectangle indicates the non-overlapping block-shifting segmentation window. Additionally, the black arrow denotes the shifting direction of the sliding window. For the target that occupies more than one sliding window, the detection window is split into red rectangles A and B. In this scenario, we need to merge them according to the geometrical relationship of the two samples and draw a bounding box of the ship. Additionally, the rectangles marked red and green are generated by two different detection networks shown in Figure 8; thus, we should also merge these detection results. Supposing that the center coordinates (x, y), width w, and height h of the split detection windows A and B are known a priori, which are defined by (x A , y A , w A , h A ) and (x B , y B , w B , h B ), respectively, then they should satisfy the two principles given below: where · 1 is L1-norm. The first inequality sets constraint on the two windows in the horizontal direction, while the second one sets constraint in the vertical direction. Threshold_l is the lower bound of the distance between two detection windows, which is determined by the detection resolution and is experimentally set to 2. Meanwhile, Threshold_h is the higher bound of the distance between two detection windows distance, and is set to be If the two detection windows satisfy merge principles given in (4) and (5), then the new detection windows are defined by where x min , y min , x max , and y max denote the left, top, right, and bottom coordinates of the bounding box, respectively.
After that, we define the new detection window to draw bounds of ships in the PolSAR image, where, x min_c , x max_c , y min_c , y max_c denote the coordinates of the detection window in the PolSAR image, x min , x max , y min , y max denote the coordinates of the detection window in the segmented samples, W index , H index denote the width and height of the segmented samples, respectively, and Ss is the stride.
Experimental Results
In the following discussions, experimental results of four measured datasets are presented to show the validity and the generality of the proposed method. Firstly, we illustrate the necessity of multi-look processing for heterogeneous PolSAR data before applying the detection algorithm by comparing the detection results of different number of looks. Meanwhile, we analyze the influence of azimuth ambiguity on ship detection performance. Because the ground truth provided by the automatic identification system (AIS) is unavailable, we discriminate between ships and their ambiguities by comparing the multi-frequency data [12], and assess the UAVSAR data by comparing images of the same scene at different time instants.
Results of AIRSAR Japan Dataset
The L-band dataset covers an area of the inland sea named Kojimawan, which is close to the Tamano City in Japan. It was acquired on 4 October 2000 using the NASA/JPL AIRSAR instrument. The extracted image has 797 × 741 pixels, corresponding to a resolution of 3.33 × 4.63 m (Range × Azimuth). Figure 9 shows the Pauli RGB image of this dataset, where 21 ships are marked by red rectangles. Obviously, the PolSAR image is too large for DCNN. Therefore, we segment the image into smaller slices by the sliding-window technique, where the stride is set as 64 pixels and the size of a slice is 64 × 64. Then, the CNN-based classifier discussed in Section 2.2 is applied for ship subsamples extraction. The CNN-based classifier discussed in Section 2.2 achieves the state-of-the-art classification performance with 99.8% accuracy on the real-measured data, and is utilized for ship subsamples extraction. After that, the modified Faster R-CNN is applied to ship detection. In the training stage, it takes about 3 h to train an accurate modified Faster R-CNN model. For illustration, Figure 10 shows typical detection results with Faster R-CNN, Figure 10a-d refer to the detection results of the original PolSAR image and Figure 10e-h refer to the detection results after multi-look processing with 9 looks. From Figure 10, it is observed that all the ships are concisely detected and marked with red and green rectangles, which are generated by feature maps of the last and the second last convolutional layers, respectively. It is worth noting that the Faster R-CNN, which generates proposals from Conv3 is termed deep Faster R-CNN, and shallow Faster R-CNN generates proposals from Conv2 (Conv2 and Conv3 are convolutional layer shown in Figure 7). Figure 10a,e shows that the all ships are clearly detected by the deep Faster R-CNN and can be individually distinguished, while the shallow Faster R-CNN detector miss the labeled A ship. Meanwhile, the large-size ship in Figure 10c,g is detected by shallow and deep Faster R-CNN, while the small ship in the right of Figure 10c,g is only detected by the shallow Faster R-CNN. The detection windows labeled A and B with respect to Figure 10a,e, and Figure 10b,f correspond to one ship, and thus they should be merged into a single window. Additionally, the detection proposals generated by feature maps from different convolutional layers should also be merged. As shown in Figure 10, there are two missed detections by using single-level feature, while robust detection performance can be achieved by using multi-level features. Figure 11 are false alarm, missed ship, and roughness-detected ship, respectively. In Figure 11a, four missed ships and no false alarms occur. Figure 11b shows that 20 ships are detected with two false alarms, and one small ship is misdetected. Note that the clutter is detected by the deep Faster R-CNN as a ship, but it is corrected in the shallow Faster R-CNN, probably because of the strong energy of the clutter and the lack of train samples with clutter. The ship detection result of the modified Faster R-CNN is depicted in Figure 11c, where 21 ships are detected with two false alarms. No missed detections occur in this case. By comparing the detection result of the traditional Faster R-CNN, the modified Faster R-CNN achieves a better detection performance for multi-size ships by combining different feature maps. Figure 11d shows the ship detection result with modified CFAR, which applies the segmentation-based CFAR detector using truncation statistics for multi-look intensity (MLI) SAR imagery [8]. For the modified CFAR detector, the detection window, truncation ratio, confidence level, subsampling factor, and false alarm rate are set to 300 × 300, 5%, 99.9%, 4, and 10 −8 , respectively [8]. As shown in Figure 11d, all ships are correctly detected; however, the modified CFAR detector misses 2 ships and four false alarms appear due to strong clutter. Figure 11e presents the ship detection result of the SPWH detector. The SPWH detector is based on the assumption that sea clutter presents a homogeneous polarimetric behavior, and there are only two kinds of scatterers (i.e., sea, ship) in the scene [12]. We can see that major ships were clearly detected by this detector. However, there exist many false alarms marked using red dash circles, and these false alarms may be caused by severe clutter. It is indicated that the sea with abnormal polarimetric characteristics would generate false alarms, and we cannot simply suppose that only two kinds of scatterers existed in the scene. Ships do not have too much appearance information in PolSAR images, and their useful visual features (e.g., brightness and edge) can be easily captured by Conv1. Figure 11f shows the ship detection performance of the shallow Faster R-CNN detector with the proposals generated by the Conv1 in RPN. There are a lot of partial structures of large ships that have not been detected. It is worth noting that the shallow Faster R-CNN generates proposals by the Conv1 in RPN that would consume a large amount of memory, which seriously reduces the speed of target detection model training and testing. Figure 11e shows the ship detection result of the fully convolutional network-based ship detector; there are 5 false alarms and no misdetected ships. Meanwhile, some clutters are wrongly detected as a part of ships marked with greed dotted circles. The detection performance shown in Figure 11e demonstrates that the ship detector based on a fully convolutional network can't mitigate the influence of the clutter. The fully convolutional network-based ship detector can output pixel-wise segmentation results [22] (sea, coast, and ship). The parameters of the fully convolutional network-based ship detector are adopted from the reference [28], while the fully convolutional network-based ship detector utilizes the same training data for the proposed ship detector. There are, in total, 31,892 samples with the size of 64 × 64 for training the ship detector based on fully convolutional network. In Figure 11, it is shown that the proposed modified Faster R-CNN detector had superior performance compared to the traditional Faster R-CNN and the modified CFAR detector with the improvement of detection probability.
The training data was generated from Pauli decomposition. To demonstrate the validity of the training data generated from Pauli decomposition, we analyze the ship detection performance with training data generated from a different decomposition. Figure 12a shows the ship detection result with training data generated from Cloude decomposition [29], there are 13 false alarms marked with red dash ellipses and no ship missed detections. Figure 12b shows the ship detection result with training data generated from Huynen decomposition [29]; there are 14 false alarms marked with red dash ellipses and 1 missed ship was marked with a pink ellipse. By comparison, it is shown that the modified Faster R-CNN with the training data generated by Pauli decomposition has the best ship detection results.
Additionally, we analyzed the influence of the number of looks on the detection performance. Figure 13 shows the detection results of the proposed detector after multi-look processing with 9 looks, 25 looks, and 49 looks, respectively. Compared to the detection result of the original PolSAR image, the detection results after multi-look processing are more accurate. Figure 10d,h show partial ship detection result of the original and multi-look processed PolSAR images, respectively, which indicate that multi-look processing can suppress speckle noise and improve the detection performance. Compared to Figure 13, the bounding box marked by the green dash ellipse in Figure 11 became rougher. With an increasing number of looks, however, some weak ships may have been misdetected as clutter because the multi-look processing make it look more like clutter, as shown in Figure 13c. Therefore, the modified Faster R-CNN detector has better performance after multi-look processing with 9 or 25 looks for the heterogeneous PolSAR images. To further validate the proposed method, the detection probability P d [12] and the figure of merit (FoM) [30] are introduced to perform performance evaluation quantitatively; i.e., Remote Sens. 2019, 11, 2862 15 of 27 where N td is the number of true detections, N f a is the number of false alarms, and N gt is the number of ground-truth targets. From Table 1, it is shown that the proposed ship detector has performance superior to the traditional Faster R-CNN and the modified CFAR, achieving high accuracy with P d = 100%, FoM = 91.7% for the Japan dataset.
The experiment is carried out on a personal computer with a 3.60-GHz Intel Core i7 processor and 64.00-GB RAM. The processing time of the shallow Faster R-CNN detector, the deep Faster R-CNN detector, proposed ship detector, the modified CFAR detector, and the shallow Faster R-CNN using Conv1 in RPN takes 2.53s, 2.71s, 3.03s, 201.9s, and 3.97s, respectively. The modified CFAR detector is a segmentation-based CFAR detection algorithm based on truncated statistics for multi-look intensity (MLI) SAR imagery. It takes around 195.3s for image segmentation due to the high computation complexity of the modified EM (Expectation Maximization) algorithm. On the contrary, all the parameters of the proposed ship detector are trained off-line, and thus the test stage takes much less time than the CFAR detector. A comparison between the execution time in Table 1 demonstrates that the proposed ship detector has a faster detection speed for complex and challenging sea clutter situations. In addition, we analyzed the influence of azimuth ambiguity on the detection performance. For the C-band measured dataset of the same scene, the extracted image has 785 × 693 pixels, and the Pauli image is shown in Figure 14a, where the targets marked by red rectangles are ships, and those marked by a cyan rectangle are ambiguities. There are 20 ships and 8 ambiguities.
The detection results of the shallow Faster R-CNN, deep Faster R-CNN, proposed ship detector, proposed ship detector after multi-look processing, the modified CFAR detector, and the ship detector based on fully convolutional network are presented in Figure 14b-e, respectively. For the modified CFAR detector, the detection window, truncation ratio, confidence level, subsampling factor, and specifics false alarms are separately set by 300 × 300, 5%, 99.9%, 4, and 10 −8 [8]. Meanwhile, the parameters of the modified CFAR are the same for other test dataset. There is one false alarm marked with red dotted ellipse and one missed ship marked with pink circle in Figure 14b. As is shown in Figure 14c, there are 3 false alarms and one missed ship. The false alarms are marked by red dotted ellipses shown in Figure 14d, and there are no missed detections. As we can see from Figure 14e, the ship detection performance has improved after multi-look processing, and there are two false alarms. Figure 14f shows that there are 17 false alarms and 2 missed ships. Meanwhile, 7 ambiguities marked by green dotted circles are misclassified as ships. Figure 14e shows that there are 13 false alarms and no missed detections. Although the ship detector based on a fully convolutional network can mitigate the influence of the azimuth ambiguities, it introduces more false alarms due to strong clutter. Compared to the modified CFAR detector, the proposed ship detector has better ability in distinguishing the ambiguities and ships because it can accurately extract different features of ships and ambiguities in the scattering intensity. Quantitative analysis on the ship detection results is listed in Table 2, which demonstrates that the proposed ship detector has performance superior to the modified CFAR detector, the fully convolutional network based ship detector, and the proposed ship detector using a multi-level feature that has better detection performance than traditional Faster R-CNN. Due to the existence of ambiguities having an adverse impact on ship detection, it is recommended that the dataset should undergo ambiguity removal beforehand.
Result of UAVSAR Gulfco Area A Dataset
The detection results on the AIRSAR data where ships are distributed, targets have demonstrated the effectiveness of the proposed detector. In this part, we further analyze the detection performances on the UAVSAR Gulfco area A dataset, where the ships are compactly distributed. The dataset is acquired by NASA/JPL L-band, quad-pol UAVSAR over a bay area in Gulfco in 2010. The extracted image is 249 × 223 pixels in size with a resolution of 7.2 × 5 m (Azimuth × Range). This image contains 39 ships in the scene. Figure 15 shows the Pauli image for reference, where the ships are marked by red rectangles. Additionally, the ships marked by green solid circles in Figure 15 are relatively compacted, which are difficult to detect by conventional Faster R-CNN. Figure 16 shows ship detection result of partial samples. It is observed that the deep Faster R-CNN were prone to take compacted ships as single ship while the shallow Faster R-CNN could detect all the compacted ships, as shown in Figure 16a,b. Figure 17a-e shows the final ship detection result of the shallow Faster R-CNN, the deep Faster R-CNN, the proposed ship detector, the modified CAFR ship detector, and the fully convolutional network based ship detector, respectively. All the ships are accurately detected without false alarms and missed detections for the shallow Faster R-CNN, the proposed ship detector, the modified CFAR ship detectors, and the fully convolutional network based ship detector. However, Figure 17b shows that there were three missed ship marked with pink circles, and three small ship are detected as one marked with green dotted ellipses. The modified CFAR achieves satisfying performance because the PolSAR data presents a homogeneous polarimetric behavior. Meanwhile, the fully convolutional network-based ship detector shows that it performed well in ship compactly distributed condition, as well as in homogeneous area. This experiment also verified that the proposed detector is capable of detecting compactly distributed ships accurately. Moreover, it proves that the deep Faster R-CNN is not suitable for small and compactly distributed ship detection. Detailed detection result of the four ship detectors can be found in Table 3.
Result of UAVSAR Gulfco Area B Dataset
The ship detection results on the AIRSAR and UAVSAR Gulfco area A datasets have demonstrated the validity and generality of the proposed ship detector. However, there are no coasts in the above datasets. To verify that the proposed ship detector can suppress the negative impact of coast on the detection result, we performed experiments on the UAVSAR Gulfco area B dataset. This L band dataset is also a product of NASA/JPL UAVSAR system acquired in Gulfco. The extracted image is 2021 × 1209 pixels in size with a resolution of 7.2 × 5 m (Azimuth × Range), and there are 22 ships in the scene. Figure 18 shows the Pauli image for reference, where ships are marked by red rectangles. Meanwhile, the targets marked by yellow rectangles are not ships with referred ground truth shown in the image. After obtaining sub-samples through the sliding-window technique, the DCNN based classifier is applied to extract samples containing ships. Figure 19a shows that most ships were detected, two false alarms marked with red dotted circles, and one miss detected ship marked with pink circles. Figure 19b shows that most ships are detected and two false alarms presented. Figure 19c shows the merged ship detection results of the proposed ship detector, where all the ships are detected with 2 false alarms marked by red dotted ellipse. Due to the resolution of the PolSAR image being comparatively low, the proposed ship detector could not learn sufficient fine features and false alarms appeared in the detection result. Meanwhile, the detection results of the modified CFAR and the fully convolutional network-based ship detector shown in Figure 19d,e further demonstrate the superiority of the proposed ship detector. The segmentation result shown in Figure 19e demonstrates that the fully convolutional network performs well, the lakes and rivers are very clear. The sea, ship, and coast are marked with blue, yellow, and green color, respectively. However, there are some false alarms which occurs because the characteristic differences between ship and some coast are too small. Detailed ship detection performance comparisons of the five detectors are shown in Table 4. Note that though there is no clutter in the detected area and ship size is moderate, the detection performance of the traditional Faster R-CNN is consistent with the proposed algorithm.
Result of AIRSAR Taiwan Area Dataset
To further demonstrate the effectiveness of the proposed modified Faster R-CNN ship detector and to verify the performance of the proposed method in inshore scenery, we perform experiments on the AIRSAR Taiwan area dataset in L band. Figure 20 shows the Pauli RGB image of the AIRSAR Taiwan area dataset and the extracted image is 1527 × 1277 pixels in size with a resolution of 2.5720 × 1.6655 m (Azimuth × Range). Figure 20 shows a complex and challenging sea situation for ship detection. There are multiple small weak ships appearing in the image, and many ships spread over the inshore. There are about 132 ships marked with red rectangle by visual inspection. Figure 21 demonstrates that the proposed ship detector can provide a more excellent performance than the traditional Faster R-CNN, the modified CFAR, and the fully convolutional network-based ship detector. The proposed ship detector is sensitive enough to clearly detect and distinguish small and close located ships. It is worth noting that there were 14 false alarms observed around the coast edge because coast and ships have many similar image features in low-resolution PolSAR images. Moreover, the proposed ship detector completely missed the 8 ships because some samples contain ships were wrongly classified as coast. Compared with the traditional faster R-CNN and proposed ship detector, the performance of the modified CFAR and fully convolutional network-based ship detector was poor. There were many false alarms due to the complex inshore condition. Meanwhile, compared with the segmentation result shown in Figure 19e, the segmentation result shown in Figure 21e were worse, especially for coast. This situation may occur because there were no similar coastal samples in the training samples. However, the proposed ship detector performed well in such inshore areas. Detailed ship detection performance comparisons of the five detectors are shown in Table 5.
Discussion
In this paper, we developed a modified Faster R-CNN ship detector for PolSAR images. Compared with previous ship detection algorithms for PolSAR, the modified Faster R-CNN ship detector could capture the difference between the ship and clutter. Therefore, it performed well and effectively detected ships of multiple size. Four ship detection experiments performed on the measured PolSAR images in different condition demonstrates the effectiveness of the proposed ship detector. Meanwhile, the proposed ship detector had the ability to mitigate the influence of the azimuth ambiguities on the ship detection performance. Simultaneously, the modified Faster R-CNN ship detector had good performance in inshore scenery, expanding the scope of application of the proposed algorithm. However, the ship detection result presented in the last experiment shows that some small ships near land were more easily misdetected, and some coasts would be recognized as ships using the proposed ship detector. This might have occurred because the characteristic difference between ship and coast is very small in low resolution PolSAR images. In the future, we will introduce more additional features and use deep learning to improve the accuracy of ship detection for PolSAR.
Conclusions
In this paper, a DCNN based ship detection algorithm for PolSAR images is proposed. To mitigate the influence of the coast on ship detection, a three-class classifier based on DCNN was utilized to accurately extract samples containing ships. Compared with conventional Faster R-CNN, the modified Faster R-CNN could generate proposals of differing size from multi-level feature maps of the last two convolutional layers. Experimental results of four measured datasets have shown that the improvement in Faster R-CNN facilities fast and accurate detection performance for ships of differing size, especially for the compactly distributed ships and small ships. Additionally, we investigated the influence of multi-look processing, polarimetric decomposition methods and azimuth ambiguities on the detection performance for PolSAR images. Moreover, we performed an experiment on inshore scenery to demonstrate the effectiveness of the proposed ship detector.
Future works will focus on the methods of combining the deep learning and Bayesian theory to extract the structure, texture, and statistical characteristics of the ship, and further improve the detection performance. | 8,863.4 | 2019-12-02T00:00:00.000 | [
"Engineering",
"Computer Science",
"Environmental Science"
] |
On CSQ-normal subgroups of finite groups
Abstract We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.
Basic definitions and preliminary results
The lemma presented below is crucial in the sequel. The proof is a routine check, and we omit its details. Lemma 2.2. Suppose that every proper subgroup of a group G is nilpotent but G itself is not nilpotent. Then (1) There exist some primes p and q such that jGj D p˛qˇ.
(2) G has a normal Sylow q-subgroup Q; if q > 2, then exp.Q/ D q and if q D 2, then exp.Q/ Ä 4; G also has a cyclic Sylow p-subgroup P D hai. ; c a p 2 ; c a p 1 i, namely, Q D hOEc; a; OEc; a a ; ; OEc; a a p 1 i.
As in [8], a minimal nonsupersolvable group is a nonsupersolvable group whose proper subgroups and quotients are supersolvable.
Lemma 2.3. Suppose that a group G is minimal nonsupersolvable. Then G is isomorphic to a group of the form G t for 1 Ä t Ä 6, where the groups G t are defined in the following way.
(II) G 2 D ha, c 1 i and jG 2 j D p˛r p and p˛ 1 kr 1, where˛ 2. a p˛D c r where the exponent of t .mod r/ is p˛ 1 . (III) G 3 D ha; b; c 1 i and jG 3 j D 8r 2 and 4 j r 1, where the exponent of s .mod r/ is 4. (IV) G 4 D ha, b, c 1 i and jG 4 j D p˛Cˇr p and p maxf˛;ˇg j r 1, whereˇ 2. a p˛D b pˇD c r , i D 1, 2, : : : , p; where the exponents of t and u .mod r/ are p˛ 1 and pˇ, respectively. (V) G 5 D ha; b; c; c 1 i and jG 5 j D p˛CˇC 1 r p and p maxf˛;ˇg j r 1.
where the exponents of t, v and u .mod r/ are p˛ 1 , pˇand p, respectively. (VI) G 6 D ha; b; c 1 i, jG 6 j D p˛qr p and p˛q j r 1, p j q 1,˛ 1.
where the exponents of t, v .mod r/ are p˛ 1 and q, respectively, and the exponent of u .mod q/ is p.
Proof. (a) By the hypothesis, H is S -quasinormal in hH; H g i for all g 2 G. Then for any x 2 G, we have that H x is S -quasinormal in hH x ; H gx i=hH x ; .H x / g x i for all g 2 G. Then one checks easily that W G ! G, defined by is a bijective map. Since g x runs over G as g does for fixed x, we get that H x is S-quasinormal in hH x ; .H x / g x i for all g x 2 G. Thus H x is a CSQ-normal subgroup of G.
(b) By the hypothesis, H is S-quasinormal in hH; H g i for all g 2 G. By [5, Theorem 1], we know that H is subnormal in hH; H g i for all g 2 G, so H is subnormal in G by Wielandt's theorem.
Main results
Let Z be a complete set of Sylow subgroups of a group G, that is, for each prime p dividing the order of G, Z contains exactly one Sylow p-subgroup of G. Let Z\E D fP \ E j P 2Zg.
Theorem 3.1. Let G be a group and Z be a complete set of Sylow subgroups of G. Suppose that E E G such that G=E is nilpotent and G is G 1 -free. If every cyclic subgroup of a Sylow subgroup of E contained in Z \ E is a CSQ-normal subgroup of G, then G is nilpotent.
Proof. Assume that the result is false, and let G be a counterexample with least .jGj C jEj/. Let Hence all cyclic subgroups of K p contained in Z are CSQ-normal in H , and thus H and its normal subgroup K satisfy the hypothesis. By the minimal choice of jGj C jEj, H is nilpotent. By Lemma 2.2, we may assume that G D P Q, where Q is a normal Sylow q-subgroup of G and P is a cyclic Sylow p-subgroup of G.
Suppose that N C G. We shall prove that .G=N; EN=N / satisfies the hypothesis. Clearly, .G=N /=.EN=N / Š G=EN is nilpotent and G=N is G 1 -free. Let H=N be a cyclic subgroup of a Sylow subgroup of EN=N \ ZN=N . Then we may assume H D hxN i and hxi is a cyclic subgroup of a Sylow subgroup in E \ Z. By the hypothesis, hxi is CSQ-normal in G and by Lemma 2.1 .b/, H=N is CSQ-normal in G=N . Then .G=ˆ.G/; E=ˆ.G// satisfies the hypothesis of the theorem. The minimality of jGjCjEj implies that G=ˆ.G/ is nilpotent and so is G, a contradiction. Thusˆ.G/ D 1 and so G Š G 1 , again a contradiction. This shows that there exists no counterexample, so the result is true.
Remark 3.2. We cannot replace the condition "cyclic subgroup of Sylow subgroup" by "minimal subgroup of a Sylow subgroup" in Theorem 3.
Obviously, the pair .G; E/ satisfy the hypothesis. Nevertheless, it is not nilpotent.
Remark 3.3. The condition of "G is G 1 -free" cannot be removed. For example, let G D S 3 and choose E D A 3 . Then the pair .S 3 ; A 3 / satisfy the hypothesis of Theorem 3.1. Nevertheless, S 3 is not nilpotent.
Corollary 3.4. Let G be a group and Z be a complete set of Sylow subgroups of G. If every cyclic subgroup of a Sylow subgroup of G contained in Z is a CSQ-normal subgroup of G, then G is nilpotent.
Proof. By the proof of Theorem 3.1, we just need to check that G Š G 1 . By the hypothesis, we have that a p-Sylow To prove Theorem 3.6, we need the following Lemma 3.5.
Lemma 3.5. Let G be a group and Z be a complete set of Sylow subgroups of G. Suppose that P is a Sylow psubgroup of G contained in Z, where p is a prime divisor of jGj with .jGj; p 1/ D 1. If every maximal subgroup of P is CSQ-normal in G, then G=O p .G/ is p-nilpotent and hence G is solvable.
Proof. Assume that the result is false and let G be a counterexample of smallest order. Let P 1 be a maximal subgroup of P . By the hypothesis, P 1 is CSQ-normal subgroup of G. Then P 1 is subnormal in G by Lemma 2.4, and thus P 1 Ä O p .G/ D 1. Hence P is a cyclic subgroup of order p. Since N G .P /=C G .P / . Aut .P /, we get that the order of N G .P /=C G .P / must divide .jGj; p 1/ D 1. Then N G .P / D C G .P /. Thus G is p-nilpotent by [1, Burnside's theorem] , a contradiction. We conclude that there is no counterexample and Lemma 3.5 is proved.
Theorem 3.6. Let G be a group and Z be a complete set of Sylow subgroups of G. Suppose that G is G t -free with t 2 f1; 2; 6g and every maximal subgroup of any non-cyclic Sylow subgroup of G contained in Z is CSQ-normal in G. Then G is supersolvable.
Proof. Assume that the theorem is false and let G be a counterexample of smallest order. We proceed in a number of steps.
If every Sylow subgroup of G contained in Z is cyclic, then every Sylow subgroup of G is cyclic, thus G is supersolvable. Next we assume that there is a non-cyclic Sylow p-subgroup contained in Z.
Let p D min .G/ and P be a Sylow p-subgroup of G contained in Z. If P is cyclic, then G is p-nilpotent, so G is solvable. If P is not cyclic, then G=O p .G/ is p-nilpotent by Lemma 3.5, thus G is solvable. Hence we have Step 1.
Step 2. G has a unique minimal normal subgroup N andˆ.G/ D 1.
Let N be a minimal normal subgroup of G, then ZN=N be a complete set of Sylow subgroups of G=N . Let PN=N 2 Syl p .G=N /, where P 2 Z and PN=N is non-cyclic. (Of course, P is non-cyclic.) Assume that T =N be a maximal subgroup of PN=N . Then T D T \ PN D .T \ P /N . Suppose that T \ P D P 1 . Then P 1 \ N D T \ P \ N D P \ N . Hence jP W P 1 j D jPN=N W P 1 N=N j D jPN=N W T =N j D p: By the hypothesis, P 1 is CSQ-normal in G, so P 1 N=N D T =N is CSQ-normal in G=N by Lemma 2.1 .b/. Thus G=N satisfies the hypothesis. By the choice of G, we obtain that G=N is supersolvable. Similarly, if N 1 is another minimal normal subgroup of G. Then G=N 1 is also supersolvable. Now it follows that G Š G=N \ N 1 is supersolvable, a contradiction. Hence, N is the unique minimal normal subgroup of G. If N Ĉ.G/, then the supersolvability of G=N implies the supersolvability of G. Hence,ˆ.G/ D 1. Therefore, we have Step 2.
Step 3. N D O p .G/ D P , C G .N / D N and jGj D p n r˛1 1 r˛2 2 r˛s s , the Sylow r i -subgroup of G is cyclic, where 1 Ä i Ä s,˛i 1.
By Step 1 and Step 2, we know that N is an elementary abelian p-subgroup and N D F .G/ D O p .G/ Ä P , so C G .N / D N . Assume that N < P . Given a maximal subgroup P 1 of P , by the hypothesis, P 1 is a CSQ-normal subgroup of G, then P 1 is subnormal in G by Lemma 2.4, so P 1 Ä O p .G/ D N < P . If N D P 1 C G, we get that P has a unique maximal subgroup, so P is cyclic and hence so is N . By Step 2, we obtain that G=N is supersolvable, hence so is G, a contradiction. Therefore, we have N D P . Suppose that R i is a non-cyclic Sylow r i -subgroup of G contained in Z for some natural number i , 1 Ä i Ä s, and jR i j D r˛i i . Then˛i 2, so we can choose 1 6 D R i1 to be a maximal subgroup of R i 2 Syl r i .G/. By the hypothesis, R i1 is CSQ-normal in G, so R i1 is subnormal in G by Lemma 2.4, so 1 6 D R i1 Ä O r i .G/. By the uniqueness of N , this is impossible. Hence R i is cyclic, and thus all Sylow subgroups B of G are cyclic except B D P . Hence we have the assertion in Step 3.
Step 4. Let E be a maximal subgroup of G. We show that jG W Ej D jP j D p n or rˇi i , whereˇi IJi . Then E satisfies the hypothesis, so E is supersolvable.
Since G is solvable, jG W Ej D p j or rˇi i , where j Ä n,ˇi IJi . Suppose that jG W Ej D p j . By Step 2 and Step 3, it is easy to show G D NE and N \ E D 1, so E D R 1 R 2 R s and j D n, where R i 2 Syl r i .G/ (1 Ä i Ä s). It is clear that E satisfies the hypothesis by Lemma 2.1 .a/, so E is supersolvable.
Step 5. Final contradiction. By Step 2 and Step 4, we know that G is minimal nonsupersolvable. On the other hand, by Step 4 and the hypothesis, G is not isomorphic to any group G i in Lemma 2.3. We conclude that there is no minimal counterexample and Theorem 3.6 is proved.
If we remove "non-cyclic" in the hypothesis of Theorem 3.6, we can get the following Theorem.
Theorem 3.7. Let G be a group and Z be a complete set of Sylow subgroups of G. Suppose that G is G 1 -free and G 6 0 -free, where G 6 0 . G 6 and jG 6 0 j D pqr p , that is, the case˛D 1. If every maximal subgroup of every Sylow subgroup of G contained in Z is a CSQ-normal subgroup of G, then G is supersolvable.
Proof. By the proof of Theorem 3.6, we only need to check G Š G 2 and G Š G 6 , where jG 6 j D p˛qr p and p˛q j r 1, p j q 1,˛ 2. Assume that G Š G 2 . Using the same description as in Lemma 2.3, let V 1 D ha p i. Then it is a maximal subgroup of P . By the hypothesis where the exponent of t .mod r/ is p˛ 1 . Thus r divides Therefore, R i normalizes V 1 and, of course, c i normalizes V 1 . Since i was arbitrary, we conclude that V 1 is normalized by P and R, where P 2 Syl p .G/, R 2 Syl r .G/. If˛ 2, then 1 6 D V 1 C G, which is impossible. If˛D 1, then G Š G 1 , a contradiction. Hence G is not isomorphic to G 1 . As in a similar argument above, we also get that G is not isomorphic to G 6 , where jG 6 j D p˛qr p and p˛q j r 1, p j q 1,˛ 2. The proof is completed.
Corollary 3.8. [9, Theorem 2] Let G be a group with the property that maximal subgroups of Sylow subgroups are -quasinormal in G for D .G/. Then G is supersolvable.
Proof. By the proof of Theorem 3.6 and Theorem 3.7, we only need to check that G Š G 1 and G Š G 6 0 , where jG 6 0 j D pqr p and pq j r 1, p j q 1. Assume that G Š G 1 . By Lemma 2.3, we have G 1 D PQ, where jP j D p and jQj D qˇ.ˇ 2/. By Step 2 and Step 3 of Theorem 3.6, Q is a minimal normal subgroup of G 1 . Choosing Q 1 to be a maximal subgroup of Q, by the hypothesis, we obtain that Q 1 is -quasinormal in G 1 . Then O q .G/ Ä N G .Q 1 /, so P normalizes Q 1 , and thus 1 ¤ Q 1 C G, contrary to the minimality of Q. Hence G © G 1 . Using a similar argument as above, we also get that G is not isomorphic to G 6 0 . The proof is completed. Proof. Assume that the Theorem is false and let G be a counterexample of smallest order.
Assume first that G has odd order. Since G is a QCLT -group, by [6], we have that G is supersolvable. Now we assume that 2 j jGj. By Lemma 3.5, we have that G is solvable. For any 1 ¤ N E G, if 2 − jG=N j, then G=N is a QCLT -group of odd order and hence G=N is supersolvable. Suppose that 2 j jG=N j. Without loss of generality, we assume that every maximal subgroup of a Sylow 2-subgroup of G=N is of the form P 1 N=N , where P 1 is a maximal subgroup of a Sylow 2-subgroup of G. Then P 1 is CSQ-normal in G by hypothesis, so P 1 N=N is CSQ-normal in G=N by Lemma 2.1 .b/. Hence the quotient group G=N satisfies the hypothesis. By the choice of G, we have that G is a solvable outer-supersolvable group. Then, by [7, Theorem 7.1], G D ML, where M is a maximal subgroup of G, M \ L D 1, L is an elementary abelian p-group and is also the unique minimal normal subgroup of G with order p˛,˛> 1, the Sylow p-subgroup of M is an abelian p-group andˆ.G/ D 1.
If jG 2 j Ä 4, where G 2 2 Syl 2 .G/, then G 2 is a cyclic subgroup or an elementary abelian 2-subgroup. It follows that G is S 4 -free, then G is supersolvable by [10, Theorem 4], a contradiction. Hence we may choose 1 ¤ P 1 to be a maximal subgroup of G 2 . By hypothesis, P 1 is a CSQ-normal subgroup of G. Then P 1 is subnormal in G by Lemma 2.4, thus 1 ¤ P 1 Ä O 2 .G/, hence L Ä O 2 .G/, so we get p D 2. By [7, 6.1, Main lemma], we also get O 2 .G/ D F .G/ D L.
Let M 2 be a Sylow 2-subgroup of M . Then G 2 D M 2 L is a Sylow 2-subgroup of G. Assume that P 1 is a maximal subgroup of M 2 N containing M 2 . Then M 2 < P 1 since jLj D 2˛, where˛> 1. Then P 1 is CSQ-normal in G by the hypothesis, so P 1 is subnormal in G by Lemma 2.4. Thus P 1 Ä O 2 .G/ D L, hence G 2 D M 2 L D P 1 L D L is an elementary abelian Sylow 2-subgroup of G. It follows that G is S 4 -free, so G is supersolvable by [10, Theorem 4], a contradiction. Hence the minimal counterexample does not exist. Therefore G is supersolvable.
Theorem 3.11. Let G be a QCLT -group. If every 2-maximal subgroup of a Sylow 2-subgroup of G is CSQ-normal in G. Then G is supersolvable.
Proof. The proof is similar to Theorem 3.10 and omitted here. | 4,390.4 | 2016-01-01T00:00:00.000 | [
"Mathematics"
] |
Robust Real-Time Detection of Laparoscopic Instruments in Robot Surgery Using Convolutional Neural Networks with Motion Vector Prediction
: More than half of post-operative complications can be prevented, and operation performances can be improved based on the feedback gathered from operations or notifications of the risks during operations in real time. However, existing surgical analysis methods are limited, because they involve time-consuming processes and subjective opinions. Therefore, the detection of surgical instruments is necessary for (a) conducting objective analyses, or (b) providing risk notifications associated with a surgical procedure in real time. We propose a new real-time detection algorithm for detection of surgical instruments using convolutional neural networks (CNNs). This algorithm is based on an object detection system YOLO9000 and ensures continuity of detection of the surgical tools in successive imaging frames based on motion vector prediction. This method exhibits a constant performance irrespective of a surgical instrument class, while the mean average precision (mAP) of all the tools is 84.7, with a speed of 38 frames per second (FPS)
Introduction
According to the World Health Organization (WHO), complications in inpatient surgical operations occur for at most 25% of the patients, and at least half of the cases in which surgery led to harm or damage are considered preventable [1]. This means that improvement of surgical performance can lead to better outcomes of surgical operations. Surgical performance can be improved through sophisticated remote manipulation of the robot [2][3][4], but surgical feedback also has a positive effect on surgical performance [5]. While manual evaluation methods such as the objective structured assessment of technical skills (OSATS), and the global operative assessment of laparoscopic skills (GOALS) can assess the surgical skills and are beneficial in terms of their improvements, it is both time and labor consuming, because surgeries could last multiple hours [6,7]. Manual assessment is subjective to observer bias and can lead to subjective outcomes [8]. Detection of surgical instruments is one of the indicators used for the analysis of surgical operations and it can be useful for the effective and objective analysis of surgery [9]. This also helps prevent surgical tool collision by informing the operator during the procedure [10].
Various approaches have been published on surgical tool detection. Cai et al. [11] imaged markers, which were placed on surgical instruments with the use of two infrared cameras. Kranzfelder et al. [12] presented an approach based on radiofrequency identification (RFID) for real-time tracking of Kranzfelder et al. [12] presented an approach based on radiofrequency identification (RFID) for realtime tracking of laparoscopic instruments. However, at present, there is no proper and reliable antenna system for routine intraoperative applications [12]. However, detection tools utilizing markers interfere with the surgical workflow and require modifications of the tracked instrument [13].
Efforts have been expended to develop vision-based and marker-less surgical tool detection using feature representations, based on color [14,15], gradients [16], or texture [17]. Speidel et al. [18] segmented the instruments in images and recognized their types based on three-dimensional models. Many researchers have also addressed surgical tool detection with the use of convolutional neural networks. Putra et al. [19] proposed for the first time the use of a CNN for multiple recognition tasks on laparoscopic videos. Several works [20][21][22] of surgical tool detection by CNNs have been proposed as a part of the M2CAI 2016 tool presence detection challenge [23]. Jin et al. [24] performed surgical tool localization and phase recognition in cholecystectomy videos based on faster R-CNN. Bodenstedt [25] proposed a new method to detect and to identify surgical tools by calculating a bounding box using a random forest algorithm, and then, extracting multiple features from each bounding box. Shvets et al. [26] introduced a method of robotic instrument semantic segmentation based on deep learning, in both binary and multiclass settings. However, these studies dealt with tool detection in a frame-wise manner, but did not employ time information, and did not detect tools in real time.
In this study, we address the issue of tool detection in laparoscopic surgical videos. Our method is faster and more accurate than cutting-edge technologies [20][21][22]24], and it can be applied during surgery or real-time analyses. We propose a new method to detect the surgical tool in laparoscopic images using YOLO9000 [27] and detect missing surgical tools based on motion vector prediction.
Surgical Tool Detection
The proposed algorithm consists of two stages. The first step aims to detect the surgical tool used in the current frame based on YOLO9000. The second step is to check for the presence of the surgical tools that were not detected in the first step, and to detect them additionally ( Figure 1).
Figure 1.
Flow chart of the proposed algorithm. The top rectangle is the detection step of the surgical tool in the current frame using YOLO9000, and the rest in the upper-right direction pattern corresponds to the missing tool detection step.
Detection with YOLO9000
The proposed method detects a surgical tool using YOLO9000, which is based on a convolutional neural network (CNN). CNN usually draws feature maps from input images using convolutional and pooling layers. In the convolutional layer, the filter extracts the pattern corresponding to each filter in the entire image area based on a convolution operation. Alternatively, the pooling layer generally reduces the size of the output of the preceding convolutional layer, thereby reducing the size of feature map inputs to the next layer, and consequently reduces the total number of parameters required for training. Maximum pooling and average pooling are mainly used for CNN.
You Only Look Once (YOLO) is one of CNN-based detection methods and is suitable for real-time processing. As the general region-based CNN identifies the region-of-interest directly from every input image, it requires considerable computation to detect the position of an object. As a result, it is difficult to detect an object in real time. However, YOLO divides all input images into S × S grid cells. Additionally, the size of the bounding box is set in advance. To be specific, the bounding box is preset by clustering using the box size of the ground truth in the training dataset. Therefore, during training or testing, only B pre-defined bounding boxes are calculated for each grid cell. This is a major difference between YOLO and region-based CNNs, such as the faster R-CNN, and this is the reason why YOLO can detect objects in real time.
The algorithm we used for the purposes of this study is YOLO9000, which is the second of the three versions of YOLO. YOLO9000 uses small grid cells and changes layers to improve accuracy over the previous versions of YOLO. Figure 2 shows the difference between the first version (V1) [28] and the second version (V2) of YOLO. In V1, S is 7 and B is 2, but S is 13 and B is 5 in V2. V2 uses more bounding boxes compared to V1. This is because the size of one grid cell is reduced by increasing the number of grid cells. As a result, it is easy to detect smaller objects. In V1, the configuration of each grid cell in the last layer is (5 × B + C), but it is (5 + C) × B in V2. C is the number of classes. In V1, the probability that a grid cell corresponds to each class is calculated separately from the probability that each bounding box contains an object. By multiplying these two values, the class to which each bounding box corresponds can be determined. In V2, however, class and object probabilities are obtained for each bounding box unit. Furthermore, the fully connected layer of V1 is replaced with the convolutional layer in V2. Therefore, it is designed so that it does not lose spatial information. Finally, unlike V1, V2 uses batch normalization on the convolutional layer to enhance the learning effect in the mini batch. Leaky ReLU [29] is also applied as an activation function for nonlinearity between layers, and maximum pooling is applied. Based on the differences, we applied YOLO9000, that can better preserve the spatial location information of tools for surgical tool detection.
corresponds to the missing tool detection step.
Detection with YOLO9000
The proposed method detects a surgical tool using YOLO9000, which is based on a convolutional neural network (CNN). CNN usually draws feature maps from input images using convolutional and pooling layers. In the convolutional layer, the filter extracts the pattern corresponding to each filter in the entire image area based on a convolution operation. Alternatively, the pooling layer generally reduces the size of the output of the preceding convolutional layer, thereby reducing the size of feature map inputs to the next layer, and consequently reduces the total number of parameters required for training. Maximum pooling and average pooling are mainly used for CNN.
You Only Look Once (YOLO) is one of CNN-based detection methods and is suitable for realtime processing. As the general region-based CNN identifies the region-of-interest directly from every input image, it requires considerable computation to detect the position of an object. As a result, it is difficult to detect an object in real time. However, YOLO divides all input images into S × S grid cells. Additionally, the size of the bounding box is set in advance. To be specific, the bounding box is preset by clustering using the box size of the ground truth in the training dataset. Therefore, during training or testing, only B pre-defined bounding boxes are calculated for each grid cell. This is a major difference between YOLO and region-based CNNs, such as the faster R-CNN, and this is the reason why YOLO can detect objects in real time.
The algorithm we used for the purposes of this study is YOLO9000, which is the second of the three versions of YOLO. YOLO9000 uses small grid cells and changes layers to improve accuracy over the previous versions of YOLO. Figure 2 shows the difference between the first version (V1) [28] and the second version (V2) of YOLO. In V1, S is 7 and B is 2, but S is 13 and B is 5 in V2. V2 uses more bounding boxes compared to V1. This is because the size of one grid cell is reduced by increasing the number of grid cells. As a result, it is easy to detect smaller objects. In V1, the configuration of each grid cell in the last layer is (5 × B + C), but it is (5 + C) × B in V2. C is the number of classes. In V1, the probability that a grid cell corresponds to each class is calculated separately from the probability that each bounding box contains an object. By multiplying these two values, the class to which each bounding box corresponds can be determined. In V2, however, class and object probabilities are obtained for each bounding box unit. Furthermore, the fully connected layer of V1 is replaced with the convolutional layer in V2. Therefore, it is designed so that it does not lose spatial information. Finally, unlike V1, V2 uses batch normalization on the convolutional layer to enhance the learning effect in the mini batch. Leaky ReLU [29] is also applied as an activation function for nonlinearity between layers, and maximum pooling is applied. Based on the differences, we applied YOLO9000, that can better preserve the spatial location information of tools for surgical tool detection.
(a) Although YOLO9000 adjusts the size of the grid cell and uses identity mapping to detect small objects, it is still difficult to detect small-sized surgical tools, because the input image is resized to 416 × 416, which is typically a smaller size compared to the original image. To solve this problem, the third version of YOLO [30] detects objects at three scale levels according to the residual skip connection and upsampling. In addition, multiple label classifications are possible. As a result, the object detection ratio increases, but the computational time also increases, and the speed decreases. For this reason, the third version of YOLO is not suitable for surgical tool detection in real time. The surgical tool detection problem consists of seven classes and requires a single-label classification in real time. Therefore, in the proposed method, it is performed by applying YOLO9000, and the missing tools are additionally detected through motion vector prediction with tool mapping.
Missing Tool Detection with Motion Vector Prediction
The missing tool detection process is subdivided into the following steps-a tool mapping and a tool redetection. In the tool mapping step, the presence of a missing tool is checked. To be specific, the tools identified in the current frame (t) are compared to that of the previous frame (t−1), based on the number and class. If one or more of the tools of this frame (t) have the same class as the tools of the previous frame (t−1), the tool that is closest to the tool of the previous frame (t−1) is considered as the same tool in the current frame (t). Conversely, if a tool only exists in the previous frame (t−1), it is determined that a missing tool exists.
Once the existence of the missing tool is confirmed, motion vector prediction is performed as shown in Figure 2. As the YOLO9000 classifies the surgical tool using a predetermined bounding box, if the main feature of the surgical tool is located at the boundary of the bounding box due to the movement of the surgical tool, it cannot be detected. Therefore, the proposed algorithm predicts the position of the surgical tool in the current frame using the position of the surgical tool in the previous two frames. This prediction is based on the center point of the surgical tool. More specifically, the motion vector (MV) of the surgical tool is calculated using the position of the surgical tool in the previous two frames (Equation (1)).
By adding the value of this motion vector to the position vector of the previous frame (( −1 , −1 )), the position in the current frame ((̂,̂)) is predicted (Equation (2)).
Tool detection is performed again with the use of the trained network by inputting the cropped image at the pre-determined size based on the predicted position of the tool. The size of the newly Although YOLO9000 adjusts the size of the grid cell and uses identity mapping to detect small objects, it is still difficult to detect small-sized surgical tools, because the input image is resized to 416 × 416, which is typically a smaller size compared to the original image. To solve this problem, the third version of YOLO [30] detects objects at three scale levels according to the residual skip connection and upsampling. In addition, multiple label classifications are possible. As a result, the object detection ratio increases, but the computational time also increases, and the speed decreases. For this reason, the third version of YOLO is not suitable for surgical tool detection in real time. The surgical tool detection problem consists of seven classes and requires a single-label classification in real time. Therefore, in the proposed method, it is performed by applying YOLO9000, and the missing tools are additionally detected through motion vector prediction with tool mapping.
Missing Tool Detection with Motion Vector Prediction
The missing tool detection process is subdivided into the following steps-a tool mapping and a tool redetection. In the tool mapping step, the presence of a missing tool is checked. To be specific, the tools identified in the current frame (t) are compared to that of the previous frame (t−1), based on the number and class. If one or more of the tools of this frame (t) have the same class as the tools of the previous frame (t−1), the tool that is closest to the tool of the previous frame (t−1) is considered as the same tool in the current frame (t). Conversely, if a tool only exists in the previous frame (t−1), it is determined that a missing tool exists.
Once the existence of the missing tool is confirmed, motion vector prediction is performed as shown in Figure 2. As the YOLO9000 classifies the surgical tool using a predetermined bounding box, if the main feature of the surgical tool is located at the boundary of the bounding box due to the movement of the surgical tool, it cannot be detected. Therefore, the proposed algorithm predicts the position of the surgical tool in the current frame using the position of the surgical tool in the previous two frames. This prediction is based on the center point of the surgical tool. More specifically, the motion vector (MV) of the surgical tool is calculated using the position of the surgical tool in the previous two frames (Equation (1)).
By adding the value of this motion vector to the position vector of the previous frame ((x t−1 , y t−1 )), the position in the current frame ((x t ,ŷ t )) is predicted (Equation (2)).
of 13
Tool detection is performed again with the use of the trained network by inputting the cropped image at the pre-determined size based on the predicted position of the tool. The size of the newly input image is set to be less than or equal to 416 × 416, which is the size of the input image of YOLO9000, so that the smaller objects can also be visible more easily. Comparison of the second result to the first result obtained based on the tool detection process, and if the intersection of the union (IOU) of the bounding box of the two results is more than 0.5, we regard that the same tool is detected twice. Accordingly, we discard the second result.
Experimental Conditions and Results
We performed experiments on Ubuntu 16.04 using a GPU NVIDIA GeForce GTX 1080, with 16 GB of memory, and a CPU Intel core i7-4770K. The training dataset was created with the use of vertical flip, horizontal flip, or both, to generate the 1st to the 7th videos at m2cai16-tool-locations, thus resulting in 7492 images in total ( Figure 3). In addition, the 10th video of m2cai16-tool-locations was used as the validation set. Regarding the test set, the 8th and 9th videos from m2cai16-tool-locations [31] and the videos 11-15 of the m2cai16-tool dataset [32] were used. The number of each class and the total number of images included in training and test videos are shown in Table 1.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 13 to the first result obtained based on the tool detection process, and if the intersection of the union (IOU) of the bounding box of the two results is more than 0.5, we regard that the same tool is detected twice. Accordingly, we discard the second result.
Experimental Conditions and Results
We performed experiments on Ubuntu 16.04 using a GPU NVIDIA GeForce GTX 1080, with 16 GB of memory, and a CPU Intel core i7-4770K. The training dataset was created with the use of vertical flip, horizontal flip, or both, to generate the 1st to the 7th videos at m2cai16-tool-locations, thus resulting in 7492 images in total ( Figure 3). In addition, the 10th video of m2cai16-tool-locations was used as the validation set. Regarding the test set, the 8th and 9th videos from m2cai16-toollocations [31] and the videos 11-15 of the m2cai16-tool dataset [32] were used. The number of each class and the total number of images included in training and test videos are shown in Table 1. 13.37). The weight used in training was pre-trained using visual object classes (VOC), and nonmaximal suppression (NMS) [28] was applied.
We compared the performance of the proposed method with results presented in other studies conducting experiments on the same dataset. Table 2 and Figure 4 show the performance estimates for our proposed algorithm, for the winner of the 2016 M2CAI Tool Presence Detection Challenge, and for the algorithm based on the Faster R-CNN [33]. We also compared the performance of the proposed method-the algorithm using the second version of YOLO and motion vector prediction-with the results obtained in our previous work [34] for the algorithm using the first version of YOLO. Moreover, we performed the comparison of the proposed algorithm with the deformable part models (DPM) [35] and EndoNet [19], which used different datasets to detect surgical tools. The performance comparison was conducted based on the mAP estimates [24]. As shown in Table 2, the proposed method has a higher mAP than the alternative algorithms including the winners of the M2CAI Tool Presence Detection Challenge. This observation was obtained based on the average of all considered tools. Figure 4 shows the mAP values for each class of algorithms, except for the Raju study. The proposed algorithm showed lower performance than some algorithms for such surgical instruments as hook and clipper, but the mAP of all classes was over 80, showing uniform performance regardless of class. We compared the performance of the proposed method with results presented in other studies conducting experiments on the same dataset. Table 2 and Figure 4 show the performance estimates for our proposed algorithm, for the winner of the 2016 M2CAI Tool Presence Detection Challenge, and for the algorithm based on the Faster R-CNN [33]. We also compared the performance of the proposed method-the algorithm using the second version of YOLO and motion vector predictionwith the results obtained in our previous work [34] for the algorithm using the first version of YOLO. Moreover, we performed the comparison of the proposed algorithm with the deformable part models (DPM) [35] and EndoNet [19], which used different datasets to detect surgical tools. The performance comparison was conducted based on the mAP estimates [24]. As shown in Table 2, the proposed method has a higher mAP than the alternative algorithms including the winners of the M2CAI Tool Presence Detection Challenge. This observation was obtained based on the average of all considered tools. Figure 4 shows the mAP values for each class of algorithms, except for the Raju study. The proposed algorithm showed lower performance than some algorithms for such surgical instruments as hook and clipper, but the mAP of all classes was over 80, showing uniform performance regardless of class. Table. 2, except the Raju method. Table 3 compares the speed of the proposed algorithm against that of three different algorithms-two algorithms with high performance according to the results provided in Table 2, and an algorithm using random forests [25]. Algorithms using random forests automatically generate bounding boxes and determine the instrument type of the bounding box. The speed comparison is based on frames per second (FPS) and allows estimating the accuracy of each algorithm. The accuracy estimate of each algorithm was based on the values provided in corresponding papers, therefore, Table 2, except the Raju method. Table 3 compares the speed of the proposed algorithm against that of three different algorithms-two algorithms with high performance according to the results provided in Table 2, and an algorithm using random forests [25]. Algorithms using random forests automatically generate bounding boxes and determine the instrument type of the bounding box. The speed comparison is based on frames per second (FPS) and allows estimating the accuracy of each algorithm. The accuracy estimate of each algorithm was based on the values provided in corresponding papers, therefore, different criteria were considered. Considering the alternative algorithms with similar average mAP, it can be seen that the proposed algorithm is approximately 7 times faster. Moreover, the proposed algorithm has approximately 1.71 times faster speed and 1.72 times higher accuracy than the random forest algorithm. The results of the proposed method are shown in Figure 5. If a tool identified in the previous frame (a) is not found in the current frame (b), the missing tool detection algorithm is applied. (c) is the result of missing tool detection. After the presence of the missing tool is recognized, a white O symbol is displayed in the upper left corner of the image (c, d). Taking Figure 5 as an example, we can describe in more detail that an irrigator is detected in the previous frame (a), however, in the current frame, no surgical tools were detected through YOLO9000 (b). Therefore, through the surgical tool mapping applied on the previous frame and the current frame, it is recognized that the missing tool exists. This is indicated by the white O symbol in the upper left corner of the image. Thereafter, the missing irrigator is detected through the motion vector predicting step, and the class of the detected tool is displayed under the white O symbol.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 13 different criteria were considered. Considering the alternative algorithms with similar average mAP, it can be seen that the proposed algorithm is approximately 7 times faster. Moreover, the proposed algorithm has approximately 1.71 times faster speed and 1.72 times higher accuracy than the random forest algorithm. The results of the proposed method are shown in Figure 5. If a tool identified in the previous frame (a) is not found in the current frame (b), the missing tool detection algorithm is applied. (c) is the result of missing tool detection. After the presence of the missing tool is recognized, a white O symbol is displayed in the upper left corner of the image (c, d). Taking Figure 5 as an example, we can describe in more detail that an irrigator is detected in the previous frame (a), however, in the current frame, no surgical tools were detected through YOLO9000 (b). Therefore, through the surgical tool mapping applied on the previous frame and the current frame, it is recognized that the missing tool exists. This is indicated by the white O symbol in the upper left corner of the image. Thereafter, the missing irrigator is detected through the motion vector predicting step, and the class of the detected tool is displayed under the white O symbol. Table 4 compares precision, recall, and F1 scores, according to whether the missing tool detection algorithm is applied or not. Application of missing tool detection allows the precision to be reduced by approximately 0.63%, the recall by 4.95%, and the F1 score by approximately 2.35%. The reason Table 4 compares precision, recall, and F1 scores, according to whether the missing tool detection algorithm is applied or not. Application of missing tool detection allows the precision to be reduced by approximately 0.63%, the recall by 4.95%, and the F1 score by approximately 2.35%. The reason for the precision decrease is attributed to the erroneous detection of a tool as a missing tool in YOLO9000. Accordingly, an additional detection process is executed.
Error Analysis
In the object detection task, errors can be classified as false positive and false negative. A false positive is that the ground truth is false, but the test result is true. In other words, a non-existent surgical tool is detected. For example, the background is erroneously detected as a surgical tool, or the class of the surgical tool is identified incorrectly. A false negative, on the other hand, means that the ground truth is true, but the test result is false. Therefore, it can be concluded that a surgical tool exists, but cannot be detected. for the precision decrease is attributed to the erroneous detection of a tool as a missing tool in YOLO9000. Accordingly, an additional detection process is executed.
Error Analysis
In the object detection task, errors can be classified as false positive and false negative. A false positive is that the ground truth is false, but the test result is true. In other words, a non-existent surgical tool is detected. For example, the background is erroneously detected as a surgical tool, or the class of the surgical tool is identified incorrectly. A false negative, on the other hand, means that the ground truth is true, but the test result is false. Therefore, it can be concluded that a surgical tool exists, but cannot be detected. Figure 6 shows false positives and false negatives observed in detecting surgical instruments using only YOLO9000. The above two images are examples of false positives. More specifically, the background was detected as a surgical tool in the upper left image, and a hook was detected incorrectly as a bipolar in the upper-right image. In this case, the nonexistent bipolar is detected, and existing hook is not detected. Consequently, both false positive and false negative are increased by 1. The bottom images are examples of false negatives. The image on the left is an example of failure to detect a grasper, and the image on the right is an example of failure to detect a hook. Figure 7 shows the error in each considered surgical video when using YOLO9000 only, and when using both YOLO9000 and missing tool detection. Each of the six pictures represents an error in each video. However, m2cai16-tool-location videos are displayed together because the total Figure 7 shows the error in each considered surgical video when using YOLO9000 only, and when using both YOLO9000 and missing tool detection. Each of the six pictures represents an error in each video. However, m2cai16-tool-location videos are displayed together because the total number of frames is small. The numbers on the vertical axis represent the number of errors. For example, if the number of surgical instruments erroneously detected in the same frame is two, the error is also registered as two. The bright blue region of the graph represents a false positive, and the yellow dot region represents a false negative. The orange line indicates the total number of errors. In each figure, the bar on the left shows the error when using only YOLO9000, and that one on the right shows the result obtained using missing tool detection together with YOLO9000.
error is also registered as two. The bright blue region of the graph represents a false positive, and the yellow dot region represents a false negative. The orange line indicates the total number of errors. In each figure, the bar on the left shows the error when using only YOLO9000, and that one on the right shows the result obtained using missing tool detection together with YOLO9000.
As shown in the figure, when using only YOLO9000, most errors are false negatives. It can be explained by the fact that there are many errors due to missing tools. To solve this problem, we additionally applied the missing tool detection algorithm. As a result, the total number of errors decreased, as shown in the right graph. In addition, the number of false negatives also decreased. On the other hand, the number of false positives increased, because wrongly detected surgical tools were judged to be missing tools and consequently, were redetected accordingly. Figure 8 shows an example of error caused by missing tool detection. The left image is the result obtained in the previous frame. In the previous frame, a grasper was detected correctly through missing tool detection. However, a part of the background was detected as a specimenbag. As a result, in the current frame (right image), the specimenbag was judged as a missing tool through mapping. Correspondingly, the background was detected incorrectly as a specimenbag again due to applying the missing tool detection algorithm. As shown in the figure, when using only YOLO9000, most errors are false negatives. It can be explained by the fact that there are many errors due to missing tools. To solve this problem, we additionally applied the missing tool detection algorithm. As a result, the total number of errors decreased, as shown in the right graph. In addition, the number of false negatives also decreased. On the other hand, the number of false positives increased, because wrongly detected surgical tools were judged to be missing tools and consequently, were redetected accordingly. Figure 8 shows an example of error caused by missing tool detection. The left image is the result obtained in the previous frame. In the previous frame, a grasper was detected correctly through missing tool detection. However, a part of the background was detected as a specimenbag. As a result, in the current frame (right image), the specimenbag was judged as a missing tool through mapping. Correspondingly, the background was detected incorrectly as a specimenbag again due to applying the missing tool detection algorithm. Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 13 (a) (b) Figure 8. Example of errors in surgical tool detection using YOLO9000 and missing tool detection (a) The specimenbag was detected incorrectly in the previous frame, (b) The incorrectly detected specimenbag is judged as the missing tool, hence, it is redetected by applying the missing tool detection algorithm in the current frame.
Discussion and Conclusions
In this paper, we proposed the new method of detecting and classifying surgical instruments in laparoscopic images. This method has two main advantages-it can be used during real-time operations, and it is robust in comparison to the existing methods.
Firstly, the proposed method can detect surgical tools in real time by using the object detection system YOLO9000. Unlike other methods, You Only Look Once (YOLO) does not allow for finding the region of interest (ROI). Conventional methods aim to identify the ROI from an input image and thereafter, to classify each ROI. However, applying YOLO allowed for the diminishing of the time required to calculate the ROI. YOLO divides an input image into a set of grid cells and then, performs classification of each grid cell. Owing to this key feature of YOLO, the proposed algorithm can detect surgical tools in real time (Table 3).
Moreover, the proposed method is deemed to be robust. In other words, the proposed method demonstrates the uniform and excellent performance in the detection of surgical instruments of all classes. Based on the results provided in Table 2 and Figure 4, it can be concluded that in comparison to other algorithms, the proposed method has a uniform mean average precision (mAP)-over 80for all classes of surgical instruments, and the highest average mAP with respect to all considered surgical tools. As shown in Figure 4, while the performance of other algorithms with the similar mAP deteriorates for certain classes, the performance of the proposed algorithm is plotted as a flat graph, which confirms its high robustness.
Achieving the robustness of the proposed algorithm is possible owing to the use of the upgraded version of YOLO-YOLO9000. As mentioned earlier, YOLO has a high processing speed, as grid cells are considered instead of ROI. However, it has the problem of lacking accuracy in the first version of YOLO. This can be seen by comparing the performance results of [34] and [24] in Table 2. The study [34] is dedicated to the detection of surgical instruments using the early version of YOLO, and [24] is a study in which surgical instruments were detected applying the faster R-CNN, a typical algorithm using ROI. The results presented in Table 2 and Figure 4 show that the performance of the early version of YOLO is lower than that of the approach based on ROI identification. YOLO9000 has come out to solve these problems. As shown in Figure 2, compared to the earlier version of YOLO, YOLO9000 has subdivided the input image into smaller grid cells resulting in more sophisticated detection.
Another reason for the robustness of the proposed algorithm is that it enables improvements to the detection performance of successive surgical tools owing to the prediction of missing tools. Missing tool detection leads to better performance, as it enables the redetection of surgical tools that have been present in the previous frame, but are not detected in the current frame. As YOLO9000 uniformly divides the input image into grid cells, detection performance may deteriorate when the Figure 8. Example of errors in surgical tool detection using YOLO9000 and missing tool detection (a) The specimenbag was detected incorrectly in the previous frame, (b) The incorrectly detected specimenbag is judged as the missing tool, hence, it is redetected by applying the missing tool detection algorithm in the current frame.
Discussion and Conclusions
In this paper, we proposed the new method of detecting and classifying surgical instruments in laparoscopic images. This method has two main advantages-it can be used during real-time operations, and it is robust in comparison to the existing methods.
Firstly, the proposed method can detect surgical tools in real time by using the object detection system YOLO9000. Unlike other methods, You Only Look Once (YOLO) does not allow for finding the region of interest (ROI). Conventional methods aim to identify the ROI from an input image and thereafter, to classify each ROI. However, applying YOLO allowed for the diminishing of the time required to calculate the ROI. YOLO divides an input image into a set of grid cells and then, performs classification of each grid cell. Owing to this key feature of YOLO, the proposed algorithm can detect surgical tools in real time (Table 3).
Moreover, the proposed method is deemed to be robust. In other words, the proposed method demonstrates the uniform and excellent performance in the detection of surgical instruments of all classes. Based on the results provided in Table 2 and Figure 4, it can be concluded that in comparison to other algorithms, the proposed method has a uniform mean average precision (mAP)-over 80-for all classes of surgical instruments, and the highest average mAP with respect to all considered surgical tools. As shown in Figure 4, while the performance of other algorithms with the similar mAP deteriorates for certain classes, the performance of the proposed algorithm is plotted as a flat graph, which confirms its high robustness.
Achieving the robustness of the proposed algorithm is possible owing to the use of the upgraded version of YOLO-YOLO9000. As mentioned earlier, YOLO has a high processing speed, as grid cells are considered instead of ROI. However, it has the problem of lacking accuracy in the first version of YOLO. This can be seen by comparing the performance results of [34] and [24] in Table 2. The study [34] is dedicated to the detection of surgical instruments using the early version of YOLO, and [24] is a study in which surgical instruments were detected applying the faster R-CNN, a typical algorithm using ROI. The results presented in Table 2 and Figure 4 show that the performance of the early version of YOLO is lower than that of the approach based on ROI identification. YOLO9000 has come out to solve these problems. As shown in Figure 2, compared to the earlier version of YOLO, YOLO9000 has subdivided the input image into smaller grid cells resulting in more sophisticated detection.
Another reason for the robustness of the proposed algorithm is that it enables improvements to the detection performance of successive surgical tools owing to the prediction of missing tools. Missing tool detection leads to better performance, as it enables the redetection of surgical tools that have been present in the previous frame, but are not detected in the current frame. As YOLO9000 uniformly divides the input image into grid cells, detection performance may deteriorate when the main feature is located at the boundary of the grid cell. This situation can occur, for example, as the surgical tool moves. Therefore, it is possible to improve the detection performance by predicting the motion trajectory of the surgical tool and adjusting the position of the grid cell correspondingly. Figure 7 shows the difference in error estimates depending on the presence or absence of the missing tool detection algorithm. The results provided in Table 3 also demonstrate the improved performance owing to this algorithm.
In conclusion, for the purpose of this study we applied two algorithms-YOLO9000 and missing tool detection-to perform the robust detection of surgical instruments in real time. Although the proposed method allows for the diminishing of the error of YOLO9000 by using missing tool detection, the detection error still exists. In particular, missing tool detection requires information from previous frames; therefore, if YOLO9000 detects a surgical tool incorrectly in the previous frame, it consequently affects the current frame.
To solve these problems, it is necessary to use missing tool detection in training. For example, we can obtain a better performance of the proposed method by checking the occurrence of a missing tool in training and adaptively adjusting the probability of the surgical tool presence in the previous frame. Alternatively, a method of using information from previous frames in training through time-sequence techniques such as long short-term memory (LSTM) [36] may be helpful for improving the performance. Finally, increasing the accuracy of the dataset may enable improvements to the detection performance. In this paper, we used an open dataset, which does not reflect information if a surgical tool appears small or obscured; consequently, the detection performance of the proposed method can be improved further if this problem is addressed. | 9,497.6 | 2019-07-18T00:00:00.000 | [
"Engineering",
"Medicine",
"Computer Science"
] |
‘ The idea of the University ’ and the ‘ Pretoria Model
The article is authored by the Dean of Faculty of Theology at the University of Pretoria, celebrating the Faculty’s centenary in 2017. The exposition of the argument is unfolded on the basis of Ricoeur’s threefold mimesis of prefiguration, configuration and reconfiguration. The earliest decisive statement with regard to the nature of the Faculty, and which is eagerly pursued, was made by the Rev. M.J. Goddefroy in 1888, epitomising theological training as of academic deference, that is as a Faculty at a university and not a seminary. This has been the fibre of Theology at the University of Pretoria and intellectual inquiry is an uncompromised value. The article is a critical reflection on the past century and an orientation towards the next hundred years, identifying the essence of what a real Pretoria Model could and should be and looking ahead to the next century. ‘History is not a destination, but an orientation’, sounds like a refrain in the article. The enterprise is contextual with regard to time and space. The assessment is subsequently done in terms of this continent and this century, that is Africa and the 21st century. The conclusion of the article is that the Pretoria Model fills a unique niche in theological inquiry at public universities competing for a position among the top 500 on the ranking of world universities.
Introduction
The title of this article comes across as rather pretentious.This is however, not erudite at all.It is rather a bit of a tongue in the cheek remark of locating the article within a certain context which is not only to be understood in terms of the second century of existence of the Faculty of Theology at the University of Pretoria, but more importantly, in which the classical paradigm of the Faculty finds its identity and relevance.It is a recognition of its diachronically rootedness in the Western tradition of scholarly education.
The informed reader will immediately recognise the opening phrase in the title of the article, as the title of the renowned book of John Henry Newman (1809Newman ( -1890)), The idea of the university (1982).The historian G.M. Young has ranked this book with Aristotle's Ethics among the most valuable of all the works on the aim of education.Arthur Quiller-Couch told his students at Cambridge that, 'of all the books written in these hundred years there is perhaps none you can more profitably thumb and ponder.' (See Martin Svaglic in his Introduction to The idea of the university [Newman 1982:vii]).
There is an allusion to another important publication by John Henry Newman, and that is to his Apologia pro vita sua (2005).Newman, a highly influential figure in the Church of England, stunned the Anglican community in 1845 when he left his position as vicar of St. Mary's, Oxford, to join the Roman Catholic Church and set up a university for Catholics in Ireland.No one took greater offence than Charles Kingsley who responded with a scathing attack on Newman's faith and honour, which inspired his brilliant response in his spiritual autobiography.The depths and nature of Christianity, together with the Latin in the title ('A defence of one's life') have insured its status as a classic.
The expression, 'Pretoria Model', was first used by Conrad Wethmar (2000) in his rethinking of theological education at Pretoria, since the two sections (of the NGK 1 and the NHK 2 ) have merged to a single multi-ecclesial 3 Faculty.Wethmar (1997) foresaw two decades ago quite a challenge for 1.Nederduitse Gereformeerde Kerk and in English, Dutch Reformed Church (DRC).
3.Note: not ecumenical.
The article is authored by the Dean of Faculty of Theology at the University of Pretoria, celebrating the Faculty's centenary in 2017.The exposition of the argument is unfolded on the basis of Ricoeur's threefold mimesis of prefiguration, configuration and reconfiguration.The earliest decisive statement with regard to the nature of the Faculty, and which is eagerly pursued, was made by the Rev. M.J. Goddefroy in 1888, epitomising theological training as of academic deference, that is as a Faculty at a university and not a seminary.This has been the fibre of Theology at the University of Pretoria and intellectual inquiry is an uncompromised value.The article is a critical reflection on the past century and an orientation towards the next hundred years, identifying the essence of what a real Pretoria Model could and should be and looking ahead to the next century.'History is not a destination, but an orientation', sounds like a refrain in the article.The enterprise is contextual with regard to time and space.The assessment is subsequently done in terms of this continent and this century, that is Africa and the 21st century.The conclusion of the article is that the Pretoria Model fills a unique niche in theological inquiry at public universities competing for a position among the top 500 on the ranking of world universities.theological education in the Western world, but for South Africa in particular: In spite of all this, and understandably so, the South African debate is characterized by its own particular issues and emphases.These issues and emphases are to a large extent related to the new political dispensation that developed in South Africa.(pp. 415-416) What Wethmar did not foresee in his 'Pretoria Model' are the changes in the international academic landscape and the impact it has on faculties of Theology worldwide.
The fourth allusion in the title is of course the centenary of the Faculty of Theology.The Faculty of Theology at the University of Pretoria (UP) was established in 1917. 4It did not develop from a seminary as was the case of Stellenbosch and Potchefstroom, but developed as a Faculty with full academic status at the university since its inception, making this the oldest fully fledged Faculty of Theology in South Africa. 5 Of the total number of eleven faculties of Theology at universities in South Africa, today only four 6 remain as proper faculties of Theology.I will argue that the worldranking of universities has opened up a new challenge and even a niche for a new approach to Theology in the 21st century.I propose that the 'Pretoria Model' is given a new dimension and perhaps defines the nature of theology at the University of Pretoria for the time to come.
The exposition of the argument will be unfolded on the basis of Ricoeur's (1984:52-87) threefold mimesis of prefiguration, configuration and reconfiguration.This means that the idea of a university is therefore not understood as following everything, but rather as preceding everything.Immanuel Kant (1963:20) states in the preface to the second edition of his Critique of Pure Reason, that reason 'constraining nature to give answer to questions of reason's own determining', or as 'an appointed judge who compels the witnesses to answer questions he has himself formulated.' The earliest decisive statement with regard to the nature of the Faculty, and which is eagerly pursued, was made by the Daar is uitdruklike voorwaardes aan die Raad van die TUK gestel: dat ten minste een van die teologiese professore 'Hollandssprekend' moes wees, dat by die aanstelling van professore 'rekening wordt gehouden met de beginselen der Ned Herv Kerk in ZA', dat die kerklike professor in rang gelyk aan universiteitsprofessore sou wees, dat die 'verdeling der vakken" in oorleg met die kerklike professor sal geskied, en dat die Hervormde teologiese studente as universiteitstudente sal geld.Dit is aanvaar en die Hervormde teologiese opleiding was 'n werklikheid.(Loader 1989:427).This has been the fibre 7 of Theology at the University of Pretoria and intellectual inquiry is an uncompromised value of the Faculty and the line I follow in unfolding the argument. 8As a sort of tacit presupposition, the unfolding will be executed to the point where the Pretoria Model finds a niche in its own right at a public university competing for the top 500 positions of research-intensive world universities.
5.The University of Pretoria, formerly known as the
This article does not pretend to be a historical exposition of the Faculty over the past one hundred years. 9It is a critical reflection by the Dean on the past century and an orientation towards the next hundred years, identifying the essence of what a real Pretoria Model could and should be and looking ahead to the next century. 10History is not a destination, but an orientation will sound like a refrain in this article and during the centenary.It is a humble endeavour to make sense of the past in the light of the future.
Obviously, this enterprise should be contextual with regard to time and space.The assessment is subsequently done in terms of this continent and this century, that is, Africa and the 21st century.This article ultimately proposes that the Pretoria Model fills a unique niche in theological inquiry at public universities competing for a position among the top 500 on the ranking of world universities.
8. This of course is not a commonly accepted fact.Wethmar cites John Wycliffe who rather vehemently took the opposite position when he wrote: 'Universities, with their programmes of study, their degrees, and their professorships, are products of vain heathenism; they are as much good to the church as the devil is.' (1997:427).
9. See inter alia the following contributions in this regard: Van The origin of many medieval universities can be traced back to the Christian cathedral or monastic schools, 11 which appeared as early as the 6th century and were run for hundreds of years as such before their formal establishment as universities during the high medieval period (Wikipedia contributors 2016).Andrew Louth (2004:70) identifies a certain monk, Bede of Northumbria, to be the first scholar to equip monastic schools for education, he also authored textbooks on grammar and rhetoric, the two subjects together with dialectic that constituted the trivium, the introductory part of the medieval curriculum.These were the early beginnings of the eighth century.This introduction enabled the learners to read, write and think in Latin and to enable them subsequently to have access to the scriptures.
Beyond the trivium lay the quadrivium which entailed music, arithmetic, geometry and astronomy.They completed the artes liberals -the so-called liberal arts -which is still a familiar term used at modern universities.The monastic schools' aim was to enable monks to fulfil their vocation as monks and to come to know God, to praise him and to love him.This is encapsulated in the term contemplatio which consisted of the four steps of lectio → medidatio → oratio → contemplatio.This reading, thinking, pondering ultimately led the monks to contemplation: to looking to God, to be aware of God's presence (Louth 2004:70).The human intellect was seen as not only doing things, but getting beyond them and knowing reality.Discerning God, is perhaps what it was all about.Louth (2004) makes the following important conclusion from this: Right from Aristotle, and indeed earlier, the acknowledgment of the supreme value of contemplation, and the need that there be those who may devote their time to this, has been linked to acknowledgment that human beings are not simply earth-bound entities.(p.77) Although I will later attempt to define theology within the context already referred to, it is nevertheless important to allude to the pre-Christian era in this regard, not so much to find the roots of university, but rather to indicate what a university is all about.The Ionic philosophers already tried to explain the ultimate problems of the origin of the universe.They asked the question of what is fundamental to all things, or as the Milesians put it, the basic substance or Arche.Thales of Miletus (c.624-546 BC) reduced everything to water, Anaximander (c.610-545 BC) was of the opinion the Arche of all things is the boundless and Anaximenes (c.585-528 BC) held the opinion that breath and air encompass everything (Zeller 1963:32).Since the earliest times, humans have had the urge to penetrate to the absolute in order to understand the whole.
The key expression in coming to grips with what the understanding of reality (read: university) is all about accepting what has been said by Kant (see the above citation), is Anselm's fides quaerens intellectum or 'faith seeking understanding'.The theologian's task is not to determine the object of inquiry, but to be guided by the inherently rationality of the object itself. 12This concept has its antecedent already in the theology of Augustine (MacDonald 2010:1012): 'Unless we believe these things, we would do nothing at all in this life' (Augustine 1996:130).A measure of faith is a sine quo non when one wants to come to grips with reality.This is the proper epistemic approach to reality, which transcends the empirical senses.Yet, reason plays the primary role in furnishing depth of understanding to what we believe in faith.MacDonald (2010) recapitulates this point effectively when he says that: Augustine affords reason the primary role of furnishing depth of understanding or knowledge to what we believe in faith even if we only can achieve full understanding or knowledge, and thus perfect happiness, in the life to come.(p.1012) MacDonald (2010MacDonald ( :1013) ) uses this argument to contend that this allows theology at a secular university, because all disciplines have certain epistemic authorities.The question is not whether a discipline is grounded in certain presuppositions, but rather which authoritative teaching they are grounded in.
For Cardinal John Henry Newman (1982) it is clear that Theology is a branch of knowledge and that universities should teach universal knowledge: But this, of course is to assume that Theology is a science, and an important one: so I will throw my argument into a more exact form.I say, then, that if a University be, from the nature of the case, a place of instruction, where universal knowledge is professed, and if in a certain University, so called, the subject of Religion is excluded, one of two conclusions is inevitable,either, on the one hand, that the province of Religion is very barren of real knowledge, or, on the other hand, that in such a University one special and important branch of knowledge is omitted.(p.16) The argument for Newman is that knowledge is an end in itself and not for the sake of one or other ulterior motive.The university appeals to common sense and not some ecclesiastical rules and only then is it a place at which it can make humans fit for the world. 13 However, the universality and unity of the scientific disciplines has turned out to be only a phantom and although the very concept of truth is in danger of losing its place in the modern university, Ebeling (1981:16-18) argues, it has an intrinsic relationship to human life and is preserved in both the person of the scientist who conducts the research and 12.But in relation to this Subject, we are at once confronted with the problem of knowledge.All speaking and hearing in the Church of Jesus Christ entirely rests upon and is connected with the fact that God is known in the Church of Jesus Christ; that is to say, that this Subject is objectively present to the speakers and hearers, so that man in the Church really stands before God.If it were not so, if man did not really stand before God, if God were not the object of his perception, viewing and conception, and if he did not know God -whatever we understand by 'know'-then he could not speak and hear about Him.Then everything declared and heard in the Church would have no Subject and would be left in the air like an empty sound.(Barth, Bromiley & Torrance 2004:3).
13.For a masterfully exposition and re-examination of the thoughts of Newman, see Jaroslav Pelikan (1992).
in the impact of that research on the environment and is therefore indispensable.Religion is a major determinant in human life (Van de Beek 2012:84).
MacDonald (2010:995) cites Donald Wiebe claiming that theology is intrinsically driven by at least some sort of a priori commitment to 'an independent subject matter -that is, God, the gods, the Transcendent, Ultimate Reality, and so on.'World views are templates that govern the social construction of a symbolic universe.Michael Polanyi developed the expression tacit knowledge as a central part of knowledge in general in order to express what we look for and have some idea about what else we may want to know: 'we can know more than we can tell.' (Polanyi 1966:6).Subsequently, tacit knowledge indicates shared values and tradition, rather than scepticism and lies at the heart of scientific discovery.
Western societies have made fundamental errors in believing that an objective body of knowledge exists and is waiting to be discovered, secondly that the actual possession of such knowledge is neutral and value-free and thirdly that the pursuit of knowledge benefits all human endeavour rather than just a specific class (Grenz & Olson 1996:313).Thus, the argument goes, theology cannot produce valid knowledge (Van de Beek 2012:83).
In a well-researched and argued paper, 'Why the university needs theology', Edna McDonagh puts up four reasons to address this question, namely historical, cultural, societal and intellectual grounds.She is of the opinion that 'a combination of ignorance and arrogance is undermining the role of the humanities, including theology, in the intellectual enterprise of many universities ' (2006:141).The historical grounds are not only mentioned because theology was an embryotic part of Western universities, but also because scientific dialogue is impossible without the Judeo-Christian heritage of the different disciplines.She (McDonagh 2006) gives a backhand compliment to Richard Dawkins in acknowledging that reality needs a multi-dimensional approach and asserting that: [E]ven in the very latest anti-religious writings of scientist Richard Dawkins the scientific arrogance and theological ignorance expose the need for a dialogue with university theology which he refuses or has no opportunity to address.(p.142) The cultural grounds deal with the sources of human beliefs and practices in their historical context, otherwise they are mere shallow surveys of current lifestyles.Ritual practices of both the past and the present should be engaged with.It is noteworthy that many secular studies nowadays base their methods of interpreting texts, on earlier Jewish and Christian approaches.On societal grounds McDonagh (2006:145) argues that many professional disciplines like food science, engineering and medicine are significant social practices and interact with religion through the medium of morality.Theology contributes not only to the social cohesion of society, but shapes the value system too.This all escalates into the intellectual ground when it becomes clear that theology (and philosophy) yield certain ultimate questions about human and cosmic life and death.This is of course 'subject to critical intellectual exploration and scrutiny if they are not to lapse mere self-deception and superstition' (McDonagh 2006:148).
Configuration
'The house of religious studies is full of strange beds and even stranger bedfellows' (Hart 2002:93).It is rather important to distinguish between different forms of theological tuition and learning.The scope of this article is not a general one, but very focused on theology as a science 14 taught at a secular university, with or without ecclesial sanction (although with recognition).William Hart (2002:94) differentiates between Theology (upper case) and theology (lower case but with italics).Theology with a capital 'T' refers to a devotional, confessional, and dogmatic enterprise, that is, very much church-based.On the other hand, theology with a small 't' and written in italics, refers according to Hart, to a liberal, academic, and humanistic enterprise, that is very much based on philosophy.'Theology is fideistic; theology is fallibilistic.'However, there is a tertium datur too: a theology with a small 't' and non-italicised.Hart commends this option to a post-Theological culture.
In his latest publication, Knowledge and Christian belief, Alvin Plantinga, by using the tools of modern epistemology, argues for a rational and warranted theology; 'Christians not only can be but also are justified in holding their characteristic beliefs' (2015:45) and it is in this line that I (Buitendag 2014) endorse the QANU Report on the Quality Assurance of Netherlands Universities. 15Van de Beek (2012:86-89) argues for a 'filled neutrality' in the study of Theology at a public university.This makes provision for all religions and philosophical world views, assessed by their own internal critique.
In my mind, theology and religious studies are not birds of the same feather.Similarities can so easily be over accentuated and differences glossed over.There is a major difference in epistemology.The assumptions of modernistic liberal understanding have been challenged from different angles and 'the presumptive epistemic privilege of the scholar has been shaken as the epistemological foundations upon which it was based have crumbled' (Cady 2002:113).Each of us inhabits a particular place and time and that limits research and making it provisional.No scholar is above the data, but 14.In his The conflict of the faculties, Kant distinguished the philosophical or liberal arts faculty from the professional faculties of law, medicine and theology.A faculty of theology was defended within a university, not for its independent engagement in the pursuit of knowledge, but for the professional training of ministers.However, it is unsatisfactory to divide reason and sensibility: 'Humans live in one world, of which reason, understanding and sensibility must together provide a coherent and plausible conceptual interpretation' (Ward 2009:88).
15.It is important for theology to be present in secular universities.It has a very positive role to play in providing reflective enquiry into fundamental questions of human nature and existence, and in exploring the approaches to those questions within one or more major and historically crucial religious traditions.Theology has therefore to be conserved as an autonomous discipline with its own theorybuilding and methodology, independently of the external approach of religion by religious studies and of its more instrumental use for ministerial training, and also irrespective of the commitment to church policies.(QANU 2013:8).
is in relation to it.The academic and cultural trends of the last 50 years oppose abstraction and the universalisation of knowledge.Abstract analysis has made place for contextual relationality.Kathryn Tanner (2002:206) aptly states: 'In a search for truth humbled by the recognition of constant change and limitations of perspective, this cultural contest would require the widest possible purview.' I would like to conclude my argument with a citation by Denys Turner (2005) with regard to the place of theology at a university: And that precisely is the reason why any university should want to have in its midst the presence of theologians: for 'Religious Studies' people ask only the same old sorts of questions that the anthropologists, or psychologists, or historians, or sociologists ask, as it happens about religions, whatever they are.Whereas theologians ask distinctive questions all of their own that no one else would have thought of asking, questions of such oddity that you are obliged, as a first sort of task, to demonstrate that they can be legitimately asked at all -like Leibniz's question, 'Why is there something rather than nothing?(pp.36-37) Although there are both 'strange beds' and even 'stranger bedfellows', I would like to distinguish between the different models all using the same adjective 'theological': theological training, theological education and theological inquiry.
Theological training is carried out by a church, and financially supported by the relevant denomination(s).Obviously there is much emphasis on the praxis of the denomination and very little or perhaps no independent thinking happens.The training is for a fixed period after which the candidate is licensed by the church.But these schools, sometimes even seminaries, are independent and not linked to a university.This is outside the scope of this article.Theological education is of a much higher standard, and institutions offering it are often accredited by Higher Education as a seminary.Whereas the previous has the emphasis on praxis, this model has theory as well and proper study of the confessions and creeds is done.The focus is broader than only the denomination, and society is seen as the context of the ministry.This is a lifelong education, and continuous teaching and learning normally takes place.A more advanced form, is a Christian university.In Africa it becomes an increasingly popular development for excelling seminaries. 16 The at the university.It accepts the challenge to compete internationally and adheres to the demands of the worldranking systems with the core criteria of publish or perish.Its focus is the scholarly world and it realises that 'glocalisation' is the route to go; it contributes to global scholarly debates from a local perspective.The following concise table lists the differences between the two, although binary forces: The Pretoria Model is fit to taking up this challenge.The latest InCites data 17 shows that the Faculty at the University of Pretoria is ranked position #25 in the world with regard to research done by religious institutions as per the Web of Science categories.This position is based on the (1) articles on the Web of Science, (2) Normalized Citation Impact, (3) Times Cited, and (4) International Collaborations.The following graphs indicate both the four South African faculties of theology 18 as well as the three international Faculties the Faculty at Pretoria has chosen to benchmark itself against. 19 The point at stake here is that a new grammar has been developed for theology as a science.The challenge for a Faculty of Theology at a research-intensive university is to publish where it is noted, that is Scopus, The Scientific Electronic Library Online (SciELO) SA and the Norwegian list (Tshilidzi 2016:34) Theology is a scholarly endeavour by believers in the public sphere in order to come to grips with multi-dimensional realities (being) in a manner that matters (bread).
These definitions will be fleshed out in the next and last section, before some final concluding remarks.
Refiguration
The case for theological education cannot be finally made once and for all.It needs to be made again and again, because what theology and theological education are called to do, varies in each social setting and cultural circumstance (Brueggemann 1991:100).
Research universities in the 21st century cannot be singlepurpose institutions anymore, but must rather be pluralistic The summit agreed inter alia that: • Higher Education is a public good.
• Democratic citizenship and the right to dignity critically underpin the mandate of our public universities.• Universities have a developmental role to play in redressing inequalities in broader society.• Curriculum change is at the core of university transformation initiatives.• Transformation of universities is multidimensional and complex.• The term transformation must continue to be interrogated and discussed at deeper levels.• Workers are an integral part of the communities of public universities.
During the Mini-Lekgotla of the Faculty of Theology on the 4 th December 2015, Prof Kobus Krüger 28 was invited to 27.In a rather cynical way, Stefan Collini (2012:Loc 62) refers to the 'trinity' signalling the position of universities today in Britain: 'funding', 'impact' and 'access'.
28.There was not a published paper presented only his personal notes which were given to the Dean.The indicated paragraphs quoted freely from that.
provide direction to the possible positions the Faculty could go towards in the future with regard to its values of inclusivity and diversity.As an introduction, he alluded to three entangled sets of problems that compel humanity today to rediscover and return to the root and nature of things.
• Firstly there is the ecological crisis.Humankind's scientific developments and their technological applications and extensions have become a problematic force in the overall tissue of reality.At the level of popular culture plain materialism, not coinciding with, yet related to science, poses an enormous problem and challenge to theology.• Then there is the social crisis with its many faces, reminding us that injustice towards children and women, minorities and majorities and the socially exposed and weak of all kinds are today as prevalent as at any time in the past.• Thirdly, there is the loss of legitimacy of all traditional religious and other value systems, even when they are propped up laboriously, sometimes aggressively, in some parts of the world.All religions are in a crisis.Humanity has entered a new kind of culture, global in spread but shorn of ultimate meaning.
Like ancient Polynesian way finders over vast stretches of ocean, Krüger said, humanity today will have to draw on all dimensions of human experience and knowledge; remember past stretches of water covered and islands passed on the way here; be able to read the tides and the winds of the present moment; and have a good understanding of the groundswell, the deep currents in the ocean of human consciousness.We have entered a new axial age, and it may be time for an exciting new start.
The challenge for the Faculty of Theology at Pretoria is therefore to be globally competitive, yet locally relevant.Richard Starcher (2004) of the Nairobi of the Evangelical Graduate School of Theology, found that: [R]esearch participants most often expressed a desire to grow in competence (knowledge or skill) in connection with a desire to be of greater service to Africa or the African Church.(p.211) With regard to the relevance of theology in South Africa, Anthony Balcomb (1998:68) distinguishes subsequently between theologies of bread and theologies of being.The first type is engaged in the reconstruction of the South African society and the latter type struggles with the quest for identity in a society dominated by Western values.Relevance is therefore not only an ethical question, but an ontological as well as an epistemological one.Deconstruction of the heritage of the past century and engaging in the world debate from an That this challenge has been appropriated by the Faculty, is evident from inter alia a recent report from the Head of the Department of Practical Theology, Prof. C.J. Wepener (2016), to the Dean: The aim of practical theological research is a better understanding of faith practices as well as the continuing renewal of a theory for praxis.Ultimately Practical Theology wants to make a contribution regarding the healing of individuals, society and creation which for us includes issues such as justice, reconciliation, inclusivity, equality, poverty alleviation -in essence the meaningful reconnection of individuals and communities to themselves, each other, creation and God.(Unofficial email by C.J.W. to J.B).
The 'shape and size' of the Faculty of Theology has been indicated by the University's Executive as a matter that should be revisited.The Vice-Principal: Institutional Planning therefore formally requested the Dean on 9 March 2015 by an email 30 to conduct an investigation into the possibility of transforming certain research clusters into managerial units, that is, departments, with the potential implication of reducing the number of departments in the Faculty (Ströh 2015).
The following Terms of Reference 31 were set by the Executive: • To review the current structure of the Faculty and suggest possible changes to improve its organisational efficiency and research productivity in support of the University's strategic goals.(Buitendag 2016).
relationships between the Faculty of Theology and church partners), particularly in relation to research, teaching and learning, and professional training.Also, to suggest possible ways of overcoming these challenges.
It was a sine qua non throughout these discussions was that the integrity and independence of the Faculty should be maintained as well as the six established disciplines of Theology.The restructuring is therefore to be seen as a managerial issue in order to improve the operational efficiency of the Faculty.Based on a Faculty Lekgotla (Pure Joy, 10-11 March 2016), the Dean prepared a report to the effect of reducing the current six departments to five and to rename both the departments and the Faculty.
The following changes are proposed 32 (Buitendag 2016:3-4): • Gateway To … 34 'History is not a destination, but an orientation'.It is important not only to interpret the past, but to come to terms with it as well.Like any human, the Faculty has a twopronged genealogy, the line of the fatherly ancestry and the line of the motherly ancestry.In terms of the Pretoria Model and the discussed reconfiguration, it is decisive to identify the core traits in the fibre of the Faculty.In Wethmar's mind, this is undoubtedly the issue of either the simplex ordo (NGK) or the duplex ordo (NHK) and the clear choice of the former (Wethmar 2000:425).This however, is much more complex than presented here.Neither the NGK nor the NHK had a pure application of either model.No distinction was later 35 made between church subjects (Dogmatics and Practical Theology) and the others.In both sections of the Faculty, the respective churches played a crucial role in the appointment of all academic staff and in the case of the NHK, they dismissed a New Testament professor 36 whose actions would be in a duplex ordo dispensation, inappropriate.Since the amalgamation of the two sections in 2000, it was clearly stated in the agreements with the churches that academic appointments would be made according to university's rules and regulations, with the only provisoo that denominational allocated positions would be filled from the ranks of that church, but appointed by a Recruitment and Appointment Committee of the University.I would rather contend that the Pretoria Model is in its fibre a hybrid with more traits of the duplex ordo, except for the distinction of church subjects vis-à-vis academic subjects and that the current complement of lecturers are all believers and even licensed ministers of a number of different denominations.(vgl. Valeton [1909] se kritiek hierop, uitgewerk in sy bespreking van die verskillende rigtings en die standpunt van die etici daarteenoor), en tegelyk 'n regsinnigheid wat standpunt teen die liberale teologie ingeneem het.Daarom moet verwag word dat die Hervormde teologie, soos bedrywe aan die fakulteit te Pretoria, die karakter van die "derde opsie" en meer bepaald dié van die etiese teologie sou vertoon.' (Loader 1989:423).
of pursuing truth as an encounter.Postfoundationalist approaches are noted in many publications by the Faculty.
In my view (Buitendag 2014), the Postliberal Theology of the Yale School gives very much vocabulary to express this crucial trait of the Pretoria Model.This approach permits space for different and authentic voices, each in their own right.
In my mind it is clear that the Faculty has to continue to closely collaborate with different churches, religious institutions and different religions.It is also clear in my mind that academic excellence is not negotiable and that churches would have to add a certain amount of denominational flavour to the theological inquiry offered at the Faculty.If theology really wants to serve the church, it should have 'certain degree of freedom in relation to the official structures of the church' (Wethmar 2012:81).This implies a new application of the duplex ordo in the sense that all six disciplines are academic, yet ecclesiastical.
By means of an approach of constructive dialogue, a Faculty Theology at a public university has to contribute to human's urge to comprehend nature or rather reality.I concur with David Ford (2007) when he states that: Academic or public theology seeks wisdom in relation to questions, such as those of meaning, truth, beauty and practice, which are raised by, about and between the religions and are pursued through engagement with a range of academic disciplines.(p.117) Truth-seeking is intrinsic to the inquiring mind and characterises theology as well, or as Ford puts it, 'speaking the truth in love' (Ford 2005:727).This is perhaps what Wethmar (1997) sensed when he stated that: Christian theology will no longer retain its position at statefunded universities for traditional religious or ideological reasons but it will have to justify its presence in academic and moral terms.(p.416) However, Van de Beek (2012:85) warns against a metareligious moral framework which so-called 'objective' researchers apply in investigating their subject matter.A public university should never become idiosyncratic.
The Faculty of Theology has therefore engaged in critical multidisciplinary and transdisciplinary research on a wide spectrum of strategic academic and societal interests ranging from social cohesion, social ethics and leadership, missional church to narrative pastoral care and to actual biblicalhermeneutical challenges to the influential science-theology discourses.Much of the research has as its focus the problem of poverty, the challenges of reconciliation and the need for restorative justice, involving key role players from different sectors of society, industry and academia.
Prof Kobus Krüger (2015) has concluded his argument at the said Mini-Lekgotla of the Faculty with the following blessing: http://www.hts.org.zaOpen Access Clearly the Faculty has arrived at a moment of truth.It could become a pioneering Faculty, exploring new academic and religious ways in the Republic of South Africa, Africa, and wider.I believe the Faculty is strategically well-positioned, administratively in excellent hands and academically excellently equipped to fulfil that role.My very best wishes accompany you.
In the 2013 Faculty Plan, the following introductory paragraph led the vantage thinking of the author and is perhaps the leitmotif of his thinking (Buitendag 2012): The
4.
The first two theology students -P.J.J. Venter and M.M.J. Basson -were registered in 1917, although the institutionalisation of the Faculty was only finalised by April 1918.The first lecturers were Dr J.H.J.A. Greyvenstein and Rev E. MacMillan.Profs A.C. Paterson and H.T. Reinink took responsibility for the classics.This was the embodiment of the agreement with the church:
Figure 1 :
Figure 1: Research footprint of benchmarking faculties of Theology.
The Departments of Church History and Church Polity and the Department of Dogmatics and Christian Ethics will merge.• The Department of Science of Religion and Missiology will be converted to a Department of Religion Studies.• The name of the Faculty is to change to the Faculty of Theology and Religion (Afrikaans: Fakulteit Teologie en Religie and Sepedi: Lekala la Thutatumelo le Bodumedi).• The Faculty will comprise of five departments with the following proposed names: Rev. M.J. Goddefroy in 1888, epitomising theological training as of academic deference, that is as a Faculty at a university and not a seminary: Transvaal University College (TUC) had been established in 1908 under the direct influence of General Jan Smuts and commenced lectures in Kya Rosa with 32 students and 4 professors.The focus was on the classics, law and the sciences.Two of these four professors (Paterson and Reinink) were later affiliated to the Faculty of Theology.General Smuts was the first scholar to obtain an honorary doctorate from the University of Pretoria (13 December 1930) (cf.University of Pretoria, 2016a; University of Pretoria 2016b).6The following universities used to have faculties of Theology: Unisa, University of the Western Cape, Rhodes University, Fort Hare University, Zululand University, University of KwaZulu-Natal and Limpopo University.In most cases these faculties dissolved into the Faculty of Humanities as departments or schools of religious studies.
third category is what I see as a new challenge, yet a niche for theology.Theological inquiry is what Hart calls theology spelled in lower case (no italics) which has a critical approach in its methodology.It is open for contestation, interdisciplinary, multidisciplinary and even transdisciplinary research and wants to contribute to humans' search for understanding and meaning.It is not essentially ecclesiastical, perhaps not even ecumenical, but scientific in nature.It tries to be a worthy dialogue partner among the different sciences 16.A very good example is St Paul's University in Nairobi.As vision it states is to be 'a university of academic excellence based on Christian principles producing graduates in various fields for global service' and as mission it wants, 'to develop servant leaders by imparting knowledge, skills and values through creative methods of education, research and Christian spiritual formation.'('Vision & Mission', on St Paul's University webpage).
Table 1 :
Differences in models.
and of course the Thomson Reuters' Web of Science, previously referred to as the Institute for Scientific Information (ISI), and the International Bibliography of the Social Sciences (IBSS).The three most important indices measuring the world ranking position of universities are currently the Academic Ranking of World Universities 20 (ARWU), The Times Higher Education 21 (THE) and the Quacqaurelli Symonds 22 (QS), each with its own criteria: The league table was originally compiled and issued by Shanghai Jiao-tong University in 2003, the first global ranking with multifarious indicators (Shangai Rankings 2016).21.'TheTimes Higher Education World University Rankings, founded in 2004, provide the definitive list of the world's best universities, evaluated across teaching, research, international outlook, reputation and more.' (THE 2016).22.QS Quacquarelli Symonds was founded in 1990 and has established itself as the leading global provider of specialist higher education and careers information and solutions.(QS2016).23.The SCImago Journal & Country Rank is a portal that includes the journals and country scientific indicators developed from the information contained in the Scopus® database (Elsevier B.V.).24.Group 17 of the Classification of Educational Subject Matter (CESM) is 'Philosophy, Religion and Theology' and contributes 5.96% to the total publications of South African universities and is ranked in the 8th position of all fields (Tshilidzi 2016:14).25.Although the Faculty of Theology is the smallest faculty at the University (1.4% of students and 1.5% of lecturers), it delivers more than 12% of the article output of the University of Pretoria.theologicaljournal in South Africa and affiliated to the Faculty of Theology at the University of Pretoria (SJR 2016).The journal in the third position, Verbum et Ecclesia 26 is affiliated to the Faculty of Theology at the University of Pretoria as well.
of Religion, 1980-2015
26.Strangely enough, Verbum et Ecclesia is listed under the category of 'Sociology andPolitical Science' and not 'Religious Studies' as the rest.InternaƟonal Benchmarking
This means that universities have to become agents of change and 'the critical source of equalisation of chances and democratisation of society by making possible equal opportunities for people'(Cloete et al. 2015:2).
Table 3 :
The five Theological SA journals with an international footprint.
Baie dankie vir die gesprek wat ons verlede wek gehad het tov Teologie by UP.Ek stel dit graag op skrif dat UP Bestuur groot waardering het vir die besondere bydrae wat deur jou Fakultieit gelewer word.Dit is ook so deur die Rektor oorgedra met die vorige prestasie rondte met Dekane.Wat die toekoms van die Fakulteit aanbetref is dit baie duidelik deur die Rektor aan my en Norman oorgedra dat ons Teologie as 'n onafhanklike Fakulteit wil hou.Daar is tans oor die hele UP 'n aantal inisiatiewe besig om te kyk na die bestuurseenhede waarbinne dissiplines funksioneer en die voorstel is dat ons bestuurseenhede skep wat belyn is met fokus areas 'cluster van dissiplines' wat 'n kritiese massa verteenwoordig en nie klein [en] baie bestuursomgewings skep nie.Dit is dan die versoek dat julle as Fakulteit met 'n voorstel kom oor hoe ons hiermee vorentoe [kan] gaan.Nogmaals baie dankie vir die baie goeie werk.Groete, Anton.(Personal e-mail by A.S to J.B). 31.See the report of the Dean to the Academic Planning Committee (APC) of 09 February 2016 Loader 37has indicated convincingly that the nature of the Faculty since its inception, was very much based on the Dutch Ethical Theology which most probably today is very much the character of the Pretoria Model, which is neither liberal, nor orthodox but finds a dialectical third option 34.The Faculty's Centenary Committee has decided that this is the strapline for the celebrations.It implies not only a gate, but an open gate inviting the traveller to proceed.The early Christians were known as 'The Way'.With this the Faculty wants to endorse its mission of inclusivity and wants to take along marginalised people of the past, whether of race, of gender, of ideology, of language or whatever.Therefore, it is a confession of our erroneous exclusivity of the past as well.The old wooden gates of the University are symbolically placed in a fixed open position in front of the building of the Faculty.35.The two so-called church subjects only started at UP in 1952 and 1967 respectively.General Jan Smuts, Prime Minister of the Union of South Africa requested the then Vice-Chancellor of the University of Pretoria, Prof. C.H. Rautenbach a previous member of theFaculty of Theology (1939-1948), to visit St. Andrews University and to duplicate the Scottish structure of departments at UP.The Presbyterian legacy of the Faculty has become integral to the Faculty because of this fact and not because of the initial lecturers in 1917.
Greyvenstein, Engelbrecht en Wolmarans), en dat hulle hul geledere sou versterk met hulp uit dieselfde oord (getuige die hulp van Obbink en die koms van Gemser en Van Selms).Dit is des te meer begryplik aangesien die etiese teologie alles kon bied wat vir Hervormers belangrik was: distansie van die gereformeerde teologie, afwysing van die bevindelikheid van die "evangelischen" last message of the late President Paul Krüger to the people of the old Zuid-Afrikaansche Republiek in the Transvaal during his exile in Switzerland in the final days of theAnglo-Boer War (1899-1902), was that they should gather from the past what was good and of value and build a future on it.However praiseworthy, it should be turned upside down in real business and strategic thinking: visualise the future and build a history accordingly.(p. 2) 'Ars longa, vita brevis', is the slogan on the cornerstone of the Theology Building on the campus of the University of Pretoria.Life is short, but art forever.And so is theology here to remain.Or to conclude with another Latin expression: 'ex Africa semper aliquid novi.'There is always something new from Africa.May this Pretoria Model as ars theologica Africae be a gateway to the Kingdom.Nkosi Sikelel' iAfrika! | 10,365.6 | 2016-12-02T00:00:00.000 | [
"Philosophy"
] |
Permutation testing in high-dimensional linear models: an empirical investigation
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates. Permutation-based tests are valuable in particular because they can be highly robust to violations of the standard linear model, such as non-normality and heteroscedasticity. Moreover, in some cases they can be combined with existing, powerful permutation-based multiple testing methods. Here, we propose permutation tests for models where the number of nuisance coefficients exceeds the sample size. The performance of the novel tests is investigated with simulations. In a wide range of simulation scenarios our proposed permutation methods provided appropriate type I error rate control, unlike some competing tests, while having good power.
Introduction
We consider the problem of testing hypotheses about coefficients in linear models, where the outcome may be non-Gaussian and heteroscedastic, and the number of nuisance coefficients exceeds the sample size. By the nuisance coefficients we mean the coefficients which are not tested by the particular test at hand, but still need to be dealt with since they lead to confounding effects. In recent decades, the literature on permutation methods has strongly expanded (Tusher et al., 2001;Meinshausen et al., 2011;Hemerik and Goeman, 2018a;Ganong and Jäger, 2018;Berrett et al., 2018;He et al., 2019;Albajes-Eizagirre et al., 2019;Hemerik et al., 2019;Rao et al., 2019). While the permutation test dates far back (Fisher, 1936), most of the permutation tests in the presence of nuisance were published in the last four decades. To our knowledge, the existing methods are limited to low-dimensional nuisance. For the high-dimensional case, an approach similar to a permutation test is proposed in Dezeure et al. (2017).
Permutation tests for low-dimensional linear models are valuable for two main reasons. First, they are robust to violations of certain standard assumptions, such as normality and homoscedasticity. Under non-normality, they often have higher power than a classical parametric test (Anderson and Legendre, 1999;Kowalski, 1972). Under heteroscedasticity, they often provide better type I error control than parametric tests. Second, when the outcome is multidimensional, a permutation-based test can be combined with existing permutationbased multiple testing methods, which tend to be relatively powerful, since they take into account the dependence structure of the outcomes (Meinshausen, 2006;Meinshausen et al., 2011;Hemerik and Goeman, 2018a;Hemerik et al., 2019). For example, under strong positive dependence among p-values, the Bonferroni-Holm multiple testing method (Holm, 1979) is greatly improved by a permutation method (Westfall and Young, 1993). Permutation methods are particularly popular in omics research and neuroscience (Winkler et al., 2014). This is partly due to the fact that permutation-based multiple testing methods take into account the dependence among, for example, genes or voxels Hemerik and Goeman, 2018a).
Exact permutation tests, i.e.. tests with level exactly equal to the nominal value α, are only available if the outcome is Gaussian Langsrud, 2005), if all nuisance parameters are known (Anderson and Robinson, 2001) or if the nuisance variables are discrete (so that we can permute within blocks). Otherwise, permutation tests are only asymptotically exact.
For the low-dimensional general linear model, with identity link but not necessarily Gaussian or homoscedastic residuals, several different permutation tests have been proposed. The main approach that these methods have in common, is to permute residuals after regressing on the nuisance covariates. There are different ways to permute the residuals. Instead of permutation in the strict sense, the residuals may also be randomly sign-flipped, under the assumption that the residuals are symmetric. For overviews of the available methods, see Anderson and Legendre (1999), Anderson and Robinson (2001), Winkler et al. (2016) and in particular Winkler et al. (2014).
Among the existing permutation methods, the ones that often perform best with respect to type I error control and power, are the procedures commonly referred to as the Freedman-Lane method (Freedman and Lane, 1983) and the Smith method. The latter procedure is named after a reviewer (O'Gorman, 2005;Winkler et al., 2014). Compared to all other methods, the Freedman-Lane approach is most commonly used. It tends to provide excellent type I error control, even if the number of nuisance covariates approaches the sample size.
Because the existing permutation tests require estimating the nuisance coefficients using maximum likelihood, these methods cannot be used when the number of covariates exceeds the sample size. It is of interest to somehow extend these methods to high-dimensional linear models. A seemingly natural way to do this, is to replace the least squares estimation by some type of regularized estimation, e.g. ridge estimation.
However, extending the existing methodology to the high-dimensional setting is not straightforward. For example, the Freedman-Lane method requires re-estimating the nuisance each time the data have been permuted. This can quickly become computationally challenging in the high-dimensional setting. Moreover, it is not obvious what test statistic should be used within the permutation test. For example, the usual F -and Wald statistics are not available in the high-dimensional setting. As in the low-dimensional case, a suitable choice of the test statistic is essential for the validity of the test.
In recent years, important theoretical advances have been made in the field of inference in high-dimensional linear models. Although there is a vast literature on regularization methods such as ridge regression, most existing results on testing in such models are quite recent (for a partial overview, see Dezeure et al., 2015). Several of these tests have proven asymptotic properties. In particular, the method in Zhang and Zhang (2014) has been shown to be asymptotically optimal under certain assumptions (Van de Geer et al., 2014). The method in Bühlmann et al. (2013) tends to be more conservative, but requires less assumptions to provide asymptotic type I error control. Dezeure et al. (2017) propose a bootstrap approach, which is related to the method in Zhang and Zhang (2014) .
The known theoretical properties of these methods are asymptotic and rely on complex assumptions and sparsity. The test by Zhang and Zhang (2014) can be rather anti-conservative in settings where a substantial fraction of the coefficients are non-zero. Moreover, these methods are not based on permutations. Hence they do not generally have the above-mentioned advantages, such as robustness against certain violations of the standard linear model. An exception is the bootstrap method in Dezeure et al. (2017), which tends to be more robust to such violations.
We propose two novel tests, which, to our knowledge, are the first permutation tests in the presence of high-dimensional nuisance. One is an extension of the low-dimensional method in Freedman and Lane (1983) and the other is somewhat related to a method by Kennedy (Kennedy, 1995;Kennedy and Cade, 1996). The method based on Freedman and Lane (1983) requires performing ridge regression in every permutation step, but we do this in a computationally efficient way.
Using simulations we show that our methods provide appropriate type I error rate control in a wide range of situations. In particular, we illustrate empirically that our tests have the above-mentioned robustness properties. The methods in this paper have been implemented in the R package phd, available on CRAN.
This paper is built up as follows. In Section 2 we discuss exact permutation tests, which are available when the nuisance parameters are known. We discuss permutation testing in settings with low-dimensional, unknown nuisance in Section 3. This section contains some novel remarks which will be used in Section 4. There, we propose permutation tests for highdimensional settings. We assess the performance of our methods with simulations in Section 5. An analysis of real data is in Section 6.
2 Known nuisance 2.1 Notation throughout the paper We consider the general linear model where X is a n × d matrix of covariates of interest, Z an n × q matrix of nuisance covariates and ǫ an n-vector of i.i.d. errors with mean 0 and non-zero variance, which are independent of the covariates. Here the rows of X, Z and Y are i.i.d.. The matrix Z is assumed to have full rank with probability 1. We will often focus on the case that d = 1. Let the variables Y ∈ R, X ∈ R d and Z ∈ R q be such that their joint distribution coincides with that of the rows of (Y , X, Z).
The parameter β ∈ R d is of interest and γ ∈ R q is a nuisance parameter. We want to test the null hypothesis H 0 : β = 0 ∈ R d . Here 0 might be replaced by another constant: the extension is straightforward.
Let w be a positive integer, which will denote the number of random permutations or other transformations. In this paper, all permutation p-values are of the form or, in case of a two-sided test where both small and large values of T 1 are evidence against where T 2 , ..., T w ∈ R are statistics computed after random permutation and T 1 is a statistic based on the original, unpermuted data. The methods in this paper only differ with respect to how T 1 , ..., T w are computed.
Exact permutation tests
When the nuisance parameter γ is known, then E Z (Y ), the expected value of Y given Z under H 0 , is known. Hence, under H 0 , the errors ǫ coincide with the observed residuals e = Y − E Z Y . However, the distributional shape of the errors is not generally known, so that there exists no exact test of H 0 in general. When the distribution of the errors is known to be invariant under a group of permutations or other transformations, then we do obtain an exact test. More precisely, suppose that under for all g ∈ G, where G is a group of transformations g : R n → R n . See e.g. Hemerik and Goeman (2018b) for the definition of a group in the algebraic sense. Examples of such G are given below. The exact test is then obtained as follows. Let T be a function from the sample space of (X, Z, Y ) to R, large (absolute) values of which are evidence against H 0 . For example, T could be an F -statistic. For every 1 ≤ j ≤ w, define T j = T (X, Z, Y * j ), where with g j ∈ G a random transformation of the vector of residuals e. Here, we draw g 2 , ..., g w uniformly from G, with replacement. We take g 1 to be the identity, so that T 1 corresponds to the original data. We draw with replacement for convenience, although drawing without replacement is also allowed (Hemerik and Goeman, 2018b). The p-value is then (1) or (2), as required by the context. See Algorithm 1. Writing α ∈ (0, 1) for the desired confidence level, we reject H 0 when the p-value is at most α. Under H 0 , the resulting rejection probability is at most α. Under mild assumptions such as continuous residuals, if the transformations are drawn without replacement and α is a multiple of 2w −1 , then the rejection probability is exactly α (Hemerik and Goeman, 2018b).
In practice, G is usually taken to be a group of permutation maps or a group of signflipping transformations (Winkler et al., 2014). In case we use permutation, G consists of all maps g : R n → R n of the form (e 1 , ..., e n ) → (e π(1) , ..., e π(n) ),
To obtain an exact test, we require (3) to hold. In case G contains permutations, (3) is satisfied if e 1 , ..., e n are independent and identically distributed. Note that we then need no assumption on the shape of the errors ǫ. This means that the test is still exact if the errors ǫ are not normal, i.e., the test is robust to non-normality. If sign-flipping is used, it suffices to assume that the errors ǫ are independent and symmetric around 0. The errors can have different distributions, however. In particular they are allowed to have very different variances, i.e., the test is robust to heteroscedasticity.
Unknown, low-dimensional nuisance
Here we discuss existing permutation methods that can be used when the nuisance parameter γ is unknown and has dimension smaller than n. For this setting an appreciable number of permutation methods have been proposed (Winkler et al., 2014), most of which are asymptotically exact under mild assumptions (Anderson and Robinson, 2001). We will focus on two methods, which inspire the methods in Section 4. Section 3.1 also contains some novel remarks, which will be important in Section 4.1.
The existing permutation methods all provide p-values according to formulas (1) and (2), but differ with respect to how permutation is used to obtain T 1 , ..., T w . Although we will often write 'permutation', sign-flipping can also be used, as explained in Section 2.2. All methods in this paper consist of the following steps.
1. Compute a test statistic T 1 based on the original data.
2. Compute a test statistic T 2 in a similar way, but after randomly permuting certain residuals. Repeat to obtain T 3 , ..., T w .
Most of the existing permutation methods use residualization of Y or X with respect to the nuisance Z. The residual forming matrix is All tests in Section 3 involve the residuals RY ∈ R n . When d = 1 we will sometimes consider RX ∈ R n , which is assumed to be nonzero with probability 1. In Section 3 we assume Z contains a column of 1's. This implies that the entries of RX and RY sum up to 0.
Note that if we use permutation, we can write the transformed residuals g(RY ) as P RY , where P is an n × n matrix with exactly one 1 in every row and column and elsewhere 0's. In case of sign-flipping, P is instead an n × n diagonal matrix with diagonal elements in {1, −1} (Winkler et al., 2014). We write P 1 , ..., P w to distinguish the w random permutation matrices. Here P 1 is the identity matrix and P 2 , ..., P w are random.
The Freedman-Lane method
The Freedman-Lane permutation method (Freedman and Lane, 1983) is known to provide excellent type I error control, with both its level and power staying very close to the parametric F -test, under the Gaussian model. The test statistic T 1 is based on the unpermuted model Y = Xβ+Zγ+ǫ. The other statistics are obtained after randomly transforming the residuals. That is, for 2 ≤ j ≤ w the statistic T j is based on the model (P where the same test statistic, say T , is used as for computing T 1 . Thus where T is a suitable test statistic, the choice of which we now discuss. In Section 2 we saw that when the nuisance parameters are exactly known, the permutation test controls the type I error rate regardless of the choice of T . Here, however, it is usually important to use an asymptotically pivotal statistic, i.e., a statistic whose asymptotic null distribution does not depend on any unknowns under H 0 (Kennedy and Cade, 1996, p.926-927, Winkler et al., 2014, p.382, Hall and Titterington, 1989, Hall and Wilson, 1991. A pivotal statistic T will always involve estimation of the nuisance parameters. Thus, after every permutation, the nuisance parameters need to be estimated anew. Note that T should for example not be taken to be an estimate of β, since that is not a pivotal statistic. Instead one can use the F -statistic or Wald statistic. These are equivalent: the resulting p-value (1) will be the same.
In case X is one-dimensional, the F -statistic is also equivalent to the square of the partial correlation (Fisher, 1924;Agresti, 2015), which is used in Anderson and Robinson (2001). The partial correlation is the sample Pearson correlation of RY and RX, Here we used that the sample means of RY and RX are 0. If we use the partial correlation in the Freedman-Lane permutation test, this means that we take T (X, Z, Y ) = ρ RY , RX , so that (4) and (5) become where R(P j R + H) could be simplified to RP j R, since RH = 0. The numerator in (6) is The Freedman-Lane test with T defined by (9) remains unchanged if in (9) we replace i (RX) 2 i by 1 or by the constant i X 2 i . Indeed, T 1 , ..., T w will just be multiplied by the same constant. Thus, with respect to the permutation test, the statistic (6) If X has been centered around 0, then this equals where µ x denotes the n-vector with entries equal to the sample mean of X. This is the sample correlation of RY and X and is called the semi-partial correlation. If we take T to be the semi-partial correlation, then (4) and (5) become T 1 = ρ RY , X and where R(P j R+H) could be simplified to RP j R. Note that we could simply leave the constant i (X i − µ x ) 2 out without changing the result of the permutation test. Although for centered X the statistics (6) and (11) are equivalent, their counterparts in the high-dimensional setting are not, as will be discussed in Section 4.1.
The Kennedy method
The Kennedy method (Kennedy, 1995;Kennedy and Cade, 1996;Winkler et al., 2014) residualizes both Y and X with respect to Z. The outcome residuals are then permuted. Apart from the initial residualization step, the Kennedy method performs no nuisance estimation. The test statistics are where 2 ≤ j ≤ w. In the usual formulation of the Kennedy method, X is assumed to be one-dimensional, but generalizations are conceivable. The Kennedy method is similar to the Still-White procedure (Gail et al., 1988;Levin and Robbins, 1983;Still and White, 1981), which only residualizes Y .
In the simulations of Winkler et al. (2014), the Freedman-Lane method provided better type I error control than the Kennedy method. This is explained theoretically in Anderson and Robinson (2001). Heuristically, the reason is that the Freedman-Lane method repeats the residualization after every permutation, thus mimicking the computation of the original statistic T 1 . In Anderson and Robinson (2001) it is shown that the permutation tests by Freedman andLane (1983), Ter Braak (1992), Kennedy (1995) and Manly (1997) are asymptotically equivalent to each other and are asymptotically exact.
High-dimensional nuisance
When the nuisance parameter γ has dimension q ≥ n, the discussed permutation methods cannot be used. Here, these approaches are adapted to obtain tests which can account for high-dimensional nuisance. We consider the case that X is one-dimensional, i.e., d = 1, although generalizations where X is high-dimensional are conceivable. We assume that the entries of Y , X and Z have expected value 0. Consequently, the intercept is 0.
All existing tests rely on residualization steps, where Y or X is regressed on Z. A natural way to adapt this step to the high-dimensional setting, is to instead estimate the residuals using some type of elastic net regularization. We will consider ridge regression. For minimizing prediction error, ridge regression is often preferrable to Lasso, principal components regression, variable subset selection and partial least squares (Hastie et al., 2009;Frank and Friedman, 1993).
Compared to the methods in Section 3, using ridge regression comes down to replacing the projectionsŶ = HY andX = HX by ridge estimatesH λ Y andH λ X X, with λ, λ X > 0. Here, for λ ′ > 0,H which satisfiesH and similarly for X. The values λ, λ X are the regularization parameters, whose selection will be discussed. Using ridge regression, the residuals becomeR λ Y andR λ X X, wherẽ R λ = (I −H λ ) andR λ X = (I −H λ X ). The last two rows of Table 1 outline the permutation schemes that we will consider in Sections 4.1 and 4.2. The first two rows summarize the existing methods that have been discussed in Section 3. This table is analogous to Table 2 in Winkler et al. (2014) and allows easy comparison of the new methods with the existing methods discussed in Winkler et al. (2014).
Although Table 1 outlines the permutation schemes that we will use, several crucial specifics remain to be filled in. For example, several choices of the regularization parameters λ and λ X can be considered. Moreover, the computational challenge of performing nuisance estimation in every step will need to be addressed. Finally and importantly, we must determine what test statistics are suitable to use within our permutation tests.
Freedman-Lane HD
As discussed in Section 3.1, the low-dimensional Freedman-Lane method is known to provide excellent type I error control and power. Here we will provide an extension to the case of
Method
Model after permutation Freedman-Lane high-dimensional nuisance. We will refer to this test as Freedman-Lane HD. The permutation scheme that we use is analogous to that of Freedman-Lane and is shown in the third row of Table 1. As in the Freedman-Lane method, after every permutation, we will require nuisance estimation to compute T j . We will choose ridge regression to do this. Note however that when many permutations are used, performing a ridge regression after every permutation can be a large computational burden. We will therefore compute λ only once, for the unpermuted model. We take λ to be the value that gives the minimal mean cross-validated error; see Section 5.1 for more details. After each permutation, we then use the same parameter λ in the ridge regression. Thus, after the j-th permutation, to compute the new ridge residuals, we will only need to pre-multiply the transformed outcome (P jRλ +H λ )Y byR λ . We only need to computeR λ once. Owing to this approach, essentially we need to perform ridge regression only once.
An important consideration is the test statistic T used within the permutation test. The usual F -statistic and Wald statistic are only defined when the nuisance is low-dimensional. Extending these definitions to the high-dimensional setting with q ≥ n is problematic. For example, a Wald-type statistic would require an unbiased estimate of β and a variance estimate. The partial correlation (6), however, is more naturally generalized to the q ≥ n setting: we can replace the residuals RY and RX by the ridge residualsR λ Y andR λ X X. Similarly we can generalize the semi-partial correlation (11), by replacing RY byR λ Y . This gives the following test statistics, which generalize the partial correlation (6) and the semi-partial correlation (11) respectively: Here, µ 1 , µ 2 and µ x are n-vectors whose entries are the sample means ofR λ Y ,R λ X X and X respectively. In Section 3.1 we reasoned that if X has been centered, (6) and (11) are equivalent with respect to the permutation test. This does not apply to (16) and (17). In simulations, using the statistic (17) tended to result in somewhat higher power than using the statistic (16). In Section 5 we consider both methods.
In case the generalization of the partial correlation is used, the test statistics T 1 , ..., T w on which Freedman-Lane HD is based are Here µ j is an n-vector whose entries are the sample mean ofR λ (P jRλ + H λ )Y . For the version based on the generalization of the semi-partial correlation, the statistics are As usual, T 1 is just T j with P j = I n . The pseudo-code for the version based on semi-partial correlations is in Algorithm 2.
If q < n, as λ ↓ 0, the test converges to the test for λ = 0, which is the classical Freedman-Lane method. In the wide range of simulation settings considered in Section 5, the Freedman-Lane HD method stayed on the conservative side, in the sense that the size was less than α. This may due to the fact that if λ > 0 and 2 ≤ j < k ≤ w, the correlation between Y and Y * j is strictly larger than the correlation between Y * j and Y * k , where Y * j := (P jRλ +H λ )Y . This inequality is proved in the Supplementary Material.
As discussed, to perform the test, λ and henceR λ need to be computed only once. Thus, like the low-dimensional Freedman-Lane procedure, the test requires nuisance estimation after every permutation, but this is not a large computational burden. The method is often computationally feasible even when many millions of permutations are used; see Section 5. It is also worth mentioning that there exist approximate methods for reducing the number of permutations while still allowing for very small, accurate p-values (Knijnenburg et al., 2009;Winkler et al., 2016).
Algorithm 2 Freedman-Lane HD (version based on semi-partial correlations)
1: ComputeH λ = Z(Z ′ Z + λI q ) −1 Z ′ and the residual forming matrixR λ = I −H λ . Here λ is taken to give the minimal mean cross-validated error (see main text). 2: Let T 1 = ρ R λ Y , X , the sample Pearson correlation of the Y -residuals with X. 3: for 2 ≤ j ≤ w do
Double residualization
Here we propose a test that we refer to as the Double Residualization method. The method is somewhat related to the Kennedy procedure discussed in Section 3.2, but not analogous. The Kennedy method residualizes both Y and X and proceeds to permute the Y -residuals. Here we replace the least squares regression by ridge regression. Moreover, unlike Kennedy's permutation scheme, we keepH λ Y in the model; see Table 1. The test statistic that we use within the permutation test is the sample correlation. Thus, the test is based on the statistics where 2 ≤ j ≤ w. The difference between (22) and (19) is that (19) contains an additional R λ . The pseudo-code for the Double Residualization method is in Algorithm 3. We take λ and λ X to be the values that give the minimal mean cross-validated error; see Section 5.1 for more details. For fixed q, as n → ∞, the Double Residualization method becomes equivalent to the Kennedy method and the Freedman-Lane method if the penalty is o P (n 1/2 ), as shown in the Supplementary Material. The case that q > n is investigated in Section 5.
Let T j = ρ (P jRλ +H λ )Y ,R λ X X , where the random matrix P j encodes random permutation or sign-flipping. 5: end for 6: The two-sided p-value p equals (2). 7: return p
Simulations
We used simulations to gain additional insight into the performance of the new tests, as well as existing tests. The simulations were performed with R version 3.6.0 on a server with 40 cores and 1TB RAM. In Section 5.2 we consider scenarios where the outcome Y follows a standard Gaussian high-dimensional linear model. In Section 5.3 we consider non-standard settings with non-normality and heteroscedasticity. We consider simulated datasets where the covariates have equal variances. It is well-known that when the data are not standardized, this can affect the accuracy of the model obtained with ridge regression (Bühlmann et al., 2014, p.257).
Simulation settings and tests
We considered the model in Section 2.1, where the variable of interest was one-dimensional, i.e., β ∈ R. In every simulation, the covariates had mean 0 and variance 1. They were sampled from a multivariate normal distribution with homogenous correlation ρ ′ , unless stated otherwise. The errors ǫ had variance 1. The intercept was γ 1 = 0, i.e., Y had mean 0. The tested hypothesis was H 0 : β = 0. The sample size in the reported simulations was n = 30. We obtained comparable results for other sample sizes. The estimated probabilities in the tables are based on 10 4 repeated simulations, unless stated otherwise.
As the set G of transformations we took the group of n! permutations, unless stated otherwise. The penalty λ was chosen to give the minimal mean error, based on 10-fold cross validation. The penalty λ X was chosen analogously. To compute the penalties, we used the cv.glmnet() function in the R package glmnet. We used [10 −5 , 10 5 ] as the range of candidate values for the penalty. The penalty obtained with cv.glmnet() is scaled by a factor n, so we multiplied this penalty by n to obtain λ. We included an intercept in the ridge regressions, but excluding the intercept gave very similar results.
All tests used were two-sided. The tests corresponding to the columns of the tables in this section are the following.
"FLH1" is the Freedman-Lane HD test defined in Section 4.1, with test statistics T 1 , ..., T w based on the generalized partial correlation as in (19). "FLH2" is the same, except that T 1 , .., T w are based on the generalized semi -partial correlation as in (21). "DR" is the Double Residualization method of Section 4.2. Each of these tests used w = 2 · 10 4 permutations.
"BM" is a high-dimensional test based on ridge projections, proposed in Bühlmann et al. (2013). This test is based on a bias-corrected estimate |β corr | of |β| ∈ R and an asymptotic upper bound of its distribution. We used the implementation in the R package hdi (Dezeure et al., 2015).
"ZZ" is a high-dimensional test based on Lasso projections, proposed in Zhang and Zhang (2014). This method constructs a different bias-corrected estimateb of β, which has an asymptotically known normal distribution under certain asumptions, such as sparsity. For this test we also used the hdi package. We could not include this test, in the simulations with a very high number of nuisance parameters, since it is computationally very time-consuming when q is large, as also noted in Dezeure et al. (2015). We expect the test to have good power in these settings.
"BO" is the bootstrap approach in Dezeure et al. (2017), which is also implemented in the hdi package. We set the number of bootstrap samples per test to 1000 and considered the robust version of the method. We used the shortcut, which avoids repeated tuning of the penalty. Still, the method was very slow, so that we used 10 3 instead of 10 4 repeated simulations of this method per setting. Also, we did not include the test in the simulations with very large q.
Gaussian, homoscedastic outcome
We first consider some settings with a moderately large number of nuisance coefficients, q = 60. We first simulated an anti-sparse setting with γ 2 = ... = γ 60 = 0.05. We took ρ ′ = 0.5. The estimated level and power of the tests described above, for different p-value cut-offs α, are shown in Table 2. The tests rejected H 0 if the p-value was smaller than the α. The level of a test should be at most α. Table 2 shows that the test by Zhang and Zhang (2014) was rather anti-conservative. Especially for small α, its level was many times larger than α. This is partly due to the antisparsity. Indeed, the test by Zhang and Zhang (2014) only has proven asymptotic properties under a sparsity assumption. The bootstrap approach of Dezeure et al. (2017) was much less liberal, but still seemed to be somewhat anti-conservative for small α. Of the other tests, Freedman-Lane HD 2 often had the most power. The Double Residualization method had relatively low power when α was small, e.g. 0.001. Table 2: Anti-sparse setting with ρ ′ = 0.5, n = 30, q = 60. Power is shown for β = 1.5. We also considered a setting with very high correlation ρ ′ = 0.9, see Table 3. We took γ 2 = γ 3 = 1 and γ 4 = .... = γ 60 = 0. The first 4 methods provided appropriate type I error control. For small cut-offs α, the method by Zhang and Zhang (2014) was relatively powerful, but also seemed to be somewhat anti-conservative. This method seems more suitable for settings where q is many times larger than n. Among our permutation methods, Freedman-Lane HD 2 had the best power, while incurring few type I errors. The method by Bühlmann et al. (2013) was relatively conservative. We also performed simulations with a very large number of nuisance variables (q = 1000). We first took γ 2 = γ 3 = 1, γ 4 = ... = γ 10 = 0.2, γ 11 = ... = γ 1000 = 0. See Table 4 for simulations with ρ ′ = 0.5 and Table 5 for simulations with ρ ′ = 0.9. All permutation methods provided appropriate type I error control. Double Residualization had relatively high power for large cut-offs α, but not for small cut-offs. The method by Bühlmann et al. (2013) had relatively good power for ρ ′ = 0.5 but low power for ρ ′ = 0.9.
Method
We also performed simulations where γ was very anti-sparse, e.g. with γ 2 = 1, γ 3 = ... = γ 800 = 0.002 and ρ ′ = 0.9. We also considered negative coefficients and we varied the orders of magnitude of the coefficients and the errors ǫ and the sample size. We also considered settings where there were multiple independent clusters of correlated covariates. Also in these settings, the type I error rate was controlled.
Violations of the Gaussian model
As discussed in for example Section 2.2, permutation tests can be robust to violations of the standard linear model, such as non-normality and heteroscedasticity. The power of parametric methods is often substantially decreased when the residuals have heavy tails. The power of the permutation tests is more robust to such deviations from normality. This is illustrated in Table 6. Here, the data distribution was the same as in the setting corresponding to Table 3, except that the errors ǫ were not standard normally distributed, but had very heavy (cubed exponential) tails, scaled such that the errors had standard deviation 1. Note in Table 6 that the permutation and bootstrap methods still had roughly the same power as at Table 3, while the power of the tests by Bühlmann et al. (2013) and Zhang and Zhang (2014) was strongly reduced compared to Table 3. As a second type of violation of the standard linear model, we considered heteroscedasticity. We simulated errors ǫ i which were normally distributed, but with standard deviation proportional to the absolute value covariate of interest, |X i |. We again took γ 2 = γ 3 = 1, γ 4 = ... = γ 60 = 0. We took ρ ′ = 0 for illustration, since in that case the test by Bühlmann et al. (2013) had higher power than the permutation methods in this specific setting, but was anti-conservative for small α.
In the simulations underlying Table 7, we did not use sign-flipping, which is known to be robust to heteroscedasticity (see Section 2.2). Surprisingly, our tests nevertheless provided appropriate type I control. We also performed these simulations with sign-flipping instead of permutation (results not shown), which further reduced the level of our tests, but also somewhat reduced the power.
We conclude from the simulations of Section 5 that our tests are rather robust to several types of model misspecification. The method from Zhang and Zhang (2014) was often relatively powerful, but was quite anti-conservative in several scenarios. The bootstrap approach of Dezeure et al. (2017) was also anti-conservative in some scenarios, but much less so. The method from Bühlmann et al. (2013) tended to be relatively conservative.
Data analysis
We analyze a dataset about riboflavin (vitamin B2) production with B. subtilis. This dataset is called riboflavin and is publicly available . It contains normalized measurements of expression rates of 4088 genes from n = 71 samples. We use these as input variables. Further, for each sample the dataset contains the logarithm of the riboflavin production rate, which is our one-dimensional outcome of interest. We (further) standardized the expression levels by subtracting the means and dividing by the standard deviations. We also shifted the outcome values to have mean zero. For every 1 ≤ i ≤ 4088, we tested the hypothesis H i that the outcome was independent of the expression level of gene i, conditional on the other expression levels. We used the same tests as considered in the simulations. This time we used w = 2 · 10 5 permutations per test.
The results of the analysis are summarized in Table 8. The columns correspond to the same methods as considered in Section 5. For every method, the fraction of rejections is shown for different p-value cut-offs α. The fraction of rejections is the number of rejected hypotheses divided by 4088, the total number of hypotheses. The hypotheses that were rejected, were those with p-values smaller than or equal to the cut-off α.
With most methods we obtain many p-values smaller than 0.05. This is not the case for the test by Bühlmann et al. (2013), which is known to be relatively conservative. After Bonferroni's multiple testing correction, we reject no hypotheses with any method, suggesting there is no strong signal in the data. Van de Geer et al. (2014) also obtained such a result with this dataset.
Discussion
We have proposed novel permutation methods for testing in linear models, where the number of nuisance variables may be much larger than the sample size. Advantages of permutation approaches include robustness to certain violations of the standard linear model and compatibility with powerful permutation-based multiple testing methods. We have proposed two novel permutation approaches, Freedman-Lane HD and Double Residualization. Within these approaches some variations are possible, with respect to how the regularization parameters are chosen and which test statistics are used. Our methods provided excellent type I error rate control in a wide range of simulation settings. In particular we considered settings with anti-sparsity, high correlations among the covariates, clustered covariates, fat-tailedness of the outcome variable and heteroscedasticity. The simulation study was limited to settings with multivariate normal covariates. Future research may address more scenarios.
We compared our methods to the parametric tests in Bühlmann et al. (2013) and Zhang and Zhang (2014) and to the bootstrap approach in Dezeure et al. (2017). Our tests tended to have higher power than the method by Bühlmann et al. (2013). The test by Zhang and Zhang (2014) had relatively good power, but was rather anti-conservative in several scenarios, for example under anti-sparsity and heteroscedasticity. The bootstrap approach of Dezeure et al. (2017) was also anti-conservative in some scenarios, but less so. Our permutation tests tended to be less powerful than that method, but provided appropriate type I error control in all scenarios. Moreover, our permutation tests were computationally much faster.
sinceH λ −H 2 λ is positive definite. We then also have Note that since P jRλ Y is a random permutation ofR λ Y . Similarly we have and cov(Y * k , Y * j ) = var(H λ Y ). | 9,221.8 | 2020-01-06T00:00:00.000 | [
"Mathematics"
] |
Effects of Plasma Treated Alumina Nanoparticles on Breakdown Strength, Partial Discharge Resistance, and Thermophysical Properties of Mineral Oil-Based Nanofluids
Mineral oil has been chosen as an insulating liquid in power transformers due to its superior characteristics, such as being an effective insulation medium and a great cooling agent. Meanwhile, the performance of mineral oil as an insulation liquid can be further enhanced by dispersing nanoparticles into the mineral oil, and this composition is called nanofluids. However, the incorporation of nanoparticles into the mineral oil conventionally causes the nanoparticles to agglomerate and settle as sediment in the base fluid, thereby limiting the improvement of the insulation properties. In addition, limited studies have been reported for the transformer oil as a base fluid using Aluminum Oxide (Al2O3) as nanoparticles. Hence, this paper reported an experimental study to investigate the significant role of cold plasma treatment in modifying and treating the surface of nano-alumina to obtain a better interaction between the nano-alumina and the base fluid, consequently improving the insulation characteristics such as breakdown voltage, partial discharge characteristics, thermal conductivity, and viscosity of the nanofluids. The plasma treatment process was conducted on the surface of nano-alumina under atmospheric pressure plasma by using the dielectric barrier discharge concept. The breakdown strength and partial discharge characteristics of the nanofluids were measured according to IEC 60156 and IEC 60270 standards, respectively. In contrast, the viscosity and thermal conductivity of the nanofluids were determined using Brookfield DV-II + Pro Automated viscometer and Decagon KD2-Pro conductivity meter, respectively. The results indicate that the 0.1 wt% of plasma-treated alumina nanofluids has shown the most comprehensive improvements in electrical properties, dispersion stability, and thermal properties. Therefore, the plasma treatment has improved the nanoparticles dispersion and stability in nanofluids by providing stronger interactions between the mineral oil and the nanoparticles.
Introduction
Since 1892, mineral oil has been used as an insulation medium due to its excellent insulating properties and has effectively served as a dielectric coolant [1]. One of the reasons that mineral oils have been chosen as a transformer oil is the ability to transfer heat more effectively than solid-based insulating materials, where solid insulations typically have issues, such as containing void impurities and poor thermal conductivity. Besides, mineral oil also has improved self-healing after failure, making it suitable for power transformer insulation [2]. Previously, significant progress had been made in improving the electrical breakdown strength and heat transfer of mineral oils by dispersing a certain number of nanoparticles into the mineral oil to create a liquid called nanofluid or nano-transformer oil [3]. The main purpose of exploring nanofluids is to enhance the insulation and thermal properties, consequently prolonging the power transformer's lifespan and minimizing the pre-breakdown phenomenon.
Even though the surfactants approach can avoid premature sedimentation, the precise number of surfactants required to maximize nanofluids' insulation properties remains a question. The most suitable and effective type of surfactants is also the main challenge in overcoming the agglomeration issue [17,18].
Recently, plasma discharge has been introduced as a surface modification technique to improve the compatibility in nanomaterials application. Plasma is a state of matter formed through the photoionization process that can be exhilarated using high voltage sources. Previously, plasma treatment has been utilized to improve the compatibility between the nanoparticles and solid-based polymer. Likewise, the main purpose of this treatment is to overcome the agglomeration of the nanoparticle and obtain a uniform dispersion of the nanoparticles into the polymer matrix. Plasma treatment is typically used to functionalize a certain chemical functional group on the surface of nanoparticles, which effectively anchors a new covalent bond during the mixing process of nanoparticles into base fluids. Besides, the plasma treatment is also useful to strengthen the covalent bond of the nanoparticles by producing radical species such as an oxygen-containing compound and a hydroxyl group. Thus, the combination of plasma treatment and nanoparticles seems to have a great outcome in terms of the insulation properties' enhancement, such as an increase in the breakdown strength and partial discharge resistance of the nanofluids due to the advantages and benefits of this technique. Plasma is also an alternative method of the treatment process that does not require a chemical solvent to functionalize the surface of the nanoparticles. Therefore, this could be another reason for choosing plasma as a modification technique.
Previously, Musa et al. [19] pointed out that atmospheric pressure plasma treatment was effective in forming uniform dispersion of nanoparticles within the polymer matrix. Besides, this technique was also attributed to forming strong covalent bonds with the molecules of the base insulating materials [19]. Yan et al. [20] also conducted a comprehensive study to investigate the dielectric breakdown strength of epoxy resin filled with atmospheric pressure plasma-treated nano-silica. The results showed that plasma treatment was a great technique to improve the compatibility of the nanoparticles and the polymer matrix, improving the dielectric breakdown strength. Furthermore, Awang et al. [21] revealed that the partial discharge resistance of nanomaterials was highly achievable by treating the nanofillers with cold plasma compared with the pure insulating materials.
The implementation of plasma treatment on the nanoparticles in preparing nanofluid seems necessary to explore intensively since this technique has great potential to improve the dispersion of nanoparticles, indirectly enhancing the insulation and thermal properties of the nanofluids. Currently, a limited number of studies have been conducted regarding the performance of plasma treatment in improving the properties of nanofluids. Thus, it seems necessary to fill this gap by exploring the effectiveness of plasma treatment in modifying the surface morphology of nano-alumina before it is dispersed into mineral oil.
In this work, cold atmospheric pressure plasma treatment was used to treat Al 2 O 3 nanoparticles to enhance the AC breakdown strength, viscosity properties, and thermal conductivity of nanofluids using helium gas as discharge working gas. Some researchers tackled agglomeration problems in nano-mixtures by using thermal non-equilibrium atmospheric-pressure plasma to change the nano-silica surface [22]. Meanwhile, other researchers claimed that plasma-treated nanoparticles with the desired surface functionality could interact strongly with liquid molecules that are better dispersed into the base fluid to form a stable suspension [23]. The interaction and compatibility between alumina nanoparticles and mineral oil can be improved using the cold atmospheric pressure plasma method.
Hence, this paper introduces plasma-treated nano alumina into mineral oil-based nanofluids to enhance the AC breakdown strength and partial discharge resistance and boost two important thermophysical properties: viscosity and thermal conductivity. Nano transformer oil has the potential for better heat transfer characteristics relative to conventional transformer oils used for cooling purposes [24].
Materials and Methods
The base fluid used in this work was Hyrax Hypertrans mineral oil supplied by Hyrax (Klang, Malaysia), which is good as a dielectric and coolant. It has a density of 0.895 g/mL and a minimum dielectric strength of 30 kV. The Alumina (Al 2 O 3 ) nanofiller was purchased from Sigma Aldrich (Petaling Jaya, Malaysia) with an average particle size of 13 nm. Nanofluid samples were prepared with 0.01 wt%, 0.05 wt%, 0.1 wt%, and 0.3 wt%, respectively. In this work, plasma was applied to the nanoparticles for surface modification to prevent early sedimentation in oil and improve the dielectric properties. The alumina nanofillers were treated using atmospheric pressure plasma in the plasma chamber that applied the dielectric barrier discharge (DBD) concept. These plasma discharges were applied on the alumina nanofiller to form functionalized surfaces of major reactive species.
The plasma discharges were applied on the surface of the nanoparticles to avoid early sedimentation in the oil. A 50 Hz power supply produced the cold atmospheric air pressure plasma with a maximum of 10 kVrms of applied voltage, and the output power consumed was 9 to 10 W. The plasma setup consisted of two glass plates, and the nanoparticles were placed on the plates. A tin-coated copper coil electrode was mounted 2 mm above the top of the nanoparticles layer. Helium gas was used as the working gas for discharge. The duration of the treatment was 30 min. The nanoparticles were stirred for 30 s for every 5 min of surface treatment to obtain a homogenous plasma treatment as recommended and indicated in the reference [12]. The schematic diagram of the experimental setup for dielectric barrier discharge (DBD) plasma treatment is shown in Figure 1a, while the setup for the DBD chamber is shown in Figure 1b. After the treatment, the treated nanoparticles were combined with the base oil according to the two-step method. The two-step method is the most economical method of producing nanofluids on a broad scale, as nanoparticles' synthesis techniques have already been scaled up to industrial production standards [24]. In this experiment, as shown in Figure 2, the two-step method was used to prepare mineral oil-based nanofluid, where the nanoparticles were first weighed. Nanoparticles were initially distributed in mineral oil. The mixture was stirred within 30 min with a magnetic stirrer and then sonicated to ensure good dispersion of the mixtures. Next, the alumina nanofillers with different concentrations of 0.3 wt%, 0.1 wt%, 0.05 wt%, and 0.01 wt% mass fraction were added to the 100% by weight of mineral oil to study the impact of nanoparticles concentration. The samples were then dried in a vacuum oven at 60°C for at least 24 h [11].
AC Breakdown Voltage
The breakdown voltage test was carried out in compliance with the IEC 60156 standard. The configuration of the electrode consists of two spherical brass electrodes with a gap of 2.5 mm. The AC voltage (50 Hz) with an increased rate of 20 kV/s was applied until a breakdown occurs. Three sets of six measurements of breakdown tests were recorded for each type of nanofluid. The results were analyzed using Weibull analysis. Figure 3 shows the oil test set to run the AC breakdown voltage for alumina nanofluids. Figure 4 shows the average AC breakdown voltage for mineral oil-based plasmatreated and untreated alumina nanofluids. Meanwhile, the average AC breakdown voltage for mineral oil-based 0.1 wt% of plasma-treated, untreated, and cetyl trimethylammonium bromide (CTAB) treated alumina nanofluids is shown in Figure 5. The results showed 48.37 kV, 55.77 kV, 46.35 kV, and 43.05 kV for untreated alumina nanofluid of 0.3 wt%, 0.1 wt%, 0.05 wt%, and 0.01 wt% samples, respectively. Previously, Kong et al. [25] and Tendero et al. [26] carried out work to modify alumina nanoparticles using the atmospheric pressure plasma treatment method. The plasma-treated alumina nanofluid showed 53.30 kV, 58.28 kV, 54.35 kV, and 47.47 kV for 0.3 wt%, 0.1 wt%, 0.05 wt%, and 0.01 wt% samples, respectively. For comparing purposes, the plasma-treated alumina nanofluid obtained the highest result compared to the CTAB-treated and untreated nanofluid samples for 0.1 wt%, as illustrated in Figure 5. The overall enhancement of the AC breakdown voltage for alumina nanofluids relative to pure mineral oil can be seen in Table 1. Plasma-treated nanofluids have a higher increased AC breakdown voltage than pure mineral oil, untreated nanofluids, and CTAB-treated nanofluids. However, the results have shown that the AC breakdown voltage for all nanofluids is higher than the pure mineral oil, which is in line with the outcomes obtained by Yuzhen et al. [27], Zhou et al. [28], and Du et al. [29].
Weibull Analysis
Weibull analysis can be used to estimate the breakdown voltage obtained from AC breakdown data for lower failure probabilities with two-parameter functions [30]. For example, Figure 6a shows the two-parameter Weibull analysis of the AC breakdown voltage of pure mineral oil and mineral oil-based untreated alumina nanofluids with 95% confidence intervals. At the same time, the Weibull analysis method of AC breakdown voltage for mineral oil-based plasma-treated alumina nanofluids is shown in Figure 6b.
Moreover, alumina nanoparticles could significantly increase the AC breakdown voltage of the mineral oil. The enhancement of the breakdown voltage at a concentration of 0.1 wt% nanoparticle is remarkable. The AC breakdown voltage of Al 2 O 3 nanofluids increases with the increase in particle concentration. Since 0.1 wt% of both untreated and treated alumina nanofluid samples show the highest breakdown voltage in each category, one type of 0.1 wt% alumina nanofluid containing the surfactant (CTAB) was used for comparison purposes. The nanofluid with the addition of surfactant was used in this experiment to determine if it contributes a great deal to the breakdown voltage. As illustrated in Figure 6c, it is clear that 0.1 wt% alumina nanofluid with CTAB indicates the lowest voltage value of 56.33 kV, and the plasma-treated alumina sample has the highest breakdown voltage value. Therefore, the results obtained from the Weibull analysis had about the same value as their mean voltage. The summary of scale and shape parameters of breakdown voltage results for alumina nanofluids from the Weibull probability analysis are shown in Table 2. Figure 7 shows the comparison between the present experimental data and the previous findings of the AC breakdown strength. Table 3 depicts the detail of previous studies according to the type of nanofluid and the effective loading of nanoparticle in enhancing the AC breakdown strength. It is shown that the plasma treatment implemented in the present work is the most promising technique that effectively improves the AC breakdown voltage of the nanofluids incorporated with 0.1 wt% of nano-alumina, followed by the CTAB surfactant technique, which also increased the AC breakdown voltage by more than 50% of the pure mineral oil. Moreover, the variation of nanoparticles used with different effective loadings of nanoparticles exhibits less than a 50% improvement.
Partial Discharge Characteristics
Phase-resolved PD patterns of 0.01 wt%, 0.05 wt%, 0.1 wt%, and 0.3 wt% of Al 2 O 3 nanofluids were shown in Figures 8-11, respectively. Discharge occurrences in mineral oil were repeatable in both positive and negative half-cycles. In addition, only one or two discharge pulses were produced during the power cycle. Furthermore, the polarity effect can also be shown by the discharge in the mineral oil, which tends to have much more negative pulses than the positive pulse in the cycle, as also claimed in the previous research by Makmud et al. [16]. Meanwhile, Figure 12 shows the average PD magnitude for all alumina nanofluid samples. As illustrated in the figure, pure mineral oil shows the highest average PD magnitude, at about 676 pC, while the lowest is shown by 0.01 wt% plasma-treated alumina nanofluid, which is about 106 pC. The other samples obtained a lower average PD magnitude compared to pure mineral oil, and this trend is in line with the previous studies by Makmud et al. [16] and Nagendran et al. [36]. Likewise, plasma-treated nanofluid samples show a lower average PD magnitude compared to the untreated samples. For 0.01 wt% alumina nanofluids, the plasma-treated sample has a lower average PD magnitude of about 106 pC than the untreated sample at about 330 pC.
Furthermore, for 0.05 wt% nanofluids, the average PD magnitude charge values are about 379 pC and 147 pC, respectively, for untreated and plasma-treated samples. As usual, a sample with surfactant (CTAB) was used for comparison purpose. The 0.1 wt% has been determined to be mixed with surfactant owing to the fact that this amount resulted in a higher AC breakdown strength. With 0.1 wt% alumina and surfactant, the sample exhibited a higher value of average PD magnitude, at about 170 pC, compared to untreated and plasma-treated samples at about 166 pC and 151 pC, respectively. Lastly, for 0.3 wt% samples, the untreated and plasma-treated nanofluids show an average PD magnitude of about 177 pC and 176 pC, respectively. These results demonstrate that the addition of alumina nanoparticles into the mineral oil would certainly enhance its PD characteristics, as also revealed by Muangpratoom et al. [37], Mohamad et al. [38], and Jacob et al. [39]. The total number of partial discharges (PDs) of all alumina nanofluid samples is illustrated in Figure 13. The highest PDs number is shown by pure mineral oil, which is about 4506, while the lowest value is shown by 0.01 wt% plasma-treated alumina nanofluid, which is about 112. The lower the number of PDs, the better the sample, but the average of the PD magnitude must be emphasized. Figure 14 shows the comparison between present experimental data and previous findings of the average PD magnitude. Table 4 represents the detail of previous findings regarding the type of nanofluids and effective loading of nanoparticles to minimize the PD magnitude. Significantly, the plasma treatment on the surface of nanoparticles effectively improves the PD endurance, which proved that incorporating 0.01 wt% of plasma-treated alumina into mineral oil reduced the average PD magnitude of pure mineral oil by 84.32%. However, compared to other results obtained in previous findings, all the configurations of untreated and surfactant nanoparticles only showed less than a 34.69% reduction of the PD magnitude.
Viscosity
Viscosity is one of the most critical parameters studied since it can influence both the nanofluids' heat transfer and electrical properties [24]. Viscosity testing was performed on the oil samples using the Brookfield DV-II + Pro Automated viscometer, manufactured by Brookfield Engineering Laboratories (Middleboro, MA, USA) as shown in Figure 15, using the CP-42 spindle based on the ISO 3104 standard [41]. In this paper, the rheometer measured the viscosity at temperatures of 40 • C and 60 • C. Figure 16a shows the average viscosity of Al 2 O 3 nanofluid samples at 40 • C. The alumina nanofluids showed that the higher the concentration of nanoparticles, the higher the viscosity of the sample. This was also collectively revealed by Yu et al. [42] and Wong et al. [43]. It was clearly shown that the sample with the highest percentage of nanoparticles, which was 0.3 wt%, resulted in the highest viscosity readings for both untreated and plasma-treated samples with values of about 13.76 mPas and 12.71 mPas, respectively.
The alumina nanofluid with CTAB was used for comparison purposes. With the value of 10.53 mPas, the sample with CTAB did not aid much in reducing the viscosity of nanofluids. The value showed a significant change compared to 0.1 wt% alumina UNF with a value of about 9.85 mPas, while the 0.1 wt% alumina PTNF showed a value of 9.80 mPas. Between these three 0.1 wt% samples, the plasma-treated sample was still the best, with a value of 9.80 mPas; 0.01 wt% alumina UNF and 0.01 wt% alumina PTNF are 9.49 mPas and 9.46 mPas, respectively. In contrast, 0.05 wt% alumina UNF and 0.05 wt% alumina PTNF values are 9.53 mPas and 9.50 mPas, respectively.
The viscosity results of alumina nanofluids at 60 • C, as shown in Figure 16b, show that the higher the concentration of nanoparticles, the higher the sample's viscosity. The 0.3 wt% is the highest percentage of nanoparticles used, showing the highest viscosity readings for both untreated and plasma-treated samples with the values of 8.54 mPas and 8.26 mPas, respectively. The same as at 40 • C, the sample with surfactant (CTAB) was used for comparing 0.1% nanoparticles with untreated and plasma-treated samples. With a value of 5.69 mPas, the sample with surfactant did not help much in reducing the viscosity of nanofluids. The value indicates no substantial difference relative to the untreated 0.1 wt% with a value of 5.66 mPas, while the plasma-treated 0.1 wt% indicates a value of 5.61 mPas.
The 0.01 wt% alumina UNF and 0.01 wt% alumina PTNF samples, respectively, gave the values of 5.33 mPas and 5.26 mPas. Meanwhile, 0.05 wt% alumina UNF and 0.05 wt% alumina PTNF samples obtained values of 5.47 mPas and 5.47 mPas, respectively. As mentioned before, lower-concentration nanoparticles have a negligible impact on the viscosity of mineral oil. As illustrated in Figure 16, both untreated and plasma-treated alumina nanofluids at 0.01 wt% and 0.05 wt% did not show any significant changes due to a smaller concentration of nanoparticles having a negligible effect on the viscosity of mineral oil [4].
Thermal Conductivity
Dispersing nanoparticles in fluids is an efficient way to improve the thermal conductivity of nanofluids. In this paper, the relationship between thermal conductivity and viscosity of mineral oil-based alumina nanofluids in a temperature range from 40 • C to 80 • C under different nanoparticles weight fractions of 0.01 wt%, 0.05 wt%, 0.1 wt%, and 0.3 wt% were addressed.
Thermal conductivity and viscosity are the essential thermophysical properties of any nanofluids affecting their heat transfer performance. Temperature and volume fractions significantly affect the thermal conductivity and viscosity characteristics of mineral oilbased alumina nanofluids. In this paper, the researchers used a KD2-Pro thermal property analyzer with a heating element and thermistor on the KS-1 sensor needle for thermal conductivity measurements, as shown in Figure 17a. Hence, to keep the temperature within the range, a water bath, as shown in Figure 17b, helped to heat and maintain the temperature value required for the thermal purpose. Figure 18a-d shows that the thermal conductivity of alumina nanofluids increased with an increase in nanoparticle concentrations at elevated temperatures compared to pure mineral oil, and these results agreed with the conclusion made by Xiang et al. [44]. The 0.1 wt% alumina with CTAB nanofluid has higher thermal conductivity than pure mineral oil and untreated nanofluids but shows lower thermal conductivity than the plasma-treated nanofluid.
TEM Analysis
The structure of the sample and dispersion of the nanofillers within the sample can be observed and further studied using JEOL JEM-2100F transmission electron microscope (TEM), manufactured by JEOL Ltd. (Akishima, Tokyo, Japan) as such in Figure 19. Furthermore, the sample preparation of nanofluids for TEM analysis is easy and not complicated as only a small drop of nanofluids was placed onto a TEM grid and was allowed to dehydrate at room temperature. For sample preparation for the transmission electron microscope, nanofluid samples are first mixed with distilled water, with a ratio of 1:10 in volume [45]. Using the CTAB as a surfactant, the alumina nanofluids with surfactant were observed to have a high level of agglomeration, as shown in Figure 20a. Meanwhile, in Figure 20b, without any chemical treatment in an untreated nanofluid, the size of agglomerated particles and the number of primary particles in a nanoparticle cluster was significantly decreased. However, the stirrer and sonication do not seem to be an effective method to break down the size of the alumina nanoparticle clusters. As shown in Figure 20c, the plasma treatment was the most effective method to deagglomerate the alumina nanoparticle dispersions in mineral oil.
Discussion
In this work, there are two types of mineral oil-based nanofluids prepared, namely plasma-treated mineral oil-based nanofluids and untreated mineral oil-based nanofluids. However, a CTAB-treated nanofluid was also prepared with 0.1 wt% nanoparticles for comparison purposes. These four types, including pure mineral oil, were compared to their performances for AC breakdown voltage, partial discharge, viscosity, and thermal conductivity characteristics. The weight percentage of alumina added into the mineral oil were 0.01, 0.05, 0.1, and 0.3 wt% only. Meanwhile, the weight percentage of CTAB added was 0.075 wt% of the alumina nanofluids [35].
For AC breakdown tests, both 0.1 wt% plasma-treated alumina nanofluids indicate the highest breakdown voltage than other samples. The Weibull analyses also show the same trend as AC breakdown voltage results. Ionization in cold atmospheric pressure plasmas is not very high but nevertheless very effective in generating high concentrations of reactive radicals, as many researchers have chosen this approach to modify the surfaces of nanoparticles. Consequently, the plasma surface modification treatment of alumina nanoparticles has led to higher AC breakdown voltage. The 0.1 wt% plasma-treated nanofluids have the highest enhancement in about 45.25% compared to pure mineral oil. Such apparent breakdown voltage enhancement based on the addition of plasmatreated nanoparticles has suggested a significant solution to improve the breakdown voltage of the mineral oil, which has been reported to decrease after specific years of service [46]. It is noteworthy that the results obtained indicate that this simple plasma treatment method can enhance the interfacial interaction, thus increasing the breakdown voltage of the nanofluids. The enhancement behavior of AC breakdown voltage with increased nanoparticles concentration can be explained due to the relaxation time constant and polarization of nanoparticles in the nanofluids. This was also explained by Wang et al. in reference [47]. In addition, the polarization produces charges that can change the potential distribution around the nanoparticles in the nanofluids. After that, dielectric nanoparticles' polarization changes them into potential wells necessary to capture free electrons [48]. The breakdown strength of transformer nanofluids is often correlated with additional traps from the dispersed nanoparticles, which work to capture electrons and reduce the energy of electrons travelling through the transformer oil. This mechanism was believed and claimed by several researchers [47,48]. The effect from that is the possibility that other electron production could be reduced, and thus the distortion of the electric field in transformer oil by electronic charge could also be reduced, thus increasing the breakdown voltage [29].
The plasma-treated samples show enhanced PD characteristics through the PD tests compared to pure mineral oil, untreated nanofluids, and CTAB-treated nanofluids. The presence of alumina nanoparticles in mineral oil resulted in higher viscosity than pure mineral oil. This indication was also pointed out by Jin et al. [11]. The number of PDs increases with an increasing weight percentage of alumina nanoparticles, as Makmud et al. [16] claimed. According to Jin et al.'s [14] findings, nanoparticles in mineral oil can absorb those additives such as moisture, acidity, and impurities due to oxidation on their surfaces. Consequently, the PD magnitude and PD's number of the nanofluids were smaller than pure mineral oil, as also concluded by Jin et al. [14] and Kurimsky et al. [49]. A higher weight concentration of alumina nanoparticles can be considered worse for transformer applications based on partial discharge characteristics. A concentration above 0.1 wt% significantly influences PD magnitude and the number of PDs of the nanofluids. Agglomerated nanoparticles can explain this behavior above a certain weight concentration in mineral oil [15].
The phenomenon leading to a breakdown of liquid insulation is called a streamer, which normally consists of a positive and negative streamer. In transformer oil, the initiation of the streamer usually occurs when electrons generated by field emission at the needle tip are induced. Then, local expansion is created and forms a low-density form. As a result, electrons can speed up, and the ionization process appears to be multiplied by the charge and helps the discharge channel expand. It is noteworthy that the development of a low-density zone is indeterminate and causes different propagation traces. According to space charge theory, a positive space charge zone is generated and developed because of the enormous difference in the mobility of ions and electrons. These positive space charges distort the previous electric field distribution in the oil that the electric field at the needle tip is diminished. While the electric field at the head of the ionized zone is enhanced, this causes the ionization to occur further, and the streamer channel under positive excitation is more likely to elongate towards the ground than the negative cycles [50].
Meanwhile, the PD pattern in oil found that the negative-polarity PDs occur much more than that positive-polarity PDs. As Liu et al. [32] explained, PD with negative polarity always appears near the needle electrode with a corona-type structure. In addition, the positive ions and free electrons have been generated due to the ionization near the tip of the needle as per the space charge theory. The positive ion is moved relatively slowly in the oil, which gathered near the tip, greatly heightened, and forced the electric field between the negative tip and positive ions, causing the PD to occur much more frequently. The free electron is caused by ionization growth and is more likely to expand along the electric field line, and consequently forms a negative charge layer with penetrated distribution [51]. After all the explanations above, it can be said that the space charge effect is mainly caused by significant differences in mobility between electrons and ions [50].
A study by Yuzhen et al. [52] proved that the moisture content, acidity, and impurities due to oxidation could encourage a negative effect on the dielectric strength of mineral oil. In contrast with the PD magnitude, the pulse repetition rate is more sensitive to those additives. The additional nanoparticles added into the mineral oil can absorb those additives to their surface, henceforth contributing to the smaller number of PDs in alumina nanofluids than in the mineral oil. Based on the overall results, the plasma-treated nanoparticles in the nanofluids could have greater characterization in adsorbing those additives than the untreated samples, thus improving the PD characteristics by reducing the total discharge magnitude compared to the pure mineral oil.
The viscosities of alumina nanofluids show a similar trend at temperatures of both 40 • C and 60 • C. Adding nanoparticles into the mineral oil has created an extraordinary impact on the thermal performance of the mineral oil [53][54][55]. The highest nanoparticle concentration was 0.3wt% in alumina nanofluids, with the highest viscosity values. This behavior can be interpreted by the increased nanofluids concentration, which directly influences internal viscous shear stresses [56]. However, the increasing nanoparticle concentration could affect the viscosity and deteriorate the nanofluids' heat transfer system [57]. A higher concentration can also contribute to the higher agglomerated cluster of nanoparticles in nanofluids, which can be considered one reason for higher viscosity [58].
Comprehensive studies in using surfactant as a stabilizer at high temperatures are still lacking. The studies of surfactants used at high temperatures are extremely important, affecting the physical properties of the surfactants and the nanoparticles [59]. Meanwhile, the excessive surfactant used in nanofluids could change the nanofluid characteristics, such as viscosity and thermal conductivity, and will be an apprehensive issue in nanofluid applications [60]. As mentioned above, this strongly supports the idea that the surfactant should be eliminated in nanofluids. Since the nanoparticle's sizes are very small, the attractive forces between the particles can cause them to agglomerate. Furthermore, the plasma-treated nanofluids show lower viscosity values since the plasma treatment offers increased surface energy of the treated nanoparticles in mineral oil, thereby resulting in a good result with good suspension stability and lower viscosity.
Moreover, dispersing plasma-treated nano-alumina into the mineral oil has reduced the viscosity of the nanofluids compared to the untreated nanoparticles. Incorporating untreated nanoparticles with mineral oil tends to form an agglomerated dispersion of nanoparticles, which typically affects the viscosity of the nanofluids. This issue can be solved by treating the surface of nanoparticles using plasma discharge. The interfacial region formed through the plasma functionalization technique would improve the compatibility between nanoparticles and mineral oil molecules [20]. The enhancement of surface compatibility may result in enhancing the distribution of nanoparticles into mineral oil uniformly. The uniform dispersion of nanoparticles into the mineral oil would cause the viscosity of the nanofluids to reduce. In addition, the viscosity of nanofluids is also affected by the number of well-dispersed nanoparticles.
Meanwhile, the contents of additive materials such as nanoparticles have also influenced the viscosity of the nanofluids. However, plasma treatment is an alternative method proven in this study to reduce the viscosity of the nanofluids incorporated with a particular quantity of nanoparticles. The results also showed that the behavior of nanofluids below 0.3 wt% represents Newtonian fluids. In contrast, the viscosity behavior of nanofluids with 0.3 wt% nanoparticles caused them to start to become non-Newtonian fluids. Plasmatreated alumina has an effective ability in improving the viscosity of nanofluids compared to other nanoparticles because it has a very weak shear rate dependence of their viscosity. Besides, alumina is more preferable as nanoparticles due to its mass-to-volume ratio, which is among the lowest compared to other nanoparticles such as silica and titania. Thus, the plasma-treated and untreated alumina are preferred to be dispersed into the based fluids.
Based on the viscosity tests, the viscosities of both untreated and plasma-treated nanofluids have also decreased at an elevated temperature, similar to pure mineral oil. As mentioned by Jiang et al. [61], it can be elucidated that the higher the temperature, the lower the viscosity due to the increase in thermal conductivity. The downward trend in viscosity when the temperature increases can be explained by a weakening intermolecular attraction between the mineral oil and the nanoparticles [57]. Additionally, higher temperature also influenced the Brownian motion of nanoparticles and decreased nanofluid viscosity [58]. Thus, it has been found that viscosity depends strongly on both temperature and concentration. Furthermore, a previous research work stated that the formation of nanofluids has no significant effect upon the viscous resistance, but viscosity might have affected the development of streamers in that insulating liquid [62].
Furthermore, the thermal conductivity of mineral oil was enhanced with the addition of plasma-treated nanoparticles. The thermal conductivity of alumina nanofluids increased with the increase in nanoparticle concentrations and temperatures. In line with the results obtained by Bao et al. [63], higher nanoparticle surfaces, nanoparticle interaction, nanoparticle cluster, and Brownian motion of nanoparticles are among the significant factors that contributed to the thermal conductivity enhancement in alumina nanofluids when the nanoparticle concentrations were increased accordingly. In addition, the thermal conductivity of alumina nanofluids also increased with temperature, and this justification agreed with the results reported by Shah et al. [64]. This condition could be explained by the fact that the increased temperature results in decreased viscosity, contributing to the Brownian motion to escalate and thus affect the convection process in nanofluids [58]. The 0.1 wt% alumina with a CTAB nanofluid has higher thermal conductivity than pure mineral oil and untreated nanofluids but shows lower thermal conductivity than the plasma-treated nanofluid. Applying surfactant in nanofluids can cause the surface of the nanoparticles to be coated. It is noteworthy that the amount of surfactant in nanofluid is not limited by thermal conductivity, but the surfactant may cause physical or chemical instability problems [65].
Meanwhile, plasma-treated alumina nanofluids considerably enhance the thermal conductivity compared to other samples, including pure mineral oil, since the plasma treatment can convert the alumina nanoparticles to disperse much easier in the base oil [66]. Hence, plasma-treated alumina nanofluids exhibited better thermal properties than untreated alumina nanofluids and pure mineral oil. Plasma discharge occurred due to the ionization of the discharge gas, producing reactive species such as photons and electron clouds. The reactive species collide with the air molecules contained in the treatment chamber to form radical species, typically hydroxyl and oxygen-containing functional groups. The functionalized reactive species on the surface of nanoparticles could then react with the aluminum atoms, which produce a new and strong covalent on the interfacial region when the nanoparticles dispersed into the based fluids. This would create a new relaxation process that might reduce the transportation charge due to the formation of the interfacial region [67]. This interfacial region is key in improving insulation properties due to its role in trapping the charges distributed in the nanofluids. The mechanism of trapping the charges would reduce the accumulated space charge and eventually minimize the distortion of the local electric field [68]. This brings positive implications to the insulation properties, such as improving the breakdown strength and the partial discharge resistance of the nanofluids.
Conclusions
The electrical properties, dispersion stability, and thermal properties of mineral oilbased alumina nanofluids have been improved using cold atmospheric pressure plasma treatment. The easily operated atmospheric pressure plasma method has been successfully implemented to modify the surface of alumina nanoparticles. Their morphological analysis showed an improvement in the structure of the nanoparticle, according to the TEM analysis. In addition, the effect of ion and electron bombardment onto the surface of the nanoparticles can be regarded as changes in morphology. Therefore, the plasma treatment of the nanoparticles has resulted in a homogeneous dispersion and stability in nanofluids as this treatment provided stronger interactions between the mineral oil and the nanoparticles.
The electrical performances of mineral oil-based nanofluids with alumina nanoparticles have been successfully investigated and analyzed. The addition of alumina could help in improving the electrical properties of conventional mineral oil. The CTAB was chosen as a surfactant used for comparison purpose with the untreated and plasma-treated nanofluids. On top of that, the surfactant is one of the traditional methods to modify nanoparticles' surface in order to reduce the agglomerated clusters in nanofluids. However, it has been found that it has retained many drawbacks. The 0.1 wt% alumina nanofluids recorded the highest breakdown strength as compared to 0 wt%, 0.01 wt%, 0.05 wt%, and 0.3 wt% nanofluids, respectively. It can be concluded that the increase in the weight percentage of nanoparticles up to about 0.1 wt% could increase the breakdown voltage of the nanofluids, but samples show the reduced breakdown strength at a higher weight percentage (0.3 wt%) due to the agglomerated nanoparticles. The plasma-treated samples of alumina nanofluids have been proved to have better breakdown strength than pure mineral oil, untreated samples, and CTAB-treated nanofluids. The results were also supported by the Weibull analysis, with the same trend of improvement.
Meanwhile, partial discharge characteristics of alumina-based nanofluids were performed at the applied voltage of 20 kVrms. PD magnitude and the number of PDs were depicted, and the results showed that the plasma-treated samples had lower PD magnitude and a lesser total number of PDs compared to the untreated and CTAB-treated nanofluids. Hence, plasma-treated nanofluids are believed to have excellent potential to be used as power transformer oil in practice. In short, electrical tests showed an improved breakdown strength and PD characteristics of the plasma-treated alumina-based nanofluids. The mineral oil-based nanofluids with 0.1 wt% of plasma-treated alumina showed great improvements in electrical performances. A higher concentration of more than 0.1 wt% has resulted in deteriorated breakdown strength and PD resistance characteristics.
A higher percentage of nanoparticles used in a sample has resulted in a higher viscosity as well. However, the plasma-treated samples showed lower viscosity than untreated nanofluids and CTAB-treated nanofluids with an increase in temperature, thus showing that the plasma-treated nanofluids also had excellent heat transfer properties. Additionally, the higher the alumina nanoparticles added to the base fluid, the higher the thermal conductivity of the nanofluids. Based on the results obtained, the thermal conductivity was enhanced with the increase in temperature. This behavior can be explained by the Brownian motion of the nanoparticles in the nanofluids. Besides, 0.1 wt% of plasma-treated alumina nanofluids have also shown better improvements in thermal and dispersion stability. Furthermore, CTAB as a surfactant did not help much in solving the agglomeration issue. Therefore, with the elimination of the surfactant, plasma treatment can be an alternative and environmentally friendly method to modify the surface of the nanoparticles without using any chemical solutions.
Furthermore, the important conclusion for future research is to identify the effects of plasma treatment on the zeta potential and the stability of the nanoparticles dispersed in the base fluids. In addition, the effect of plasma treatment on the pH value of nanofluids could not be neglected. Therefore, it ought to be covered in future works in order to characterize the significance of plasma treatment in enhancing the insulation and thermophysical properties of plasma treatment nanofluids. | 9,069.2 | 2021-06-28T00:00:00.000 | [
"Physics"
] |
Sparse alternatives to ridge regression: a random effects approach
In a calibration of near-infrared (NIR) instrument, we regress some chemical compositions of interest as a function of their NIR spectra. In this process, we have two immediate challenges: first, the number of variables exceeds the number of observations and, second, the multicollinearity between variables are extremely high. To deal with the challenges, prediction models that produce sparse solutions have recently been proposed. The term ‘sparse’ means that some model parameters are zero estimated and the other parameters are estimated naturally away from zero. In effect, a variable selection is embedded in the model to potentially achieve a better prediction. Many studies have investigated sparse solutions for latent variable models, such as partial least squares and principal component regression, and for direct regression models such as ridge regression (RR). However, in the latter, it mainly involves an L1 norm penalty to the objective function such as lasso regression. In this study, we investigate new sparse alternative models for RR within a random effects model framework, where we consider Cauchy and mixture-of-normals distributions on the random effects. The results indicate that the mixture-of-normals model produces a sparse solution with good prediction and better interpretation. We illustrate the methods using NIR spectra datasets from milk and corn specimens.
Introduction
In a calibration of near-infrared (NIR) instrument, we model some chemical compositions of interest from a set of observations as a function of their NIR spectra, which are measured on several hundreds or thousands wavelengths (variables). In the calibration, we deal with the situation where the number of variables exceeds the number of observations and the variables exhibit extremely high multi-collinearity. With these characteristics of the data, we have two inherent problems in building a calibration model. Firstly, we have a problem in estimating model parameters as standard ordinary least squares (OLS) regression will fail in this situation, and secondly, some variables may not contribute towards better prediction.
To deal with the first problem, many calibration models have been proposed and shown to work well. These models can generally be categorised into two main groups. The first one is by regressing the response on linear combinations of the original variables (called latent variables or components) and the second one is directly regressing the response on the (original) variables. The first category includes partial least squares (PLS) regression and principal component regression (PCR) and the second category includes ridge regression (RR) and lasso regression. To deal with the second problem, wavelength selection or variable selection has been advocated to improve prediction (e.g. [25]). Many strategies have been proposed, including genetic algorithm (e.g. [2,20]), forward selection (e.g. [9]), self-organising map [5], and boundary subset selection [23]. See, for example, Ref. [1] for some strategies of variable selection.
Dealing with both problems separately can be sub-optimal in building a prediction model, as some selection methods are not optimal to be used with a particular calibration model. For example, forward selection method may result in a configuration of variables that does not produce better prediction than 'best subset' selection method in RR. To overcome this, recent studies suggested sparse alternatives to the calibration models [3,7,15,17]. The term 'sparse' refers to the model parameters, where some of them are zero estimated (or very close to zero), and the other parameters are estimated naturally to be away from zero. Effectively, the contribution of some variables are cancelled and the prediction model relies on the other variables that have non-zero parameter estimates. This is done in a single framework within the calibration model.
Many studies recently have investigated some sparse alternatives for PLS and PCR, mostly involving L 1 -norm penalisation or lasso [26]. For example, Chun and Keles [4] developed a sparse PLS method by imposing sparsity in the dimension reduction step. Fu et al. [8] proposed an elastic net, a combination of ridge-type and lasso-type penalties, that imposes sparse solution within PLS. Lee et al. [16] proposed a shrinkage of singular values for principal component analysis to produce sparse loadings. Lee et al. [17] modified the NIPALS algorithm in PLS, by incorporating lasso method to produce sparse loadings.
The above studies have focused on sparse solutions for latent-variable models. For direct regression models such as ridge regression, the main sparse alternative has been the lasso regression [26] or similar models with L 1 -norm penalty to the model objective function. Although they produce a sparse solution, the models share some concerns including interpretation of the model estimates in extremely multicollinear data.
In this paper, we propose some sparse alternatives to the ridge regression within a random effects model framework by demonstrating that a sparse solution can be achieved by modifying the distributional assumption of the random effects. The first one is a linear model where the random effects are assumed to follow a Cauchy distribution. The second one is a linear model where we assume that the random effects follow a mixture distribution of three normals. The three normal distributions correspond to those random effects that have negative, zero, and positive estimates to create a sparse solution. We compare this model to some existing models within random effects model framework such as ridge regression and lasso regression. The main results indicate that the Cauchy random effects model does not necessarily produce a sparse solution. The results also indicate that the mixture-of-normals random effects model will produce a sparse solution with interesting interpretation and a good prediction. We illustrate the application of our proposed models using NIR calibration from milk and corn datasets.
Methods
In this section, we discuss the different random effects models and how their distributional assumptions are modified to produce a sparse solution. In Section 2.1, we outline a general setting of random effects models. In Section 2.2 we describe the RR model and some current models that produce a sparse solution. We present the Cauchy and mixture-of-normals random effects models in Sections 2.3 and 2.4, respectively.
General setting
Let X be a matrix of NIR spectra of p variables from n observations. So the matrix X is of size n × p with n p. We assume that each variable has been centred to have zero mean. Let y be an n-vector of response variable, and let β be a p-vector of regression model parameters. We also assume that the vector y is centred to have zero mean. We model the response y as where ε ≡ {ε k }, k = 1, . . . , n, is an n-vector of the error term. We assume ε to follow a normal distribution with mean zero and variance covariance matrix = σ 2 I n , where I n is the identity matrix of size n. Our main interest is to estimate the regression parameters β.
It is well known that the solution of OLSβ LS = (X T X ) −1 X T y is not applicable in our case because (X T X ) is not invertible in the case of n p. Even if (X T X ) is invertible in the case of n > p, the estimates of β LS are highly unstable because of the extreme multi-collinearity between the columns of X . To deal with this problem, it is natural to make a distributional assumption on β so that we formulate the estimation problem in the context of random effects model. For example, if we assume β to follow a normal distribution N(0, σ 2 β ), we have a RR model (Section 2.2.1). It is of our interest in this paper to modify this assumption on the random effects to obtain a sparse solution for β, which will be described in Sections 2.2.2 and 2.4.
Let p(β) denote the distribution of β. In the context of random effects model, the estimation of β is based on an extended likelihood [22] or h-likelihood [18]. Let θ denotes the variance(s) and other parameters. The log-likelihood of the parameters can then be written as log L(β, θ) = log p(y | β) + log p(β). ( The estimates of β can be obtained by maximising log L(β, θ) in Equation (2). Regardless of the distribution of the random effects β, the conditional distribution of y given β is a normal distribution with mean E(y | β) = X β and variance , so that the first term in the log-likelihood is given by In our formulation, the RR can be viewed as a random effects model where the random effects β are assumed to follow a normal distribution (see the next section). To obtain sparse alternatives for RR, it is natural to modify the distributional assumption of the random effects and consider other distributions that have fatter tails than the normal distribution. Before we discuss about the modification, we briefly review the RR and other current models that produce sparse solutions from the random effects model framework in the next section. The proposed new sparse alternatives to the ridge regression will be presented in Sections 2.3 and 2.4.
It is interesting to note that Equation (2) can have a Bayesian interpretation. From a Bayesian perspective, p(β), p(y | β), and L(β, θ) can be considered as prior, likelihood, and posterior, respectively. We will come across this form again in the next several sections, in particular Equations (4), (7), (8), and (12).
Normal random effects (RR)
To view the RR from within the random effects model framework, we assume that the regression parameter β follow a normal distribution with zero mean and variance covariance matrix . We also assume that β is independent of ε. Combining this with the conditional log-likelihood (3), the log-likelihood of the parameters can be written as where θ ≡ { , D}.
At fixed values of θ, we take the first derivative of the log-likelihood log L with respect to β Setting this to zero and solving it for β, we obtain the estimates of β aŝ where the subscript N inβ N indicates that the estimates are under the normal distribution assumption on β. By considering that ≡ σ 2 I n and D ≡ σ 2 β I p , the estimates for β N can be rewritten intoβ where λ ≡ σ 2 /σ 2 β . This is the RR estimates as first proposed by Hoerl and Kennard [11]. The estimation of λ can be done via cross-validation or through minimising Akaike's information criterion (AIC).
One thing to note is that the RR estimates in Equation (6) are not sparse, i.e. there is no clear separation between zero and non-zero estimates. To put forward sparse alternatives for the RR, we assume β to follow some distributions which put a density mass around zero and have fatter tails (for non-zero estimates). A natural choice would be to consider a Laplace distribution, which is known to have fatter tails than the normal distribution ( Figure 1). The result of this assumption would be the well-known Lasso regression as described in the next section.
Laplace random effects
A distribution that we commonly assume on the random effects β to produce a sparse solution is the Laplace distribution ( Figure 1, right panel, dotted line). Specifically, we assume β to follow a Laplace distribution with location 0 and scale σ v , or where | · | denotes the modulus or absolute value. Combining this with the conditional loglikelihood (3), the log-likelihood of the parameters can be written as There is one thing to note from the estimation of β from the log-likelihood in Equation (7). The first derivative of the last term in the log-likelihood, log p(β), does not contain β. In fact, the first derivative is −1/σ v for positive β and 1/σ v for negative β. There are some alternative ways to estimate β in this case (e.g. [28]). In this study, we resort to the algorithm discussed in the original paper of Tibshirani [26] and Hastie et al. [10] which is implemented in the R package lars. The package also implements the estimation of σ v via cross-validation.
Cauchy random effects
The first alternative model that we consider is a random effects model where the random effects are assumed to follow a Cauchy distribution. This distribution is illustrated in Figure 1 (left), in comparison to the normal distribution. The Cauchy distribution has fatter tails than the normal distribution, which makes it an intuitive first alternative towards obtaining a sparse solution.
Specifically, we consider the random effects β to follow a Cauchy distribution with location 0 and a scale σ s , or where β is assumed to be independent to ε. Combining p(β) with the conditional distribution of y in Equation (3), the log-likelihood of the parameters is given by (8), an additional step is needed to approximate the log-likelihood by a quadratic form [22, pp. 464-466]. However, we can derive a more stable estimation as follows. First, note that the log likelihood of the random effects β i is given by The first derivative of the log-likelihood is given by where Secondly, we combine the expression for (β) in Equation (9) with the derivation of loglikelihood log L in Equation (8) at fixed θ to obtain At fixed θ, we set this equation to zero and solve it for β to obtain the estimates of β aŝ where the subscript C inβ C denotes the Cauchy distribution assumption on the random effects β. With a starting value β 0 C , the estimation of β C is done alternately at fixed value of θ by first computing D −1 s and then calculatingβ C as in Equation (10). The estimation of error variance σ 2 is done robustly byσ and the estimation of σ 2 s is done through cross-validation.
Mixture-of-normals random effects
Previous approaches to obtain a sparse solution relied on the assumption that the model parameters follow a distribution that put some mass at zero and has fatter tails (for example, Laplace distribution). With this assumption, some parameters receive heavy shrinkage towards zero in the estimation, while allowing the other parameters to be estimated naturally away from zero. In the RR, assuming a (single) normal distribution with zero mean produces random effects estimates that are shrunk towards the zero mean. To obtain a sparse solution, we need to support some parameters to be naturally estimated away from zero by constructing a random effects distribution that contains non-zero means.
Hence, a natural immediate extension to obtain a sparse solution is to assume that the parameters β follow a mixture of three normal distributions. The first and third components of the mixture are assumed to have negative and positive means, respectively, and the second component to have zero mean. The second component with zero mean is the one that will put shrinkage on some estimates towards zero and give a sparse solution.
Specifically, we assume that the parameters β ≡ {β i } follow a mixture distribution where g = 3 is the number of components in the mixture distribution, π j is the mixing proportion with 0 ≤ π j ≤ 1 for all j and j π j = 1, μ j is the jth mean of normal component, constrained to have μ 1 < 0, μ 2 = 0, μ 3 > 0, and σ 2 βj is the jth variance of normal component in the mixture distribution.
To estimate the parameters, we first rewrite the model (1) as for k = 1, . . . , n. Defining θ ≡ {μ j , σ 2 βj , π j , = σ 2 I n , j = 1, 2, 3}, and combining the expressions in Equations (3) and (11), the contribution of observation k to the extended likelihood of β in Equation (2) can be written as where p j (·) is a normal density function with mean μ j and variance σ 2 βj . At fixed θ , taking the derivative of log L k (β, θ) with respect to β gives us We define and P j as a diagonal matrix of size p × p with diagonal entries p ij for i = 1, . . . , p. The quantity p ij is the probability of β i to belong to mixture component j.
Expression (13) can be written as Combining for k = 1, . . . , n, we arrive at with = σ 2 I n and D j = σ 2 βj I p . Equating the above expression to zero yields the estimatê We can infer that, as a result of assuming a mixture distribution on the distribution of random effects β, the expression forβ M in Equation (17) contains an additional term that would shift a group of parameter estimates to their corresponding μ j , depending on their probability to belong to the mixture component j. For example, if β i has a higher probability to belong to the group j = 3 with a positive mean, the estimate will be shrunk towards μ 3 , and not zero. As a result, we have a non-linear shrinkage. The expression forβ M in Equation (17) reduces to the ridge regression estimateβ N in Equation (5), if μ j = 0 and σ 2 βj = σ 2 β for all j = 1, 2, 3.
The estimation of θ is done jointly with the estimation of β M in an iterative manner. We use non-standard expectation-maximisation algorithm, where the estimation of random effects is done in the maximisation step instead of the expectation step. The advantage is that the quantities inβ M and θ ≡ {μ j , σ 2 βj , π j , = σ 2 I n , j = 1, 2, 3}, are in closed form expression (tractable). To obtain a sparse solution, σ 2 β2 is constrained at a small value, typically in the order of 10 −4 -10 −5 of the estimates of σ 2 β1 or σ 2 β3 , and we constrain σ 2 β1 = σ 2 β3 . Referring to Figure 1 (right), this means that the middle component would be a 'spike'. The variances associated with non-zero means (σ 2 β1 and σ 2 β3 ) are estimated via cross-validation.
Datasets
In our study, we illustrate the above methods using two datasets. The first one is a dataset from a calibration of NIR instruments with spectra from milk batches as previously described in [9,14]. Seventy milk batches were drawn from a production line in milk processing factory, and their fat concentrations were measured. On each milk batch, NIR spectrum was scanned between 829 and 1145 nm with wavelength resolution of 2.45 nm, creating a spectra matrix of 70 rows (observations) and 130 variables (wavelengths). Figure 2 (left) shows the spectra of the 70 milk batches after being centred on their respective variable means. The second dataset is from corn specimen described in Eigenvector.com website [13]. The dataset consists of NIR spectra from 80 corn specimens measured on two spectrometers (mp5 and mp6). The wavelength range is 1100-2498 nm at 2 nm intervals (creating 700 variables). The moisture, oil, protein and starch values for each of the corn specimen were measured. So, we have four calibration models for each spectrometer, with a total eight calibration models in this dataset. Figure 2 top-right and bottom panels show the spectra of the 80 corn specimens that have been centred to have zero column means. The results of analysis on the corn dataset are presented in the supplementary material.
Cross-validation
In the cross-validation, we split n observations into two subsets. The first one is a training set with n t observations, in which we estimate the regression parameters. The second one is a validation set with n v observations, where we estimate the predicted fat concentration using the regression parameters obtained in the training set. In each regression method, we calculate the root mean square errors of prediction (RMSEP) where γ represents a relevant tuning parameter, the summation is done over the n v observations in the validation set, andŷ k is the predicted fat concentration using the parameter estimates from the estimation set. The use of cross-validation to estimate a tuning parameter is appropriate in our NIR calibration problem. It can be shown that an estimate of tuning parameter based on the cross validation also maximises its profile likelihood. In a general case where the number of variables increases at a higher rate than the number of samples, careful consideration is needed to the choice of method to estimate tuning parameter (see, for example, [6,27]).
Results
In this section, we present the results of our analysis on the milk dataset; the results on the corn dataset are presented in the supplementary material, except the summary of prediction error which are presented in Section 4.4. Figure 3 shows the results of cross-validation and the estimates of normal random effects. The figure indicates that the optimal λ is estimated at exp{−9}. The estimatesβ N (from the training set) in Figure 3 suggest that we cannot obtain a sparse solution; the estimates are all non-zero. From variable selection point of view, we do not have a simple interpretation of the estimates as all of the wavelengths are taken into account in the prediction. The estimatesβ N follow approximately a normal distribution (not shown), reflecting our assumption on β N . Figure 4 presents the results of cross validation and random effects estimates under the Cauchy and Laplace random effects models. For the Cauchy random effects model, the estimate of σ 2 s is exp{4}, which minimises the validation residual sum of squares. The figure shows some parameters that are estimated away from zero while the others are estimated near zero. When we 'zoom in' to the estimatesβ C around zero, these estimates are not zero exactly, but only distributed tightly around zero (see Figure 1 in the supplementary material, top-left panel). This indicates that the Cauchy distribution with fatter tails allows some estimates to be away from zero, but not enough to shrink some estimates to zero. The behaviour of the estimatesβ C around zero is similar to that of the normal random effectsβ N .
Cauchy and Laplace random effects models
For the lasso regression, Figure 4 indicates that the estimate of λ L ≡ 1/σ v is exp{−5.079}. The algorithm to estimate the random effects was implemented in 'steps', hence the value of λ L evaluated cannot be made equally spaced. Looking at the bottom-right figure on the estimateŝ β L , we have a sparse solution where many random effects are shrunk to zero, and the others are non-zero estimated. Unlike the characteristics of the estimatesβ C , some of the estimates under the lasso regressionβ L are zero estimated. In practice, the estimates are very small (in the order of 10 −7 -10 −5 ) and reported as zero.
Mixture-of-normals random effects model
For the mixture-of-normals random effects model, the estimates of σ 2 βj for j = 1, 3, are presented in Figure 5. Based on the cross-validation, the variances σ 2 β1 = σ 2 β3 are estimated at exp{5}. The estimatesβ M are presented in the right panel of the figure and exhibit a sparse solution, where some estimates are shrunk to zero.
Compared to the lasso regression solution, the solution under mixture-of-normals random effects has less number of zero estimates. The estimates of mixture proportion π j 's are 0.471, 0.113, and 0.416 for j = 1, 2, 3. So, the number of zero estimates are approximately 11% out of 130 wavelengths. The estimated means of the mixture components μ j 's are −25.4 and 28.7 for j = 1, 3 (the middle component is constrained to have zero mean). This is reflected in the estimatesβ M where they are separated into three groups as displayed in Figure 5.
From Figure 5, we have an interesting note. There are six regions in the wavelength that have 'blocks' of non-zero random effects estimates, three in each sign. It has been suggested in the context of PLS regression that selecting regions of wavelengths, rather than selecting individual wavelengths, can potentially give better prediction (e.g. [19,21,24]) or give better stability of the estimates [12]. These studies support the notion that within the NIR regions of wavelength, there are some intervals where the main information lie.
Our results based on the mixture-of-normals random effects model in the milk data seem to support this idea. Although we do not model explicitly the spatial information between wavelengths, the existing correlation structure between wavelengths and the mixture model assumption on the random effects have resulted in accentuating the regions of wavelengths that positively or negatively associated with the fat concentration. This result is not specific only to this dataset. Similar interpretation can be inferred in different calibration models in the corn dataset (presented in the supplementary material).
Prediction
To check whether the models are reasonable to be used in real application, we compare the predicted fat concentration in the validation set to their observed value under different models as presented in Figure 6 for the milk dataset. The predicted fat concentrations are based on the The description for elastic-net and adaptive lasso models are presented in the supplementary material.
parameter estimates obtained in the training set. In general, all of the models that we consider in this study suggest a good prediction. The figure indicates that the Laplace random effects model exhibits the lowest RMSEP, while the RR exhibits the highest RMSEP in the milk dataset. The different RMSEP's for the different calibration models in the corn and milk datasets are presented in Table 1. Overall, the different calibration models indicate a good prediction error. It is not categorically conclusive that one model is always superior to the other models. Some reduction of prediction error that we can observe from those datasets are marginal. The mixtureof-normals random effects model tend to have lower prediction error in majority of calibration models.
Discussion
In this study, we have investigated some sparse alternatives for RR in NIR calibration problem from random effects approach. This approach gives us the flexibility in modifying the distributional assumption of the parameters to obtain a sparse solution. We concentrate on the distributions that put more density mass around zero, but still allow some random effects to be estimated away from zero. In this paper, we investigate the Cauchy, and mixture-of-normals distributions for the random effects as alternatives to the normal distribution, and briefly review lasso regression as a well-known alternative.
In a strict sense, assuming Cauchy distribution for the random effects does not produce a sparse solution, as none of the variables is shrunk to zero. However, apart from the Laplace distribution, the Cauchy distribution is another immediate natural alternative to the normal distribution. It has fatter tails that we expect to allow some random effects to be estimated away from zero. Although some parameters are estimated away from zero, the model does not generally improve the prediction compared to the RR.
We found that the mixture-of-normals random effects model is a better alternative to the RR compared to the Cauchy and Laplace random effects models. In the mixture-of-normals random effects model, the estimates form a sparse solution and, with extremely high multicollinearity presents, the estimates have a more intuitive interpretation compared to those of the Cauchy or Laplace random effects model. Our results suggest that the model shows a good prediction in a cross validation.
Conclusion
The challenges in calibration of NIR instruments have recently been dealt with sparse regression models. We investigated a novel sparse alternative to RR within a random effects model framework where we assume the random effects to follow a mixture of three normal distributions. This assumption has resulted in a sparse solution where some estimates are zero estimated. Compared to the RR or lasso regression, the mixture-of-normals random effects model has a more intuitive interpretation with relatively better prediction. 1 | 6,549.2 | 2015-01-02T00:00:00.000 | [
"Computer Science"
] |
SpatialVOC2K: A Multilingual Dataset of Images with Annotations and Features for Spatial Relations between Objects
We present SpatialVOC2K, the first multilingual image dataset with spatial relation annotations and object features for image-to-text generation, built using 2,026 images from the PASCAL VOC2008 dataset. The dataset incorporates (i) the labelled object bounding boxes from VOC2008, (ii) geometrical, language and depth features for each object, and (iii) for each pair of objects in both orders, (a) the single best preposition and (b) the set of possible prepositions in the given language that describe the spatial relationship between the two objects. Compared to previous versions of the dataset, we have roughly doubled the size for French, and completely reannotated as well as increased the size of the English portion, providing single best prepositions for English for the first time. Furthermore, we have added explicit 3D depth features for objects. We are releasing our dataset for free reuse, along with evaluation tools to enable comparative evaluation.
Introduction
Research in image labelling, description and understanding has a long tradition, but has recently seen explosive growth. Work in this area is most commonly motivated in terms of accessibility and data management, and has a range of different specific application tasks. One current research fo-cus is detection of relations between objects, in particular for image description generation, and the research presented here contributes to this line of work with a new dataset, SpatialVOC2K, 1 in which object pairs in images have been annotated with spatial relations encoded as sets of prepositions, specifically for image-to-text generation. We start below with the source datasets from which we obtained the images, bounding boxes, and candidate prepositions (Section 2), followed by an overview of directory structure and file schemas (Section 3), and a summary of the annotation process (Section 4) and spatially relevant features (Section 5). We describe the two evaluation tools supplied with the dataset (Section 6), and finish with a survey of other datasets with object relation annotations (Section 7).
Source Data
Our main data source for SpatialVOC2K was the PASCAL VOC2008 image dataset (Everingham et al., 2010) in which every object belonging to one of 20 object classes is annotated with class label, bounding box (BB), viewpoint, truncation, occlusion, and identification difficulty (Everingham et al., 2010). Of these annotations we retain just the BB geometries and the class labels (aeroplane, bird, bicycle, boat, bottle, bus, car, cat, chair, cow, dining table, dog, horse, motorbike, person, potted plant, sheep, sofa, train, tv/monitor).
We also used Rashtchian et al.'s VOC'08 1K corpus (2010), which has 5 descriptions per im-age obtained via Mechanical Turk for 50 images from each VOC2008 class, in order to determine an initial set of candidate prepositions for our annotations (for details see Section 4). Due to quality control measures, the VOC'08 1K descriptions are of relatively high quality with few errors.
For SpatialVOC2K, we selected all images from the VOC2008 data that had two or three object bounding boxes (BBs), meaning that images contained exactly two and three objects from the VOC2008 object classes, respectively. We also selected all images with four and five BBs where three were of normal size and the remainder very small (bearing the VOC2008 label 'difficult'). This selection process resulted in a set of 2,026 images with 9,804 unique object pairs. Numbers of BBs in images were distributed as follows: For each image, we then (i) collected additional annotations (Section 4) which list, for each ordered object pair, (a) the single best, and (b) all possible prepositions that correctly describe the spatial relationship between the objects; and (ii) computed a range of spatially relevant features from the image and BB geometries, BB labels, and image depth maps (Section 1). All annotations and features are included in this dataset release.
SpatialVOC2K Structure and Schemas
The overall structure and file conventions of the SpatialVOC2K dataset mirror those of the VOC2008 dataset where possible: All files in the Annotations directory start with a line that is simply the original annotations from VOC2008. In the Best subdirectory, the remaining lines have the pattern Object 1 Object 2 Preposition, where Object 1 and Object 2 are the exact word strings, including any subscripts, of the object labels in the first line in the file, and Preposition is the single best preposition chosen by annotators for the two given objects presented in the given order (more about object order in Section 4 below). Each pair of annotated objects is thus associated with exactly two prepositions in the Best files, the best humanselected preposition for each order. The following is a simple example of a Best file: In the All directory, files have the same structure except that in the preposition lines, instead of a single preposition, there are as many prepositions as were selected by the human annotators as possible for a given ordered object pair. The Spatial Features files also have the same basic structure, except that instead of prepositions, there are 19 feature-value pairs (explained in Section 5) for each ordered object pair (some feature values differ depending on object order), e.g.: In the following three sections, we explain how we obtained the preposition annotations and spatial features, and how the metrics encoded by the evaluation tools are defined.
ones. This gave us 38 English prepositions: V 0 E = { about, above, across, against, along, alongside, around, at, atop, behind, below, beneath, beside, beyond, by, close to, far from, in, in front of, inside, inside of, near, next to, on, on top of, opposite, outside, outside of, over, past, through, toward, towards, under, underneath, up, upon, within } To obtain prepositions for French, we first asked two French native speakers to compile a list of possible translations of the English prepositions, and to check these against 200 sample images randomly selected from the complete set to be annotated. This produced 21 prepositions which were reduced to 19, based on evidence from previous work (Muscat and Belz, 2015), by eliminating prepositions that were used fewer than three times by annotators (en haut de, parmi). After the first batch of 1,020 images had been annotated, we furthermore merged prepositions which co-occur with another preposition more than 60% 3 of the times they occur in total (á l'interieur de, en dessous de), in accordance with the general sense of synonymity defined in previous work (Muscat and Belz, 2017). We found this kind of cooccurrence to be highly imbalanced, e.g. the likelihood of seeingá l'interieur de given dans is 0.43, whereas the likelihood of seeing dans giveń a l'interieur de is 0.91. We take this as justification for mergingá l'interieur de into dans, rather than the other way around, and proceed in this way for all prepositions. The process leaves a final set of 17 French prepositions: V F = {à côté de,á l'éxterieur de, au dessus de, au niveau de, autour de, contre, dans, derrière, devant, en face de, en travers de, le long de, loin de, par delà, près de, sous, sur} We also reduced the set of 38 English prepositions, using the same elimination process, starting with prepositions that occurred fewer than three times (toward, towards, about, across, along, outside, outside of, through, up). A further 12 prepositions were merged into others (within, inside, inside of, beside, alongside, by, against, upon, atop, on top of, beneath, under), yielding a final set of 17 English prepositions: V E = { above, around, at, behind, below, beyond, close to, far from, in, in front of, near, next to, on, opposite, over, past, underneath } As discussed in more detail in previous work (Muscat and Belz, 2017), we make the domainspecific assumption that there is a one-to-one mapping from each preposition to the SR it denotes (whereas an SR can map to multiple prepositions). While our machine learning task is SR detection, we ask annotators to annotate our data with the corresponding prepositions (a more humanfriendly task).
We used the above preposition sets in collecting annotations as follows. For each object pair O i and O j in each image, and for both orderings of the object labels, L i , L j and L j , L i , the task for annotators was to select (i) the single best preposition for the given pair (free text entry), and (ii) the possible prepositions for the given pair (selected from a given list) that accurately described the relationship between the two objects in the pair, given the template L 1 is L 2 (is becomes et for French). Even though in annotation task 1, annotators were not limited in their choice of preposition, they did not use any that were not in the list of prepositions offered in annotation task 2 (a few typos we corrected manually). As it would have been virtually impossible to remember the exact list of prepositions and only use those, we interpret this as meaning that annotators did not feel other prepositions were needed.
We used average pairwise kappa to assess interannotator and intra-annotator agreement as described in previous work (Muscat and Belz, 2017). First, figures for the first batch of French annotations (1,020 images with 2 or 3 objects in BBs 4 ). For single best prepositions (annotation task 1), average inter-annotator agreement was 0.67, and average intra-annotator agreement was 0.81. For all possible prepositions (annotation task 2), average inter-annotator agreement was 0.63, and average intra-annotator agreement was 0.77.
For the second batch of French annotations (1,006 images with 3, 4 or 5 BBs), average interannotator agreement for single best prepositions (annotation task 1) was 0.33, and average intraannotator agreement was 0.66. For all possible prepositions (annotation task 2), average interannotator agreement was 0.3, and average intraannotator agreement was 0.62. A possible reason for the lower annotator agreement on batch 2 is that as the number of dominant objects in an im- Area of overlap of bounding boxes normalized by the area of the smaller bounding box.
[0, 1] F 7: Distance between centroids divided by sum of square root of areas/2 (approximated average width of bounding boxes).
[0, ∼20] F 8: Position of Objs relative to Objo expressed as one of 4 categories, depending on the angle with the vertical axis.
[∼-40, ∼+40] age increases, the annotation task becomes more difficult; we also used different annotators for the second batch which may be a contributing factor. 5 nington et al., 2014) for the object labels. 6 F2-F14 are visual features measuring various aspects of the geometries of the image and two bounding boxes (BBs). Most features express a property of just one of the objects, but F4-F9 express a property of both objects jointly, e.g. F6 is the normalized BB overlap. F17 and F18 are the average pixel-level depth value within the BB of Obj s and Obj o , respectively. Pixel-level depth values were computed via the method described in (Birmingham et al., 2018), which uses depth maps computed with monoDepth 7 (Godard et al., 2017) .
Evaluation Tools
SpatialVOC2K includes two evaluation tools which we have used in all previous work involving similar data. The two tools, systemAccuracy and relationPrecision implement the following two methods, respectively.
System-level Accuracy: There are four different variants of system-level Accuracy, denoted Acc(n), n ∈ {1, 2, 3, 4}. Each variant returns Accuracy rates for the top n outputs returned by systems, in the sense that a system output is considered correct if at least one of the reference prepositions (the human-selected prepositions from the dataset annotations) can be found in the top n prepositions returned by the system (for n = 1 this yields standard Accuracy).
Weighted Average Per-preposition Precision: This measure, denoted Acc P , computes the weighted mean of individual per-preposition precision scores. The individual per-preposition precision for a given system and a given preposition p is the proportion of times that p is among the corresponding human-selected prepositions out of all the times that p is returned as the top-ranked preposition by the system.
Related Datasets
A number of datasets are available that incorporate annotations representing relations between objects in images. Types of relationships that have been annotated include actions (e.g. person kicks ball), other verbal relations (person wears shirt), spatial relations (person on horse), and comparative relations (one car bigger than another). In this section, we provide a brief overview of available datasets with relation annotations, in terms of their stated purpose (application task), the types of relations included, the range of spatial prepositions included, as well as size and other properties of the dataset. Table 2 has a summary of the datasets.
Visual Phrases (Sadeghi and Farhadi, 2011) was the first image dataset with object relation annotations, and used the concept of a visual phrase (VP) which is defined as a bounding box that surrounds two objects in an image. Out of 17 different types of VPs annotated in the data set, 13 comprise 2 objects, and 4 comprise one object. However, there are 120 predicates per object category.
Visual and Linguistic Treebank (Elliott and Keller, 2013) contains 341 images that are annotated with regions (362 in total) and visual dependency representations, which unfold to a total of 5,748 spatial relations (from a set of 8) and are aligned to the dependency parse of the image description. This setup allows for the prediction of actions as well as spatial relations (using a set of 8 manual created rules).
Scene Graphs (Johnson et al., 2015) is a dataset of 5,000 human-generated scene graphs grounded to images; scene graphs describe objects and their relationships.
ViSen (Ramisa et al., 2015) associates sets of (object 1, preposition, object 2) triples with images, where the triples have been extracted from parses of the image descriptions in MSCOCO (Lin et al., 2014) and Flickr30k (Young et al., 2014). Prepositions covered include all those extracted from the image descriptions including non-spatial ones. By far not all descriptions contain prepositions so not all images have spatial relation annotations; the task addressed is preposition prediction, not spatial relation prediction.
Visual Relationships Dataset (VRD) (Lu et al., 2016) contains 5,000 images, 100 object categories, 6,672 unique relationships, and 24.25 relations per object category. Scant information is available about how the dataset was created other than that relations broadly fit into the categories action, verbal, spatial, preposition and comparative.
Visual Genome (Krishna et al., 2017) contains 108K images, split into 4M regions, corresponding to 108K scene graphs and about 4K region graphs, 1.5M object-object relations, 40K unique relations, and an average of 17 relations per image and 0.63 relations per region. | 3,389.4 | 2018-09-07T00:00:00.000 | [
"Computer Science"
] |
Scanning Tunneling Spectroscopy of Subsurface Ag and Ge Impurities in Copper
We investigate single Ge and Ag impurities buried below a Cu(100) surface using low temperature scanning tunneling microscopy. The interference patterns in the local density of states are surface scattering signatures of the bulk impurities, which result from 3D Friedel oscillations and the electron focusing effect. Comparing the isoelectronic d scatterer Ag and the sp scatterer Ge allows to distinguish contributions from impurity scattering and the host. Energy-independent effective scattering phase shifts are extracted using a plane wave tight-binding model and reveal similar values for both species. A comparison with ab-initio calculations suggests incoherent sp scattering processes at the Ge impurity. As both scatterers are spectrally homogeneous, scanning tunneling spectroscopy of the interference patterns yields real-space signatures of the bulk electronic structure. We find a kink around zero bias for both species that we assign to a renormalization of the band structure due to many-body effects, which can be described with a Debye self-energy and a surprisingly high electron-phonon coupling parameter $\lambda$. We propose that this might originate from bulk propagation in the vicinity of the surface.
I. INTRODUCTION
Scattering at impurities in a solid crucially affects material properties like electrical or thermal conductivity. Almost a century ago, the empirical Linde rule already related the residual resistivity of a dilute alloy ρ with the valence difference ∆Z between host and impurity species by ρ ∝ (∆Z) 2 [1]. As compound in a dilute Cu alloy, e.g., Ge shows a 27 times higher residual resistivity than Ag [1][2][3]. Complementary to macroscopic transport measurements, the scanning tunneling microscope (STM) yields access to the atomic scale that allows to investigate the scattering properties of single impurity atoms. This was first performed in the early days of STM in 2D scattering experiments of noble metal surface states, e.g. on Cu(111) or Au(111) [4][5][6]. The resulting Friedel oscillations contain information about both the defect scattering properties as well as the host. For example, on the one hand, the STM characterized a surface magnetic impurity with its Kondo signature and its scattering phase shift in the scattering pattern of a metal surface state [7][8][9][10][11][12]. On the other hand, by measuring the energy-dependent wave length of the scattering pattern at step edges, the dispersions of the surface states of Cu(111) and Au(111) were observed in real space [4,6]. The Fourier analysis of standing wave patterns, termed as quasiparticle interference (QPI), characterizes a materials' surface 2D band structure as well as available scat- *<EMAIL_ADDRESS>tering channels [13][14][15][16]. In specific sample systems, 2D QPI can be used to study parts of the 3D band structure [17,18].
Of peculiar interest are properties exceeding a single electron dispersion that describe many-body effects, e.g. electronic interactions with phonons where self-energy corrections cause a characteristic kink around the Fermi level. Especially metal surface states as prototypical 2D system were investigated in detail [19][20][21], e.g. by angleresolved photoemission spectroscopy (ARPES) [22][23][24][25]. By means of STM, the life times [26,27] as well as the electron-phonon coupling parameter λ and the selfenergy Σ [28] of surface states were determined. QPI also gave access to other many-body effects including coupling to surface plasmons [29] and different phonon modes [30][31][32]. As another approach by STM, Landau level spectroscopy offered access to 2D sample systems and their renormalized bands due to electron-phonon coupling [33,34].
In 3D, first, subsurface properties in metals were explored through quantum well states [35][36][37]. Then electron focusing was found to be a powerful tool to access bulk properties with an STM in real space on the atomic scale. Due to the anisotropy of a metal's band structure, the electrons propagate directionally through the bulk and form interference patterns at the surface. This was found at single magnetic impurities characterizing the host's Fermi surface [38], at noble gas cavities [39][40][41][42] and point-like subsurface defects [43]. The electron focusing effect was theoretically described [44] and applied at impurities in different contexts for the spectral signature of the Kondo effect at single atoms [45][46][47], for the two-band superconducting gap of Pb [48], and for quantum well states within layered systems [49].
In this study, we map the surface signatures of nonmagnetic impurity atoms buried in Cu(100). The scattering patterns of the isoelectronic d scatterer Ag and the sp scatterer Ge are compared in order to distinguish contributions from the impurity and the host. We extract similar energy-independent effective scattering phase shifts for both impurity species. Scanning tunneling spectroscopy (STS) reveals the energy-dependence of the electron focusing patterns, which act as real-space signature of the isoenergy surfaces of the host's 3D band structure due to the spectral homogeneity of the scattering phase. Most of the detected patterns is reproduced by electronic structure simulations, except from spectral anomalies intriguingly located at the Fermi energy. These can be described as the signature of a Debye self-energy that is discussed as bulk electron-phonon coupling in the vicinity of the surface.
A. Topographic signature of subsurface impurities
The experiments were performed with home-built STMs operating at a temperature of T ≈ 6 K and a base pressure of p < 5 × 10 −11 mbar. We investigate dilute Cu surface alloys with < 1% of Ge or Ag impurities, respectively. In a first step of sample preparation, Cu(100) single crystals are cleaned by cycles of Ar + sputtering and annealing. Subsequently, Cu and the impurity material are simultaneously deposited from two electron beam evaporators. The sample preparation is described in detail in Supplementary Note S1.
Both species of non-magnetic impurities feature picometer-high Friedel oscillations as surface signature due to electron focusing. A large scale topography in Fig. 1a shows interference patterns of Ge impurities at the Cu(100) surface. Each pattern corresponds to a single subsurface impurity causing a standing wave pattern of scattered electrons that propagate to the surface. The surface signatures have four-fold symmetry as defined by the crystal surface orientation and the anisotropic Cu band structure. The latter determines a specific angle under which the electrons propagate from the impurity towards the surface. Thus, a laterally more extended surface pattern corresponds to an impurity located deeper below the surface. Strong bright contrast are surface adatoms while dark contrast is assigned to surface layer impurities (termed '1st layer impurities' hereafter). The topographic contrast in the local density of states (LDOS) for subsurface impurities is with a few picometers a small fraction of a monoatomic step. (For more information see Supplementary Note S1).
In Fig. 1b, we present the surface signatures of Ag and Ge impurities from 3rd to 7th monolayer (ML) in Cu(100). The topographic contrast of a single impurity can be identified and assigned a depth using atomic resolution data (c.f. Supplementary Note S2). With increasing depth, the picometer-high corrugations increase in lateral size. Each four-fold pattern has its characteristic shape of maxima and minima due to constructive and destructive interference. Comparing both species, we find the topographic signatures to be very similar in both shape and amplitude. We can reproduce the experimental data with a tight-binding plane wave model adapted from Ref. [38] which uses an effective scattering phase shift η to characterize the shape of the interference pattern (for detailed information, see Appendix A). The average best-fit effective scattering phase shifts of η Ag = (1.32 ± 0.04)π and η Ge = (1.23 ± 0.05)π match the similarity of both species as observed in topography data.
B. Spectroscopic signature of subsurface impurities
We resolve the energy-dependence of the electron focusing patterns by using scanning tunneling spectroscopy. For each voltage, STS probes the interference pattern of the subset of states with wave vectors of the corresponding energy. Data was processed with topography normalization to obtain spectroscopic information for a constant height contour. For analyzing the change in LDOS due to the impurity, we subtract averaged spectra of the pristine Cu surface far away from the buried atom from the differential conductance around the impurity. As the topographic patterns only show a height contrast of a few picometers, the remaining spectroscopic signal shown in the following corresponds to approximately 1% of LDOS modulation obtained in the raw data.
We find the spectroscopic signatures of buried impurities to be very similar for both species, Ag and Ge, which agrees with the findings for the topography data. In Fig. 2 we show a 7th ML Ag impurity along with its spectroscopic signature. In the topography, the four-fold symmetry is well-resolved. A spectroscopic line section through the pattern along the crystal's [010] axis is presented in Fig. 2c. The color-code depicts the difference in differential conductance ∆dI/dU with respect to the pristine Cu surface. The main characteristic is an inwards movement of the positions of maxima and minima due to energy dispersion. A higher electron energy leads to a shorter wave length which fulfills the same interference condition for shorter distances. Dispersion is also the dominating effect in simulated spectroscopy data, calculated using the tight-binding model (Fig. 2b). The general shape of the simulation, which is given by the positions of maxima and minima lines, matches well with the experiment (Fig. 2c).
A spectroscopy data set of a 5th ML Ge impurity is shown in Fig. 3 with topography, spectral section and tight-binding simulation. As for Ag, we find the spectroscopic signature of a Ge impurity to be governed by electron dispersion with good agreement between experimental and calculated patterns. A single effective scattering phase can describe the data in the whole energy range without any strong additional resonances at element-specific energies. As for the topographies, the spectroscopy data for Ag and Ge is very similar for the same impurity depths.
An additional spectroscopic feature is found for both species at the Fermi level. In Fig. 2c and Fig. 3c, a bending of the interference pattern can be seen around 0 eV bias voltage where the pattern shifts towards the center in an immediate jump as if it experiencing a small phase shift. Considering a larger energy interval, the dispersion is unaffected by this anomaly. We observed these characteristics in multiple data sets for both species and different depths, including a Ge impurity buried in the 18th ML (c.f. Supplementary Note S4). The additional feature is not found in simulations of the tight-binding model, so it is beyond the scope of this single-particle band structure calculation.
III. AB-INITIO CALCULATIONS
Complementary to the experiment and the simplified tight-binding model, we performed ab-initio calculations using density functional theory (DFT) as implemented in the full potential Korringa-Kohn-Rostoker Green function (FP-KKR-GF) method [50] with the local density approximation (LDA) as parameterized by Vosko, Wilk and Nusair [51]. The theoretical and numerical approach is similar to that used in Refs. [38,44,47,49] and is described in more detail in Supplementary Note S3.
In Fig. 4, we show surface spectral sections along the crystal symmetry axis as calculated from the KKR-DFT potentials. Figure 4a and Fig. 4b show a 7th ML Ag impurity and a 5th ML Ge impurity, corresponding to the experimental sections presented in Fig. 2c and Fig. 3c.
The calculated spectra show richer patterns than the tight-binding model because the full crystal potential is considered. The pattern shape shows more detailed features than an almost linear dispersion and the LDOS amplitude modulates with energy. The total amplitude of the signal for Ge is multiple times higher than for Ag.
Comparing ab-initio calculation and experiment, the Ag data shows good qualitative agreement reproducing the overall pattern shape. With only small corrections to the ab-initio calculations' parameters (e. g. a shift of the energy scale by 150 mV or slightly corrected scattering phase shifts), the positions of the pattern's minima and maxima for the Fermi level match also quantitatively (c.f. Supplementary Note S3). For Ge, the patterns differ from each other. The calculation's rich features in the center including the contrast inversion from positive to negative with increasing energy are not found in the experiment, which presents a pattern that does not change qualitatively with energy and only shows a small dispersive shift. The pattern shape of the ab-initio data in the outer region (r > 8Å) resembles better the overall experimental pattern shape and is also similar to the Ag data. This different behavior for Ag and Ge data holds also for spectroscopic sections of other depths of both species.
A. Contributions of orbital components
Surface interference patterns are detected by STM even for atoms buried many layers below the surface despite the fact that non-magnetic impurities are weak scatterers. By the specific design of this experiment, we probe only the contributions of coherently scattered electrons for which the incoming and the scattered waves interfere constructively or destructively at the surface. The shape and size of a pattern are determined by two main ingredients: firstly, the scattering event, i.e., the scattering properties of the impurity atom and the electronic states it interacts with and, secondly, the electron propagation between surface and impurity.
In the experiment, we find the topographic signature of both impurity species to be very similar. From the literature, one would expect to find severely different scattering characteristics as the species differ strongly in both residual resistivity as well as the predicted scattering channels. In scattering theory, the scattering process at an impurity is described by its influence on host states being scattered. These electron wave functions are expanded in spherical harmonics, usually limited to s, p, and d orbitals. The influence on their asymptotic behavior by the impurity potential is parametrized by orbital-dependent scattering phases which are the main contribution to the scattering matrix T . These considerations are essential to the DFT-KKR ab-initio calculations, where the difference of element-specific scattering matrices determines by its amplitude how strong the scattering is in the respective channel for a specific impurity in a specific host. In other words, defects scatter especially in those channels, where the impurity differs most from a host atom. In this framework, strong scattering means that the host's states of a specific orbital character are especially disturbed and it does not describe scattering during bulk state propagation in the pure host or how many states of the respective orbital character are present. For the transition metal Ag in the isoelectric Cu, scattering at a 3d virtual bound state gives rise to the low residual resistivity [52]. As the resonance state is located far from the Fermi energy [53], leading to only little interaction with the electrons at the Fermi level, a small scattering amplitude of d scattering is predicted. For the sp impurity Ge in Cu, the perturbations of the crystal potential due to the significant additional local valence charge [53] of three additional electrons in s and p orbitals constitutes the main scattering process, leading to higher scattering rates especially for electrons of s and p character.
These predicted scattering intensities agree with the scattering amplitudes calculated in our ab-initio calculations (see Supplementary Note S3). While the scattering amplitude for Ge in Cu is three to four times higher for s and p orbital characters than for the d contribution, all Ag scattering amplitudes are half or less of the smallest value for Ge. This is reflected in the calculated LDOS amplitudes (see Fig. 4) where for Ge the signal is up to a factor of 7 higher than for Ag in the same depth. Even more strikingly, also the calculated pattern shape strongly differs between both species (c.f. Supplementary Figure S6).
While ab-initio calculations and experiment match for Ag impurities, there are large deviations for Ge. In order to explain these differences, the importance of the orbitals for the scattering process leads us to investigate if LDOS features of the simulations can be assigned to specific orbital components. For this, it has to be noted that the ab-initio calculations contain two orbital-dependent components, namely the impurity scattering as well as the propagation of Cu bulk states within the crystal lattice. For the latter, we can apply the tight-binding model (c.f. Appendix A). We determine the orbital character of the host metal's Bloch states in order to analyze how different orbital contributions are distributed over the Fermi surface and how this affects the electron focusing patterns at the crystal surface.
In Fig. 5a the contributions of Cu sp and d states in an exemplary interference pattern are shown as line sections as calculated with the tight-binding model. For each orbital, both propagation paths to and from the impurity are described by the orbital-specific propagator. For equal scattering amplitudes for sp and d states, the surface signal of d electrons is around 60% of the whole signal and, therefore, larger in amplitude than the combined sp contributions. At the outmost angles, the maximum at 12Å is only found in the d signal. This is representative for the signatures of impurities in all depths. In the center of the pattern, contributions from all electronic orbitals superimpose, while in the most outward region, the surface pattern is strongly dominated by d contributions.
In more detail, we can link this observation on a simulated topography to the host's Fermi surface: the interference patterns are constituted by bulk electrons that propagate from the impurity to the crystal surface in the direction of their group velocity. Electron focusing describes the fact that flat regions of the Fermi surface accumulate states with a certain propagation angle and, thus, cause a strong surface LDOS signal [38,44]. Figure 5b shows that for Cu(100) the focusing regions are especially the flat facets near the 110 directions (between the necks) with a focusing angle of 30 • to 40 • . The regions in 100 direction and around the necks ( 111 ) show smaller focusing angles. From the tight-binding model, we determine the orbital character of states at different regions of the Fermi surface as shown in Fig. 5c in agreement with previous calculations [52,54]. For all areas contributions from all orbitals are present with varying intensity. We find that the regions dominated by d character (bright) coincide with the flat focusing regions, whereas the neck and belly regions show stronger contributions from s and p (dark) whose smaller focusing angle points more towards the center of the interference pattern. Consequently, the orbital-resolved characteristics of the Fermi surface support what has already been visualized in the simulated orbital-resolved interference pattern.
With this knowledge, we can interpret the differences in the data of buried Ge atoms. In the ab-initio calculations, the outer, weak-contrast dispersion-like features are assigned to electrons with d character. In the center area, a very dominant feature from sp (because of strong sp scattering at the Ge impurity) masks a weak d electron background. As in the experiment such a sp feature is not visible, the signal of the experimental Ge topography is attributed to d electrons, which is supported by DFT in the outer regions. As our experiment is only sensitive to coherently scattered electrons interfering at the surface, we conclude that Ge shows such coherent scattering only for Cu electrons with d character and attribute the missing sp signal to additional incoherent processes in the sample system, which are not being considered in the ab-initio calculation.
We propose that these incoherent scattering processes occur at the impurity while we assume incoherence introduced during electron propagation to play only a minor role. Previous ab-initio studies have found strongly kdependent relaxation times for bulk electrons regarding electron-phonon interactions for different regions of the Fermi surface [54] with shorter times at necks and in 100 directions and longer times at flat regions which could explain stronger damping for the low angle regions than for high angles. However, as the relaxation times for room temperature range from 18 fs to 54 fs for different parts of the Fermi surface, the corresponding mean free paths are up to an order of magnitude larger than the propagation distance between surface and impurity in our low-temperature experiment. At low temperatures and including electron-electron interaction, bulk electron coherence has been assumed to be several dozens of nanometer even for energies up to 1 V from the Fermi energy [55,56]. Therefore, the coherence lengths are too large for the sp contributions to be damped by scattering within the propagation distance of only few nanome- ters. Instead, we suggest that the sp scattering process at the Ge impurity is partially not coherent which would strongly reduce the signal in our experiment. Within these considerations, the substantially increased residual resistivity of Ge impurities in Cu with respect to Ag could be attributed to decoherent scattering of sp electrons at the impurity.
Having discussed the origin of the differences between ab-initio calculations and experimental data for Ge, it remains the question why Ag and Ge show almost identical surface signatures in the experiments. For Ag, our DFT calculations and literature describe sp scattering to be less dominant than d scattering and a similar effective phase shift for all orbital contributions. This agrees with the simulated LDOS data that does not exhibit such a strong feature as Ge, but instead shows dispersive lines over the whole lateral range. These consist of all orbital characters and especially d electrons as these are the strongest orbital contribution in the electron focusing propagation. For Ag, the DFT calculation matches with the experimental data. When comparing both species, the KKR scattering phases for Ag are similar to the Ge scattering phase for the d orbital which is, in this case, the only imaged orbital channel. Hence, this can explain why the experimentally acquired topographies resemble each other for both species.
B. Signatures of Many-Body Effects
So far the analysis has shown that the surface signatures of buried impurities are also determined to a large extent by the bulk electron properties. This allows to compare scattering at two weak scatterers with different properties, here Ag and Ge impurities, and to separate the contributions from the specific impurity and general properties of the host. Thus, we use the real-space spectroscopic data to characterize the electronic structure of the Cu host around the Fermi level.
Similarly to the analogous STS studies for 2D surface states, here, we perform an experiment for standing waves of 3D Cu bulk electrons reflected at sub-surface point defects. In previous studies for single bulk impurities in Cu [45,46], the Kondo signatures of buried magnetic atoms were investigated. As magnetic impurities induce a phase shift around zero bias due to the Kondo resonance, an analysis of features from the host with weaker impact was not possible.
Analysing the spectroscopic data of the non-magnetic atoms Ag and Ge in Fig. 2 and and Fig. 3, respectively, the main observation in the range from −300 mV to 300 mV is a reduction of the interference pattern's lateral size for increasing bias voltage. This can be directly attributed to the dispersion relation of Cu bulk electrons as visualized in the tight-binding model (c.f. Figs. 2b, 3b). The reduction of the wave length for higher energies, which leads to a smaller ring structure, is the real space mapping of increasing electron momentum for higher energy.
In addition to this expected observation, the experimental data shows significant deviations from the simple, almost-linear bulk dispersion around the Fermi level. A bending of the pattern shape around zero bias is detected for both species in an energy range of approximately ±30 mV. This energy scale is common for lattice vibrations and it is known for the dispersion in momentum space that electron-phonon interaction leads to a renormalization of electron band structure, often manifested as 'kink' in the corresponding energy interval around the Fermi level [57]. We propose that in our experiment we map the real space signature of electronic coupling to phonon modes of the host.
In many-body theory, electron-phonon coupling is described by electron-like quasiparticles that include the interaction with phonons in their dispersion relation by self-energy corrections. These are determined by the Eliashberg function α 2 F (ω) or the averaged electron-phonon coupling parameter λ [57] whose cou-pling strength is given on the one hand by the available electron and phonon states, i.e. the respective densities of states, and on the other hand by the matrix element linking the two. While the real part of the self-energy shifts the center energy for a given k-value, the imaginary part causes a broadening in the spectral function due to finite quasiparticle lifetimes. In order to estimate the effect of such a band structure renormalization on the real space signatures, we implement the real part of the self-energy into the tight-binding model. For the Cu phonons, we use the Debye model with an Eliashberg function α 2 F (ω) = λ(ω/ω D ) 2 for ω < ω D and zero elsewhere, and the Debye frequencyhω D =30 meV [58,59]. The influence of the imaginary part of the self-energy is investigated in a simple 1D toy model with linear dispersion. We find broadening especially for states with energies E ≥ ω D , but no indications for strong changes in λ or the overall pattern shape (see Appendix B). Figure 6 shows the results and a comparison to the experimental data of 7th ML Ag and 5th ML Ge impurities. The tight-binding simulations including electronphonon coupling reveal distinctive features, especially for |E| <hω D (Fig. 6b and 6e). The patterns exhibit strong deviations from the simulations without many-body effects ( Fig. 2b and 3b) around the Fermi level, which are the real space signature of the well-known kink in momentum space. Comparing calculated and experimental data, we find good agreement for both species. For example, for the Ge pattern (Fig. 6d), the maxima almost join at around 25 meV before bending outward again, which is reproduced in the calculation (Fig. 6e). In the simulations, discontinuities are present at ω D , which are linked to the used Debye model that introduces an abrupt cut in the phonon density of states. For a real Cu phonon spectrum, the self-energy shows a smoother course that leads to weaker features at ω D (c.f. Supplementary Note S6). Furthermore, the simulation assumes a temperature of T = 0 K, while the experimental data is smoothened by thermal broadening on the scale of a few millivolts, blurring possible features at the Debye energy. The comparison in Fig. 6c and Fig. 6f shows the shift of the spatial position of the pattern's maximum with energy, as labelled in the 2D data. Good agreement is obtained with almost constant values for |E| >0.1 eV and a steep step within [−ω D , ω D ].
To describe the experimental data, we use an electronphonon coupling parameter of λ = 5.0, which is very high compared to the Cu bulk value λ Cu = 0.15 or even materials with strong coupling like PbBi alloys (λ ≈ 3.0) [57,60]. A calculation similar to Fig. 6 with the bulk value λ Cu does not reproduce the experimental data (c.f. Supplementary Note S5). Although the tight-binding model does not include all interactions and therefore is not expected to quantify exactly the experimentally found phenomena, this large deviation needs to be discussed.
Instead of coupling with delocalized bulk phonons, the spectroscopic features could be linked to local bulk vi-brational modes induced by the impurity atom at the impurity site or extended over several nanometers around the defect. However, as Ag is significantly heavier than Ge, different local vibrational modes would be expected, but both species' signatures show a similar strength of deviation from the single-particle dispersion. Furthermore, also electronic resonances, e.g. originating from a hybridization of bulk states with the impurity, which generally cause a phase shift, would very unlikely reveal a resonance exactly at the Fermi level for both species.
In the literature, the Cu bulk coupling parameter λ shows a directional variance of a factor of 2-3, leading to values as λ(k) = 0.08...0.23 [54,61,62]. Although our model uses the simplifications of no k-dependence and particle-hole symmetry in the self-energy, this alone cannot account for a factor of 30 between λ = 5.0 and the bulk value. According to ab-initio calculations, the bulk Eliashberg function α 2 F (ω) generally follows the phonon density of states without unusually large coupling of particular parts of the phonon spectra to electronic states [63]. Yet, our experiment is very specific about electron k values, as every point (x, y) probes only a specific region of the isoenergy contour with the corresponding angle of group velocity, so the general statement might not hold for an electron focusing signal.
We propose that the vicinity of the surface enhances the electron-phonon coupling parameter for our experiment. Missing translational symmetry breaks the momentum conservation perpendicular to the surface which opens up additional scattering processes with more available (bulk and surface) phonon modes as well as more available final electronic states.
Electron-phonon coupling of metal surface states has extensively been studied by surface-sensitive techniques [20,21]. For various systems, Mo(110) [23], Cu(111) [22,24,64,65], Cu(110) [66] as well as the Pb(110) bulk state [24], values of λ similar to the respective λ bulk were obtained by ARPES [57]. In STM measurements, many-body effects due to electron-phonon coupling of the Ag(111) surface state and other 2D systems were quantified by the coupling parameter λ and the self-energy which were found to match the literature values from ARPES and the bulk [28,33,34].
Further studies have shown that electron-phonon coupling can be enhanced compared to an average parameter λ, because the coupling of specific electronic and phonon modes can show strong variations as well as an energy-dependence [67,68]. Different interactions within the electronic surface band, with bulk electrons as well as with bulk phonon states and surface modes contribute unequally to the lifetime of surface states [26,27,69], e.g. for Cu(111) with strong coupling to the surface Rayleigh mode and interaction with specific bulk phonons [65,70]. By extracting the Eliashberg function an enhanced λ was obtained for the Be(1010) surface due to coupling to low energy surface modes [25]. These findings were crucial to understand the very high value of λ ≈ 1 for the Be(0001) surface [13,[71][72][73][74][75], four times higher than the bulk value [57]. Strong variations of the electron-phonon coupling parameter are also discussed for quantum well systems, e.g. thin Ag films [76][77][78][79][80].
It becomes clear that for a full picture of electronphonon interaction, all available final electronic states, available phonon modes, and the matrix elements for the scattering processes have to be taken into account at a state-specific level. This can play a key role in our experiment because we investigate a complex 3D system, which is dominated by the bulk band structure and additionally influenced by the vicinity of the surface and the atomic defects. Although the origin of the high electronphonon coupling value of λ ≈ 5 remains unclear, such an enhanced phase space of possible interactions might be a reason why the simulations including a self-energy from many-body effects can describe the experimentally observed features.
V. CONCLUSIONS
In summary, we perform a 3D scattering experiment at single non-magnetic impurities in a metal, detecting surface signatures of impurities buried up to 17 monolayers below the Cu(100) surface. The interference patterns at the surface characterize both impurity scattering properties of Ag and Ge as well as the host electronic structure of Cu. Analysing the topographic patterns with a plane wave tight-binding model, we extract similar effective scattering phase shifts for both impurity species. Following a comparison with ab-initio calculations, we propose that incoherent sp scattering at Ge impurities is crucial for the main scattering channel of this dilute alloy. As a result, the interference patterns of Ge impurities resemble those of Ag.
Due to the spectral homogeneity of impurity scattering, the surface signatures act as real space probe of the host's electronic dispersion, which we are able to map in good agreement with electronic structure calculations. We resolve small corrections in the form of a distinct bending of the interference pattern around the Fermi level that can be described with a Debye self-energy. It visualizes in real space the quasiparticle band structure of renormalized Cu bulk bands including many-body interactions. The high value of the electron-phonon coupling parameter λ could result from state-specific interactions and the vicinity of the surface in the investigated bulk system.
The used experimental approach can be versatilely applied to other systems to investigate scattering properties of subsurface impurity atoms as well as electronic properties of the host material. While for magnetic impurities the Kondo signature masks the host's features at the Fermi level, non-magnetic impurities or inherent defects can be functionalized to probe the electronic structure of both bulk and surface nanostructures even close to zero bias. For a simple material such as a noble metal, we unveil non-trivial features that we propose to be emerging from phonons coupling to electrons. As the miniaturization of nanoelectronic devices continues, the presented approach can be a useful tool to understand fundamental processes on the atomic scale in order to identify electronic interactions.
Appendix A: Description of surface signatures with tight-binding model The surface signatures are analyzed and reproduced with a tight-binding plane wave (TB) model adapted from Ref. [38]. It describes the interference of an outgoing electron wave and an incoming wave scattered at the impurity (see Fig. 7). The Bloch states are assumed to be plane waves without considering the lattice periodic part, but including the dispersion of the Cu bulk band structure, as calculated in a tight-binding calculation [81,82]. For simplicity, the scattering event is reduced to an energy-independent, orbital-independent effective scattering phase shift η imp that the wavefunction collects at the impurity and a corresponding unitary scattering matrix T = exp(i · η imp ). The change in LDOS with respect to the pure Cu surface is given with the Green's function G 0 as propagator and x imp as the position by The LDOS(x, ) at the surface exponentially decays into the vacuum towards the STM tip. We use the effective scattering phase shift η imp of the TB model to describe and quantify the shape of the experimental surface signatures. It can take values between 0 and 2π and is assumed to be constant for different bulk impurity depths. This is reasonable as for bulk conditions the surroundings of an impurity are always identical, independent of location within the single crystal. The other free parameters of the model are the height of the tip h above the sample, the distance a surf between surface layer and vacuum, and the depth of the impurity d which only takes discrete integer values (Fig. 7).
The typical distances in scanning tunneling microscopy are about 5Å to 8Å where shorter distances lead to more laterally high-frequency features because of larger transmission of k || [83]. Taking the bias voltage and current set points into consideration, we choose h = 5Å for Ag and h = 7Å for Ge data sets which proves to reproduce well the general appearance of interference patterns (cf. Figs. 8 and 9). The tip-sample distance h does not have strong influence on the simulated topographies as a large change of h only leads to a change of roughly 0.1π in phase shift which is about the size of the error bar for the extracted phase shift. 7. Sketch of the tight-binding plane wave model. Surface interference patterns result from interference between incoming (blue) and outgoing (red) electron waves, which oscillate within the crystal and experience a scattering phase shift ηimp at the impurity (yellow). The tip probes the surface signature with a distance-dependent exponential decay. This distance is labeled with h. The depth of the impurity is given by d.
The surface layer is referred to as the 'first layer'.
The surface layer spacing is set to a surf = a [100] = 181 pm in a rough approximation of the crystal potential [84]. Small changes in depth can be compensated by a shift in effective phase shift η imp because the phase contribution of additional propagation distance (Fermi wave length λ Cu = 4.6Å) cancels with the new η imp . A shift of 0.1 ML in depth corresponds to approximately −0.14π in phase shift. Therefore, as the parameters of the TB model are not independent of each other, there is not exactly one resulting parameter set. However, the lateral size of the surface signature which has to match with the focusing directions confines this flexibility to very few monolayers. The depth of an impurity d is deduced from images with atomic resolution (for more information see Supplementary Note S2). The depth is restricted to discrete integer values as impurities only sit substitutionally in Cu atomic lattice points.
The effective phase shift in the TB model includes all phase contributions within the solid, even if they do not occur at the impurity. Firstly, this is a phase shift from the transmission from the vacuum to the metal crystal [85]. Secondly, unlike the phase shift in the KKR framework, the TB model assumes propagation within the impurity cell which leads to a phase contribution. These contributions are identical for both impurity species, so the phase shift difference between them is independent of the contributions' absolute values. In Fig. 8 the surface signatures of Ag impurities from 3rd to 7th ML in Cu(100) are shown. The left column depicts the experimental topographies already presented in Fig. 1b in the main text. With increasing depth, the picometer-high corrugations increase in lateral size. Each four-fold pattern has its characteristic shape of maxima and minima due to constructive and destructive interference. The center column (Fig. 8b) depicts simulated topographies calculated with the TB model with a best-fit scatter- ing phase, reproducing their experimental counterparts in size and shape. The sections (Fig. 8c) along the [010] direction also indicate accurate agreement between experimental and simulated data. The deviations for the 7th ML originate from the atomic resolution superposed with the bulk focusing signal. We find an average effective scattering phase shift of η Ag = (1.32 ± 0.04)π. Figure 9 shows the surface signatures of another nonmagnetic impurity, Ge. Figure 9a shows experimental topographies in monolayers 3-7. The simulated 2D TB topographies (Fig. 9b) and sections of experiment and calculation (Fig. 9c) show good agreement. We obtain an average effective scattering phase shift of η Ge = (1.23 ± 0.05)π. The tight-binding model proves to be a reliable tool to describe the surface patterns of subsurface, nonmagnetic impurities. This can be especially useful when ab-initio calculations are not available or for deeper layers where computational cost increases strongly for DFT.
Appendix B: Electron-phonon coupling toy model
In the implementation of electron-phonon coupling in the tight-binding model, as described in the main text, we have only included the real part of the self-energy, which is responsible for the shift in center energy in the spectral function with respect to the single-particle system. Here, we analyze the role of the imaginary part for the spectral function in real space using a simple 1D toy model. We approximate the quadratic dispersion of a free electron to be linear in the considered energy interval around the Fermi energy (E F =7 eV). The interaction with Debye phonons is introduced via a self-energy calculated from an Eliashberg function α 2 F similar as described in the main text.
The resulting renormalized spectral function in momentum space is shown in Fig. 10a for λ = 5.0. The typical kink at the Debye energyhω D =30 meV as well as the broadening due to quasiparticle interactions for energies E > 0 eV are found as known from the literature [57].
Via Fourier transform, we obtain the real space representation of the Green's function propagator and calculate a simulated STS pattern for an impurity in 7ML with effective scattering phase η = 1.0π. Because the Friedel oscillations' amplitude in the 1D model is constant even for large distances, we include an additional damping term ∼ r −3 (with distance r from impurity to surface position) into the LDOS. This accounts for a 3D propagation from impurity to the surface like in the experimental patterns.
For a propagator with only the real part of the selfenergy, as implemented in the tight-binding model, we obtain a pattern of constant intensity with energy with a characteristic kink around the Fermi level (Fig. 10b). As this toy model is spatially isotropic and, thus, does not favor a certain electron focusing angle, there are multiple oscillations in the surface pattern. The smaller amplitude with larger distance only results from the additional 3D damping term.
Including the full self-energy (Fig. 10c), the imaginary part reduces the signal strength due to the finite lifetime. For E > ω D , the amplitude is attenuated by approximately 50% while close to the Fermi level, the patterns remains almost unchanged. The whole pattern shape (i.e. the position of minima and maxima) is almost identical to the case with only e(Σ), as depicted in Fig. 10d where for each line the spectral function is normalized to 1.
From the study of the toy model, we conclude that our implementation of many-body effects into the Cu tight-binding model can describe the basic effects of electron-phonon coupling for the STS spectra. We do not claim exact quantitative accuracy for the tight-binding model. After all, despite describing well the overall topographic and spectroscopic signatures for different impurity species, it is a simple model that does not include all effects of the solid.
S1. SURFACES OF DILUTE CU ALLOYS
The samples, Cu(100) with dilute Cu alloys in the topmost layers, were prepared in a home-built UHV preparation chamber with a base pressure of p = 5 × 10 −11 mbar. The Cu(100) single crystals were cleaned by cycles of sputtering by Ar + ions with an energy of 700 eV and annealing to 680 K. In the last cycles the sputtering and annealing times were reduced and the temperature was lowered to 630 K in order to flatten the surface without causing segregation of bulk defects towards the surface. The surface quality was checked by low-energy electron diffraction, Auger electron spectroscopy and STM which presents the sample as clean with terraces of a width of up to a few 100 nm. Dilute alloys in the 20 topmost layers are fabricated by co-deposition of 20 ML copper and < 1% silver and germanium, respectively, by two electron beam evaporators. Cu is evaporated at 1 ML/min.
In order to achieve very small ratios of composition, the impurity evaporator is equipped with a stepper motor which allows shutter opening times of 100 ms. During evaporation, the sample is held at a temperature of T≈100 K. In order to restore a flat surface that can be investigated by STM, the sample is flashed to T = 520 K for 3 seconds after growth.
Subsequently, it is immediately transferred into the low temperature STM.
The surfaces of dilute Cu alloys show different patterns at the surface corresponding to different defects. An example of a topography with Ag impurities is shown in Fig. S1 which is similar to the large-scale topography for Ge presented in the main text (cf. Fig. 1a). Many second layer Ag impurities are visible as strong contrast white dots with surrounding black rings. In the left center two impurities are buried, one rather close to the surface and one deeper impurity with clear four-fold pattern. Additionally, signatures of clusters presenting richer patterns are found (e.g. center, bright white contrast) which can either be linked to subsurface impurity clusters or nanocavities of residual argon gas from the sputtering process.
The four-fold signature for single, buried impurities are the consequence of electron focusing. Electrons within the crystal propagate corresponding to their group velocity which is given by the gradient of band structure [1]. Hence, for flat regions on the isoenergy con- directions, leading to a weak signal at the surface. This effect is depicted for two sections of the Cu Fermi surface in Fig. S2. The electrons dominantly propagate in directions where group velocity vectors accumulate, leading to surface interference patterns above buried impurities. In semiconductors or other materials with comparably low charge carrier density, subsurface dopant atoms can be mapped by STM in a different mechanism. The donor's extended Coulomb potential around the impurity site can be modified by switching the dopant's charge state by tip-induced band bending [2,3]. This mechanism is excluded for the impurities investigated here, buried in the metal Cu. The charge carrier density is significantly higher and the Thomas-Fermi screening length as short as 0.55Å, so that any charged region is screened on short length scales. In Fig. S3 three different types of single impurities in Cu(100) are shown in topography and line sections. The signature of first monolayer impurities is a depression for Ge (and also previously, e.g. Co [4]) with an amplitude of typically 30 pm. Second ML defects, only covered by one monolayer of Cu, reveal a bright spot surrounded by a dark ring.
The electronic contrast is typically 10-15 pm. As a reference also a 7th ML impurity with picometer-high signature is included in the data set. Due to very good imaging conditions in the presented data set, the typical heights for the features are exceeded.
A. Determination of impurity depth
The depth of an impurity is deduced from STM topographies with atomic resolution.
The center position of the surface interference pattern with respect to the surface lattice determines if the impurity is located in an odd or even crystal monolayer. The surface pattern is always centered around the buried atom due to symmetry. If the surface signature coincides with a surface atom, then the impurity sits perpendicular to the surface below this surface atom. Hence, with Cu being an fcc single crystal, the impurity is located in an odd monolayer. Here, the surface layer is counted as first layer. If the surface signature's center is located between surface atoms, then the impurity is positioned in an even crystal monolayer. An example for such an analysis is shown in Fig. S4a. The surface interference pattern of this impurity is centered around a surface atom (marked with a cross), so the impurity is located in an odd crystal monolayer.
Additional information for the determination of an impurity atom's depth is taken from the lateral pattern size which is restricted by the focusing angle, i.e., the main directions of electron focusing. Because of this, for a full data set in which all depths are available, the patterns can be ordered by size and then assigned a crystal monolayer. Alternatively, tight-binding calculations (see Appendix A in the main text) can be performed for different depths, for each fitting the best effective scattering phase shift. As the impurity positions are limited to a discrete number of crystal layers and by atomic resolution data further reduced to only even or odd layers, the comparison of simulation and experimental data reveals the impurity's depth. For the exemplary depth analysis in Fig. S4, in (b) the experimental data is compared with a tight-binding simulation for a third monolayer ('3ML') impurity. The patterns match far better than the candidates of 5th ML and 7th ML in subfigure (c). For deeper layers, the main weight of the interference pattern is shifted towards larger distances, whereas for the 3rd ML the main signal is located in the center peak.
For data sets where no atomic resolution was obtained, the depth is determined by comparison with tight-binding simulations of various depth with the average effective scattering phase shift, assuming a constant scattering phase shift for all bulk layers. Once the layer is identified (e.g. comparison of lateral size, ratios in contrast pattern), in a next step an [5][6][7]. The interference patterns for residual sputter gas (Ar, Ne) can be distinguished from the patterns used in our analysis as they show richer surface interference patterns with larger lateral extent (e.g. in Fig. S1).
For the dilute alloys, the concentration of impurities is usually < 1%, so that impurity atoms can hardly form clusters. In some topographies we find clusters of Ag or Ge with rich surface signatures which are easily distinguished from point-like scattering centers which show clearly defined four-fold interference patterns confined to approximately 1.5 Friedel oscillations [1].
Nevertheless, the tip quality is crucial for resolving the surface signatures of buried impurities. They show apparent heights of few picometers in topography which correspond to LDOS modulations of around only 1% in spectra. Data sets with reproducible, well-defined interference patterns as shown in the main text can be recorded with a suitable sharp tip.
For dull tips, we obtain broader features which make it more difficult to distinguish between subsurface structures and other defect contrasts, which is why we exclude these from the analysis.
S3. AB-INITIO CALCULATIONS AND SCATTERING PHASE SHIFTS
The ab-initio calculations are performed using DFT as implemented in the full potential Korringa-Kohn-Rostoker Green function (FP-KKR-GF) method [8] with the local density approximation LDA [9]. First, the electronic structure of 18 layers fcc Cu slab with two additional vacuum regions (3 vacuum layers on each side of the Cu slab) are taken along the (001) direction. The decimation technique [10,11] is adopted to simulate the semi-infinite substrate to avoid size artifacts in the charge density. The experimental lattice parameter a = 3.61Å was considered without surface relaxations, which are negligible. Then each impurity is embedded underneath the surface together with its neighboring atoms, defining a cluster of atoms, where the charge is allowed to be updated during self-consistency. The induced charge density is then computed in the vacuum at h = 3.61Å above the surface, proportional within the Tersoff-Hamman approach [12] to the tunneling signal measured with STS. While the self-consistent calculations required 40 × 40 k-points in the two-dimensional Brillouin zone, the theoretical STS spectra were obtained with a set of 200 × 200 k-points.
The calculations are performed to obtain simulations of the experimental spectroscopy data and energy-dependent scattering phase shifts at the different impurity species. As the former results are discussed in the main text, here we mainly focus on the phase shifts at the Fermi energy.
We obtain scattering phases δ for host and impurity species consistent with previous studies [13]. The values of phase shifts at the Fermi energy are listed in Tab. I. A comparison between 5th ML and 3rd ML shows only tiny changes for the different depth. This indicates a depth-independent scattering phase shift which supports the assumption in our analysis for extracting the phase shift from experimental data.
With the tight-binding model (c.f. Appendix A in the main text), we parametrize the experimental surface patterns with a single effective scattering phase shift η imp which describes the phase relation of incoming and scattered wave. This parameter is determined by the scattering potential of the impurity. The corresponding quantity used in quantum scattering theory is the scattering phase shift δ which is linked to the scattering matrix t by t = −(1/ √ E) sin(δ) exp(iδ). In a Cu crystal with Bloch electron states, the scattering amplitude and phase due to an impurity are given by the complex number ∆t = t imp − t Cu which is the difference of the impurity scattering matrix with respect to the host [14]. The experimentally determined effective scattering phase shift η imp corresponds to arg(∆t). The scattering amplitude, i.e., the amplitude of the complex scattering matrix difference, is contained in the height of electronic contrast measured by STM. However, electronic contrast is very difficult to quantify as transmission strongly depends on absolute tip-sample distance and tip shape. In the calculations, Ge shows as an impurity in Cu a three to four times higher scattering amplitude for s and p orbitals than the d orbital contribution. For Ag, the orbital components only vary by a factor of two, with all amplitudes being half of the Ge's value for d orbitals or less. The energy-dependence of scattering phases for s, p, and d orbital characters are shown in Fig. S5 for Cu, Ag, and Ge. The phase around the Fermi level is approximately constant.
The strongest energy-dependence from −1 eV to +1 eV show the s and p orbitals of Ge. The scattering amplitude, i.e., the absolute value of difference of the complex scattering matrices of Ge and Cu, of these orbitals is 3-4 times higher than for the d orbitals.
Resulting from the ab-initio calculations, we obtain simulated spectroscopic sections as shown in Fig. S6 which also comprises the data shown in the main text. While the lateral sizes of the surface signatures are similar for both species for a specific depth, Ag and Ge differ strongly in LDOS amplitude and pattern shape.
As discussed in the main text, for Ag we find good agreement between ab-initio calculations and the experimental data. In order to obtain a match for the overall shape and lateral size of the interference pattern, in the ab-initio calculations either the scattering phase shifts have to be slightly corrected or the energy scale has to be shifted by 150 mV. Such an energy shift is known from the literature to be possible for metallic electronic states as obtained from LDA with respect to those measured experimentally [15]. In Fig
S4. DEEPLY BURIED IMPURITIES
Due to the electron focusing effect, the signature of buried impurities is detected by an STM despite the screening effects of the host's high charge density. While in previous data we have shown interference patterns corresponding to impurities of up to the 7th ML, in Fig. S8 we show a deeply buried Ge impurity. In Fig. S8a, the topographic surface pattern of a 18th ML impurity is presented. The four-fold ring structure of more than 3 nm diameter is clearly discriminable despite the adatoms and other buried impurities in the surrounding surface region. Because the focusing pattern is limited to distinct 1.5 wave lengths and clusters would lead to richer surface structures, we assign the pattern to a single impurity.
We identify the impurity's depth by comparison with tight-binding simulations (Fig. S8b) where we obtain good agreement.
In Fig. S8c and Fig. S8d, the spectroscopic signature is shown for two energy ranges.
For ±300 mV (Fig. S8c), the dominant feature is the shrinking of the ring-like structures for higher energies. This is understood by electronic dispersion. For high absolute values of Spectroscopic section similar to (c) with smaller energetic range. Around the Fermi level, an additional bending of the pattern is found that is assigned to electron-phonon coupling.
energies, the signal is more difficult to detect as the tunnel current noise is also increasing.
For these long propagation distances, there might be additional effects by electron-electron scattering for energies further from the Fermi level. As the impurity is located 30Å below the crystal's surface, the electrons in the interference pattern have travelled coherently 7 nm through the Cu crystal. In Fig. S8d, we show a spectroscopic section for an energy range from −100 mV to +100 mV. As in the data before, we find an additional bending at the Fermi level due to electron-phonon coupling. Even for this depth, the renormalized band structure of interacting electrons is resolved in spectroscopy.
S6. SPECTROSCOPIC SIGNATURES AND PHONON SPECTRUM
In Fig. S10, a comparison of the spectroscopic signatures of a 7th ML Ag impurity and a 5th Ge impurity are shown for different phonon spectra. The tight-binding simulations including a self-energy based on the Debye model (Fig. S10a,d) are also shown in Fig. 6 in the manuscript. Here, they are compared with calculations using a self-energy based on the Cu phonon spectrum. One finds that, firstly, the Debye model approximation of an abrupt cut-off at the Debye energy leads to discontinuous line shape. Therefore, the self-energy and the simulated STS pattern for the real Cu phonon spectrum reveal a smoother transition around the Debye energy. Secondly, the simulation assumes a temperature of T = 0K. The experimental data is recorded at T = 6K, so the experimental data is thermally broadened, which is included in the spectroscopic sections shown in Fig. S10(c,f). | 13,039.6 | 2021-09-07T00:00:00.000 | [
"Physics"
] |
Street Network Models and Measures for Every U.S. City, County, Urbanized Area, Census Tract, and Zillow-Defined Neighborhood
OpenStreetMap provides a valuable crowd-sourced database of raw geospatial data for constructing models of urban street networks for scientific analysis. This paper reports results from a research project that collected raw street network data from OpenStreetMap using the Python-based OSMnx software for every U.S. city and town, county, urbanized area, census tract, and Zillow-defined neighborhood. It constructed nonplanar directed multigraphs for each and analyzed their structural and morphological characteristics. The resulting data repository contains over 110,000 processed, cleaned street network graphs (which in turn comprise over 55 million nodes and over 137 million edges) at various scales — comprehensively covering the entire U.S. — archived as reusable open-source GraphML files, node/edge lists, and GIS shapefiles that can be immediately loaded and analyzed in standard tools such as ArcGIS, QGIS, NetworkX, graph-tool, igraph, or Gephi. The repository also contains measures of each network’s metric and topological characteristics common in urban design, transportation planning, civil engineering, and network science. No other such dataset exists. These data offer researchers and practitioners a new ability to quickly and easily conduct graph-theoretic circulation network analysis anywhere in the U.S. using standard, free, open-source tools.
Introduction
Urban planners and transportation engineers have examined and modeled street networks for decades to explore household travel behavior, accessibility and equity, urban form and design patterns, connectivity, and centrality . Complex networks such as street networks have also been explored from the perspective of statistical physics to assess structure and performance [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. However, large volumes of cross-sectional street network data-in a format well-suited for graph-theoretic analysis-have often been difficult to come by, especially in an open-source, scalable, automatable way. This paper presents a new data repository to address this gap. It describes a research project that downloaded raw OpenStreetMap street network data for the entire U.S., cleaned these data, then constructed graph-theoretic models of these data at multiple scales for fast and rigorous urban analysis. It then calculated dozens of metric and topological measures of each network, nationwide. These models and measures can save researchers weeks or months of ad hoc data collection and analysis. However, they are even more useful for urban planners and policymakers who often lack the technical capacity to write their own API scripts in custom query languages or implement their own network science algorithms to understand the built form and urban circulation.
This new data repository provides four significant value-additions for urban science and analytics. First, the repository contains graph-theoretic models in common reusable formats, immediately suited data [77]. It is an open-source, worldwide, collaborative mapping project. OpenStreetMap provides geospatial information about streets and intersections, along with attribute data about road types, names, and (sometimes) speeds, widths, and numbers of lanes. However, its data cannot by default be automatically extracted into a graph-theoretic object for network analysis [78]. Furthermore, the network topology must be substantially cleaned to correctly represent nodes exclusively as intersections and dead-ends. Prior to this wider project, no tools or data repositories enabled the automatic, at-scale, configurable acquisition of OpenStreetMap data and construction of graph-theoretic data objects for analysis.
Methods
Given this background and motivation, this project originally developed a new open-source Python-based software toolkit called OSMnx [45]. OSMnx can download data from OpenStreetMap using configurable user queries, then construct a nonplanar, directed multigraph, and finally clean the topology [79]. Python was chosen to develop this tool for three reasons. First, Python is one of the most popular programming languages in the world, giving it a broad audience. Second, Python offers particularly simple and straightforward syntax, making it easy for newcomers to learn and lowering the scientific barriers to entry. Third, it has become a standard language for data science research and practice, with an extensive ecosystem of related packages for scientific, network, and geospatial analysis. Finally, other similar tools in this space include dodgr (an R tool for distance calculations on weighted directed graphs), shp2graph (an R tool for converting spatial networks into igraph objects) [80], pandana (a Python tool for network accessibility queries) [81], the Urban Network Analysis Toolbox plugin for ArcGIS and Rhino [82], and GISF2E (a Python tool that processes shapefiles into edge lists) [78]. However, none of these offer the end-to-end capabilities of OSMnx to download network data directly, build models, clean the topology, and conduct statistical analyses and simulations.
To construct this data repository, this project used OSMnx to download network data and construct graphs for the drivable street networks of every U.S. city/town, county, urbanized area, census tract, and Zillow-defined neighborhood (Zillow is a large online real estate database company that defines neighborhood boundaries in many cities and towns). It saved these graphs as shapefiles, GraphML files (a standard, open-source format for graph serialization), and node/edge lists. Finally, it analyzed these networks to assess the geometric, topological, and morphological characteristics of U.S. street networks and how they reflect various urban planning eras, transportation technologies, economic conditions, and design paradigms. These study sites are presented in Figure 1.
Graph Production
To produce the data in the repository, we loaded five publicly-available input datasets defining these study sites into OSMnx version 0. [84][85][86].
Zillow is a prominent real estate database company, and their boundaries dataset covers large U.S. cities. One at a time, for each city, county, urbanized area, tract, and neighborhood boundary defined in the above shapefiles, we downloaded the drivable public street network within its boundaries from OpenStreetMap using OSMnx. To acquire these raw data, OSMnx buffers each boundary polygon by 500 m then downloads the streets within this geometry, filtering them based on attribute data. It then constructs a nonplanar directed multigraph. In the case of one-way streets, a directed edge is added from the origin node to the destination node. However, for bidirectional streets, reciprocal directed edges are added in each direction between the two nodes.
Next, OSMnx cleans the graph's topology to retain nodes only at intersections and dead-ends (detailed below). However, the full edge spatial geometry and length are retained in the cleaned graph. Then, it calculates node degrees and node types before truncating the graph to the original boundary polygon. This buffer/truncate workflow attenuates perimeter effects [87] and guarantees that true intersections are not incorrectly considered pseudo-nodes or dead-ends if an incident edge links to a node outside the boundary polygon. The final graph may be strongly connected, weakly connected, or neither. If it is not connected, OSMnx returns all connected components as a single graph object.
To clean the graph's topology, OSMnx only retains nodes that represent the junction of multiple streets, as depicted in Figure 2. First, it identifies all non-intersection pseudo-nodes (i.e., all those that simply form an expansion graph). Next, it removes these pseudo-nodes while maintaining the true spatial geometry and attribute data of the street segment between the true intersection nodes. In strict mode, OSMnx considers two-way "intersections" to be topologically identical to a single street that bends around a curve. Conversely, to retain these intersections when the incident edges have different OpenStreetMap IDs, we can use OSMnx's non-strict mode. This cleaning step is critical to this dataset, providing additional value beyond extraction of data from OpenStreetMap itself by producing models more suitable to urban design/morphology and transportation analysis by representing intersections/dead-ends as nodes and linear blocks' sides as edges. Once we have constructed and cleaned the graph, we use OSMnx to save it to disk as node/edge lists (formatted as comma-separated values), as ESRI shapefiles to work with in GIS software, and as a GraphML file (an open-source, standard format for serializing graphs) to work with in common network analysis software packages such as NetworkX, Gephi, graph-tool, or igraph [88][89][90]. OSMnx's saved shapefiles include separate node and edge layers. When saving shapefiles, OSMnx simplifies the network to an undirected representation but preserves one-way origin-destination directionality as edge attributes for subsequent GIS-based routing applications.
Graph Analysis
Finally, for this repository we calculate several metric and topological measures of each of these networks, common in the urban design, transportation planning, and network science disciplines. These measures include each network's area (km 2 ), mean average neighborhood degree, mean average weighted neighborhood degree, average circuity, average clustering coefficient, average weighted clustering coefficient, average degree centrality, edge density (m/km 2 ), average edge length (m), total edge length (m), count of intersections, intersection density (per km 2 ), count of dead-ends, proportion of nodes that are dead-ends, count of three-way intersections, proportion of nodes that are three-way intersections, count of four-way intersections, proportion of nodes that are four-way intersections, average node degreek, count of edges m, count of nodes n, node density (per km 2 ), maximum and minimum node PageRank (a measure of node importance based on the structure of incoming edges), proportion of edges that self-loop, street density (m/km 2 ), average street segment length (m), total street length (m), count of street segments, and average number of streets per node.
Data and Code Availability
These data are freely available online at the Harvard Dataverse at https://dataverse.harvard. edu/osmnx-street-networks. This repository includes the graphs of the street networks for every U.S. city, county, urbanized area, census tract, and Zillow neighborhood as a GraphML file, node/edge shapefiles, and node/edge lists. These files can be loaded into any standard GIS software or network analysis package. It also contains the analytical measures for every street network. The datasets are available in the following two repositories: All the code to download and analyze these street networks with OSMnx (version 0.8.1) is open-source and available on GitHub at https://github.com/gboeing/dataverse-street-networks. The OSMnx software itself is also open-source and freely available for download and installation from GitHub (https://github.com/gboeing/osmnx), the PyPI package repository (https://pypi.org/ project/OSMnx/), and the Anaconda package repository (https://anaconda.org/conda-forge/osmnx).
Discussion
This paper described a new urban science data repository constructed from raw OpenStreetMap data that provides four significant value-additions. First, the repository contains graph-theoretic models in common reusable formats, immediately more useful than typical raw geometry data downloads out of the box. Second, these models all have meaningful spatial extents (municipalities, counties, urbanized areas, census tracts, and neighborhoods) that correspond to administrative boundaries or social units for urban analysis and simulation. Third, these graphs have substantially cleaned-up topologies such that nodes exclusively represent intersections and dead-ends and edges represent the street segments connecting them. Fourth, this repository contains dozens of metric and topological measures calculated for each graph-no such database previously existed. These measures can be used to analyze the urban fabric's texture and walkability (via intersection density, node/edge density, and average street segment length), connectivity (via average number of streets per node and circuity), and network resilience and importance (via centrality measures and PageRank).
In total, this data repository contains over 110,000 street networks which in turn collectively comprise over 55 million nodes and over 137 million edges. While these data fill a gap in helping researchers quickly ramp-up graph-theoretic street network analyses in the U.S. without having to spend weeks developing their own ad hoc data collection, modeling, and analysis workflows, they fill a larger gap in opening up these scientific modes of urban analysis to planners and policymakers without the individual technical or institutional capacity to do so otherwise. Yet to use these data accordingly, they must reasonably model the real world. Validation of these data can be considered from two perspectives. The first considers how faithfully the OpenStreetMap data represent the real-world street network. The second considers how faithfully the repository's graphs in turn represent the OpenStreetMap street network.
Regarding the former perspective, various authors have explored this subject in detail [76,[107][108][109][110][111][112][113][114]. OpenStreetMap's road data quality is generally quite high--for example, Garmin consumer GPS devices can use OpenStreetMap roads data for navigation. Although data coverage varies worldwide, it is generally good when compared to corresponding estimates from the CIA World Factbook. In the US, OpenStreetMap imported the 2005 TIGER/Line roads in 2007 as a foundational data source. Since then, numerous corrections and improvements have been made. More importantly, many additions have been made beyond what TIGER/Line captures, including richer attribute data describing the characteristics of features and finer-grained codes for classifying streets. Of course, much of these data are crowd-sourced and user-generated, and errors thus occasionally exist. However, the data are validated and vetted by the OpenStreetMap community, resulting in high quality overall. Most relevant to this project's study area, the U.S. network is essentially complete on OpenStreetMap [76].
Regarding the latter perspective, we comprehensively tested the final dataset's quality, adapting the methodologies of [76,78] against three reference datasets: the TIGER/Line roads, Google Earth satellite imagery, and the OpenStreetMap raw source data. The first step uses QGIS to compare these data spatially against the TIGER/Line roads shapefile in a random sample of 100 cities to identify any edges appearing in one of these datasets but missing in the other. Discrepancies were then checked one at a time to ensure they correctly matched the OpenStreetMap source and secondarily against Google Earth satellite imagery for real-world verification. Finally, tests are performed on each graph to ensure they can be loaded, analyzed, and routed. The validation confirmed that this project's algorithms reconstructed the OSM data properly with nodes exclusively at intersections and dead-ends.
Comprehensive documentation for using OSMnx is available at https://osmnx.readthedocs.org and tutorials, examples, and demonstrations are available at https://github.com/gboeing/osmnxexamples. To reuse this dataset, researchers can install OSMnx according to the installation instructions in the documentation. Then, they can load the GraphML files using OSMnx's load_graphml function. The graphs may be similarly loaded in NetworkX, graph-tool, igraph, and other similar network analysis tools. To load these graphs with Gephi, first load the GraphML file in OSMnx, re-export it using OSMnx's save_graphml function with argument gephi=True (to add additional customization for Gephi compatibility), then open the exported file in Gephi. The shapefiles may be loaded in standard fashion in any GIS software, such as QGIS, ArcGIS, or geopandas.
Funding: This research received no specific external funding. | 3,249.4 | 2019-03-01T00:00:00.000 | [
"Geography",
"Computer Science"
] |
Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays
In this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we first decompose the considered Clifford-valued neural network into 2m2n real-valued systems. Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks.Then, by designing a novel state-feedback controller and constructing a proper Lyapunov function, we study the global asymptotic synchronization of the considered neural networks. Finally, a numerical example is presented to show the effectiveness and feasibility of our results.
Introduction
Clifford algebras, which were invented by mathematician W. K. Clifford, are algebras generated from vector spaces with quadratic forms and are unitary associative algebras.They contain real numbers, complex numbers, quaternions, and several other hypercomplex systems as special cases.Clifford algebras have important applications in a variety of fields, including geometry, theoretical physics, and digital image processing [1].Clifford-valued neural networks generalize real-valued, complex-valued, quaternion-valued, and octonion-valued neural networks and so on.Since the Clifford-valued neural networks can use multistate activation functions to process multilevel information and require much fewer connection weight parameters of the networks, they have recently been an active research area [2][3][4][5].Due to the noncommutativity of Clifford numbers' multiplication, it brings great difficulties to the research of Clifford-valued neural networks.At present, the results of research on Clifford-valued neural networks are still rare, especially, for the nonautonomous ones.
On the one hand, it is well known that, in the design and implementation of neural networks, the existence of periodic solutions or almost periodic solutions of nonautonomous neural networks is as important as the existence of equilibrium points of autonomous neural networks.At the same time, we know that, even if all the time-varying coefficients in a neural network are periodic functions (such as connection coefficients, connection weight functions, external inputs, and time delays, etc.), if their periods are incommensurable, then, for such a neural network, it is also impossible to have a periodic solution.Therefore, studying the almost periodicity of neural networks is more practical and important than studying the periodicity of neural networks.At present, the periodicity has been extensively studied as an important dynamic property of various neural networks.However, there has been no paper published on the almost periodicity of Clifford-valued neural networks yet.
On the other hand, the synchronization of nonlinear systems has become an important research topic due to its potential applications in various fields such as secure communication, image encryption, information science, and so on.Particularly, recently, many authors have studied the synchronization problem for various neural network systems [6][7][8][9][10][11][12][13][14][15].For example, the synchronization problem for chaotic memristor-based neural networks with time-varying delays 2 Complexity was studied in [11].The global asymptotic synchronization problem of nonidentical fractional-order neural networks with Riemann-Liouville derivative was investigated in [12].The synchronization of an inertial neural network with time-varying delays was investigated in [13].The finitetime cluster synchronization of coupled fuzzy cellular neural networks with Markovian switching topology, discontinuous activation functions, proportional leakage, and time-varying unbounded delays was studied in [14].The global exponential almost periodic synchronization of quaternion-valued neural networks with time-varying delays was investigated in [15].But until now, the results of the synchronization of Cliffordvalued neural networks have not been reported.
In summary, it is meaningful to study the almost periodicity and the synchronization problem of Clifford-valued neural networks.Therefore, our main purpose of this paper is to investigate the problem of the existence of almost periodic solutions and global asymptotic synchronization of Clifford-valued CNNs with discrete delays.To the best of our knowledge, this is the first paper to study such a problem for Clifford-valued neural networks with discrete delays.Our methods of this paper can be used to study other types of Clifford-valued neural networks.
The rest of this paper is organized as follows: in Section 2, we introduce some basic concepts, notations, and lemmas and give a model description.In Section 3, we study the existence of almost periodic solutions of Clifford-valued CNNs with discrete delays.In Section 4, we investigate the global asymptotic almost periodic synchronization of Clifford-valued CNNs with discrete delays.In Section 5, we give an example to demonstrate the effectiveness and feasibility of our results.In Section 5, we give a conclusion.
Preliminaries and Model Description
The real Clifford algebra over R is defined as where For simplicity, when one element is the product of multiple Clifford generators, we will write its subscripts together.For example, 4 5 7 9 = 4579 .Denote Λ = {0, 1, 2, . . ., , . . ., 12 ⋅ ⋅ ⋅ }, and then we have where ∑ is short for ∑ ∈Λ and A is isomorphic to R 2 .For any = ∑ ∈ A, the involution of is defined as where In view of = (−1) and then A = (−1) [⋅] .In addition, for any ∈ A, we can find a unique satisfying ⋅ = (−1) [⋅] for = (−1) [⋅] .Therefore, and Throughout this paper, A , R × , A × represent the dimensional real Clifford vector space, the set of all × real matrices, and the set of all × real Clifford matrices.We define the norm of In this paper, we consider the following Clifford-valued cellular neural network with discrete delays: where = 1, 2, . . ., , and corresponds to the number of units in the neural network; () ∈ A denotes the activation of the th neuron at time ; () > 0 represents the rate with which the th unit will reset its potential to the resting state in isolation when disconnected from the network and external inputs at time ; (), () ∈ A represent the strengths of connectivity without and with time delay between cells and at time , respectively; , : A → A are the activation functions of the signal transmission; () ∈ A is an external input on the th unit at time ; () ≥ 0 is the transmission delay at time .
The initial values of (8) are where 8) can be transformed into the following equation: with the initial value: Definition (see [16]).A function ∈ (R, R ) is said to be almost periodic on R, if, for any > 0, it is possible to find a real number = () > 0 such that, for any interval with length (), there is a number = () in this interval such that |( + ) − ()| < .
Denote by (R, R ) the set of all almost periodic functions on R; then (R, R ) is a Banach space with the supremum norm ‖‖ = ∑ =1 sup ∈R | ()|.
Denote by (R, A ) the set of all such functions.Consider the following linear system where According to [16], one can easily get the following lemma.
The Existence of Almost Periodic Solutions
In this section, we study the existence and uniqueness of almost periodic solutions by the contracting mapping principle.
In order to obtain our results, we introduce the following assumptions.
(H 1 ) For , = 1, 2, . . ., , , ∈ (R, R + ), , , ∈ (R, A) and for each 1 en system of ( ) has a unique almost periodic solution in the region Proof.For ∀Φ ∈ X, we consider the following system: Since ( 1 ), it follows from Lemma 3 that system (24) has a unique almost periodic solution We define a mapping : X 0 → X as follows: We first prove that (X 0 ) ⊂ X 0 .To this end, for each Φ ∈ X 0 , we have which implies Φ ∈ X 0 .Hence, (X 0 ) ⊂ X 0 .Then, we prove that is a contracting mapping.In fact, for every Φ, Ψ ∈ X 0 , we have Hence, : X 0 → X 0 is a contracting mapping.Therefore, by the Banach fixed point theorem, there exists a unique point Φ * ∈ X 0 such that Φ * = Φ * ; that is, system (14) has a unique almost periodic solution.In view of Remark 4, we know that system (8) has a unique almost periodic solution.
The proof is complete.
Almost Periodic Synchronization
In this section, we will investigate the global asymptotic synchronization problem of Clifford-valued CNNs with discrete delays.To this end, we consider the system (8) as the drive system and design the response system as where ∈ ([−, 0], A), () ∈ A represents the state of the response system, () is a state-feedback controller, and the rest notation is the same as those in system (8).
Let () = () − (); then, from ( 8) and ( 29), we obtain the following error system: where () = () − ().To realize the global asymptotic synchronization of the drive-response system, we choose the following state-feedback controller where = 1, 2, . . ., , : R → R + , : R → A, ℎ : A → A. By using a similar approach of transforming system (8) into system ( 14) and adopting the similar notation there, system (30) can be transformed into the following real-valued system: > 0, Remark .Under the premise that system (8) has an almost periodic solution, the synchronization of almost periodic system (8) and almost periodic system (29) is called the almost periodic synchronization.
(34) en the drive system ( ) and the response system ( ) implement global asymptotical almost periodic synchronization.
Proof.By Theorem 6, system (8) has an almost periodic solution.In order to show that system (8) and system (29) are globally asymptotically synchronized, we consider a Lyapunov function where Calculating the derivatives of 1 and 2 along the solutions of system (32), we have and Therefore, lim →+∞ 1 () = 0.By the definition of 1 (), we obtain that lim →+∞ | () − ()| = 0, for all ∈ Λ.Hence, the drive system (8) and the response system (29) are globally asymptotically synchronized.The proof is complete.
A Numerical Example
In this section, we present an example to illustrate our results.
Conclusion
In 2 (Ｎ) Ｔ 12 1 (Ｎ) Ｔ 12 2 (Ｎ) neural networks into 2 2 real-valued systems and by designing a new state-feedback controller.Our results are new and our methods can be used to study other types of Cliffordvalued neural networks. | 2,437.4 | 2019-05-12T00:00:00.000 | [
"Mathematics"
] |
A Duflo Star Product for Poisson Groups
Let $G$ be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of $G$ provided by an Etingof-Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on $G$. This recovers and generalizes Duflo's theorem which gives an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra $\mathfrak{a}$ and the subalgebra of ad-invariant in the symmetric algebra of $\mathfrak{a}$. As our proof relies on Etingof-Kazhdan construction it ultimately depends on the existence of Drinfeld associators, but otherwise it is a fairly simple application of graphical calculus. This shed some lights on Alekseev-Torossian proof of the Kashiwara-Vergne conjecture, and on the relation observed by Bar-Natan-Le-Thurston between the Duflo isomorphism and the Kontsevich integral of the unknot.
Introduction
Let K be a field of characteristic 0 and G be a Lie, algebraic or formal group over K. A multiplicative Poisson structure on G is a Poisson structure such that the multiplication map G × G → G is a Poisson map. This leads to the notion of Poisson Lie, Poisson algebraic or Poisson formal group depending on the context. If O(G) is the Hopf algebra of C ∞ , regular or formal functions on G then a multiplicative Poisson structure on G turns O(G) into a Poisson Hopf algebra.
A quantization of G is a Hopf algebra which is a quantization of O(G) as a Poisson algebra and whose coproduct reduces to the one of O(G) at = 0.
In [11] Etingof-Kazhdan associate to any Drinfeld associator a functorial way to quantize Lie bialgebras and Poisson formal groups. Their construction can be applied to Poisson Lie and algebraic groups as well. Our main result is the following (Theorem 4.2 below): If a is a finite-dimensional Lie algebra, then G = a * as an abelian group is a Poisson algebraic group, the Poisson structure on O(G) = S(a) being induced by the Lie bracket of a. The Poisson center is identified with the sub-algebra of invariant S(a) a . On the other hand one can show that the quantization of G = a * can be specialized at = 1, and becomes isomorphic to the enveloping algebra of a. Hence we get Duflo's theorem [9] as a corollary: In fact there are two constructions of a quantization of G in [11]: the first one comes from a natural construction of a certain fiber functor out of a coalgebra in a braided monoidal category constructed from a Drinfeld associator. This construction is not, however, functorial, and the authors then modify it in an appropriate way to make it so.
Our first result (Theorem 4.1) is a fairly simple graphical proof that the restriction of the star product of the first construction to the Poisson center of O(G) is undeformed, i.e., the same as the original product. This result alone guarantee the existence of a quantization of G fulfilling the conclusion of Theorem 1.1.
The second step is to show that the two constructions yields isomorphic algebras (and in fact, isomorphic Hopf algebras). This isomorphism is higly non-trivial and depends on the underlying associator. Its existence relies on the fact that the two fiber functors at hand are isomorphic as monoidal functors. However, the proof of this fact given in [11] appears to be incorrect: the isomorphism between those functors given there is not monoidal due to the contribution of certain non-trivial associativity constraints. Taking the associativity constraints into account and correcting this construction requires a detailed discussion of dualities in categories constructed from Drinfeld associators and a generalization of a result by Le-Murakami on the behaviour of the Kontsevich integral under taking parallels of tangles (Proposition 3.4). In particular, one has to modify the ordinary coevaluation map in the Drinfeld category using a very specific element closely related to the Kontsevich integral of the unknot, which explains its relation with the diagrammatic Duflo isomorphism of [3].
For the sake of concreteness we work with Lie bialgebras in the category of vector spaces, but our proof also applies in the following situation: if g is a Lie bialgebra in a linear symmetric monoidal category S which is dualizable as an object of S, then one can define the algebra of functions over the Poisson formal group of g as the object S(g * ) equipped with its standard multiplication and the coproduct induced by the Baker-Campbell-Hausdorff formula. Then Theorem 1.1 is also valid in this setting. In particular we get a version of the Duflo Theorem for dualizable Lie algebras in arbitrary symmetric monoidal categories.
We note that an analog of Theorem 1.1 holds for Kontsevich's deformation quantization of an arbitrary Poisson manifold M , which also implies Duflo's theorem [5,13,17]. While it is true for duals of finite-dimensional Lie algebras, to the best of the author's knowledge it is not known whether Kontsevich's star product on a Poisson group seen as a Poisson manifold is isomorphic to the one coming from Etingof-Kazhdan construction (if for the former one uses Tamarkin's construction [20,21], and if one chooses the same associator in both cases). An affirmative answer to this question would thus give another proof of our result. Another motivation for this paper is Alekseev-Torrossian proof of the Kashiwara-Vergne conjecture [2]. Roughly speaking they show that solutions of this conjecture are essentially the same as universal twist-quantizationà la Drinfeld of duals of finite-dimensional Lie algebras. The Kashiwara-Vergne conjecture implies (but is much stronger than) Duflo's theorem. This raises the question of whether there is a direct proof of Duflo's theorem in Etingof-Kazhdan formalism and whether it can be generalized to other Poisson groups. This paper is thus an affirmative answer to this question.
Poisson groups
To any finite-dimensional Lie algebra g over K is associated a formal group, whose algebra of functions is by definition the dual U (g) * of the enveloping algebra. This is a topological Hopf algebra, which as an algebra is identified with the degree completion S(g * ) of the symmetric algebra of g * , and whose coproduct where BCH is the Baker-Campbell-Hausdorff series.
If G is a Lie or algebraic group with Lie algebra g then the algebra O(G) of C ∞ or regular functions on G is a Hopf algebra with coproduct 1 Let I be the augmentation ideal of O(G), i.e., the ideal of functions vanishing at the identity. Then the Hopf algebra of functions on the formal group associated with g is isomorphic to the I-adic completion of O(G).
A multiplicative Poisson structure on a formal, Lie or algebraic group G is a Poisson bracket on O(G) for which the coproduct is a map of Poisson algebra. In that case we say that O(G) is a Poisson-Hopf algebra. A quantization of G is an Hopf algebra (O (G), , ∆ ) over the ring of formal power series K[[ ]] such that: A Lie bialgebra structure on g is a linear map δ : g → ∧ 2 g such that the dual map is a Lie bracket on g * and A multiplicative Poisson structure on G induces a Lie bialgebra structure on g, and conversely if g is a Lie bialgebra then the cobracket induces a multiplicative Poisson structure on G [6].
Let d be the double of g. As a vector space this is g ⊕ g * and its Lie bracket is determined by the following conditions: • the inclusions g → d and g * → d are Lie algebra maps, • the canonical pairing on d is ad-invariant.
By the PBW theorem, there is a vector space isomorphism which turns U (g) into a d-module (this coincides with the universal Verma module M − of the next section) hence d acts on the algebra of function on the formal group of g. If g is the Lie algebra of a Lie or algebraic group G, then this action is by vector fields on G, hence it can be globalised to an action of d on O(G) is the Lie and algebraic setting as well (this is the so-called dressing action [18]). A key fact for the constructions in the next sections is that the Poisson bracket on O(G) can be expressed as follows: let x i be a basis of g and x i be the dual basis of g * , then In particular, the following holds [18]:
Two quantizations of G
In this section we recall the main construction of [11], in a slightly different form inspired by [19]. Let G be a Poisson group, g its Lie bialgebra and d the Drinfeld double of g and t ∈ d ⊗2 the canonical element.
The Drinfeld category
Let A be the category whose objects are d-modules and whose morphisms are defined by Let Φ be a Drinfeld associator over K. Recall that this is a group-like element of the formal completion K X, Y of the free associative algebra on two generators, satisfying the pentagon and the hexagon equation [8]. LetΦ be the image of Φ through the algebra morphism by the action ofΦ and a map Then A with its ordinary tensor product, associativity constraint α and commutativity constraint β is a braided tensor category.
We will need a few results about duality in A. Note that A is not a rigid category since we allow infinite-dimensional modules, for which the coevaluation involves infinite sums, and in particular not every map in A has a well defined transpose. However, it is easily checked that in all our computations involving duality, only finitely many terms of the coevaluation map will contribute. The existence of a suitable rigid structure on the sub-category of A consisting of finite-dimensional modules is discussed in [4,7,12], and in a different language but using a different normalization that we will need in [14,16].
Note that for a d-module V , the ordinary evaluation and coevaluation are morphisms in A but the presence of the non-trivial associativity constraints implies that they fail to satisfy the zig-zag identity required in order to define a duality in a monoidal category. Namely, writẽ where S is the antipode of U (d). Then the action of ν induces an automorphism of the identity functor in A so that for any V ∈ A where ev (resp. coev) is the K[[ ]]-linear extension of the standard map V * ⊗ V → K (resp. K → V ⊗ V * ).
Remark 3.2. The element ν is essentially a specialization of the Kontsevich integral of the unknot, and can be shown to be independent of the choice of the associator Φ [15]. induces a duality in A. Note that for any choice of α, β the dual of V is its dual as a d-module and the dual of a map is also its ordinary dual. As objects in A we have but both sides are dual to V ⊗W in an a priori different way. In other words, the chosen duality induces a canonical automorphism given by which fails to be the identity in general. This fact is closely related to the failure of the Kontsevich integral to be compatible with the operation of taking parallel for arbitrary tangles, which has been investigated by Le-Murakami [16], who show the following result: since ν = 1 + O( ) it has a unique square root ν Using this result, we prove: Proposition 3.4. For any choice of an associator, there exists α, β such that for the corresponding duality, the canonical isomorphism Proof . Let Φ, Φ be two associators and A, A the braided monoidal categories constructed from them. By [8,15] there exists a strong monoidal structure J on the identity functor inducing a braided monoidal equivalence The morphism J is given by the action of a symmetric, d-invariant element in U (d) ⊗2 [[ ]], still denoted by J, which is given by a universal formula, i.e., can be chosen independently of d.
In particular, if one chooses any even associator Φ one can transport the duality from A to A using this equivalence. Namely we define then this duality corresponds to the choice (see, e.g., [7]). For this choice of duality, the isomorphism W * ⊗ V * → (V ⊗ W ) * is given by where we used the fact that by Theorem 3.3 the analog morphism is the identity in A . Now since any associator Φ is group-like, we have (S ⊗ S ⊗ S)(Φ) = Φ −1 . Therefore, the element (S⊗S)(J −1 ) satisfies the same twist equation as J, and since we choose J to be the specialization of an universal twist it follows from [8] that there exists an invertible central element u ∈ U (d) [[ ]] such that Now by definition (J V,W ) * is given by the action of (S ⊗ S)(J), and using the fact that J is symmetric, the map (3.1) is given by the action of (u −1 ⊗ u −1 )∆(u). Finally, setting makes this map trivial.
Two f iber functors
Let M + = Ind d g 1 and M − = Ind g g * 1 be the universal Verma modules. By the PBW theorem as vector spaces M + ∼ = U (g * ) and M − ∼ = U (g), which implies that M ± are coalgebras. We denote by 1 ± the image of 1 through those isomorphisms. Define functors F and F from A to the category vect of topologically free K[[ ]] modules by Proposition 3.5. The functors F and F are naturally isomorphic to the forgetful functor sending a d- respectively.
The following observation is key to the present construction: Proposition 3.6. Equipped with their original coproduct and counit, M ± are cocommutative coalgebras in A.
Recall that if A is any tensor category, a coalgebra structure on an object C turns the functor Hom A (C, −) into a monoidal functor. If A is braided and if C 1 , C 2 are two coalgebras in A, then the tensor product C 1 ⊗ C 2 has a natural coalgebra structure (the braided tensor product) given by Hence, the functor F has a natural monoidal structure which we denote by J . One checks that J is actually invertible, i.e., the functor F is strong monoidal. One can then formally dualize this structure to obtain a monoidal structure on F . Namely, let J be the map defined by x ⊗ y −→ Remark 3.9. If one chooses a different duality, then it still follows from Proposition 3.4 that these two algebra structures are isomorphic.
Finally, we obtain Proposition 3.10. The map given by induces a natural monoidal isomorphism between F and F .
Proof . As in [11,Proposition 9.7] this follows from the identity = which holds thanks to Proposition 3.8. We note that this in [11] this identity is claimed to be true with the ordinary coevaluation instead of the one coming from Proposition 3.4, which is not correct.
Quantization of G
The same proof as for Proposition 3.7 implies: Proposition 3.11. The algebra of function on G equipped with the dressing action of d and its original algebra structure, is a commutative algebra in A.
Hence, let O (G) = F (O(G)) and O (G) = F (O(G)). Since both functors are monoidal those are algebras in vect , and since those functors are monoidally equivalent these algebras are isomorphic. The main result of [11,19] is: is given by 2 Remark 3.14. It is of course important that the algebra structure that we consider is part of a Hopf algebra structure, i.e., that we consider quantizations of G as a Poisson group and not just as a Poisson manifold. Yet it is sufficient for our purpose that the coproduct exists, which is why we refer the reader to [11,19] for its construction.
Remark 3. 15. To be precise, the construction of [11] uses the functor Hom A (M − , M * + ⊗ −) applied to the coalgebra M − . The authors then show that this defines a functorial quantization of the Lie bialgebra g and then define the quantization of the formal group of g as Hom A (M − , M * + ⊗ M − ) * . The construction presented here is the correct way of dualizing the whole construction in order to obtain O (G) as the image of an algebra in A, and coincides with the one given in [19]. Indeed, in loc. cit. the author starts with the braided tensor product of two copies of O(G), and then applies the monoidal functor V → V g to it. By Frobenius reciprocity this is Replacing the second copy of O(G) by its formal completion which, as an algebra in A is by definition M * − one sees that the two constructions are the same. Remark 3.16. Strictly speaking, what is claimed in [11] is the existence of an Hopf algebra isomorphism between F (M − ) and Hom A (M − , M * + ⊗ M − ). Once again, this claim is valid if one uses the modified coevaluation of Proposition 3.4 instead of the ordinary one in the construction of an isomorphism between these functors. The proof of this claim can then be adapted to our setting in a straightforward way.
The center of O (G)
In this section we show the following: The rest of this section is devoted to the proof of Theorem 4.1. We start with a few general facts about coalgebras in a braided monoidal category. Lemma 4.3. Let C 1 , C 2 be two coalgebras in a braided tensor category A. Then the counit of C 1 induces a coalgebra morphism from the braided tensor product C 1 ⊗ C 2 to C 2 .
Proof . We have: Therefore, the counit of C 1 induces a monoidal natural transformation from the functor Hom A (C 2 , −) to the functor Hom A (C 1 ⊗ C 2 , −), hence for every algebra A in A an algebra morphism ρ : Hom A (C 2 , A) −→ Hom A (C 1 ⊗ C 2 , A).
Indeed, for all f, g ∈ Hom A (C 2 , A) where is the product in Hom A (C 1 ⊗C 2 , A) induced from the monoidal structure on Hom A (C 1 ⊗ C 2 , −) and from the product of A, and where is defined similarly for Hom A (C 2 , A).
Lemma 4.4. If C 2 is cocommutative and A is commutative, then the image of ρ is in the center of Hom A (C 1 ⊗ C 2 , A).
Proof . Let f ∈ Hom A (C 2 , A) and g ∈ Hom A (C 1 ⊗ C 2 , A). Then Using the commutativity of A and the cocommutativity of C 2 this equals given as the composition of ρ with the PBW isomorphism, restricts to an algebra isomorphism S(a) a ∼ = U (a) a .
Remark 5.3. It is known that the even part of a universal Duflo isomorphism for Lie algebras is uniquely determined and coincide with the original Duflo element introduced in [9]. Hence, in the case of an even associator one recovers the original Duflo isomorphism. | 4,558.4 | 2016-04-28T00:00:00.000 | [
"Mathematics"
] |
Titanium Nitride Nanodonuts Synthesized from Natural Ilmenite Ore as a Novel and Efficient Thermoplasmonic Material
Nanostructures of titanium nitride (TiN) have recently been considered as a new class of plasmonic materials that have been utilized in many solar energy applications. This work presents the synthesis of a novel nanostructure of TiN that has a nanodonut shape from natural ilmenite ore using a low-cost and bulk method. The TiN nanodonuts exhibit strong and spectrally broad localized surface plasmon resonance absorption in the visible region centered at 560 nm, which is well suited for thermoplasmonic applications as a nanoscale heat source. The heat generation is investigated by water evaporation experiments under simulated solar light, demonstrating excellent solar light harvesting performance of the nanodonut structure.
Introduction
The emerging field of thermoplasmonics uses metal nanoparticles (NPs) and metal metamaterial structures as nanoscale heat sources when excited at their localized plasmon resonance wavelength through incident light absorption [1,2]. This has been employed for various applications, such as cancer therapy, photothermal imaging, photothermal and hot-electron enhanced chemistry, and applications based on solar light harvesting [3]. Solar light is a very important source of environmentally clean and sustainable energy. Thermoplasmonic systems are particularly interesting for solar light harvesting applications, such as thermophotovoltaics and solar water evaporation (SWE). Since ancient times, SWE has been a fundamental technology for potable water production [4,5]. This technology has gained even more attention nowadays due to its great potential for addressing global challenges, such as clean water shortage (e.g., people in remote areas during the flooding season, fisherman on an unexpected long trip on the sea), desalination, and wastewater treatment [6][7][8][9]. Generally, in SWE, sunlight is absorbed by a photothermal material (i.e., absorber), which is converted into heat to vaporize water [10]. Due to their broad absorption range, carbon nanomaterials, such as amorphous carbon, graphene, and carbon nanotubes, are high-efficiency solar light absorbers. Although their low emissivity is a limiting factor for achieving high-efficiency photothermal conversion, various carbon-based materials and structures have demonstrated good SWE performance [9,[11][12][13][14].
Pioneering research utilizing thermoplasmonics for SWE employed solar harvesting with metal NPs dispersed in a liquid [15][16][17]. Typically, noble metal NPs, such as Au, Ag, Pt, and Pd, have been employed because of their widespread use in plasmonics and strong light absorption at the localized surface plasmon resonance [10,15,17]. However, their high cost and narrow absorption range are hindrances for practical SWE deployment. Recently, titanium nitride (TiN) has been demonstrated as a highly stable plasmonic material that is much cheaper than noble metals [18][19][20][21][22][23][24][25]. TiN NPs have been reported to be promising for solar harvesting applications, in which efficient nanoscale heat generators with a wide spectral absorption range are highly desirable [21,26,27]. Employing these advantages, TiN has been demonstrated as an excellent photothermal material for SWE [21][22][23][28][29][30]. Furthermore, since evaporation occurs at the liquid-air interface, and heat is generated in the bulk liquid, the volumetric heating method usually achieves low energy conversion efficiency due to the heat loss [5,28]. Therefore, recent SWE studies have employed floating structures, in which the photothermal material is immobilized on a substrate that floats in water. Using this approach, significant improvements of the SWE efficiency have been achieved [9,11,14,[30][31][32].
In this work, we present a low-cost method for fabricating a novel nanostructure of TiN, i.e., nanodonut. The TiN nanodonuts exhibit strong and spectrally broad localized surface plasmon resonance absorption in the visible region that provides excellent photothermal conversion performance. We demonstrate the effectiveness of the TiN nanodonuts as broad-band thermoplasmonic heat generators for SWE under simulated solar light using the floating substrate approach by depositing the TiN nanodonuts on a polymer membrane.
Synthesis of TiO 2 Nanoparticles from Ilmenite Ore
TiO 2 NPs were synthesized by a three-step process described as follows: Step 1: Ilmenite ore was firstly crushed and ground into fine powder with particle sizes in the range of 50-75 µm. Then, 10 g of the powder was transferred into a 250 mL plastic beaker containing 70 mL of HF 20% solution. The suspension was continuously stirred for 5 h at room temperature. The obtained slurry suspension (i.e., filtrate) was separated from the deposited solid residual.
Step 2: 30 mL KCl 4 M solution was slowly added to the filtrate, resulting in a white K 2 TiF 6 precipitate. In the next step, the precipitate was separated and dissolved in water by heating up the suspension to 80 • C until a saturated solution was achieved, which was then filtered and rapidly cooled down to room temperature to form again K 2 TiF 6 precipitate. This step was used to eliminate the impurities and purify the K 2 TiF 6 precipitate. The precipitate was dried in air at 105 • C for 2 h.
Step 3: 5 g of K 2 TiF 6 precipitate was dissolved in 500 mL of distilled water by heating up to 80 • C. Then, NH 3 solution (4 M, prepared from ammonium hydroxide 28% solution) was slowly added until pH = 9. This hydrolysis reaction produced Ti(OH) 4 , which was then annealed at 550 • C for 3 h to obtain TiO 2 .
Synthesis of TiN by Nitridation of TiO 2 in NH 3
Nitridation of TiO 2 to obtain TiN has been reported by several research groups [33][34][35][36][37]. In our approach, for each experiment, 1 g of TiO 2 NPs was loaded into a ceramic boat and placed at the center of a quartz-tube furnace (PTF 12/50/610, Lenton, UK). One end of the tube was connected to the gas inlet (N 2 , NH 3 ). The other end was connected to a mechanical vacuum pump. Initially, the quartz tube was evacuated to reach a vacuum of 10 −2 mbar and then pre-heated to 250 • C. The tube was purged several times by N 2 (99.99%) to remove contaminants. Thereafter, the temperature in the furnace was increased to either 700 or 900 • C, both at a ramping rate of 3 • C min −1 . After the temperature was stabilized, NH 3 gas was introduced into the furnace at a flow rate of 1000 sccm for 1 h. Finally, the furnace was cooled down to 100 • C in NH 3 ambient, and further to room temperature in N 2 before unloading the sample.
Material Characterizations
The morphology of the materials was studied by Field-Emission Scanning Electron Microscopy (FE-SEM) and High-Resolution Transmission Electron Microscopy (HR-TEM) using Hitachi S4800 (Ibaraki, Japan) and JEOL ARM-200F (Tokyo, Japan) systems, respectively. The crystalline structure of the materials was investigated by X-Ray Diffraction (XRD) using a Bruker diffractometer (D8 Advance Eco, Bruker, Billerica, MA, USA) equipped with a Cu Kα X-ray radiation source. The optical absorption spectra were acquired by using a JASCO V-750 UV-VIS spectrophotometer (Easton, MD, USA). Chemical compositions of the materials and the binding energy of the elements were determined by X-Ray Photoelectron Spectroscopy (XPS) using a XR4 Thermo Scientific Spectrometer (Waltham, MA, USA) equipped with an Mg-Kα X-ray radiation source.
Solar Water Evaporation Experiments
For each experiment, 20 mg of the powder (TiO 2 , TiON, TiN or nanocarbon) was dispersed in ethanol and sonicated for 10 min. Using the drop-coating method, the powder was deposited on a polymer membrane (Novatexx 2471, Freudenberg, 5 cm in diameter). The membrane was immersed in water contained in a 100 mL glass beaker and was kept afloat at a distance of~5 mm below the water surface, which was the equilibrium position of the membrane when it floated. It is worth noting that due to the non-uniform mass distribution, the membrane might be slightly tilted. To address this issue, a thin fabric string was used to keep the entire membrane in the horizontal position. The evaporation was investigated by monitoring the weight change of the system (glass beaker, water and the membrane) under simulated solar light generated by a Xenon arc lamp (60 W, Guangzhou Lightech Auto Lighting Co., Ltd. Guangdong, China) with an illuminance of 550 W m −2 , which is equivalent to an illuminance of 0.55 sun of natural solar light. The temperatures of the environment, the surface of the membranes and the liquid were measured using a BETEX 1230 Infrared Thermometer (Bega Special Tools, Vaassen, the Netherlands).
Results and Discussion
The hydrofluoric acid leaching of ilmenite ore produces TiO 2 NPs with sizes in the range of 70-160 nm, as shown in the SEM micrograph in Figure 1a. The presence of TiO 2 material is confirmed by XRD and XPS analyses shown in Figures 1d and 1e, respectively. The XRD pattern from the obtained powder (Figure 1d, bottom pattern) is consistent with that of the polycrystalline TiO 2 containing both anatase and rutile phases [38]. The XPS spectrum of the Ti 2p core-level (Figure 1e, bottom spectrum) shows two peaks at binding energies of 464.0 and 458.2 eV. These peaks are the characteristic doublet state of Ti 2p (i.e., Ti 2p 1/2 and Ti 2p 3/2 , respectively) in TiO 2 [39]. Following annealing in NH 3 at 700 • C for 1 h, a slight coalescence of the NPs is observed (Figure 1b). The annealing strongly affects the crystalline structure and chemical composition, as shown in the spectra in Figure 1d-f. In the XRD pattern (Figure 1d), the R(110) and A(200) peaks observed for TiO 2 vanish and a new peak at 43.3 • appears. This peak represents the (200) plane of TiN cubic structure [40], and is further confirmed by the HR-TEM image shown in Figure 2a. The co-existence of both TiO 2 and TiN results in the N-Ti-O bonds, causing the broadening of the Ti 2p peaks to the lower binding energy side, as shown in Figure 1e (middle spectrum) [39]. The presence of those bonds is also demonstrated by the broad and asymmetric N 1s peak shown in Figure 1f (middle spectrum) [39]. The XRD and XPS analyses indicate that the nitridation of the TiO 2 at 700 • C was incomplete, resulting in TiO 2 -TiN composite (hereafter denoted as TiON). After nitriding at 900 • C in NH 3 for 1 h, the NPs exhibit distinct changes in morphology: the NPs transform into an entirely different structure with the shapes of nanodonuts having outer diameters in the range of 80-120 nm, and inner diameters ranging from 30 to 60 nm (Figure 1c and Figure S1,). In the XRD pattern shown in Figure 1d, the diffraction peaks of TiO 2 entirely disappear, and only TiN peaks are observed [27]. This is further supported by the results obtained by HR-TEM shown in Figure 2b. Furthermore, the two peaks at 461.0 and 455.3 eV in the Ti 2p XPS spectrum (Figure 1e) and the peak at 396.5 eV in the N 1s spectrum (Figure 1f) are consistent with the binding energies of Ti-N bonds in stoichiometric TiN [39]. Therefore, we conclude that by annealing in NH 3 at 900 • C, the TiO 2 was completely nitridized and transformed into TiN.
The nitridation of TiO 2 in NH 3 ambient was previously explained by Gou et al. [42]. According to the study, at 900 • C, the nitridation takes place via the formation of TiN 1−x O x and releases H 2 O vapor and N 2 gas. With increasing the reaction time, the oxygen atoms of TiN 1−x O x are gradually substituted by the nitrogen atoms. Eventually, TiO 2 is nitridized to TiN [42]. Importantly, the authors observed the formation of mesopores with diameters in the range of 20-40 nm after the nitridation. This is consistent with formation of the cavities, which results in the nanodonuts; this can be attributed to the release of H 2 O vapor and N 2 gas. In addition, it has been reported that the incorporation of nitrogen atoms during the nitridation process can cause an expansion and contraction of the particles [43,44], which can be another factor that promotes the formation of the nanodonut structure. Nevertheless, this assumption requires further studies for clarification.
The UV-VIS diffuse reflectance spectra of the materials are shown in Figure 3a. The TiO 2 NPs have an absorption edge at 410 nm, which corresponds to a bandgap of 3.0 eV (using the Tauc method). The absorption of the TiON NPs exhibits a significant red shift that results in a bandgap of 2.1 eV. The TiN nanodonuts manifest a broad plasmon resonance spectrum in the visible region with a peak centered at 560 nm. This is in contrast to resonance peaks commonly observed for TiN, which are in the far-red and near infrared ranges. For instance, Traver et al. [40]. These examples demonstrate a nonmonotonic relationship between the particle size and the plasmon resonance of TiN NPs. We speculate that the peak resonance at 560 nm, in this case, may arise from the structure of the nanodonut NPs, which requires further exploration. Importantly, the broad plasmon resonance spectrum of the TiN nanodonuts corresponds well with the solar spectral range where sunlight provides the highest flux ( Figure S2, Supporting Information). This is highly desirable for the solar light harvesting applications. respectively) under continuous-wave (cw) illumination of simulated solar light generated by a Xenon arc lamp with illuminance of 550 W m -2 . The measurements were performed in air at a relative humidity of 72% and an ambient temperature of 31 • C. The results demonstrate that, after 9 min of cw illumination, the temperature of the blank membrane increases from 31 to 45 • C and stabilizes thereafter. Higher temperatures are acquired for the TiO 2 and TiON membranes (i.e., 48 and 53 • C, respectively), which can be explained by the improved light absorption (Figure 3a). For the TiN membrane, the temperature reaches 60 • C, indicating its higher photothermal conversion efficiency.
The use of TiN nanodonuts as nanoscale heat generators was tested by studying their SWE performance under cw illumination of simulated solar light with illuminance of 550 W m −2 . For this purpose, the membranes were immersed in water and kept at a position of about 5 mm below the water surface. Water evaporation was investigated by monitoring the weight change under continuous cw simulated solar illumination. The results are shown in Figure 3c, demonstrating a linear decrease in weight after 10 min of cw illumination. From these plots, the evaporation rates are calculated, which are presented in Table S1, Supporting Information. For the TiN membrane, an evaporation rate of 0.045 g min −1 is achieved. Taking into account the diameter of the glass beaker (~5 cm) gives an evaporation rate of 1.38 kg h −1 m −2 . This rate is comparable to evaporation rates obtained for various other materials, which are typically in the range of 1.0-1.9 kg h −1 m −2 , despite our lower illuminance (Table 1). This suggests the high light harvesting efficiency of the TiN nanodonuts. In addition, the TiN nanodonuts outperform carbon and graphene NPs under similar experimental conditions (Table S1 and Figure S3, Supporting Information). Furthermore, it is worth mentioning that the TiN membrane was used for a considerable number of experiments (i.e., above 30) in various experimental conditions (e.g., under simulated solar light, under natural solar light, in fresh water and in salt water with a concentration of 35 g L −1 ) with total illumination time above 30 h. The data reported in Figure 3c were acquired after the membrane had been used for more than 25 h. No considerable change in the evaporation rate (as well as the formation of air bubbles presented in the next part) was observed. This indicates an excellent stability of the TiN nanodonuts. RGO-Sodium alginate-CNT aerogel Self-floating 1.0 1.622 [13] 2D GO film Cellulose-wrapped Polystyrene foam 1.0 1.45 [46] Carbon black coated PMMA nanofiber on PAN nanofiber Self-floating 1.0 1.3 [47] Bi-layered rGO film Polystyrene foam 1.0 1.31 [48] Carbon nanotubes Porous Silica 1.0 1.32 [49] Flame-treated wood Self-floating 1.0 1.05 [50] Carbonized mushrooms Polystyrene foam 1.0 1.475 [51] Importantly, we observed that within 30 s of illumination, bubbles were formed at the TiN membrane surface (Figure 4). Under continuous cw illumination, the bubbles expanded their volume and eventually detached from the membrane surface and moved to the water-air interface, where the air contained in the bubbles was released (Videos S1 and S2, Supporting Information). Only sporadic bubbles were observed for the TiON membrane and no bubble was observed for the blank and the TiO 2 membranes ( Figure S4, Supporting Information). This can be explained by the higher temperature of the TiN membrane (i.e., 60 • C), as shown in Figure 3b. The bubble formation due to the thermoplasmonic effect has been described in detail by Baffou et al. [2,52]. Two important conclusions emerge from their analysis: (i) the bubbles contain air, and (ii) the NPs generate a high localized temperature in the range of 200-220 • C, which is required to initiate bubble generation [2,3,52]. From their second conclusion, the bubble formation observed in our work suggests that the local temperature obtained for the TiN nanodonuts under cw illumination could be significantly higher than the measured value at the surface of the TiN membrane (i.e., 60 • C). This seeming discrepancy can be attributed to the fact that the infrared temperature probe has a spot size of about 2 mm and thus provides a spatially averaged value, while the bubble formation occurs locally. We note that bubble formation caused by the thermoplasmonic effect has been observed for Au NPs by many research groups [2,15,17,53]. However, this phenomenon has not been reported for TiN, although high local heat has been suggested for various TiN nanostructures under simulated solar light illumination [19,21,23,[27][28][29].
Conclusions
In summary, we have demonstrated a low-cost and feasible approach for the fabrication of TiN nanodonuts that exhibit strong and broad plasmon resonance absorption in the visible region centered at 560 nm. The SWE performance was studied using a floating structure prepared by drop-coating the TiN nanodonuts on a polymer membrane. Using simulated solar light with an illuminance of 550 W m −2 , our experiments reveal two important observations. First, the TiN nanodonuts provide an evaporation rate of 1.38 kg h −1 m −2 . This value is comparable to previously reported rates obtained for higher illuminance, proving that the TiN nanodonuts are highly efficient light harvesting materials. Second, the formation of the bubbles at the membrane surface is observed, providing firm evidence of high local heat generated by the TiN nanodonuts, which has not been previously reported.
Supplementary Materials: The following are available online at https://www.mdpi.com/2079-499 1/11/1/76/s1, Figure S1: Representative TEM images of TiN nanodonuts. The particle and cavity sizes were measured using Gatan Micrograph Suite ® software, Figure S2: UV-Vis absorption spectrum of TiN nanodonuts and solar emission spectrum, Figure S3: SWE performance of the synthesized photothermal materials (TiO 2 , TiON and TiN) in comparison with the graphene nanoplatelets and carbon nanopowders, Figure S4: Photographs of (a) blank polymer membrane, (b) TiO 2 membrane, (c) TiON membrane and (d) TiN membrane taken after 600 s of exposure to simulated solar light generated by the Xenon arc lamp with an illuminance of 550 W m -2 , Table S1: Evaporation rate of water without the membranes, the blank membrane and the membranes deposited with photothermal nanomaterials ( | 4,495.4 | 2020-12-31T00:00:00.000 | [
"Physics",
"Materials Science"
] |
Optical and Magnetic Properties of Fe Doped ZnO Nanoparticles Obtained by Hydrothermal Synthesis
Diluted magnetic semiconductors Zn 1−x Fe x O nanoparticles with different doping concentration (x = 0, 0.01, 0.05, 0.10, and 0.20) were successfully synthesized by hydrothermal method.The crystal structure, morphology, and optical and magnetic properties of the samples were characterized by X-ray diffraction (XRD), energy dispersive spectrometer (EDS), high-resolution transmission electron microscopy (HRTEM), Raman scattering spectra (Raman), photoluminescence spectra (PL), and the vibrating sample magnetometer (VSM). The experiment results show that all samples synthesized by this method possess hexagonal wurtzite crystal structure with good crystallization, no other impurity phases are observed, and the morphology of the sample shows the presence of ellipsoidal nanoparticles. All the Fe successfully substituted for the lattice site of Zn and generates single-phase Zn 1−x Fe x O. Raman spectra shows that the peak shifts to higher frequency. PL spectra exhibit a slight blue shift and the UV emission is annihilated with the increase of Fe concentration. Magnetic measurements indicated that Fe-doped ZnO samples exhibit ferromagnetic behavior at room temperature and the saturationmagnetization is enhanced with the increase of iron doping content.
Introduction
Diluted magnetic semiconductors (DMSs) are referred to as nonmagnetic semiconductors in which a small fraction of host cations are replaced by transition metal or rare-earth ions, with both spin and charge degrees of freedom in a single material [1,2].In recent years, DMSs have been under intense research due to their potential applications in spinbased multifunctional electronic devices, such as ultraviolet absorbers, optoelectronics, spin field-effect transistors, fieldemission devices, gas sensors, nonvolatile memory devices, and quantum computer [3][4][5][6][7][8].Of all the oxide diluted magnetic semiconductors, the transition metal (TM) doped ZnO has been identified as a promising one, because the host material ZnO is a chemically and thermally stable -type II-VI compound semiconductor with a wide band gap energy (3.37 eV) and a large exciton binding energy (60 meV) [9][10][11].During the past years, transition metal doped ZnO has been doped into the ZnO lattice to modulate the local electronic structure and cause dramatic changes in their optical and electromagnetic properties [12][13][14][15].Various methods have been used to synthesize TM doped ZnO nanoparticles: some experimental results observed the room temperature ferromagnetism in ZnO : Fe system, but the experimental results were contradictory, and the theoretical explanation about the origin of the magnetism is still not mature [16][17][18][19][20].However, there are very few reports on the magnetic behavior of transition metal doped ZnO synthesized using hydrothermal method.Thus, in this paper, our aim is to synthesize Zn 1− Fe O nanoparticles with different concentration using hydrothermal method and to study their structural, optical, and magnetic properties.
In this paper, diluted magnetic semiconductors Zn 1− Fe O nanoparticles with different doping consistency ( = 0, 0.01, 0.05, 0.10, and 0.20) were synthesized by hydrothermal method.And the crystal structure,
Experimental
Zn 1− Fe O ( = 0, 0.01, 0.05, 0.10, and 0.20) nanoparticles were prepared by hydrothermal method.All materials were of analytical grade and used without further purification in this study.In a typical experiment, zinc acetate (Zn(CH 3 COO) 2 ⋅2H 2 O, 99.0%, AR) and ferric nitrate (Fe(NO 3 ) 3 ⋅9H 2 O, ≥99.0%,AR) were mixed together according to the required amounts of the corresponding chemical reagents and dissolved into absolute alcohol under magnetic stirring at room temperature.Then cetyltrimethylammonium bromide (CTAB, ≥99.0%,AR) was added to the above solution; meanwhile, sodium hydroxide (NaOH, ≥96.0%,AR) was dissolved into absolute ethanol and introduced into the above solution.After being stirred for 30 min, the mixture was transferred into a 45 mL Teflon lined stainless steel autoclave.The hydrothermal synthesis was heated to 180 ∘ C and maintained for 24 h in an oven and then cooled down to the room temperature naturally.The obtained products were washed with distilled water and absolute ethanol several times and dried at 60 ∘ C for 24 h.Finally, the samples were obtained.
The crystalline structures of the samples were examined by a rotating-target X-ray diffractometer (Japan Rigaku D/Max-2400) equipped with graphite monochromatized CuK radiation ( = 1.54056Å, 40 kV, 100 mA).The samples were scanned in the angular range from 10 to 90 ∘ (2) with scanning rate 0.005 ∘ /s and step size 0.02 ∘ .The morphology and microstructure of the samples were observed through transmission electron microscopy (TEM, Japan JEOL JEM 1200EX), the corresponding selected-area electron diffraction (SAED), and high-resolution transmission electron microscopy (HRTEM, JEM-2010).The chemical composition of the products was verified by energy dispersive spectroscopy (EDS) at an acceleration voltage of 200 keV in TEM.Raman spectral measurements at room temperature in the energy region between 100 and 1500 cm −1 were carried out using a micro-Raman spectrometer (HR800) with 525 nm line of He-Ne ion laser as exciting light source.Photoluminescence (PL) spectra were performed at 266 nm wavelength using a PerkinElmer spectrophotometer with a He-Cd laser as excitation source.Magnetic hysteresis loops were investigated at room temperature using a vibrating sample magnetometer (VSM, Lakeshore 7304) with an applied field from −12000 Oe to 12000 Oe.
Results and Discussion
The phase purity and crystal structure of the Zn 1− Fe O samples were examined by XRD. Figure 1 0.20) nanoparticles.It is clearly observed from the pattern that all the diffraction peaks can be well corresponding to the diffractions of ( 100), ( 002), ( 101), ( 102), ( 110), ( 103), ( 200), ( 112), (201), and (202) planes of single-phase hexagonal wurtzite structure with the space group 6 3 mc, respectively.All the diffraction peaks are in good agreement with the values of the standard spectrum (JCPDS 01-079-2205).In addition, there are no traces of impurity or secondary phases within the detection limit of XRD and there are no obvious diffraction patterns of Fe species such as Fe, Fe 2 O 3 , and Fe 3 O 4 in the samples where the doping atomic percentage is from 1% to 20%.These results indicate that all Fe ions were incorporated in the lattice of the host crystals, the products consist of pure phase, and no characteristic peaks can be found from other impurities.For Fe-doped ZnO dilute magnetic semiconductors, the peak position of the doped ZnO samples shifts to lower angles compared with pure ZnO, and also there is a decrease in the intensity of peaks with the Fe doping concentration.This shifting as well as decrease in intensity of the characteristic peak clearly indicates the successful incorporation of Fe in the ZnO matrix, which can be attributed to the difference of ion radius of Zn 2+ (0.74 Å) comparing with that of Fe 3+ (0.64 Å).It is indicated that Fe ions occupy the Zn ions sites in the hexagonal wurtzite structure and no impurity phase appears.
The morphology and microstructure of the samples were observed through HRTEM.The images of all samples reveal the presence of randomly distributed ellipsoidal shape nanoparticles.Figure 2(a) shows the HRTEM image of the Zn 0.95 Fe 0.05 O; it can be seen that the sample consists of ellipsoidal shape particles, and well dispersed with smooth surface and uniform size, the diameter of the nanoparticles ranges from 10 to 40 nm, with an average diameter approximately 25 nm.The crystalline quality improves since CTAB promotes the establishment of a net surface charge onto the nanocrystals preventing their aggregation.which is in good agreement with the d-spacing of (002) planes of hexagonal wurtzite ZnO structure.The value of lattice spacing is greater than that of pure ZnO (0.26 nm).The HRTEM analysis is consistent with the XRD results, which further indicates that all the Fe ions successfully substituted for the lattice site of Zn 2+ in the hexagonal wurtzite structure and no impurity phase appeared.
In order to determine the elements of the prepared samples, EDS analysis was performed.Figure 3 shows the EDS patterns of Zn 0.95 Fe 0.05 O sample.The EDS spectrum indicates that the as-prepared nanoparticles mainly contain Fe, Zn, and O three elements.The characteristic peaks of O appeared at 0.5 keV and the characteristic peaks of Zn appeared at 1 and 8.7 keV.The characteristic peaks of Cu appeared at 0.9, 8 and 8.9 keV.The Fe signal at 0.7, 6.4, and 7.1 keV was observed in the Fe-doped ZnO nanoparticles.Apart from that, the Cu and C peaks in the EDS originate from the TEM micromesh grid.The EDS results further verify XRD conclusion; this indicates that Fe-doped ZnO diluted magnetic semiconductor was successfully synthesized by hydrothermal method and Fe 3+ in the sample occupied the place of Zn 2+ .
Raman spectra are a versatile technique for detecting the incorporation of dopants and the resulted defects and lattice disorder in the host lattice.In order to further confirm the phase transition and the defect chemistry variation after Fe-doped ZnO, Raman spectra of the as-prepared products were measured with an excitation wavelength of 532 nm at room temperature.Wurtzie structure ZnO as a -type II-VI semiconductor with the space group 6 3 mc, has zone center optical phononmodes: Γ opt = 1 + 2 1 + 1 + 2 2 [21], where 1 , 1 , and 2 are Raman active and 1 is Raman forbidden. 1 and 1 modes are polar and split into the transverse optical (TO) and longitudinal optical (LO) phonons, and 2 mode consists of two modes: 2 high which is associated with the vibration of oxygen atoms and 2 low attributed to the Zn sublattices.
Room temperature Raman spectrum of all the synthesized samples is presented in Figure 4.The spectra reveal that all the major peaks which are the characteristics of vibrational modes in ZnO exist in all samples.For all the samples, Raman peak at 332 cm −1 is attributed to the second order Raman mode arising from zone boundary phonons 2 high- 2 low, the peak at 381 cm −1 is assigned to the fundamental optical mode 1 TO, and the peak at 444 cm −1 is the 2 high mode, whereas peak at about 478 cm −1 is thought as originated from two phonon process, which correspond to 1 TO + 2 low mode.Moreover, for the Zn 0.99 Fe 0.01 O and Zn 0.95 Fe 0.05 O samples, a broad hump at 574 cm −1 is 1 LO symmetry modes [11,22,23].And for the Zn 0.90 Fe 0.10 O and Zn 0.80 Fe 0.20 O samples, a broad peak centered at 640 cm −1 is related to intrinsic host-lattice defects after doping and it is also a powerful evidence to prove Fe 3+ occupation at Zn 2+ sites in the ZnO lattice [24,25].Besides, with increasing the content of Fe 3+ doping in the samples, there is shift in all peaks towards higher frequency region, broaden asymmetrically and weakened peak intensity.This shift can be due to strain, phonon confinement by boundaries, and the force constant changes caused by the less defects or impurities.
In these modes, the 2 high peak in all the samples is attributed to the standard mode in wurtzite structure, which indicates that Fe-doped ZnO nanoparticles keep a good hexagonal ZnO structure.Moreover, 2 high mode is very sensitive to the stress in the crystal [24].From Figure 4, the peaks at 444 cm −1 of 2 high mode are lowered in the intensity with the more Fe content, which due to the radius of Fe 3+ (0.063 nm) smaller than radius of Zn 2+ (0.074 nm), and after being doped with Fe 3+ , it can cause the lattice expansion, defects, and the stress increase [26].
Figure 5 depicts PL spectra of Fe-doped ZnO nanoparticles at room temperature.For comparison, PL spectrum of undoped ZnO sample is also given.The pure ZnO sample contains six main emission peaks, including three obvious broad bands centered at 390, 440, and 490 nm and three comparatively weak emission peaks at 420, 460, and 525 nm, respectively.The 1% sample exhibits similar emission to pure ZnO.This illustrates that the Zn 0.99 Fe 0.01 O sample displays nearly the same structure of pure ZnO.But the emission peak position of doped sample exhibits a slight blue shift with the increase of Fe 3+ concentration, and this is attributed to defects or the oxygen vacancies in ZnO induced by Fe 3+ doping.
In addition, the visible light (VL) emission band is also suppressed with the increase of the Fe 3+ concentration.The strong ultraviolet (UV) emission band at 390 nm (3.18 eV) and the weak violet emission peak located at 420 nm (2.95 eV) originate from excitonic recombination corresponding to the near-band-edge emission (NBE) of wide band gap of ZnO, because of the quantum confinement effect [27].The strong blue emission bands centered at 440 nm (2.8 eV) and the weak blue emission peak at 460 nm (2.69 eV) are attributed to the transitions between the shallow donor levels of the interstitial Zn to the top of the valence band [14] or the transitions between shallow acceptor levels of oxygen vacancies and shallow donor levels of zinc vacancy [28].The blue-green bands centered at 490 nm (2.55 eV) for samples are ascribed to the transition between the deep donor level of oxygen vacancy, which is close to the bottom of the conduction band of about 0.8∼0.9eV, to the valence band [28,29].The weak green emission peak at 525 nm (2.36 eV) is possibly assigned to positively charged electron transition and surface traps mediated by defects in the band gap [30].PL spectrum analysis further illustrates that Fe ions are probably incorporated into the ZnO host matrix in the doped ZnO sample.
The related PL intensity of doped sample decreases rapidly with the increase of Fe doping concentration compared with undoped ZnO, and the emission peak position intensity of 20% Fe-doped ZnO sample was annihilated; this is because the photogenerated electrons preferentially occupy the Fe ion induced trap centers, resulting in the quenching of luminescence [14].
Figure 6 shows the magnetic hysteresis (M-H) loops of the Zn 1− Fe O nanoparticles with different doping consistency ( = 0, 0.01, 0.05, 0.10, and 0.20) measured at room temperature.The magnetic hysteresis loops of ZnO and lower doped ZnO ( = 0.01 and 0.05) samples pass origin of coordinates, and the remanent magnetization (M r ), and coercivity (H c ) are zero.It suggests that these samples show paramagnetic behaviors at room temperature.While the higher doped ZnO ( = 0.10 and 0.20) samples exhibit obvious ferromagnetic behaviors.The saturation magnetization values are 0.74 emu/g and 1.74 emu/g and the coercive force values are 90 Oe and 78 Oe, respectively, for ZnO ( = 0.10 and 0.20).It is evident from Figure 6 that a transition from the paramagnetic state to the ferromagnetism state occurs.The saturation magnetization of Zn 1− Fe O nanoparticles increases with the increasing of Fe doping concentration compared with pure ZnO.
The room temperature ferromagnetism of the Zn 1− Fe O nanoparticles could arise from two possible sources.One is extrinsic magnetism and the other is intrinsic magnetism.Extrinsic source includes the formation of clusters of transition elements or secondary phase.Exchange interactions come under intrinsic source of magnetism.But the XRD results of the Zn 1− Fe O nanoparticles suggest no traces of impurity or secondary phases (these parasitic phases include the Fe clusters and any other phases like Fe 2 O 3 , Fe 3 O 4 , etc.).Thus, the possibility of ferromagnetism due to the clusters of transition elements or secondary phases in the samples could be ruled out.Hence, the obtained ferromagnetism is an intrinsic magnetic property of the Zn 1− Fe O nanoparticles.It is evident from the XRD analysis that Fe is incorporated into the ZnO lattice.In view of the Fe 3+ ions substituted into ZnO lattice, the origin of magnetism in the samples is due to the exchange interaction between local spinpolarized electrons (such as the electrons of Fe 3+ ions) and the conductive electrons.Such interaction can lead to the spin polarization of conductive electrons.Consequently, the spin-polarized conductive electrons undergo an exchange interaction with local spin-polarized electrons of Fe 3+ ions.Thus, after a successive long-range exchange interaction, almost all Fe 3+ ions exhibit the same spin direction, resulting in the ferromagnetism of the material [31].
Conclusions
(1) Diluted magnetic semiconductors Zn 1− Fe O nanoparticles with different concentration ( = 0, 0.01, 0.05, 0.10, and 0.20) have been synthesized by hydrothermal method.The samples possess hexagonal wurtzite crystal structure with good crystallization, no other impurity phase appeared, and the morphology of samples is ellipsoidal shape nanoparticles with good dispersion.
(2) All the Fe 3+ successfully substituted for the lattice site of Zn 2+ and generates single-phase Zn 1− Fe O.The Raman spectra of the Zn 1− Fe O nanoparticles occurs red shift, and the UV emission of photoluminescence spectra is annihilated with the increase of Fe 3+ concentration.The ferromagnetic behaviors are found for all doped samples at room temperature.
Figure 2(b) shows a typical HRTEM image of Zn 0.95 Fe 0.05 O nanoparticles.The resolved lattice plane extending through the image confirms that the particle is crystallized.
Figure 6 :
Figure 6: The magnetic hysteresis loops of the Zn 1− Fe O nanoparticles. | 3,928.4 | 2014-01-01T00:00:00.000 | [
"Materials Science",
"Chemistry"
] |
Selection of suitable reference genes for normalization of quantitative RT-PCR in peripheral blood samples of bottlenose dolphins (Tursiops truncatus)
Quantitative RT-PCR is often used as a research tool directed at gene transcription. Selection of optimal housekeeping genes (HKGs) as reference genes is critical to establishing sensitive and reproducible qRT-PCR-based assays. The current study was designed to identify the appropriate reference genes in blood leukocytes of bottlenose dolphins (Tursiops truncatus) for gene transcription research. Seventy-five blood samples collected from 7 bottlenose dolphins were used to analyze 15 candidate HKGs (ACTB, B2M, GAPDH, HPRT1, LDHB, PGK1, RPL4, RPL8, RPL18, RPS9, RPS18, TFRC, YWHAZ, LDHA, SDHA). HKG stability in qRT-PCR was determined using geNorm, NormFinder, BestKeeper and comparative delta Ct algorithms. Utilization of RefFinder, which combined all 4 algorithms, suggested that PGK1, HPRT1 and RPL4 were the most stable HKGs in bottlenose dolphin blood. Gene transcription perturbations in blood can serve as an indication of health status in cetaceans as it occurs prior to alterations in hematology and chemistry. This study identified HKGs that could be used in gene transcript studies, which may contribute to further mRNA relative quantification research in the peripheral blood leukocytes in captive cetaceans.
Function
Gene Name Table 2); therefore all 15 HKGs were included in the analysis of reference gene suitability. Figure 1 illustrated the variable transcript levels in the 15 HKGs with the lowest mean Cq values (21.06) in ACTB, and the highest (32.14) in SDHA. Transcript levels were used to establish two arbitrary categories: those that were highly transcribed (mean Cq values < 25 cycles) including ACTB, B2M, GAPDH, RPL4, RPL8, RPL18, RPS18, and RPS9, and those with lower transcript levels (mean Cq values > 25 cycles) including HPRT1, LDHA, LDHB, PGK1, SDHA, TFRC and YWHAZ. All HKGs showed a small difference (< 5 cycles) between the maximum and minimum Cq values.
Gene transcript stability in 75-sample group. The geNorm algorithm demonstrated good stability of all tested HKGs (Table 3). M values, average pair-wise variation of a given gene with all other control genes, were lower (0.178-0.682) than the program's default limit of 1.5. RPL18 and RPS18 were the most stable genes followed by RPL8, RPL4, and RPS9. The optimal number of reference genes for normalization was established using pairwise variation values (V) between two sequential normalization factors while employing an increasing number of genes. The optimal number was determined to be less than 3 based upon V 2/3 value of 0.084 (< 0.15 is the default cut-off) ( Fig. 2A), indicating that the addition of one more HKG would not significantly improve reliability. NormFinder analysis identified HPRT1 as having the best stability (0.357) followed by RPL4 (0.390) and PGK1 (0.408) ( Table 3). BestKeeper analysis determined the SD Cq value of all HKGs (0.540-0.783) were < 1 indicating these genes were basically stably expressed. The three most stable genes, according to their SD Cq value ,were RPL4, TFRC and RPS9 ( Table 3). The best choice in comparative Δ Ct method was PGK1, HPRT1 and RPL4. RefFinder identified RPL4, HPRT1 and PGK1 as being superior (Table 3, Fig. 3A).
Gene transcript stability in 35-and 55-sample groups. In both 35-and 55-sample groups the M values in geNorm of all studied HKGs were lower than the program's default limit (M = 1.5), and the SD Cq value in BestKeeper were < 1. V 2/3 values in both groups were below to 0.15 (Fig. 2B,C). In contrast to the result in 75-sample group, geNorm algorithm identified PGK1, ACTB and LDHA to be the most stable HKGs in both groups. BestKeeper showed similar results in high-ranking HKGs (RPL4, TFRC, RPS9, B2M and HPRT1) in three groups. NormFinder and comparative Δ Ct method identified HPRT1, PGK1 and RPL4 to be the best-three HKGs in all three groups. The RefFinder comprehensive rankings placed PGK1, HPRT1 and RPL4 as being highly ranked HKGs in all three groups (Tables 3-5, Fig. 3).
Discussion
RNA transcript stability plays a crucial role in qRT-PCR-based studies due to pre-analytical variations, especially degradation by endogenous RNases and unintentional transcription of individual genes after blood drawing. Without proper preservation, copy number of individual mRNA transcripts in blood can change more than 1000-fold during storage and transport 20 . Two common methods for stabilizing blood leukocyte RNA are to use PAXgene Blood RNA vacutainer tube and RNAlater. Previous study compared RNA transcript stability in blood leukocytes collected directly into PAXgene tubes or transferred immediately in RNAlater, and showed both methods were clearly appropriate for RNA stabilization in blood based on good quantity, integrity and purity of isolated RNA 21 . PAXgene tube has been successfully used in blood collection of sea otters (Enhydra lutris) to measure differential transcript levels of select immune function genes 20 . PAXgene tubes have the advantage of minimal sample manipulation and immediate exposure of the cells to RNA stabilizing agents, but require collection of 2.5 mL of blood. The present study used RNAlater. Smaller blood volume (0.5 mL) needed for RNAlater would facilitate sample collection and transport. Besides, a small difference between the maximum and minimum Cq values of each HKG indicates good quality of RNA stabilization and the consequent procedures in the current study. Amplification efficiency is an important factor in gene transcript studies using qPCR. When efficiency is not close to 100% (doubling of PCR products per cycle), the calculation the gene quantification requires corrected 22 . Δ Δ Ct and Δ Δ Ct corrected may yield similar results only in the case where high quality data are available and the traditional Δ Δ Ct method would not overestimate the error 23 . The efficiency values of 15 candidate genes in the present study were within the optimal range of 95-105%. Regardless, HKG rankings were susceptible to modest variation if raw Cq values were used for stability analysis rather than corrected Cq values were used (data not shown). This suggests that proper efficiency adjustment can improve qPCR data analysis with greater accuracy.
The HKG stability orders proposed by the four different algorithms used in the current study were not identical, which has been described before 24 . BestKeeper uses raw Cq data as compared to relative transcript levels used in geNorm and NormFinder that may lead to the different outputs 24 . Comparative Δ Ct and geNorm, which use a pairwise comparison approach, are prone to select co-regulated genes and this can also influence the ranking results 25 . While NormFinder uses a model-based approach that considers systematic differences and is less likely to be impacted by co-regulated HKGs, it is sensitive to sampling errors and outliers 26 . Since different algorithms can show various HKG rankings, it has been suggested that more than one type of algorithm should be used for reference gene selection 27 . RefFinder was used in the current study to combine all four algorithms to comprehensively evaluate and rank HKGs. This approach assigns an appropriate score to each individual HKG and then calculates their geometric means to produce a final ranking. The three most stable HKGs (PGK1, RPL4, HPRT1) identified using RefFinder were also in high-ranking orders in NormFinder and comparative Δ Ct. In contrast, the top 5 reference genes identified by geNorm were all coding for ribosomal proteins that are likely to be co-regulated. It has been demonstrated that the sensitivity to co-regulation is a major weakness of the pairwise comparison approach while the co-regulation of candidate HKGs does not significantly affect the model-based approach (NormFinder) 26 . Sole utilization of ribosomal protein genes as reference genes has the potential to decrease the sensitivity of identifying changes in transcript levels of GOI in an experiment 6 . Therefore, utilization of HKGs whose encoded proteins belong to different functional classes would reduce the co-regulation effect 26 . The three most stable HKGs in the present study are responsible for different functions. PGK1, encoding for a key enzyme in glycolysis and gluconeogenesis, has previously been identified as a stable reference gene for use with human whole blood RNA and RNA derived from PBMC 28 . RPL4 encodes a protein that is a component of the 60S ribosome subunit. It has been identified as a suitable reference gene on the PBMCs with unknown pathogenic condition in pigs 29 . RPL4 and PGK1 have previously been recommended as reference gene for exfoliated cervical cells 30 . HPRT1, plays a central role in the generation of purine nucleotides through the purine salvage pathway, belonged to one of the most stable reference genes for qRT-PCR studies in human neutrophils 31 and exercise induced stress in horse PBMCs 32 .
Increasing the number of stably transcribed HKGs included in calculation will increase the efficacy of the normalization factor 3 . Previous studies have suggested there is no single reference gene that can be used for different experiments but rather a group of putative reference genes should be considered for certain specific experimental setups 27 . While inclusion of more HKGs further decreased the V values in the present study, the V2/3 value showed two genes were sufficient for data normalization. Previous study has suggested the transcript levels of a reference gene should not to be very low (Cq > 30) or very high (Cq < 15) 33 . However, appropriate reference genes were suggested to have the same transcript levels as the target gene in an experimental application in order to enhance the uniformity of the analysis 5 . According to mean Cq values, PGK1 and HPRT1 were classified in the low transcript-level group (mean Cq > 25) and RPL4 in the high transcript-level group (mean Cq < 25). Based upon these concepts, the low-level transcripts encoding PGK1 and HPRT1 would be logical reference genes for studying immune-inducible genes with typical low transcript level, and the combination of RPL4 and PGK1 would be more appropriate for higher transcript-level studies. Investigators must recognize that the proposed reference genes in this study would be suitable only when RNA is extracted from RNAlater-preserved whole blood samples of bottlenose dolphins. It has been shown that some HKGs found to be invariant in proliferating PBMC cultures were unsuitable when studied in whole blood 28,34 . For blood samples from other cetacean species, more studies are needed to identify if PGK1, HPRT1 and RPL4 are superior reference genes as well.
Immunologic studies of cetaceans with cytokine gene transcripts have been conducted on blood samples using several different HKGs as reference genes. GAPDH and YWHAZ were used in harbor porpoise studies [10][11][12] , GAPDH in bottlenose dolphins 13 , and RPS9 in bottlenose dolphins, beluga whales, and Pacific white-sided dolphins 8,14 . RPS9 could potentially be a better reference gene than GAPDH and YWHAZ in studies using bottlenose blood samples since it was ranked much higher than the other two genes in the current study.
The reliability of reference gene selection could be affected by sample size. The general recommendation for selecting reference genes using NormFinder is a minimum of 8 samples and 5-10 genes 26 , and GeNorm proposed the use of 8 reference genes and 10 samples 3 . Previous studies directed at reference gene selection in cetaceans have included 30 skin biopsy samples in striped dolphins 5 , and 20 skin biopsy samples from 7 blue whales (Balaenoptera musculus), 7 fin whales (Balaenoptera physalus) and 6 sperm whales (Physeter macrocephalus) 17 . Bovine 35 and sheep 36 studies have employed 22 and 16 neutrophil samples, respectively, for use as reference gene selection. The current study employed 75 blood samples from 7 bottlenose dolphins including clinically healthy controls and individuals with a variety of different body conditions, which has been suggested for facilitating optimal reference gene selection for a wide-range of whole blood transcript studies 37 . In addition, the analyses were conducted using randomly selected subsets of 35 and 55 samples for comparative purposes. Analyses of the 35-and 55-sample subsets using RefFinder also identified HPRT1, PGK1 and RPL4 as being the high-ranking genes, only differing in the ranking order. It indicated that a 35-bottlenose dolphin blood sample set with various body conditions could establish reliable HKGs as reference genes. This is the first comparison of sample size effect on reference gene selection to our knowledge. It should be noted that the reference gene identified here is for use in clinical bottlenose dolphin testing. For non-clinical dolphin research, the potential reference gene should be verified first for each experimental condition. Employing a similar approach in other cetacean species in the future would be both time and cost saving. Table 2). The majority of sequences were obtained from bottlenose dolphin and striped dolphin, while a few were based upon beluga whale, killer whale and fin whale (Balaenoptera physalus). Primers and corresponding UPL probes were designed using Roche UPL design software Scientific RepoRts | 5:15425 | DOi: 10.1038/srep15425 (ProbeFinder, v.2.49) ( Table 2). Primer specificity of the 15 candidate genes was confirmed by PCR using Fast-Run Hotstart PCR kit (Protech) and electrophoresis.
Methods
Quantitative PCR. Quantitative PCR was conducted in 48-well reaction plates using the Eco Real-Time PCR System (Illumina, San Diego, CA, USA). Reactions were prepared in a total volume of 10 μ L containing 3 μ L of 12-fold-diluted cDNA, 0.4 μ L of each 10 μ M primer, 0.2 μ L of UPL probe (Roche, Pleasanton, CA, USA), 5 μ L FastStart Essential DNA Probes Master (Roche) and 1 μ L of RNase/ DNase-free sterile water (Protech). The thermocycle conditions were set as follows: polymerase activation at 95 °C for 10 min, followed by 45 cycles of denaturation at 95 °C for 10 s and combined primer annealing/elongation at 60 °C for 30 s. All reactions including no template controls (NTC) and plate controls were conducted in triplicate. Plate controls contain the same reaction components on every plate. Cq data was analyzed with EcoStudy software (Illumina). A consistent Cq value across plates was obtained allowing the data consolidation from multiple plates into a single study data set. Baseline values were automatically determined for all plates using Eco Software V4.0. Thresholds for each HKG were determined manually ( Table 2). Triplicate Cq values with standard deviation (SD) < 0.5 were averaged as raw Cq values. PCR amplification efficiency (E) and R 2 for each probe and primer pair were calculated from the slope of a standard curve using the following equation: E = (10 (−1/slope) − 1) × 100%. The average of at least three E values for each HKG was used as a gene-specific E for following relative quantity transformation. This study was conducted according to MIQE (Minimum information for publication of quantitative real-time PCR experiments) guidelines 38 .
Data analysis.
Corrected Cq values (Cq corr) were transformed from raw Cq values using Δ Cq formula, Cq corr = Cq min − log 2 E −ΔCq , modified from Fu et al. 39 , where Δ Cq is the Cq value of a certain sample minus the Cq value of the sample with the highest transcript level (lowest Cq, Cq min ) of each HKG. Stability of all HKGs were evaluated and ranked using algorithms geNorm 3 , NormFinder 26 , comparative Δ Ct method 40 and Bestkeeper 41 using the web-based analysis tool RefFinder (http://www. leonxie.com/referencegene.php) 42 . Algorithm geNorm calculates the expression stability value for each gene and them performs a pair-wise comparison of this gene with the others. NormFinder ranks the set of candidate reference genes according to the least of their estimated variations. Comparative Δ Ct method compares relative transcription of pairs of genes and the stability of candidate reference genes is ranked according to repeatability among all samples. BestKeeper determines the standard deviation and the genes are rated based upon variability. RefFinder calculated the geometric mean based upon rankings obtained from each algorithm and provides the final comprehensive ranking. Thirty-five and 55 samples were randomly selected from the original 75 samples, and the HKG ranking results were compared among 35-, 55-and 75-sample groups. | 3,711.4 | 2015-10-21T00:00:00.000 | [
"Biology"
] |
Discussion on the Construction and Application of Navigation Electronic Map Quality Inspection Sample Database
In order to improve the scientificity and efficiency of quality inspection of navigation electronic map, and save the cost of quality inspection, it is necessary to establish the national navigation electronic map quality inspection sample database. In this paper, the construction goal, data acquisition technology process, and database construction method of navigation electronic map quality inspection sample database are described in detail, and the construction content and technical indicators are discussed. The quality test is carried out by combining the in-house verification with the field comparison of the navigation electronic map quality test sample database, and the test results are analyzed and evaluated. The effective application of the sample database in the quality test and evaluation of the internet navigation electronic map in the pilot area is carried out. At the same time, the application of navigation electronic map quality inspection sample database in the research of urban fine management and solid waste recycling economy ecological park planning is prospected.
Introduction
With the development of communication, electronics, network technology, and the geographic information industry, map navigation products have been widely used in people's daily life [1][2]. The mobile terminal navigation system and vehicle navigation have become necessary tools for people to travel. As a form of a public map, Internet navigation electronic map has developed rapidly in recent years. According to incomplete statistics, there are more than 40000 Internet map service websites in China. Due to the differences in service fields, service modes, and methods, there are great differences in map basic data, map display, and service functions among various Internet navigation electronic map service websites. However, when users use electronic map navigation and positioning products of different manufacturers, they find that some products often have different degrees of quality problems. Due to a large amount of data, strong timeliness, and complex data structure of navigation electronic map, in the current navigation electronic map quality detection work, for each test sample area, we need to go to the scene for benchmark data collection and field testing. The establishment of national navigation electronic map quality inspection sample database has become a problem to be solved [3]. Therefore, it is very important to develop the construction and application of a sample database for navigation electronic map quality inspection, which is of great significance to improve the scientific and efficiency of the quality detection of navigation electronic map and promote the development of the geographic information industry.
2 Data characteristics of navigation electronic map quality inspection sample database
Accuracy of point of interest retrieval
As a typical application of navigation system, the accuracy of reaching the specified target can be used as an important parameter to evaluate the navigation system [4]. In common geographic information databases, point of interest (POI) usually represents geographic points and simple related information. But in the construction of navigation electronic map quality detection sample database, users need to retrieve the accurate entrance and exit of the specified target in the process of using the navigation system, so that the system can lay the foundation for users to plan the most accurate route in a short time. Therefore, in the construction of navigation electronic map detection sample database, especially for shopping malls, hospitals and other features with large area and multiple exits, it is necessary to show the routes of entrances and exits in all directions as much as possible.
High data availability
Vehicle navigation and mobile terminal navigation system are the two most widely used directions of navigation system at present. When users use the navigation system, whether they are using cars, sharing bicycles or other modes of transportation, they are most concerned about how to reach the destination with the optimal path in a short time. Navigation electronic map is an important basis of navigation system, and the current situation of data will directly affect the accuracy of navigation. The most frequent changes in the process of car driving are traffic restriction information and dynamic traffic information. The actual traffic guidance information and traffic condition information are the two indication conditions that must be followed in the process of car driving. Whether the information in the navigation system is consistent with the field information can be used to judge whether the driving instructions based on the navigation database are effective, Therefore, the current situation of traffic restriction information and dynamic traffic information can directly determine the efficiency of navigation electronic map detection process.
Reasonable data topological relationship
In the construction of navigation electronic map quality inspection sample database, the sample area data needs to express the geographic location, shape and spatial relationship of the road information and related element data in the target area. Taking road information detection as an example, the connectivity of road network is one of the concerns of navigation electronic map detection personnel, that is, the topological relationship between the arc segment and the node in the road layer, which contains the attributes of traffic capacity. In the process of building the database, when dealing with the topological relationship of Road intersection, especially in the multilevel Road intersection, overpass deck and other places, the topological relationship of the road should be fully reflected, and the combination of the topological relationship and the traffic capacity should be paid attention to at this time. The change of traffic capacity is usually at the node, and the decrease of traffic capacity may affect the traffic degree of topologically connected roads 3 The implementation of sample database for navigation electronic map quality inspection
Technical process of sample data collection
The sample database of navigation electronic map detection has been collected in 93 cities of 31 provinces, cities and autonomous regions nationwide, and 93 sample areas have been selected. The sample areas include municipalities directly under the central government, provincial capital cities, prefecture level cities and county-level cities. The regional distribution takes into account the East, South, West, North and central regions of China, and the degree of development takes into account the urban, urban-rural integration and rural areas. The sample area size is about 3 km × 3 km. According to the standard data collection scheme of navigation electronic map quality inspection sample database, realtime road network and its ancillary information data are collected in the sample area, including road network data, administrative division data, water system data of grade 6 and above, and basic data of place name data. Collect the road, background and notes of motor vehicles in the city; Collect the data of relevant points of interest in the city, and organize and process the data.
POI collection
POI is the point of interest. Whether it is vehicle navigation or mobile terminal navigation, today's navigation systems on the market have their own POI database [5][6]. The number of POI in the navigation map, the accuracy of information and the speed of information update all seriously affect the use of a navigation system. The collection of POI should focus on the important information concerned by users, such as the accurate full name and relevant location information of interest points such as the location of the sample area government, local widely recognized landmark features, hotels, restaurants, shopping malls, transportation hubs, hospitals, gas stations, charging stations, schools, etc. In the process of field collection, it is necessary to collect the name information of POI on the basis of authoritative information, verify the location of POI or collect new POI point information on the spot, take photos on the spot, record the collection time of POI, and record the important attributes of POI, such as scenic spot level and hotel star level. It should be noted that the hotel star rating is subject to the official announcement of the tourism administration, and the Hotels with larger scale equivalent to 4 or 5 stars are classified as the secondary important category. In the process of in-house collation, the POI benchmark data is set up as a separate point layer. Based on the fields including number, name, collection and verification time, photo number and remarks, the POI benchmark data is sorted out, and the fields of classification code, importance and other important attributes are added.
Road information collection
The content of road information collection includes road network information, traffic restriction information, road guidance map information and so on.
The field work of road network information collection is mainly based on the image and the 1:10000 road data in the sample area to carry out on-site verification and mapping, and record the driving track in the whole process to complete the collection of road morphology and structure. In the process of field work, we should focus on collecting the level and code of high-level roads, and refer to the official data for confirmation and on-site verification before the survey. In the process of office work arrangement, it is necessary to establish the line layer of road information separately, specify the direction of road acquisition as the traffic flow direction, and draw all the road elements collected and verified by the field work in the survey area on the image according to the field work track information and 1:10000 road data. In the road information layer, key fields such as reference name, road code, level, one-way restriction, one-way restriction time domain, number of lanes and important one-way line are added.
In navigation electronic map data, structure information, one-way traffic information, and intersection traffic restriction information are combined to express traffic restriction information. It can be divided into important one-way lines and all intersection restriction information, among which important one-way lines, including roundabout, single lane road, often match with traffic restriction information. In the field work, 1:10000 data is used as the base map to collect and identify the single lane, note its time domain, road section range, flow direction and other information, and collect and number the photos related to the single lane information. The basic traffic restriction information includes no left, no right, no U-turn and no straight. In the office work, it is necessary to establish a point layer for traffic restriction information, and add key fields such as road level, restriction information description and vehicle type in the layer.
Background and annotation information collection
The background element information of navigation electronic map data involves administrative division, water system, railway and green space information, and the annotation information involves road name and number, public facilities name and other information. In the construction of navigation database, the background and annotation information need to refer to the basic 1:10000 data acquisition, field verification and photo recording, and the internal industry should build a separate layer and set up the number, name, acquisition / update time, photo number and other fields.
Application test of navigation electronic map quality inspection sample database
Organize the quality inspection practitioners to carry out the quality inspection test by combining the in-house verification and field comparison in the navigation electronic map quality inspection sample database as a group, and analyze and evaluate the test results. The evaluation methods and experimental results are as follows:
Evaluation method
The score of test results is calculated according to the proportion of errors and omissions of different levels, and the score is shown in the formula (1).
S 2 =100-[a 1 *(12/t)+a 2 *(4/t)+a 3 *(1/t)]
(1) In formula (1), S 2 is the score of mass element; a 1 is the number of serious errors; a 2 is the number of large errors; a 3 is the number of general errors; t is the adjustment factor of deduction.
The comprehensive score of elements is calculated by weighted average according to the detection index, and the calculation method is shown in the formula (2).
In formula (2), S 1 is the score of the corresponding mass element; S 2i is the score of the corresponding mass sub elements; P i is the weight of corresponding quality sub elements, which can be adjusted according to the emphasis of inspection; n is the number of quality sub elements contained in the quality element. For a sample area, the formula for calculating the weighted score of all unit results is: In formula (3), S 1 is the data quality score of a sample area; S 1i is the score of each mass element; P i is the weight of each quality element can be adjusted according to the emphasis of inspection; n is the number of quality elements contained in the unit achievement.
Analysis of experimental results
Based on the evaluation method of this paper, six influential Internet navigation electronic map service websites are selected to carry out the experiment. The sample area of the experiment is mainly in Prefecture and county-level cities. Six cities are randomly selected from the sample database of navigation electronic map quality detection. In each sample area, according to the complexity of road and poi, the area of not less than 4 square kilometers is cut as the sample area of the actual test.The data in the navigation electronic map quality inspection sample database obtained by field measurement is taken as the reference data of the sample area. Tile map sample data is obtained online and realtime by ordinary users through the official websites of various map service providers. In the experiment, the query function provided by the website is used to query the POI data one by one, and compare with the benchmark reference data to determine the integrity and consistency of the data. The integrity and correctness of the road data are verified by using the line planning function. The test results are shown in Figure 1. The above test results show that the quality evaluation method based on the navigation electronic map quality inspection sample database can not only evaluate the quality of Internet navigation electronic map service well, but also reflect the fine differences in data and services of various Internet map service providers.
Application of sample database data in urban fine management
Urban management is the coordinated control behavior of all the activities of the operation and development of the city. Fine management is a management concept and technology that originated from Japanese enterprises in the 1950s, which has been applied to all kinds of social organizations [7]. Urban fine management is to introduce the concept of fine management into urban management. In order to implement fine management in a city, it is necessary to refine the management of underground pipe networks, roads, bridges, buildings and other objects of underground, ground, and above ground space. With the passage of time, the city is constantly changing. The navigation electronic map quality inspection sample database data can more clearly and objectively display and mine the information of urban geospatial-related elements. The timely updated geographic information data can realize the regular observation of large urban areas, and help to grasp the panorama and historical changes of the city. It will greatly promote the application of geographic information data in all aspects of urban fine management. Using high timeliness geospatial information to carry urban management business information, truly restore urban road construction and other information, spatially and sequentially process urban management related business data, and carry it into the urban space-time environment based on geographic information data, so as to provide data support for urban meticulous management.
Application of sample database data in the planning of solid waste recycling economy ecological park
Industrial Park is an important entry point for the development of circular economy and sustainable development. [8][9]. By using the limited available site space and concentrating all kinds of municipal solid waste treatment facilities, the construction of a circular economy eco-industrial park for municipal solid waste treatment can not only reduce the resistance caused by scattered-site selection, but also improve the joint treatment and disposal level of various types of municipal solid waste, at the same time, it is also conducive to the construction of material, energy and water resources recycling cascade utilization system, which is an effective mode to solve the problem of "garbage siege" in large and medium-sized cities with the land shortage. Using the navigation electronic map quality inspection sample database to obtain the surrounding features information and spatial distribution of the park, to provide basic data support for the planning of the park land layout structure. Combined with the surrounding road planning, congestion information, the process characteristics of each project, and the material supply and demand relationship between projects, the optimal layout of all kinds of land and projects in the park is realized, it provides a scientific and effective plan for the planning and construction of the solid waste park.
Summary
As an important foundation of the navigation system, the quality of the navigation electronic map will directly affect the user's evaluation of the navigation system. It is the key to guaranteeing the quality of all kinds of electronic navigation system products to strictly control the quality of navigation electronic maps by adopting the industry technical standards and Technical Specifications issued by state organs. The quality inspection of navigation electronic map in some pilot areas has been confirmed. Through scientific and feasible methods, we can establish a multi-level navigation electronic map quality inspection sample database covering the whole country, and carry out the application of navigation electronic map quality inspection sample database, which can save the inspection cost on the basis of ensuring the authenticity and reliability of navigation electronic map data inspection results Improve inspection efficiency, and continuously improve the quality of navigation electronic map, Internet map service products, and navigation terminal products. At the same time, the establishment of a year-by-year updated navigation electronic map quality testing sample database can not only serve the quality control of Internet map quality testing. It can also be applied to the research of urban fine management, carbon emission monitoring and management, solid waste recycling economy ecological park planning, and so on. It provides a new idea for the above research. | 4,187.4 | 2021-01-01T00:00:00.000 | [
"Computer Science"
] |
$AdS_2 \times S^6$ versus $AdS_6 \times S^2$ in Type IIB supergravity
We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form $AdS_{2}\times S^{6}$ warped over a Riemann surface $\Sigma$ in terms of two locally holmorphic functions on $\Sigma$. We construct the general Ansatz for the bosonic supergravity fields and supersymmetry generators compatible with the $SO(2,1)\oplus SO(7)$ isometry algebra of space-time, which extends to the corresponding real form of the exceptional Lie superalgebra $F(4)$. We reduce the BPS equations to this Ansatz, obtain their general local solutions, and show that these local solutions solve the full Type IIB supergravity field equations and Bianchi identities. We contrast the $AdS_{2}\times S^{6}$ solution with the closely related $AdS_6\times S^2$ case and present our results for both in parallel. Finally, we present a preliminary analysis of positivity and regularity conditions for $AdS_{2}\times S^{6}$, but postpone the construction of globally regular solutions to a subsequent paper.
Introduction
Half-BPS solutions to Type IIB supergravity were obtained recently for a space-time of the form AdS 6 × S 2 warped over a Riemann surface [1][2][3][4]. The motivation for that work was the construction of holographic duals to five-dimensional superconformal field theories (SCFTs). The SO(2, 5) ⊕ SO(3) isometry algebra of the space-time manifold extends to invariance under the corresponding real form of the exceptional Lie superalgebra F (4), which is the unique superconformal algebra in 5 space-time dimensions.
A closely related problem is to construct solutions to Type IIB supergravity whose spacetime is of the form AdS 2 × S 6 warped over a Riemann surface Σ. The isometry algebra SO(2, 1) ⊕ SO(7) now extends to a different real form of the exceptional Lie superalgebra F (4), which is one of the superconformal algebras in 2 dimensions with 16 supercharges [5,6]. The relation between these two problems is similar to the one encountered between gravity duals to Wilson loops [7] and interface solutions [8]. Experience with such relations through "double analytic continuation" between supergravity on spaces with AdS p ×S q and AdS q ×S p factors reveals that their solutions are closely related mathematically, yet their physical space-time structure is quite different. The existence of half-BPS warped AdS 6 ×S 2 solutions to Type IIB supergravity therefore motivates the search for warped AdS 2 × S 6 solutions.
The study of AdS 2 holography provides further motivation for the search for AdS 2 × S 6 supergravity solutions. Holography on two-dimensional Anti-de Sitter space-time is arguably less well understood than its higher-dimensional counterparts due in part to certain exotic features of AdS 2 . They include the presence of multiple disconnected time-like boundary components, the suppression of finite-energy excitations due to strong gravitational backreaction [9,10], and the ambiguity in identifying the natural CFT dual either as conformal quantum mechanics or as two-dimensional boundary conformal field theory. Much recent focus has been on analyzing the gravitational backreaction on AdS 2 , and on possible relations with dilaton gravity and the Sachdev-Ye-Kitaev model (see [11] and references therein).
In this paper, we construct the local form of half-BPS solutions to Type IIB supergravity for warped AdS 2 × S 6 following the strategy used for AdS 6 × S 2 . We derive the reduced BPS equations for the general Ansatz dictated by SO(2, 1)⊕SO (7) isometry for the fields of Type IIB supergravity. These equations are very closely related to the reduced BPS equations for the AdS 6 ×S 2 case, but differ by subtle and crucially important signs and factors of i = √ −1. We provide a detailed comparison between the mathematical equations for both cases.
Using methods which are analogous to the ones developed to solve the reduced BPS equations for the AdS 6 × S 2 case, we construct the general local solutions for the AdS 2 × S 6 case in terms of two locally holomorphic functions A ± on the Riemann surface Σ. The differences between the AdS 2 × S 6 and AdS 6 × S 2 solutions are again subtle, but crucial, and to facilitate direct comparisons we discuss both cases in parallel. To solve the reduced BPS equations, we make use of the solution to the axion-dilaton Bianchi identities, but derive the Bianchi identity for the 3-form field strength from the BPS equations. To complete the discussion, we verify that the full set of Type IIB field equations are satisfied when the bosonic supergravity fields are given by the solutions to the BPS equations and axion-dilaton Bianchi identities. We show this for the AdS 2 × S 6 and AdS 6 × S 2 cases in parallel, and thus provide this check also for the solutions constructed in [1].
The solutions obtained for the supergravity fields satisfy the BPS and field equations, but they become physically viable only after certain reality, positivity and regularity conditions are enforced. We obtain the constraints on the functions A ± required by physical positivity and regularity conditions on the supergravity fields, and exhibit crucial differences between the AdS 2 × S 6 and AdS 6 × S 2 cases. We discuss the possibility of performing a "double analytic continuation" of the global AdS 6 × S 2 solutions constructed in [2,3] to the present case of AdS 2 × S 6 . Although such continuations are found to satisfy the field equations, they appear to be neither supersymmetric nor physically regular. Therefore, the construction of global AdS 2 ×S 6 solutions must be conducted independently of the AdS 6 ×S 2 case. With that objective in mind, we derive the explicit forms of the two-form and six-form potentials for the AdS 2 × S 6 and the AdS 6 × S 2 solutions. For the AdS 6 × S 2 case the two-form potential was a valuable indicator for brane sources in the physically regular solutions constructed in [2,3], and we expect the six-form potential to play a similar role for AdS 2 × S 6 .
Solving the physical positivity and regularity conditions, constructing global solutions, obtaining their holographic CFT dual, developing a brane interpretation, and exploring potential relations with (p, q) string webs in analogy to the (p, q) five-brane webs for AdS 6 ×S 2 solutions, are important topics left to subsequent work.
The remainder of this paper is organized as follows. In section 2 we review Type IIB supergravity and introduce the general SO(2, 1) ⊕ SO(7)-invariant Ansatz. In section 3 we reduce the BPS equations to this Ansatz. In section 4, we solve the reduced BPS equations in terms of two locally holomorphic functions on Σ. In section 5 we obtain the expressions for the supergravity fields of the solutions in terms of the holomorphic data, compare with the AdS 6 × S 2 solutions, and analyze their behavior under SU (1, 1) symmetry. In section 6 we verify that the solutions to the BPS equations obey the field equations for both AdS 2 ×S 6 and AdS 6 × S 2 cases. In section 7 we derive the physical positivity and regularity conditions, as well as discuss their implications for global solutions. In section 8, we discuss the relation between AdS 6 × S 2 and AdS 2 × S 6 provided by double analytic continuation. We conclude in section 9. In appendix A, a basis for the Clifford algebra adapted to our Ansatz is presented. Details of the derivation of the BPS equations are given in appendix B, of the two-and six-form potentials in appendix C, and of the Ricci tensor components in appendix D.
2 AdS 2 × S 6 × Σ Ansatz in Type IIB supergravity In this section we begin by reviewing the salient features of Type IIB supergravity needed in this paper, and then obtain the SO(2, 1) ⊕ SO(7)-invariant Ansatz for the bosonic supergravity fields and the generator of supersymmetry transformations.
Type IIB supergravity review
The bosonic fields of Type IIB supergravity consist of the metric g M N , the complex-valued axion-dilaton field B, a complex-valued two-form potential C (2) and a real-valued four-form field C (4) . The field strengths of the potentials C (2) and C (4) are given as follows, The field strength F (5) satisfies the well-known self-duality condition F (5) = * F (5) . Instead of the scalar field B and the 3-form F (3) , the fields that actually enter the BPS equations are composite fields, namely the one-forms P, Q representing B, and the complex 3-form G representing F (3) , given in terms of the fields defined above by the following relations, Under the SU (1, 1) ∼ SL(2, R) global symmetry of Type IIB supergravity, the Einsteinframe metric g M N and the four-form C (4) are invariant, while B and C (2) transform as, where SU (1, 1) is parametrized by u, v ∈ C with |u| 2 − |v| 2 = 1. The field B takes values in the coset SU (1, 1)/U (1) q and Q plays the role of a composite U (1) q gauge field. The transformation laws for the composite fields are as follows [12], Equivalently, one may formulate Type IIB supergravity directly in terms of g M N , F (5) , P, Q and G provided these fields are subject to the Bianchi identities [12,13].
The fermionic fields are Weyl fermions with opposite 10-dimensional chirality, namely the dilatino λ satisfying Γ 11 λ = λ and the gravitino ψ M satisfying Γ 11 ψ M = −ψ M . The crucial information for the construction of supersymmetric solutions to Type IIB supergravity are the supersymmetry variations of the fermions, respectively δλ and δψ M . The BPS equations are the conditions that the fermion fields and their variations vanish, and are given by, 1 Here, ε is the generator of infinitesimal supersymmetry transformations. It transforms under the minus chirality Weyl spinor representation of SO (1,9) and ∇ M is the covariant derivative acting on this representation. In sec. 6 we will show that the solutions with 16 supersymmetries to these BPS equations satisfy the field equations, and when formulated in terms of P, Q, G, F (5) also satisfy their Bianchi identities.
SO(2, 1) ⊕ SO(7) invariant Ansatz for supergravity fields
We construct a general Ansatz for the bosonic fields of Type IIB supergravity invariant or covariant under the SO(2, 1) ⊕ SO(7) symmetry algebra. The SO(2, 1) and SO (7) parts are realized by a geometry which contains a factor AdS 2 as well as a factor S 6 , so that the space-time is given by, warped over a two-dimensional space Σ. To produce a geometry of Type IIB supergravity, Σ has to be orientable and carry a Riemannian metric, and is therefore a Riemann surface. The resulting SO(2, 1) ⊕ SO(7)-invariant Ansatz for the metric can be written as, where f 2 , f 6 , and ds 2 Σ are functions of Σ. We introduce an orthonormal frame, The signature convention for the metric is (− + · · · +), the Dirac-Clifford algebra is defined by the relation {Γ M , Γ N } = 2η M N I 32 and the charge conjugation matrix B is defined by the relations B * B = I and BΓ M B −1 = (Γ M ) * . Repeated indices are summed over, as usual, and complex conjugation is denoted by a bar for functions and by a star for spinors. We will also use the notation Γ · T ≡ Γ M1···Mp T M1···Mp for the contraction of an antisymmetric tensor field T of rank p with a Γ-matrix of the same rank.
whereê m andê i respectively refer to orthonormal frames for the spaces AdS 2 and S 6 with unit radius and e a is an orthonormal frame on Σ only. In particular, we have, The requirement for SO(2, 1) ⊕ SO(7)-invariance restricts F (5) = 0 as well as, where the components p a , q a , and g a are complex and depend on Σ only. We have thus parametrized the entire configuration in terms of functions that have non-trivial dependence only on Σ, and it will be convenient to set up the frame and coordinates on Σ more explicitly.
We will use complex frame indices z,z with the following conventions, We introduce local complex coordinates w,w such that the metric on Σ reads, and we have, This completes the Ansatz for the bosonic fields.
SO(2, 1) ⊕ SO(7) invariant Ansatz for susy generators
Next, we decompose the supersymmetry generator spinor ε in an SO(2, 1) ⊕ SO(7)-invariant basis of Killing spinors. The Killing spinor equations on AdS 2 and on S 6 were derived in Appendix B of [7] and are respectively given by, where m and i are all frame indices. Note that∇ m and∇ i stand for the covariant spinor derivatives respectively on the spaces AdS 2 and S 6 with unit radius. The spinors χ η 1 ,η 2 α are 16-dimensional, and the parameters η 1 and η 2 can take the values ±. For each value of (η 1 , η 2 ), these equations admit solutions with a four-fold degeneracy, which is labelled by the index α = 1, 2, 3, 4. The action of the chirality matrices is given by, These equations can be understood as follows. Beginning with η 1 = η 2 = +, we pick a basis χ +,+ α for the four-dimensional vector space of spinors for fixed η 1 , η 2 such that the action of γ (1) and γ (2) are diagonal. The basis for χ η 1 ,η 2 α can then simply be defined for the remaining three values of η 1 , η 2 by the action of the chirality matrices above.
Using arguments similar to the ones used for the AdS 6 × S 2 case, we relate the complex conjugate basis spinors to the original basis by, for all values of η 1 , η 2 , and α. Since this decomposition is now canonical in terms of the degeneracy index α, we will no longer indicate it explicitly. An arbitrary 32-component complex spinor ε may be decomposed onto the above Killing spinors as follows, where ζ η 1 ,η 2 is a complex 2-component spinor for each η 1 , η 2 , and the four-fold degeneracy index is suppressed. As a supersymmetry generator in Type IIB, the spinor ε must be of definite chirality Γ 11 ε = −ε, which imposes the following chirality requirements on ζ, Finally, the charge conjugate spinor is given by, This completes the construction of the SO(2, 1) ⊕ SO(7)-invariant Ansatz.
Reducing the BPS equations
The residual supersymmetries, if any, of a configuration of purely bosonic Type IIB supergravity fields are governed by the BPS equations of (2.5). As we will discuss in more detail in sec. 6, any SO(2, 1) ⊕ SO (7) invariant Ansatz for the supergravity fields and for the 16component supersymmetry spinor as discussed in sec. 2.2 which satisfies the BPS equations will automatically solve the Bianchi and field equations, and thus automatically provides a half-BPS solution to Type IIB supergravity.
In this section, we reduce the BPS equations to the AdS 2 × S 6 × Σ Ansatz, expose its residual symmetries, and solve those reduced equations which are purely algebraic in the supersymmetry spinor components. This will produce simple algebraic expressions for the metric factors f 2 , f 6 in terms of the spinors. The remaining reduced BPS equations will be solved for the remaining bosonic fields in subsequent sections. The strategy employed here is the same as the one used in [1].
The reduced BPS equations
We use the τ matrix notation introduced originally in [14] in order to compactly express the action of the various γ matrices on the reduced supersymmetry generator ζ introduced in (2.17). Defining τ (ij) = τ i ⊗ τ j with i, j = 0, 1, 2, 3, we identify τ 0 with the identity matrix and τ i for i = 1, 2, 3 with the standard Pauli matrices. The action of these matrices on ζ may be written in components as follows, The reduced BPS equations may then be calculated using the decomposition of ε onto Killing spinors given in (2.17). The reduced dilatino equation is given by, while the reduced gravitino equations take the following form, The derivative D a acts on functions of Σ only, and is defined with respect to the frame e a of Σ, so that the total differential d Σ on Σ takes the form d Σ = e a D a , while the U (1)-connection with respect to frame indices isω a . The reduction is carried out in Appendix B.
Symmetries of the reduced BPS equations
The global SU (1, 1) symmetry of Type IIB supergravity, whose action on the bosonic fields was given in (2.3) and (2.4), survives the reduction to the SO(2, 1)⊕SO(7) invariant Ansatz. It leaves the metric functions f 2 , f 6 , ρ invariant, transforms the axion-dilaton field B and the two-form C (2) as in (2.3), transforms the reduced supersymmetry spinor ζ by ζ → e iθ/2 ζ, and transforms the composite fields of (2.4) as follows, The reduced BPS equations are also invariant under the following discrete symmetries which act only on the reduced supersymmetry generator but not on the reduced supergravity fields, Finally, charge conjugation K acts by, The chirality requirement of Type IIB restricts the spinor ζ to the subspace, The symmetries I, J , K commute with one another and may be diagonalized simultaneously. Both I and J commute with U (1) q , but K does not commute with U (1) q .
Restricting to a single subspace of J
The eigenspace of I being already restricted by the chirality condition of (3.7), we now derive the restrictions to the eigenspaces of J and K which are implied by the reduced BPS equations, following the same procedure that was used for AdS 6 × S 2 in [1]. For any value of g a , we have the following quadratic relations in ζ, provided the matrix T belongs to the following set of τ (ij) -matrices, T ∈ T = τ (00) , τ (10) , τ (20) , τ (31) , τ (32) , τ (33) (3.9) For these values of T , the combination T τ (12) σ 2 γ a is anti-symmetric for a = 1, 2 and the relation (3.8) indeed holds automatically. The reduced dilatino equation implies, p a ζ † T γ a ζ = 0 (3.10) Making use also of the chirality condition (3.7), we obtain the further equation, p a ζ † T τ (11) γ a σ 3 ζ = 0 (3.11) When both T and T τ (11) belong to T , which is the case for only a single pair of matrices, namely T = τ (20) or T = τ (31) , and assuming that p a does not vanish identically, we may combine (3.10) and (3.11) to obtain the following relations, which hold for a = 1, 2 and are equivalent to one another upon using the chirality condition.
Next, we analyze the gravitino equations. Multiplying equations (m) and (i) of (3.3) on the left by ζ † T σ p for p = 0, 3, we obtain a cancellation of the last term when T τ (12) is anti-symmetric (which is the same condition we had for the dilatino equation), In view of (3.12), the second term will cancel when T = τ (20) and T = τ (31) . so that we obtain the following relations from the remaining cancellation of the first term, and their chiral conjugates, which may be obtained by using the chirality condition.
Next, we use the general result of [8] that the bilinear equation ζ † M ζ = 0 is solved by projecting ζ onto a subspace via a projection matrix Π that anti-commutes with M . Thus, we must find a projector Π with the following properties, The solutions to these equations are τ (32) , τ (23) , τ (32) σ 3 , and τ (23) σ 3 . These four possibilities are pairwise equivalent under the chirality relation. The projector Π = τ (32) precisely corresponds to the symmetry J , so imposing a restriction on the spinor space by this operator is the only consistent restriction. Therefore, we will impose the restriction, which solves all the above bilinear relations for either choice of ν, but not both.
We may solve the projection relations given in (3.7) and (3.16) in terms of two independent complex-valued one-component spinors α and β. Denoting the components of ζ by ζ abc , where a, b label the τ -matrix basis, while c labels the chirality basis in which σ 3 is diagonal, and a, b, c take values ±, we have,
The reduced BPS equations in component form
To decompose the reduced BPS equations in a basis of complex frame indices z,z, we use (2.11) along with the following basis of γ-matrices compatible with a diagonal σ 3 , Using (3.17) the reduced dilatino equations become, The gravitino equations which are purely algebraic in α, β,ᾱ,β are given by, while the gravitino equations which are differential in α, β,ᾱ,β are given by, In addition, we have the complex conjugate equations to all of the equations above. Note that since G and P are complex-valued, we have in general (g z ) * = gz and (p z ) * = pz.
These combinations suggest that we should evaluate the covariant derivatives D z (αᾱ ± ββ) out of the differential equations (3.21) for α, β,ᾱ,β, and we find, Eliminating all flux dependences between (3.22) and (3.23), we may integrate the resulting relations, to obtain the following expressions for the radii, where c 2 and c 6 are integration constants.
Solving the remaining algebraic gravitino equations
To obtain the results of the previous subsection, we have taken only pairwise linear combinations of the algebraic gravitino equations. Here, we take the orthogonally conjugate pairwise linear combinations. To guarantee that the four resulting bilinear equations are equivalent to the original four algebraic gravitino equations, we must have that the determinant of the two linear combinations is αᾱ + ββ = 0. Therefore, we multiply the first equation by α and the second by −β, so that the terms in D z f 2 and D z f 6 cancel out, and we are left with, 1 2c 2 The last equation may be simplified with the help of the first and yields, Recall that ν is allowed to take either value ν = ±1, but not both.
Summary and comparison to AdS 6 × S 2
In this subsection, we summarize the remaining reduced BPS equations for the AdS 2 ×S 6 case and present the result in parallel with the corresponding results for the remaining reduced BPS equations obtained for the case AdS 6 ×S 2 in [1]. To this end we introduce the quantities K and c to distinguish between the two cases as follows, With the help of these quantities the remaining reduced BPS equations take on a remarkably unified form. The remaining reduced dilatino equations are, along with their complex conjugates. The radii in terms of the spinors α, β are given by, The remaining algebraic relation between the spinors and the fluxes is given by, along with its complex conjugate. The remaining differential equations on the spinors are, along with their complex conjugates.
Local solutions to the BPS equations
The BPS equations have been reduced to the AdS 2 × S 6 × Σ Ansatz and solved for the radii f 2 and f 6 in the previous section. In this section, the remaining equations, namely the dilatino BPS equations of (3.28), the remaining algebraic gravitino equation of (3.30) and the four differential equations (3.31), will be completely solved locally on Σ in terms of two locally holomorphic functions A ± on Σ. Thus we will obtain expressions for all bosonic supergravity fields that satisfy the BPS equations in terms of A ± .
Eliminating the reduced flux fields
We start from the equations summarized in sec. 3.7 and keep K and c as defined in (3.27) for easier comparison with the AdS 6 × S 2 case. We begin by eliminating the reduced flux fields g z , gz and their complex conjugates in favor of p z , pz and their complex conjugates using the dilatino BPS equations of (3.28). The algebraic relation (3.30) becomes, The differential equations (3.31) take the following form, Equations (4.1) and (4.2) are the remaining relations to be solved. Their solution will give α, β, f 2 , f 6 , ρ, p z and therefore B as well as the flux field g z , gz and their complex conjugates via the reduced dilatino equations.
Integrating the first pair of differential equations
Next, we use the expressions for p z , pz, q z and their complex conjugates in terms of the axiondilation field B via the relations (2.2) and (2.10) to solve the first two equations of (4.2) in terms of holomorphic functions. To do so, we multiply the first equation of (4.2) by α and the second equation of (4.2) by β, switch to conformally flat complex coordinates (w,w) on Σ as introduced in (2.13), and use (2.2) and (2.10) to express p z and q z in terms of B, By taking suitable linear combinations we obtain the following equivalent equations, These equations are solved in terms of two independent holomorphic 1-forms κ ± , as follows, Inverting (4.5), we obtain the spinor components α, β, and their complex conjugatesᾱ,β, The right side of all four equations involves only the holomorphic data κ ± and the B-field and their complex conjugates. It remains to solve for the fields ρ and B.
Preparing the second pair of differential equations
Next, we express the third and fourth equation of (4.2) in terms of B, ρ and the local complex coordinates (w,w), and obtain the following set of equations, The spinors α, β and their complex conjugates, as well as the derivatives of f ρᾱ 2 and f ρβ 2 may be evaluated in terms of B, ρ, and κ ± and their first derivatives using (4.2). After some simplifications, we obtain the following equivalent system of equations, where we have used the following abbreviation for the phase angle ϑ, The dependence of the algebraic relation (4.1) on α and β may also be eliminated using (4.6), while p z , pz may be expressed in terms of B, and we find the equivalent relation, Equations (4.8) and (4.10) are supplemented by their complex conjugates.
Although on the face of it the remaining equations (4.8) and (4.10) depend on both κ ± and their complex conjugates, the conformal invariance of these equations tells us that the dependence is actually only through the combination ρ 2 /κ − and the ratio, In terms of these variables, the equations take the following form, where we now have, as well as the equation resulting from (4.10), In summary, we have prepared the remaining reduced BPS equations in the form of complex differential equations (4.12) and (4.14) along with their complex conjugate equations.
Decoupling by changing variables
In this subsection, we will perform two consecutive changes of variables to decouple the remaining equations.
First change of variables, from B to Z
A first change of variables replaces B by a complex field Z and is designed to parametrize the phase e iϑ in (4.13) without the square root required from its definition. We make the following rational change of variables to eliminate B in terms of a complex function Z, which will allow us to express e iϑ and f 2 as rational functions of Z and its complex conjugate, The equations (4.12) now take the form, Taking the difference of these two equations eliminates the dependence on ρ 2 /κ − , while taking their sum gives, where we have changed variables from ρ toρ in the following way, Finally, eliminating B in favor of Z in the algebraic flux equation (4.14) as well, we obtain, It remains to solve the system of equations (4.18), (4.19), and (4.21).
Second change of variables, from Z to R, ψ
A second change of variables is inspired by the form of equation (4.19), in which the norm of Z and its phase enter in distinct parts of the equation. We express the complex field Z in terms of two real variables, its absolute value R and phase ψ, as follows, In terms of these variables (4.19) takes the form, while (4.18) becomes, (4.24) and (4.21) becomes, The three equations (4.23), (4.24), and (4.25) are the basic starting point for the complete solution of the full system of reduced BPS equations.
Decoupling the equations for ψ andρ 2
Adding equations (4.24) and (4.25) cancels the terms proportional to ∂ w R, and concentrates the entire R-dependence of this sum in an overall multiplicative factor of (1 + K 2 R) 2 . Omitting this factor, the sum becomes, Equations (4.23) and (4.26) involve only ψ andρ 2 but not R. Up to factors of K 2 , this system is the same as the system in [1], and we will solve it with the same methods. Adding twice (4.23) to (4.26) eliminates the term proportional to e −iψ , and we obtain, Clearly, this equation involves only the following specific complex combination ofρ 2 and ψ, where we have included a factor of K in the definition of ξ for later convenience. In terms of ξ we may express (4.27) as follows, where we have used the relation κ + = λκ − . The integrable structure of the system of equations (4.18), (4.19), and (4.21) has therefore been exposed clearly with the help of this sequence of changes of variables. Indeed, equation (4.29) involves only the field ξ, which is the combination ofρ and ψ entering (4.28). Having obtained ξ, equation (4.27) may be solved forρ and ψ. Finally, havingρ and ψ, equation (4.24) becomes an equation for R only, and we will see below that it can be solved as well.
Solving for ψ,ρ 2 , and R in terms of A ±
Having decoupled the reduced BPS equations in the preceding subsection, we will solve the decoupled equations in the present section. We begin by solving (4.29) for ξ, then obtain ψ, ρ 2 , and R as described above. We introduce locally holomorphic functions A ± such that, Given the one-forms κ ± , the functions A ± are unique up to an additive constant for each function.
With the conventions used to define ξ and A ± , the equations governing ξ in terms of A ± are identical to those of the AdS 6 × S 2 case, and we import their solution from [1], Note thatρ and ψ are directly determined by ξ using equation (4.28).
To solve for R, we begin with equation (4.24) before using (4.23) to eliminate the term proportional to e −iψ . We then divide the resulting equation by R, and find, Changing variable from R to a new variable W , which we conveniently define by, renders equation (4.32) linear in W with an inhomogeneous part, We note that this equation is now independent of K 2 and therefore coincides with the corresponding equation for the AdS 6 × S 2 case, whose solution we import from [1], where we have defined κ 2 and G through, Since ∂ w B is a holomorphic 1-form, there exists a locally holomorphic function B, defined up to the addition of an arbitrary complex constant. This completes the solution of the decoupled reduced BPS equations for the fields ψ,ρ, and R.
Supergravity fields of the local solutions
The general local half-BPS solution to Type IIB supergravity with SO(2, 1) ⊕ SO (7) symmetry can now be expressed in terms of the locally holomorphic functions A ± introduced above. Here we will translate from the local solution of the reduced BPS equations to the supergravity fields and discuss some of the immediate properties of the solutions.
For comparison we present the AdS 6 × S 2 and AdS 2 × S 6 cases in parallel. The five-form field strength and all fermion fields vanish. The remaining bosonic fields in both cases are distinguished merely by the parameter Λ = K 2 . The metric Ansatz and Λ are given by, The remaining fields in both cases are given by, where vol 2 is the volume form on AdS 2 of unit radius for Λ = −1 and the volume form of S 2 with unit radius for the case Λ = 1. The metric functions f 2 , f 6 , ρ, and C and the dilaton-axion field B are all functions on Σ.
The metric functions
The metric functions f 2 , f 6 , and ρ are naturally expressed in terms of composite quantities κ 2 and G defined in (4.36), and the function R obtained by eliminating W between equations (4.33) and (4.35). The latter is given in terms of κ 2 and G by, To obtain the explicit expressions for the metric functions, we begin by eliminating α and β from the combinations (f 6 ± 3 ν f 2 ) 2 in favor of κ ± and f using (3.29) and (4.6), and we find, Changing variables from B to Z using (4.15) and (4.16), solving for f 2 and f 6 , and expressing the result in terms of |Z| 2 = R, we obtain, To calculate ρ 2 we express the result of (4.20) for ρ 2 in terms ofρ 2 , use (4.28) to obtainρ 2 in terms of ξ, and (4.31) to express ξ in terms of L, which in turn is given by, Expressing the result in terms of R, G and κ 2 , we find, Alternatively, after making use of (5.2), and eliminating ρ 2 from f 2 2 and f 2 6 , we have, Some care will be needed with the choice of the branch of the square root, which will be discussed in detail in section 7.
The axion-dilaton
The axion-dilaton field B is obtained using its expression of (4.15) in terms of Z, eliminating Z in favor of R and ψ using (4.22), and eliminating ψ in favor of ξ and L using (4.31), Multiplying numerator and denominator by |κ − | 2 and using (5.5) to eliminate L yields, One verifies that this field automatically satisfies |B| < 1 provided κ 2 (1 − R 2 ) > 0.
Two-form and six-form flux potentials
The evaluation of the two-form flux potential C (2) and of its magnetic dual six-form flux potential C (6) on the solutions to the BPS equations is considerably more involved than for the other supergravity fields. Here we shall summarize the result, and relay an account of the detailed calculations to appendix C. As a byproduct, the calculations of the flux potentials will prove that the solutions to the BPS equations for 16 supersymmetries together with the Bianchi identities for the P, Q one-forms, imply the Bianchi identity and field equation for the three-form field G.
Consider the three-form F (3) and dual seven-form F (7) field strengths defined by, where denotes the Poincaré dual. It is a standard result that the Bianchi identity for the field F (3) is given by dF (3) = 0. By inverting the relation between F (3) and G one deduces the well-known Bianchi identity for G, which takes the form, where P and Q are given in terms of B by (2.2). The field equation for G is equivalent to the condition dF (7) = 0. Here we shall be interested only in solutions to the field equations for which F (5) = C (2) ∧F (3) = 0, so that the field equation for G reduces to, The closure conditions on the three-form F (3) and on the seven-form F (7) may be solved locally in terms of flux potentials C (2) and C (6) by, In view of the SO(2, 1) ⊕ SO(7) isometry algebra of AdS 2 × S 6 and the SO(5, 2) ⊕ SO(3) isometry algebra of AdS 6 × S 2 , we have the following Ansatz for C (2) , C (6) and G, where vol 2 and vol 6 denote the volume forms of the maximally symmetric spaces of unit radius respectively of the two-dimensional and six-dimensional factors of the space-time.
Integrating these equations for our solutions results in the following flux potentials, where W ± are locally holomorphic functions defined up to a constant by A ± ∂ w B = ∂ w W ± .
SU (1, 1) transformations induced on the supergravity fields
The action of the global SU (1, 1) symmetry of Type IIB supergravity on the supergravity fields, as given in (2.3), is induced by an action of SU (1, 1) ⊗ C on A ± , in parallel with the AdS 6 × S 2 case of [1], where we have parametrized SU (1, 1) by u, v ∈ C with |u| 2 − |v| 2 = 1 and a is a complex constant. The transformation of B is given by, These transformations leave κ 2 and G and consequently also the metric functions invariant. The condition F (5) = 0 is also left invariant. They transform B as given in (2.3), while C and M transform as follows, Consistently with the SU (1, 1) action of (2.3) and (2.4), F (3) and F (7) transform as follows, where the first transformation law follows from the second equation in (2.3) and F (3) = dC (2) .
Verifying the field equations
Whether the BPS equations for 16 residual supersymmetries imply the full set of Bianchi identities and field equations for the form fields P, Q, G, F (5) , the space-time metric, and the spin connection is, in general, an open problem. In our solution of the BPS equations, we have assumed the expression for the spin connection in terms of the metric, and we have assumed that the Bianchi identities for P, Q, given by, have been solved in terms of the axion-dilaton field B by the first two equations in (2.2). The Bianchi identity for the F (5) field is trivially satisfied since in our solutions we have F (5) = 0 as well as G ∧Ḡ = 0. But the Bianchi identity for the field G in (5.11) was not assumed from the outset and instead has been shown in subsection 5.3 to result from the solution to the BPS equations and the Bianchi identity for P, Q.
In this section we show that the field equations of Type IIB supergravity are obeyed for the general local solution obtained in section 5. We continue to treat the AdS 2 × S 6 × Σ and AdS 6 × S 2 × Σ cases in parallel, and establish the Type IIB field equations for both cases. In particular, we verify the field equations for the warped AdS 6 solutions obtained in [1], a result that was not completely obtained in that paper. The full Type IIB supergravity field equations for the bosonic fields are [12,13], To show that these equations are satisfied, we start with Einstein's equations and then turn to the field equations for B and the three-form flux. We will need the components of the Ricci tensor, which are derived for general AdS p × S q × Σ warped products in appendix D. We will use the labels p and q for the dimensions of the AdS and S parts of the geometry throughout this section, as well as f A and f S for their respective radii. The general procedure for verifying the field equations is to reduce them to a form where they only involve quantities for which we have given explicit expressions in terms of the holomorphic data in sec. 5, and then verify them via a strategy that will be explained in sec. 6.4.
Einstein's equations
For easier reference we reproduce here the explicit expressions for the components of the Ricci tensor along Σ, with f A , f S , p and q defined in appendix D, We will also use the explicit expansions of P and G, where vol 2 is the canonical volume form on AdS 2 of unit radius for AdS 2 × S 6 × Σ and on S 2 of unit radius for AdS 6 × S 2 × Σ.
Components along Σ
The ww component of Einstein's equations in (6.2) simplifies to, Evaluating G P Q wḠ wP Q amounts to contracting two volume forms on the two-dimensional space, for which the difference in signature between AdS 2 and S 2 is crucial. We thus find, G P Q wḠ wP Q = 2Λρ 2 g z (gz) * (6.6) Using the expression for the components of P in (3.28) and thatK/K = Λ, the ww components of Einstein's equations then become, With (C.2) this can be further evaluated to ρ 2 g z (gz) * = −16Λf 4 (∂ w B)(∂ wB ), and the ww component of Einstein's equations consequently becomes, Note that f 4 dBdB is the Poincaré metric on the disc, and SU(1, 1) invariant.
Using the expansions of P and G in (6.4) and again that contractions of G produce overall factors as given in (6.6), the ww component of Einstein's equations becomes, For the components of Einstein's equations in (6.2) along the six-dimensional space, AdS 6 for the case of AdS 6 × S 2 and S 6 for the case of AdS 2 × S 6 , the only non-vanishing contributions are coming from the Ricci tensor and the last term. We thus find, M, N along AdS 6 /S 6 (6.14) With (6.10), (C.2) and (6.12), we find, For the components along the six-dimensional spaces, AdS 6 and S 6 , we thus have, for S 6 (6.16) The three-form field G has non-vanishing components along the two-dimensional space AdS 2 /S 2 , and the corresponding components of Einstein's equations therefore become, The contraction of G in the last term has already been evaluated in (6.10). Explicitly evaluating the second term with M, N along AdS 2 /S 2 produces a contribution similar to the last term, only with a different numerical coefficient. A factor Λ again originates from the difference in signature between AdS 2 and S 2 . The components of Einstein's equations along AdS 2 /S 2 become, For the components along the two-dimensional spaces, AdS 2 and S 2 , we thus have,
Axion-dilaton field equations
We now turn to the axion-dilaton equation. We will perform the index contractions as contractions of spacetime indices instead of frame indices, without introducing new notation.
The equation then reads, With the definitions of P and Q in (2.2), we find, The connection term in the covariant derivative evaluates to, This leaves only the term involving G to be evaluated. We find, where (C.2) was used to obtain the second equality. Using (6.12) and (4.6) shows, The complete equation of motion, after dividing by 2g ww f 2 , becomes,
The 3-form flux field equation
The field equation for the 3-form field G with vanishing F (5) reads, We have already presented one proof that this field equations holds for our solution in section 5.3, by showing that the form F (7) is closed. Here, we provide a second proof, obtained by direct evaluation. Analyzing (6.26), we see that the last two terms vanish unless M, N are both along AdS 2 for the AdS 2 × S 6 case or correspondingly along S 2 for the AdS 6 × S 2 case. The only nontrivial components of the entire equation are when M, N are either both on S 2 /AdS 2 , or one of them on S 2 /AdS 2 and one on Σ. In the latter case, (6.26) reduces to an equation that is satisfied automatically due to metric compatibility of the connection on S 2 /AdS 2 . It therefore only remains to consider the case with both components on S 2 /AdS 2 . For notational convenience we will introduce coordinate indices µ, ν, which correspond to AdS 2 for the AdS 2 × S 6 case and to S 2 for the AdS 6 × S 2 case. We will also again perform index contractions as contractions of spacetime indices, without introducing additional notation.
When M, N = µ, ν are both along S 2 /AdS 2 , the field equation reads, Evaluating the connection terms in analogy with (6.22), the field equation becomes, Gw µν − P wḠwµν + (w ↔w) (6.28) We now use the expansion (6.4) along with (C.2) to replace, With (6.12), we then find, The equation of motion, after dividing by 4iΛKf 2 2β /ᾱ and separating off the volume form on the two-dimensional space, consequently becomes, Evaluating the derivatives and using the components of Q as defined in (2.2) yields, With P w = f 2 ∂ w B, Pw = f 2 ∂wB as well as,
Explicitly evaluating the equations
To summarize, the non-trivial components of Einstein's equations take the form given in (6.8) for the ww component, in (6.13) for the ww component, in (6.16) for the AdS 6 /S 6 components, and in (6.19) for the AdS 2 /S 2 components. The equation for the axion-dilaton scalar takes the form given in (6.25) and the non-trivial components of the equation for G are given in (6.32) with (6.33).
We will now describe the strategy to verify that these equations are satisfied. We use the explicit expressions for the metric functions in (5.7), for B in (5.9), and for the components of the Ricci tensor. This reduces the field equations to a set of equations involving only the holomorphic functions and their derivatives, as well as R, G and κ 2 along with their derivatives. We will avoid using the explicit definition for G or R, since G involves an integration that we have not performed for generic A ± while the definition of R involves a square root with a corresponding choice of branch that we do not wish to specify explicitly. The first step will be to make the expressions algebraic in R and G, i.e. to eliminate all their derivatives. From the definitions for G in (4.36) and for R in (5.2), we straightforwardly derive, The ∂w derivatives of R and G are obtained by complex conjugation. Repeatedly using these relations to reduce the rank in derivatives acting on R and G, we can eliminate all derivatives of G and R. We now use the definition of R in (5.2) to eliminate G, by setting, Using also the explicit definition of κ 2 , we have at this point reduced Einstein's equations to relations involving only the holomorphic functions and their differentials along with R. G and its derivatives as well as the derivatives of R are eliminated completely. Straightforward evaluation now shows that the equations are indeed satisfied for both, the AdS 6 and AdS 2 cases, with the corrsponding choices of Λ and K as well as of p and q for the dimensions of the AdS and S parts of the geometry. This shows that the local solution to the BPS equations presented in sec. 5 solves the field equations of Type IIB supergravity as well. We point out that, for the discussion of the BPS equations, c was assumed real and R constrained to be positive by its definition as absolute value of Z in (4.22), but that neither of these constraints appear to be necessary for the equations of motion to be satisfied.
We close this section with a comment on the sign of G. It is generally true that, for a solution to Type IIB supergravity, flipping the sign of G produces another solution, since G appears quadratically in the equations of motion. In general, supersymmetry is not preserved under this sign flip, since the BPS equations do depend on the sign of G. For our solutions, however, flipping the sign of G again produces a supersymmetric solution. This may be seen from the fact that a sign reversal in G corresponds to a special case of the SU (1, 1) transformations discussed in sec. 5.4. Choosing u = −1 and v = 0 indeed leaves all supergravity fields invariant except for the two-form potential C (2) , on which it induces a sign flip that results in a sign reversal on G. The sign-flipped solution is therefore again in our class of supersymmetric solutions, although with a different form of the Killing spinors, which depend on the A ± directly.
Reality, positivity, and regularity conditions
The solutions obtained for the supergravity fields of the case AdS 2 × S 6 in the previous section satisfy the BPS equations, but are physically viable solutions only after certain reality, positivity, and regularity conditions are enforced on the supergravity fields of the solutions. In this section we establish these conditions and uncover their implications on the functions A ± . We set Λ = −1 throughout this section.
Reality and positivity conditions
For an acceptable solution with appropriate signature, the metric is real-valued and the functions f 2 2 , f 2 6 ρ 2 positive on Σ. There are no reality constraints on the fields B and C (2) , but B is restricted by the condition of positive coupling constant, |B| < 1. We now extract the necessary and sufficient conditions on κ 2 , G, and R for these properties to hold.
Recalling that the functions κ 2 and G, which were defined in (4.36), are real-valued by construction, and that R is real and non-negative by construction, (5.2) implies, In particular, κ 2 and G need to have opposite signs. Assuming positive ρ 2 , the positivity of f 2 2 and f 2 6 in (5.4) furthermore requires, With this assumption ρ 2 , given in (5.4), is real and can be made positive by appropriately choosing the sign of the constant c. To verify |B| ≤ 1 we calculate f 2 using (4.16), 2) implies f 2 ≥ 1. The reality and positivity conditions are therefore given by (7.1) and (7.2).
Inversion and complex conjugation
The space of allowed triplets (κ 2 , G, R) naturally divides into two branches, according to whether the conditions (7.1) and (7.2) are realized for R > 1 or R < 1. We shall refer to these branches as B ± , defined by, These two branches are mapped into one another by an involution, which is a combination of complex conjugation, reversal of the complex structure on Σ, and reversal of the indices ± on the functions A ± , given by, combined with R → R −1 . This transformation leaves eq. (5.2) invariant and reverses the sign of κ 2 and G. It leaves the metric functions f 2 2 , f 2 6 and ρ 2 invariant and complex conjugates the fields B and C,
Global regularity and boundary conditions
By inspection of the metric functions f 2 2 , f 2 6 , and ρ 2 in (5.4), it is manifest that a supergravity solution considered on a compact subset U of Σ for which (κ 2 , G, R) maps to a compact subset of either B + or B − (but not both) is locally regular in U . If the supergravity solution considered throughout a compact surface Σ is such that (κ 2 , G, R) maps to a compact subset of either branches B + or B − then the supergravity solution is globally regular on Σ.
If Σ has a non-empty boundary, ∂Σ, additional regularity conditions have to be satisfied on ∂Σ. We assume geodesic completeness of the space-time manifold allowed for a supergravity solution, so that the boundary of space-time is at infinite geodesic distance (modulo issues of the Minkowski signature of the AdS 2 -factor). The only way we know how to realize this when Σ has a boundary is by closing off the sphere S 6 , namely f 2 6 → 0, while keeping f 2 2 finite. In view of the expression obtained from (5.4) for the ratio, this corresponds to the boundary condition R = 1. As R → 1, factors of 1 − R in the expressions for the metric functions vanish at a number of places, and having a regular limit therefore imposes additional constraints: From the expression for f 2 2 in (5.7), we see that finiteness of the AdS 2 radius needs G = O ((1 − R) 3 ) as the boundary is approached. Similarly, from the finiteness of ρ 2 we then conclude that κ 2 = O(1 − R). The boundary ∂Σ is therefore mapped to the common boundary of the two branches B ± , namely κ 2 = G = 0 and R = 1. Lastly, in view of (5.2) we also have the constraint that ∂ w G = O((1 − R) 2 ).
Implications of regularity and boundary conditions
In this subsection we will discuss some immediate implications of the global regularity conditions for the structure of the solutions.
No smooth solutions for compact Σ without boundary
Assuming that G is smooth, there are no globally regular solutions on a compact surface Σ without boundary. The argument is parallel to the one already given for the case AdS 6 × S 2 . It is based on the following differential equation, which readily follows from the definitions of κ 2 and G in (4.36). If G is smooth, then on a compact surface without boundary, the integral of the left side over Σ must vanish. But the sign of κ 2 is constant throughout Σ so the integral of the right side cannot vanish, which is in contradiction to our assumptions. Hence such globally regular solutions cannot exist. We are thus left with two options: either Σ has a non-empty boundary, or Σ is compact without boundary and the functions A ± have singularities in Σ.
No smooth solutions for compact Σ with boundary
We show that for smooth G and an arbitrary Riemann surface Σ with non-empty boundary ∂Σ, the conditions G| ∂Σ = 0 and sgn(κ 2 ) = −sgn(G) can not be satisfied simultaneously. We start from (7.8) and solve this equation along with the boundary condition G| ∂Σ = 0 to obtain the following integral equation, Here, G(w, z) is the scalar Green function on Σ, which is symmetric G(z, w) = G(w, z) and vanishes on the boundary ∂Σ, ∂ w ∂wG(w, z) = −πδ(w, z) G(w, z)| w∈∂Σ = 0 (7.10) As shown in detail in sec. 2.3 of [3], for any two points w, z in the interior of Σ, the function G(w, z) is strictly positive. H(w) is a harmonic function. Since G(w) vanishes on the boundary by assumption, and by construction the Green function G(w, z) vanishes for w ∈ ∂Σ, then H itself must also vanish on ∂Σ, and we have By the min-max principle for harmonic functions, H(w) takes its minimum and maximum values on the boundary of Σ. Since H(w) = 0 for w ∈ ∂Σ, this implies that H(w) = 0 both on ∂Σ and in the interior of Σ. But this is incompatible with sgn(κ 2 ) = −sgn(G), due to the positivity of the Green function G(w, z), which implies that the integral term in (7.9) is strictly positive for the branch B + with κ 2 > 0 and strictly negative for the branch B − with κ 2 < 0. Thus, no regular supergravity solutions exist when G vanishes on ∂Σ.
Double analytic continuation
In this section we study the relation between AdS 2 × S 6 and AdS 6 × S 2 via double analytic continuation of the space-time manifold metrics in more detail, and discuss the implications from the perspective of the solutions to the BPS equations. At the level of the geometry, one may perform an analytic continuation from AdS 6 × S 2 to AdS 2 × S 6 via 2 and these continuations can be extended straightforwardly to the remaining bosonic supergravity fields. This does not produce a ten-dimensional spacetime of the desired signature, since the eight-dimensional symmetric space has changed signature from mostly plus to mostly minus while the metric on Σ remains positive definite, but it does formally produce a solution to the equations of motion. We may therefore wonder whether we can recover the analytic continuation of the globally regular AdS 6 × S 2 × Σ solutions constructed in [2,3] as a special case of the AdS 2 × S 6 × Σ solutions presented in sec. 5. In the remainder of this section we will show that this is indeed the case, but that the result is neither regular (even leaving aside the signature issue) nor supersymmetric.
The construction in [2,3] started from Σ a disc, realized as the upper half plane. The holomorphic functions A ± were given by, where w is a complex coordinate on the upper half plane, s n a collection of points inside the upper half plane and p a set of poles of the differentials ∂ w A ± on the boundary of the upper half plane. With a suitable choice of the integration constant implicit in G, this produced, We can assume the same choice of holomorphic data as input for the AdS 2 ×S 6 ×Σ solutions. The expressions for κ 2 and G in terms of the locally holomorphic functions are the same for AdS 2 × S 6 × Σ and AdS 6 × S 2 × Σ, such that we realize (8.3) in both cases. Eq. (5.2) then implies ΛR > 0 in the interior of the upper half plane and ΛR → 1 on the boundary, and we choose the branch 0 < ΛR ≤ 1. This implies that R is positive for AdS 6 × S 2 × Σ and negative for AdS 2 × S 6 × Σ. We note that negative R was not acceptable for solving the BPS equations, where R was positive by construction. But, as noted at the end of sec. 6, neither R nor the constant c are constrained by the equations of motion. So at the level of the equations of motion these AdS 2 × S 6 configurations are acceptable, and we have, The expressions for the supergravity fields in (5.7), (5.9) and (5.15) depend on R only through this combination ΛR. The form of the axion-dilaton B in (5.9) is, in fact, exactly the same for AdS 2 × S 6 × Σ and AdS 6 × S 2 × Σ. The metric functions in (5.7) are real provided that c is chosen real for AdS 6 × S 2 × Σ and imaginary for AdS 2 × S 6 × Σ, to compensate for the phase in √ ΛG. They only differ between AdS 2 × S 6 × Σ and AdS 6 × S 2 × Σ through their signs: while f 2 2 , f 2 6 and ρ 2 all have the same sign for AdS 6 × S 2 × Σ, the sign of f 2 2 and f 2 6 is opposite to that of ρ 2 for AdS 2 × S 6 × Σ. This is precisely as expected for solutions connected by the analytic continuation in (8.1). The gauge potential C in (5.15) differs only by an overall factor of i between AdS 2 × S 6 × Σ and AdS 6 × S 2 × Σ. This produces the expected behavior under a Wick rotation for the three-form field strength, where one of the components along S 2 becomes timelike and picks up a factor of i. We have thus recovered the analytic continuation of the global AdS 6 × S 2 × Σ solutions to AdS 2 × S 6 × Σ via (8.1), which is simply realized by the same choice of locally holomorphic functions.
This naive analytic continuation does, however, not lead to physically regular solutions. Aside from the inappropriate signs for the metric functions, it is still the two-dimensional space that collapses on the boundary of Σ. This was the desired behavior for the AdS 6 ×S 2 ×Σ case, with the collapsing S 2 smoothly closing off spacetime. But it is not desirable for the AdS 2 × S 6 × Σ solutions to have the AdS 2 cap off on ∂Σ. Moreover, the solutions are not supersymmetric, since we do not recover them from the BPS equations where R ≥ 0 was required by construction. The loss of supersymmetry under Wick rotation may be understood from the change in the Clifford algebra due to the changed signature in the twoand six-dimensional spaces. The construction of physically regular supersymmetric solutions will therefore have to be revisited, with the regularity conditions and constraints spelled out in sec. 7.
Conclusion
We have constructed the general local form of solutions to Type IIB supergravity that are invariant under SO(2, 1) ⊕ SO(7) and sixteen supersymmetries. The geometry takes the form AdS 2 × S 6 warped over a two-dimensional Riemann surface Σ, and the local form of the solutions is strikingly similar to the AdS 6 × S 2 case considered in [1]. The entire solution is summarized, in parallel with the AdS 6 × S 2 case, in sec. 5, and we have verified for both cases that the solution to the BPS equations also satisfies the field equations of Type IIB supergravity in sec. 6. The differences between the local solutions for AdS 2 × S 6 and AdS 6 × S 2 are subtle, and encoded entirely in sign flips at various places.
To obtain physically acceptable solutions additional positivity and regularity conditions have to be imposed on the general local form of the solutions. We have presented a preliminary analysis of these conditions for AdS 2 × S 6 in sec. 7. Subtle but crucial differences between the solutions for AdS 2 × S 6 and AdS 6 × S 2 appear to render ineffective the strategy followed in [3] to obtain global solutions for AdS 6 × S 2 . An analytic continuation of the physically regular AdS 6 × S 2 solutions to AdS 2 × S 6 , discussed in sec. 8, gives rise to field configurations which solve the field equations, but are neither regular nor supersymmetric. The construction of physically regular AdS 2 × S 6 solutions therefore poses an interesting new problem, which we hope to come back to in a follow-up paper.
One may speculate about the possible brane interpretation of warped AdS 2 ×S 6 solutions. The physically regular AdS 6 ×S 2 solutions constructed in [3] have a compelling interpretation in terms of the conformal limit of (p, q) 5-brane webs. A similar interpretation may be expected for physically regular AdS 2 solutions to Type IIB supergravity in terms of webs of (p, q) strings. It will be interesting to see whether AdS 2 solutions with this interpretation can be found within our SO(2, 1) ⊕ SO(7) invariant Ansatz.
A Clifford algebra basis adapted to the Ansatz
The signature of the space-time metric is chosen to be (− + · · · +). The Dirac-Clifford algebra is defined by {Γ A , Γ B } = 2η AB I 32 , where A, B are the 10-dimensional frame indices. We construct a basis for the Clifford algebra that is well-adapted to AdS 2 × S 6 × Σ Ansatz, with the frame labeled as in (2.8), where a convenient basis for the lower dimensional Dirac-Clifford algebra is as follows, We will also need the chirality matrices on the various components of AdS 2 × S 6 × Σ, The 10-dimensional chirality matrix in this basis is then given by, The complex conjugation matrices in each component are defined as follows, where in the last column we have also listed the form of these matrices in our particular basis. The 10-dimensional complex conjugation matrix B satisfies, .6) and in this basis is given by,
B Derivation of the BPS equations
In reducing the BPS equations, we will use the following decompositions of ε and B −1 ε * , where we use the abbreviations, in τ -matrix notation. We will also need the chirality relations,
B.1 The dilatino equation
Reduced to the Ansatz, and using the above decomposition, the dilatino equation is, where we have used the following simplifications for the inner products, Using the expression for ζ and reversing the sign of η 2 , we extract an equation satisfied by the ζ-spinors, and recover the reduced dilatino BPS equation announced in (3.2).
B.2 The gravitino equation
The gravitino equation is, where A, B are the 10-dimensional frame indices.
B.2.1 The calculation of (d + ω)ε
The spin connection components for a generic space-time of the form AdS p × S q × Σ are worked out in appendix D. Here we quote results for the case of p = 2 and q = 6, and in particular we reproduce equation (D. 5), which gives the relevant spin connection components, along with ω a b whose explicit form we will not need. The hats refer to the canonical connections on AdS 2 and S 6 , respectively. We replace the covariant derivative of the spinor along the AdS 2 and S 6 directions by the corresponding group action, SO(2, 1) and SO (7), as defined in (2.14). The additional term that appears in going from ∇ to∇ is due to the warp factors in the ten-dimensional metric. The covariant derivatives along AdS 2 and S 6 , respectively, are given by, as well as ∇ a ε along Σ. Using the Killing spinor equations (2.14) to eliminate the hatted covariant derivatives, as well as the equation Γ a = γ (1) ⊗ γ (2) ⊗ γ a , we have, As we will show, each term in the gravitino equation contains Γ A χ η 1 ,η 2 , which we argue are linearly independent. Therefore, we will require that the coefficients vanish independently along the various directions of AdS 2 , S 6 , and Σ.
B.2.2 The calculation of gB −1 ε *
The relevant expression is as follows, We make use of the following identities, where γ ab ≡ iε ab σ 3 and ε 89 = +1. Projecting along the various directions, we obtain,
B.2.3 The complete gravitino BPS equation
We now assemble the reduced gravitino equations. Requiring the coefficients of Γ A χ η 1 ,η 2 to vanish independently, then rewriting the relations using the τ -matrix notation, we have, whereω a = (ω 89 ) a is the spin connection along Σ, and we have used the fact Γ 89 = iσ 3 .
Eliminating the star using the definition (B.2), then multiplying the (m) and (i) equations by τ (11) , we recover the system of reduced gravitino BPS equations announced in (3.3).
C Calculation of the flux potentials
In this appendix, we present the calculations of the reduced flux potentials C and M.
C.1 Calculation of the flux potential C
Expressing the field strength G in terms of g a , the equations for the derivatives of the potential C are given by, Converting G into P and then into derivatives of B using (2.2) and (3.28) yields, along withḡ z = (gz) * andḡz = (g z ) * , and we obtain the following expressions, We will now apply the same changes of variables used to solve the BPS equations. In the derivation of C as well as M, it will be useful to have the derivatives of B andB expressed in terms of the new variables, and these derivatives are given by,
C.1.1 Expressing variables in terms of holomorphic functions
Recall that we have, as well as the expressions for B in (4.15) and f 2 in (4.16). Using these, along with the rearrangement formula following from (4.28), we write (C.3) as, Next, we define the combinationC +λC by its derivative with respect to w as, where P w is given by, Using ξ(1 − |λ| 2 ) = L to eliminate ξ and then changing variables via Z 2 = Re iψ , we find, The combinations of R and ∂ w W can be expressed in terms of W defined in (4.33) and its derivative ∂ w W . The latter is given by equation (4.34), from which we eliminateρ in favor of ξ, as well as eliminate ξ in favor of L and λ, to obtain, Using the relation e iψ = K 2L /L to express the derivative i∂ w ψ in terms of L, then separating the dependence of L andL, we find, The last term inside the square brackets can be replaced using the differential equation for W in (C.11), which upon expressing ψ in terms of L takes the form, Eliminating this term between (C.11) and (C.12) and integrating the result, we find, Therefore, we have, with some holomorphic function K 1 , Proceeding analogously forC, and using the equations for ∂ w ξ and ∂ wξ , we find, for some holomorphic function K 2 . To determine K 2 , we equate the two different expressions forC +λC, eliminate the dependence on W and separate holomorphic and anti-holomorphic dependences to obtain, where K 0 is an arbitrary complex constant. Eliminating ξ and L leads to (5.15).
C.2 Calculation of the reduced flux potential M
To evaluate M, we proceed in analogy with the calculation of C. Reducing G (3) to P and then expressing this quantity in terms of derivatives of B using (2.2) and (3.28) yields, Using (C.5) and (C.4) to express α/β and the derivatives of B andB in terms of Z, λ and ρ 2 , as well as the following expression, we find, after some simplifications, Significant cancellations occur when combining these results into the following form, Combining the relations, Recognizing a total derivative in the expression for ∂ w (M −λM), we may rearrange the result as follows, Extracting a total derivative again significantly simplifies the expression, and we have, where S w is given by, Using the relation ∂ w L = (1 − |λ| 2 )∂ w A − , we find a remarkable cancellation of the factor (1 − |λ| 2 ), and recover an expression which, after converting Z andZ to R and ψ using (4.22), is given as follows, Next, we make use of the identity Le iψ = ΛL, and then use ∂ w G = −L∂ w A − to obtain the following expression, Using the definition of R as well as κ 2 = −∂ w ∂wG, this can be rewritten as follows, The first term already is in integrated form, and the last two terms are of degree at most two in A + and A − and of degree at most one in ∂ w A + and ∂ w A + , and they may be integrated in their holomorphic dependence on w.
C.2.1 Integrating forM −λM
We introduce two locally holomorphic functions, W ± such that One may then verify by straightforward evaluation that the second term in (C.29) can be integrated as follows For the remaining term we use repeatedly the relation ∂ w L = ∂ w A − −λ∂ w A + and find Combining (C.31) and (C.32) with the expression for S w in (C.29) shows that we have thus integrated S w . Coming back to the expression for ∂ w (M −λM) in (C.25), we can thus integrate forM −λM. After a number of simplifications and using thatλL − L = (1 − |λ| 2 )(Ā + − A − ), we find where V 1 is a so far arbitrary locally holomorphic function. The terms of degree −1 inλ combine to a purely anti-holomorphic function and can be absorbed into V 1 .
C.2.2 IntegratingM
To fix the so far unspecified locally holomorphic function, we go back to the expression for ∂ wM in (C.20). Using (C.23), and combining all the derivative terms, it can be rewritten as To evaluate the terms in the derivative further, we perform the variable changes to R and ψ and then to L, which yields Using thatλL − L = (1 − |λ| 2 )(Ā + − A − ) and ∂ w G = −L∂ w A − , yields We thus have The terms in the second line are again of degree at most two in A ± and at most one in ∂ w A − , and can be integrated straightforwardly. We find This completes the integration and we conclude that with a locally holomorphic function V 2 . To fix V 1 and V 2 , we equate the two expressions for M in (C.40) and (C.33) and isolate the holomorphic and anti-holomorphic dependences. This yields The final form of M then becomes where W ± are defined up to complex constants by (C.30).
D Curvature for AdS p × S q × Σ warped products To compute the curvature for the AdS 6 × S 2 and AdS 2 × S 6 cases in parallel, we generalize the setting to AdS p × S q warped over a Riemann surface Σ, with metric The functions ρ 2 , f 2 A , f 2 S depend only on Σ and dŝ 2 AdSp , dŝ 2 S q are respectively the SO(2, p − 1) and SO(q + 1)-invariant metric of unit radius on AdS p and S q .
Withê m andê i denoting the orthonormal frames for the unit radius AdS p and S q , respectively, we make the following choice for the orthonormal frame, e m = f Aê m m = 1, · · · , p e i = f Sê i i = p + 1, · · · , p + q (D. 2) combined with e z , ez for Σ as defined in (2.13). We collectively denote the frame indices by A, B. The frame metrics are given as in (2.11) for Σ and η mn = diag [− + · · · +], δ ij = diag [+ · · · +]. Denoting the connection 1-form by ω A B , the torsion equations are, The connection forms of the symmetric spaces, denoted by a hat in analogy to the notation for the frame, are defined by the analogous vanishing torsion conditions. The connection components on Σ are given by ω z z = dw ∂ w ln ρ − dw ∂w ln ρ (D.4) We use the notation of (2.13) for the frame-covariant derivative when no connection is needed, and analogous notation when a connection is needed, e.g. D z v a = ρ −1 (∂ w v a + ω a w b v b ). The remaining components are then, where we use the notation |D a ln f | 2 ≡ (D a ln f )(D a ln f ) and square brackets denote antisymmetrization of the enclosed indices, e.g. δ m [A η B]n = δ m A η Bn − δ m B η An . Furthermore, where the normalization is such that R (2) = −1 when ρ 2 = y −2 corresponds to the Poincaré metric on the upper half space. The components of the Ricci tensor (in frame index convention) are defined by R AB = R C ACB , and the non-vanishing ones are given by, | 17,892 | 2017-12-12T00:00:00.000 | [
"Mathematics"
] |
Probing light higgsinos in natural SUSY from monojet signals at the LHC
We investigate a strategy to search for light, nearly degenerate higgsinos within the natural MSSM at the LHC. We demonstrate that the higgsino mass range μ in 100−160 GeV, which is preferred by the naturalness, can be probed at 3σ significance through the monojet search at 14 TeV HL-LHC with 3000 fb−1 luminosity. The proposed method can also probe certain region in the parameter space for the lightest neutralino with a high higgsino purity, that cannot be reached by planned direct detection experiments at XENON-1 T(2017).
Introduction
One of the key theoretical motivations for low-energy supersymmetry (SUSY) is that it provides a framework for a light Higgs boson without invoking unnatural fine-tuning of theory parameters. However, recent discovery of a Standard Model (SM) Higgs-like particle with the mass around 125 GeV [1,2], in conjunction with non-observation of supersymmetric particles, have largely excluded the most studied parameter range within the minimal supersymmetric Standard Model (MSSM), for which the naturalness criterion is satisfied. If the observed resonance is to be identified with the lightest CP-even Higgs boson of MSSM, heavy multi-TeV stops and/or large Higgs-stop trilinear soft-breaking coupling are required to achieve sufficient enhancement of the predicted Higgs mass [3][4][5][6][7][8]. Furthermore, null results on gluino searches at the LHC so far have pushed the lower limit on gluino mass above the TeV scale [9][10][11][12]. All these significantly jeopardize the naturalness of MSSM with a standard sparticle spectrum. Therefore, it is imperative to consider the possibly hidden parameters space where the theory maintains naturalness, and look for other strategies for verifying such natural SUSY models at the LHC [13][14][15][16][17]. In this work, we investigate the possibility of monojet signals induced by light higgsinos at 14 TeV high-luminosity LHC(HL-LHC) as a probe of natural SUSY.
The justification for light, nearly degenerate higgsinos within the natural MSSM comes from the following consideration. In the MSSM, the minimization of the tree-level Higgs potential leads to the relation [18]: where m 2 H d and m 2 Hu represent the weak scale soft SUSY breaking masses of the Higgs fields, and µ is the higgsino mass parameter. A moderate/large tan β 10 is assumed in the last approximate equation. In order to avoid large fine-tuning in eq. (1.1), µ and m Hu must be of the order of ∼ 100 − 200 GeV, which implies light higgsinos. At the same time, the electroweak gaugino mass parameters M 1,2 are preferred to be of the similar order as the heavy gluino mass parameter M 3 and large Higgs-stop trilinear coupling A t is JHEP02(2014)049 needed [19][20][21][22]. Hence, generically we have µ ≪ M 1,2 and the mass splittings between the lightest chargino and the lightest two neutralinos at leading order are determined by [27] This in turn implies that light electroweak gauginos in the natural MSSM are nearly degenerate higgsino-like states with a mass differences of about 3 − 10 GeV (for M 1 = M 2 ∼ 0.5 − 2 TeV). Therefore, a direct search for light higgsinos may serve as a sensitive probe of the natural MSSM. For such light higgsinos the electroweak production rates for Z →χ 0 and W ± →χ ± 1χ 0 2 are expected to be reasonably large, reaching pb-level at the LHC. However, since the light higgsinos are nearly degenerate, the products of their subsequent decays,χ ± 1 → W ± * χ0 1 andχ 0 2 → Z * χ0 1 , will carry small energies and, hence, the currently adopted search strategy for electroweak gauginos through their direct pair production is not applicable to this case [23,24]. Recently, a new search channel based on the wino pair production with a same-sign diboson plus missing transverse energy ( / E T ) final state has been proposed for the 14 TeV LHC in [25]. Also, it has been pointed out that for mχ± 1 − mχ0 1 1 GeV the wino may have a long life-time and such long-lived charged particle is already excluded by the LHC data [26].
Calculations and discussions
We study the detection of the light higgsinos via monojet searches at the LHC in the following processes (see figure 1 for the corresponding Feynman diagrams): In these processes a hard jet radiated from initial partons recoils against the invisible missing transverse energy from soft decay productes and this can be used as a handle to tag the higgsino pair production. Because of the small mass splitting (∆m ∼ 3 − 10 GeV)
JHEP02(2014)049
betweenχ ± 1 ,χ 0 2 andχ 0 1 , all three channels (jχ + 1χ − 1 ,jχ 0 1χ 0 2 and jχ ± 1χ 0 1,2 ) share the same topology in the detector. As a result, the monojet production rates within the natural MSSM are greatly enhanced. In addition, when µ ≪ M 1,2 , these processes are largely insensitive to other SUSY parameters but higgsino mass µ. Therefore, we do not consider the production of stops and gluino in this paper, which contribute to the fine-tuning in more complicated and model-dependent way [19][20][21][22]. The current constraints on the mass limits of stop and gluino in natural SUSY have been discussed in [28][29][30][31][32][33]. The sleptons and first two generation squarks are irrelevant for our analysis and we assume them to be heavy.
Since the monojets have a distinctive topology of events with a singly high p T hadronic jets and large missing / E T , their relevance to the search for the pair production of weaklyinteracting particles have been exploited at the LHC [38,39]. The SM backgrounds to the above monojet signature are dominated by the following four processes: (i) pp → Z(→ νν) + j, which is the main irreducible background with the same topology as our signals; (ii) pp → W (→ ℓν)+j, this process fakes the signal only when the charged lepton is outside the acceptance of the detector or close to the jet; (iii) pp → W (→ τ ν) + j, this process may fake the signal since a secondary jet from hadronic tau decays tend to localize on the side of / E T ; (iv) pp → tt, this process may resemble the signal, but also contains extra jets and leptons. This allows to highly suppress tt background by applying a b-jet, lepton and light jet veto.
For the QCD background, the misreconstruction of the energy of a jet in the calorimeters can cause an ordinary di-jet event with large missing energy to mimic the signal. An estimation of the QCD background based on the full detector simulation can be found in [34]. By fitting the jet energy response function (JERF) using the method in [35], the authors of [36] found that the multijet background in the supersymmetric monojets analysis at 14 TeV LHC can be reduced to a negligible level by requiring a large / E T cut, such as / E T > 200 GeV . Since other dominant backgrounds have / E T > 200 GeV, we set / E T > 500 GeV as in [37], where the cuts for the monojet events are optimized for 14 TeV LHC, thus we can safely neglect the QCD background in our calculation (the pile-up effects at 14 TeV HL-LHC have not been considered in the work, due to lack of the exact detector configurations.). The diboson backgrounds and single top background are not considered in our calculations due to their small cross sections compared to other backgrounds.
In the calculations we assume M 1 = M 2 = 1 TeV and use the Suspect [40] and SUSY-HIT [41] to calculate masses, couplings and branching ratios of the relevant sparticles. The parton level signal and background events are generated with MadGraph5 [42]. We perform parton shower and fast detector simulations with PYTHIA [43] and Delphes [44]. We cluster jets using the anti-k t algorithm with a cone radius ∆R = 0.7 [45]. In order to obtain reasonable statistics, a generator level event filter was applied which imposed a partonlevel cut of p T > 120 GeV on the first leading jet for signals and W/Z + j backgrounds. It should be noted that the jet veto cuts can significantly affect the QCD corrections to the backgrounds [46]. To include the QCD effects, we generate parton-level events of Z/W + j with up to two jets that are matched to the parton shower using the MLM-scheme with merging scale Q = 60 GeV [47]. Due to the tt events containing a large number of jets, we need not generate the events with the extra hard partons, which will be strongly rejected by the jets veto [37]. Although the additional jet may come from the decays ofχ ± 1 or χ 0 2 , they are too soft to pass our strict p T cut on the leading jet adopted in the following analysis. So there is no need to generate the higgsinos pairs without additional parton in the final state. Besides, our signal simulation is exclusively based on eq. (2.1) so that double counting will not arise in our calculation.
In figure 2, we display the cross section of pp →χ ± implies that signals with the same initial states have approximately same cross sections. Therefore, the total production rate is amplified and can reach nearly pb-level. In figure 3 we show the normalized distributions of a reconstructed leading jet p T (j 1 ) and / E T of the signals and backgrounds. From the upper panel one can see that for p T (j 1 ) > 200 GeV the signals have harder p T (j 1 ) spectrum than the backgrounds. The greater value of µ corresponds to an increase in the average p T of the jet. The difference in peaks of the signals (∼ 120 GeV) and tt background (∼ m t /2) is caused by the parton-level cut p T (j 1 ) > 120 GeV. From the lower panel one observes that the signals have the larger / E T than the backgrounds. Thus, a hard cut on / E T will be effective to reduce the backgrounds. According to the above analysis, events are selected to satisfy the following criteria of monojet searches [38,39], and the cuts for / E T and p T (j 1 ) are optimized for 14 TeV LHC [37]: (i) We require large missing transverse energy / E T > 500 GeV; (ii) The leading jet is required to have p T (j 1 ) > 500 GeV and |η j 1 | < 2; events with more than two jets with p T above 30 GeV in the region |η| < 4.5 are rejected; (iii) We veto the second leading jet with p T (j 2 ) > 100 GeV and |η j 2 | < 2; (iv) A veto on events with an identified lepton (ℓ = e, µ, τ ) or b-jet is imposed to reduce the background of W + j and tt. We use the b-jet tagging efficiency parametrisation given in [48] and include a misidentification 10% and 1% for c-jets and light jets respectively. We also assume the τ tagging efficiency is 40% and include the mis-tags of QCD jets by using Delphes. Table 1. Cut flow of the signal events for µ = 100, 200 GeV at 14 TeV LHC with L = 100 fb −1 .
The cross section of tt is normalized to the approximately next-to-next-to-leading order value σ tt = 920 pb [49].
In table 1, the resulting cut-flow for signal and background events is presented, for a centre-of-mass energy of 14 TeV and an integrated luminosity of 100 fb −1 . After the cuts P T (j 1 ) > 500 GeV and / E T > 500 GeV, the Z + j and W + j backgrounds are reduced by O(10 −4 ), while the signals only by O(10 −2 ). The lepton and light jet veto will suppress W j backgrounds by extra two orders. For tt background, we have not included the hadronic channels due to its large jet multiplicity and small / E T . We impose the third jet veto as the requirement of the ATLAS collaboration [38,39], which is not used in the paper [37]. We also checked that our results are consistent with those obtained in ref. [50] by setting the same values of cuts and collider energy. The Z(νν) process is still the dominant background after all cuts.
In figure 4 we display the dependence of the signal significance S/ √ B on the higgsino mass µ at 14 TeV HL-LHC for various luminosities, L = 1000, 2000, 3000 fb −1 . The overall background B including the systematic errors is calculated through the formula [37]. With an increase of µ the significance drops fast due to the reduction in the signal cross sections. At L = 3000 fb −1 , the range µ ∼ 100 − 160 GeV, favored by the naturalness, can be probed at 3σ significance. However, it should be mentioned that, since the realistic detector performances of the HL-LHC are still not available, we can expect our analysis can be improved by optimizing signal extraction strategies and better understanding of the backgrounds uncertainties through the dedicated analysis of the experimental collaborations at HL-LHC. As a complementary searches for the light higgsinos, we also investigate the probing ability of the dark matter direct detections. We computed the dark matter observables by using the package MicrOmega [51] and scan the following parameter space: 100 GeV ≤ µ ≤ 200 GeV, 0.6 TeV ≤ mQ Other irrelevant mass parameters are taken as 2 TeV. The above parameters are further constrained by: (1) Measurements of B → X s γ and B s → µ + µ − processes at 2σ level [52,53]; (2) Higgs mass in the range 123-127 GeV [54,55]; (3) LHC searches for H/A → τ + τ − [56]; (4) Direct search results of stop/sbottom pair productions at the LHC [33]; (5) LEP data [58,59] and (6) Electroweak precision measurements [57].
We note that, in the natural MSSM, the thermal relic density of the light higgsinolike neutralino dark matter is typically low due to the large annihilation rate in the early universe. This makes the standard thermally produced WIMP dark matter inadequate in the natural MSSM. In order to provide the required relic density, several alternative ways have been proposed [60][61][62][63][64][65], such as choosing the axion-higgsino admixture as the dark matter [66,67]. In this case, the spin-independent neutralino-proton scattering cross section σ SI p must be re-scaled by a factor Ωχ0 1 h 2 /Ω PL h 2 [66,67], where Ω PL h 2 is the relic density measured by Planck satellite [68]. However, it should be mentioned that, if the naturalness requirement is relaxed, the heavy higgsino-like neutralino with a mass about 1 TeV can solely produce the correct relic density in the MSSM [69,70]. Of course, all these analyses are performed by assuming a standard ΛCDM model.
The results for the spin-independent higgsino-proton scattering cross section are shown in figure 5 and compared with the current limits from XENON-100, LUX [71,72] and future reach projections of XENON-1T [73]. We also present the 3σ probing sensitivity of the higgsino mass µ by our proposed monojet strategy at the LHC with L = 3000 fb −1 . From figure 5 we can see that even with the scale factor Figure 5. Scatter plot of samples survived the constraints from (1)- (6) in the text. The horizontal lines show the 90% C.L. bound from XENON100 [71], future sensitivities at LUX [72] and XENON1T [73], respectively. The vertical dashed line is the sensitivity of monojet signals at 3σ significance at 14 TeV LHC with L = 3000 fb −1 .
with a high higgsino purity can not be covered by the XENON-1T(2017). In this case, our proposed monojet searches may be used to probe such a light higgsino-dominant neutralino with mass up to ∼ 160 GeV at 14 TeV LHC for L = 3000 fb −1 .
Conclusion
In this paper, we studied a strategy for searching light, nearly degenerate higgsinos in the natural MSSM. Our results showed that for L = 3000 fb −1 , the higgsino mass range µ ∼ 100 − 160 GeV favored by the naturalness may be probed at 3σ significance through the monojet searches at 14 TeV LHC. Also, this method can probe certain area in the parameter space for the lightest neutralino with a high higgsino purity, that cannot be reached by planned direct detection experiments at XENON-1T(2017). | 3,906 | 2014-02-01T00:00:00.000 | [
"Physics"
] |
Short-Term Electricity Consumption Forecasting Based on the EMD-Fbprophet-LSTM Method
Short-term electricity consumption data reflects the operating efficiency of grid companies, and accurate forecasting of electricity consumption helps to achieve refined electricity consumption planning and improve transmission and distribution transportation efficiency. In view of the fact that the power consumption data is nonstationary, nonlinear, and greatly influenced by the season, holidays, and other factors, this paper adopts a time-series prediction model based on the EMD-Fbprophet-LSTM method to make short-term power consumption prediction for an enterprise’s daily power consumption data. .e EMD model was used to decompose the time series into a multisong intrinsic mode function (IMF) and a residual component, and then the Fbprophet method was used to predict the IMF component. .e LSTMmodel is used to predict the short-term electricity consumption, and finally the prediction value of the combined model is measured based on the weights of the single Fbprophet and LSTM models. Compared with the single time-series prediction model, the time-series prediction model based on the EMD-Fbprophet-LSTM method has higher prediction accuracy and can effectively improve the accuracy of short-term regional electricity consumption prediction.
Introduction
In the new electricity market, the members of the electricity market need to remain stable in the market in order to make the highest possible profit, and this profit is closely related to the accurate forecasting of electricity consumption [1]. e demand for electricity consumption by customers is affected by many uncertainties, and an accurate forecasting model has an important role in improving the operation and planning of the power system, the main purpose of which is to help plan future power consumption and power load, so that a balance is achieved between power consumption and power production in order to reduce operating costs and resource waste [2]. In order to build a reasonably sized, safe, and reliable power system, electricity sales companies or agency platforms are now allowed to sell electricity to industrial or residential customers, optimizing the grid structure, enabling spatial segmentation of the electricity consumption market, and ensuring reliability of supply [3].
By improving the accuracy and reliability of short-term electricity consumption prediction, the response speed of the grid to unexpected situations can be improved, the operational efficiency of the transmission and distribution network can be improved, the power consumption planning of the grid can be refined, and daily maintenance costs can be reduced [4].
Current forecasts of electricity consumption are generally divided into short-term forecasts, medium-term forecasts, and long-term forecasts, with the medium-term and long-term forecasts mainly focusing on monthly and above time scales of electricity demand, while the short-term forecasts are for demand within a day [5]. Traditional forecasting methods are based on mathematical methods, such as regression analysis, ARIMA model, and exponential smoothing [6]. e autoregressive moving model (ARIMA) is often applied to short-term time series with strong regularity and periodicity, and literature [7] adopts the ARIMA model for short-term prediction and evaluation of a month's power load data in Dayton, and, by comparing the relative errors, the prediction value of the model is found to be more accurate. Reference [8] applied the exponential smoothing method for medium-term and long-term demand forecasting, which is suitable for large areas with relatively little uncertainty, and some seasonal factors can also be included in the model. ese methods are simple and easy to use, but when encountering nonlinear and unstable electricity consumption data, the forecast results are not highly accurate and prone to various problems [9]. Artificial intelligence methods have been proposed, which will effectively solve the accuracy problem in load forecasting, including BP neural networks (ANNs) [10] and support vector machines (SVMs) [11]. Reference [12] adopts the support vector machine (SVM) model to forecast the medium-term and long-term electricity consumption in Jibei region, taking into account the economic environment and the downstream environment of the industrial chain, through which the complexity of the calculation is reduced, the speed of the calculation is accelerated, and the accuracy of the prediction is improved. Reference [13] proposes an improved BP neural network prediction model, which effectively improves the convergence and prediction accuracy by batch-processing the data. Although a single intelligent algorithmic model has good adaptability to nonlinear and unstructured electricity consumption data and the accuracy of prediction can be improved to some extent by deeply mining the inherent patterns of electricity consumption data, its prediction results are difficult to promote the use, so many scholars use combinatorial models to improve the robustness of the model and the accuracy of prediction [14]. Reference [15] proposes a model for predicting regional electricity consumption based on gray prediction and stochastic forest combination method, which considers the interaction between electricity consumption and economic indicators. Reference [16] constructs a prediction model based on random forest (RF) and deep belief network (DBN) to simplify the structure of electricity prediction model by unbiased optimization identification of variables, which helps to improve the training rate and generalization ability of the model. Combinatorial forecasting method is greatly influenced by random factors, and multiple factors work together on electricity consumption, so preprocessing of data is needed before forecasting, and the fluctuating characteristics of electricity consumption data can be well analyzed by decomposition. Reference [17] proposed a short-term load prediction model based on GM (1, 1) and EMD combinatorial model, which better adapts to the randomness and periodicity of load and significantly improves the accuracy of prediction. In literature [18], the time series is decomposed by wavelet function, and different models are built for predicting the time series on different scales, and the complete prediction result is obtained by sequence reconstruction, which improves the prediction accuracy and the modeling efficiency. Reference [19] proposes a prediction model based on the combination of EMD and LSTM, which can be predicted by modeling each component and is more suitable for nonlinear electricity consumption prediction than the traditional single model.
Based on the shortcomings of existing studies, such as the complexity of processing complex data and the lack of general applicability of prediction results, this paper proposes a combined prediction model to predict short-term electricity consumption. Since short-term electricity consumption data is a nonlinear, nonstationary series consisting of multiple frequency superpositions, the volatility of electricity consumption data is the focus of research and is affected by a variety of external factors, such as daily, weekly, and seasonal cyclicality [20,21]. e previously proposed methods and models have greater complexity and uncertainty in predicting this type of data, so there is still a need for a more accurate method to target and obtain more valuable results. To this end, this paper proposes a new EMD-Fbprophet-LSTM short-term electricity consumption prediction model, which firstly uses the LSTM method to predict short-term electricity consumption and secondly uses the Fbprophet time-series model to predict electricity consumption based on the decomposition of electricity consumption by EMD. As a new and more advanced hybrid model, the EMD-Fbprophet-LSTM model takes into account the unique fluctuating characteristics of electricity demand on different time scales and the influence of factors such as weather on customer demand and provides lower forecast errors and better results when forecasting short-term electricity consumption of customers.
is study is a time-series forecast of short-term electricity consumption, with a forecast lead time of one day, taking full account of the temporal correlation between dynamic electricity consumption data. e LSTM has strong generalization ability, good learning ability for both large and small data sets, and strong advantages for the processing of nonlinear data, which can improve the accuracy of short-term power consumption prediction. e empirical mode decomposition (EMD) [22] is based on the different waveform data obtained from the electricity consumption data, and, according to the time series of the waveform data itself, it can smoothly decompose the nonlinear and nonstationary time series, which is usually decomposed into a small number of embedded mode function components (intrinsic mode functions, IMF) and a residual component, thus reducing the nonstationarity of the original data and the complexity of the time series even more, so that the periodicity and trend of the original data series can be revealed. Using the Fbprophet time-series model [23] to implement the prediction of the IMF component, the prediction results can be obtained quickly and accurately, the outliers in the time series can be handled effectively, and the seasonal and holiday factors in the time series can be taken into account. e final empirical evidence shows that the prediction of electricity consumption by combining the Fbprophet and LSTM method has a high accuracy, and the simulation results verify that it is an effective method for short-term electricity consumption prediction.
Based on the above, the important questions can be summarized as follows: (1) Disaggregation of the original short-term electricity consumption data using the EMD method (2) e Fbprophet forecasting model is used to forecast each part of the IMF, taking into account the effects of holidays and other factors, in order to obtain valid electricity consumption forecasts (3) Adopt LSTM model to forecast the short-term electricity consumption (4) Construct a combined EMD-Fbprophet-LSTM model to forecast short-term electricity consumption and compare the forecast results with those of ARIMA model and single Fbprophet model, LSTM model, and EMD-Fbprophet model to prove the validity of the model proposed in this paper e rest of the paper is presented as follows. Section 2 introduces the algorithmic principles of EMD, Fbprophet, and LSTM and constructs the EMD-Fbprophet-LSTM model proposed in this paper. Section 3 selects the electricity consumption data of an enterprise in Province Z for empirical study and compares and verifies the results to prove the accuracy of the prediction results. Section 4 gives the conclusion of this paper.
Principle of EMD Algorithm.
Empirical mode decomposition (EMD) is an adaptive time-series decomposition method that smooths the nonlinear time series x(t) into feature components with different feature scales, namely, the intrinsic mode function (IMF) component, and the residual component r(t). e decomposed resulting IMF represents the fluctuating components of different time scales implicit in the raw electricity consumption data, and its values and waveforms can well reflect the characteristics of the raw electricity consumption data. e residual term, on the other hand, represents the trend of the forecast series [24,25]. e basic steps are as follows: (1) Find the maximum and minimum points of the original signal x(t), fit the upper and lower envelope lines e max (t) and e min (t) of x(t), and calculate the mean values of e max (t) and e min (t), m(t): (2) Calculate the difference between the raw data and the mean of the envelope lines, d(t): (3) Determine the nature of d(t); if it is satisfied that the numbers of zero crosses and extreme points in d(t) are the same and the local maxima and minimal values, respectively, form envelope lines that are zero-mean, then d(t) is an IMF component. Otherwise, the above steps need to be repeated for screening. (4) Define residuals r(t):
Principles of the Fbprophet Algorithm.
e Fbprophet model is a time-series prediction tool proposed by Facebook in 2017, which carries out time-series prediction through time-series-based decomposition and machine learning fitting [26]. e Fbprophet prediction process consists of four parts: model building, evaluation of predictions, problem solving, and manual checking, which work in a sequential loop until a suitable predictive model is obtained.
e Fbprophet algorithm decomposes the time series y t into three parts, as shown in the following equation: where g t is the trend term, which represents the trend of the time series on a nonperiodic basis; s t is the seasonal term (period term); h t is the holiday term; and ε t is the error. By fitting these three items through the submodel, it can be reasonably applied to a variety of time-series predictions with regularity and can identify and adjust the anomalies in the data, effectively dealing with the jump points and periodicity of the time series, while the Fbprophet algorithm also takes into account the seasonal and holiday effects that are of concern to the prediction model and is a convenient and efficient time-series prediction tool.
Principle of LSTM Algorithm. LSTM (Long Short-Term
Memory) consists of an input layer, a hidden layer, and an output layer [27], which can effectively solve the problem of gradient disappearance or explosion due to the long time span of dependencies between information, learn and predict based on historical information, balance the temporal and nonlinear relationships of electricity consumption data, and obtain better prediction results. Figure 1 shows the network structure of LSTM.
Oblivion Gate.
e forgetting gate f t determines how much information can be passed from the previous cell state to the current cell state, with an output of 1 indicating that all information from the previous moment is retained and an output of 0 indicating that all information from the previous moment is discarded.
where f t is the oblivion gate, σ is the excitation function, taking values between [0, 1], w is the weight matrix, and b f is the deviation vector.
Input
Gate. e input gate i t updates the candidate information in the memory cell by activating the function σ to filter new input information and add it to the memory cell.
Mathematical Problems in Engineering
where i t and g t are the input gate, x t is the input vector, and b i and b c are the deviation vectors.
Update Cell
State. e output of the forgetting gate f t and the old cell state c t−1 of the previous moment form part of the updated cell state c t , while the other part consists of the output of the input gate i t and the memory cell candidate state.
where c t is the updated cell state and c t−1 is the old cell state at the previous moment.
Input Gates and Hidden Layer
Outputs. e output gate o t can be obtained by the excitation function σ. e output vector h t can be obtained by compressing and updating the cell state c t .
where o t is the output gate and h t is the output vector.
Model
Integration. e construction of a combined prediction model can combine the advantages of each single model and improve the prediction accuracy. In this paper, the weights of the models are determined using the variance method and are calculated as follows.
Calculate the variance corresponding to each prediction model.
Get the weights from the variance.
After deriving the weights, the respective predictions are multiplied by the corresponding predictions to obtain the combined predictions.
where F indicates the predicted result. F 1 , F 2 denote the separate predictions of the LSTM model and the EMD-Fbprophet model, respectively.
Model Construction.
After decomposing the time series by EMD method, the resulting IMF component can simplify the time-series forecasting model with a high degree of fit, but the lower-order IMF component is still highly volatile and cannot be simply discarded for noise reduction as it retains some of the information from the time series. Since short-term electricity consumption forecasts are influenced by complex external market factors, the Fbprophet model relies only on historical time series, it is difficult to utilize other external information related to the forecast target, and if used alone it will not achieve the desired forecast level due to insufficient information. Since the prediction accuracy of LSTM is affected by the selection of key parameters and the size of the dataset, for the predictive analysis of nonlinear time series, this paper proposes a combined LSTM-Fbprophet model for short-term electricity consumption prediction. Based on the advantages of LSTM neural network for long-time problem processing and EMD-Fbprophet algorithm for mutation point and periodic problem processing, the combined LSTM-Fbprophet algorithm can effectively improve the prediction accuracy. e modeling process is shown in Figure 2.
(1) e decomposition of the original time series into a number of IMF components and a residual component r(t) using EMD highlighting the local characteristics of the original data, which can well reflect the periodicity, trend, randomness, and other characteristics of the original data (2) Preprocessing the load data of the decomposed subseries to normalize the data integrating the prediction results, and obtaining the final prediction results
Data Description.
e dataset used in this paper is for the installation of smart meters at an enterprise in Province Z between January 1, 2019, and September 27, 2019. e sum of the users' daily electricity consumptions is 270 data samples (the data have been desensitized). To test the predictive power of the model, this paper splits the dataset into a training data sample and a predictive test data sample, using the former daily. e electricity consumption data trained the model and predicted the daily electricity consumption for the last 7 days. e mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE) were used as the indicators to assess the effectiveness of predictive models, comparative analysis of the Fbprophet model, and EMD-Fbprophet predicted results of the model.
Mathematical Problems in Engineering
In this paper, all algorithms of the proposed technique are implemented in Python 3.7.9 software.
Descriptive Analysis and Data Preprocessing.
As can be seen in Figure 3, there is a large volatility in regional daily electricity consumption data, and there are more external factors affected by changes in daily electricity consumption. Holidays have a greater impact on electricity consumption, and, during special holidays, such as around Chinese New Year, there is a significant trough in electricity consumption. Electricity consumption is significantly higher than weekend consumption, showing a cyclical variation on a weekly basis.
For missing data and anomalies, the average of the valid data before and after two weeks is used to fill in the missing and anomalous data. e preprocessing of the data does not remove data points such as holidays which cause significant changes in electricity consumption.
Experimental Results.
is paper uses the front part of the dataset as a training sample to predict the daily electricity consumption for the last 7 days; in order to prove the validity of the proposed model in the prediction model, this paper will longitudinally compare the prediction performances of ARIMA, LSTM, Fbprophet model, and the proposed LSTM-Fbprophet model to analyze the daily electricity consumption. e EMD method is used to decompose the short-term electricity consumption data after preprocessing to obtain waveforms formed by six different intrinsic modal functions (IMF) and a residual component (see Figure 4).
In Figure 4, the six IMFs are sorted according to their frequencies to show some of the periodicity of factors affecting the time series, reflecting the impact of noninfluential factors on the electricity consumption data at different scales. e higher frequency of the components in IMF1 and IMF2 can be seen as the high-frequency component of the original series and the more pronounced periodicity of the components in IMF3, which can be seen as the periodic component of the original series. e component frequencies in IMF4, IMF5, and IMF6 are low and can be considered as low-frequency components. e residual component Res, on the other hand, represents the long-term trend of the electricity consumption series.
In order to better test the accuracy of the proposed model, the ARIMA model, LSTM model, Fbprophet model, and the proposed model are used to predict the daily electricity consumption data for the last 7 days of an enterprise, respectively. e predicted results are shown in Table 1 and Figure 5. Among them, the error is positive when the predicted value is larger than the actual electricity consumption and it is negative when the predicted value is smaller than the actual electricity consumption.
Model prediction accuracy indicators used are MAPE, RMSE, and MAE, where MAPE reflects the overall level of deviation between the model prediction value and the actual value of the prediction test data sample, and the smaller the value of MAPE, the higher the prediction accuracy; RMSE reflects the degree of dispersion of error, and the smaller the value of RMSE, the better the prediction stability; MAE is the average absolute error, and the smaller the value, the higher the prediction accuracy. e models MAPE, RMSE, and MAE were obtained (see Table 2).
rough the comparison of the actual and predicted values and the statistical analysis of the error indicators, the following conclusions can be drawn.
First, the proposed model's MAPE, RMSE, and MAE are the smallest, which means that the model has better average forecast accuracy and stability than the ARIMA, LSTM, Fbprophet, and EMD-Fbprophet models.
Second, the RMSE value of ARIMA is the largest among the several models, indicating a moderate prediction performance. Fbprophet and EMD-Fbprophet models are more stable than ARIMA, and the LSTM model is second only to the model proposed in this paper in terms of accuracy. e prediction trend of the proposed model is basically consistent with the actual value, which has the highest stability and accuracy, and can better grasp the daily electricity consumption trend.
Conclusion
In this paper, a short-term electricity consumption prediction model based on the combination of EMD-Fbprophet and LSTM method is proposed. Firstly, the EMD method is used to decompose the raw data of regional daily electricity consumption, the subseries and residual series of low frequency and high frequency are obtained, and the influence of different components is distinguished to reduce the complexity, randomness, and nonstationarity of the raw data. e Fbprophet method is used to model predictions for each component. en short-term electricity consumption is predicted by a single LSTM model. Finally, the prediction results of the combined EMD-Fbprophet-LSTM prediction model are measured based on the weights obtained from the variance. In addition, in order to prove the validity and optimality of the EMD-Fbprophet-LSTM prediction model proposed in this paper, the EMD-Fbprophet-LSTM model and the prediction results of the traditional ARMA method with a single Fbprophet and LSTM model are compared and analyzed in the empirical analysis. e experimental results show that the fluctuations of the EMD-Fbprophet-LSTM optimized prediction model errors are relatively smaller, and, by distinguishing the effects of different components, the complexity, randomness, and nonstationarity of the raw data are reduced, which can effectively improve the prediction accuracy and precision, reduce the prediction errors, and have a good ability to accurately predict the short-term nonlinear electricity consumption data. Since short-term electricity consumption data are nonlinear data with strong volatility and instability and the EMD-Fbprophet-LSTM prediction model proposed in this paper can predict data with strong holiday effects and seasonal fluctuations well and can also handle outliers well, it can effectively reduce the prediction error and improve the prediction accuracy. erefore, the model can effectively forecast short-term electricity consumption, which is conducive to balancing demand-side management, guaranteeing basic electricity consumption, and helping power companies to rationally allocate power resources and providing them with more accurate decision support.
Data Availability e data were from State Grid Zhejiang Economic Research Institute and have been desensitized.
Conflicts of Interest
ere are no conflicts of interest regarding the publication of this paper. | 5,350.8 | 2021-04-12T00:00:00.000 | [
"Computer Science",
"Engineering"
] |
Attributes, Methods, and Frameworks Used to Evaluate Wearables and Their Companion mHealth Apps: Scoping Review
Background: Wearable devices, mobile technologies, and their combination have been accepted into clinical use to better assess the physical fitness and quality of life of patients and as preventive measures. Usability is pivotal for overcoming constraints and gaining users’ acceptance of technology such as wearables and their companion mobile health (mHealth) apps. However, owing to limitations in design and evaluation, interactive wearables and mHealth apps have often been restricted from their full potential. Objective: This study aims to identify studies that have incorporated wearable devices and determine their frequency of use in conjunction with mHealth apps or their combination. Specifically, this study aims to understand the attributes and evaluation techniques used to evaluate usability in the health care domain for these technologies and their combinations. Methods: We conducted an extensive search across 4 electronic databases, spanning the last 30 years up to December 2021. Studies including the keywords “wearable devices,” “mobile apps,” “mHealth apps,”
Background
Wearable technology, also known as wearable devices, includes smart electronic devices worn in close proximity to the surface of the human body.These devices can detect, analyze, and transmit information concerning body signals such as vital signs and physiological data, including step count and heartbeat [1][2][3].Smart wearable technologies and their high-performance microsensors are of growing importance for patient health monitoring and are being widely accepted into clinical use and trials [4][5][6][7].These technologies have the capability to amplify personal wellness and raise awareness in the spectrum of preventive health care.Consumers continue to rely on smart devices such as mobile phones and smartwatches to engage in healthy behavior [8][9][10].They also assist in the self-management of chronic conditions, preventive measures, and aftercare, for example, diabetes monitoring [11], rehabilitation [12][13][14], fall detection [15,16], wound healing [17], and even monitoring symptoms of long-term illness [18][19][20].Wearable technology further enhances the continuum of care within interdisciplinary communication and improves individuals' health and well-being, all in their natural mobile environment [3,21].
Commercial Wearables Versus Medical Wearables
The growing demand for health care technology, particularly wearable devices, has led to the proliferation of various medical and smart health care wearables.However, there is ambiguity in distinguishing between commercial consumer wearable devices and wearable medical devices.The European Union regulations [22] define medical devices as those intended for medical purposes such as disease diagnosis, monitoring, treatment, injury management, and physiological process modification; however, this scope does not include wearable technologies, such as smartwatches, smart bands, and mobile phone-based devices, designed primarily to provide users as tools for health monitoring and management.Fotiadis et al [23] defined wearable medical devices as self-contained, noninvasive devices with specific medical functions.Although a clear definition of wearable medical wearables remains elusive, these devices serve as a convergence point for both conventional medical device manufacturers and consumer-oriented companies aiming to enter the profitable medical market.The traditional distinction between medical and consumer-grade devices relies on the primary intention; however, we found that many commercial devices are being used opportunistically in health care and clinical trials.
Despite the expanding scope of wearable devices, unresolved concerns persist among general consumers regarding the safety, security, and usability of these devices [24][25][26][27][28]. Therefore, ensuring the fit-for-use of these technologies for specific users in clinical settings must be ascertained.The assessment of the usability of these technologies is critical to the success and adoption of wearable and mobile technology or the combination thereof.The identification and consideration of the appropriate attributes and methods for the measurement of usability as early on in the product development process can increase productivity, reduce errors, reduce user training and user support, and improve efficacy, thereby further broadening the acceptance of wearable and mobile technology by users [29][30][31].
Definition of Usability
In the literature, the definition of usability varies, with some studies equating it to assess a device's functionality, whereas others focus on aspects such as feasibility or performance.This ambiguity highlights the need for a comprehensive approach in measuring usability, considering users, devices, environment, and the actions users perform.The International Organization for Standardization (ISO) 9241 clarifies usability as "the extent to which a system, product or service can be used by specified users to achieve specified goals with effectiveness, efficiency, and satisfaction in a specified context of use" [32].It is important to recognize that usability extends beyond the immediate outcomes of use.Established standards such as ISO 9241 or other regulatory frameworks primarily view usability as a result of use, emphasizing attributes such as effectiveness, efficiency, and satisfaction.However, a holistic evaluation of usability attributes that goes beyond immediate outcomes contributes to a deeper understanding of user interactions with these technologies and their acceptance in everyday use.
For better adoption of wearables in combination with their companion mobile health (mHealth) apps in clinical settings, usability needs to be considered to safeguard the effectiveness, functionality, and ease of use of these technologies.Concerning the acceptance of wearable technologies, it has been advocated that the devices must be easy to wear, affordable, possess suitable functions, and be appealing to users [33][34][35].In such circumstances, designers, developers, and interdisciplinary researchers need to consider the development and use of such devices in a user-centered manner [36][37][38], thereby affirming that wearable technology is relative to the requirements of the users as it is a vital factor in the adoption of digital health apps and devices because it can be challenging for users owing to their health conditions.Furthermore, usability testing of these technologies allows researchers to understand how the wearable being developed meets users' requirements before being used in health interventions.
Exploring Key Attributes of Usability
Previous scientific literature disclosed the measurements of usability using different entities.These entities are defined as dimensions, components, scales, or factors of usability.According to Folmer and Bosch [39], these terms are analogous and hold the same meaning.Therefore, as defined by Wixon and Wilson [40], the term usability attribute is the characteristics of a product that can be measured.The most consistently reported usability attributes are effectiveness, efficiency, and satisfaction, which are part of the usability definition of ISO 9241-11:2018 [32,41].Existing reviews have focused on reporting the usability attributes of mobile apps in health care; however, the shortcoming of applicable attributes for wearables and their companion app poses a challenge in assessing the usability of these technologies.
Exploring Evaluation Methods of Usability
Usability assessment is instrumental in determining how well users learn and use technology to meet their goals.This includes the effectiveness and efficiency of a device and how satisfied the users are with the process.Therefore, different usability evaluation methods should be used to gather this information.Existing literature shows that different methods have been used for the testing of wearables such as field studies and laboratory experiments [42][43][44].Although laboratory experiments, field studies, and hands-on measurement are some of the most commonly used methodologies, these are sometimes difficult to apply and have drawbacks.The prevailing usability methods assess different facets of usability, each providing different data.Accordingly, the selection of methods plays a pivotal role in evaluating the desired attributes of usability.Previous reviews have investigated the usability of wearables [45][46][47] and mHealth apps independently [41,[48][49][50].These reviews examined the usability assessment of wearables or mobile apps according to specific use cases in the health care domain [51][52][53][54][55][56][57].Moreover, evaluation studies on the combination of the aforementioned devices were not taken into consideration.Research in this area continues to be fragmented, which demonstrates the importance of exploring further the requirements, functionalities, and capabilities of such wearable devices to enhance our comprehensive understanding of their use and acceptance.
Objectives
This study aims to survey the existing literature in the field of medicine and health care that reports on the usability of wearable technology, mHealth apps, or their combination.Our scoping review seeks to analyze the literature in three ways: (1) type (commercial or medical) and category (stand-alone or paired) of wearable devices and their frequency of use in studies; (2) medical use cases; and (3) usability evaluation of these technologies, specifically usability attributes, methods, and frameworks.
Framework
This study uses the framework developed by Arksey and O'Malley [58] for reporting on scoping reviews, following the recommendations for enhancement of this approach by Levac et al [59].We followed the five stages of the framework: (1) identifying the research question (RQ), (2) identifying relevant studies, (3) selecting studies, (4) charting the data, and (5) summarizing and reporting the results.In addition, the review followed the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) checklist to report the study selection process of the scoping review (Multimedia Appendix 1) [60,61].
Stage 1: Identifying the RQs
For our scoping review, we used the PICO (Population, Intervention, Comparison, and Outcome) model [62,63] shown in Table 1 to help us regulate our RQs, outline the search strategy, and identify relevant studies within the health care domain.However, for our scoping study, the control or comparison aspect of the PICO methods was eliminated because our focus was not on comparative studies or controlled exposure.This scoping review aims to accomplish its objectives by answering the following RQs: 1. RQ1: What type (commercial or medical) and category (stand-alone or paired) of wearable devices and their companion mHealth apps were implemented and how frequently were they used in the studies?The focus of the second stage of the Arksey and O'Malley framework [58] was to find the relevant studies that match the RQs and the purpose of the scoping review.We began the review with an extensive search using keywords related to the PICO model.However, this raised questions about the sensitivity and specificity of the articles, that is, retrieving and identifying relevant research topic publications.Therefore, redefining the search terms after the initial search added the advantage of prioritizing the sensitivity of the relevant article. We
Stage 3: Study Selection
For our scoping review, all types of articles ranging from journal articles to conference papers were considered, without restrictions on the period of publication.In line with the systematic review methodology, we formulated inclusion and exclusion criteria for this scoping review.The inclusion and exclusion criteria are provided in Textbox 1.This allowed us to reduce the number of papers that were included in the screening of titles and abstracts.Citavi (version 6; Swiss Academic Software GmbH) was used for the collection of the articles.
Textbox 1. Inclusion and exclusion criteria for the scoping review.
Inclusion criteria
• Language: English • Papers focused on wearables or a prototype of wearables that have used usability testing for their evaluation, where methods such as questionnaires, observations, experimental testing, or surveys were used • Papers focused on a mobile health (mHealth) app or a prototype of the mHealth app that used usability testing for its evaluation, where methods such as questionnaires, observations, experimental testing, or surveys were used
•
Papers that use either a wearable, an mHealth app, or both in a medical use case, for example, chronic diseases • Papers that use a user-centered design approach for developing wearables or mHealth apps
Exclusion criteria
• Inclusion criteria not fulfilled, for example, papers not written in English or not matching any of the secondary inclusion criteria • Papers with the theme or topic of augmented reality and virtual reality, which may also include usability studies (eg, Google Glass) • Papers that have only used audio and visual wearable aids (ie, without additional support from smartphones) • Papers purely focused only on the technical aspects, technical descriptions, or features of wearables or mobile apps or PDAs in the development and testing processes of materials; self-developed sensors; or wearable sensors such as accelerometers, gyroscopes, or inertial measurement unit
•
Papers that are focused mainly on medical professionals rather than patients, for example, describing algorithms or methods used for the optimization of viewing medical data (such as electrocardiogram and electroencephalogram) We followed the recommendations from Daudt et al [64] for interdisciplinary teamwork in scoping reviews: we incorporated reviewers from different disciplines and backgrounds such as health services research, usability engineering, and medical informatics.The reviewers were divided into 2 groups such that each group had members with diverse backgrounds and expertise.Furthermore, an expert not involved in the screening reviewed mismatched publications from the groups and made discrete decisions for the inclusion and exclusion of articles.Each team member independently reviewed the titles, abstracts, and full text of the publications assigned to them.Studies were considered for the full-text reading if the inclusion criteria were met and cross-verified among team members.
Stage 4: Charting the Data
At this stage, the data from the included studies were extracted.The review team collectively designed a structured data-charting format aligned with the RQs of the scoping review.Each team member individually extracted relevant characteristics from the included studies and adapted them to the data-charting format.Disagreements between the reviewers were resolved through discussions and feedback.The characteristics extracted from the included studies that are associated with the aim of this scoping review are as follows: (
Stage 5: Summarizing and Reporting the Results
To effectively summarize and organize the extracted data, a comprehensive search of the relevant literature was conducted to identify suitable articles to structure the examination and analysis.Two relevant literature sources were identified to fulfill our objectives.We aimed to find a suitable classification system that could effectively categorize various wearable devices.The classification proposed by Seneviratne et al [65], which provides a comprehensive survey of commercial wearable products grouped into 3 categories-accessories, e-textiles, and e-patches-served as a helpful tool for our analysis.In addition, we used the usability taxonomy hierarchy proposed by Alonso-Ríos et al [66] for our analysis.This taxonomy provided a comprehensive framework for organizing usability attributes in a logical and meaningful order.
We present our findings by integrating descriptive tables and graphical illustrations of the outcomes.These figures and graphics helped our analysis to directly connect the findings to the objectives of our review and identify the gaps in the literature.In our study, we illustrate the frequencies and percentages of the findings in coherent data visualizations, emphasizing the analysis and reporting of data and giving them a comprehensive meaning.
Eligible Studies
Our search yielded 382 records, including articles about wearables, mHealth apps, or their combination; research about the implementation of these technologies in medical use cases; and evaluations of their usability.Overall, 323 records were evaluated for the initial screening of titles and abstracts after eliminating duplicates.From these, 132 full-text papers were found, of which 62 were excluded, resulting in 69 studies whose data were charted per the study questions.Following the final text reading, a single study had to be excluded from this scoping review because it did not meet the predefined inclusion criteria, despite the presence of relevant keywords in the paper.The process of selection of articles for the scoping review can be seen in the PRISMA-ScR diagram shown in Figure 1.
Wearable Devices and Their Frequency of Use
Most studies (57/68, 84%) used a combination of wearables and mobile apps.Overall, 12% (8/68) of the studies used wearables in conjunction with other technological devices such as smartphones, computers, recording devices, or PDAs; however, these devices were used independently from the wearables.Furthermore, the data extraction indicated that two-thirds of the studies (45/68, 66%) used commercially available wearables for their evaluation studies, of which approximately half of the studies (21/45, 47%) used Fitbit (Fitbit Inc.) devices as their source of data tracking and collection.Our data further showed that only 11% (5/45) of the studies used wearable devices that were certified as medical devices.In addition, only 18% (12/68) of the studies used a self-developed wearable prototype and a mobile app for data tracking and monitoring.
From the included studies, 9% (6/68) of the studies reported using only wearables in their studies.Of these 6 studies, 5 (83%) used commercially available wearable devices such as Fitbit and Samsung Gear S3 (Samsung Electronics Co, Ltd), whereas 1 (1%) study reported using a self-developed wearable prototype.However, 7% (5/68) of outliers were detected where 60% (3/5) of the studies mentioned using only a mobile app; 20% (1/5) of the studies reported using only a smartphone; and in 20% (1/5) of the studies, smartphone was used as a wearable device by attaching a 3D-printed phone holder around the user's neck [67].Although this is typically not defined as a wearable, the outcome of this study proved imperative in determining the different devices and variables used for evaluation.We used a classification system consisting of 6 distinct groups to categorize the diverse use of wearable technologies and mobile apps (with, without, or a combination thereof).They are (1) only wearables (eg, stand-alone wearables such as Fitbit and Garmin [Garmin Ltd]), (2) wearables+companion apps (eg, Garmin tracker+corresponding Garmin mobile app), (3) smartphone as wearables (eg, smartphone used in close proximity to the skin to track physiological data), (4) wearables+connectivity (not companion) apps (eg, wearables paired with connectivity apps for Bluetooth connection and not for presenting data), (5) wearables+other technologies (eg, Garmin+laptops, recording units, and PDAs), and ( 6) others (only smartphone or only app).
The specified categories and the corresponding studies included in this review are presented in Table 2.
In most studies, the validation, accuracy, and certification of the used wearables were not thoroughly discussed, despite these aspects being considered essential in good research practices.
Although some studies briefly touched upon validation or accuracy, they did not necessarily indicate that the wearables had undergone certification, such as Food and Drug Administration approval or Conformité Européenne mark.Authors of the included studies often omitted reporting the inaccuracies and validation limitations of consumer-grade wearables, particularly when usability was of significant importance.Instead, the accuracy of wearables was often assumed based on the authors' validation of wearables' selection through peer-reviewed research and their alignment with traditional instruments for measuring health data.The list of included studies along with the extracted information can be found in Multimedia Appendix 3 [43,.
Most of the wearables (35/68, 51%) covered in the review were wrist worn, such as wristbands or smartwatches.However, only 9% (6/68) of the studies used multiple wearables, such as a smartwatch and chest belt or multiple wrist-worn wearables.Table 3 presents the data on the different categories of the types of wearable devices extracted from the included studies.More than half of the studies (48/68, 71%) deployed stand-alone mobile apps, which implies that users or patients collected health information using wearables and apps without sharing it with their professionals.Overall, 68% (46/68) of the studies determined that Bluetooth connections were the primary means of connectivity for wearables and the mobile apps that accompanied them.Data from the extracted studies revealed no linkage between the technologies; hence, outliers (4/68, 6%) were also recognized.
Medical Use Cases and Reported Data
Our data showed that approximately half of the studies (32/68, 47%) focused on participants with chronic illnesses or disorders, indicating the importance of wearable technologies in managing and monitoring chronic conditions.The remaining 53% (36/68) of the studies encompassed various other medical use cases such as wellness, mental health, rehabilitation, sleeping disorders, otolaryngology, and preventive measures.
Most studies (40/68, 59%) routinely collected physiological data from users or patients.The most commonly collected health data revolved around physical activity, encompassing metrics such as steps taken, stairs climbed, and inertial measurement units.Approximately 35% (24/68) of the health data gathered in the studies focused on cardiac measurements, including electrocardiogram, heart rate variability, heart rate, or blood pressure.In addition to physical activity and cardiac measurements, other data types were also collected, albeit to a lesser extent.Sleep data accounted for 25% (17/68) of the collected information, and brain activity data, such as electroencephalogram recordings, constituted 4% (3/68) of the data.Furthermore, biosignals, including measurements such as skin conductance and respiration rate, were captured in 18% (12/68) of the studies.Other health data and observations such as acoustics, posture, blood glucose, and weight were also monitored in approximately 21% (14/68) of the cases, indicating the broad range of parameters that wearables can track and analyze.
In addition to physiological data, a small proportion of the studies (4/68, 6%) included in our analysis also collected nonphysiological data that were not directly linked to health parameters.These data contained various variables such as the number of cigarettes consumed per day, location data, and dietary intake.Although not directly related to traditional health measurements, the inclusion of such data provides a broader context and enables a more holistic understanding of individuals' behaviors and lifestyle factors.
Usability Attributes
The studies included in this review used various terms such as usability characteristics and attributes, which we consider to be synonymous.Therefore, we applied the usability attributes from the extracted data to the usability taxonomy [66].We found that satisfaction (34/68, 50%), ease of use (27/68, 40%), user experience (16/68, 24%), perceived usefulness (18/68, 26%), and effectiveness (15/68, 22%) were the most commonly used attributes for assessing usability.Although user experience is acknowledged as the overarching term encompassing XSL • FO RenderX usability, conceptualizing user experience as a facet of usability captures the comprehensive perception arising from interactions with devices.This extends beyond the mere use of the device, encapsulating the entirety of the experience or the anticipated use of the technologies.Furthermore, we identified 32% (22/68) of the studies that simply reported usability or perceived usability.Moreover, our findings further indicate that out of the 29 identified usability attributes, 6 (21%) can be classified as quality attributes.Table 4 shows the mapping of the attributes identified in the review to the attributes defined in the usability taxonomy.These particular usability characteristics possess qualities that are directly related to the overall quality and performance of the technologies used in the studies.Table 5 presents the quality and product attribute matrix of the attributes ascertained in the review and the defined attributes from the ISO norm 25010 [134].A detailed explanation of the different attributes in Tables 4 and 5 can be found in Multimedia Appendix 4 [66].a The rows list all the usability attributes identified in the scoping review and the columns list the first-level usability attributes from Alonso-Ríos et al [66], with each checkmark symbol indicating a match based on their description and their sublevel attributes.The last column lists the number of studies using the term from that row.
Compatibility
Performance efficiency Functional suitability The rows list all the attributes identified in the scoping review and the columns list the quality and product attributes from ISO norm 25010 [134], with each checkmark symbol indicating a match based on the description of the attributes.The last column lists the number of studies using the term from that row.b Overlapping attributes also identified as usability attributes.
Efficiency
In addition, during the data extraction process, we obtained insights into the elements and factors that affect the evaluation of usability.Among the 68 included studies, 52 (76%) reported these elements and factors, which played a crucial role in shaping and guiding the measurement of usability.Notably, acceptance (21/68, 31%) emerged as the most commonly used element or factor in assessing usability, indicating its significance in understanding users' acceptance and adoption of wearable technologies.
Usability Evaluation Methods and Frameworks
Only 12% (9/68) of the studies outlined using some sort of framework for usability evaluation.User-or human-centered design (7/68, 10%) was the most commonly used framework.Our findings revealed that more than half of the studies (37/68, 54%) collected data using the mixed methods approach.Only 15% (10/68) of the articles used only qualitative methods.These data collection methods included interviews, focus group discussions, thinking-aloud protocols, cognitive walkthroughs, open-ended discussions, Wizard of Oz, and free-text writing.Approximately two-thirds of the studies (21/68, 31%) used quantitative approaches for data collection during evaluation studies.The System Usability Scale (SUS) outnumbered other usability questionnaires (17/68, 25%) such as the Mobile Application Rating Scale, Net Promoter Score, Single Ease Question, NASA Task Load Index, and Technology Acceptance Model.However, a large percentage (21/68, 31%) of the articles used self-developed surveys or self-reporting questionnaires.Only one-fourth of the articles (16/68, 24%) further implemented statistical analysis including task completion, number of errors, descriptive statistics, or Google Analytics for the assessment of usability.Consequently, only a small proportion (3/68, 4%) of the included studies performed heuristic evaluation as a form of expert evaluation.
Principal Findings
Our data suggest that the evaluation of wearables for medical purposes was largely conducted without direct integration with mobile apps.Although some studies used smartphones as a means of connecting with the wearables, users were not assigned companion apps for data viewing.This limits the analysis and data visualization capabilities of the data collected within the studies.Wrist-worn devices were the most common type of wearables identified in the studies, indicating the convenience XSL • FO RenderX of using this type of wearables for measuring physical activities in a research setting.We also found that most studies (21/68, 47%) reported the use of consumer-grade fitness and activity trackers from Fitbit, and only a handful of the studies (5/68, 7%) implemented medical-grade wearable devices.A small number of the studies (10/68, 15%) investigated the data collection and use of the wearable in the aspects of aftercare of patients, wellness, and rehabilitation.
We noted the absence of standards or guidelines to facilitate the analysis of the usability of wearables, mobile apps, or their combination.Although user-and human-centered design frameworks were mentioned in a few studies (7/68, 10%), they are guiding the design and development of systems and devices focusing on users and their needs but not the usability of these devices.Despite the fact that many wearable technologies were included in the study, no usability evaluations of multiple devices, the combination of devices, or multidevice interfaces were reported.
Only a little more than one-third of the included publications (22/68, 32%) in our review explicitly reported the measurement of usability or perceived usability.Some studies (8/68, 12%) primarily focused on assessing the measurement of usability or perceived usability as user perceptions of the devices, attitudes, and compliance using different qualitative or quantitative methods [71,89,91,95,97,98,102,129].However, it is worth noting that these studies encountered a challenge in clearly differentiating the evaluation of the usability of the wearable device from that of the accompanying mobile app.Consequently, the intended purpose of the evaluation may have been limited in these studies.Therefore, we address the term usability, a broad term that encompasses various factors including technology and user acceptability.Studies might have reported on usability alone either due to missing expertise or due to a high-level summarization of various aspects they investigated.To help mitigate this, we incorporated and synthesized a set of attributes or subattributes to measure the capability and performance of a system based on the extracted data.
Our analysis showed that a subset of usability studies lacked testing with the intended target group and instead relied on healthy adults as participants.Despite the absence of explicit acknowledgment of this limitation in the included studies, it raises concern regarding the extent to which the devices and apps under investigation adequately address the unique needs and requirements of the target users, particularly individuals with chronic health conditions.This observation is in line with the findings reported in previous studies [135][136][137][138][139][140][141][142][143][144], emphasizing the concern regarding the devices and apps under investigation that adequately meet the unique needs and requirements of the target users.
Wearables
Most of the studies (45/68, 66%) in our review used consumer-grade wearables.This matches the observations of other studies [145][146][147][148][149][150] that investigated commercially available wearables and reported a wide variety of purposes, ranging from digital diagnostic tools to sports tracking to remote monitoring.Niknejad et al [151] and Ferreira et al [152] reported that consumer-grade wearables have been used to foster self-awareness among users.In contrast, we observed that the studies using consumer-grade wearables in our corpus focused on their use for monitoring chronic conditions such as diabetes, obesity, cardiology, and cancer.
We found that wearables are gradually being used more widely in health care and clinical settings.As stated in the previous paragraph, this is true for consumer-grade wearables such as Fitbit, Jawbone, Apple, and Garmin [153][154][155][156][157].However, concerns about the safety, reliability, and accuracy of these devices persist.In their work, Piwek et al [146] raised concerns about wearables in terms of user safety, emphasizing the need to better address the reliability and security of the data collected from these devices.Considering the inherent lack of emphasis on user safety in consumer wearables, it is imperative to acknowledge the importance of adhering to standard safety and privacy protocols.This includes ensuring ethical transparency and providing appropriate education to users regarding the privacy and information security risks they may encounter when using such devices [24,158,159].In addition, the use of consumer wearables in health care settings remains somewhat ambivalent at present [160,161].Although our review did not specifically address these concerns, we acknowledge that these factors significantly affect the usability of wearable technologies, whether used independently or with companion mHealth apps.Similar to Piwek et al [146], who pointed out acceptance challenges of wearables concerning safety and security, we believe that a structured framework with clear definitions and well-defined methods would allow bringing wearables into more diverse practices in the health care system, encouraging a broader adoption and implementation of use cases with high and tested usability.
Studies by Niknejad et al [151], Dimou et al [162], and Yang et al [163] proposed different categorization approaches for wearables, considering factors such as industry relevance (eg, health care or fashion) or wearable placement on the body.However, owing to the wide variety of wearables available in the market, establishing a standardized classification or hierarchy for these different types of wearables becomes challenging.Thus, to help designers and developers, a standardized classification or hierarchy would be helpful when selecting wearables for specific use cases.
Usability Attributes
Many studies in our corpus did not explicitly state the usability attributes they evaluated.Some mentioned generic terms such as usability or user experience, but did not define them further for their specific cases.As we have argued, more specific usability attributes can facilitate the development of more appropriate requirements and clearer identification of problems in usability studies.This matches observations in related areas.Meyer et al [164] analyzed usability evaluation practices in wearable robotics and recommended better distinguishing between the different usability dimensions and including qualitative measures for identifying a wider range of usability issues.Chiauzzi et al [139] examined the use of wearable XSL • FO RenderX devices for long-term chronic disease management.Patient concerns regarding technical difficulties and the appeal of the devices were identified, but their investigation did not address usability attributes such as device comfort and usefulness.Furthermore, the authors emphasized the importance of wearables being perceived as usable and generating comprehensible data to facilitate wider adoption among patients.
Among the 29 identified attributes in our review, 6 (21%) attributes were found to be more suitable for capturing the quality or product-related aspects of the technologies investigated in this study (Table 5).However, determining the most appropriate attributes for wearables and their associated mobile apps can be challenging because of the potential overlap between the product and inherent attributes, such as effectiveness and satisfaction (Table 5).This finding is consistent with Bakhshian and Lee [165], who argued that consumers' attitudes and purchase intentions toward wearable technology are influenced by both product attributes and inherent attributes, including functional, expressive, and esthetic characteristics.In contrast, other studies have explored the design attributes and their influence on user interactions and acceptance of different types of wearables for specific use cases, such as electroencephalogram systems [166], autism spectrum disorders [167], sports applications [168], and haptic feedback wearable robots [169].The importance of assessing usability based on user interactions with wearable devices and their associated app remains crucial, amid the emphasis on the design and quality attributes of wearables.
Our data highlight the importance of considering supplementary attributes such as wearability, perceived usefulness, and connectivity when evaluating individual wearables and companion mobile apps.Consistent with our findings, the existing literature also emphasizes the significance of incorporating auxiliary attributes beyond the conventional usability factors such as effectiveness and satisfaction to enhance the acceptance of wearable devices.The aforementioned supplementary attributes identified in the literature include characteristics such as comfort, user-friendliness, affordability, useful features, and appealing design [33][34][35]136].It is imperative to incorporate these attributes into the evaluation process to ensure comprehensive assessments of usability and user acceptance in both wearables and companion mobile apps.Although a few studies provide a general overview of wearable attributes related to design and product quality, there is limited research that specifically focuses on the usability attributes of wearables.Although some reviews have identified specific usability attributes for mHealth apps used in various use cases [41,[170][171][172][173][174][175][176], these are insufficient when evaluating the combined use of wearables and companion apps because of the complex and multifaceted features and interactions involved.
Our results revealed diverse informal terminology used to describe usability, performance, and quality aspects of the technologies examined in the studies.This variability in terminology posed challenges in accurately distinguishing and classifying the terms based on their usability characteristics.We adopted an existing usability taxonomy from the literature to address this issue and ensure consistency in data interpretation [66].
Usability Evaluation Methods and Frameworks
Our analysis revealed that only 9 studies incorporated the userand human-centered design framework in the design and development of prototypes.These studies specifically targeted specific user populations and assessed usability attributes such as satisfaction, ease of use, and effectiveness as part of their evaluation process.Although usability frameworks are available individually for the design and development of wearables and mobile apps [32,[177][178][179][180][181][182], a usability evaluation framework for the combination of these technologies or multi-interface devices is unavailable.
In our scoping review, most of the included studies (57/68, 84%) used qualitative methods, with interviews being the primary method.This corresponds with other studies reporting on evaluation methodologies [183][184][185].A survey on the evaluation of physical activity apps highlighted that a substantial number of studies specifically used a mixed methods approach, including randomized controlled trials, to assess the acceptability and evaluate the usability of wearable technologies, with or without companion mobile apps [186].This approach has gained popularity because of its comprehensive nature and ability to capture diverse perspectives.Among the combinations of methods used, questionnaires and interviews have emerged as commonly used techniques [75,[187][188][189].
Among the 68 studies included in our review, only one-third (20/68, 31%) used a standardized usability questionnaire to evaluate perceived usability.These questionnaires comprise a predefined set of questions presented in a specific order and format, with established scoring rules based on respondents' answers [190].The SUS questionnaire [191] was used most frequently among the studies analyzed.Although SUS was originally designed as a generic tool for usability assessment across a broad range of digital interfaces and software apps, it may not include items tailored to the specific characteristics and challenges posed by wearable technology.Wearables often involve prolonged and continuous interaction with the user, making aspects such as device comfort and user experience crucial; however, these aspects are not comprehensively addressed by the SUS.Researchers have proposed different adaptations of usability questionnaires tailored to assess the usability of wearables or mobile apps [192][193][194].Although this helps to better evaluate the particularities of wearables and mobile apps, they lack items assessing novel usability considerations such as ergonomics, comfort, real-time data feedback, and interaction with the wearable independently or combined with their associated mobile app, which has been identified as important factors by studies [33,73,195,196].The investigation of these aspects, which are crucial for most systems and apps, has been limited and partial.These observations may be attributed to various factors, including inadequate awareness of available usability questionnaires, the perception that these questionnaires do not align with their specific study, or the belief that the items or constructs within the questionnaires do not adequately reflect the purpose of their evaluation.
Concluding Analysis
We have shown that health care professionals and the medical technology industry acknowledge the importance of high or XSL • FO RenderX adequate usability in new medical equipment, including wearables and mobile apps.In addition, our results highlight the shortcomings in the evaluation and reporting of usability for wearable technologies, necessitating further research on human factors and usability.Literature reviews emphasize concerns regarding the lack of standardized study methodology reporting, guidelines for evaluating usability, and the absence of frameworks or theories for designing comprehensive usability assessments [151,[197][198][199].According to the reviews conducted by Khakurel et al [27] and Keogh et al [144], the current literature lacks a comprehensive usability evaluation method that effectively addresses usability issues throughout the entire life cycle of a wearable device, from the early development stages to product release.Considering the significance of reliability and wearability in wearable devices, it is imperative to establish traceability in the usability evaluation process.Although researchers are actively engaged in assessing usability, further research is required to identify potential usability attributes, develop suitable evaluation methods and frameworks, and successfully integrate these effective assessments into practice.
Limitations
The goal of this scoping review was to investigate wearable devices and their frequency of use in studies as well as their combination with mHealth apps within the medical domain.Our findings may not completely capture the breadth of usability attributes and their effectiveness in wearables across different contexts.Wearables and their companion apps have demonstrated utility in various use cases and recreational activities, including industrial settings, gaming, museums, and entertainment.By limiting our search to health care-related keywords, we may have excluded valuable insights and perspectives from these alternative domains.Future research could broaden the search criteria to include diverse contexts and use cases beyond health care.This will allow for a more holistic exploration of the potential and effectiveness of usability attributes across different industries and settings.This study did not aim to synthesize evidence on the effectiveness of usability evaluation methods.Instead, it focused on capturing the diversity of the available literature, encompassing various objectives, critical usability measures, and methods.Consequently, this study primarily serves as an exploratory investigation and provides suggestions for future research in the field.
Conclusions
Our scoping review sheds light on the types and categories of wearable devices, frequency of wearables used in the medical context, their use cases, and the evaluation of their usability.With a wide array of wearables and mHealth apps available, health care providers and manufacturers face the challenge of selecting devices and apps that are effective and user-friendly.The evaluation of usability is crucial for ensuring user engagement and the success of these technologies.As our scoping review shows, there is a lack of standardized frameworks for classifying usability attributes and their subattributes as well as structured evaluation guidelines for wearable technologies.This gap in usability and user experience research hinders the understanding of strengths and limitations in the field of wearable technologies.Therefore, further research is needed to address these limitations and enhance the comprehension of researchers in this field.
Multimedia Appendix 2
Search strategies for the 4 databases.
Multimedia Appendix 3
List of the included studies and extracted information.
Multimedia Appendix 4
Short description of the different attributes in Tables 4 and 5.
Figure 1 .
Figure 1.PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) flow diagram of the selection process for the scoping review.
Table 3 .
Categorization of the type of wearable devices according to the classification of wearable devices by Seneviratne et al[65] ordered by their frequency of use in studies (n=68).Studies, n (%) Devices Description Categorization of the type of wearables 26 (38) Wrist bands Wrist-worn devices with fitness tracking capabilities or other functionalities, generally without a bands, Upper arm bands, e-Patches, Sensor patches Study includes >1 wearable device (any type) >1 wearable device in the study 5 (7) Straps Chest straps, belts, upper arm bands (in contrast to wristworn bands), or knee straps equipped with sensors for health tracking or other functionalities Other accessories 5 (7) Smart garments Main clothing items that also serve as wearables, such as shirts, pants, and undergarments epatches that can be adhered to the skin for either fitness tracking or haptic applications e-Patches 3 (4) Wrist bands, Upper arm bands, e-Patches, Sensor patches Does not fit the categories Outliers 2 (3) Foot or hand-worn Shoes, socks, insoles, or gloves embedded with sensors e-Textiles 1 (1) Smart jewelry Jewelry designed with features such as health monitoring and handless control Other accessories a e-tattoo or e-skin Tattoos with flexible and stretchable electronic circuits to realize sensing and wireless data transmission e-Patches -Smart eyewear Spectacles or contact lenses with sensing, wireless communication, or other capabilities Head-mounted devices -Headsets or earbuds Bluetooth enables headsets or earplugs.Sensor-embedded hats and neck-work devices are also found in research products Head-mounted devices a Not available.
Table 1 .
The PICO (Population, Intervention, Comparison, and Outcome) method applied to our review.
Table 2 .
Wearable devices, mobile apps, and their combination along with their frequency of use in studies (n=68).
Table 4 .
[66]ix mapping of the attributes identified in the scoping review and the usability taxonomy[66]a .
Table 5 .
[134]ty and product attributes identified in the scoping review that match the attributes from the International Organization for Standardization (ISO) norm ISO/International Electrotechnical Commission (IEC) 25010[134]a . | 9,403.8 | 2023-08-25T00:00:00.000 | [
"Medicine",
"Computer Science"
] |
GaN Based HEMT Power Amplifier Design with 44.5dBm Output Power Operating at 5-7GHz
The next-generation wireless communication systems including satellite, radar, and mobile communications need application-specific power amplifiers that can operate at very high frequencies and high power with the overall minimum power consumption from the system. To meet such stringent requirements there is a rising interest in amplifier designs based on GaN transistors. This paper presents an improved design of a high power amplifier based on GaN HEMT transistor operating at the frequency band 5GHz – 7GHz with optimized output power level. The presented design is based on a 12 Watt Discrete Power GaN on SiC HEMT from TriQuint. In this manuscript, we have considered the stability of the amplifier for the whole operating frequency band, its input and output matching impedance, gain, and maximum output power. The design of the Radio Frequency (RF) power amplifier and its overall performance are carried out using an advanced design system (ADS). The simulation results of the device stability and the output power level achieved provides a good comparison with the parameters and specifications of the device used. For better correlations in the simulation results and measurements, the accuracy of passive element designs are also considered. The simulation and experiment results show that the designed high power amplifier has achieved an output power level of 44.5 dBm at 1 dB compression point.
INTRODUCTION
ower amplifier is considered a key module for any mobile or wireless communication system [1]. Therefore, its stability at the operating frequency band, output power level, and the Power Added Efficiency (PAE) are always considered during its design. The performance of many semiconductor devices can provide a limitation over various operational frequencies thereby reducing the performance of the power amplifier required for the specific application. The technologists have developed high-performance materials to handle the high communication domain.
GaN-based materials can tolerate high power density. This property not only allows the development of micro devices with similar output power performance but also provide higher impedances as well. The availability of higher impedance makes it easier for the circuit designer to match the impedance of the system which reduces extra cost requirements and the complexity such as required by the conventional materials like GaAs. Furthermore, the property of high voltage can greatly reduce the requirement of voltage conversion which may lead to high power-added efficiency. Hence the overall cost of the system design will also be reduced.
RELATED WORK
The careful design of the power amplifier make it capable and efficient for operating in wideband applications at higher frequency. The optimized power efficiency and output power levels can improve the amplifier's performance that will lead to improving the system's efficiency with the limited power conditions especially for those operating in the aircraft and space environments. Moreover, this wide band operation can also be very useful for future 4G/5G mobile communication systems. Due to the promising electrical properties of GaN HEMT power amplifiers, it is considered to be an appropriate choice of use for high thermal conditions and high operating voltages [5].
The mobile communication systems and radar systems need an output power level higher than 20W [8]. The performance of GaN is far superior to the GaAs both in terms of output power and power-added efficiency operating at the frequency bandwidth 1GHz to 12GHz. AlGaN/GaN technology-based power amplifier biased at 20V for the X band application provided an output power between 21W to 28.5W for the frequency range from 8-10.5 GHz . The peak performance of this amplifier design provided an output power of 30W for the frequency ranging 8.5-9GHz [6,9]. A 10W power amplifier achieved an output power level of 42.03dBm at 2.4GHz [9]. In one application of a GaN based amplifier also achieved a highly efficient and stable design which attained 35dBm output power with a wide band of 30 to 500MHz [11]. In another work, GaN material based amplifier achieved an output power level of 20W for radio frequency applications [7]. In another work supported by the European Defense agency GaN HEMT amplifier achieved an output power level of 46dBm at the drain bias voltage of 25V. Further, at 9GHz when the bias voltage was increased to 32V the achieved output power reached the level of 47.7 dBm. The large-signal model design of the power amplifier presented in [12,13] achieved an output power of 41.43dBm while operating at the frequency range of 1-3GHz. The drain bias voltage was set to 28V. Using the GaN-based power devices and by setting the drain bias voltage to an appropriate level the optimized output power levels can be achieved with better power-added efficiency.
METHODOLOGY
The major steps considered for designing a power amplifier on a 12 Watt Discrete Power GaN on SiC HEMT from TriQuint to achieve an optimized output power include. (1) Calculating the stability of the amplifier at the given frequency band, (2) Impedance matching network design, (3) Power amplifier characterization, and (4) Design optimization.
Stability Factor
The circuit shown in Fig. 1 is designed to obtain the bias point for the amplifier, the DC IV characteristics of the device are obtained as a drain to source voltage (VDS) from 0V to 50V is varied and the corresponding drain to source current (IDS) values are obtained respectively.
Biasing Network design
Drain and gate biasing networks are designed using a microstrip substrate [14], where the physical and substrate parameters are measured in LineCal, the center frequency was set at 6GHz. The measured values of the biasing networks are summarized in Table 1.
Stability vs Frequency
The next step of the amplifier design is to evaluate the stability of the device with the frequency for maximum gain and maximum gain matching impedances (Fig. 2) for the load and source [16]. The RF frequency selector is set to 6GHz and then the Sparameters, stability factors, maximum available gain, and stability circles are calculated through simulation. The stability of the amplifier is very essential and the amplifier must be stable for the whole operating frequency band otherwise the amplifier will be an oscillating circuit [17,18,19,20]. The scattering parameters are calculated to evaluate the stability, it can be calculated by the following equation [15].
It can be seen that K > 1 in equation (1). These parameters can be calculated using the Advanced Design System (ADS) [13]. In Fig. 3 stability factor K, and the Geometric stability factors µ_source and µ_load are found to be greater than 1 showing the amplifier is unconditionally stable from 5GHz-7GHz. If either mu_source or mu_load is K>1, the circuit is unconditionally stable.
SIMULATION RESULTS
Design and simulations of the power amplifier are carried out using the ADS. The simulation results of the device stability and the output power level achieved provides a good comparison with the parameters and specifications of the devices used. Fig.4 shows the maximum available gain, associated power gain, and dB (S21) when input and output networks are matched. 5 shows the forward transmission (S21) forward transmission is a signal at port 2 for an input signal for port 1, and the reverse transmission signals showing S12 = 7dB for the 5GHz to 7GHz and S12 reverse transmission of -35dB, Fig. 6 shows the constant voltage wave ratio. Table 2 in terms of operating frequency and the output power levels.
CONCLUSIONS
Power amplifiers are considered to be a vital part of any modern communication systems. GaN-based HEMT power amplifier design can provide better output power levels to meet the high operating voltages requirements. This paper presents an improved design of a high power amplifier based on GaN HEMT transistor operating at the frequency band 5GHz -7GHz with optimized output power level. The presented design is based on a 12 Watt discrete power GaN on SiC HEMT from TriQuint. In this manuscript, we have considered the stability of the amplifier for the whole operating frequency band, its input and output matching impedance, gain, and maximum output power. The design of the RF power amplifier and its overall performance are carried out using the ADS. The simulation and experiment results show that the designed high power amplifier has achieved an output power level of 44.5 dBm at 1 dB compression point. | 1,908.2 | 2021-10-01T00:00:00.000 | [
"Engineering",
"Computer Science"
] |
Mechanical Properties and Strength Characteristics of Rock–Coal–Rock Assemblages under Different Peripheral Pressures
: To investigate the deformation and damage characteristics of internal coal bodies of small pillars under different pressures, rock–coal–rock assemblage samples were subjected to the conventional triaxial compression test to analyze the mechanical behavior characteristics under different pressures. The results showed that, with the increase in peripheral pressure, the peak strength and modulus of elasticity of the assemblage specimens increased, the range of fracture compaction stage gradually decreased, and the specimen was gradually transformed from brittle to ductile. With an increase in peripheral pressure, the residual strength gradually increased, and the strength decay coefficient gradually decreased. The strength decay coefficient decreased the most at 0–10 MPa, and this decrease slowed down after exceeding 15 MPa. When the peripheral pressure was 0 MPa, the damage degree of the coal pillar was larger. With the increase in peripheral pressure, the number of cracks in the coal column increased, the damage degree increased more, and mixed damage characteristics of tension–shear were found. Based on the Hoek–Brown criterion, the strength criterion applicable to the specimen of rock–coal–rock combination was obtained through numerical fitting iteration, which provides an experimental and theoretical basis for realizing the stability control of small coal columns.
Introduction
With the gradual depletion of shallow mineral resources, resource development is constantly moving towards deeper parts of the earth, and the exploitation of kilometer-deep wells has gradually become the new normal of resource development [1,2]. In recent years, a large number of engineering practices have proven that the destruction of coal-rock is not only affected by the respective mechanical parameters of coal rock but also related to the structure of the coal-rock assemblage. The top plate, coal pillar, and bottom plate together form a rock-coal-rock assemblage, a ternary body mechanics equilibrium system. With the optimization of mining methods, its stress state is constantly changing [3]. The damage to the rock-coal-rock assemblage is not only affected by the damage to coal-rock monomers but also by the structure of the rock-coal-rock assemblage. In the high-stress environment in deep parts of mines, many disasters are essentially the result of the overall destructive destabilization of the rock-coal-rock assemblage system [4]. The deformation and damage characteristics of small coal pillars in deep parts of mines are a scientific problem that urgently needs to be solved.
At present, many scholars at home and abroad have carried out uniaxial and conventional triaxial compression tests on single rock bodies, coal bodies, and coal-rock binary and ternary combinations, and have conducted in-depth studies on the deformation and damage of coal-rock binary and ternary combinations. Liu et al. [5] conducted uniaxial and triaxial compression tests at 8,16, and 25 MPa on coal-rock monoliths using MTS815 to investigate the strength and deformation characteristics of coal-rock under different peripheral pressures. Zheng et al. [6] analyzed the effect of the number of layers on the compressive properties of coal-rock binary assemblage through uniaxial compression experiments. They used a stress monitoring system, DIC, and acoustic emission system to collect and analyze the stress-strain characteristics, the evolution of the surface strain field, and the acoustic emission characteristics during the experimental process. Weijian Yu et al. [7] analyzed the loading damage law of rock-coal-rock assemblage with different height ratios using a uniaxial loading test. Zhu et al. [8,9] used computerized tomography and X-ray scanning to analyze microscopic defects in concrete specimens, thereby predicting and identifying changes in the strength properties of concrete and reinforced concrete structures. Chen Guangbo et al. [10] carried out axial compression tests on 19 binary and ternary composites with different coal-rock ratios and combinations to investigate their effects on the mechanical properties and damage mechanisms. Zuo Jianping [11] and Song Hongqiang [12] investigated the post-peak progressive damage characteristics of rock-coal-rock assemblages using a nonlinear model and a stress-strain relationship model and examined the brittleness characteristics of rock-coal-rock assemblages through uniaxial and triaxial tests. Guo Dongming et al. [13], Dou Linming et al. [14], Liu Bo et al. [15], Fa et al. [16], and Liu et al. [17] conducted uniaxial compression tests on coal-rock monoliths and their binary assemblages to analyze the mechanical properties of the assemblages and the positive correlation between the strength of the intermediate coal body and the overall strength. Yang YJ et al. [18] and Liu QS et al. [19] investigated the deformation and damage characteristics of coal-rock binary assemblies under conventional triaxial action. Zuo et al. [20] analyzed the deformation and damage characteristics of rock-coal-rock assemblies with a weak coal inclusion by means of uniaxial and triaxial tests, and Guo et al. [21] analyzed the effect of different coal thicknesses on the mechanical behavior and damage characteristics of rock-coal-rock assemblages with a PFC2D numerical simulation. Recently, many scholars have proposed a variety of strength criteria to characterize the stability of rock strength by means of conventional triaxial compression experimental data. Raflai [22] characterized the stability of rock structures by means of a representative strength damage criterion. For example, the Mohr-Coulomb strength criterion proposed by Labuz et al. [23] can be used to describe the shear damage pattern of the material under positive stress. The H-B criterion and GH-B strength criterion proposed by Hoek et al. [24,25] can further accurately respond to the intrinsic properties of the rock body and the effect of structural surfaces on the strength of the rock body.
Most of the abovementioned scholars' research is based on coal-rock monomers and coal-rock binary combinations and has achieved much in terms of deformation and failure characteristics under uniaxial or conventional triaxial compression tests. With the increase in mining depth, due to the existence of high stress at greater depths, many coal-rock structures under different confining pressure conditions are damaged based on the rockcoal-rock ternary structure of the roof, coal pillar, and floor. However, there is a lack of research on rock-coal-rock ternary combinations under different confining pressure conditions, and on the m i and s empirical parameters of the Hoek-Brown strength criterion suitable for rock-coal-rock combinations.
This paper presents a structural model of a rock-coal-rock ternary assemblage on the basis of previous research, as shown in Figure 1. Conventional triaxial compression tests were conducted on the rock-coal-rock assemblage to study its mechanical properties and damage characteristics under different peripheral pressure conditions to reveal its strength characteristics and damage trends, obtain the strength criterion of the ternary assemblage based on the modification of H-B, predict the damage trend, and provide a further theoretical basis for understanding the destructive behavior of the small coal pillars and the fissure evolution of small coal pillars in deep coal mines.
Preparation of Rock-Coal-Rock Composite Specimen
The coal and rock used in the test were taken from the 21,216 working face of the Xieqiao mining area in Huainan, Anhui Province. The mining level is −810 m, the average coal thickness is 3.0 m, and the direct roof and direct bottom are coarse sandstone. The coarse sandstone stones and coal pillars were processed into cylinders with a diameter of 50 mm and different heights by scoring machines, cutting machines, and grinding machines. During processing, the non-parallelism and non-perpendicularity of the end faces of coal-rock single specimens and coal-rock composite specimens are required to meet the requirements of GB/T23561. . According to the theoretical model of rock-coalrock combination in Figure 1, the coarse sandstone and coal pillar were bonded to the standard specimen of Φ50 mm × 100 mm using high-strength mica glue in the following order: coarse sandstone, coal pillar, coarse sandstone. Among them, the height ratio of coarse sandstone and coal pillar is strictly guaranteed to be 1:1:1, as shown in Figure 2. At the same time, the uniaxial compression samples of rock and coal were prepared, and the basic physical and mechanical parameters of coal-rock mass were measured, as shown in Table 1. The combination specimen was labeled GCG-B-A; G represents coarse sandstone, C represents coal pillar, B represents confining pressure, and A represents the specimen number. For example, GCG-0-1 is the uniaxial compression test of sample No. 1 of rockcoal-rock under 0 MPa confining pressure.
Preparation of Rock-Coal-Rock Composite Specimen
The coal and rock used in the test were taken from the 21,216 working face of the Xieqiao mining area in Huainan, Anhui Province. The mining level is −810 m, the average coal thickness is 3.0 m, and the direct roof and direct bottom are coarse sandstone. The coarse sandstone stones and coal pillars were processed into cylinders with a diameter of 50 mm and different heights by scoring machines, cutting machines, and grinding machines. During processing, the non-parallelism and non-perpendicularity of the end faces of coal-rock single specimens and coal-rock composite specimens are required to meet the requirements of GB/T23561. . According to the theoretical model of rockcoal-rock combination in Figure 1, the coarse sandstone and coal pillar were bonded to the standard specimen of Φ50 mm × 100 mm using high-strength mica glue in the following order: coarse sandstone, coal pillar, coarse sandstone. Among them, the height ratio of coarse sandstone and coal pillar is strictly guaranteed to be 1:1:1, as shown in Figure 2. At the same time, the uniaxial compression samples of rock and coal were prepared, and the basic physical and mechanical parameters of coal-rock mass were measured, as shown in Table 1. The combination specimen was labeled GCG-B-A; G represents coarse sandstone, C represents coal pillar, B represents confining pressure, and A represents the specimen number. For example, GCG-0-1 is the uniaxial compression test of sample No. 1 of rock-coal-rock under 0 MPa confining pressure.
Preparation of Rock-Coal-Rock Composite Specimen
The coal and rock used in the test were taken from the 21,216 working face of the Xieqiao mining area in Huainan, Anhui Province. The mining level is −810 m, the average coal thickness is 3.0 m, and the direct roof and direct bottom are coarse sandstone. The coarse sandstone stones and coal pillars were processed into cylinders with a diameter of 50 mm and different heights by scoring machines, cutting machines, and grinding machines. During processing, the non-parallelism and non-perpendicularity of the end faces of coal-rock single specimens and coal-rock composite specimens are required to meet the requirements of GB/T23561. . According to the theoretical model of rock-coalrock combination in Figure 1, the coarse sandstone and coal pillar were bonded to the standard specimen of Φ50 mm × 100 mm using high-strength mica glue in the following order: coarse sandstone, coal pillar, coarse sandstone. Among them, the height ratio of coarse sandstone and coal pillar is strictly guaranteed to be 1:1:1, as shown in Figure 2. At the same time, the uniaxial compression samples of rock and coal were prepared, and the basic physical and mechanical parameters of coal-rock mass were measured, as shown in Table 1. The combination specimen was labeled GCG-B-A; G represents coarse sandstone, C represents coal pillar, B represents confining pressure, and A represents the specimen number. For example, GCG-0-1 is the uniaxial compression test of sample No. 1 of rockcoal-rock under 0 MPa confining pressure. The test instruments were a Hai Chuang high-tech HC-U81 multi-functional concrete ultrasonic detector and a TYJ-1500 M rock mechanics testing machine, as shown in Figures 3 and 4. The sampling interval of the HC-U81 wave velocity meter is 0.025~2000 µs, the sampling length is 512 points~2048 points, the receiving sensitivity is no higher than 10 µV, the acoustic time measurement range is 0~99,999 µs, the amplitude measurement range is 0~170 dB, the emission pulse width is 0.1~100 µs, and the depth measurement range is 5~500 mm. In the test, the longitudinal vibration transducer of the composite structure was used to clamp the two ends of the specimen. The sound wave is emitted from one end of the transducer and received from the other end so as to record the average sound velocity of the wave through the specimen, measuring its homogeneity and the amount of defects. The maximum axial force of the TYJ-1500 M rock mechanics test machine is 2000 kN, the accuracy of the test force was controlled to within ±1%, the resolution of the test force, deformation, and confining pressure is 1/180,000, the maximum displacement of the axial piston is 150 mm, the displacement accuracy is controlled to within ±5% FS, the displacement resolution is 5µm, the axial deformation measurement range is 0~10 mm, the deformation measurement accuracy is controlled to within ±5% FS, the maximum confining pressure is 100 MP, and the confining pressure accuracy is controlled to within ±2%. The test instruments were a Hai Chuang high-tech HC-U81 multi-functional concrete ultrasonic detector and a TYJ-1500 M rock mechanics testing machine, as shown in Figure 3 and 4. The sampling interval of the HC-U81 wave velocity meter is 0.025~2000 µs, the sampling length is 512 points~2048 points, the receiving sensitivity is no higher than 10 µV, the acoustic time measurement range is 0~99,999 µs, the amplitude measuremen range is 0~170 dB, the emission pulse width is 0.1~100 µs, and the depth measuremen range is 5~500 mm. In the test, the longitudinal vibration transducer of the composite structure was used to clamp the two ends of the specimen. The sound wave is emitted from one end of the transducer and received from the other end so as to record the average sound velocity of the wave through the specimen, measuring its homogeneity and the amount of defects. The maximum axial force of the TYJ-1500 M rock mechanics test ma chine is 2000 kN, the accuracy of the test force was controlled to within ±1%, the resolution of the test force, deformation, and confining pressure is 1/180,000, the maximum displace ment of the axial piston is 150 mm, the displacement accuracy is controlled to within ±5% FS, the displacement resolution is 5µm, the axial deformation measurement range is 0~10 mm, the deformation measurement accuracy is controlled to within ±5% FS, the maximum confining pressure is 100 MP, and the confining pressure accuracy is controlled to within ±2%. The test instruments were a Hai Chuang high-tech HC-U81 multi-functional concrete ultrasonic detector and a TYJ-1500 M rock mechanics testing machine, as shown in Figures 3 and 4. The sampling interval of the HC-U81 wave velocity meter is 0.025~2000 µs, the sampling length is 512 points~2048 points, the receiving sensitivity is no higher than 10 µV, the acoustic time measurement range is 0~99,999 µs, the amplitude measurement range is 0~170 dB, the emission pulse width is 0.1~100 µs, and the depth measuremen range is 5~500 mm. In the test, the longitudinal vibration transducer of the composite structure was used to clamp the two ends of the specimen. The sound wave is emitted from one end of the transducer and received from the other end so as to record the average sound velocity of the wave through the specimen, measuring its homogeneity and the amount of defects. The maximum axial force of the TYJ-1500 M rock mechanics test ma chine is 2000 kN, the accuracy of the test force was controlled to within ±1%, the resolution of the test force, deformation, and confining pressure is 1/180,000, the maximum displacement of the axial piston is 150 mm, the displacement accuracy is controlled to within ±5% FS, the displacement resolution is 5µm, the axial deformation measurement range is 0~10 mm, the deformation measurement accuracy is controlled to within ±5% FS, the maximum confining pressure is 100 MP, and the confining pressure accuracy is controlled to within ±2%.
Test Scheme
Before the triaxial compression experiment, the homogeneity of the rock-coal-rock standard sample was detected by the wave velocity instrument to prevent the experimental error caused by the sample-making process. The test results of the wave velocity instrument are shown in Table 2 below. The five samples GCG-0-1, GCG-5-3, GCG-10-3, GCG-15-3, GCG-20-3 were found to have higher sound velocity and smaller average sound velocity error, and better homogeneity. The TYJ-1500 M rock mechanics testing machine was used to apply axial pressure to the specimen, and the computer system was used to detect the data changes in real-time. Firstly, the specimen was installed, the heat-shrinkable pipe sleeve was used at the junction of the specimen and the pressure pad, and the hot air gun was used to shrink the fixed effect to prevent the penetration of the confining pressure oil body from affecting the strength of the specimen. At the interface between the specimen and the lower pressure pad and the upper pressure block, black insulating tape was used to further increase the compactness. Secondly, the specimen was fixed using the eight-jaw extensometer, and the axial extensometer was installed. The axial deformation data of the specimen was collected by the axial extensometer. The specimen was installed as shown in Figure 5. The loading process was controlled by load, and the loading rate was kept at 0.02 kN/s until the specimen was loaded. The loading rate of confining pressure in the triaxial compression test was 0.5 MPa/s.
Analysis of Mechanical Properties of Coal-Rock-Coal Combination
The results of the triaxial compression test are shown in Table 3 below. E is the elastic modulus, and the linear slope is obtained by calculating the elastic stage of the stressstrain curve of the corresponding sample. The σ1, σ3, and σr express the axial peak strength,
Analysis of Mechanical Properties of Coal-Rock-Coal Combination
The results of the triaxial compression test are shown in Table 3 below. E is the elastic modulus, and the linear slope is obtained by calculating the elastic stage of the stress-strain curve of the corresponding sample. The σ 1 , σ 3 , and σ r express the axial peak strength, confining pressure, and residual strength of the composite specimen, respectively, and ε is the axial peak strain of the composite specimen. According to the experimental results shown in Tables 1 and 3, the relationship between the elastic modulus and confining pressure of different coal-rock combinations can be obtained, as shown in Figure 6. It can be seen from this figure that, under the confining pressure of 0 MPa, the elastic modulus of the single rock is higher than that of the coal-rock combination, and the elastic modulus of the single coal is the smallest. When the confining pressure is less than 15 MPa, the elastic modulus of the coal-rock combination is linear with the confining pressure. The size of the elastic modulus of the combination increases with the increase in the confining pressure, and the increase is more intense in the 5-10 MPa stage. In the 10-15 MPa stage, the increasing trend becomes smaller. At more than 15 MPa, the elastic modulus changes little and remains almost unchanged. The stress-strain curves under different confining pressure conditions obtained through the triaxial compression test are shown in Figure 7. The samples shown in Figure 7 are GCG-0-1, GCG-5-3, GCG-10-3, GCG-15-3, and GCG-20-1. The elastic modulus of GCG-10-3, GCG-15-3, and GCG-20-1 is 11.02, 12.23, and 12.52 GPa, respectively. It can be seen from Figure 7 that the change in coal-rock combinations can be presented as a crack The stress-strain curves under different confining pressure conditions obtained through the triaxial compression test are shown in Figure 7. The samples shown in Figure 7 are GCG-0-1, GCG-5-3, GCG-10-3, GCG-15-3, and GCG-20-1. The elastic modulus of GCG-10-3, GCG-15-3, and GCG-20-1 is 11.02, 12.23, and 12.52 GPa, respectively. It can be seen from Figure 7 that the change in coal-rock combinations can be presented as a crack compaction stage, elastic stage, yield stage, and post-peak softening stage. With the application of confining pressure, the change in the crack compaction stage is not obvious. The initial stage of 10 MPa and 15 MPa is caused by the slow loading rate. The actual compaction stage has been greatly shortened compared with 0 MPa and 5 MPa. In the uniaxial compression test on the single coal and single rock samples, the post-peak stage of the stress-strain curve is almost at 0, and the sudden stress drop causes the residual strength to almost reach 0. Under a confining pressure of 5 MPa~20 MPa, the yield stage of the coal-rock combination is more obvious than that under the confining pressure of 0 MPa, and there is an obvious ductile failure phenomenon in the post-peak softening stage. According to Paterson et al. [26], the rock needs a larger confining pressure if it is to realize the transition from brittleness to ductile rupture. The size of the confining pressure is no less than 70 MPa. However, in this experiment, under the confining pressure of 5 MPa, there is a change in characteristics from brittleness to ductility. The reason for this may be that the strength of the middle coal body is low, and with the application of confining pressure, the strength of the coal body is greatly affected. The destruction of the coal-rock combination is mainly affected by the change in the strength of the middle coal body [7], which leads to the ductile transformation of the coal body being reflected in the coal-rock combination as a whole.
According to the test results in Table 3, the relationship between confining pressure and axial peak strength, and axial peak strain can be obtained, as shown in Figures 8 and 9. Figure 8 shows that, with the increase in confining pressure, the axial peak strength of the coal-rock combination gradually increases. In the stage of 0~10 MPa, the peak strength changes greatly, and the peak strength changes slowly in the stage of 10~15 MPa. After 15 MPa, the peak strength changes are not obvious. It can be concluded that 10~15 MPa is a critical area where the peak strength is affected under the confining pressure of the coal-rock combination. Beyond this area, the peak strength change will slow down.
From Figure 9, it can be concluded that when the confining pressure is less than 15 MPa, the axial peak strain of the combination increases linearly with the increase in confining pressure. Under the condition of 0~10 MPa confining pressure, the peak strain growth trend is relatively slow. When the confining pressure reaches 10~15 MPa, the peak strain increases sharply. When the confining pressure is higher than 15 MPa, although the peak strain decreases abruptly, the change is relatively slow. It can be seen that the confining pressure of 15 MPa is a critical value for the change in peak strength and peak strain of the coal-rock combination, and 10~15 MPa is the critical range of change. The stress-strain curves under different confining pressure conditions obtained through the triaxial compression test are shown in Figure 7. The samples shown in Figure 7 are GCG-0-1, GCG-5-3, GCG-10-3, GCG-15-3, and GCG-20-1. The elastic modulus of GCG-10-3, GCG-15-3, and GCG-20-1 is 11.02, 12.23, and 12.52 GPa, respectively. It can be seen from Figure 7 that the change in coal-rock combinations can be presented as a crack compaction stage, elastic stage, yield stage, and post-peak softening stage. With the application of confining pressure, the change in the crack compaction stage is not obvious. The initial stage of 10 MPa and 15 MPa is caused by the slow loading rate. The actual compaction stage has been greatly shortened compared with 0 MPa and 5 MPa. In the uniaxial compression test on the single coal and single rock samples, the post-peak stage of the stress-strain curve is almost at 0, and the sudden stress drop causes the residual strength to almost reach 0. Under a confining pressure of 5 MPa~20 MPa, the yield stage of the coal-rock combination is more obvious than that under the confining pressure of 0 MPa, and there is an obvious ductile failure phenomenon in the post-peak softening stage. According to Paterson et al. [26], the rock needs a larger confining pressure if it is to realize the transition from brittleness to ductile rupture. The size of the confining pressure is no less than 70 MPa. However, in this experiment, under the confining pressure of 5 MPa, there is a change in characteristics from brittleness to ductility. The reason for this may be that the strength of the middle coal body is low, and with the application of confining pressure, the strength of the coal body is greatly affected. The destruction of the coal-rock combination is mainly affected by the change in the strength of the middle coal body [7], which leads to the ductile transformation of the coal body being reflected in the coal-rock combination as a whole.
(a) GCG-0-1 stress-strain curve ( b) GCG-5-3 stress-strain curve According to the test results in Table 3, the relationship between confining pressure and axial peak strength, and axial peak strain can be obtained, as shown in Figures 8 and 9. Figure 8 shows that, with the increase in confining pressure, the axial peak strength of the coal-rock combination gradually increases. In the stage of 0~10 MPa, the peak strength changes greatly, and the peak strength changes slowly in the stage of 10~15 MPa. After 15 MPa, the peak strength changes are not obvious. It can be concluded that 10~15 MPa is a critical area where the peak strength is affected under the confining pressure of the coalrock combination. Beyond this area, the peak strength change will slow down. According to the test results in Table 3, the relationship between confining pressure and axial peak strength, and axial peak strain can be obtained, as shown in Figures 8 and 9. Figure 8 shows that, with the increase in confining pressure, the axial peak strength of the coal-rock combination gradually increases. In the stage of 0~10 MPa, the peak strength changes greatly, and the peak strength changes slowly in the stage of 10~15 MPa. After 15 MPa, the peak strength changes are not obvious. It can be concluded that 10~15 MPa is a critical area where the peak strength is affected under the confining pressure of the coalrock combination. Beyond this area, the peak strength change will slow down. From Figure 9, it can be concluded that when the confining pressure is less than 15 MPa, the axial peak strain of the combination increases linearly with the increase in confining pressure. Under the condition of 0~10 MPa confining pressure, the peak strain growth trend is relatively slow. When the confining pressure reaches 10~15 MPa, the peak strain increases sharply. When the confining pressure is higher than 15 MPa, although the peak strain decreases abruptly, the change is relatively slow. It can be seen that the confining pressure of 15 MPa is a critical value for the change in peak strength and peak strain of the coal-rock combination, and 10~15 MPa is the critical range of change. Figure 10 shows the failure mode of the composite specimens under different confining pressures. The integrity of the composite specimen is different under different confining pressure conditions. Five typical failure samples were selected, namely, GCG-0-1, GCG-5-3, GCG-10-3, GCG-15-3, and GCG-20-1, and their macroscopic failure modes were analyzed. It can be seen that the failure mode of middle coal pillars was mostly tensileshear mixed failure and that of the upper and lower strata was mostly shearing failure. Under the condition of uniaxial compression, the middle coal body of the GCG-0-1 sample was seriously damaged. The red dotted line marks a large caving area, showing obvious brittle splitting failure characteristics, and the crack propagation is randomly distributed. Under the triaxial compression test, with the increase in confining pressure, the failure mode of the middle coal body began to alleviate, and the crack propagation angle began to become relatively small, no longer showing complex failure characteristics under the uniaxial compression test. When the confining pressure was 5 MPa, the integrity of the GCG-5-3 sample was the best, the crack propagation angle was small, the upper and lower strata had less crack development, and the failure range was mainly concentrated in the middle part of the coal. When the confining pressure was 10 MPa, the integrity of the GCG-10-3 sample was reduced, and the middle coal body had many cracks, but there was no large area of collapse, although the upper and lower rock masses were seriously damaged. When the confining pressure was 15 MPa, the integrity of the GCG-15-3 sample was improved, the damage to the upper and lower rock mass was reduced, and the middle coal pillar showed a small area of caving. When the confining pressure was 20 MPa, the integrity of the GCG-20-1 sample was improved and showed essentially the same failure form as GCG-15. It can be seen that, when the confining pressure is 10-15 MPa, the failure mode of the composite changes greatly. When the confining pressure exceeds 15 MPa, the change mode slows down. It can be seen that the failure mode of middle coal pillars was mostly tensile-shear mixed failure and that of the upper and lower strata was mostly shearing failure. Under the condition of uniaxial compression, the middle coal body of the GCG-0-1 sample was seriously damaged. The red dotted line marks a large caving area, showing obvious brittle splitting failure characteristics, and the crack propagation is randomly distributed. Under the triaxial compression test, with the increase in confining pressure, the failure mode of the middle coal body began to alleviate, and the crack propagation angle began to become relatively small, no longer showing complex failure characteristics under the uniaxial compression test. When the confining pressure was 5 MPa, the integrity of the GCG-5-3 sample was the best, the crack propagation angle was small, the upper and lower strata had less crack development, and the failure range was mainly concentrated in the middle part of the coal. When the confining pressure was 10 MPa, the integrity of the GCG-10-3 sample was reduced, and the middle coal body had many cracks, but there was no large area of collapse, although the upper and lower rock masses were seriously damaged. When the confining pressure was 15 MPa, the integrity of the GCG-15-3 sample was improved, the damage to the upper and lower rock mass was reduced, and the middle coal pillar showed a small area of caving. When the confining pressure was 20 MPa, the integrity of the GCG-20-1 sample was improved and showed essentially the same failure form as GCG-15. It can be seen that, when the confining pressure is 10-15 MPa, the failure mode of the composite changes greatly. When the confining pressure exceeds 15 MPa, the change mode slows down.
Residual Strength Analysis
Residual strength is an important aspect affecting the elastic-brittle-plasticity of rock. The higher the residual strength, the easier it is for the rock to show a higher peak load in the plastic rock sample [27]. With the increase in confining pressure, the brittleness of the overall failure of the composite specimen decreases, and the plasticity increases. At this time, the bearing capacity of the composite is basically composed of the internal friction force (i.e., residual strength) generated by the positive pressure and the strength adhesion of the specimen itself [28]. According to the experimental results in Table 3, the relationship between the confining pressure and the combined sample as shown in Figure 11 can be made. It can be seen from the diagram that the residual strength of the coal-rock combination is almost positively correlated with the confining pressure. When the confining pressure exceeds 15 MPa, the change trend decreases.
Residual Strength Analysis
Residual strength is an important aspect affecting the elastic-brittle-plasticity of rock. The higher the residual strength, the easier it is for the rock to show a higher peak load in the plastic rock sample [27]. With the increase in confining pressure, the brittleness of the overall failure of the composite specimen decreases, and the plasticity increases. At this time, the bearing capacity of the composite is basically composed of the internal friction force (i.e., residual strength) generated by the positive pressure and the strength adhesion of the specimen itself [28]. According to the experimental results in Table 3, the relationship between the confining pressure and the combined sample as shown in Figure 11 can be made. It can be seen from the diagram that the residual strength of the coal-rock combination is almost positively correlated with the confining pressure. When the confining pressure exceeds 15 MPa, the change trend decreases. The strength attenuation coefficient is an important index that reflects the brittleness of rock. It is a mechanical index that characterizes the post-peak strength attenuation behavior of rock based on the triaxial mechanical properties test proposed by Peng Jun [29]. The formula of the rock strength attenuation coefficient is as follows: The strength attenuation coefficient is an important index that reflects the brittleness of rock. It is a mechanical index that characterizes the post-peak strength attenuation behavior of rock based on the triaxial mechanical properties test proposed by Peng Jun [29]. The formula of the rock strength attenuation coefficient is as follows: In the formula, D s is the strength attenuation coefficient, and its value range is 0~1; σ 1 is the peak strength, σ r is the residual strength, and ∆σ is defined as the difference between the peak strength and the residual strength. The calculation results are shown in Table 4 below. From Figure 12, it can be observed that the curve depicts a general downward trend. This trend indicates that as the confining pressure increases, the strength attenuation coefficient of the combination gradually decreases while maintaining a high residual strength.
Notably, when the confining pressure ranges from 0-10 MPa, the strength attenuation coefficient of the combination sample experiences the most significant reduction. This observation highlights the heightened sensitivity of the strength attenuation coefficient to variations in confining pressure. Additionally, the findings reveal the combination's pronounced brittleness characteristics under conditions of uniaxial compression. Furthermore, the plasticity of the combination exhibits a gradual increase with escalating confining pressure.
H-B Strength Criterion
The Hoek-Brown strength criterion is an empirical formula for predicting rock fracture. It can reflect the inherent characteristics of rock mass and the influence of the structural plane and stress state on rock mass strength. The Hoek-Brown strength criterion can predict trends in scatter data and explain the influence of the lower stress zone, tensile stress zone, and minimum principal stress on rock mass strength. Its expression is
H-B Strength Criterion
The Hoek-Brown strength criterion is an empirical formula for predicting rock fracture. It can reflect the inherent characteristics of rock mass and the influence of the structural plane and stress state on rock mass strength. The Hoek-Brown strength criterion can predict trends in scatter data and explain the influence of the lower stress zone, tensile stress zone, and minimum principal stress on rock mass strength. Its expression is In the formula, σ c is the uniaxial compressive strength of the sample, and the value is the average value of the peak stress of the sample under 0 MPa confining pressure. σ 3 represents different confining pressure strengths, m i and s are Hoek-Brown empirical constants, which can be obtained by a uniaxial experiment. If there is a lack of laboratory data, empirical values can be taken. The value range of m i is 0~25 according to the look-up table, and the value range of s is 0~1. Combined with the triaxial compression test data of the coal-rock combination, the least square method can be used to calculate the fitting parameters in MATLAB software. The fitting formula is as follows: After calculation, the fitting parameters can be obtained: m i = 9.923, s = 0.786.
GH-B Strength Criterion
The Hoek-Brown strength criterion is suitable for intact rocks, but actual rocks generally comprise disturbed loose and broken bodies. In order to make the original criterion more suitable for evaluating the strength of rock masses, Hoek et al. [25] introduced the integrity coefficient related to rock mass on the basis of the Hoek-Brown strength criterion in the 1990s, and proposed an improved generalized Hoek-Brown strength criterion. Its expression is In the formula, σ c is the uniaxial compressive strength of the sample, σ 3 is the strength of different confining pressures, and m b , s, and a are empirical parameters.
The triaxial compression data are fitted by the GH-B strength criterion, and the fitting formula is as follows: σ 1 = σ 3 + 43.92(0.096σ 3 + 0.867) 0.842 (5) After calculation, the fitting parameters were m b = 4.234, s = 0.867, a = 0.842. The fitting curves of the two strength criteria are shown in Figure 13. The results of the above fitting calculations show that the H-B criterion fitting parameter m i is 9.923, and the GH-B criterion fitting parameter m b is 4.234. The difference between the two is 5.698, which is very large. The value of s is less than 1 in both criteria; the difference between them is 0.099, so the fitting value of s is reasonable. According to [30], the complete sandstone parameter m i value range should be between 13 and 21, the m i value of coal should be between 3 and 7 [3], and the m i value of the fitted combination should be between the two, which further proves the correctness of the experimental results. It can be seen from Figure 13 that the curve fitted by the H-B strength criterion is better than the curve fitted by the GH-B strength criterion. The fitting degree of the H-B criterion is R 2 = 0.9433, while the fitting degree of the GH-B criterion is R 2 = 0.9209. Therefore, we can conclude that the H-B strength criterion is more suitable for describing the strength characteristics of the rock-coal-rock combination in a triaxial compression test. Figure 13 that the curve fitted by the H-B strength criterion is better than the curv by the GH-B strength criterion. The fitting degree of the H-B criterion is R 2 = 0.943 the fitting degree of the GH-B criterion is R 2 = 0.9209. Therefore, we can conclude H-B strength criterion is more suitable for describing the strength characteristic rock-coal-rock combination in a triaxial compression test. However, because rock-coal-rock is a ternary combination, the parameters in the H-B strength criterion are different from the values for individual rock s Therefore, the least square method and numerical iteration were carried out in M to obtain the most suitable m and s values, as shown in Table 5. The m and s valu solved after iteration, and the fitting degree reached 0.9500. The smaller the m valu closer it is to the test value, and the larger the s value is, the higher the fitting de The fitting curve after iterative solutions based on the H-B criterion can be used scribe the strength characteristics of the rock-coal-rock ternary combination mor rately. However, because rock-coal-rock is a ternary combination, the parameters m and s in the H-B strength criterion are different from the values for individual rock samples. Therefore, the least square method and numerical iteration were carried out in MATLAB to obtain the most suitable m and s values, as shown in Table 5. The m and s values were solved after iteration, and the fitting degree reached 0.9500. The smaller the m value is, the closer it is to the test value, and the larger the s value is, the higher the fitting degree is. The fitting curve after iterative solutions based on the H-B criterion can be used to describe the strength characteristics of the rock-coal-rock ternary combination more accurately.
Conclusions
Based on the conventional triaxial test of the rock-coal-rock ternary combination under the mapping of deep small coal pillars, the relationship between the confining pressure and the related parameters, such as peak strength, peak strain, strength attenuation coefficient, and residual strength, was analyzed in depth. The following conclusions were obtained: (1) The uniaxial compression test on rock-coal-rock specimens showed that, under uniaxial loading conditions, the middle coal body was seriously broken and the degree of discreteness was large, which led to the overall failure and instability of the combination; this is the main reason for the serious deformation of small coal pillars.
With the further expansion of cracks, it is possible to cause roof and floor damage; (2) Under the condition of triaxial loading, the failure strength of the composite increased with an increase in confining pressure. The combined coal samples were dominated by shear failure, and some of the rock samples produced shear surfaces consistent with the coal samples. With an increase in confining pressure, the combination showed obvious characteristics of ductility; (3) By comparing the relationship between different confining pressure conditions and elastic modulus, peak strengths, peak strains, and residual strengths, it can be seen that the confining pressure of 10-15 MPa is a critical area for the strength change in the combination. After exceeding 15 MPa, the deformation trend of the combination became relatively slow. With an increase in confining pressure, the attenuation coefficient of rock strength gradually decreased, and in the range of 0~10 MPa, the at-tenuation coefficient of rock strength decreased rapidly, showing that the combination is more sensitive to confining pressure; (4) Based on the Hoek-Brown strength criterion, the empirical parameter values m i and s suitable for rock-coal-rock combination were solved using a numerical fitting iteration, which can more accurately predict the change in strength characteristics of the combination, and provide a theoretical basis for the width, stability control, and support design of small coal pillars. | 9,622.2 | 2023-08-16T00:00:00.000 | [
"Materials Science"
] |
Rapid Change in Articulatory Lip Movement Induced by Preceding Auditory Feedback during Production of Bilabial Plosives
Background There has been plentiful evidence of kinesthetically induced rapid compensation for unanticipated perturbation in speech articulatory movements. However, the role of auditory information in stabilizing articulation has been little studied except for the control of voice fundamental frequency, voice amplitude and vowel formant frequencies. Although the influence of auditory information on the articulatory control process is evident in unintended speech errors caused by delayed auditory feedback, the direct and immediate effect of auditory alteration on the movements of articulators has not been clarified. Methodology/Principal Findings This work examined whether temporal changes in the auditory feedback of bilabial plosives immediately affects the subsequent lip movement. We conducted experiments with an auditory feedback alteration system that enabled us to replace or block speech sounds in real time. Participants were asked to produce the syllable /pa/ repeatedly at a constant rate. During the repetition, normal auditory feedback was interrupted, and one of three pre-recorded syllables /pa/, /Φa/, or /pi/, spoken by the same participant, was presented once at a different timing from the anticipated production onset, while no feedback was presented for subsequent repetitions. Comparisons of the labial distance trajectories under altered and normal feedback conditions indicated that the movement quickened during the short period immediately after the alteration onset, when /pa/ was presented 50 ms before the expected timing. Such change was not significant under other feedback conditions we tested. Conclusions/Significance The earlier articulation rapidly induced by the progressive auditory input suggests that a compensatory mechanism helps to maintain a constant speech rate by detecting errors between the internally predicted and actually provided auditory information associated with self movement. The timing- and context-dependent effects of feedback alteration suggest that the sensory error detection works in a temporally asymmetric window where acoustic features of the syllable to be produced may be coded.
Introduction
During the development of speech production, different sorts of sensory feedback help to coordinate the movements of the respiratory, laryngeal, velopharyngeal, and articulatory subsystems. Cutaneous and/or somatosensory information on the status of multiple articulators and auditory information related to produced speech constitute important sources of feedback for speech motor control [1]. Various studies employing auditory feedback alteration have suggested that acoustic information is critical as regards learning and maintaining vowel production [2,3] and voice pitch control [4,5]. Evidence has also been obtained from humans and non-human primates showing that neural activity in the auditory cortex is modulated by self-produced vocalization [6,7,8,9]. In concert with these studies, theoretical models of speech acquisition and production have been proposed, which hypothesize that speech targets represented in auditory space are achieved using an articulatory-to-auditory map trained on self-produced auditory feedback [10,11]. However, debate continues as to whether such neural mechanisms also help to ensure stability in rapid and complex speech motor control [12,13], aside from the well-studied reflexive adjustment of voice volume or pitch based on auditory information [5,14,15,16,17,18]. Certain aspects of the effects of auditory feedback on speech articulation have been examined using the delayed auditory feedback (DAF) paradigm [19,20,21,22,23] where various types of speech disfluencies are induced, e.g., increased articulatory error, lengthened duration, augmented volume, and increased funda-mental frequency. Similarly, a vocal duration reduction with an accelerated auditory feedback delay has also been reported [24]. However, the mechanisms that underlie these effects elicited by constant exposure to unusual feedback delay remain unclear. Auditory feedback may serve as an immediate source for the dynamic control of speech articulation, analogous to the wellknown rapid adjustment of labial constriction based on cutaneous and/or somatosensory information [25,26,27,28,29].
In this study, we examined the online control mechanism for articulatory lip movement by suddenly shifting the auditory feedback timing in the ahead-of-time or delayed direction, and/or replacing the feedback syllable by other syllables, during the repetition of bilabial plosives /pa/. Labial distance trajectories under altered and normal feedback conditions were compared within a single cycle of lip closing/opening movement subsequent to the auditory alteration. Statistical analysis revealed that a quickened lip closing/opening movement was clearly elicited when the auditory feedback preceded the real production by 50 ms. On the other hand, such change was not significant when the feedback was provided more than 50 ms before the real production or was delayed, and/or when the feedback syllable was replaced by /Wa/ or /pi/. These results suggest (1) an underlying mechanism that detects errors between anticipated and actually provided auditory consequences for the rapid modification of subsequent movements, and (2) a temporally asymmetric window for detecting auditory errors in which acoustic features of the syllable to be produced may be coded.
Ethics Statement
All participants gave their written informed consent to participating in this study, which was approved by the Research Ethics Board of NTT Communication Science Laboratories.
Participants
Ten adults (seven males and three females) aged from 21 to 39 participated in the experiments. All the participants were native speakers of Japanese and exhibited no obvious speech difficulties as judged by the experimenters. Figure 1A is a schematic diagram of the auditory feedback alteration system. The speech sounds produced by a participant are converted into voltage signals by an electret condenser microphone (Sony ECM-G3M driven by an Earthworks Microphone Preamp 1021). The signals are then filtered (NF 48 dB/oct filter P-85 in the phase-linear low pass mode) with a cutoff frequency of 6 kHz, and digitized at a sampling frequency of 16 kHz (Systems Design Service DASBOX Model-16/100). A At the beginning of the trial, the participants heard a sequence of seven click tones with an interval of 200 or 300 ms through earphones. After hearing the final (seventh) click tone, the participants produced syllables at a rate identical to that indicated by the click tone sequence. No click tone was presented during the production period. Participants heard the unaltered speech feedback during the first two repetitions. The normal speech feedback was blocked after the second repetition, and /pa/, /Wa/, or /pi/ sound was presented once at 2150, 2100, 250, 0, +50, +100, or +150 ms from the predicted third repetition onset. doi:10.1371/journal.pone.0013866.g001 custom made program for altering the input speech signals with a buffer size corresponding to 10 ms is run on a workstation. The processed signals are then converted to voltage signals (Systems Design Service DASBOX-16) and filtered (NF 48 dB/oct filter P-85 in the phase-linear low pass mode) with a cutoff frequency of 6 kHz. Finally, the voltage signals are converted into acoustic sounds and fed back to the participant bilaterally using earphones (Etymotic Research earphones ER-4S driven by Sony audio mixer SRP-X6004).
Apparatus
In the experiment, the participants sat on a chair and were asked to insert the earphones as deeply as possible in the ear canal. A microphone mounted in a floor stand was located close to the left ears of the participants who were asked to keep their heads in a fixed position throughout the experiments. The participants heard their own unaltered speech picked up by the microphone through the earphones while vocalizing an /a/ sound in their natural way. They were then asked to adjust the gain of the microphone so that they heard their own speech sounds most naturally. The participants were also asked to adjust the sound level of the pink noise they heard through the earphones, which was produced by a noise generator (Bruel & Kjaer Type 1405), while vocalizing an / a/ sound in their natural way, so that, as far as possible, they did not perceive their own bone-conducted auditory feedback, but without experiencing stress. The sound level of the noise chosen by the ten participants in the experiments was 61.562.75 dBSPL as measured by a probe microphone (Etymotic Research Probe Microphone ER-7C).
We chose an in-the-ear transducer with a view to eliminating the participants' own air-conducted auditory feedback most effectively. However, the occlusion effect caused by the in-ear earphone can influence the bone conduction threshold. The occlusion effect is the result of the acoustic energy created by the vibration of the walls of the external ear canal in response to a bone conducted signal trapped in the ear. When the tip of the earphone is fitted deeper in the ear canal, there is less opportunity for vibrations to occur and the occlusion effect is reduced [30]. This is why the participants were asked to insert the earphones as deeply as possible in the ear canal.
The three-dimensional motion of the upper and lower lips was measured with an optical motion capture system (Qualisys Qqus) at a sampling frequency of 250 Hz. Six low mass, retro-reflective markers with a diameter of 4 mm were placed on the vermilion borders of the upper and lower lips in the midsagittal section, the bridge and the tip of the nose, and the left and right side of the forehead, as shown in Fig. 1B. Two digital cameras placed on the left and right in front of the participant emitted infrared light that was reflected from the markers and back to the cameras. The position data of the four markers other than those on the upper and lower lips were used to calculate the relative positions of the lips with respect to the participant's head.
Experimental procedures
In each trial in this experiment, the participants were asked to produce an isolated syllable /pa/ seven times while maintaining a constant speech rate. For each trial, the auditory feedback corresponding to the third repetition of /pa/ was altered by shifting the timing and/or replacing the type of syllable, while the subsequent feedback was blocked. A comparison of the articulatory lip movement under each altered condition with that under a normal condition enabled us to evaluate the effect of auditory feedback alteration on speech motor control more precisely than previous studies based on DAF. As for speech errors produced when employing DAF, their speech rate dependence can also be disputed in the light of certain controversial results [22,23]. Therefore, two speaking rates (200 and 300 ms per syllable) were employed in our experiment in order to examine the speed dependence of the effect.
The experiment consisted of five test blocks and one control block. Each test block consisted of forty-six trials, where twentythree different feedback conditions were employed for two different repetition rates (200 and 300 ms per syllable). Of the twenty-three feedback conditions, twenty-one were altered conditions where one of three syllables (/pa/, /Wa/, or /pi/) was presented at seven different timings (2150, 2100, 250, 0, +50, +100, or +150 ms in relation to the onset of the third repetition), one was a blocked condition (no feedback after the second repetition), and one was unaltered. The control block consisted of twenty trials with unaltered feedback conditions, half of which were conducted at 200 ms per syllable and half at 300 ms per syllable.
In the experiment, the control block was introduced first, which took about 5 minutes, followed by five test blocks, each of which took about 10 minutes. There was a short break between each block. During the test blocks, the order of the feedback conditions applied to each participant was shuffled block by block. In the control block, the two syllable rates were alternated trial by trial. Figure 1C depicts the trial protocol. At the beginning of the trial, the participants heard a sequence of seven guide click tones with a fixed interval of 200 or 300 ms through their earphones. After hearing the final (seventh) click tone, the participants were asked to produce syllables at a syllable rate identical to that indicated by the click tone sequence. No click tone was presented during the production period. As illustrated in Figure 1C, the participants heard unaltered speech feedback while producing the first two repetitions. The burst onset timing of the first two repetitions was detected by thresholding the segmental power of the signals calculated every 4 ms. The burst onset timing of the third repetition was predicted before it was produced, based on the interval between those of the first two repetitions. The normal speech feedback was blocked after the second repetition, and the sound /pa/, /Wa/, or /pi/, spoken by the corresponding participant, was presented once either at 2150, 2100, 250, 0, +50, +100, or +150 ms from the predicted third repetition onset. These sound stimuli /pa/, /Wa/, and /pi/ were recorded by the participants just before they undertook this task. Note that this method enabled us to investigate not only the effect of speech sound alteration, but also the effect of the early feedback of speech sound, which was impossible to examine using the previously employed online signal modification methods [17,18,19,20].
Tasks
When preparing these stimuli, the participants repeated /pa/, /Wa/, and /pi/ in their most natural way. While the participants were producing these syllables, the burst onset timing of one syllable was detected in the same way as in the experiments, and 200 ms of the signals from the detected onset were stored for each of the three syllables, while preserving the amplitude ratio among the syllables. Examples of the stored syllables for a participant are shown in Fig. 2A. When these pre-recorded syllables were presented in the experiments, the sound pressure level was adjusted by the computer program in every trial, based on that of the second repetition, so that the inter-syllabic ratio of the sound pressure level for /pa/, /Wa/, and /pi/ was maintained correctly as each participant produced these syllables in his or her natural way. Figure 2B shows examples of auditory feedback signals presented to a participant under three different conditions during the experiments, while repeating /pa/ seven times at a rate of 300 ms per syllable. In Figs
Data analysis
The time varying three-dimensional labial distance (LD) was calculated from the marker position data. For each participant, the LD trajectories of all trials were temporally aligned at the predicted third repetition onset by referring to the simultaneously recorded acoustic signals. The mean LD trajectory of five trials was obtained for each of forty-six different conditions in the five test blocks (twenty-three feedback types, two speech rates). The While the participant was producing /pa/, /Wa/, or /pi/ repeatedly, the burst onset timing of one syllable was detected in the same way as in the experiments, and 200 ms of the signals from the detected onset were stored while preserving the amplitude ratio among the syllables. When presenting these pre-recorded syllables in the experiments, the sound pressure level was adjusted by the computer program for every trial, based on that of the second repetition, so that the inter-syllabic ratio of the sound pressure level for /pa/, /Wa/, and /pi/ was maintained correctly as the participant produced the syllables in his or her natural way. (B) Examples of auditory feedback signals presented to a participant under three different conditions during the experiments, while he or she produced /pa/ seven times at a rate of 300 ms per syllable. In each pair of panels, Bi to Biii, the participant's speech signals are illustrated at the top, with the thick vertical line indicating the predicted onset of the third repetition. The corresponding auditory feedback signals are in the lower panels in Bi-Biii, with the thick vertical line indicating the onset of the altered auditory feedback signal. The auditory stimuli presented in Bi, Bii and Biii were /pa/ at 2100 ms, /Wa/ at 0 ms and /pi/ at +50 ms from the predicted onset of the third repetition, respectively. doi:10.1371/journal.pone.0013866.g002 mean trajectory of ten trials from the control (normal feedback) block was also obtained for the two speech rates.
The auditorily induced change in the labial movement was represented by a lag that provided the maximum cross-correlation between the LD trajectories under the altered and control conditions within the post-stimulus period. Note that this method was more stable and consistent than that using the displacement error or the velocity error, maybe because of the inter-participant variability in the time course of lip opening-closing cycle (see Figure S1). In Fig. 3 To adjust for the phase difference between the trajectories of the altered and control conditions before alteration onset, the lag within the pre-stimulus period arg max R pre m ð Þ (also shown in Fig. 3) was calculated and subtracted from arg max R post m ð Þ. The pre-stimulus period was set at the same length as the post-stimulus period. The cross-correlation function R pre m ð Þ was calculated in the same way as R post m ð Þ.
Results
Labial distance trajectory Figure 4 shows sample LD trajectory data during the production of /pa/ at a speech rate of 300 ms per syllable. The auditory feedback conditions shown from the top to bottom panels were as follows: pre-recorded /pa/ was presented once at 2150, 2100, 250, 0, 50, 100, 150 ms from the predicted third repetition onset. The solid vertical line in each panel indicates the onset timing of the auditory stimulus, while the dotted vertical line indicates the predicted third repetition onset. The solid curve in each panel shows the mean LD trajectory for five trials over the test blocks. The mean trajectory for ten trials in the control (normal feedback condition) block is shown as a dotted curve.
By comparing the two trajectories in each panel, the mouth opening movement subsequent to the auditory stimulus onset appeared generally to occur sooner for the 250 ms stimulus presentation. While a similar hasty movement was also observed for the 2150 and 2100 ms conditions, the effect seemed to be weaker. The deviation between the trajectories under each of the delayed feedback (50, 100, 150 ms) and control conditions was much smaller. Similar results were obtained for all ten participants.
In Fig. 4, the open and filled horizontal bars in each panel indicate the pre-and post-stimulus periods, respectively, for calculating the lag of the maximum cross-correlation between the LD trajectories under the altered and control conditions. The lag value may not necessarily reflect the exact amount of time shift, but will at least help to indicate which of the two series is leading the other, irrespective of which component of the amplitude, period, or phase of the LD trajectories was dominant in the difference. As observed in the top three panels in Fig. 4, the difference between the LD trajectories in the altered and control conditions tended to increase with time after the auditory alternation onset. Since such differences may be produced by a progressive accumulation of voluntary and involuntary effects, it would be difficult to specify the direct causal effect of auditory alteration on the LD trajectory. Therefore, in this study, we focused on the LD trajectory during a short period after the auditory alteration. The following subsection presents a statistical evaluation of the differences between LD trajectories under each of altered and control conditions. Figure 5 shows the lag corresponding to the maximum crosscorrelation (N = 10; error bar: standard error) between the LD trajectories under the altered and control conditions within the post-stimulus period, obtained by subtracting those within the prestimulus period. The minus value of the lag reflects an ahead-oftime shift of the articulatory lip movement compared with the control, and vice versa. The top and bottom panels show the results obtained when the speech rates were 200 and 300 ms per syllable, respectively. Each color indicates the syllable presented as a stimulus. ''No'' indicates a condition where no feedback was presented after the production of the second repetition. The condition indicated as ''normal'' refers to a comparison of the normal feedback trials during the test blocks and those in the control block, which reflects the variance in the baseline speech rate of each participant throughout the experiment.
Auditorily induced rapid change in articulatory movement
For 22 altered conditions at each speech rate, the statistical significance of the difference from the ''normal'' condition was evaluated with a two-sided paired t-test (dF = 9 for all comparisons, with the Bonferroni adjustment). A statistically significant change (p,0.05) was found only when syllable /pa/ was presented 50 ms prior to the onset of syllable production for a rate of 300 ms per syllable. Under this condition, the auditory feedback alteration resulted in an ahead-of-time shift of the articulatory lip movement according to Fig. 5 (a minus lag value). A comparable large negative mean value was also found in Fig. 5 with a 50 ms preceding presentation of syllable /Wa/ at a rate of 300 ms per syllable. However, the difference from the normal condition was not statistically significant (p.0.05) owing to the variation across subjects. Also from Fig. 5, the maximum positive mean values were found for a 50 ms delayed presentation of syllables /pa/ and /Wa/ at a rate of 300 ms per syllable. However, these were also statistically insignificant (p.0.05). For a speech rate of 200 ms per syllable, the effects of auditory feedback alteration on the articulatory lip movement were found to be insignificant under all the conditions tested (p.0.05).
From the experimental results, we concluded that an ahead-oftime shift in the articulatory lip movement emerged rapidly when the auditory feedback preceded the real syllable production by 50 ms. However, too early a manipulation (2150 and 2100 ms) of the auditory feedback did not significantly affect the subsequent articulatory lip movement. The delayed feedback also produced no significant change. Syllables that were not identical to those of the speech task (/Wa/ and /pi/) had no significant effect even when they were fed back 50 ms prior to the real syllable production. Finally, the articulatory changes were not significant for the faster speech rate (200 ms per syllable) under any of the alteration conditions tested.
Time-asymmetric effect of auditory feedback alteration
The experimental results obtained in the current study showed that the ahead-of-time and delayed auditory feedback affected the articulatory lip movement in a time-asymmetric manner during repetitive syllable production. Significantly hastened articulation at around 120 ms from the auditory alteration onset occurred when the auditory stimulus was presented 50 ms prior to the onset of syllable production. Taken together with the hypothetical feedforward and feedback mechanisms of speech motor control [31], the hastened articulation could be regarded as a sort of rapid compensatory articulation in the time domain, which was induced by a sensory error caused by the progressive auditory input. However, the feedback alteration effect was not significant when the feedback timing was earlier (2150 and 2100 ms). This fact seemed to suggest that an internal simulation of the auditory consequences of speech motor commands is not completed 100 ms prior to the initiation of the articulatory lip movement.
More interestingly, our experimental result revealed that no delayed feedback had a significant effect on the subsequent lip movement. One possible explanation for this result may be an imperfect masking of the air-and bone-conducted auditory feedback. In our experiment, an in-ear earphone was used to realize the effective isolation of the air-conducted feedback of the participants' own speech output. In addition, a masking noise was delivered to their ears to disturb the sensation and/or perception of the air-and bone-conducted feedback to a certain degree. However, even a small amount of natural feedback might still reduce the effect of sensory error on the motor control compared with ahead-of-time feedback alteration. This might result in the insufficient effect of the delayed auditory feedback.
Another possible mechanism for the temporally asymmetric effect could be related to the response attenuation in the auditory cortex resulting from self-produced vocalization [6,7,8,9]. The precise temporal processing properties of such auditory attenuation on the time course of speech production, however, are less well understood. Further experimental and theoretical investigations are required to clarify the precise mechanisms underlying the time-asymmetric effect of auditory feedback alteration on the speech articulatory movement obtained in our experiment.
Context dependence of auditorily-induced response
The experimental results showed that the auditory feedback of /Wa/ and /pi/ did not significantly change the subsequent lip movement, irrespective of the timing of the feedback. Taking this fact together with the hypothetical feedback-feedforward error correction mechanism [31], articulatory compensation in the time domain might be considered rather insensitive to an auditory input whose acoustic feature is not identical to that of the internal prediction.
The results also revealed of the effect of /Wa/ had a larger mean value than that of /pi/ being fed back 50 ms prior to /pa/ production at a rate of 300 ms per syllable, though both were statistically insignificant. One suspected cause is that /pi/ has a smaller relative acoustical power than /Wa/. In the experiment, the auditory feedback amplitude of each syllable was dynamically adjusted so that its syllabic power ratio to the syllable /pa/ to be produced by each participant was matched with that in his/her natural production. (See the Task subsection for details.) Figure 6 shows the relationship between the relative syllabic power of the auditory feedback and the difference in the magnitude of auditorily-induced articulatory change on a participant-by-participant basis (N = 10). If the magnitude of the articulatory change were dependent on the power of the auditory feedback, the data in Fig. 6 would exhibit a negative correlation. However, the correlation coefficient for ten participants was found to be low (r = 0.54, p = 0.11, dF = 8). Therefore, the smaller mean value of the effect of /pi/ feedback did not appear to result from its smaller amplitude.
Another possible cause of the smaller mean effect of the /pi/ feedback could be related to a larger acoustic deviation of /pi/ from /pa/ compared with that of /Wa/, in the light of the evidence showing that the auditory cortex responded differently to self-produced and externally produced speech sounds during speech production [9]. The auditory input of /pi/ while producing /pa/ might not be processed as a self-produced sound because of the large difference in vowel quality between /a/ and /i/ such as the location of the formants, despite the invariant feature of the initial /p/ independent of the following vowel [32].
Speech rate dependency of response
The experimental result showed that none of the altered auditory feedback tested under the faster speech condition (200 ms per syllable) induced significant articulatory changes. So far little has been reported about the dependence of the auditory alteration effect on speech rate. There have been conflicting results regarding the speech-rate dependence of DAF-induced disfluencies, where speech errors were found to decrease [23] or increase [22] as the speaking rate increased. Most of the speech errors both the above studies involved various suprasyllabic features, which may not be a direct consequence of the short-latency auditory-motor response as obtained in our experiment. Further investigation is required to untangle the sources of the complex speech errors induced by DAF, and to understand the mechanism underlying the speechrate dependence of the auditory-motor response.
A study on the accuracy with which speakers repeat a monosyllable in time with an external rhythm suggested two underlying processes depending on the repetition rate [33]. At a rate of 1 to 3 times per second, speakers could compensate for a discrepancy in timing between a syllable and the external guide tone in an adjacent or neighboring utterance (''ongoing processing''), while at a rate of 4 to 6 times per second, such one-by-one processing did not work (''holistic processing''). Considering our experimental condition in the light of Hibi's work, a rate of 200 ms per syllable is classified as holistic processing where the one-by-one adjustment of utterances was impossible. On the other hand, a rate of 300 ms per syllable (equivalent to 3.3 times per second) can be classified as either ongoing or holistic processing. Such a difference in the underlying processing strategy might have caused the speech rate dependence of the auditory-motor response obtained in our experiment. However, the speech task used in our experiment was very different from that used in Hibi's work in that the participants were required to repeat the syllable in a self-paced manner with no external rhythm provided while speaking. Another processing mechanism may be involved in the self-paced rhythmic production.
Language dependency of response
From the viewpoint of rhythmic properties, languages are considered to be classified as stress-, syllable-, or mora-timed, although a quantitative measure of speech rhythm has not been Figure 6. Magnitude difference in auditory-induced articulatory change against relative acoustical power of auditory feedback. The abscissa is the relative acoustical power between /Wa/ and /pi/. The ordinate is the difference between the mean lag shown in Fig. 5 for /Wa/ and /pi/ feedback 50 ms prior to the production onset under a rate of 300 ms per syllable. The correlation coefficient for ten participants was r = 0.54 (p = 0.11, dF = 8). doi:10.1371/journal.pone.0013866.g006 established. While the results of the current study were obtained from Japanese speakers, it would also be interesting to consider whether the same behavior occurs in other language speakers. Language-specific aspects of temporal organization of the kinematics of lower lip-jaw articulation have been compared between English, French, and Japanese, which are assumed to be examples of stress-, syllable-, and mora-timed languages, respectively [34]. They have used reiterant speech task in which speakers were required to replace each syllable of a target phrase with a single syllable such as /ba/ or /ma/, while trying to maintain the rhythmic character of the original [35]. They have found highly linear relation between peak velocity and displacement in lower lip movement for all three languages, and concluded that the dynamics could be modeled as a universal second-order system with language-specific parameter settings. It is therefore inferred that, as far as the repetitive syllable production task is concerned, the auditory-motor effect observed in the current study would be expected to occur also in speakers other than Japanese.
Conclusion
A rapid auditorily induced change in articulatory lip movement was found when auditory feedback preceded real syllable production by 50 ms when isolated syllables were spoken repeatedly at a rate of 300 ms per syllable. The change was not significantly induced when the feedback occurred earlier than 50 ms or was delayed, and/or the feedback syllable was replaced by other syllables. The results suggested that a compensatory mechanism detected sensory errors between the internally predicted and actually provided auditory information associated with the self-produced speech, by using a temporally asymmetric window in which acoustic features of the syllable to be produced may be coded. This study provides evidence that the temporal dynamics of articulatory lip movement must be correctly maintained not only with somatosensory feedback resulting from peripheral motor activation but also with auditory feedback of selfproduced speech. Figure S1 Inter-participant variability in the time course of lip opening-closing behaviors. The solid and dotted curves indicate temporal patterns of the labial distance (left panels) and their first time-derivatives (right panels) under altered feedback and control conditions, respectively, during the repetitive production of /pa/ at a rate of 300 ms per syllable for each participant (P1 -10). In the altered condition, the auditory feedback /pa/ was presented 50 ms prior to the predicted production onset. The thick vertical line indicates the onset timing of the auditory stimulus, and the dotted vertical line indicates the predicted third repetition onset. The pre-and post-stimulus periods used in the cross-correlation analysis are highlighted by the light and dark gray rectangles, respectively. As comparing the graphs of different participants, the displacement and its velocity patterns varied, and the timing of initiation of behavioral changes (e.g., temporal shift) by the feedback alteration were also different across the participants. Because of these variability, the kinetic variables such as the displacement and its time derivative were not useful to extract the common behavioral change across participants. In the main analysis, we therefore hired cross-correlation value as a lag-lead index because of robustness to the inter-participant behavioral variability. Found at: doi:10.1371/journal.pone.0013866.s001 (0.20 MB TIF) | 7,397.6 | 2010-11-08T00:00:00.000 | [
"Linguistics"
] |
Testing f ( R )-Theories by Binary Pulsars
Using the Post-Keplerian parameters to obtain, in the Minkowskian limit we obtain constraints on f(R)-theories of gravity from the first time derivative of the orbital period of a sample of binary stars. In the approximation in which the theory is Taylor expandable, we can estimate the parameters of an an analytic f(R)-theory, and fulfilling the gap between the General Relativity prediction and the one cames from observation, we show that the theory is not ruled out.
Introduction
Astrophysical systems like Neutron Stars (NS), coalescing binary systems, Black Holes (BHs), and White Dwarfs (WDs), are the most promising to study the gravitational waves (GWs) emision.Indeed, studying the binary system B1913+16, known as the Hulse-Taylor binary pulsar, the first time derivative of the orbital period was measured to be different from zero [13,18], as predicted by General Relativity (GR) when gravitational radiation is emitted.This measurements was confirmed by study in other relativistic binary systems.The agreement between GR and the observation is at the order of ∼ 1%.However, using the Extended Theories of Gravity (ETG) it should be possibile to explain the observational results as shown in [10,12] where, starting from a class of analytic f (R)-theories it is possible evaluate the first time derivative of the orbital period and compare it with the data.This approach permit both to test the ETGs both to explain the gap between observation and the theoretical prediction.This paper was organized as follow: in Sec. 1 we calculate the quadrupole emission for an analytic f (R)-Lagrangian using the weak-field limit; in Sec 2 we compare the theoretical prediction with the observed data.Finally in Sec 3 we give our conclusions and remarks.
The First Time Derivative of the
Orbital Period in the f (R)-Theories The simplest extension to GR is the f (R)-gravity, in which, the Lagrangian is an arbitrary function of Ricci scalar [2].Starting from the field equations in f (R)gravity (for details see [2,16,4,5]) where it is possibile, in the Minkowskian approximation of an analytic f (R)-Lagrangian1 , to compute the quadrupole emission due to GWs [10,11].Furthermore, it is possible calculate the energy momentum tensor of gravitational field in f (R)-gravity that assumes the following form To be more precise, the first term, depending on the choice of the constant f 0 , is the standard GR term, the second is the f (R) contribution.It is worth noticing that the order of derivative is increased of two degrees consistently to the fact that f (R)-gravity is of fourthorder in the metric approach [10].
In this contest, we can write the total average flux of energy due to the GWs integrating over all possible directions as dE dt where we point out that for f 0 → 0 and f 0 → 4 3 , the previous equation becomes that is the prediction of GR [14,17].In order to evaluate the above expressions for the flux it is necessary to form explicit expressions for ...
Q ij for the system under consideration.For our purposes we consider a binary pulsar system.If we assume a Keplerian motion of the stars in the binary system, wherewe m p is the pulsar mass, m c the companion mass, and µ = m c m p m c + m p is the reduced mass, it is possible to compute the time average of the radiated power computing the first time derivative of the orbital period [11] Ṗb = − 3 20 where is the orbital eccentricity and T is the orbital period of the binary.
Methodology and Data Analysis
Knowing exactly the Lagrangian that describes the system, we can predict the orbital period decay, however,we want understand how well the relativistic binary systems can fix bounds on f (R) parameters using eq.( 7), and getting an estimation of the second derivative of the Lagrangian with respect to Ricci scalar, f 0 .We use the following prescription, the difference between the first derivative of the binary observed period variation ( Ṫb Obs ± δ) and the theorethical one obtained by GR, ∆ Ṫb = Ṫb Obs − ṪGR , is fulfilled imposing that: where δ is the experimental error, that we propagate on the Ṫb Obs , into an uncertainty on f 0 ±δ .In this way, the extra contribution to the loss of energy due to the emission of GWs radiation in the ETGs regime can provide to fill the difference between theory and observations.We select a sample of Observed Relativistic Binary Pulsars (see their references reported in Tab. 1 of [11]) for which we compute the correction Ṫb f (R) , the difference ∆ ṪGR between Ṫb Obs and ṪGR (equal to the correction −f 0 Ṫb f (R) ), the corresponding f 0 solution of (8), the interval centered on f 0 and finally, the interval centered on f 0 and computed from the difference: , all results are reported in Tab. 1.In Fig. 1 we show, for sake of convenience, in logarithmic scale, the absolute values of f 0 reported in Tab. 1
ṪGR
. There are six binaries in tables, for which the ETGs are not ruled out 0.04 ≤ f 0 ≤ 38, getting 0.5 ≤ Ṫb Obs ṪGR ≤ 1.5.For those systems the difference between ṪGR and Ṫb Obs can be explained adding an extra contribution that comes out from the f (R)-thoery.Instead for most of binaries we have f 0 values that can surely rule out the theory, since taking account of the weak field assumption we obtain 38 ≤ f 0 ≤ 4 × 10 7 .From this last values to the first ones, there is a jump of about four up to five order of magnitude on f 0 .The origin of these strong discrepancies, perhaps, is due to the extreme assumption we made, to justify the difference between the observed Ṫb Obs and the predicted ṪGR using the ETGs.
Table 1: Upper Limits of f 0 correction to ṪGR of binary relativistic pulsars assuming that all the loss of energy is caused by Gravitational Wave emission.We reported the J-Name of the system,the difference ∆ ṪGR between Ṫb Obs and ṪGR equal to the correction −f 0 Ṫb f (R) , the correction Ṫb f (R) , the corresponding f 0 solution of ( 8), the interval centered on f 0 and computed from the difference ,where f 0 ±δ ,are the corresponding solutions of ( 8) taking account of the experimental errors ±δ on the observed orbital period variation Ṫb Obs .
Discussion and Remarks
In this paper, we develop expressions for quadrupole gravitational radiation in f (R)-gravity theory using the weak field technique and apply these results, which are applicable in general, to a sample of a binary pulsars, though their orbits are eccentric.Here, we seen that, where the GR theory is not enough to explain the gap between the data and the theoretical estimation of the orbital decay, there is the possibility to extend the GR theory with a generic f (R)-theory to cover the gap.According to eq. ( 7),we have selected a sample of relativistic binary systems for which the first derivative of the orbital period is observed, we have computed the theoretical quadrupole radiation rate, and finally we have compared it to binary system observations.From Tab. 1, it is seen that the first five systems have masses determined in a manner quite reliable, while for the remaining sample, masses are estimated by requiring that the mass of the pulsar is 1.4M and, assuming for the orbital inclination one of the usual statistical values (i = 60 • or i = 90 • ), and from here comes then the estimate of the mass of the companion star.So a primary cause of major discrepancies, not only for the ETGs, but also for the GR theory, between the variation of the observed orbital period and the predicted effect of emission of gravitational waves, could be a mistake in the estimation of the masses of the system.In addition, other causes may be attributable to the evolutionary state of the system, which, for instance, if it does not consist of two neutron stars may transfer mass from companion to the neutron star.In our sample, there are only five double NS that can be used to test GR and ETGs.Taking into account of the strong hypothesis we made, the ETG correction to ṪGR can also include the galactic acceleration term correction ( [7], [8]).Here, we give a preliminary result about the energy loss from binary systems and we show that, when the nature of the binary systems can exclude energy losses due to trade or loss of matter, then, we can explain the gap between the first time derivative of the observed orbital period and the theoretical one predicted by GR, using an analytical f (R)-theory of gravity.
ṪGR
. We must note that for five binaries the ETGs we are probing is not ruled out 0.04 ≤ f 0 ≤≈ 38, for those systems the difference between ṪGR and Ṫb Obs is tiny, indeed we get 0.5 ≤ Ṫb Obs ṪGR ≤ 1.5.Instead for most of binaries we have f 0 values that can surely rule out the theory, since taking account of the weak field assumption we obtain 38 ≤ f 0 ≤ 4 × 10 7 .From this last values to the first ones, there is a jump of about four up to five order of magnitude on f 0 .
PSRJ2129+1210CFigure 1 :
Figure 1: In figure there are shown, for sake of convenience, in logaritmic scale, the absolute values of f 0 reported in Tab. 1 versus the ratio Ṫb Obs | 2,254 | 2014-12-04T00:00:00.000 | [
"Physics"
] |
Photoacoustics of single laser-trapped nanodroplets for the direct observation of nanofocusing in aerosol photokinetics
Photochemistry taking place in atmospheric aerosol droplets has a significant impact on the Earth's climate. Nanofocusing of electromagnetic radiation inside aerosols plays a crucial role in their absorption behaviour, since the radiation flux inside the droplet strongly affects the activation rate of photochemically active species. However, size-dependent nanofocusing effects in the photokinetics of small aerosols have escaped direct observation due to the inability to measure absorption signatures from single droplets. Here we show that photoacoustic measurements on optically trapped single nanodroplets provide a direct, broadly applicable method to measure absorption with attolitre sensitivity. We demonstrate for a model aerosol that the photolysis is accelerated by an order of magnitude in the sub-micron to micron size range, compared with larger droplets. The versatility of our technique promises broad applicability to absorption studies of aerosol particles, such as atmospheric aerosols where quantitative photokinetic data are critical for climate predictions.
U nderstanding fundamental processes that govern the reaction dynamics of gas phase, aerosol and cloud processes is crucial for the advancement of global atmospheric chemistry modelling [1][2][3][4][5][6][7][8][9][10][11][12][13][14] . Much of the chemistry occurring in the Earth's atmosphere is driven by sunlight. Photochemical reactions, in which aerosol particles or droplets act as the active reaction medium, can be highly complex because they are influenced by optical phenomena, transport properties and surface effects 2 . Optical phenomena play a fundamental role in light-initiated particle processes since the radiation flux within the particles determines the activation rate of the photochemically active species.
Focusing of electromagnetic radiation inside small particles leads to an enhancement of the overall light intensity, compared with the intensity of the incident radiation and to structuring and localization of the internal optical fields [15][16][17][18][19][20][21][22][23] . These phenomena depend strongly on the particle size, the particle composition and the wavelength of electromagnetic radiation. The fundamental influence of the enhanced electromagnetic energy density on the rate of photochemical reactions in micro-and nanodroplets has been recognized and calculations have provided limited evidence for enhanced photochemical rates [24][25][26][27] . Experimental results remain inconclusive concerning the influence of light enhancement on the kinetics, mainly because direct observation of the actual photoactive step was not possible 23,[28][29][30][31][32][33][34] . The observation of size-dependent effects in ensembles of aerosol or emulsion droplets is often hindered because the droplet size distribution cannot be varied and determined with the necessary accuracy. However, even single-droplet techniques have so far not provided size-dependent photolysis rates because the direct measurement of the population decay of the photoactive substance was not possible.
Elastic light scattering is sensitive enough to allow measurements on single sub-micron-sized droplets, but the information content is not specific enough to extract size-dependent rates. Raman spectroscopy, by contrast, could provide specific information but it comes with the disadvantage of low sensitivity (long averaging times), which would make its application to study processes in single submicrometre droplets where nanofocusing becomes important very challenging. Single-droplet fluorescence studies require a fluorescing compound, which strongly restricts its applicability. Furthermore, the fluorescence depletion is not always a reliable measure of the population decay of the photoactive species because of varying quenching efficiencies. The recently presented cavity ring-down studies on single droplets provide information on the extinction but not directly on the droplet absorption 35,36 . Even in combination with light scattering measurements, the determination of rates in nanodroplets is likely prohibited by the uncertainty of the derived absorption.
This study reports the direct observation of light nanofocusing on the photokinetics in nanometre-to micron-sized droplets in the ultraviolet/visible (UV/VIS) range. To this end, we introduce single-droplet photoacoustic (PA) absorption spectroscopy, allowing the direct detection of the population decay of the photoactive substance. PA spectroscopy has been successfully used for the investigation of ensembles of aerosol particles [37][38][39][40] , but its applicability to single aerosol particle studies has been controversial and has not previously been realised experimentally. Here we demonstrate the feasibility of single-droplet PA spectroscopy in combination with laser trapping, and provide direct experimental evidence for the size-dependence of the photolysis rate in model aerosol droplets due to nanofocusing effects. The results are compared with simulations using classical cavity electrodynamics.
Results
Principle of single-droplet PAs. The two experimental set-ups, using a microphone and a quartz tuning fork, respectively, for resonant single-droplet PA measurements, are sketched in Fig. 1a,b (see Methods). For the droplet absorption experiments, we use a l ¼ 445 nm excitation laser (Nichia laser diode NDB7112E) of variable power (0.3-40 mW) modulated at the resonance frequency of the PA-resonator and the tuning fork, respectively. The resonance frequency and the Q-factor of the PA-resonator and the tuning fork are 3.97 kHz and B8.9, and 32.7 kHz and B8,000, respectively ( Supplementary Fig. 1). The power of the excitation laser is recorded by a power meter after passing the PA cell and the tuning fork, respectively ( Supplementary Fig. 2). The amplified PA signals are averaged over either 30 ms or 200 ms. For single-particle trapping, we use a counter-propagating optical tweezer built from a continuous laser beam of l ¼ 660 nm of B200 mW (Laser Quantum, Opus 660) ( Supplementary Fig. 2). Such multiple beam optical traps allow trapping of sub-micron droplets, and combine the advantage of a comparatively simple set-up with high trapping stability and tight particle confinement (o100 nm) [41][42][43] . Droplets are trapped by gradient forces pointing towards the trap centre for all translational degrees of freedom. Single droplets are captured in the trap centre from a plume of aerosol generated by a nebulizer (see Methods). The droplet size is determined from laser light elastically scattered by the droplet 41,44 (see Methods, Supplementary Fig. 3). Figure 1e shows an example for light scattering measurements for droplet sizing. In the microphone set-up (Fig. 1a), the trap centre is located in the middle of the PA-resonator above the microphone 45 . The trapping and excitation lasers enter and exit the cell through wideband, anti-reflective windows coated for the respective wavelengths. The CMOS camera for particle imaging and light scattering measurements is placed perpendicular to the excitation and trapping laser. The aerosol inlet and outlet are on the side of the PA cell outside the resonator.
In the tuning fork set-up (Fig. 1b), the droplet is trapped between the tines of the fork with collinearly aligned excitation laser and trapping laser beams. The CMOS camera for particle imaging and light scattering measurements is placed opposite the tines of the fork. Figure 1c,d shows images of a single droplet trapped in between the tines and of a droplet ensemble flowing through the tines, respectively. The principal attractiveness of the tuning fork derives from its high detection sensitivity (very high Q-factors) and low sensitivity to environmental acoustic noise 46 . In our set-up, we mainly profit from the ease of combining it with laser trapping and light scattering measurements, as well as from the fact that it is chemically inert.
PA response of a single droplet. Figure 2 provides typical noise levels, background signals and a proof for single-droplet detection. Figure 2a illustrates the noise level and the background signal for the empty trap with the trapping laser on. With the excitation laser off ( À 5 soto0 s), the background signal (average) and noise level (1 s.d.) are B2.2±1.2 mV. Once the excitation laser is turned on at time t ¼ 0 s, a background signal of BS ¼ 5.3 mV with a noise level of NL ¼ 1.7 mV is recorded. The background signal is caused by excitation laser light scattered from the cell walls and hitting the microphone. Blocking the trapping laser (that is, disabling the trap) leaves the noise, as well as the background unchanged. Figure 2b shows the same as Fig. 2a but with a single VIS441/tetraethylene glycol (TEG) solution droplet in the trap. The PA signal reaches a maximum (S max ) just after the excitation laser is turned on and then decreases exponentially as the VIS441 absorber undergoes photolysis. In Fig. 2b, the trap is disabled at ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10941 t ¼ 7 s which leads to the immediate loss of the droplet and to a decrease of the PA signal to the background signal BS. This proves that the signal between 0 soto7 s indeed comes from a single droplet. The signal to noise ratio S NL ¼ S max À BS NL depends on the power P of the excitation laser, the concentration of the solution and the droplet size. Figure 3 shows exemplary experimental data for solution droplets of different size excited with different laser powers P. With the tuning fork set-up, we find an improvement in the S NL ratio of a factor of B3 compared with the microphone set-up. Note that the PA signal is caused by absorptive heating of the droplet and subsequent heat transfer to the surroundings. Evaporation of the solvent does not occur.
Detection limit. The minimum absorbance detectable with the single-particle PA set-ups at a given power of the excitation laser can be estimated from the PA signal and the single-droplet absorbance assuming that the noise level NL is the detection limit (see Methods, Calculation of droplet absorbance). As an example, we use the PA signal at t ¼ 0 (S max ) of the 530 nm droplet shown in Fig (S max À BS) ¼ 33.3 mV corresponds to an equivalent absorbance of A ¼ 1.8 Â 10 À 5 . From the measured NL of the 530 nm droplet of NL ¼ 1.7 mV, we derive a minimum absorbance A min ¼ 9 Â 10 À 7 detectable with the microphone set-up. The improvement in S NL by a factor of B3 for the tuning fork set-up reduces the detection limit to A min B3 Â 10 À 7 , a minimum detectable absorption coefficient of a min ¼ 0.0074 Â 10 À 6 m À 1 or a minimum detectable absorption cross-section C abs,min ¼ 0.0037 mm 2 (laser power of 2.8 mW and averaging time of 200 ms) (see Methods equations (2)-(4)). The equivalent particle radius of 146 nm corresponds to a probe volume of 13 al. This far exceeds the performance of typical spectrometers (A min B10 À 3 -10 À 4 ), and is at least comparable to the most sensitive laser spectroscopic absorption measurements for macroscopic probe volumes. Note that in our set-up, this sensitivity is achieved for small (attolitre) probe volumes and very short (oo1 s) measurement times. Both can be further improved by increasing the laser power. Size-dependent photokinetics. The photokinetics in small droplets do not follow simple pseudo first order kinetics because the light intensity distribution inside the droplets is time dependent; that is, because of the concentration dependence of the nanofocusing. Therefore, we use the same initial concentration for all experiments so that the first half-life can be used as a measure for the size-dependence of the photokinetics. With our PA set-up, we directly measure the decay in absorption resulting from the population decay of the photoactive substance. Diffusion is so fast in the droplets (B10 mm 2 s À 1 ) that concentration gradients cannot build up and homogeneous concentrations for the solute can be assumed at all times. A model for the droplet photokinetics under these conditions is provided in Methods (Calculation of droplet photokinetics).
The model prediction (full blue line in Fig. 4a) shows a strong droplet size-dependence with a maximum in the inverse first halflife 1 t 1=2 at a droplet radius of B0.5 mm. Pronounced increases in 1 t 1=2 and fluctuations due to resonances are observed over the droplet size range from B50 nm to B1.2 mm. In this size range, the increase of the rate is caused by the enhancement of the internal electromagnetic field intensity through focusing of the light inside the droplet. Figure 4b shows the distribution of the light intensity inside a B0.5 mm droplet at t ¼ 0 s. The enhancement of the overall intensity and the local variation of the intensity are pronounced. The inverse half-life at a droplet radius of B0.5 mm is increased by a factor of B2.5 compared with the infinitely small droplet limit. The kinetics in these small droplets is no longer influenced by nanofocusing inside the droplet or light scattering by the droplet as visualized by the internal field intensity in Fig. 4c. The inverse half-life of larger droplets (46 mm) exhibits only a weak size-dependence but decreases continuously (towards zero for infinitely large particles). The rate for these large droplets is determined by the balance between the decay of the absorber and the rise of the decay rate with time. As the photolysis proceeds, the penetration depth of the light and hence the internal field intensity increases. As in the case of very small droplets, nanofocusing is not important for very large droplets. Large droplets essentially represent the behaviour of thin bulk films with the same effective thickness as the droplet. The 1 t 1=2 increases by a factor of B10 for a 0.5 mm compared with a 13 mm droplet, which implies a substantial increase in the rate of sub-micron-size droplets relative to bulk. The dashed red line in Fig. 4a simulates the behaviour of a hypothetical droplet excluding the influence of nanofocusing and light scattering but still accounting for the droplet-size-dependent absorption (see Methods, Calculation of droplet photokinetics). This curve represents bulk behaviour. The comparison with the full blue line clearly shows the pronounced influence of light focusing on the rate in the sub-micron to micron size range.
The statistically evaluated experimental first half-lives (black circles in Fig. 4a) are determined from time-dependent PA measurements (see Methods, Statistical analysis). The experimental results clearly follow the size-trend predicted by the model (full blue line). The pronounced maximum of 1 t 1=2 at a droplet size of B0.5 mm is clearly visible even though the data scatter notably below B1 mm (Supplementary Fig. 6) mainly because of the uncertainty in the droplet size determination (Methods, Droplet Sizing). Our experimental data show somewhat higher values of the inverse half-life for larger droplets than the model prediction. Deviations from the model assumptions including modified PA response in large droplets 47 could potentially account for this. We have recently introduced a broad-band scattering method for accurate sizing of submicrometre particles, which will allow us in future to significantly reduce the size uncertainty in the submicrometre range (unpublished data). However, already at the current level of accuracy, the data in Fig. 4a provide the first direct observation of the strong influence of nanofocusing of light on the photokinetics in droplets.
Discussion
The experimental results in Fig. 4 confirm a strong size-dependence of the rate of photochemical reactions in droplets. This optical phenomenon shows the most pronounced effect in the submicrometre to micrometre droplet size range for electromagnetic radiation in the UV to VIS range, that is, for the relevant frequency range in atmospheric processes. Classical cavity electrodynamics provides a semi-quantitative description of the kinetics for our ideal model system. The photokinetics of our model system is representative of typical atmospheric aerosols; that is, of typical optical properties of these particles. For example, similar quantitative results are predicted for aqueous droplets (Supplementary Fig. 7). The acceleration of the kinetics we find in the visible range is predicted to be even more pronounced in the UV range of the solar spectrum ( Supplementary Fig. 7). Many aerosol particles are non-spherical. However, for particles with different shapes but the same volumes one finds quantitatively similar nanofocusing effects as for droplets. Nanofocusing also affects surface reactions since the strong intensity enhancement in forward direction shown for the internal field in Fig. 4b extends to the external field near the surface (not shown). The ability to measure and thus quantify the kinetics of the light-induced step in photochemical reactions in aerosol particles is of fundamental importance for atmospheric chemistry, where chemical processes are largely driven by sunlight. The diverse and complex processes (for example, transport and surface phenomena) in atmospheric aerosol particles require direct measurement methods as the one introduced here because simple models are of limited applicability.
The introduction of single-droplet PA spectroscopy in the present study finally makes the direct observation of the photoactive step possible. Single-droplet PA was previously deemed not feasible because of sensitivity and background issues. Here we demonstrate the viability of this new method and its very high sensitivity (C abs,min ¼ 0.0037 mm 2 ) enabling studies even of single nanodroplets (10 al). PA spectroscopy provides a general absorption method that can be used in any frequency range. The combination with laser trapping lets us follow the evolution of individual droplets under controlled conditions over extended periods of time (up to several days). This versatility enables fundamental studies on many different droplet systems relevant to atmospheric and technical processes. The investigation of droplet photokinetics is just one example where this new broadly applicable single-droplet method can make an important contribution.
Methods
PA measurements with microphone. The PA cell is made of brass and consists of a longitudinal PA-resonator (length 40 mm, diameter 4 mm), which is connected to two buffer volumes with acoustical baffles for sound insulation (Fig. 1a) 45 . A sensitive microphone (EK 23029, Knowles) is used with a custom-made preamplifier. The output signal is recorded by a lock-in amplifier (Stanford, SR 830).
PA measurements with tuning fork. The distance between the two tines of the tuning fork (Q 32.768 kHz TC 38, AURIS) is 300 mm. Each tine has a width of 600 mm, a thickness of 340 mm and a length of 3.8 mm. The quartz tuning fork acts as the resonant acoustic transducer, which generates an electric signal on resonant excitation by an acoustic wave due to the piezoelectric effect 46 . The signal recording is identical to the microphone set-up except for the more precise reference frequency adapted to the higher Q-factor.
Aerosol generation and materials. To study photokinetics in single droplets, solutions of the photoactive dye VIS441 (Cyanine dye with formula NaC 17 H 25 N 3 O 5 S 3 and molar mass 470, QCR solutions) in TEG solvent (ACROS organics, 99.5%) are nebulized with a medical nebulizer (Pari, PARI Boy SX). A concentration of 4.55 gl À 1 VIS441 in TEG is used. For measurements on pure solvent droplets, pure TEG is nebulized. The Supplementary Fig. 4 shows an UV/VIS spectrum of a bulk solution of VIS441 in TEG and of pure TEG solvent, respectively. Droplet sizing. The particle size is determined from excitation laser light scattered elastically by the droplet. The scattered light intensity is collected for scattering angles between 76.5˚and 103.5˚and focused onto a CMOS camera (Thorlabs, DCC1645C, 1280 Â 1024 pixels) using a camera objective (Super Carenar, focal length ¼ 50 mm, f-number ¼ 1.7). The particle size is retrieved by fitting calculated phase functions to experimental ones using Mie theory 41,44 . The sizing of sub-micron-sized droplets is difficult because only few fringes are left in the scattering pattern (for example, Fig. 1e). Larger particles exhibit brighter scattering images and many more fringes ( Supplementary Fig. 3), which makes sizing easier. We estimate uncertainties in the droplet radius of about half the wavelength.
Calculation of droplet absorbance. The PA signal S is assumed to be proportional to the power P abs absorbed by the droplet, which is located at the centre of a Gaussian excitation laser beam (beam waist radius of 87 mm and cross-section q L ¼ 11,889 mm 2 ) with incident power P I 0 is the intensity incident on the droplet and C abs is the droplet's absorption cross-section. The equivalent absorbance A due to absorption is given by For a single droplet in the PA cell, the equivalent absorption coefficient is given by, where V res ¼ 0.5 cm 3 is the volume of the PA-resonator. The absorption cross-section of the droplet is calculated from the Mie theory 44 with a refractive index of the surroundings equal to 1: Here a n and b n are the scattering coefficients, x ¼ 2pa l is the size parameter, a is the droplet radius, l its wavelength of light in vacuum, o is the angular frequency of the light, e and m are the permittivity and the permeability, respectively, of the droplet, and m ¼ n þ ik is the droplet's complex index of refraction at the wavelengths of the excitation laser (l ¼ 445 nm). The latter is determined from UV/VIS absorption and refractometric measurements of VIS441/TEG bulk solutions and a pure TEG solution using Kramers-Kronig inversion. The refractive index of the VIS441/TEG solution for a dye concentration 4.55 gl À 1 and the pure TEG solvent are n þ ik ¼ 1.463 þ i Á 0.0062 and n s þ ik s ¼ 1.460 þ i Á 0.0000, respectively. The refractive index of the VIS441/TEG solution (dye concentration 4.55 g l À 1 ) in the UV/VIS range is provided in the Supplementary Fig. 5. For other dye concentrations (see photokinetics), it is assumed to depend linearly on the dye concentration.
Calculation of droplet photokinetics. The droplet photokinetics is described by the following rate equation p. Here r denotes the location within the droplet and I is the local field intensity. Both I and s depend on the complex index of refraction, which in turn depends on the number density N, so that the rate law is no longer pseudo first order. The power absorbed by the droplet is given by the rate of absorption integrated over the droplet's volume V Assuming fast diffusion, that is, N 6 ¼ NðrÞ, we obtain: where f ¼ p Á I 0 =hn is the product of incident photon flux and reaction probability. Equation (7) is integrated using a 4th order Runge-Kutta method with the time-dependent PA signal given by equation (1). The corresponding inverse first half-lives of the PA signal as a function of droplet radius are shown as a full blue line in Fig. 4a.
To illustrate the effect of nanofocusing, we compare the above model (full blue line in Fig. 4a) with a model that neglects the influence of nanofocusing (dashed red line in Fig. 4a). This model is obtained from equations (5) and (6) C abs ¼ N t ð Þ Z I r ð Þ I 0 s r ð ÞdV ð8Þ by inserting the small particle limit 44 for s and a Beer-Lambert expression for the intensity distribution within the particle where 'ðrÞ ¼ r cos y þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 2 À r sin y ð Þ 2 q is the absorption path length at distance r from the centre of the particle and at polar angle y relative to the incident beam direction.
Statistical analysis of experimental photolysis data. To account for the uncertainties both in the particle radii and in the decay half-lives of the experimental data set ( Supplementary Fig. 6), we perform a two-step maximum likelihood analysis. First, the distribution of particle radii D a ð Þ ¼ P g i ðaÞ is analysed assuming a normally distributed error for the size determination, with a constant s.d. of s a ¼ 220 nm. The local extrema in D at a k divide the size range into sections with a lower and an upper half for each cluster of data, which are combined into a single section for isolated data points. For each section, we finally obtain the most probable values for particle radius and the inverse half-life as weighted averages over the particles with weights given by, This implies normally distributed errors for the experimental inverse half-lives with s.d. s t,i ranging from about 10% for the most accurate measurements to about 50% for measurements with S NL oo10 (typically small particles). The error bars in Fig. 4a were obtained by s.e. propagation. | 5,569.2 | 2016-03-16T00:00:00.000 | [
"Environmental Science",
"Physics"
] |
Alternation of inverse problem approach and deep learning for lens-free microscopy image reconstruction
A lens-free microscope is a simple imaging device performing in-line holographic measurements. In the absence of focusing optics, a reconstruction algorithm is used to retrieve the sample image by solving the inverse problem. This is usually performed by optimization algorithms relying on gradient computation. However the presence of local minima leads to unsatisfactory convergence when phase wrapping errors occur. This is particularly the case in large optical thickness samples, for example cells in suspension and cells undergoing mitosis. To date, the occurrence of phase wrapping errors in the holographic reconstruction limits the application of lens-free microscopy in live cell imaging. To overcome this issue, we propose a novel approach in which the reconstruction alternates between two approaches, an inverse problem optimization and deep learning. The computation starts with a first reconstruction guess of the cell sample image. The result is then fed into a neural network, which is trained to correct phase wrapping errors. The neural network prediction is next used as the initialization of a second and last reconstruction step, which corrects to a certain extent the neural network prediction errors. We demonstrate the applicability of this approach in solving the phase wrapping problem occurring with cells in suspension at large densities. This is a challenging sample that typically cannot be reconstructed without phase wrapping errors, when using inverse problem optimization alone.
A lens-free microscope is a minimalist setup for in-line holography [1][2][3] . The lens-free records only intensity measurements in the sensor plane, the image of the sample is obtained through computation. A simple procedure consists in back-propagating the measurements, but in the absence of phase information, the reconstructed image is degraded by so-called 'twin-image' artefacts 4 . To overcome the lack of information, various inverse problem approaches have been used to better reconstruct the sample image, i.e. forward model based algorithms, which perform either parameter fitting and/or regularization with a gradient descent scheme [5][6][7][8] . However, if the optical thickness of the sample exceeds /2 , the reconstructed image is still largely incorrect, as the phase values are reconstructed modulo 2π whereas true values can exceed this range. This is the case for cells in suspension and cells undergoing mitosis. Their images are systematically reconstructed with phase wrapping errors. This problem considerably limits the application of lens-free microscopy in live cell imaging. At low cell concentrations, it is possible to apply a simple positive phase constraint to correct the phase wrapping errors 9 . But at large cell concentrations, the accumulation of phase wrappings errors in the reconstruction prevents the use of this method. Recent publications have introduced the use of convolutional neural network (CNN) to address phase unwrapping in digital holography microscopy [10][11][12][13][14][15] . The results obtained by Zhao et al. 13 demonstrate that the CNN solution is robust to unwrap phase containing heavy noise and aliasing. A successfull unwrapping phase images of living mouse osteoblast up to phase shift of 13π has been shown. In the work of Ren et al. 15 , the CNN solution applied to digital holography allows to reconstruct phase directly from the hologram. Different deep learning approaches have been successful in improving lens-free holographic reconstruction results 16,17 but they do not address phase wrapping issues. A specific CNN could be trained to transform a lens-free reconstructed image into an image free of phase wrapping, as obtained with a quantitative phase imaging technique [18][19][20] . A similar approach have been used to transform images between different imaging techniques 21,22 . However, the performance of image reconstruction using CNN is compromised by the problems of hallucination, generalization and adversarial fragility 23 . The hallucination problem deals with insufficient network training, resulting in systematic CNN prediction errors. The generalization problem is a result of overtraining, where the CNN fails Scientific Reports | (2020) 10:20207 | https://doi.org/10.1038/s41598-020-76411-9 www.nature.com/scientificreports/ to process unseen data. At last, in the adversarial fragility problem the CNN can produce widely differing results after adding imperceptible variations to the input. In sum, deep-learning is a data-driven approach which can deliver an outcome very close to the reality, however with an intrinsic lack of confidence in the results owing to the above-mentioned problems.
In order to perform phase unwrapping in lens-free microscopy with a CNN based-solution and address issues of deep learning, here we propose an approach that alternates between the deep learning and inverse problem approach (see Fig. 1). We start the process with a first incorrect reconstruction of the cell sample image. The result is then fed into a CNN, which is improving the reconstruction by removing phase wrapping errors. The CNN prediction is next used as the initialisation of a second reconstruction. The latter returns the final result. In the best case, the alternation approach can lead to an accurate result found trough the CNN prediction which better initializes the inverse problem approach. If the CNN returns an inaccurate prediction with no concordance to the measurements, we expect that the second reconstruction algorithm will retrieve a solution with a better data fit. Note that this approach differs from the three methods based on deep learning recently reviewed in 24 . Our alternation approach is not an end-to-end deep learning engine, it does not predict the sample image from the raw acquisition. It is neither a single-pass physics-informed deep learning engine, applied only once after inversion of the raw acquisition 16,24 . Nor is it a physics-informed deep learning engine, running the regularization in place of a regular gradient-descent scheme 25,26 .
In this paper, we demonstrate the applicability of the proposed alternation approach in solving the phase wrapping problem that occurs in lens-free holographic reconstruction. The approach has been specifically developed for the reconstruction of images of cells in suspension. It has first been developed and assessed on simulations and next validated on experimental acquisitions.
Results
Validation on simulated datasets. Figure 2 shows the outcome of the proposed three-step reconstruction algorithm for three examples of the synthetic validation set corresponding to different cell densities-low, medium and high. The number of cells contained within the entire 1000 × 1000-pixel image were 1001, 2547 and 4569 corresponding respectively to densities of 358, 909 and 1627 cells/mm 2 . Note, the hologram of the high density case is speckle-like. As expected, objects recovered by the first (old) reconstruction, shown in Fig. 2c are degraded, with the presence of numerous wrapping errors in the OPD map (occurring when L exceeds /2 ). Absorption maps A show cells outlined with absorbing circle artefacts. In the high density case, the first holographic reconstruction results are barely intelligible. In comparison, L and A images predicted by the CNN (Fig. 2d) are better matched to the ground-truth images. The final (new) reconstruction results ( Fig. 2e) have similar appearance as the CNN results. Figure S1 shows the convergence plots for these reconstructions, namely the data fidelity criterion, the regularization criterion and their sum as a function of the iterations (see Eqs. 3, 4 and 5). Notably, Fig. S1 shows that the CNN used for phase unwrapping systematically introduces a large deviation between the prediction of the model and the measurements. This error is corrected by the third step, which improves data matching and allows for a low regularization term. The peak signal-to-noise ratio (PSNR) values measured between results and ground truth are given in Fig. 2. The CNN increases the PSNR values by almost a factor two in comparison with the first reconstruction. The PSNR measured on the final reconstruction are slightly lower than what obtained on the CNN prediction. In order to better assess these results, Fig. 3 shows a quantitative comparison between reconstructed and ground truth values for the three different cell densities presented above. The values of the real and imaginary part of the cell refractive index, n r_recons and n i_recons respectively, were obtained from the reconstructions (see Eq. 7) and compared to their ground truth values. For the first reconstruction, even at low concentrations, there is no correlation between reconstructed and ground truth values. In comparison, the results obtained with the CNN and the second reconstruction are linearly correlated with the ground truth values. For the n r_recons values, we found good correlations up to index values of 0.05 and up to a cell density of 900 cells/mm 2 (Fig. 3a,c). The slopes of the linear regressions are in the range of 0.84 to 0.96 and the coefficients of determination R 2 are all larger than 0.75. The best results are obtained with the second reconstruction which is slightly better than the CNN output. At the highest tested cell density of 1618 cells/mm 2 (Fig. 3e), values are correlated up to index values of 0.03. Regarding n i_recons , the reconstructed imaginary part of the cell refractive index, the results correlate with the ground truth values only at the low concentration of 360 cells/mm 2 (Fig. 3b). The slopes of the linear regressions are about 0.6 and the coefficients of determination R 2 about 0.7. Again the results obtained with the second reconstruction are slightly better than what was obtained with the CNN. Fig. 4). Distance Z was determined to be 1830 µm , a network was trained for this distance. In the absence of reference measurements obtained with quantitative phase imaging techniques 18,19 , we can only discuss the reconstructed images in a qualitative way. Figures 4 and 5 show that the results obtained on experimental data are in line with the results In agreement with the simulated data, the last reconstruction step improves the matching between our model and measured data (see convergence plot in Fig. S1). This improvement brought by the third step can also be seen on the resulting image. Figure 4j points out errors introduced by the CNN but corrected by the third step. Fluorescence microscopy was used to validate the positions and the shapes of the cells in the reconstructed images. Based on the comparison between the two modalities, we conclude that reconstructions from our alternation approach recover well the low density sample and give satisfactory results at high densities. The red boxes in Fig. 5 show typical discrepancies which appear at large cell density in the presence of the largest cells. This in agreement with the simulation which pointed out that the CNN is effective at large cell density only up to a given refractive index value (Fig. 3c,d). With these results, we can therefore conclude that the alternation approach is effective up to a concentration of ∼ 1000 cells/mm 2 , in agreement with results of the simulation study.
As a generalization test, we applied the proposed alternation reconstruction approach to the acquisitions of different cell lines in suspension. Supplementary figures depict the reconstruction of cell culture in suspension . The CNN performs phase unwrapping while the last reconstruction step improves the matching between the model prediction and the measurement (see Fig. S1). As a second test, we applied the method to the reconstruction of a sample not considered during the CNN training, namely the acquisitions of an adherent mammalian cell line. Figure 6 shows the results obtained on the acquisition of adherent PC12 cells treated with neuron growth factor (NGF). Distance Z for this experiment was evaluated at 3500 µm , a dedicated CNN was trained at this distance. Interestingly, in this case it is possible to clearly distinguish the three different steps of the alternation approach and their impact on the image reconstruction. After the first holographic reconstruction, the image appears degraded (Fig. 6a,d,h,l). The large thickness of the cells results in several phase wrapping artefacts. The neuron heads are reconstructed with negative values (see blue profile in Fig. 6g). Finer morphological features are not well reconstructed, for instance the neurites which are www.nature.com/scientificreports/ only 1 to 3 μm wide. The CNN prediction performs well phase unwrapping at the location of the neuron cell body (see orange profile in Fig. 6g), but the complexity of the scene is lost. The CNN prediction presents only rounded spots with positive phase values (Fig. 6b,e,i,m). Details such as the neurites are lost in the process (see orange profile in Fig. 6k). Obviously these details were not present in the training dataset, the CNN output is thus facing here a generalization problem. In addition, the CNN predicts the presence of rounded spots that are not present in the scene (see orange profile in Fig. 6o). The CNN output is thus facing here a hallucination problem. Notably, the final reconstruction corrects these CNN predictions (see green profiles in Fig. 6k,o). This example shows the good complementarity of the two algorithms. The CNN addresses the phase unwrapping and the final reconstruction retrieves the finer details that are lost in the CNN prediction. The PC12 cells could therefore be well reconstructed using the alternation approach whereas the complexity of these images was not accounted in the CNN training data set. As a last example, Fig. S5 depicts a case, namely the culture of adherent fibroblast cells, where the three steps approach was not successful. We observe errors introduced by the CNN that are not corrected by the last reconstruction. In particular, in Fig. S5c the CNN outputs two cells (red arrow A in Fig. S5c) whereas the first reconstruction present only one (Fig. S5b). In this case, the last reconstruction does not recover a single cell image (red arrow A in Fig. S5d) and outputs two cells instead. This last example indicates that the alternation method does not fully generalize when applied to samples of adherent cell culture.
Discussion
In this article, we introduce a novel reconstruction approach, based on alternations between an inverse problem approach and deep learning using CNN to improve lens-free image reconstruction. We have designed the CNN to perform phase unwrapping on the acquisition of cells in suspension. CNN has been trained on synthetic datasets and we demonstrate the generalization to real samples. On a sample of PC3 cells in suspension, we show an effective phase unwrapping up to phase shift of 5 π . With this method we succeeded in reconstructing cells in suspension at large cell densities of up to ∼ 1000 cells/mm 2 . This allows us to observe 35,000 cells simultaneously in a field of view of 30 mm 2 with our lens-free system. According to simulations, at this concentration, the method is quantitative for the determination of the cell refractive index (real part). Alternatively to the other CNN-based lens-free microscopy techniques 17,18 , our final image is obtained with a reconstruction step following the CNN prediction. As an advantage, this last reconstruction can correct the prediction of the CNN when www.nature.com/scientificreports/ it is not in agreement with the measured data. In some cases, this third step allows the reconstruction of sample different from the original training data. As an example, we have shown that our approach is successful in reconstructing the image of PC12 adherent cells. However, the alternation approach was not successful when tested on the acquisition of adherent fibroblast cells. Hence, the proposed alternation approach does not generalize to the large domain of adherent cell culture. In sum, the novel CNN-based solution allows to reconstruct the image of the cells in suspension free of phase wrapping errors. It extends thus the applicability of lens-free microscopy to the live imaging of cells in suspension. www.nature.com/scientificreports/
Method
The proposed alternation approach is a three-step algorithm (see Fig. 1). A first holographic reconstruction is initialized using a null sample, leading to the computation of a first guess of the sample image. The result of the first reconstruction is used as the input for a convolutional neural network, which has beforehand been trained to correct the object phase image from wrapping errors. The CNN is not trained with experimental image data, but instead with synthetic images. The network output is next used as initialization of the last holographic reconstruction step. In the following, we detail the different steps of the reconstruction algorithm and describe the synthetic CNN training. Next we present how we assess the reconstructions of the simulated floating cells in a quantitative manner. Finally we describe the lens-free setup and the cell lines used for the experimental validation.
Holographic reconstruction. The holographic reconstruction generates an object description from intensity measurements. It relies on a given physical description of the object and a forward model which allows to predict the measurements for a given object (see "Physical model"). The reconstructed object is obtained with an inverse problem approach, namely a gradient-based iterative process minimizing a given criterion (see "Inverse problem approach").
Physical model. Partially coherent illumination is diffracted by the object as shown in Fig. 7. The intensity of the generated interference pattern (hologram) at a distance Z behind the sample is recorded with a camera. The light field, at wavelength , is described as a complex scalar field and the illumination light is described by a plane wave with normal incidence and with intensity normalized to one. The transmission of the sample is assumed to be directly related to L the optical path difference (OPD) and A its (negative) absorption coefficient. The light field E after the sample is: i being the imaginary unit. By using the Fresnel propagator, h Z (r) = 1/(i Z) exp(iπr 2 /( Z)) , and taking into account the partial coherence of the light source by a convolution kernel K, and the uniform light intensity B ("background"), a direct model of the intensity measurement of image I is set as: where '*' is the convolution operator. I(L, A) is the measurement used in the subsequent data processing, it is sampled by the sensor. The unknowns L and A, have the same size as I. There are particular difficulties related to the lens-free setup. First, for any integer N, L + N results in the same transmission and consequently the same measurements. This will give rise to wrapping problems, as the reconstruction of L will be known modulo values only. Second, the phase of the light field is not recorded by the detector. Therefore "half " of the information is lost during the detection process, giving rise to so-called 'twin-image' artefacts 4 . Furthermore, high intensity frequencies are lost due to partial coherence of the source, i.e. non-point and multi-spectral source. This is reflected in the forward model by the convolution kernel K. In this study, to compute such a kernel K, we perform two simulations on a Dirac object, one with total source coherence and one with partial source coherence (source dimension is taken into account and source spectrum is discretized, see Table 1 for source characteristics) giving rise to measurements I total and I partial . K is extracted by deconvolving I partial from I total .
Inverse problem approach. The inverse problem approach used to retrieve the object from intensity measurements is formulated as a regularized optimization problem. A criterion ǫ implementing a data fidelity term and a regularization term ζ for the unknowns L and A is set as: Where I(L, A) is the direct model (see Eq. 2) and I meas is the intensity measurement. As shown in Fig. 1, two reconstruction steps are performed in the proposed algorithm. The first reconstruction is intended to be a fast www.nature.com/scientificreports/ step, with kernel K of Eq. (2) set to a Dirac distribution, limited to a low number of iterations (20) and with no attempt to phase unwrapping. For this first reconstruction the regularisation term is: The first term of Eq. (4) is the total variation applied to the complex light field E to favor sharp edges. The spatial derivative of this term is not sensitive to jumps of L and will not propagate wrapping artefacts. The second term is a sparsity constraint on L. The third term limits the absorbance of the object to positive values. In comparison with the first reconstruction, the second reconstruction performs a larger amount of iterations (70) and takes into account the coherence of the illumination source, using a kernel K. In addition, the regularization term is more complex. This is the optimization scheme that has been previously published in 20 . The regularization term in the second reconstruction is set to: Compared to Eq. (4), the first term is now expressed with variable L, the OPD. This is possible since the object is assumed to have been unwrapped by the performed CNN step. The third term favors a smooth map of A and the last term implements the constraint that the unwrapped OPD must be positive. As shown previously 7 , the gradient of ǫ(L, A) can be analytically computed. The minimization of the criterion is performed by a conjugate gradient optimizer.
CNN for phase unwrapping of lens-free acquisition. The CNN step (see Fig. 1) takes place between the two holographic reconstruction steps and is processing the results of the first reconstruction to correct phase wrapping errors. Indeed, data fidelity term being insensitive to phase wrapping error, a regularized criterion such as defined in Eq. (3) will present local minima, which cannot be handled by gradient-based optimization.
To overcome these local minima, we have trained a CNN to perform specifically phase unwrapping. The CNN needs to be trained on a set of input/target object pairs with phase wrapping errors. To this aim, we generated synthetic images of cells in suspension and the corresponding first reconstructions.
Synthetic data. We generated synthetic images representing cells in suspension, with homogeneous spheres of random radius and with complex refractive index (see Fig. 8 and see Table 1). The relationship between OPD L, the absorption coefficient A and the refractive index of the cell n, the refractive index of the surrounding medium n medium and the thickness of the cell T is given by: Based on Eq. (2), the intensity measurement images I in the sensor plane are simulated for a given sample-tosensor distance Z, coherence of the illumination source and background B. Furthermore, to mimic the noise in the acquisition process, Poisson noise is added to the simulated hologram I. The number of cells is chosen randomly between 500 and 5000 (corresponding to a density range of 179-1792 cells/mm 2 ). Their radii are uniformly drawn between 5 to 20 µm , real and imaginary parts of the refractive index are drawn from a uniform distribution between 0.01 to 0.05 and 0 to 0.005 respectively. Figure 8 shows example images of the synthetic data. The results of the holographic reconstruction differ notably from the ground truth images, due to wrapping errors and incomplete physical modelling (kernel K is set to Dirac in the forward model). This result is T(x, y) Im(n − n medium ) = −2π T(x, y) �n i www.nature.com/scientificreports/ foreseeable and not a problem per se. The reconstruction merely aims at producing a valid object to be used as an input for the CNN network.
Training of CNN. We constructed a simple CNN network consisting of 20 repetitions of a three layers pattern, namely a convolution layer ( 5 × 5 pixel, 32 features), a batch normalization layer and a ReLU activation function (see a sketch of the CNN structure in Fig. 9). The final layer before the regression layer was a convolution layer with 2 features (L and A outputs) so as to match the ground truth image dimensions. The network does not perform any dimension changes, allowing images of any size to be used as training input. To train a CNN for unwrapping lens-free reconstructed phase images, the ground truth consisted of a synthetic dataset of 1000 image pairs ( 1000 × 1000 pixels for L and A) of cells in suspension. The CNN input contains the corresponding reconstructed images ( L recons and A recons ). Two sets of vignettes (size 121 × 121 ) were extracted randomly from the reconstructed images and used during the CNN training. CNN training was implemented with the Matlab deep learning library using the Adam optimizer. We used 12,800 sets of vignettes per epoch (a set being a vignette couple (L recons , A recons ) as input and a corresponding vignette couple as ground truth). Learning rate was set to 0.0001 and training was conducted over 10 epochs, lasting 10 h on a PC workstation with a single NVIDIA GTX Titan GPU.
Evaluation of the results obtained on synthetic datasets. The simulated reconstructions have been quantitatively compared to the known ground truth, considering the cell relative refractive index values. From the reconstruction (L recons , A recons ) , it is possible to retrieve for each cell the real imaginary parts of the relative refractive index according to the formula: Figure 8. Overview of the synthetic data generation method. A pair of synthetic images (ground truth) is generated, representing cells in suspension (L denotes the optical path difference and A the absorption). Using Eq. (2), the simulated intensity measurement image I is obtained for a given sample-to-sensor distance Z. The first reconstruction applied to I generates the simulated images L recons and A recons . The presented images are 400 × 400 pixels ( 1.67 µm pitch) crops of an image with 10 3 cells corresponding to a density of 358 cells/mm 2 . www.nature.com/scientificreports/ where k is the index of the cell, S (k) the integration domain calculated knowing the position and radius of the cell, and V (k) the cell volume.
Description of the lens-free setup. To evaluate the alternation reconstruction method on experimental data, we carried out measurements using a Cytonote lens-free setup (Iprasense). Illumination is provided by a monochromatic LED source (at wavelength = 457 nm with a spectral width of 20 nm ) located 50 mm away from the sample. A CMOS detector of 6.4 × 4.6 mm 2 with 3840 × 2748 pixels ( 1.67 µm pitch) was used to measure the diffraction patterns at a distance Z = 1−4 mm from the sample.
Description of the cell samples. PC3 cells were cultured in RPMi 1640 medium, containing 10% fetal bovine serum, 50 ng/mL geneticine and 1% of PenStrep. Cells were passed twice a week, using a 1:6 dilution. Cell density for experiments was typically 1 × 10 5 cells/mL. PC3 cells contained a GFP expressing vector. PC12 cells were cultured in proliferation medium, consisting of RPMi 1640 medium, supplemented with 10% Hi Horse Serum, 5% fetal bovine serum and 1% of PenStrep. They have been passed twice a week at a 1:10 dilution. To perform differentiation into a neuronal phenotype, cells were plated at a density of 1 × 10 4 cells/mL in differentiation media, consisting of RPMi medium supplemented with 1% Hi Horse Serum and 50 ng/mL NGF. | 6,220.2 | 2020-11-19T00:00:00.000 | [
"Physics"
] |
The LHS 1678 System: Two Earth-Sized Transiting Planets and an Astrometric Companion Orbiting an M Dwarf Near the Convective Boundary at 20 pc
We present the TESS discovery of the LHS 1678 (TOI-696) exoplanet system, comprised of two approximately Earth-sized transiting planets and a likely astrometric brown dwarf orbiting a bright ($V_J$=12.5, $K_s$=8.3) M2 dwarf at 19.9 pc. The two TESS-detected planets are of radius 0.70$\pm$0.04 $R_\oplus$ and 0.98$\pm$0.06 $R_\oplus$ in 0.86-day and 3.69-day orbits, respectively. Both planets are validated and characterized via ground-based follow-up observations. HARPS RV monitoring yields 97.7 percentile mass upper limits of 0.35 $M_\oplus$ and 1.4 $M_\oplus$ for planets b and c, respectively. The astrometric companion detected by the CTIO/SMARTS 0.9m has an orbital period on the order of decades and is undetected by other means. Additional ground-based observations constrain the companion to being a high-mass brown dwarf or smaller. Each planet is of unique interest; the inner planet has an ultra-short period, and the outer planet is in the Venus zone. Both are promising targets for atmospheric characterization with the JWST and mass measurements via extreme-precision radial velocity. A third planet candidate of radius 0.9$\pm$0.1 $R_\oplus$ in a 4.97-day orbit is also identified in multi-Cycle TESS data for validation in future work. The host star is associated with an observed gap in the lower main sequence of the Hertzsprung-Russell diagram. This gap is tied to the transition from partially- to fully-convective interiors in M dwarfs, and the effect of the associated stellar astrophysics on exoplanet evolution is currently unknown. The culmination of these system properties makes LHS 1678 a unique, compelling playground for comparative exoplanet science and understanding the formation and evolution of small, short-period exoplanets orbiting low-mass stars.
Introduction
Small planets (<4 R ⊕ ) are frequently found around low-mass stars, which are in turn the most common stars in the Galaxy (Henry et al. 2006). The preponderance of small planets on short-period orbits around M dwarfs is revealed in statistical analyses of both ground-based radial velocity survey discoveries (Bonfils et al. 2013) and transiting planets from the Kepler survey (Dressing & Charbonneau 2013Hardegree-Ullman et al. 2019). High-priority individual systems discovered using dedicated ground-based transit surveys (e.g., from MEarth, Irwin et al. 2009, andTRAPPIST, Jehin et al. 2011) added to this haul of planetary systems. These systems, with small host stars and relatively deep planet transits, present some of the best opportunities for detailed characterization of small-planet bulk compositions and atmospheres. This M dwarf advantage led to these stars being a focus of exoplanet searches with the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015), although it is not the sole purpose of the mission. TESS is performing a nearly all-sky survey to identify exoplanet systems around the nearest, brightest stars. These are most compelling for follow-up characterization studies to measure masses and investigate atmospheres with, e.g., the Hubble Space Telescope (HST) and the James Webb Space Telescope (JWST). M dwarfs are brightest in the red-optical to near-infrared wavelength range, though still fainter than more massive main sequence stars. With this in mind, TESS uses a broadband filter that ranges from 600 to 1000 nm, the red end of silicon CCD sensitivity. With ongoing discoveries from TESS and its improved sensitivity to these ubiquitous stars, our ability to focus on characterizing these exoplanet systems is improved compared to the Kepler mission.
Scattered among these bright nearby systems discovered by TESS are those uniquely poised for interesting follow-up observations. These include some of the closest and brightest M dwarf systems: LTT 1445 A (Winters et al. 2019), GJ 357 (Luque et al. 2019), and AU Microscopii (Plavchan et al. 2020). TESS has also revealed small planets orbiting bright M dwarfs with extreme orbital architectures, like the ultra-short-period LHS 3844 (Vanderspek et al. 2019) in an 11 hr orbit. Kreidberg et al. (2019) demonstrated the feasibility of characterizing such a planet's atmosphere, or lack thereof, by measuring the thermal emission coming from LHS 3844 b using Spitzer. M dwarf multiplanet systems amenable to detailed characterization have also been uncovered by TESS. Both the L 98-59 (Kostov et al. 2019a) and LP 791-18 (Crossfield et al. 2019) systems are comprised of multiple planets of different sizes orbiting bright nearby M dwarfs. These systems include small, relatively cool planets that are key for detecting atmospheres in transit. Planets in both systems are priority targets for early science observations with the JWST.
Continuing this stream of M dwarf planet discoveries from TESS is the LHS 1678 system. Here we present a holistic characterization that includes an in-depth analysis of the host star's properties, the identification of a wide-orbit, low-mass companion, and the characterization of two Earth-sized planets and a third small planet candidate in a compact system.
TESS Observations, Candidate Identification, and Vetting
LHS 1678 (TIC 77156829, TOI-696, L 375-2, LTT 2022, NLTT 13515) was observed by TESS in Sector 4 from UT 2018 October 19 to November 14 (25.95 days), in CCD 1 of Camera 3, and in Sector 5 from UT 2018 November 15 to December 11 (26.31 days), in CCD 2 of Camera 3. LHS 1678 data were collected at 2 minutes cadence because the star was prioritized for high-cadence measurements as part of the Cycle 1 Guest Investigator Program G011180, 40 the Cool Dwarf target catalog (Muirhead et al. 2018), 41 and the TESS Candidate Target List (CTL; Stassun et al. 2018b). LHS 1678 was also observed in Sectors 31 and 32 at 2 minutes cadence, after the majority of the analyses here were performed. We briefly discuss preliminary findings from the full four-sector TESS data set in Section 7.1. Aside from the aforementioned section, we focus our analyses on TESS Sectors 4 and 5 data only.
TESS 2 minute cadence data were processed into target pixel files (TPFs) and subsequent light curves by the NASA Ames Science Processing Operations Center pipeline (SPOC; Jenkins et al. 2016). The light curves revealed a star with little variability above the TESS noise level (indicating a lack of surface activity such as star spots) over nearly two months of continuous observations and exhibited no evidence for flares. The light curves were searched for periodic, transit-like signals using the Transiting Planet Search module (TPS; Jenkins et al. 2010) and revealed two candidate planet signals that passed a 40 Differential Planet Occurrence Rates for Cool Dwarfs -PI: C. Dressing. Details of approved TESS Guest Investigator Programs are available from https://heasarc.gsfc.nasa.gov/docs/tess/approved-programs.html. 41 http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/AJ/155/180 series of data validation tests (Twicken et al. 2018;Li et al. 2019). The TESS pipeline identified two candidates, TOI-696.01 and .02, with periods of 0.86 and 14.76 days, respectively, and transit depths that corresponded to planets with radii approximately 1 R ⊕ for an early M dwarf host star (see Section 3). Based on this, we began independent vetting and validation studies of the candidates to determine if the system should be prioritized for further follow-up.
Following our team's established procedures (Kostov et al. 2019a;Gilbert et al. 2020) we used the DAVE vetting tool (Kostov et al. 2019b) to identify potential sources of false positives and verify the results of the SPOC pipeline validation tests. We verified that the transits associated with TOI-696.01 were on-target, and there were no differences in odd-and evennumbered transits. The phase-folded sets of odd-and evennumbered transits showed similar depth and shape, and there was no evidence for a secondary eclipse indicative of an eclipsing binary. Our DAVE vetting of TOI-696.02 was less straightforward. There were only two transits per sector at the 14.76 day SPOC-identified period, so centroid estimates and odd/even checks were not meaningful. However, the analysis did reveal additional transit-like signals at 1/4 the period identified by the TPS pipeline. We also used preliminary host star parameters as input to the publicly available statistical validation tool vespa (Morton 2015) to estimate the numerical probability that the identified candidates were false positives (see also Section 6). The vespa analysis indicated a low falsepositive probability (FPP) for TOI-696.01 (∼1%) but a high probability (∼75%) that TOI-696.02 at the 14.76 day period was a false positive, resulting from the residual transit-like signals also identified in the DAVE vetting.
Following this lead, we examined the SPOC data validation reports for TOI-696.02 and found similar evidence for excess signal at 1/4 the originally identified period in the phased light curve. We then performed two independent planet candidate searches in an attempt to recover the TPS candidates at the same periods. Using both a modified version of the Quasiperiodic Automated Transit Search (QATS; Carter & Agol 2013;Kruse et al. 2019) and Transit Least Squares (TLS; Hippke & Heller 2019a search pipelines, we identified transiting planet candidates with periods of 0.86 days and 3.69 days, recovering TOI-696.01 at the same period and identifying TOI-696.02 at one-quarter the original period, consistent with the excess signal identified in our vetting and validation efforts. With the SPOC team, we investigated the details of the TPS candidate search to reconcile the period difference for TOI-696.02. The discrepancy was traced to statistical tests and threshold settings in TPS (Seader et al. 2013) that were failed (but only marginally) by TOI-696.02 at the shorter period. While the multiple event statistic (MES, a detection statistic tuned to measure the detection strength of periodic transit-like signals) for the candidate was higher at a period of 3.69 days, there were more individual transits and their contributions to the MES were not sufficiently consistent to pass additional statistical tests in TPS. This resulted in a period of 14.76 days being favored, where fewer individual transits contributed to the MES, but in a more consistent way. With fine tuning, TPS does recover the candidate with higher MES at 3.69 days, consistent with our independent QATS and TLS searches. We verified that the shorter 3.69 day period for TOI-696.02 produced reliable and consistent results in reanalyses using both DAVE and vespa. For the subsequent analyses presented in this paper we adopt periods of 0.86 and 3.69 days, respectively, for the planet candidates TOI-696.01 and .02.
Observed Parameters
We report measured astrometric, kinematic, photometric, and spectroscopic properties of LHS 1678 in Table 1, both taken from the literature and observed in this work.
Literature astrometry data come from Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2016Collaboration et al. , 2018Lindegren et al. 2018), the most current release at the time of our analyses. The most recent Gaia Early Data Release 3 (EDR3; Lindegren et al. 2021) parallax is only 0.1% different; an update to EDR3 is not expected to have significant scientific return. Photometric data come from Gaia DR2, Winters et al. (2015), the TESS Input Catalog Version 8 (TIC v8; Stassun et al. 2019), the Two Micron All-Sky Survey (2MASS; Cutri et al. 2003;Skrutskie et al. 2006), and the Wide-field Infrared Survey Explorer (WISE) AllWISE data release (Wright et al. 2010;Cutri et al. 2014). The BP and RP bandpasses are slightly different in Gaia EDR3 (Riello et al. 2021), showing up as a 0.02 magnitude difference for LHS 1678. We opt to use the DR2 photometry for comparison to previous works that use the DR2 magnitudes (e.g., in Section 7.5). Radial velocities (RVs) come from observations using the CHIRON spectrograph on the Small and Moderate Aperture Telescope System (SMARTS) 1.5 m at the Cerro Tololo Inter-American Observatory (CTIO, CTIO/SMARTS 1.5m) and High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph on the European Southern Observatory (ESO) 3.6 m. The details of the RV observations and analysis are described in the context of system follow-up in Section 4.3. Kinematic information is derived by combining astrometric information and RVs. Our methodology is described in the context of possible thick disk membership in Section 3.3. Spectral types come from Reid et al. (2007) and the Pecaut & Mamajek (2013) color-temperature table. 42 We complement these results with our own, derived following the procedure of Henry et al. (2002) using a spectrum taken on 2005 January 30, using the CTIO/SMARTS 1.5 m Ritchey-Chrétien Spectrograph (RC Spec; Figure 1). These methods yield results within 0.5 subtypes of each other at M2.0 to M2.5.
Photometric metallicity relations from Bonfils et al. (2005;their Equation (1); K , V, K ), Mann et al. 2013 (their Equation (29); J, K as per V − K < 5.5), and Kesseli et al. (2019;their Equation (6); J, K ) yield estimated [Fe/H] values of −0.54, −0.36, and −0.67, respectively, for LHS 1678. As we will discuss in the context of stellar age in Section 3.3, these are in line with the star's position on the Hertzsprung-Russell (HR) diagram, spectral energy distribution (SED) fitting results, etc., all of which imply its metallicity is lower than most main sequence stars with similar effective temperature. Without an appropriate spectrum from a medium-resolution optical/nearinfrared spectrograph with an established metallicity pipeline for M dwarfs, which includes TripleSpec on the Palomar Hale 200″ telescope (Rojas-Ayala et al. 2012;Dressing et al. 2017), SNIFS on the University of Hawai'i 88″ telescope (i.e., Mann et al. 2013), and SpeX on the NASA Infrared Telescope Facility 3 m (i.e., Mann et al. 2013), we do not adopt a particular metallicity value, but rather pool together the available evidence to report that LHS 1678 is metal poor.
Stellar Fundamental Parameters
Stellar mass, rotation, effective temperature, luminosity, and radius were estimated using multiple methods. Here we describe the method used to derive the values we adopt for all subsequent analyses. All other methods and values are described in Appendix A, with the exception of a spectroscopically derived projected rotation velocity discussed in Section 4.3.
cTo estimate the stellar mass, we use the Benedict et al. (2016) mass-luminosity relations for absolute magnitudes V and K (their Equation (11)). These relations are calibrated using the individual masses of M dwarf binary components, rather than total system masses or model-based masses of single stars. For LHS 1678, we adopt the mean result of the V and K relations, M = 0.345 ± 0.014 M e .
Our methodology to derive effective temperature, luminosity, and radius is based upon that of Dieterich et al. (2014), to be presented in depth in M. L. Silverstein et al. (2022, in preparation). To derive the radius of 63 objects near the star/brown dwarf boundary, Dieterich et al. (2014) compared the BT-Settl 2011 photospheric models (Allard et al. 2012) to a variety of color combinations comprised of (VRI) B JHK S W1W2W3 photometry (subscript "B" for Bessell 1995 photometric system). Our procedure is an automated version of that code which uses V J R KC I KC instead of the Bessell system 43 and is applicable to the full range of M0V to L2.5V spectral types.
Effective temperature. By comparing an ensemble of observed colors to those extracted from the model grid we determine a best-fitting model with the smallest residuals for each of nine chosen colors. This provides an effective temperature (T eff ) for each color; we adopt the average as our result. T eff error is the standard deviation added in quadrature with 50 K, half the interval of the model grid. We note that we adopted a set model metallicity value of −0.5 for this procedure based on the photometric metallicity estimates previously described (see Section 3.1). Results from different stellar parameter estimation methods (see Appendix A) were also more consistent with each other when subsolar metallicity was assumed. The spectrum exhibits deep absorption bands from TiO, VO, and CaH from ∼6000-8000 Å, a characteristic of M dwarfs. We do not see the strong CaHn (n = 1-3) and TiO5 bands typically associated with cool subdwarfs (Gizis 1997). Following the methodology described in Henry et al. (2002), the spectrum yields a type M2.0V.
Bolometric flux. Once T eff is derived, the model spectrum closest to the final value is iteratively scaled by a polynomial until observed and model photometry match to within 0.03 mag. The modified spectrum is then integrated within the wavelength range of the filters to get a partial flux. A bolometric correction is applied based on the amount of flux that would be missing from a blackbody of the same temperature viewed within our wavelength window. Bolometric flux error is derived using the mismatch between the final model and observed magnitudes and their observational errors.
Bolometric luminosity, radius, and density. The bolometric flux is scaled by the Gaia DR2 parallax to calculate luminosity, and radius is determined using the Stefan-Boltzmann law. Density is then calculated using our derived mass and radius. In a sample of 26 stars with interferometrically measured radii, the radii derived via this method matched those obtained via longbaseline interferometry to within an average of 6%. The estimated stellar parameter values used in this work are consolidated in Table 2.
Stellar Age
A combination of high galactic motion, low magnetic activity, low metallicity, and position on the HR diagram implies that this star is part of a population older than most of the thin disk.
Galactic kinematics. Combining our measured RV and Gaia DR2 astrometry, we have derived a total galactic motion with respect to the local standard of rest (LSR; Coşkunoǧlu et al. 2011) of 94.6 ± 0.4 km s −1 (see (UVW) LSR in Table 1). This is a key property in identifying Galactic populations. Stars with total galactic motion between ∼85 and ∼180 km s −1 are likely part of the Galactic thick disk (Nissen 2004;Bensby et al. 2014). Gan et al. (2020) use a method put forth by Bensby et al. (2003Bensby et al. ( , 2014 to identify the TESS exoplanet system LHS 1815 as a thick disk member. Here we follow suit (according to Appendix A of Bensby et al. 2014), with less definitive results. TD/T is the ratio of the probability of being in the thick disk to the probability of being in the thin disk. We use our (UVW) LSR space motions to derive TD/T = 0.44. According to the metric of Bensby et al. (2014), this value indicates that LHS 1678 is likely in the thin disk, but just short of being classified an "in-between" star with galactic kinematics intermediate to the bulk of the thin and thick disk populations (0.5 TD/T 2.0). Following the metric adopted by Gan et al. (2020;0.1 < TD/T < 10), LHS 1678 is in between the two populations. We therefore conclude that the Galactic membership of LHS 1678 is uncertain, but the system is likely more kinematically heated and older than the average thin disk star.
Low magnetic activity and rotation. The TESS light curve spanning two sectors showed no signs of magnetic activity, either in the form of spot modulation or flares. We also extracted archival data from the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014;Kochanek et al. 2017;Jayasinghe et al. 2019) using the online tool 44 and the Gaia DR2 J2015.5 coordinates. The Lomb-Scargle (LS) periodograms of the 3.9 yr V-and 6.7 yr g-band data sets show no signs of rotation modulation (Figure 2), in line with our TESS findings, and only single-point outliers that cannot be confirmed as flares without higher cadence data. Our 16 yr CTIO/SMARTS 0.9 m data set, discussed in detail in Sections 3.5 and 3.6, also reveals low photometric variability and no flares and on longer timescales. Without spots in our time-series photometry, we are unable to derive a photometric rotation period. Our HARPS and CHIRON RV analyses indicate the star is a relatively slow rotator, with minimal line broadening (see Section 4.3), and we see H-α in absorption, which also points to a quiet, inactive star. We use the estimated mass of LHS 1678 and the mass-rotation relation of Newton et al. (2017;their Equation (6)) to estimate a stellar rotation period of 64 ± 22 days. We also estimate the rotation period via a ¢ R log HK -rotation relation. Using the HARPS data presented in Section 4.3, we derive a ¢ R log HK value of −6.087 ± 0.548 following the methods of Astudillo-Defru et al. (2017a), in agreement with the value of −6.08 from Rains et al. (2021). Substituting this value into the relations of Astudillo-Defru et al. (2017a) yields a rotation period (P rot ) of 221 ± 185 days. This is slower than the vast majority of M dwarf rotation periods to date; we note that this relation is not calibrated to such a low value of ¢ R log HK and this estimate is highly imprecise. We include it here, nonetheless, as part of our broad effort to estimate stellar rotation. We adopt the Newton et al. (2017) rotation period estimate of 64 ± 22 days and derive an age of 4-9 Gyr using the empirical relations of Engle & Guinan (2018) for M0-M1 dwarfs (yielding 3.9 Gyr) and M2.5-M6 dwarfs (yielding 8.5 Gyr). Because LHS 1678 is M2/M2.5 and the work of Engle & Guinan (2018) notes a lack of M1.5 to M2 dwarfs available for defining an M1.5-M2.0 relation, we use both available relations to estimate that the age of LHS 1678 is approximately 4-9 Gyr.
Low metallicity, HR-diagram position, and spectral features. Photometric metallicity estimates (Table 1, Section 3.1), better stellar parameter consensus with subsolar metallicity assumptions (Section 3.2, Appendix A), and low HR-diagram position ( Figure 3) imply that the star has a metallicity less than zero. The lack of characteristically large CaHn (n = 1-3) and TiO5 band strengths in our RC Spec spectrum ( Figure 1) suggests that LHS 1678 is not a cool subdwarf (Gizis 1997), in agreement with its position within the main sequence and its low tangential velocity . These findings are consistent with our assessments of galactic kinematics and low magnetic activity.
In aggregate, these properties indicate LHS 1678 is not a young star. As described, we estimate an age range of approximately 4-9 Gyr using rotation-age relationships. Other age considerations imply that LHS 1678 likely sits at the older end of this range.
Unusual Position on the HR Diagram
We place LHS 1678 on the HR diagram to evaluate its position in the context of M dwarfs as a whole and relative to other M dwarf exoplanet host stars ( Figure 3). With = 10.047 G and BP − RP = 2.278 from Gaia DR2, the star occupies a narrow portion of G versus BP − RP parameter space characterized by a gap in the lower main sequence. Jao et al. (2018) reported the gap in the HR diagram, revealed for the first time by highprecision parallaxes from Gaia DR2. More details on the gap and other features in the HR diagram are discussed by Jao & Feiden (2020) and Feiden et al. (2021), and the gap is successfully recovered in Gaia EDR3 ( Figure 17 of Gaia Collaboration et al. 2021). The gap, or, more accurately described, a deficit of stars, is consistent with the expected transition from partially to fully convective interiors in M dwarfs. This gap is theoretically tied to the nonequilibrium burning and mixing of 3 He in the stellar core. Core 3 He fusion leads to the development of a convective core that grows and eventually merges with the convective outer envelope (van Saders & Pinsonneault 2012; Baraffe & Chabrier 2018;MacDonald & Gizis 2018;Feiden et al. 2021). Convective mixing then transports 3 He away from the core, reducing the nuclear reaction rate and causing the core to contract and again separate from the convective envelope. This leads to the emergence of a 3 He burning instability where the core undergoes damped, periodic transitions between partial and full convection until a balance is achieved in the 3 He abundance and the star remains fully convective. This transitory phase in core energy transport leads to small, slowly varying oscillations in radius and luminosity in a narrow range of stellar masses spanning only ∼0.34-0.37 M e (van Saders & Pinsonneault 2012; Baraffe & Chabrier 2018) and manifests as the observed underdensity of stars in the HR diagram.
LHS 1678ʼs location in, or at the lower edge of, the gap implies it may be part of a population of stars that have transitioned from being partially to fully convective, exhibiting long-term radial pulsations as they migrate back and forth across the gap over the course of billions of years. It is worth noting that this transition is theoretically predicted to be close to M3.5V, but spectral type is a poor marker compared to mass and age (Jao et al. 2018). Two independent analyses designate LHS 1678 as ∼M2.0V (this work; Reid et al. 2007); at first glance, declaring this star as fully convective would seem to defy our current understanding of the transition region. It does not, however, because its observed photometry ( Table 1) is consistent with the observed location of the gap and its mass, luminosity, and radius ( Table 2) are all in agreement with multiple theoretical predictions of the parameter regime where M dwarfs undergo the 3 He burning instability. Figure 3 indicates that LHS 1678 is one of the only TESS M dwarf exoplanet systems currently known to reside in the gap. Only three other systems appear to be in or near the gap, and are reported as such for the first time here: GJ 357 is just above the gap at BP − RP ≈ 2.4, and TOI-122 and LHS 1972 (GJ 3473) lie in the red end of the gap at BP − RP ≈ 2.6 and 2.7, respectively. This redder part of the gap is more clearly illustrated in Figure D3 of Jao & Feiden (2020). The implications that gap membership has on planet formation and evolution are currently unknown. As more M dwarf planets are discovered and more precise stellar parameters become available (e.g., from Gaia DR3), trends in stellar parameters and exoplanet system properties in and near the gap should be monitored, with a focus on whether there are significant differences in the frequencies, distributions, and properties of planets. We discuss several potential impacts in Section 7. . Vertical lines denote the planet orbital periods, the 41.7 day HARPS signal to be discussed in Section 4.3, and the highest peak in the g-band LS periodogram at 192.5 days. Note that the peak in the g-band LS periodogram at one day is likely caused by observations being performed only at night in Chile and/or South Africa, and peaks at less than one day are likely associated aliases. We do not see any peaks in the V-band LS periodogram. Right: gband ASAS-SN photometry folded on the candidate 192.5 day period found using the LS periodogram. Black circles are the data binned at a 15 minutes cadence, with error bars corresponding to the standard deviation of the magnitude values in each bin. We do not see clear signs of periodicity.
Astrometric Detection of a Stellar or Substellar Companion
Sixteen years (2004-2020) of ground-based astrometry from the REsearch Consortium On Nearby Stars (RECONS) program at the CTIO/SMARTS 0.9 m telescope in Chile show compelling evidence that LHS 1678 hosts a low-mass stellar or substellar companion with an orbital period longer than the timespan defined by the data set. As initially reported by Jao et al. (2017), there is residual motion in the position of the LHS 1678 photocenter after solving for parallax and proper motion. Images of the field were acquired through the V J (henceforth simply V ) filter at airmasses <1.1, meaning that corrections required for differential color refraction were minimal. Following the prescription described in Jao et al. (2005), the position of LHS 1678 was measured relative to five reference stars in 136 images taken on 30 nights with seeing better than 1 8. Once a preliminary parallax and proper motion were measured, we subtracted the corresponding model from the data to get residuals in R.A. and decl. and fit an orbit to these residuals. Our methodology here is a least-squares approach to constraining orbital elements, as described in, e.g., Winters et al. (2017), guided by the work of Hartkopf et al. (1989). We adopt a set of starting values for the orbital period, epoch of periastron, and orbital eccentricity. We iteratively calculate an orbit and compare with the data, tweaking the starting values until we identify a best-fitting orbit. To derive our final parallax and proper motion, we subtracted the orbit model from the data and measured parallax and proper motion using the new data set. We derive a trigonometric parallax of 52.22 ± 0.86 mas and a proper motion of 992.3 ± 0.2 mas yr −1 at position angle 166°.8 ± 0°.1. The high proper motion of the star allows us to rule out any contaminating background source that could affect the astrometry. For comparison, Gaia DR2 provides a parallax of 50.28 ± 0.02 mas and proper motion of 996.9 ± 0.1 mas yr −1 at position angle 166°.1 ± 0°.1. For the majority of our analyses, we adopt Gaia astrometry. For the detailed astrometric characterization of LHS 1678 and its companion we use our RECONS values henceforth because they cover a much longer timespan than the Gaia measurements (16 yr versus 1.8 yr) and incorporate the higher-order motions due to the perturbation. Figure 4 illustrates the photocenter positions, split into R.A. (top panel) and decl. (bottom panel) axes. Solid points represent the photocenter positions each night that multiple frames were taken (typically five frames over 10-20 minutes), where error bars represent standard deviations in the positions. Open points are from nights in which only single frames were taken or kept. The four points represented by "x" symbols on each axis are from observations between 2005 March and 2009 July taken through a different V filter (because the original filter was cracked) than for the rest of the series. While the photometric results of this different filter match the original V filter to a few percent, the astrometry is affected to varying degrees, particularly in the R.A. axis, depending on the configuration of the reference stars (see Subasavage et al. 2009). In the case of LHS 1678, the effects on the photocenter positions are relatively mild. These four points are used in the initial reduction for parallax and proper motion and not in the orbital fit.
An orbital fit traced with red curves in Figure 4 has been made to the photocentric positions on both axes, using the methodology of Hartkopf et al. (1989). The perturbation is evident only in decl., implying that the projected orbit of the companion is roughly north-south during the timespan of the observations. However, it is important to emphasize that the period resulting from the orbital fit, ∼42 yr, is highly uncertain and likely underestimated because the current data do not cover enough of the orbit to constrain the orbital elements. Nonetheless, the current astrometric data imply that there is a companion of lower mass than the primary orbiting LHS 1678 with a period of at least several decades. This is long enough that it is unlikely to disturb the compact planetary system around the primary star unless the companion's orbit is highly eccentric; the primary star dominates the gravity well in the Overlaid are LHS 1678 (green star) and other TESS M dwarf exoplanet systems (blue circles). LHS 1678 is the only TESS exoplanet system so far that is associated with the observed gap in the lower main sequence. In the top panel, the gap is labeled with a blue arrow and is visually seen as the darkercolored, diagonal band, seemingly "cutting into" the main sequence from the left-hand side. The two bottom panels focus on the region around the gap and show LHS 1678ʼs association with that feature. The next closest system, GJ 357 (labeled "D"), lies just above the gap at BP − RP ≈ 2.4. TOI-122 ("H") and LHS 1972 ("J") are also close to or in a less visually obvious region of the gap at BP − RP ≈ 2.6 BP − RP ≈ 2.7. Left to right: TOI-1749, TOI-1235, TOI-1728, TOI-1899, TOI location of the planets (Kane 2019). We investigate the nature of this companion in depth in Section 7.3 and Appendix C and discuss the stability of the overall system further in Section 7.4.
Long-term Variability
The images used for long-term astrometry can also be used to evaluate the photometric variability of LHS 1678 in the V band. Each frame taken from 2004-2020 is represented by a point in Figure 5, where the flux of LHS 1678 has been compared to fluxes of five reference stars. The optical flux variations of the star are minimal, with a standard deviation from the average value of only 7.6 millimagnitudes; the high and low dotted lines represent the brightness levels at twice the standard deviation. This is, in fact, near the floor of measurements we make via the typical observational protocol at the CTIO/SMARTS 0.9 m (Hosey et al. 2015). A LS periodogram of these data also shows no signs of periodicity, in agreement with our ASAS-SN data findings in Section 3.3. We conclude that LHS 1678 shows a remarkably low level of magnetic activity, and exhibits no long-term photometric variations in V above the 1% level during the 16 yr of observations. The lack of significant variability in these verylong-term observations is consistent with the absence of spot modulation and flares in the high-precision TESS observations covering a much shorter time baseline.
Archival and High-resolution Imaging
The high proper motion of LHS 1678 allows us to inspect archival data, looking back in time when the star was elsewhere to see if there is another source at its sky position during the TESS observation epochs. The earliest archival image of the LHS 1678 field available on Aladin (Bonnarel et al. 2000) 45 is from the SuperCOSMOS Sky Survey (SCSS; Hambly et al. 2001). The image was taken in 1983 using the B j filter and a photographic plate, with a resolution of 0 67 pixel −1 . Between that epoch and its late-2018 TESS observations, with its ≈1″ yr −1 proper motion and 166°position angle, the star has moved about half an arcminute across the sky. This allows us to check for possible contaminating sources within the TESS photometric aperture and beyond, both by eye and using compiled catalog data (e.g., Gaia DR2), without fear of the star blocking a possible background source. The archival imaging revealed two faint sources within ≈1 TESS pixel of its location during Sectors 4 and 5. Figure 6 demonstrates the motion of LHS 1678 across the sky. ¢´¢ All three images are centered on the Gaia DR2 J2015.5 coordinates of LHS 1678. The red dots in (c) are the brightest Gaia sources in the field of view. However, the aperture used in our TESS data analysis is very large (≈42″ in radius) and the change in flux from the transiting planets is very small. The TESS Sector 5 TPF of LHfg cvS 1678 in Figure 6(d) was generated using tpfplotter (Aller et al. 2020) and overlays the pipeline-defined extraction aperture used to create the LHS 1678 TESS light curves. 46 Critically, it includes two significantly fainter Gaia DR2 sources (red dots, #2 and #3). Both of these sources are fully blended within the TESS photometric aperture.
The source ∼11″ to the NW of LHS 1678 (#2) is 8.751 magnitudes fainter than LHS 1678 in the RP band, the closest Gaia band to the TESS band. If this faint source is a totally eclipsing binary, it would introduce a change in flux of about 0.016% the RP flux of LHS 1678, which would be insufficient to reproduce either of the transit signals in this system, which correspond to flux changes of 0.037% and 0.074% for planets b and c, respectively. The remaining motion of the star indicates a binary system with an orbital period on the order of decades. The allowed periods and amplitude of the perturbation suggest a low-mass star or brown dwarf companion. The red line traces an orbital fit to the photocenter's motion. The four points marked with an "x" were taken in a slightly different V filter, and as such were not included in the orbital fit. The other source (#3) at ∼24″ SE of LHS 1678 is 7.272 magnitudes fainter in RP. This corresponds to a factor of ∼780 in flux, a 0.062% change in the case that the faint source is a totally eclipsing binary, sufficient to masquerade as the planet b transit and potentially as planet c. We rule out these scenarios via ground-based time-series observations that recover the transits using photometric apertures that exclude this faint star (see Section 4.2). Neither of these sources are bright enough to significantly dilute LHS 1678ʼs TESS light curve. Together they contribute only ≈0.155% of the flux in the TESS aperture.
These archival imaging analyses, at higher resolution than the TESS data, reveal there are no background sources at LHS 1678ʼs current position that would significantly contaminate the light curve or mimic the observed transits. However, bound sources beyond the resolution limits of the archival imaging (∼1″) that are comoving with LHS 1678 could still remain. Such companions could be eclipsing binaries (EBs), host the transiting bodies, or add significant flux to the light curve and dilute the transit signals, leading to a bias in the derived planet radii (Ciardi et al. 2015;Furlan & Howell 2017). To identify close-in bound companions, we observed LHS 1678 via both speckle imaging using the Southern Astrophysical Research (SOAR) High Resolution Camera (HRCam)+SOAR Adaptive Optics Module (SAM) setup and adaptive optics using the Very Large Telescope (VLT) NAOS-CONICA instrument (NaCo).
LHS 1678 was observed three times with the HRCam on the SAM (Tokovinin et al. 2016) at the SOAR 4.3 m telescope. Optical speckle data were collected on UT 2019 November 10, UT 2019 December 13, and UT 2020 January 7 in the I band (λ c = 824/170 nm), which is approximately centered on the TESS bandpass ( Table 3). The observations used integrations of 6-25 milliseconds and were acquired in blocks of 400 images. The data were processed following the procedures described in detail in Tokovinin (2018) and Ziegler et al. (2020) to produce two-dimensional speckle autocorrelation "images" and contrast sensitivity curves. The HRCam data revealed LHS 1678 to be a single star within the limits of the observations. The speckle imaging limits are presented in Table 3. Their implications for the nature of the astrometric companion described in Section 3 are described in Section C.2.
We also observed LHS 1678 using the NaCo instrument (Rousset et al. 2003;Lenzen et al. 2003) on the 8.2 m VLT Unit Telescope 1 (UT1) on UT 2019 August 17 to obtain adaptive-optics-corrected near-IR images. We acquired nine images in the Brγ filter (λ c = 2.166 μm), each with an integration time of 20 s. The frames were dithered between observations to use the science data for sky subtraction in postprocessing. We used custom software to perform bad-pixel correction, flat fielding, sky-background subtraction, image registration, and coadding. The final reduced image (Figure 7, inset) had a pixel scale of 0 013221 pixel −1 . We estimated our contrast sensitivity (Figure 7) by injecting simulated companion sources at discrete separations from the host star and scaling their luminosities until they were recovered at 5σ. The reduced data do not reveal any close-in companions within a few arcseconds of LHS 1678. Details on the limits placed on bound companions by the NaCo observations and their implications for the nature of the astrometric companion are presented in Section C.2.
Ground-based Time-series Photometry
To redetect the transit signals attributed to the TESS planet candidates, refine transit depths and ephemerides, and rule out nearby sources as contaminating nearby EBs, we pursued seeing-limited, ground-based time-series observations. These (Aller et al. 2020). The image spans 11 × 11 pixels with a pixel scale of 21″ pixel −1 . The TESS SPOC pipeline photometric extraction aperture used to produce the Sector 5 light curve is shown as red shaded squares. Numbered red dots reveal the locations of Gaia DR2 sources with sizes scaled to their ΔG relative to LHS 1678. The faint sources #2 and #3 lie within the TESS aperture. We rule out these sources as the transit hosts via dilution arguments and follow-up observations (see Section 4.1). Table 4. This includes observation dates and parameters and key analysis results for each ground-based time series. LCOGT-We obtained ten transit observations of the inner planet candidate (TOI-696.01) and three transit observations of the outer planet candidate (TOI-696.02) using the 1.0 m telescopes at three southern hemisphere sites of the Las Cumbres Observatory Global Telescope Network (LCOGT; Brown et al. 2013). Each telescope is equipped with a SINISTRO CCD camera with a pixel scale of 0.39″ pixel −1 and ¢ 26 field of view. Observations were performed in either the zs or I c filters. The images in each time series were calibrated using the LCOGT Banzai pipeline (McCully et al. 2018). The AstroImageJ software package ) was used to extract differential photometry from the images, produce light curves, and investigate nearby EBs (within ¢ 2.5 ) at the periods of the planet candidates. The aggregated results of these LCOGT observations and analyses were that six transits of the inner planet candidate were detected at the anticipated times and with the expected depth (although with a low signal-to-noise ratio (S/N)), one partial transit of the outer planet candidate was detected, and the possibility of a nearby EB causing the apparent TESS transits was ruled out at the periods of both planet candidates.
PEST-A single transit of the inner planet candidate was observed using the 0.3 m Perth Exoplanet Survey Telescope (PEST). 48 PEST carries an SBIG ST-8XME CCD camera with a plate scale of 1.2″ pixel −1 and a ¢ 31 × ¢ 21 field of view. The observations were performed in the R c filter. Image reduction, differential photometry, and light curve analyses were performed using the custom C and Python-based PEST pipeline. 49 No transit-like signal was detected at the predicted time and with the expected depth of TOI-696.01, and the data were insufficient to clear nearby EBs.
MEarth-We used seven of the eight 0.4 m telescopes in the MEarth-South telescope array (Nutzman & Charbonneau 2008;Irwin et al. 2015) at CTIO in Chile to perform defocused observations of a transit of the outer planet candidate. The MEarth-South telescopes carry Apogee U/F230 CCD cameras that produce images with a pixel scale of 0.84″ pixel −1 and ¢ 29 × ¢ 29 field of view. The observations were performed in a custom broad red-optical filter (RG715). Image reduction and aperture photometry was performed using custom software, resulting in seven individual light curves of LHS 1678 across the predicted transit time. In the combined light curve, a significant transit is detected at the predicted time and with the anticipated transit depth.
Here we detail the five LHS 1678 b observations that were excluded from our analysis. PEST 2019-07-30: The apparent event was during a time with some passing clouds, so is likely systematics driven. LCOGT 2019-08-06: The observation was not defocused, so one of the potential comparison (comp) stars was saturated, and thus not useful. The resulting best light curve scatter was too high to rule out or confirm the event. Event detection is further complicated by very little preingress baseline data. LCOGT 2020-03-14: The apparent late and too deep event seems to be driven by including a specific comp star in the comparison ensemble. Without the problematic comp star included, the scatter in the data is too high to confirm or rule out the transit. LCOGT 2020-08-03: This light curve shows a possible on-time 400 ppm event, but there is a mid-transit upswing in the tentative detection, so we elected to exclude it from the joint model. LCOGT 2020-11-10: Changes in fullwidth half-maximum (FWHM) and sky transparency at the time of expected ingress likely caused systematics that confuse any shallow transit detection. The data neither rule out or confirm the shallow event. LHS 1678 c ground-based transits that were excluded from our analysis had similar issues with observing conditions.
The ground-based time-series data indicate that the signals detected in TESS photometry are consistent with planets orbiting LHS 1678 and rule out nearby stars as sources of EB contaminants. The ground-based light curves presented here were mostly gathered before it was discovered that the outer planet is in a 3.7 day orbit, rather than the initially identified 14.8 day period (see Section 2). The exception is the 2020 March 16 MEarth light curve, which was obtained just before the star's sky position moved too far toward the Sun to be observed. These data capture a transit at half the initially identified 14.8 day period. More recent, ongoing monitoring to search for transit timing variations (TTVs), to be presented in another paper, are consistent with the outer planet having a 3.7 day orbit. We incorporate the ground-based transit detections reported here into an analysis of the exoplanet properties in Section 5. The ground-based data included in the joint analysis are marked in Table 4 and the light curves with the joint model fits are shown in Figures 12 and 13. We also include the constraints imposed by these data in our statistical validation of the planet candidates in Section 6. Notes. a All ground-based transit observations were observed as continuous time series. b This column indicates which light curves were (Y) and were not (N) used in the modeling described in Section 5. c "Late" denotes that the event was detected later than the time predicted by the ephimerides. d Point-spread Function
Spectroscopy
To check for false positives in the form of a spectroscopic binary or background EB not resolved by the previously described follow-up, we acquired eight RV measurements using the CHIRON echelle spectrograph (Schwab et al. 2010;Tokovinin et al. 2013;Paredes et al. 2021) on the CTIO/ SMARTS 1.5 m in Chile (program ID 19A-0339; see Table 8). Our measurements, spanning 410-870 nm, were taken from 2019 August 27 to September 6 using slicer mode with R ∼ 80,000. RVs were calculated assuming a v i sin of 0.53 km s −1 using the same methodology that Winters et al. (2020) applied to their TRES data. 50 As described in A. A. Medina et al. (2022, in review), we measure the v i sin as follows. We search for the maximum peak correlation via two nested-grid searches. The first searches over a v i sin range of 0-100 km s −1 , sampled at 1 km s −1 intervals, while the second samples the best value from the first search within a range of ±1 km s −1 at 0.1 km s −1 intervals. We then use parabolic interpolation to obtain the final v i sin value of 0.53 km s −1 from the second grid search. This value is within the v i sin upper limit of 1.8 km s −1 set by half the spectral resolution of CHIRON. The top panel of Figure 8 shows as an example the 7100 Å TiO bands from the 2019 August 27 spectrum and the cross-correlation function (CCF) that yields our RV measurement for that date and set of bands. RVs were derived using all six available TiO band apertures in the spectrum and by taking the weighted mean, with the exception of 2019 September 2, for which we only used the one with the highest S/N ("aperture 44"). Errors of 100 m s −1 are adopted for each measurement except that of 2019 September 2, which had a low S/N and for which we used only one TiO band, and 2019 September 6, which had a higher dispersion across different TiO band measurements. As demonstrated in Table 6, we do not detect double lines indicative of a spectroscopic binary in the individual spectra, nor any variation in RVs across the full CHIRON observation baseline that would be characteristic of a wider orbit EB or brown dwarf across a range of periods. This result is not inconsistent with the low-mass companion detected astrometrically (Section 3.5), because that companion's motion in 2019 was likely more tangential than radial (see Figure 4). See Appendix C for additional discussion on this point.
Following the TESS detection of the two candidate planets, LHS 1678 was included in a precision RV monitoring program (ESO Programme ID: 1102.C-0339) on the HARPS echelle spectrograph (Pepe et al. 2002;Mayor et al. 2003) on the ESO 3.6 m telescope at La Silla Observatory, Chile. Forty-one RV observations were collected between UT 2019 November 15 and UT 2020 March 18 with exposure times of 1800 s at a spectral resolution of 115,000. To mitigate contamination in the blue end of the stellar spectrum, the spectra were observed without the on-sky calibration fiber.
High-precision RVs were measured from HARPS spectroscopic data using the maximum-likelihood template fitting method described in Astudillo-Defru et al. (2017b). In this method, a high-S/N stellar template spectrum is constructed by shifting all observed spectra of the target star to a common RV reference frame and coadding the shifted spectra. A combined telluric spectrum is also computed by subtracting the stellar template from each observed spectrum and coadding the residuals in the rest frame. The RV for each observed spectrum is determined by finding the velocity offset that maximizes the likelihood between the spectrum and the stellar template. The telluric template is included in this process to mask out spectral regions most affected by sky contamination. The individual HARPS RVs measured using this process are provided in Table 8. The scatter in the HARPS RV measurements was 2.5 m s −1 with a median measurement uncertainty of 2 m s −1 .
To explore sources of systematic noise in the RV time series, we use standard outputs from the HARPS Data Reduction Pipeline (DRS; Lovis & Mayor 2007) and calculate stellar activity indicators for each spectrum. The DRS computes radial velocities and other diagnostics from each observed spectrum using the CCF technique. Two diagnostics that are produced are the FWHM of the CCF and the RV bi-sector span (BIS). We also measure several stellar activity indicators following the methods described in Astudillo-Defru et al. (2017b). These include the S-Index, multiple lines in the hydrogen Balmer series (Hα, Hβ, Hγ), and the sodium D doublet (NaD). We show LS periodograms of the RV time series and each additional diagnostic in Figure 9. These are computed using the LombScargle algorithm in the Python package astropy. We calculated 1% and 5% false alarm probabilities (FAPs) for each time series using a bootstrap approach.
The LS periodogram of the RV data exhibits no significant peaks (above 1% FAP), including at the known periods of the planetary signals. Several other diagnostics exhibit significant peaks at ∼1 day, consistent with the observation cadence. The peak with the highest power in the RV periodogram is at ≈42 days. We further investigated this signal and identified a coherent trend in the RV data at 41.7 days (Figure 10). This candidate signal is intriguing and could represent the stellar rotation period or a harmonic. Stellar rotation estimates of LHS 1678 (Section 3.3) are in broad agreement with this signal. The LS periodograms of several activity indicators exhibit structure at similar periods, although none are significant ( Figure 9). Alternatively, the signal could be suggestive of an additional longer-period planet in the system. Such nontransiting planets have been identified in many M dwarf systems (e.g., K2-18, GJ 357;Luque et al. 2019). We fit a Keplerian orbit model with broad input priors to further investigate this hypothesis, shown in Figure 10. The data can be represented by a Keplerian orbit model at a period of 41.7 days with some level of eccentricity, although it is poorly constrained (e = 0.2-0.6). The nature of this candidate signal remains unconstrained by the available data. Continued RV monitoring and observations with higher precision are warranted to investigate further and measure the planet masses (see Section 7).
We used our CHIRON and HARPS measurements to compute the weighted-mean RV of LHS 1678. The combined HARPS and CHIRON RV is 11.4667 ± 0.0259 km s −1 (HARPS only: 11.4669 ± 0.0259, Kervella et al. 2017;CHIRON only: 11.39 ± 0.50 km s −1 ). The absence of RV variation with time allows us to exclude the possibility of a grazing transit by nonplanetary mass companion as a false positive in our transit detections. In Section 5, we jointly combine the TESS and ground-based transit observations and HARPS RV measurements to place constraints on the planet properties, including mass upper limits.
Planet Parameter Estimation
We inferred the properties of the two planets using data from the TESS photometric time-series, ground-based transits observed by MEarth and LCOGT, radial velocities from HARPS, and the stellar parameters described in Section 3. Our analysis method follows a very similar procedure to that described in Kostov et al. (2019a) and Gilbert et al. (2020), with the addition of RV data and ground-based transits and some minor parameterization changes in the model. We obtained SPOC PDCSAP (Stumpe et al. , 2014Smith et al. 2012) instrumental systematics-corrected light curves from the Mikulski Archive for Space Telescopes (MAST) using the Python package Lightkurve (Lightkurve Collaboration et al. 2018). We note that the PDCSAP light curves from Sectors 4 and 5 used in our analysis were subject to small overestimates of the sky-background flux due to a bias in the original algorithm. 51 Fortunately, LHS 1678 is relatively uncrowded, and the transit depth in these sectors was biased to be ∼1% deeper, while the radius was biased to be ∼0.5% larger, both an order of magnitude smaller than our error bars. To estimate the planet properties, we jointly modeled the exoplanet transits from TESS and ground-based data, stellar variability in the light curves, along with other systematics and the HARPS RV data using the exoplanet package (Foreman-Mackey et al. 2020). All data sets were modeled simultaneously to preserve covariances between parameters. The ground-based photometry included in the model is listed in Table 4 with a "Y" in the "In Fit?" column.
Each TESS sector is modeled with a mean offset and a white noise variance term described using a log-normal distribution. We modeled residual stellar variability using a Gaussian process (GP) model (Foreman-Mackey et al. 2017; Foreman-Mackey 2018) that describes a stochastically driven damped harmonic oscillator with two hyperparameters, power (S 0 ) and angular frequency (ω 0 ). The ground-based light curves also include a parameter to model additional variance in the data that is not encompassed in the reported observational uncertainty, and the same GP model as the TESS data, but with independent hyperparameters. Each observatory has a Figure 8. A cross-correlation analysis focusing on strong TiO absorption bands in the CHIRON spectra of LHS 1678 reveals no evidence for double lines (top) and a single-peaked cross-correlation function (bottom). These analyses rule out very close-in, unresolved binary companions. The stability of LHS 1678ʼs RV measured by CHIRON over the full observing baseline further excludes the possibility of a spectroscopic companion orbiting across a range of masses and periods ( Table 6). The vertical, dashed lines labeled s and t in the crosscorrelation plot indicate where the sky and telluric lines would be; our template does not correlate with those lines. separate model parameter for the additional uncertainty that is added in quadrature and included in the likelihood function. The model also included the stellar and planetary parameters. The stellar inputs included the stellar density (ρ * ), the stellar radius (R * ), and quadratic limb-darkening parameters (u) parameterized following Kipping (2013) with different limb darkening for the various bandpasses. For each planet, the model included the midpoint time of first transit (T 0 ), impact parameter (b), ratio of planet radius to star radius (R p /R s ), orbital eccentricity (e), longitude of periastron (ω), and planet mass. Instead of the standard method of parameterizing the exoplanet orbits as a function of period, we opted to parameterize the model in terms of the midpoint time of the last transit, making the orbital period of a planet a deterministic parameter in the model, rather than a parameter we sample in. This parameterization yielded more efficient sampling when including the ground-based photometric data. The choice of prior probability distributions for each of these modeled parameters was the same as described in Gilbert et al. (2020) except we used a normal distribution for the time of the last transit. We also included a log-normal prior on planet mass with a wide standard deviation of 3 M ⊕ . For the RV model, we included a quadratic trend and a jitter term.
We used PyMC3 (Salvatier et al. 2016) to perform a Hamiltonian Monte Carlo sampling from the posterior model. We drew over 100,000 independent samples, a very large number, to ensure that we were able to obtain well-sampled upper limits for the planet mass distributions. The central 68th percentile of folded transit models for the TESS data are shown in Figure 11 and for the ground-based transit observations in Figures 12 and 13. The ground-based transit observations are also stacked in Figure 14 with the model overlaid to better demonstrate the successful recovery of both transits from the ground. As expected, incorporation of ground-based observations, acquired after TESS Sectors 4 and 5, yielded better Note. In the case of an equal-mass companion the spectrum would appear with double lines, which were not detected; we note this, rather than include Δ RV in that case. Mass: companion mass; K: RV semiamplitude (km s −1 ); Δ RV: change in RV (km s −1 day −1 ); Det.: detected (N = no, ? = insufficient sensitivity). Figure 9. LS periodograms of HARPS RVs, activity indicators, and other diagnostics. The 5% and 1% FAPs are shown as solid and dashed horizontal lines. The periods of the TESS candidate planets derived from our joint modeling (Section 5) are plotted as vertical dotted-dashed (planet b) and dashed (planet c) lines. The RV periodogram exhibits no significant periodic signals at those orbital periods. The strongest signal in the RV data, with a 5% FAP, appears at 41.7 days (vertical dotted line). The signal may be associated with the stellar rotation period or a harmonic, but the data are insufficient to place a firm constraint. This candidate signal does not appear with any significance in the activity diagnostics. We note that several diagnostics exhibit significant peaks at ∼1 day, consistent with the observation cadence. Figure 10. HARPS RV data folded on the candidate signal at 41.7 days, repeated across two full periods, with no binning, to better show the periodic nature. This signal may be consistent with the rotation period of LHS 1678 or a harmonic. Alternatively, the signal may be evidence of a longer-period planet in the system. To explore this hypothesis, we fit the signal with a Keplerian orbit model assuming broad input priors. We show random draws from the fit posterior as black curves. While the data can be fit with such a model, the true nature of the candidate signal at 41.7 days remains unconstrained with the available data. constraints on the model than in the case where only TESS data were used. In particular, the derived radius of the outer planet increased slightly. The median model parameters and 1σ uncertainties computed during the PyMC3 sampling are provided in Table 7. We measured radii of 0.696 ± 0.044 and -+ 0.982 0.063 0.064 R ⊕ for the inner and outer planets, respectively. Figure 15 shows the full HARPS RV time-series and best-fit model and uncertainty for RV signal and trend. No significant RV signal from the planets were detected, but we were able to compute 97.7th percentile mass upper limits for each planet, 0.35 M ⊕ for the inner, and 1.4 M ⊕ for the outer. 52 Additional parameters are listed in the bottom portion of Table 7. Figure 16 shows the posterior mass distributions and 2 and 3σ limits from the joint modeling. We adopt the 2σ upper limits because, for planets of these sizes, the 3σ values correspond to densities that are unphysical (see Section 7.2 and Figure 17).
Validation
The detection of multiple TESS transits combined with ground-based follow-up and precision RV observations provides a compelling data set that indicates there is little parameter space remaining for false positives that may mimic the transit signals. To place a numerical value on the remaining FPP and statistically validate the planets, we use the vespa tool (Morton 2015). vespa combines the host star properties, the observed TESS transits, and follow-up constraints and compares to simulated false-positive scenarios allowed by the remaining parameter space in a probabilistic framework. The output of vespa is the likelihood that the detected transit signal may be mimicked by the simulated false-positive scenarios, the FPP. We ran the algorithm on each planet candidate individually. The required inputs included the host star position, broadband photometry, and stellar parameters (see Tables 1 and 2). The depth of the second-deepest, eclipselike feature in the phase-folded light curve is also included as a required input. We also included additional constraints on background EBs from our ground-based time-series observations 53 and constraints on bound companions from archival imaging, high-resolution imaging, and RV monitoring. We find FPPs of 1.02 × 10 −5 for LHS 1678 b and 1.70 × 10 −5 for LHS 1678 c. These FPPs are low enough (=1%) to consider the planets statistically validated. In addition to the low statistical probabilities of remaining false positives, we note that our follow-up time-series observations effectively rule out all nearby stars as background EBs, and our CHIRON and HARPS RV monitoring rules out bound companions across a wide range of periods and masses. Additionally, false positives are less likely in multiplanet systems (Lissauer et al. 2012), and the FPPs estimated here could be considered upper limits. Analysis of TESS multiplanet systems indicates they may be further reduced by ∼50× by this multiplicity boost (Guerrero et al. 2021).
These considerations of false positive scenarios do not take into account the wide-orbit, astrometrically detected stellar or substellar companion. The astrometric monitoring data indicate that the companion is most likely a brown dwarf (see Section 7.3). Assuming that the companion is an early-L dwarf ≈8 mag fainter than LHS 1678 in the I c band, 54 not even a totally eclipsing binary brown dwarf could reproduce the transit depths of either planet in the similar TESS band, given the significant dilution from the primary. Furthermore, it would only account for one of the transit signals associated with LHS 1678, as a multiply eclipsing brown dwarf system at the Figure 11. TESS photometry folded on the planet periods. Purple dots are the individual 2 minute cadence measurements, and the vertical lines are 10 minute bins. The best-fit transit models described in the text are overlaid as green curves. Green shading corresponds to the central 68th percentile (1σ) range of models consistent with the data. 52 Note that the distribution used here is actually log mass, which we convert to mass for our listed values. The 2σ value is calculated at the more massive end of the distribution, corresponding to the 97.7th percentile. 53 This is in the form of the minimum separation for EBs ruled out by groundbased time-series observations, or the maximum size of the apertures used for ground-based light curve extraction: 9.8″ for LHS 1678 b and 8.3″ for LHS 1678 c (see Table 4). 54 Estimated using the color-temperature relation table at http://www.pas. rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt. Note.
a These values are poorly constrained, but are included for complete disclosure of the model output and our uncertainty considerations. observed periods would likely be unstable. If the wide companion is instead a very-low-mass star, the observed signals could be caused by a heavily diluted transiting giant planet, but such a system would be exceptionally rare and, again, only account for one of the observed signals.
Discussion
The LHS 1678 system is comprised of an older-population, magnetically quiescent M2 dwarf at 19.9 parsecs, with a wideorbit, low-mass star or brown dwarf companion, and two validated, roughly Earth-sized (0.7 R ⊕ , 1 R ⊕ ) planets in 0.9 day and 3.7 day orbits around the primary star. Via HARPS radial velocity measurements, we derive 97.7th percentile mass upper limits of 0.35 M ⊕ and 1.4 M ⊕ for planets b and c, corresponding to density upper limits of 6.0 g cm −3 and 10.6 g cm −3 , respectively. The planet radii and mass upper limits, when compared to similarly sized planets ( Table 8) and planet composition models (Marcus et al. 2010;Zeng et al. 2019), indicate they are likely to be rocky (Figure 17).
Although the presence of at least two small planets orbiting an M dwarf in a compact configuration is now known to be commonplace, several properties of the LHS 1678 system mark it as exciting in the context of current cutting-edge studies and observations. The inner planet is an ultra-short-period planet (USP; Winn et al. 2018), with a sub-day orbital period of ∼21 hr. It is a compelling candidate for JWST observations to study its atmosphere via thermal emission. The outer planet is in the Venus zone (VZ; , receiving ∼13.5× the flux of Earth, and a possible data point in studying the runaway greenhouse effect in Earth-sized planets. The relatively old age of the star presents an additional constraint that provides useful insight into planetary evolutionary processes and possible periods of past temperate surface conditions (Way et al. 2016;Way & Del Genio 2020). The system is prime to search for evidence of additional planets via further transit searches and TTVs; in Section 7.1 we discuss a third planet candidate. Both of the known planets probe models of planet formation and are prime candidates for further mass-constraining precision RV observations (Section 7.2). This system has a faint low-mass star or brown dwarf companion with an orbital period on the order of decades (Section 7.3). The system is dynamically stable such that there could be additional nontransiting planets with periods intermediate to the two known (Section 7.4). The host star is associated with the gap in the HR diagram lower main sequence tied to the M dwarf convective boundary; physical mechanisms associated with this HR-diagram position have unknown effects on exoplanet formation and evolution (Section 7.5).
Search for Additional Planets
After we completed the main analysis of the TESS and follow-up data presented here, LHS 1678 was observed for two additional sectors (UT 2020 October 21 to December 17) in Cycle 3 of the TESS extended mission, as part of Guest Investigator Programs G03228, 55 G03272, 56 G03274, 57 and G03278, 58 the Cool Dwarf target catalog (Muirhead et al. 2018), and the TESS CTL (Stassun et al. 2018b). Because at the time of writing, the complete two-cycle, four-sector set of TESS 2 minute cadence measurements for this star had not yet been searched by the SPOC pipeline, we performed our own search of this combined data set to see if any additional planet signals would be revealed. Two independent analyses were performed and are described here.
Analysis 1. We calculated a box least-squares (BLS; Kovács et al. 2002) periodogram, as implemented and optimized by and Cycle 3 (Sectors 31 and 32) 2 minute data sets. Our search confirmed the detection of the two planets found by the SPOC pipeline presented earlier in this work, and also detected an additional sub-Earth-sized transiting planet candidate with a 4.965 day orbital period. The newly detected candidate has a relatively low S/N of about 9.4 in the BLS search, so we investigated the robustness of this new signal by searching for it in the TESS full frame image (FFI) data.
We downloaded FFIs in the region around LHS 1678 using the TESScut interface (Brasseur et al. 2019) and extracted our own light curve. We corrected for systematics using a different method than the SPOC light curve, namely by decorrelating against the quaternion time series following Vanderburg et al. (2019), and still recovered the same 4.965 day signal, indicating that it is unlikely to be due to an instrumental systematic. We also extracted a light curve from a single-pixel aperture centered on the position of LHS 1678 and detected the 4.965 day transit signal as well, implying that the signal must originate within about 20″ of the position of the target star. Henceforth, we refer to the new candidate as TOI-696.03.
We then performed a Markov Chain Monte Carlo (MCMC) fit to a multicycle SPOC PDCSAP 2 minute cadence light curve to estimate TOI-696.03ʼs parameters. We removed points taken during transits of the other two planets in the system and modeled the light curve with Mandel & Agol's (2002) transit model (Figure 18, top panel). We assumed that the candidate has a circular orbit and imposed a prior on the stellar density presented in Table 2. We also imposed priors on the quadratic limb-darkening coefficients of u 1 = 0.17 ± 0.15 and u 2 = 0.44 ± 0.15 based on models from Claret & Bloemen (2011), and sampled the coefficients using the q 1 and q 2 parameterization of Kipping (2013). We explored the parameter space using the differential evolution MCMC algorithm of Ter Braak (2006), evolving 100 chains for 20,000 links, and discarding the first 1000 links to remove the burn-in phase. The MCMC yielded a period of 4.965222 ± 0.000023 days, a radius of , a time of transit of BJD = 2458806.8143 ± 0.0015, and a scaled semimajor axis (a/R * ) of 26.1 ± 0.9. The period-folded transit along with the best-fit transit model from this analysis is presented in the top panel of Figure 18.
Analysis 2. Independent of Analysis 1, we also performed a separate BLS search on the SPOC PDCSAP light curves from TESS Cycles 1 and 3, also following Kovács et al. (2002) and Vanderburg et al. (2016), and recovered LHS 1678 b's and c's signals at the periods reported earlier in this work. After masking out both signals, we found a third transit signal with a period of 4.96519 d and transit epoch of 2458414.564464 BJD at an S/N of 9.5. This corresponds to a predicted radius of ∼0.9 Earth radii and transit duration of 1.024 hr.
The signal is also recovered in the Quick-Look Pipeline (QLP; Huang et al. 2020aHuang et al. , 2020b) FFI light curves following a similar process, although with somewhat lower significance. This is likely due to the relatively short duration of TOI-696.03, which compromises the transit depth when undersampled with the longer FFI cadences.
To verify that the transit signal originates from the target star, we compute difference images from the TESS FFIs ( Figure 19) and the publicly available Python package TESSplots. 59 First, TESS-plots uses TESSCut to create a pixel cutout of the FFIs centered on the target star. Then, each transit's in-and out-of-transit cadences are identified using the signal's ephemerides, and the means of the in-and out-oftransit frames are calculated. The mean out-of-transit image represents the target star with no transits, while the difference between out-of-transit and in-transit images reveals the location of the largest source of variability during a transit. We excluded all cadences that occurred during the transit of other planets before calculating the difference images to ensure that any source of variability was indeed due to the newly identified planet candidate, TOI-696.03.
We inspected the difference images for all three signals across Cycles 1 and 3. Figure 19 shows our results for TOI-693.03 in the most recently observed sector (Sector 32). As shown in Figure 19, the location of the strongest difference for transits of TOI-696.03 coincides with the pixel of the target star, as is expected in the case of a transiting planet orbiting LHS 1678. The dots in the images show the location of nearby TIC stars, down to Δ T = 4 mag. No nearby stars within this magnitude range lie in the same pixel as the target star, indicating that the planet candidate is likely to be on-target. For the other planets in the system, LHS 1678 b and LHS 1678 c, our independent difference image result is consistent with the SPOC difference image analysis.
We fit the transit of TOI-696.03 to derive its parameters using the exoplanet toolkit. The stellar mass and radius were fit with a normally distributed prior using the values in Table 2. We used a quadratic limb-darkening model, and both period and epoch had uniform priors around the values we found from our BLS search. The resulting parameters and best-fit model are shown in Table 9 and the bottom panel of Figure 18.
A likely third planet near-resonance with LHS 1678 c. Two independent analyses of the full Cycle 1 and Cycle 3 TESS 2 minute and FFI data recover an additional planet candidate, TOI-696.03. This candidate has a period of 4.965 days and a radius of ≈0.9 R ⊕ . With currently available data, we find no reason to suspect that this signal is either an instrumental or astrophysical false positive. The transit signal is most likely consistent with the presence of another planet in the LHS 1678 system. Because we identified this additional candidate late in our analyses of the system, we were not able to collect ground-based transit follow-up observations and do not attempt to formally validate this relatively low-S/N signal here. We do note that soon after these analyses were performed, SPOC released a multisector, multicycle search result that identified planet c at the correct 3.7 day period and revealed a planet candidate, with properties matching the one independently identified here (e.g., 4.97 day period, R p ≈ 1 R ⊕ ). Ground-based time-series follow up of this candidate required for validation is ongoing using TFOP resources.
Both analyses and the SPOC multicycle search identify TOI-696.03 at a period that is within 1% of 4:3 mean-motion resonance with LHS 1678 c. In Kepler planetary systems with three or more planets, there are nine pairs of planets within 1% of 4:3 resonance; all of the pairs are in resonance chains with at least one other planet in the system (notably the Kepler-223 Mills et al. 2016 andKepler-60 Steffen et al. 2013 systems). This has been interpreted as a signature of convergent disk migration (e.g., Goldreich & Schlichting 2014; Tamayo et al. 2017). However, LHS 1678 b is far away from any resonances Table 8). LHS 1678 b and c are each labeled with three open circles with arrows connecting them from right to left to denote the 3-, 2-, and 1σ (99%, 97.7%, and 68%) mass upper limits. Lines of constant density for a variety of compositions are overlaid . Planets with densities that lie beneath the collisional stripping curve (Marcus et al. 2010;Zeng et al. 2019) should be nonphysical, so that region is shaded. The collisional stripping mass upper limits of LHS 1678 b and c are 0.419 M ⊕ and 1.51 M ⊕ , respectively. Notably, the majority of planets on this diagram are of similar density to an Earth-like rocky planet. This, combined with our mass constraints, indicates that the LHS 1678 planets are likely to be predominantly rocky. Of particular note, the 1σ mass upper limit for LHS 1678 c, which is in the "Venus zone", places it identically with Venus on the mass-radius diagram within our error bars. with the other bodies in the system. This fits into the picture that most USPs have much larger orbital separation compared to other pairs of planets in the same system (Winn et al. 2018). It is plausible that LHS 1678 b migrated in a resonant chain with the other two planets, and then continued inward toward the star via tidal orbital decay (i.e., Lee & Chiang 2017). Planets in near-resonant configurations can exhibit TTVs that can reveal the architectures and masses of planets in the system. To predict the amplitude of any putative TTVs in the LHS 1678 system, we estimated the masses of both LHS 1678 c and TOI-696.03 using the forecaster procedure from Chen & Kipping (2017) and found values of
Prospects for Future Exoplanet Characterization
Here we explore possibilities for future characterization of the two validated planets in this system, LHS 1678 b and c.
Masses. We used HARPS RV monitoring to place stringent upper limits on the masses of LHS 1678 b and c, but lacked the necessary RV precision and observing baseline to significantly measure the masses. Given current knowledge of the mass-radius relation for small planets (<1.5 R ⊕ ), it is likely LHS 1678 b and c are predominantly rocky in nature (Rogers 2015). Figure 17 places these planets in context with other small, low-mass planets. Assuming their expected densities, they join a very small sample of planets comparable in size and mass to the Earth and are compelling targets for further mass constraints to infer their bulk compositions. Using the forecaster procedure from Chen & Kipping (2017), we estimate masses of for planets b and c, respectively (matching the estimate using the relation in Kempton et al. 2018). These masses are broadly consistent with our mass upper limits (Table 7, Figure 17). They are also below the collisional stripping mass limits (0.419 M ⊕ and 1.51 M ⊕ for b and c, respectively) as described by Marcus et al. (2010) and as plotted in Figure 17 using the table from Zeng et al. (2019). 60 With the forecaster masses, assuming circular orbits around LHS 1678, and taking the remaining parameters from Tables 2 and 7, we derive radial velocity signals of approximately 0.4 and 0.8 m s −1 . Given the predicted amplitude of these signals and LHS 1678ʼs southern decl., ESPRESSO on the VLT is a current instrument with demonstrated performance capable of better refining the planet masses (Pepe et al. 2010;Suárez Mascareño et al. 2020). Definitive mass measurements of these planets will be critical for future bulk composition studies and atmospheric characterization.
Atmospheric characterization. Kreidberg et al. (2019) demonstrated the use of thermal phase curves to investigate the atmospheres of small rocky planets when they inferred from Spitzer observations that the USP LHS 3844 b, which orbits its host star in only 11 hr (Vanderspek et al. 2019), likely has no atmosphere. With an orbit of 0.86 days, LHS 1678 b falls into the USP category. Because it is likely rocky, nearby, and orbiting an even brighter M dwarf (V J = 12.5, K s = 8.3 for LHS 1678 versus V J = 15.3, K s = 9.1 for LHS 3844; Cutri et al. 2003;Skrutskie et al. 2006;Winters et al. 2015;Vanderspek et al. 2019), it provides another opportunity to investigate the Figure 18. Phase-folded light curves of TOI-696.03 identified in a search of the full two-cycle, four-sector TESS data set using two independent analyses. Top (Analysis 1): the gray and purple symbols are averages of TESS 2 minute observations in intervals of 3.6 and 12 minutes in phase, respectively. The bestfit model is plotted in red. Bottom (Analysis 2): gray and green symbols represent 2 minute cadence and 7.5 minute binned measurements, respectively. The brown symbols are drawn from the best-fit transit model from this analysis. Both analyses consistently yield a small planet candidate on a 4.965 day period. If confirmed, TOI-696.03 would be sub-Earth-sized and near the 4:3 meanmotion resonance with LHS 1678 c. Figure 19. Left: the difference between out-of-transit and in-transit images of LHS 1678 star during transits of TOI-696.03 reveal that the star is the location of the candidate transits and rule out other nearby stars as the transit host (small dots). Right: a zoom in on LHS 1678 in the difference image.
atmosphere of a small planet in an extreme orbital architecture and radiation environment. Such planets provide key constraints on the evolution of small-planet atmospheres under the influence of low-mass star space weather. Although LHS 1678 is now magnetically quiet, it was certainly active as a young star, and may have eroded or fully stripped away one or both of its planets' atmospheres.
With an insolation flux of 93.2 S ⊕ and an estimated equilibrium temperature in excess of 700 K, assuming albedos ranging from 0.0 to 0.7, LHS 1678 b may be sufficiently hot for thermal phase curve measurements using the JWST. We use the emission spectroscopy metric (ESM; Kempton et al. 2018) to investigate the planet's potential for such observations. The planet has an ESM of 3.9, indicating that three full phase curve observations with the JWST MIRI LRS mode would be required for a significant constraint on its atmosphere. However, in this case, the ESM value undersells the potential of LHS 1678 b observations using the JWST. We note that under broader assumptions of the planet's properties, the thermal emission may be significantly higher than predicted by the ESM. For example, in the case that the planet's dayside is bare rock and a tenuous or nonexistent atmosphere provides very inefficient heat redistribution (similar to LHS 3844 b), the dayside temperature could be significantly higher (>1000 K) and lead to thermal emission detectable by the JWST MIRI in a single phase curve observation. Thus, LHS 1678 b is a compelling target for future JWST observations and may become a benchmark in the study of small-planet atmospheres under the influence of extreme radiation. We also calculated an ESM of 2.0 for LHS 1678 c. This cooler, longer-period planet is a less compelling target for thermal emission measurements than its shorter-period, hotter sibling.
We also investigated both planets' prospects for transmission spectroscopy observations using the Kempton et al. (2018) transmission spectroscopy metric (TSM). We do this using two sets of possible masses. Using our 2-sigma mass upper limits (M b = 0.35 M ⊕ , M c = 1.4 M ⊕ ), we derive TSM lower limits of 22.9 and 9.9 for planets b and c; using masses calculated as described in Kempton et al. (2018;M b , we derive TSMs of 30.2 and 15.2. Kempton et al. (2018) assert that planets with TSM > 10 are compelling targets for atmospheric characterization via transmission spectroscopy measurements; this TSM threshold corresponds to a planet c mass of 1.4 M ⊕ , our 2-sigma mass upper limit.
We point out that with an insolation flux of 93.2 S ⊕ , planet b exists in an extreme radiation environment and may have no atmosphere to measure in transmission. Alternatively, it could have retained a high-mean molecular weight atmosphere, which would have a small-scale height and produce a small transmission signal. Given its significantly lower insolation flux, planet c may be a more compelling transmission spectroscopy target. In trying to understand the runaway greenhouse effect, it is important to assemble a suite of planets at different stages in the process. With an insolation flux of 13.5 S ⊕ and radius of 0.982 R ⊕ , planet c falls in the middle of the VZ range defined by . The outer limit of the VZ is defined by the distance from the star at which one expects sufficient erosion of the atmosphere to counteract the runaway greenhouse effect (∼1 S ⊕ around a 3500 K star). The inner limit of (∼25 S ⊕ ) is set by a predicted complete evaporation of oceans. Planet c is not only in the VZ, but is the same radius as Venus within uncertainties and likely rocky, given its radius and our mass upper limits. These qualities make it an especially compelling target for inclusion in runaway greenhouse effect studies, and its TSM lower limit of 9.9 speaks to its feasibility.
The Nature of the Wide-orbit Companion
RECONS long-baseline astrometry provides compelling evidence for a wide-orbit, low-mass companion in the LHS 1678 system (see Section 3.5). However, the companion has not yet been directly detected. In Appendix C we discuss in greater depth our constraints on the companion. In combination, the available observations provide constraints on its mass and luminosity that indicate it is likely a brown dwarf with a projected separation of 5 au, while not disallowing the possibility it is a Jovian planet. Because the astrometric perturbation is so far seen exclusively in the decl. axis, the orbit is highly inclined, and the semimajor axis of the system may be larger than the projected separation upper limit placed by the imaging observations (Section C.2). One additional intriguing possibility is worth noting: the high inclination of the companion's orbit also suggests the possibility that the transiting planets and companion are coplanar. With this in mind, additional astrometric data can constrain the inclination of the (so far) unseen companion's orbit, perhaps revealing a rare system in which companions of very different masses orbit in the same plane. This would be the second case in the solar neighborhood, following that found for the nearby (6.9 pc) M dwarf triple LTT 1445 (Winters et al. 2019), in which the A component harbors at least one shortperiod transiting planet and the BC pair appear to orbit one another in the same plane. LHS 1678 may join a growing ensemble of orbitally aligned systems and be key to understanding their frequency and the mechanisms that drive their formation and evolution (Christian et al. 2022).
System Stability
Studying the dynamics of planetary systems can validate the viability of the measured Keplerian orbital solution and reveal potential locations for additional planets in the system (Lissauer et al. 2011;Kane & Raymond 2014;Li et al. 2014;Kane & Blunt 2019). To test the dynamical aspects of the orbital architecture of the LHS 1678 system, we performed N-body integrations using the Mercury Integrator Package (Chambers 1999) and the system parameters in Tables 2 and 7. The methodological approach taken was similar to that described by Kane (2015Kane ( , 2019. We adopted a time step in integrations of 0.04 days, necessitated by the very short orbital period of the inner planet. A single simulation was allowed to run for 10 7 simulation years and demonstrated that the system as described is exceptionally stable, with minimal perturbative interactions between the planets. We note that because the astrometric companion would not affect the planetary system unless highly eccentric (Kane 2019), we excluded it in this simulation. The combination of the relatively small predicted masses of the planets and their proximity to the host star results in similar small Hill radii: 1.1 × 10 −4 au and 4.2 × 10 −4 au for planets b and c, respectively. These small Hill radii imply that a significant amount of viable orbital space lies between the planets where additional, perhaps nontransiting, planets could reside. To test for this, we conducted several hundred N-body integrations that randomly inserted an Earth-mass planet at locations between the two known planets and ran each integration for 10 5 simulation years. These simulations showed that an additional terrestrial planet is dynamically feasible in the semimajor axis range 0.014-0.029 au, as is the presence of candidate planet TOI-696.03 at 0.04 au (Section 7.1). Statistical studies of compact planetary systems show that they are generally dynamically filled (Fang & Margot 2013). It is therefore possible that there are additional planets within the system that are interior to the outer detected planet.
Note that we did not include TOI-696.03 in our dynamical simulations due to its candidate status and lack of mass constraints, other than to infer stability at its tentatively derived location. Given its estimated radius of ∼0.9 R ⊕ and ∼0.04 au, and assuming a mass of 0.9 M ⊕ , TOI-696.03 would have a similarly small Hill radius of 5.5 × 10 −4 au. Such a small mass and Hill radius is unlikely to have significant impact on the stability derived between planets b and c, depending on the eccentricity of the orbit for TOI-696.03 and locations of possible resonances (Hadden & Lithwick 2018;Vinson & Chiang 2018;Hadden 2019;Kane et al. 2021). Further validation of TOI-696.03 and measurements that constrain its mass and orbital properties will allow a more thorough dynamical investigation into the architecture of the system.
Potential Impacts of Association with a Gap in Lower
Main Sequence LHS 1678ʼs HR-diagram position in or at the lower edge of an observed gap in the lower main sequence is nearly unique among TESS exoplanet host stars. The gap is associated with a core 3 He instability that leads to damped, periodic pulsations in stellar radius and luminosity on the order of a few to ∼10% (van Saders & Pinsonneault 2012; MacDonald & Gizis 2018; Baraffe & Chabrier 2018). Depending on the mass of the star, these pulsations occur on timescales of ∼10 8 to 10 9 yr. Changes in stellar luminosity of a few to ∼10% may have an impact on the evolution of a close-in planet, particularly its atmosphere and surface temperature. The effect of host star luminosity changes on exoplanet climates is an open question. It is conceivable that such changes in incident radiation could push planets in appropriate parts of parameter space toward different climate states, like runaway greenhouse and surface desiccation, or in the direction of a habitable state. This is highly dependent on the planet parameters, including period and atmospheric content. M dwarf planets often present an additional challenge to understanding these effects; they are often tidally locked, which adds further complexity to their atmospheres (e.g., Yang et al. 2013;Kopparapu et al. 2016). Although the implications of such instellation changes on exoplanets need further study, they have been explored in the context of Venus and Earth and solar evolution. Modeling has shown that a 10% increase in solar luminosity could trigger an abrupt shift in the Earth's climate in the direction of a moist greenhouse and significant surface warming (Wolf & Toon 2015). These implications, and the unique stellar evolution history of the LHS 1678 system, provide the impetus to model and explore the impact of periodic stellar luminosity changes on the properties of planets orbiting HR-diagram-gap M dwarfs. This may be particularly important for LHS 1678 c, given its location in the VZ.
Conclusions
The LHS 1678 system stands out among other high-profile TESS discoveries. The star is less than 20 pc from the Sun and bright in both visible and IR wavelengths. Both validated planets are smaller than Earth, very likely rocky, and each is interesting in its own right: LHS 1678 b is an USP planet with prospects for thermal emission measurements, and LHS 1678 c is a Venus analog. The additional planet candidate in the system, TOI-696.03, is near the 4:3 mean-motion resonance with LHS 1678 c and may lead to measurable TTVs in the system with further follow-up. LHS 1678 is associated with the lower main sequence gap revealed by Gaia (Jao et al. 2018). This gap is tied to low-amplitude, long-period luminosity oscillations stemming from a core 3 He burning instability. The effects of these oscillations on exoplanet formation and evolution are unknown. LHS 1678 also has a very-low-mass, astrometrically detected substellar companion with an orbit on the order of decades. LHS 1678 complements other low-mass multiple systems where one component is known to host planets, like Kepler-296 (Barclay et al. 2015), K2-288 (Feinstein et al. 2019), and LTT 1445 (Winters et al. 2019). A complete census of each exoplanet system is key to understanding its formation and evolution. The nondetection of this companion by photometric and spectroscopic measurements highlights the difficulty in probing the full phase space of companions at the star/brown dwarf boundary and the value of long-term observing programs. The full characterization presented here and the combination of the traits revealed make the LHS 1678 system a compelling target for numerous future follow-up studies. 2000), tpfplotter (Aller et al. 2020), exoplanet (Foreman-Mackey et al. 2021Agol et al. 2020;Kumar et al. 2019;Astropy Collaboration et al. 2013Kipping 2013;Luger et al. 2019;Salvatier et al. 2016;Theano Development Team 2016), forecaster (Chen & Kipping 2017), TESScut (Brasseur et al. 2019), Quick-Look Pipeline (Huang et al. 2020a(Huang et al. , 2020b, TESS-plots (https://github.com/ mkunimoto/TESS-plots).
Appendix A Stellar Properties-Multiple Techniques
We use multiple methods to robustly determine the stellar properties of LHS 1678, with the adopted methods described in Section 3.2. Here we describe the other methods in greater depth, with results in Table 10.
For one alternate method, we employed the Ks -based relations of Mann et al. (2015Mann et al. ( , 2019 to estimate the mass, radius, and luminosity of LHS 1678. We included in these calculations the effect of stellar metallicity using a value of [Fe/H] = −0.5 for LHS 1678. We then combined the luminosity and radius using the Stefan-Boltzmann law to estimate the effective temperature. The estimated mass uncertainty follows from the probabilistic method descried in Mann et al. (2019). We estimated uncertainties on the radius, luminosity, and temperature via Monte Carlo methods assuming Gaussian measurement errors and added the systematic scatter in the Mann et al. (2015) relations in quadrature. We found stellar parameters consistent with those adopted for the analyses presented in the text and estimated using the methods of M. L. Silverstein et al. (2022, in preparation). The Mann et al. parameters are also consistent with the estimated spectral type of LHS 1678.
We also performed an analysis of the broadband SED of LHS 1678 together with the Gaia DR2 parallaxes (adjusted by +0.08 mas to account for the systematic offset reported by Stassun & Torres 2018), in order to determine an empirical measurement of the stellar radius, following the procedures described in Stassun & Torres (2016) and Stassun et al. (2017Stassun et al. ( , 2018a. We pulled the U magnitude from Mermilliod (2006), the JHK s magnitudes from 2MASS, the W1-W4 magnitudes from the WISE All-Sky Data Release (Wright et al. 2010;Cutri et al. 2012), the G BP RP magnitudes from Gaia DR2, and the NUV magnitude from the Galaxy Evolution Explorer (GALEX; Martin et al. 2005;Bianchi et al. 2011). Together, the available photometry spans the full stellar SED over the wavelength range 0.2-22 μm (see Figure 20). We exclude the GALEX point in our analysis because there appears to be excess flux, likely due to chromospheric activity commonly found in M dwarfs. All values are in Table 1, except for WISE All-Sky Data Release W1 = 8.117 ± 0.024, W2 = 7.972 ± 0.021, W3 = 7.877 ± 0.017, W4 = 7.823 ±0.117. We switch from the WISE AllWISE to All-Sky release here because we make use of W4 band, which has a higher S/N in the All-Sky release.
We performed a fit using NextGen stellar atmosphere models (Hauschildt et al. 1999), with the free parameters being the effective temperature (T eff ) and metallicity ([Fe/H]). The broadband SED is largely insensitive to the choice of g log , therefore we adopted a value of 5.0 as expected for an M dwarf. We also fixed the extinction A V ≡ 0 based on the star's proximity. The resulting fit (Figure 20) corresponds to T eff = 3550 ± 100 K and [Fe/H] = −0.5, and has a reduced χ 2 of 3.3. Integrating the (unreddened) model SED gives the bolometric flux at Earth, F bol = 1.158 ± 0.045 ×10 −9 erg s −1 cm −2 . Taking the F bol and T eff together with the Gaia DR2 parallax gives the stellar radius, R å = 0.316 ± 0.018R e . These parameter values are also consistent with those determined using the methods of M. L. Silverstein et al. (2022, in preparation). We reiterate that the three methods used in this paper to derive stellar effective temperature, luminosity, and radius fall into better agreement when all three assume subsolar metallicity, which is consistent with other properties of LHS 1678 (e.g., low HR-diagram position and large galactic velocities). We note that the stellar parameter analyses presented in Rains et al. (2021) also provide consistent results and a similar subsolar metallicity assessment.
Appendix B TESS M Dwarf Exoplanet Systems
Here in Table 11, we list the names of the M dwarf exoplanet systems presented in Figure 3 and their discovery references. Note. a On arXiv, accepted for publication in AJ. Limits on the Properties of the Astrometric Companion Here we provide the details of our approach to observationally constrain the properties of the astrometrically detected wide-orbit companion described in Sections 3.5 and 7.3. All astrometry used in this discussion comes from the RECONS team, whose data and analysis reveal the companion.
C.1. Limits Placed by Astrometry
The astrometric perturbation shown in Figure 4 is caused by movement of the photocenter of the unresolved binary orbiting its center of mass. To constrain the relative orbit between the two components, the photocentric orbit can be fit to yield the photocentric semimajor axis, α observed , which in turn can be used to estimate the mass of the unseen companion.
Following the prescription of Van De Kamp (1967), α observed can be derived using the relative semimajor axis Here, Δm is the magnitude difference between the primary and secondary in the filter used for the astrometry, in this case, V. From Kepler's third law, the semimajor axis of the relative orbit, a, of a binary with orbital period P is derived from By substituting different values of B, β, and a into the relation above (Equation (C1)), we can try to reproduce the observed semimajor axis of the photocentric orbit of LHS 1678 and its companion. The successes/failures constrain the properties we substitute in. We proceed as follows: 1. Simulated primary and secondary masses are allowed to range from 0.600 to 0.002 M e . We adopt a step size of 0.010 M e from 0.600 M e to 0.010 M e and 0.002 M e from 0.010 M e down to 0.002 M e . This sets the value of B. 2. We use the empirical M dwarf mass-luminosity relation (MLR) of Benedict et al. (2016) to convert each primary and secondary mass adopted above to an absolute magnitude V , and calculate Δm. The V values for both components are then merged into a single value for the combined light, and the total apparent magnitude (V total ) of the two components is then derived using the parallax. For secondary masses less than 0.080 M e , which is the limit of the MLR relation and approximately corresponds to the transition between stars and brown dwarfs, we assume the companion contributes no flux at V. This sets the value of β. 3. For a given M A and M B , we then calculate the relative semimajor axis a using Kepler's third law and an adopted period compatible with the observed photocentric motion. This sets the value of a.
4. Using the assigned fractional mass (B), fractional flux (β), and semimajor axis of the relative orbit (a), we determine the value of α simulated for each simulated system.
The results of the simulated photocentric semimajor axis (α simulated ) values are shown in Figure 21. Note that because the primary star is assumed to be the more massive component, the top half of each plot is not a physical solution and is shaded black.
We use the available mass and flux constraints as follows to determine the best match between the α simulated and α observed (red boxes in Figure 21). (1) Key to the simulations is the mass of the primary, which we estimate using available photometry, the RECONS parallax, and the mass-luminosity relations in Benedict et al. (2016). We estimate M = 0.38 M e using = 11.07 V , adopting an uncertainty of ±0.10 M e to allow for the lack of age and metallicity considerations in the Benedict et al. (2016) MLR (all masses below use these relations).
(2) We allow the simulated V total to fall within a range of 12.48 ± 0.10, the observed magnitude of the system.
(3) Finally, we introduce a third constraint that the difference between α simulated and α observed must be 10 mas or less for the match to be deemed successful.
Note that because both the orbital period and α observed are uncertain, we opt to explore several specific options in Figure 21. We select orbital periods of 42 yr (the value from the fit in Figure 4) and 100 yr, and photocentric semimajor axes of 17 mas (from the fit) and 100 mas. The resulting mass combinations consistent with the astrometry are enclosed in red boxes in Figure 21, where the mass of the primary is shown on the y-axis and the mass of the astrometric companion is shown on the x-axis. Shading indicates the semimajor axis of the resulting photocentric orbit.
The two left panels of Figure 21 show that for a semimajor axis of the photocentric orbit of 17 mas, the companion is a low-mass brown dwarf if the orbital period is 42 yr, and an even-lower-mass brown dwarf if the period is 100 yr. On the other hand, as shown in the lower-right panel, if the semimajor axis is 100 mas and the orbital period is a century, the companion is a more massive brown dwarf. Note that simulations of a 42 yr orbit and 100 mas semimajor axis shown in the upper-right panel yield a null result: there are no mass combinations consistent with the available astrometric data. Although the nature of the companion remains uncertain, we find that it is much more likely to be a brown dwarf than a low-mass star, and we cannot yet eliminate the possibility that it is a Jovian planet.
C.2. Limits Placed by Imaging
The nature of the companion may also be constrained using photometric and high-resolution imaging data. 61 Using VRIJHK photometry from the CTIO/SMARTS 0.9 m and 2MASS, and the relations of Henry et al. (2004), we derive a photometric distance estimate of 27.1 ± 4.2 pc. This is much further than the distance of 19.88 ± 0.01 pc (Bailer-Jones et al. 2018). Thus, the photometric data appear to eliminate a companion that is similar in mass and luminosity to LHS 1678 because it appears significantly underluminous rather than overluminous. older galactic population (see Section 3). Adopting an age of 5 Gyr, conservative mass estimates can be made for the limits of bound companions. We adopt this age and use the brown dwarf cooling models of Baraffe et al. (2003) to estimate that the NaCo observations rule out bound companions 70 M Jup at 5 au projected separations. These deep-imaging limits place strong constraints on the allowed parameter space of the astrometric companion. They indicate it is at or below the H-burning mass limit, consistent with the astrometric constraints, and likely closer than ≈5 au in projected separation.
C.3. Limits Placed by Radial Velocity
The lack of a detection in CHIRON and HARPS radial velocity data (Tables 8 and 6, and Sections 4.3, 5) over the observation baseline is consistent with a low-mass, long-period companion. The 10 day CHIRON campaign and 124 day HARPS campaign are insufficiently long in duration to identify a radial velocity shift caused by a companion with a decadeslong orbit. An object, e.g., of mass 0.08 M e, with a circular, edge-on orbit around LHS 1678 and a 42 yr period would have a semiamplitude of 1.2 km s −1 . The semiaamplitude would be 0.9 km s −1 in the case of a 100 yr period. Both seem easily detectable by CHIRON or HARPS at first glance, but the change in RV would be very gradual. We estimate that such a companion would present itself as a roughly 25 times smaller, ∼40 m s −1 shift in RV across the HARPS observation period. We do not detect such a shift. This reaffirms our conclusion that the companion is likely substellar in nature.
C.4. Could the Companion be a White Dwarf?
In the above discussion, we have assumed that the companion is a low-mass red or brown dwarf, but we must also consider the possibility that the companion is a white dwarf.
To understand which white dwarfs can be eliminated by the imaging observations, we examine those typically found in the solar neighborhood, as outlined clearly in Figure 3 in Subasavage et al. (2017). Most white dwarfs have = -10.5 16.0 V , although there are rare white dwarfs as faint as V ∼16.5. From the CTIO/SMARTS 0.9 m data, white dwarfs down to V ∼ 14.1 can be eliminated beyond 1 0, which corresponds to, roughly, the more massive half of the nearby white dwarf population. The SOAR data eliminate companions down to 0 15 brighter than I ∼ 11.7, but because white dwarfs have V − I = −0.3 to +1.9, the SOAR data only eliminate the bluest, most-massive white dwarfs. Because the NaCo observations cover the near-IR and white dwarfs are relatively blue, they are not sensitive to (m)any white dwarfs.
However, the radial velocity and astrometry can eliminate the possibility that the companion is a white dwarf. The lowestmass white dwarfs have masses of ∼0.2 M e (Kilic et al. 2007), and at the same distance such objects are much fainter than the value of = 11.07 V for LHS 1678. Thus, any such companion would contribute negligible light to the system. As described previously, the HARPS radial velocity nondetection excludes the possibility of a companion more massive than 0.08 M e in 40 to 100 yr edge-on, circular orbits. The astrometry also limits the mass of an unseen companion that contributes negligible light to the system, regardless of whether that companion is a red, brown, or white dwarf. This invisible nature means a white dwarf would contribute as much light to the astrometry as a brown dwarf, and the analysis in Section C.1 that eliminates most companions above 0.08 M e would apply to this one, as well. Thus, we conclude that the companion is very unlikely to be a white dwarf (or a more massive, but even fainter, object such as a neutron star). | 24,722.6 | 2021-10-22T00:00:00.000 | [
"Physics"
] |
A Faster Algorithm for Reducing the Computational Complexity of Convolutional Neural Networks
: Convolutional neural networks have achieved remarkable improvements in image and video recognition but incur a heavy computational burden. To reduce the computational complexity of a convolutional neural network, this paper proposes an algorithm based on the Winograd minimal filtering algorithm and Strassen algorithm. Theoretical assessments of the proposed algorithm show that it can dramatically reduce computational complexity. Furthermore, the Visual Geometry Group (VGG) network is employed to evaluate the algorithm in practice. The results show that the proposed algorithm can provide the optimal performance by combining the savings of these two algorithms. It saves 75% of the runtime compared with the conventional algorithm.
Introduction
Deep convolutional neural networks have achieved remarkable improvements in image and video processing [1][2][3]. However, the computational complexity of these networks has also increased significantly. Since the prediction process of the networks used in real-time applications requires very low latency, the heavy computational burden is a major problem with these systems. Detecting faces from video imagery is still a challenging task [4,5]. The success of convolutional neural networks in these applications is limited by their heavy computational burden.
There have been a number of studies on accelerating the efficiency of convolutional neural networks. Denil et al. [6] indicate that there are significant redundancies in the parameterizations of neural networks. Han et al. [7] and Guo et al. [8] use certain training strategies to compress these neural network models without significantly weakening their performance. Some researchers [9][10][11] have found that low-precision computation is sufficient for the networks. Binary/Ternary Net [12,13] restricts the parameters to two or three values. Zhang et al. [14] used low-rank approximation to reconstruct the convolution matrix, which can reduce the complexity of convolution. These algorithms are effective in accelerating computation in the network, but they also cause a degradation in accuracy. Fast Fourier Transform (FFT) is also useful in reducing the computational complexity of convolutional neural networks without losing accuracy [15,16], but it is only effective for networks with large kernels. However, convolutional neural networks tend to use small kernels because they achieve better accuracy than networks with larger kernels [1]. For these reasons, there is a demand for an algorithm that can accelerate the efficiency of networks with small kernels.
In this paper, we present an algorithm based on Winograd's minimal filtering algorithm which was proposed by Toom [17] and Cook [18] and generalized by Winograd [19]. The minimal filtering algorithm can reduce the computational complexity of each convolution in the network without losing accuracy. However, the computational complexity is still large for real-time requirements. To reduce further the computational complexity of these networks, we utilize the Strassen algorithm to reduce the number of convolutions in the network simultaneously. Moreover, we evaluate our algorithm with the Visual Geometry Group (VGG) network. Experimental results show that it can save 75% of the time spent on computation when the batch size is 32.
The rest of this paper is organized as follows. Section 2 reviews related work on convolutional neural networks, the Winograd algorithm and the Strassen algorithm. The proposed algorithm is presented in Section 3. Several simulations are included in Section 4, and the work is concluded in Section 5.
Convolutional Neural Networks
Machine-learning has produced impressive results in many signal processing applications [20,21]. Convolutional neural networks extend the machine-learning capabilities of neural networks by introducing convolutional layers to the network. Convolutional neural networks are mainly used in image processing. Figure 1 shows the structure of a classical convolutional neural network, LeNet. It consists of two convolutional layers, two subsampling layers and three fully connected layers. Usually, the computation of the convolutional layers occupies most of the network.
Algorithms 2018, 11, x FOR PEER REVIEW 2 of 12 algorithm can reduce the computational complexity of each convolution in the network without losing accuracy. However, the computational complexity is still large for real-time requirements. To reduce further the computational complexity of these networks, we utilize the Strassen algorithm to reduce the number of convolutions in the network simultaneously. Moreover, we evaluate our algorithm with the Visual Geometry Group (VGG) network. Experimental results show that it can save 75% of the time spent on computation when the batch size is 32. The rest of this paper is organized as follows. Section 2 reviews related work on convolutional neural networks, the Winograd algorithm and the Strassen algorithm. The proposed algorithm is presented in Section 3. Several simulations are included in Section 4, and the work is concluded in Section 5.
Convolutional Neural Networks
Machine-learning has produced impressive results in many signal processing applications [20,21]. Convolutional neural networks extend the machine-learning capabilities of neural networks by introducing convolutional layers to the network. Convolutional neural networks are mainly used in image processing. Figure 1 shows the structure of a classical convolutional neural network, LeNet. It consists of two convolutional layers, two subsampling layers and three fully connected layers. Usually, the computation of the convolutional layers occupies most of the network. Convolutional layers extract features from the input feature maps via different kernels. Suppose there are Q input feature maps of size Mx × Nx and R output feature maps of size My × Ny. The size of the convolutional kernel is Mw × Nw. The computation of the output in a single layer is given by the equation where X is the input feature map, Y is the output feature map, and W is the kernel. The subscripts x and y indicate the position of the pixel in the feature map. The subscripts u and v indicate the position of the parameter in the kernel. Equation (1) can be rewritten as Equation (2).
Suppose there are P images that are sent together to the neural network, which means the batch size is P. Then the output Y in Equation (2) can be expressed by Equation (3).
If we regard the yr,p, wr,q and xq,p as the elements of the matrices Y, W and X, respectively, the output can be expressed as the convolution matrix in Equation (4). Convolutional layers extract features from the input feature maps via different kernels. Suppose there are Q input feature maps of size Mx × Nx and R output feature maps of size My × Ny. The size of the convolutional kernel is Mw × Nw. The computation of the output in a single layer is given by the equation where X is the input feature map, Y is the output feature map, and W is the kernel. The subscripts x and y indicate the position of the pixel in the feature map. The subscripts u and v indicate the position of the parameter in the kernel. Equation (1) can be rewritten as Equation (2).
Suppose there are P images that are sent together to the neural network, which means the batch size is P. Then the output Y in Equation (2) can be expressed by Equation (3). If we regard the y r,p , w r,q and x q,p as the elements of the matrices Y, W and X, respectively, the output can be expressed as the convolution matrix in Equation (4).
Matrix Y and matrix X are special matrices of feature maps. Matrix W is a special matrix of kernels. This convolutional matrix provides a new view of the computation of the output Y.
Winograd Algorithm
We denote an r-tap FIR filter with m outputs as F(m, r). The conventional algorithm for F(2, 3) is shown in Equation (6), where d 0 , d 1 , d 2 and d 3 are the inputs of the filter, and h 0 , h 1 and h 2 are the parameters of the filter. As Equation (6) shows, it uses 6 multiplications and 4 additions to compute F(2, 3).
If we use the minimal filtering algorithm [19] to compute F(m, r), it requires (m + r -1) multiplications. The process of the algorithm for computing F(2, 3) is shown in Equations (7)- (11).
The computation can be written in matrix form as Equation (12).
We substitute A, G and B for the matrices in Equation (12). Equation (12) can then be rewritten as Equation (13).
In Equation (13), • indicates element-wise multiplication, and the superscript T indicates the transpose operator. A, G and B are defined in Equation (14). We can see from Equation (7) to Equation (11) that the whole process needs 4 multiplications. However, it also needs 4 additions to transform data, 3 additions and 2 multiplications by a constant to transform the filter, and 4 additions to transform the final result. (To compare the complexity easily, we regard the multiplication by a constant as an addition.) The 2-dimensional filters F(m × m, r × r) can be generalized by the filter F(m, r) as Equation (15) [22].
F(2 × 2, 3 × 3) needs 4 × 4 = 16 multiplications, 32 additions to transform data, 28 additions to transform the filter, and 24 additions to transform the final result. The conventional algorithm needs 36 multiplications to calculate the result. This algorithm can reduce the number of multiplications from 36 to 16.
can be used to compute the convolutional layer with 3 × 3 kernels. Each input feature map can be divided into smaller feature maps in order to use Equation (15). If we substitute U = GwG T and V = B T × B, then Equation (3) can be rewritten as Equation (16).
Strassen Algorithm
Suppose there are two matrices A and B, and matrix C is the product of A and B. The numbers of the elements in both rows and columns of A, B and C are even. We can partition A, B and C into block matrices of equal sizes as follows: According to the conventional matrix multiplication algorithm, we then have Equation (18).
As Equation (18) shows, we need 8 multiplications and 4 additions to complete matrix C. The Strassen algorithm can be used to reduce the number of multiplications [23]. The process of the Strassen algorithm is shown as follows: Algorithms 2018, 11, 159 5 of 11 where I, II, III, IV, V, VI, VII are temporary matrices. The whole process requires 7 multiplications and 18 additions. It reduces the number of multiplications from 8 to 7 without changing the computational results. More multiplications can be saved by using the Strassen algorithm recursively, as long as the numbers of rows and columns of the submatrices are even. If we use N recursions of the Strassen algorithm, then it can save 1 − (7/8) N multiplications. The Strassen algorithm is suitable for the special convolutional matrix in Equation (4) [24]. Therefore, we can use the Strassen algorithm to handle a convolutional matrix.
Proposed Algorithm
As we can see from Section 2.2, the Winograd algorithm incurs more additions. To avoid repeating the transform of W and X in Equation (16), we calculate the matrices U and V separately. This can reduce the number of additions incurred by this algorithm. The practical implementation of this algorithm is listed in Algorithm 1. The calculation of output M in Algorithm 1 is the main complexity of multiplication in the whole computation process. To reduce the computational complexity of output M, we can use the Strassen algorithm. Before using the Strassen algorithm, we need to reform the expression of M as follows.
The output M in Algorithm 1 can be written as the equation where U r,q and V q,p are temporary matrices, and A is the constant parameter matrix. To show the equation easily, we ignore matrix A. (Matrix A is not ignored in the actual implementation of the algorithm.) The output M can then be written as shown in Equation (31).
We denote three special matrices M, U and V. M r,p , U r,q , and V q,p are the elements of the matrices M, U and V, respectively, as shown in Equation (33). The output M can then be written as a multiplication of matrix U and matrix V.
In this case, we can partition the matrices M, U and V into equal-sized block matrices, and then use the Strassen algorithm to reduce the number of multiplications between U r,q and V q,p . The multiplication in the Strassen algorithm is redefined as the element-wise multiplication of matrices U r,q and V q,p . We name this new combination as the Strassen-Winograd algorithm. To compare theoretically the computational complexity of the conventional algorithm, Strassen algorithm, Winograd algorithm, and Strassen-Winograd algorithm, we list the complexity of multiplication and addition in Table 1. The output feature map size is set to 64 × 64, and the kernel size is set to 3 × 3. 9.66 × 10 9 9.65 × 10 9 4.34 × 10 9 6.65 × 10 9 4.29 × 10 9 7.63 × 10 9 1.93 × 10 9 9.37 × 10 9 128 7.73 × 10 10 7.72 × 10 10 3.04 × 10 10 4.68 × 10 10 3.44 × 10 10 6.06 × 10 10 1.35 × 10 10 7.19 × 10 10 256 6.18 × 10 11 6.18 × 10 11 2.13 × 10 11 3.29 × 10 11 2.75 × 10 11 4.83 × 10 11 9.45 × 10 10 5.55 × 10 11 512 4.95 × 10 12 4.95 × 10 12 1.49 × 10 12 2.31 × 10 12 2.20 × 10 12 3.86 × 10 12 6.61 × 10 11 4.29 × 10 12 We can see from Table 1 that, although the algorithms cause more additions when the matrix size is small, the number of extra additions is less than the number of decreased multiplications. Moreover, multiplication usually costs more time than addition. Hence the three algorithms are all theoretically effective in reducing the computational complexity. Figure 2 shows a comparison of the computational complexity ratios. The Strassen algorithm shows less reduction of multiplication when the matrix size is small, but it incurs less additions. The Winograd algorithm shows a stable performance. Moreover, the number of additions slightly decreases as the matrix size increases. For small-sized matrices, the Strassen-Winograd algorithm shows a much better reduction in multiplication complexity than the Strassen algorithm. Although it incurs more additions, the number of extra additions is much less than the number of decreased multiplications. The Strassen-Winograd algorithm shows a similar performance to the Winograd algorithm. When the matrix size is small, the Winograd algorithm shows a slightly better performance, Winograd algorithm shows a stable performance. Moreover, the number of additions slightly decreases as the matrix size increases. For small-sized matrices, the Strassen-Winograd algorithm shows a much better reduction in multiplication complexity than the Strassen algorithm. Although it incurs more additions, the number of extra additions is much less than the number of decreased multiplications. The Strassen-Winograd algorithm shows a similar performance to the Winograd algorithm. When the matrix size is small, the Winograd algorithm shows a slightly better performance, whereas the Strassen-Winograd algorithm and Strassen algorithm perform much better as the matrix size increases.
Simulation Results
Several simulations were conducted to evaluate our algorithm. We compare our algorithm with the Strassen algorithm and Winograd algorithm, measuring performance by the runtime in MATLAB R2013b (CPU: Inter(R) Core(TM) i7-3370K). For objectivity, we apply Equation (18) to the conventional algorithm and use it as a benchmark. Moreover, all the input data x and kernel w are randomly generated. We measure the accuracy of our algorithm by the absolute element error in the output feature maps. As a benchmark, we use the conventional algorithm with double precision data, kernels, middle variables and outputs. The other algorithms in this comparison use double precision data and kernels but single precision middle variables and outputs.
The VGG network [1] was applied to our simulation. There are nine different convolutional layers in the VGG network. The parameters of the convolutional layer are shown in Table 2. The depth indicates the number of times a layer occurs in the network. Q indicates the number of input feature maps. R indicates the number of output feature maps. Mw and Nw represent the size of the kernel. My and Ny represent the size of the output feature map. The size of the kernel in the VGG network is 3 × 3. We apply F(2 × 2, 3 × 3) to the operation of convolution. For the computation of the output feature map with size My × Ny, the map is partitioned into (My/2) × (Ny/2) sets, each using one computation of F(2 × 2, 3 × 3).
Simulation Results
Several simulations were conducted to evaluate our algorithm. We compare our algorithm with the Strassen algorithm and Winograd algorithm, measuring performance by the runtime in MATLAB R2013b (CPU: Inter(R) Core(TM) i7-3370K). For objectivity, we apply Equation (18) to the conventional algorithm and use it as a benchmark. Moreover, all the input data x and kernel w are randomly generated. We measure the accuracy of our algorithm by the absolute element error in the output feature maps. As a benchmark, we use the conventional algorithm with double precision data, kernels, middle variables and outputs. The other algorithms in this comparison use double precision data and kernels but single precision middle variables and outputs.
The VGG network [1] was applied to our simulation. There are nine different convolutional layers in the VGG network. The parameters of the convolutional layer are shown in Table 2. The depth indicates the number of times a layer occurs in the network. Q indicates the number of input feature maps. R indicates the number of output feature maps. Mw and Nw represent the size of the kernel. My and Ny represent the size of the output feature map. The size of the kernel in the VGG network is 3 × 3. We apply F(2 × 2, 3 × 3) to the operation of convolution. For the computation of the output feature map with size My × Ny, the map is partitioned into (My/2) × (Ny/2) sets, each using one computation of F(2 × 2, 3 × 3). (Nw) 3 3 3 3 3 3 3 3 3 My(Ny) 224 224 112 112 56 56 28 28 14 As Table 2 shows, the numbers of rows and columns are not always even, and the matrices are not always square. To solve this problem, we pad a dummy row or column in the matrices once we encounter an odd number of rows or columns. The matrix can then continue using the Strassen algorithm. We apply these nine convolutional layers in turn to our simulations. For each convolutional layer, we run the four algorithms with different batch sizes from 1 to 32. The runtime consumption of the algorithms is listed in Table 3, and the numerical accuracy of the different algorithms in different layers is shown in Table 4. Table 4 shows that the Winograd algorithm is slightly more accurate than the Strassen algorithm and Strassen-Winograd algorithm. The maximum element error of these algorithms is 6.16 × 10 −4 . Compared with the minimum value of 1.09 × 10 3 in the output feature map, the accuracy loss incurred by these algorithms is negligible. As we can see from Section 2, theoretically, the processes in all of these algorithms do not result in a loss in accuracy. In practice, a loss in accuracy is mainly caused by the single precision data. Because the conventional algorithm with low precision data is sufficiently accurate for deep learning [10,11], we conclude that the accuracy of our algorithm is equally sufficient.
To compare runtime easily, we use the conventional algorithm as a benchmark, and calculate the saving on runtime displayed by the other algorithms. The result is shown in Figure 3.
The Strassen-Winograd algorithm shows a better performance than the benchmark in all layers except layer1. This is because the number of input feature maps Q in layer1 is three, which limits the performance of the algorithm as a small matrix size incurs more additions. Moreover, odd numbers of rows or columns need dummy rows or columns for matrix partitioning, which causes more runtime.
Conclusions and Future Work
The computational complexity of convolutional neural networks is an urgent problem for realtime applications. Both the Strassen algorithm and Winograd algorithm are effective in reducing the computational complexity without losing accuracy. This paper proposed to combine these algorithms to reduce the heavy computational burden. The proposed strategy was evaluated with the VGG network. Both the theoretical performance assessment and the experimental results show that the Strassen-Winograd algorithm can dramatically reduce the computational complexity.
There remain limitations that need to be addressed in future research. Although the algorithm reduces the computational complexity of convolutional neural networks, the cost is an increased The performance of the Winograd algorithm is stable from layer2 to layer9. It saves 53% of the runtime on average, which is close to the 56% reduction in multiplications. The performances of the Strassen algorithm and Strassen-Winograd algorithm improve as the batch size increases. For example, in layer7, when the batch size is 1, we cannot partition the matrix to use the Strassen algorithm, and there is almost no saving on runtime. The Strassen-Winograd algorithm saves 52% of the runtime, a similar saving as the Winograd algorithm. When the batch size is 2, the Strassen algorithm saves 13% of the runtime, which equates to the 13% reduction in multiplications. The Strassen-Winograd algorithm saves 58% of the runtime, which is close to the 61% reduction in multiplications. As the batch size increases, the Strassen algorithm and Strassen-Winograd algorithm can use more recursions, which can further reduce the number of multiplications and save more runtime. When the batch size is 32, the Strassen-Winograd algorithm saves 75% of the runtime, while the Strassen algorithm and Winograd algorithm save 49% and 53%, respectively.
Though experiments with larger batch sizes were not carried out due to limitations on time and memory, we can see the trend in performance as the batch size increases. This is consistent with the theoretical analysis in Section 3. We conclude therefore that the proposed algorithm can provide the optimal performance by combining the savings of these two algorithms.
Conclusions and Future Work
The computational complexity of convolutional neural networks is an urgent problem for real-time applications. Both the Strassen algorithm and Winograd algorithm are effective in reducing the computational complexity without losing accuracy. This paper proposed to combine these algorithms to reduce the heavy computational burden. The proposed strategy was evaluated with the VGG network. Both the theoretical performance assessment and the experimental results show that the Strassen-Winograd algorithm can dramatically reduce the computational complexity.
There remain limitations that need to be addressed in future research. Although the algorithm reduces the computational complexity of convolutional neural networks, the cost is an increased difficulty in implementation, especially in real-time systems and embedded devices. It also increases the difficulty of parallelizing an artificial network for hardware acceleration. In future work, we aim to apply this method to hardware accelerator using practical applications. | 5,370.4 | 2018-10-18T00:00:00.000 | [
"Computer Science"
] |
A Node Embedding-Based Influential Spreaders Identification Approach
: Node embedding is a representation learning technique that maps network nodes into lower-dimensional vector space. Embedding nodes into vector space can benefit network analysis tasks, such as community detection, link prediction, and influential node identification, in both calculation and richer application scope. In this paper, we propose a two-step node embedding-based solution for the social influence maximization problem (IMP). The solution employs a revised network-embedding algorithm to map input nodes into vector space in the first step. In the second step, the solution clusters the vector space nodes into subgroups and chooses the subgroups’ centers to be the influential spreaders. The proposed approach is a simple but e ff ective IMP solution because it takes both the social reinforcement and homophily characteristics of the social network into consideration in node embedding and seed spreaders selection operation separately. The information propagation simulation experiment of single-point contact susceptible-infected-recovered (SIR) and full-contact SIR models on six di ff erent types of real network data sets proved that the proposed social influence maximization (SIM) solution exhibits significant propagation capability.
Introduction
Through years of research on how network structure affects information diffusion, researchers believe that social reinforcement and homophily are the two factors that play essential roles in the process of information going viral [1][2][3]. On the one hand, social reinforcement inside communities tends to trigger multiple exposures, and each additional exposure significantly increases the probabilities of individuals adopting social behaviors [1], which is the underlying assumption of classic information diffusion models like the LTM (linear threshold model). On the other hand, people sharing similar characteristics are more likely to form social relationships, which makes homophily factors inseparable from social contagion [3]. Let us posit that there is an underlying network over which information propagates, so the social reinforcement and homophily factors implying that both local and global structural information of the network should be taken into consideration. Except for the research on the role social reinforcement and homophily in information diffusion, researchers also discussed the role of centrality for the identification of influential spreaders in complex networks [4]. According to different types of network and different research perspectives, the evaluation criteria of node importance are also different. The research on critical node set recognition originated from the thinking of Domingos and Richardson in "viral marketing" [5,6]. Domingos and Richardson propose to make use of the customers' 'network value', which means put more promotion effort to profit from customers who may be influenced to buy by current customers or who may influence other customers [5,7]. Under this circumstance, researchers simulate word-of-mouth effects by using information diffusion models, such as such as the Linear Threshold Model (LTM), Independent Cascade Model (ICM), the triggering (TR) model, time-aware diffusion models [8]. However, three aspects need to be taken into consideration: First, selected nodes should be able to cover the whole social graph more efficiently and the node influence must be taken into consideration; Second, Recognition of key node sets requires the foundation of research on node centrality. Different centrality indexes have different computational complexity and applicable scope, which will lead to differences in experimental results of the algorithm; Three, the explosive growth of network data brings severe challenges to the identification of key nodal sets [9]. In network marketing with a limited budget, the best strategy is to show the advertisements and provide discounts to a set of customers who are likely to buy the product and able to trigger many other people (including their friends, friends of friends) to buy the product to maximize the impact [10].
In this paper's research, we propose a node-embedding algorithm and cluster nodes into subgroups base on the learned node embeddings. Giving priority to the dispersion between nodes and ensuring the relative importance of nodes, we extract the core nodes from the perspective of vector space distance. We call this strategy for identifying key node sets the CNE (cluster by network embedding) algorithm.
Related Concepts
In this section, we give and explain necessary definitions and concepts which will be used through this paper. We consider an undirected graph G = (V, E), where V is the set of nodes in G and E is the set of edges among these nodes. Matrix A = a ij n × n is the adjacency matrix used to represent graph G, where n = |V| is the number of nodes in G.
Social Influence Maximization (SIM) Problem
Given an integer k [n] and k << n, the task of social influence maximization is to identify a k-sized node set such that when the information diffusion process is over maximum number of nodes become influenced. According to this description, the social influence maximization problem (SIM) task is closely associated with information diffusion models [11].
Node Embedding
The goal of node embedding is to encode nodes into lower dimension space and approximate the similarities between nodes in original space by similarities in embedding space. By doing so, network embedding avoids performing complex inference on the entire network which is a very practical and efficient solution for downstream tasks such as node classification, clustering, link prediction, and network visualization [12].
ϕ : v ∈ V → R n * d is a mapping function from node v of V to d dimension real embedding space R n * d . To our knowledge, DeepWalk was one of the very first popular network embedding approaches proposed in recent years [13]. DeepWalk provides a universal solution for feeding a network into neural nets to undertake node representation learning. It also bridges the gap between word embedding and network embedding through the use of the Word2Vec. Inspired by DeepWalk, research such as LINE, which uses first -order and second-order proximity to formally define the large-scale information network embedding problem [14], Node2vec which is similar to DeepWalk, but the main difference is that depth first and breadth first are taken into account when walking [15], and GraRep, which is a model that learns the node representation of a weighted graph and integrates the global structure information of the graph into the learning process [16] started to boom. LINE proposes to embed both local and global context information into node representation through a carefully designed objective function and edge-sampling strategy is used during learning process to prevent exploding gradients. Node2vec uses a biased random walk to generate nodes' neighborhood information and employs the skip-gram architecture for learning node representation based on the generated neighbourhood contexts. GraRep emphases the importance of capturing k-steps relationship information between node pairs and considers various powers of the adjacency matrix in order to capture higher-order node similarity.
The intuition behind most node embedding algorithms is that more popular or connected samples should be selected more frequently during training since they are more informative [17]. Base on this intuition, we naturally extended the continuous bag of words (CBOW) algorithm of DeepWalk to a much faster and more accurate algorithm called centrality-weighted CBOW (IW-CBOW). The IW-CBOW algorithm uses nodes' importance value as prior information to guide the gradient descent optimization of CBOW towards more meaningful directions and which will also accelerates the training at the same time.
Centrality Analysis
In this paper, we only consider the network with no direction. We let the network G = (V, E), where V is the node set and E is the edge set. A = a ij n × n represents the adjacency matrix of the network, where n represents the number of nodes. If node i is connected to node j, a ij = 1, otherwise a ij = 0. Our goal is to select m nodes in the node set of the network to maximize the influence of their propagation in the network.
Next, some commonly used centrality measures and algorithms to identify key node groups based on point coloring theory are briefly introduced. Finally, the SIR propagation model is introduced.
Centrality Measure
Degree centrality, the number of neighbors connected to node i.
Closeness centrality is used to measure the average distance from one node to other nodes, where d ij represents the shortest path length between node i and node j.
Betweenness centrality, which describes the distribution of a node on the path between other nodes, where δ(s, t) represents the total number of shortest paths from node s to node j, and δ(s, t i) represents the number of shortest paths from node s to node t through i.
K-kernel, which describes the importance of nodes by their location in the network. Recursive stripping of nodes with degrees less than or equal to k in the network is performed as follows: First of all, delete the nodes with degree 1 and their connected edges in the network. At this time, new nodes with degree 1 may appear in the network, and continue to delete the new nodes with degree 1 and their connected edges. Repeat this operation until there are no more nodes with degree 1 in the network. At this time, all the deleted nodes go to constitute the first layer; next, the above deletion operation is repeated to obtain a second layer and so on, until all nodes in the network are given the value of K-kernel.
Point Coloring Theory
Bao et al. introduced the point coloring theory of graphs to solve the problem of finding key node groups. First of all, the nodes in Graph G are arranged in descending order of degrees. Next comes coloring the ordered nodes, coloring the first node with the first color, and coloring each node that is not adjacent to the preceding colored node with the same color in the order of arrangement. Then, the above coloring process is repeated with a second color and so on, until all nodes are colored.
Nodes of the same color are placed in the point set of the same selected node, and the first m nodes in the node set with the largest number of nodes are taken as key node groups. It is also possible to sort the nodes according to the kernel number, closeness centrality or betweenness centrality, and select the key node group through the coloring process described above.
Susceptible-Infected-Recovered (SIR) Model
Classic propagation models are commonly used unsupervised. Susceptible-infected-recovered (SIR) is a classic mathematical model of epidemics. SIR model divides the total population N into three categories: susceptible, infected and recovered. Users in the susceptible state are likely to be infected or influenced. Users are in infected state means that these users have already been infected or influenced. Users in the recovered state are no longer able to be infected or influenced. As is shown in Figure 1, at each time step, susceptible nodes. sort the nodes according to the kernel number, closeness centrality or betweenness centrality, and select the key node group through the coloring process described above.
Susceptible-Infected-Recovered (SIR) Model
Classic propagation models are commonly used unsupervised. Susceptible-infected-recovered (SIR) is a classic mathematical model of epidemics. SIR model divides the total population N into three categories: susceptible, infected and recovered. Users in the susceptible state are likely to be infected or influenced. Users are in infected state means that these users have already been infected or influenced. Users in the recovered state are no longer able to be infected or influenced. As is shown in Figure 1, at each time step, susceptible nodes. We use the SIR propagation model to verify the influence of the selected node group on the network. The SIR model is the most classical model in infectious disease model, including three node states, where S represents susceptible state, i.e., it has no disease and lacks immunity, I represents the infected state, i.e., the diseased node, in the process of contacting with an S-state node; this type of node transmits the disease to the s-state node with a transmission probability , and the S-state node is transformed into an I-state node at this time. R represents the removal state, i.e., a node that has immunity due to disease recovery or dies due to disease, and an I-state node becomes an R-state node with a removal rate . When the number of I-state nodes is 0, the propagation process ends and the network tends to be stable. The SIR model has two implementations: full-contact SIR, i.e., every round of I-state nodes try to infect all their neighbors, such as social networks; single-point contact SIR, i.e., each round of I-state nodes randomly select one of their neighbors to try to infect, such as a call network. In the paper, we set the key node group as the propagation source, i.e., I-state nodes. After SIR propagation model simulation, we compare the final number of R-state nodes in the network to determine the advantages and disadvantages of key node group selection. In this paper, in order to ensure the observability of experimental results, we set = 1 for full-contact SIR, and we set = 0.1 for single-point contact SIR.
The Overall Approach
We begin by explaining our strategy for effective multiple spreaders identification. Considering the definition of effective spreaders for the influence maximization problem (IMP), effective spreaders should be both influential nodes and widely dispersed nodes (lower the cost) at the same time. Taking these two essential requirements into consideration, the overall approach comprise 2 simple steps: Step 1: Learn node representations and partition target network into clusters base on the similarity between nodes in the embedding space; Step 2: Calculate the 'cores' of clusters and set them as effective spreaders.
In the first step, we propose a modified DeepWalk algorithm which makes sure influential nodes play a vital role in the embedding calculation, and k-means algorithm is applied to the embedding space to cluster the target network into non-overlapping subgroups in which the nodes share particular characteristics in common. The goal of the clustering step is to ensure that the selected spreaders naturally cover the whole target network. In the second step, we set the node which has the smallest mean distance to the rest of the nodes in the same cluster as the 'core' of the cluster, which is mainly the calculation of closeness centrality measurement. Employing closeness centrality as the measurement aims to select representative nodes to the clusters. We use the SIR propagation model to verify the influence of the selected node group on the network. The SIR model is the most classical model in infectious disease model, including three node states, where S represents susceptible state, i.e., it has no disease and lacks immunity, I represents the infected state, i.e., the diseased node, in the process of contacting with an S-state node; this type of node transmits the disease to the s-state node with a transmission probability β, and the S-state node is transformed into an I-state node at this time. R represents the removal state, i.e., a node that has immunity due to disease recovery or dies due to disease, and an I-state node becomes an R-state node with a removal rate µ. When the number of I-state nodes is 0, the propagation process ends and the network tends to be stable. The SIR model has two implementations: full-contact SIR, i.e., every round of I-state nodes try to infect all their neighbors, such as social networks; single-point contact SIR, i.e., each round of I-state nodes randomly select one of their neighbors to try to infect, such as a call network. In the paper, we set the key node group as the propagation source, i.e., I-state nodes. After SIR propagation model simulation, we compare the final number of R-state nodes in the network to determine the advantages and disadvantages of key node group selection. In this paper, in order to ensure the observability of experimental results, we set µ = 1 for full-contact SIR, and we set µ = 0.1 for single-point contact SIR.
The Overall Approach
We begin by explaining our strategy for effective multiple spreaders identification. Considering the definition of effective spreaders for the influence maximization problem (IMP), effective spreaders should be both influential nodes and widely dispersed nodes (lower the cost) at the same time. Taking these two essential requirements into consideration, the overall approach comprise 2 simple steps: Step 1: Learn node representations and partition target network into clusters base on the similarity between nodes in the embedding space; Step 2: Calculate the 'cores' of clusters and set them as effective spreaders.
In the first step, we propose a modified DeepWalk algorithm which makes sure influential nodes play a vital role in the embedding calculation, and k-means algorithm is applied to the embedding space to cluster the target network into non-overlapping subgroups in which the nodes share particular characteristics in common. The goal of the clustering step is to ensure that the selected spreaders naturally cover the whole target network. In the second step, we set the node which has the smallest mean distance to the rest of the nodes in the same cluster as the 'core' of the cluster, which is mainly the calculation of closeness centrality measurement. Employing closeness centrality as the measurement aims to select representative nodes to the clusters.
Proposed Node-Embedding Approach
The DeepWalk algorithm comprises two steps.
Step 1. Perform random walks on nodes (anchor nodes) in a graph to construct contextual node sequences of anchor nodes.
Step 2. Employ SkipGram algorithm to learn the embedding of anchor nodes based on the contextual node sequences generated in step 1.
We replace the Skipgram algorithm of DeepWalk with an extended CBOW algorithm called 'centrality-weighted-CBOW' to obtain the the proposed node-embedding approach for the multiple spreaders identification (MSI) task. To lower the affect of uneven probabilistic distribution of node centrality values, we normalize centrality values using Formula (4). Line 1 of Algorithm 1 constructs a vector C of normalized centrality values of all nodes of G and line 6 feeds these centrality values as the weights for Centrality-weighted-CBOW algorithm.
To understand why a centrality weighted strategy is employed, we need to put the node-embedding approach back into the MSI task context. As we concluded, great influence should be one of the key features shared by effective spreaders, and in a social science, individuals' characteristics can be decided or revealed by looking into its' neighbors' features. CBOW algorithm is one of the learns to predict the anchor by its context, from this kind of sociology perspective, employ CBOW algorithm to embed nodes is a reasonable choice.
window size m embedding size d walks per vertex γ walk length t Number of iterations λ Output: matrix of vertex representations M n×h . 1. C =< Normalize(?(v)) f or v ∈ V//Vector of normalized node centrality values 2. for i = 0 to λ do 3. V = shu f f le(V)//Shuffle the node set of G 4.
for v∈V do 5.
end for 8. end for Let G = (V, E) be a simple network, v i ∈ V(i = 1, 2, · · · , n) and n = |V|. As is shown in Figure 2, a normal CBOW algorithm works as a three-layer neural network, where input layer in the embedding space is h-dimension. There are two matrices, where − ℎ column of × is the h dimensional embedded vector for node .
Let's break down CBOW algorithm into the steps and explain how our extended approach works.
•
Calculate the embedded node vectors of context nodes where prime marks are used to distinguish the calculated embedded node vectors from the corresponding one hot node vectors.
•
Average the embedded node vectors to obtain = + +. . . + 2 ; • Calculate a score vector = × × ; • Turn the scores into probabilities ^= ( ); • Use gradient descent to optimize loss function ( , ) = − ∑ ( ), where is the real probability, which is actually the real one hot node vector of anchor node.
As we can see, compared to neural network models such as NLP (Natural Language Processing), the CBOW model uses linear activation functions instead of non-linear activation. In the 2nd step, it picks up the desired embeddings of input nodes by multiplying nodes' one hot vector coding with matrix ×ℎ . In the following 3rd step, CBOW algorithm averages these h dimensional embedded vectors of context nodes which forms the output of the hidden layer. This averaging operation treats all nodes equally and does not consider the differences between nodes. It only considers whether or not a node appears as the context of the anchor node. Inspired by the works on improving the word2vec model carried out by NLP researchers [20,21], we use a weighted average (Formula 6) to replace the average calculation of the 3rd step above, where the node importance calculation can be any node importance measurement. Since node importance is a critical measurement which reflects vital structural characteristics of the network, we employ node importance as the weights; by doing this, the role of important nodes will be strengthened in embedding calculation. We evaluated the performance of the algorithm using community detection as the downstream task on 2 well-known network datasets (Table 1). These 2 datasets are published with ground-truth communities, so normalized mutual information was chosen to measure the K-means clustering results in node embedding space. Node importance measures, including degree, PageRank, Betweennes and Coreness generated using k-shell decomposition analysis [22,23] were tested as the weight. To There are two matrices, where i − th column of W n×h is the h dimensional embedded vector for node vi.
Let's break down CBOW algorithm into the steps and explain how our extended approach works.
Calculate the embedded node vectors of context nodes • x where prime marks are used to distinguish the calculated embedded node vectors from the corresponding one hot node vectors.
•
Average the embedded node vectors to obtain Calculate a score vector s = v × W h×n ; • Turn the scores into probabilitiesŷ = so f tmax(s); • Use gradient descent to optimize loss function H(y,ŷ) = − n j=1 y j log(ŷ), where y is the real probability, which is actually the real one hot node vector of anchor node.
As we can see, compared to neural network models such as NLP (Natural Language Processing), the CBOW model uses linear activation functions instead of non-linear activation. In the 2nd step, it picks up the desired embeddings of input nodes by multiplying nodes' one hot vector coding with matrix W n×h . In the following 3rd step, CBOW algorithm averages these h dimensional embedded vectors of context nodes which forms the output of the hidden layer. This averaging operation treats all nodes equally and does not consider the differences between nodes. It only considers whether or not a node appears as the context of the anchor node. Inspired by the works on improving the word2vec model carried out by NLP researchers [20,21], we use a weighted average (Formula (6)) to replace the average calculation of the 3rd step above, where the node importance calculation can be any node importance measurement. Since node importance is a critical measurement which reflects vital structural characteristics of the network, we employ node importance as the weights; by doing this, the role of important nodes will be strengthened in embedding calculation. We evaluated the performance of the algorithm using community detection as the downstream task on 2 well-known network datasets (Table 1). These 2 datasets are published with ground-truth communities, so normalized mutual information was chosen to measure the K-means clustering results in node embedding space. Node importance measures, including degree, PageRank, Betweennes and Coreness generated using k-shell decomposition analysis [22,23] were tested as the weight. To accelerate training, hierarchical softmax was used instead of softmax. In the experiment, we chose degree centrality (node importance measures) as the weights of models in CBOW algorithm, corresponding to Degree_CBOW algorithm.
To further improve the performance of node embedding, we can also use PCA(Principal Component Analysis) on proposed weighted CBOW, the use of PCA is a way to make up for the defect of CBOW as a shallow model. Throughout experiment (the experimental results are shown in Table 2), applying PCA on node embeddings generated by proposed algorithm will improve the community detection result NMI (Normalized Mutual Information) at an average of 0.20% for the email-EU-core network datasets.
Key Node Selection
In this paper, we choose two types of clustering: hierarchical clustering and K-means clustering. Hierarchical clustering is the "tree" that forms a hierarchy or cluster of data objects. Hierarchical clustering includes condensed hierarchical clustering and split hierarchical clustering. In this paper, we use the aggregation hierarchy clustering and use the bottom-up strategy. First, make each node a cluster, find the two most similar clusters and merge them to form a cluster, then iteratively merge the clusters into larger and larger clusters until m clusters are formed.
K-means clustering is to randomly select m nodes in vector space, and each node represents the initial mean or center of a cluster. Each remaining node is assigned to the most similar cluster according to its Euclidean distance from the center of each cluster. Then, according to the nodes assigned to the cluster, the average value of the nodes in each cluster is recalculated. The updated average value is used as the new cluster center to redistribute all objects. Continue to iterate the above process until the allocation is stable, i.e., the clusters formed in this round are the same as those formed in the previous round.
In order to make the nodes in the selected key node group sufficiently dispersed, we choose the clustering method to divide the network into m clusters, where the parameter m (the number of seed nodes/clusters) will be determined by the 'budget' of the IMP application, the clustering algorithm, and the data sets. Suppose the 'budget' of IMP application can support m 1 seed nodes and the optimal number of clusters determined by the data from the angle of the algorithm is m 2 , then we choose m based on Formula (7). If m 1 is greater than or equal to m 2 which means the budget is enough, then the m 2 clusters' centers will be selected; otherwise, the first m important nodes of the m 2 clusters' centers will be selected.
According to the above two different clustering strategies (CNE_HC (Cluster by Network Embedding_ Hierarchical Clustering), CNE_KM (Cluster by Network Embedding_ K-means Clustering)), the network is divided differently. We select the core nodes in the class cluster after the network is divided based on the similarity between nodes. We believe that a node in a cluster is most important if it has the greatest similarity with all other nodes. The similarity between nodes based on vector representation is the distance between nodes. The smaller the distance, the more similar the nodes are. Therefore, in the cluster, we want to find the node with the smallest distance from other nodes. min(
Datasets
We have carried out experiments on several different types of real network datasets in order to verify the effectiveness of our method. The email network is the internal email network of a large European research institution. Nodes represent users in the institution and edges represent the fact that there is at least one mail exchange between users [24]. The political blogs network is a hyperlink-oriented network between US political blogs recorded by Adamic and Glance in 2005 [25]. The open flights network is extracted from Open flights.org. This network includes flights between airports in the world [26]. The Protein-Protein Interactions (PPI) network is a sub-network of human protein interaction network. Nodes represent proteins and edges represent interactions between proteins [8]. The Web-EPA (Environmental Protection Agency) network provides network data linked to www.epa.gov from a scientific network data warehouse called Network Repository, where nodes represent web pages and edges represent hyperlinks [27]. The Human Protein Vidal network is also a protein interaction network. Compared with the PPI network, the Vidal network is more sparse [28].
In order to simplify the operation, we carry out a series of preprocessing on the data set, including transforming the network into an undirected and weightless network, taking the maximum branch of the network, removing duplicate edges, self-edges and deleting isolated nodes in the network. The preprocessed network data structure information is shown in the following Table 3, in which the number of nodes, the number of edges and the average degree of the network are respectively listed.
Comparing Algorithms
We chose two kinds of benchmark algorithms for comparative analysis. The first type of benchmark algorithm is based on a centrality measure, directly selecting the first m most important key nodes as key node groups. In this paper, we have chosen four measures: Degree centrality (DC), K-kernel (KS), Betweenness centrality (BC) and Closeness centrality (CC) [29,30]. The second kind of benchmark algorithm is to select m key nodes that are not connected to each other as key node groups [31]. In this paper, a key node group identification algorithm based on point coloring theory is used. Firstly, the nodes are sorted by four measures: Degree, Kernel, Betweenness and Closeness. Then, the first m nodes in the largest independent set are selected as key node groups by using the point coloring theory, which correspond to the DCC, KSC, BCC and CCC algorithms, respectively.
The Experimental Results
In order to compare the performance of different methods in identifying key node groups, we first select m nodes as propagation sources according to a method, and then simulate the propagation process through single-point contact SIR and full-contact SIR models. When I-state nodes finally do not exist in the network, the propagation process ends, and the final number of R-state nodes is counted, which is the network range finally affected by the key node groups. The advantages and disadvantages of the key node group identification algorithm are determined by comparing the propagation range. At the same time, the experiment was repeated 500 times independently in order to ensure the reliability of the experimental results.
We introduce the relative proportion index of node group influence ∆ to measure the effect of the algorithm, where Ri represents the final number of R-state nodes after the SIR propagation simulation for the key node group selected by a certain method; RDC represents the number of R-state nodes finally obtained after SIR propagation simulation using the key node group selected by DC (Degree Centricity) (i.e., selecting the top M nodes with the largest degree). When ∆ > 0, this method is better than DC. the larger ∆, the better the effect of this method.
Finally, the influence range of the SIR simulation propagation is determined by a number of factors, including the implementation of the SIR model, the infection rate β, the number of nodes in the key node group, and the selection method of the key node group. In the network division of the CNE algorithm, in order to avoid the situation that the k-means clustering algorithm may fall into the local optimal situation, the aggregation hierarchy clustering algorithm is also adopted, and these two strategies are named CNE_KM and CNE_HC respectively. In order to undertake a comprehensive comparison, we carried out a series of cross experiments with fixed parameters.
First of all, we explored the change of the relative proportion index of node group influence ∆ with the infection rate β on the basis of different key node group identification algorithms. In the single-point contact SIR model, we set the infection rate β from 0.1 to 0.5 while making the number of nodes in the key node group 1%, 3% and 5% of the total number of nodes in the network dataset. The experimental results are shown in Figure 3. From the experimental results, we can find that in the single-point contact SIR model: (1) In the case of few key node groups (1%), when the infection rate β is very small, i.e., β = 0.1 as shown in the figure, the effects of CNE_HC and CNE_KM are not particularly ideal. With the increase of infection rate, the experimental results of CNE_HC and CNE_KM gradually improve and are better than other algorithms. (2) When the number of nodes in the key node group is 3% and 5%, the experimental results of CNE_HC and CNE_KM are better than other algorithms on the whole in terms of the impact on the whole network under the condition of different infection rates β. (3) With the increase of infection rate β, the difference in the impact of various key node group identification algorithms on the entire network will gradually decrease, and information such as disease information will be easily spread in the network. However, the experimental results of CNE_HC and CNE_KM still maintain good results and are superior to other methods.
At the same time, we studied the performance of different methods in the full-contact SIR model. The experimental results are shown in Figure 4. In the full-contact SIR model, every round of I-state nodes try to infect all its neighbor nodes, so the model has extremely strong information transmission capability. In order to facilitate our observation of the experimental results, we set the removal rate µ = 1. From the experimental results in Figure 4, we find some conclusions different from the single-point contact SIR model.
(1) In Email, Openflights, PPI networks, regardless of the number of nodes in the key node group is 1%, 3% or 5%, and regardless of the infection rate, CNE_HC and CNE_KM perform well and are superior to other algorithms on the whole. (2) There are obviously different rules from the other four datasets in the Web-EPA and Vidal datasets.
In Web-EPA and Vidal, when the infection rate β is very small, i.e., β = 0.1, the experimental results of CNE_HC and CNE_KM are not ideal. With the increase of infection rate, the experimental results of CNE_HC and CNE_KM gradually improve, and catch up with and surpass other algorithms in the later stage.
Next, we explore the relationship between the number of nodes m in key node groups and the relative proportion index of node group influence ∆ based on different key node group identification algorithms through experiments. We set the infection rate β = 0.2 in single-point contact SIR (removal rate µ = 0.1) and full-contact SIR (removal rate µ = 1) models, respectively, and set the number of nodes in the node group to be 1%, 1.5%, 2%, 2.5%, 3%, 3.5%, 4%, 4.5% and 5% of the total number of nodes. The experimental results are shown in Figure 5. CNE_HC and CNE_KM have excellent effects and are superior to other algorithms in most cases. With the increase of the number of nodes m, the effect on the whole network increases significantly. Next, we explore the relationship between the number of nodes m in key node groups and the relative proportion index of node group influence Δ based on different key node group identification algorithms through experiments. We set the infection rate = 0.2 in single-point contact SIR (removal rate = 0.1) and full-contact SIR (removal rate = 1) models, respectively, and set the number of nodes in the node group to be 1%, 1.5%, 2%, 2.5%, 3%, 3.5%, 4%, 4.5% and 5% of the total number of nodes. The experimental results are shown in Figure 5. CNE_HC and CNE_KM have excellent effects and are superior to other algorithms in most cases. With the increase of the number of nodes m, the effect on the whole network increases significantly. In order to try to explain the above experimental results, we calculated the geodetic distances between the nodes of key node groups in the network, and measured the differences between the distances by introducing the distance relative proportion index .
Email-Eu-Core Network-1% nodes Email-Eu-Core Network-3% nodes Email-Eu-Core Network-5% nodes Open Flights Network-1% nodes Considering various factors, the performance of CNE_HC and CNE_KM are still satisfactory. Finally, we conducted another experiment to analyze the performance of NE_HC and NE_KM in terms of infected network speed. Since the full-contact SIR model is very easy to transmit information and cannot distinguish the infection rate of different algorithms, we only carried out experiments on the single-point contact SIR model in this group of experiments. We set the infection rate = 0.2, divided the range that will ultimately affect the network (i.e., the number of nodes in the R-state) by the number of rounds that will eventually be needed to infect the entire network as the infection speed . At the same time, in order to compare the infection speed of each method, we define the speed relative proportion index , where vi represents the speed of a method infecting the network, represents the speed of DC (Degree Centricity) infecting the network. The experimental results are shown in Figure 6. In order to try to explain the above experimental results, we calculated the geodetic distances between the nodes of key node groups in the network, and measured the differences between the distances by introducing the distance relative proportion index K, where, d i represents the average geodesic distance between node i and all nodes in the network, and d DC represents the geodesic distance of DC (Degree Centricity) infecting the network.
Considering various factors, the performance of CNE_HC and CNE_KM are still satisfactory. Finally, we conducted another experiment to analyze the performance of NE_HC and NE_KM in terms of infected network speed. Since the full-contact SIR model is very easy to transmit information and cannot distinguish the infection rate of different algorithms, we only carried out experiments on the single-point contact SIR model in this group of experiments. We set the infection rate β = 0.2, divided the range that will ultimately affect the network (i.e., the number of nodes in the R-state) by the number of rounds that will eventually be needed to infect the entire network as the infection speed v. At the same time, in order to compare the infection speed of each method, we define the speed relative proportion index Φ, where v i represents the speed of a method infecting the network, v DC represents the speed of DC (Degree Centricity) infecting the network. The experimental results are shown in Figure 6. From the above results, we found that CNE_HC and CNE_KM in the Email, Polblogs, Openflights and PPI networks performed well in terms of the speed of infection network as a whole. In the Web-EPA and Vidal networks, although the performance is not the best, it also reaches a medium level. At the same time, it can be seen that the point coloring algorithm (DCC) based on degree centrality has the highest propagation speed. This experimental result inspires us that in sparse networks, we may obtain better results in infection speed by using the most basic degree centrality.
Conclusions
This paper proposed a network representation learning-based solution for the influence maximization problem (IMP). The solution was designed based on the innate understanding that each selected seed node should be influential enough by itself, and all the seed nodes should be more dispersed in the network topology. So it extended the CBOW algorithm from NLP by using node centrality as weights to guide the training and then clusters the network nodes into subgroups in learned vector space and selects the 'center' of subgroups as seed set for the IMP solution. Since IMP From the above results, we found that CNE_HC and CNE_KM in the Email, Polblogs, Openflights and PPI networks performed well in terms of the speed of infection network as a whole. In the Web-EPA and Vidal networks, although the performance is not the best, it also reaches a medium level. At the same time, it can be seen that the point coloring algorithm (DCC) based on degree centrality has the highest propagation speed. This experimental result inspires us that in sparse networks, we may obtain better results in infection speed by using the most basic degree centrality.
Conclusions
This paper proposed a network representation learning-based solution for the influence maximization problem (IMP). The solution was designed based on the innate understanding that each selected seed node should be influential enough by itself, and all the seed nodes should be more dispersed in the network topology. So it extended the CBOW algorithm from NLP by using node centrality as weights to guide the training and then clusters the network nodes into subgroups in learned vector space and selects the 'center' of subgroups as seed set for the IMP solution. Since IMP is an NP-hard problem, the proposed solution was compared with seven baseline IMP solutions on six commonly used network datasets. Experiment results show that the solution outperforms the baseline algorithm in transmission speed and network coverage in information propagation simulation.
The IMP problem has high application value, so research on the existing IMP solution's real-world applications will be vital. For real applications, the research on multi-layer networks and temporal networks IMP is critical. The proposed approach aimed to recognize seed sets in simple networks so that we will put more research effort into the IMP solution for multi-layer and temporal networks in the future. | 9,598.4 | 2020-09-10T00:00:00.000 | [
"Computer Science"
] |
The de Novo Reference Genome and Transcriptome Assemblies of the Wild Tomato Species Solanum chilense Highlights Birth and Death of NLR Genes Between Tomato Species
Wild tomato species, like Solanum chilense, are important germplasm resources for enhanced biotic and abiotic stress resistance in tomato breeding. S. chilense also serves as a model to study adaptation of plants to drought and the evolution of seed banks. The absence of a well-annotated reference genome in this compulsory outcrossing, very diverse species limits in-depth studies on the genes involved. We generated ∼134 Gb of DNA and 157 Gb of RNA sequence data for S chilense, which yielded a draft genome with an estimated length of 914 Mb, encoding 25,885 high-confidence predicted gene models, which show homology to known protein-coding genes of other tomato species. Approximately 71% of these gene models are supported by RNA-seq data derived from leaf tissue samples. Benchmarking with Universal Single-Copy Orthologs (BUSCO) analysis of predicted gene models retrieved 93.3% of BUSCO genes. To further verify the genome annotation completeness and accuracy, we manually inspected the NLR resistance gene family and assessed its assembly quality. We find subfamilies of NLRs unique to S. chilense. Synteny analysis suggests significant degree of the gene order conservation between the S. chilense, S. lycopersicum and S. pennellii genomes. We generated the first genome and transcriptome sequence assemblies for the wild tomato species Solanum chilense and demonstrated their value in comparative genomics analyses. These data are an important resource for studies on adaptation to biotic and abiotic stress in Solanaceae, on evolution of self-incompatibility and for tomato breeding.
S. chilense occurs on the southern edge of the wild tomato species range, in southern Peru and northern Chile. It belongs to the section Peruvianum, which contains four closely related wild tomato species, of which S. chilense forms a monophyletic subclade (Pease et al. 2016). S. chilense split from S. peruvianum about 1 mya (Arunyawat et al. 2007;Städler et al. 2008). Since then, the species has migrated southward and colonized diverse arid habitats both in mountainous and coastal terrain bordering the Atacama desert characterized by low temperatures or extreme aridity, respectively (Böndel et al. 2015) (Figure 1).
S. chilense has been used in studies on drought (Xia et al. 2010), salt (Zhou et al. 2011;Martínez et al. 2012) and cold tolerance (Nosenko et al. 2016), pathogen resistance and resistance gene evolution (Stam et al. 2017(Stam et al. , 2019, as well as adaptation to extreme environments (Fischer et al. 2013;Böndel et al. 2018). As an outcrossing species it has been used to understand self-incompatibility in the tomato clade (Igic et al. 2007). The species is characterized by high levels of genetic diversity (Arunyawat et al. 2007;Städler et al. 2008;Böndel et al. 2015) probably due to existence of seed banking (Tellier et al. 2011).
S. chilense is also being used as a resource in tomato breeding; genes from S. chilense have been successfully introgressed to enhance resistance to the fungal pathogen Verticilium dahliae (Tabaeizadeh et al. 1999) and to the Tomato Mosaic Virus Y (Verlaan et al. 2013).
To corroborate the quality of our reference genome and to demonstrate its value for future genomic studies, we compared the NLR family in S. chilense with those in S. lycopersicum and S. pennellii. Canonical pathogen resistance genes in plants belong to the NLR family (Nod-like receptor or Nucleotide binding site, leucine rich repeat containing receptor) (Jones et al. 2016). NLRs are modular and contain an N-terminal domain, which can be a Toll-Interleukin Receptor (TIR) or a Coiled Coil (CC) domain, followed by a Nucleotide Binding Site (NBS) domain and several Leucine Rich Repeats (LRR). Complete NLRs have all three domains, whereas partial NLRs lack one or the other. Complete as well as some partial NLRs are involved in signaling of the plant immune system (Baggs et al. 2017). TIR-and CC-domaincontaining NLRs are called TNL or CNL, respectively; CNL are often grouped in subclasses.
Comparative studies in S. lycopersicum and some wild relatives revealed interspecific differences in NLRs (Andolfo et al. 2014). For example, S. lycopersicum and closely related S. pimpinellifolium, contain respectively 326 and 355 NLRs, while S. pennellii contains only 216 putative NLRs (Stam et al. 2016). These differences in the NLR repertoire are thought to be the result of a birth and death process (Michelmore and Meyers 1998) and could possibly be explained by differences in pathogen pressure.
METHODS AND MATERIALS
De novo genome sequence assembly for S. chilense LA3111 Seeds were obtained through the tomato genome resource center (TGRC, UC Davis). DNA was extracted from leaves of one adult plant from accession LA3111 (plant number 3111_t13) using the Qiagen DNAeasy kit following the instructions of the supplier. The sequencing was conducted at Eurofins Genomics (Ebersberg, Germany) using standard library preparation protocols for four different libraries. Two standard paired-end libraries were produced with insert sizes of 300 bp and 500-550 bp and two libraries were prepared for mate pair sequencing, with insert sizes of 8 kb and 20 kb. The 500 bp fragment library was sequenced using a MiSeq protocol, and overlapping pairedend reads (55%) were stitched to longer single reads using the software PEAR v0.9.8 . Remaining unstitched clusters (45%) were retained as paired-end reads. The other three libraries were sequenced on Illumina HiSeq2500 sequencers at Eurofins Genomics. Construction of the mate-pair-like library was done at Eurofins Genomics using their proprietary protocol. Other libraries were constructed using commercially available kits (NEBNext Ultra DNA Library Prep Kit for Illumina, article number E7370) according to the manufacturer's instructions. In brief, 1 mg of DNA was fragmented using a Covaris Instrument (Covaris Inc., Woburn, MA) according to manufacturer's instructions. End-repair, A-tailing and ligation of indexed Illumina Adapter, size selection and amplification was performed accordingly. The resulting fragments were cleaned up and quantified. Libraries were loaded on the cBot (Illumina, San Diego, CA) and cluster generation was performed using manufacturer's instructions. Sequencing of paired-end reads of 125 bp read length was performed on a HiSeq2500 machine (HiSeq Control Software 2.2.38) using HiSeq Flow Cell v4 and TruSeq SBS Kit v4. Raw data were processed using RTA v.1.18.61. CASAVA v.1.8.4 was used to generate FASTQ-files. In total we generated 134 Gb of raw data (Table S1), which would correspond to . 130x coverage assuming a 950 Mb genome size, as was estimated by Eurofins Genomics using k-mer analysis using their proprietary protocol. In addition we used GenomeScope (Vurture et al. 2017) on our paired-end illumina HiSeq read data (recommended settings, k-mer size 27). We used the Celera assembler (CAv8.3; https://sourceforge.net/projects/wgs-assembler/files/wgs-assembler/wgs-8.3) and stitched and unassembled MiSeq read data to generate contigs. The fragment correction module and the bogart unitigger of the Celera assembler were applied with a graph and merge error rate of 5%. Minimal overlap length, overlap and merge error rates were set to 50 bp and 6% each, respectively. The resulting contigs were linked to scaffolds by SSPACE v2 (Boetzer et al. 2011) using all four libraries available for la3111_t13. Scaffolds were further processed by five iterations of GapFiller v2.1.1 and corrected by Pilon v1.21 in full-correction mode (Boetzer and Pirovano 2012;Walker et al. 2014).
De novo assembly of S. chilense leaf transcriptome Twenty four Illumina paired-end read RNA-Seq libraries were generated for 12 S. chilense plants from populations LA3111 and LA2750. Replicates were obtained by propagating plants vegetatively. Total RNA was extracted from leaf tissue samples from multiple mature plants under normal and stress (chilling, 6h at 4°) conditions using the RNeasy Plant Mini Kit (Qiagen GmbH, Hilden, Germany) and purified from DNA using the TURBO DNA-free Kit (Ambion, Darmstadt, Germany). RNA concentration and integrity were assessed using a Bioanalyzer 2100 (Agilent Technologies, Waldbroon, Germany). The preparation of random primed cDNA libraries has been performed by GATC Biotech AG (Konstanz, Germany) according to their internal and proprietary SOP. Sequencing on a HiSeq 2500 in paired end mode with a read length of 2 · 100 bases was also conducted by GATC Biotech AG.
RNA-Seq library contamination with non-target species and organellar RNA was assessed using FastQ Screen v0.5.2 (http:// www.bioinformatics.babraham.ac.uk/projects/fastq_screen/) with 100000 read sub-sample and a database consisting of UniVec database and reference genome sequences of Homo sapiens, Escherichia coli, Nicotiana tabacum (NCBI) and Fusarium graminearum (ftp:// ftpmips.helmholtz-muenchen.de/fungi/Fusarium/F_graminearum_ PH1_v32). Quality of all RNA-Seq libraries were assessed using FastQC v0.11.2 (Andrews 2010). Adapters, reads with average quality below 30 and low quality (, 30) bases at the read termini were trimmed using Trimmomatic v0.35 (Bolger et al. 2014a). Only paired reads with minimum after-processing length of 70 bp were retained and used for assembling transcriptomes. Data for each population (six individuals and 12 RNA_seq libraries per population) were assembled de novo using Trinity v2.3.2 (Grabherr et al. 2011), SOAPdenovo-Trans v1.0.4 (Xie et al. 2014) and Oases-Velvet (v0.2.08/ v1.2.08) (Schulz et al. 2012); the redundancy acquired from pooling the three assemblies was reduced using the EvidentialGene pipeline (Gilbert 2013); SOAPdenovo-Trans assembly was conducted using k-mer sizes from 29 to 79 with a step size of 10. Oases-Velvet assembler was run with k-mer sizes from 25 to 73 with a step size of 12. Trinity assembly was conducted using the k-mer size of 25, the default and the only size supported by this assembler. Oases and SOAP assemblies obtained with each k-mer size were pulled together and clustered using CD-HIT-EST v4.6.5 and identity parameter set at 100% (Li and Godzik 2006). The contigs output by CD-HIT-EST and contigs resulting form the Trinity assembly were combined together and clustered using the EvidentialGene pipeline. Because FastQ Screen analyses identified organellar (chloroplast and mitochondrial) RNA as the major source of the RNA-Seq library contamination (up to 15%; Figure S1), contigs resulting from the assembly of organellar sequences were identified using BLAST similarity searches (ncbi-blast v2.6.0+; e-value 1e-70) against the chloroplast-and mitochondria-encoded proteins of three Solanaceae species: S. lycopersicum, S. pennellii and N. tabacum, and were excluded from the resulting de novo transcriptome assemblies.
Gene model prediction
We applied a previously described consensus approach (Wang et al. 2014) to derive gene structures from the S. chilense draft genome. Briefly, de novo gene finders Augustus v3.2.3 (Stanke et al. 2006), Snap v1.0beta (Korf 2004) and GeneID v1.4.4 (Parra et al. 2000) were trained on a set of high confidence models that were derived from the LA3111 and LA2750 transcriptome assemblies. Existing matrices for eudicots and S. lycopersicum were used for predictions with Fgenesh v1.6 (Salamov and Solovyev 2000) and GlimmerHMM v3.0.1 (Majoros et al. 2004), respectively. Predictions were weighted by a decision tree using the JIGSAW software v3.2.10 (Allen and Salzberg 2005). Spliced alignments of known proteins and S. chilense transcripts of this study were generated by the GenomeThreader tool v1.6.6 (Gremme et al. 2005). We used current proteome releases (status of August 2016) of Arabidopsis thaliana, Medicago truncatula, Ricinus communis, S. lycopersicum, Glycine max, Nicotiana benthiamiana, Cucumis sativa and Vitis vinifera. Spliced alignments required a minimum alignment coverage of 50% and a maximum intron size of 50 kb under the Arabidopsis splice site model. Next, de novo and homology predictions were merged to top-scoring consensus models by their matches to a custom reference blastp database comprising Arabidopsis, Medicago, S. lycopersicum and S. pennellii proteins. In a last step, we annotated the top-scoring models using the AHRD ("A human readable description")-pipeline (Wang et al. 2014) and InterProScan v5.21 (Zdobnov and Apweiler 2001) to identify and remove gene models containing transposon signatures. The resulting final models were then classified into high scoring models if they showed at least 90% of alignment consistency for both query (S. chilense) and subject (custom plant database gene as described above), an evalue of 1e-30 or better and at least 60% of the bitscore of the blastp comparison.
To obtain an additional RNA-seq support for the predicted gene models, raw RNA-seq data were processed (adapter and quality trimming) using Trimmomatic v0.35 (Bolger et al. 2014a) and aligned to the S. chilense genome sequence assembly using STAR v2.5 (Dobin et al. 2013). Read pairs aligned to exonic regions of predicted gene models were summarized per gene using featureCounts (Liao et al. 2014). To account for differences in library sizes, the resulting count matrix was normalized using DeSeq2 (Love et al. 2014). Genes represented by at least ten normalized counts (i.e., read pairs) in at least three samples were considered expressed.
Functional gene annotation and assignment to the GO term categories were performed using Blast2GO v 4.1 (Conesa and Götz 2008) based on the results of InterProScan v5.21 (Zdobnov and Apweiler 2001) and BLAST (ncbi-blast v2.6.0+) (Altschul et al. 1997) similarity searches against the NCBI non-redundant sequence database. KEGG pathway orthology assignment of protein-coding genes was conducted using KAAS (Moriya et al. 2007). The completeness of the S. chilense genome and transcriptome sequence assemblies and annotation was assessed using Benchmarking with Universal Single-Copy Orthologs (BUSCO v3) analysis (Simão et al. 2015). As an additional criterion for assessing genome assembly and annotation, we evaluated the composition and quality of the NLR gene model prediction in S. chilense.
Loci encoding putative NLR genes were identified using NLRParser (Steuernagel et al. 2015) with cut-off thresholds as described before (Stam et al. 2016). We manually inspected all regions with NLR motifs and updated the annotated open reading frames where this was required. The improved annotation was based on presence of NLR motifs and expression evidence (from the RNA-seq data). For example, in some cases the automated annotations contained introns that led to exclusion of NLR domains or missed adjacent annotated NLR domains, whereas our RNA-Seq confirmed that these domains were transcribed. In these cases we either removed annotated introns or selected alternative predicted ORFs to contain the largest number of NLR domains, without introducing frame shifts. Only 15 NLR genes required manual curation based on the RNA-Seq data aligned to the reference genome. In ten instances, frame shifts made it impossible to enhance the gene model. For these genes, the computationally predicted CDS were retained. The remaining 211 predicted NLR gene models showed to be well resolved and did not require any correction. Functional clades were assigned based on protein sequences of the NBS domain. BLASTp searches (cutoff e-value 10 230 ) were used to match the S. chilense NLRs with the nearest previously assigned NLRs (Andolfo et al. 2014). For example, the clade of the best hit in other tomato species was assigned to the S. chilense gene. In the majority of cases, this gave unequivocal results. In one instance, members of our new clade matched two previously defined clades equally well; this clade thus has double naming (CNL1/CNL9). The NLRs in two identified clusters did not match any NLRs that had been clustered previously. In these cases, new cluster numbers were assigned (CNL20, CNL21).
To assess synteny between the S. chilense, S. lycopersicum and S. pennellii genomes, orthologous pairs of protein-coding genes were identified using reciprocal BLAST searches with an e-value threshold of 10 230 and maximum target sequence number 50. For S. lycopersicum and S. pennellii, the longest splice variant for each gene was used as a BLAST input. Duplicated BLAST matches were filtered out. Only gene pairs confirmed by bidirectional BLAST searches were retained and used as an input for synteny analyses. A spatial distribution of resulting orthologous gene pairs was analyzed and gene blocks conserved between genomes (syntenic) were identified using iADHoRe v3.0.0.1 (hybrid mode with minimum syntenic block size = 3; (Proost et al. 2012)). For tandem arrays of genes, a single representative was retained in syntenic blocks. To compare, we also conducted synteny analyses using DAGchainer (r02-06-2008; Haas et al. 2004) with the following parameters: a constant match score of value 12 (-Z 12), gap penalty equal to 1 (-g 1), minimum chain length equal five colinear genes (-A 5) and allowing neighboring genes within a single chain to be no more than ten genes apart (-D 10).
Phylogenetic analyses
We mapped our sequence data as well as data from all nine publicly available S. peruvianum and presumed S. chilense data ( We extracted two types of loci. First, we extracted the sequence at six CT loci (CT066, CT093, CT166, CT179, CT198, CT268) for all 12 accessions. These are single-copy cDNA markers developed and mapped in Tanksley et al. (1992), which have previously been used to investigate the evolutionary relationships between wild tomato species (e.g., Arunyawat et al. 2007;Rose et al. 2011;Böndel et al. 2015). To account for heterozygosity, two alleles were constructed randomly per individual. A concatenated alignment was prepared and manually checked. We added to this alignment 53 sequences obtained by Sanger sequencing in previous work on S. chilense and S. peruvianum (Städler et al. 2008). These sequences originate from S. chilense or S. peruvianum accessions as identified by the TGRC (UC Davis, USA) according to the taxonomic key in Peralta et al. (Peralta et al. 2008). S. ochranthum (accession LA2682) was used as an outgroup. The phylogentic reconstruction (Figure 2A) was obtained by the Maximum Likelihood method (ML; with GTR+Gamma+I model and 1000 bootstrap replicates) as implemented in RaxML (Stamatakis 2014).
Second, we reconstructed the sequences for the coding regions of the chloroplast for each of the 12 samples listed above and our LA3111 sample. These sequences were aligned and a phylogenetic tree was constructed using PhyML (Guindon et al. 2010) (ML, GTR, extracted. Single-gene alignments were concatenated; the resulting super alignment was used as in input for RaxML to construct the ML tree (1000 bootstrap replicates). The branch length is shown as expected number of substitutions per site and bootstrap values are reported on each tree node. S. ochranthum was used as an outgroup. The sequence IDs containing chil and peru represent Sanger sequences from S. chilense and S. peruvianum individuals, respectively, followed by the accession/ individual number. The sequences with IDs containing SRR-and ERR-numbers followed by the accession number were extracted from previously generated whole genome data. B) Phylogeny constructed based on chloroplast SNP data extracted from S. chilense LA3111 (in bold and marked with gray rectangle) and previously sequenced S. peruvianum whole genome sequence data. Chloroplast sequences were aligned to the S. pennellii reference genome. The tree was built using resulting alignments and PhyML (GTR, NNI, BioNJ, 1000 bootstrap replicates). The branch length is shown as expected number of substitutions per site and bootstrap values are reported on each tree node. a Sequences of individuals with IDs containing SRR1572692, SRR1572693, SRR1572694, SRR1572695 and SRR1572696 were obtained from Lin et al. (2014). b Sequences with IDs containing ERR418084, ERR418094, ERR418097 and ERR418098 originate from 100 Tomato Genome Sequencing Consortium (2014). Individual SRR1572696 was reported as S. chilense in the main text of the paper (ref) and as S. peruvianum in the supplementary, which contain all original data. The original classification of the sequences with IDs ERR418097 and ERR418098 as S. chilense has been later withdrawn from the CGN database.
RESULTS AND DISCUSSION
First S. chilense genome sequence assembly Species within the Peruvianum group have diverged relatively recently and exhibit high intraspecific genetic and phenotypic diversity (Pease et al. 2016). Hence, species assignment of individuals from this complex can be ambiguous (Zuriaga et al. 2008). To confirm that our newly sequenced plant is indeed S. chilense, we performed phylogenetic comparisons of our sequenced individual and publicly available sequence data from S. chilense and S. peruvianum. We find that all robustly assigned S. chilense accessions (Städler et al. 2008) and our LA3111 individual cluster together into a well-supported monophyletic group (Figure 2A Additionally, we reconstructed the chloroplast phylogeny of the members of the S. peruvianum clade. All previously sequenced samples formed a polyphyletic group, which is a topology known for the species S. peruvianum, whereas our S. chilense sample forms a separated branch ( Figure 2B). Thus, phylogenetic analyses of both nuclear-and plastidencoded genes confirm that data presented in this study are the first instance of a S. chilense genome sequence assembly.
S. chilense LA3111 genome and transcriptome statistics
The final contig assembly comprised 150,750 contigs ranging from 1 to 162 kb totalling 717.7 Mb of assembled genome sequence with a N50 of 9,755 bp. After further processing, the 81,307 final scaffolds span a total size of 914 Mb with a N50 of 70.6 kb (Table 1). Of them, 111 scaffolds of total length 730 kb contain exclusively organellar genes and potentially represent the S. chilense chloroplast and mitochondrial genomes (Table S7). Our total genome size is very similar to the size calculation using k-mer analysis (950 Mb) and a bit larger than the estimates obtained by GenomeScope (Vurture et al. 2017) (721 Mb, Figure S2). The genomes for S. lycopersicum (Tomato-Genome-Consortium 2012) and S. pennellii (Bolger et al. 2014b) and are estimated to be 900 and 940 Mb, respectively. GenomeScope has been shown to underestimate the size for very heterozygous species like S. chilense (e.g., for oyster, which is also highly heterozygous, flow cytometry, k-mer analyses and GenomeScope analyses esitmated 637, 545 and 471 Mb respectively (GenomeScope manual; Vurture et al. 2017). Therefore, we expect the genome size of S. chilense to be in the range of 900-950 Mb.
The resulting transcriptome assemblies contain 41,666 and 35,470 transcripts for LA3111 and LA2750, respectively (Table 2). Despite the fact that both S. chilense transcriptome assemblies were derived from a single tissue and only two conditions (normal and cold-stress), they are 93.3% (LA3111) and 94.2% (LA2750) complete according to the BUSCO analyses (Table S2). Our data included RNA-Seq libraries for 24 S. chilense individuals. High variation of gene expression withinand between populations in the wild plant species might have contributed to the relative richness of the resulting transcriptome assemblies.
We predicted 25,885 high-confidence (hc) gene loci that show good coverage and high homology to known proteins of other tomato species. Besides their support by homology, approximately 71% (18,290) of the hc genes are additionally supported by RNA-seq data derived from leaf tissue samples. Complementary to the set of hc models, we report the presence of 41,481 low confidence (lc) loci to maximize gene content information. Functionality for some of the lc models (6,569) is suggested by transcriptome evidence from the leaf RNA-seq data.
Completeness and gene model validation
The completeness of the assembled genome was assessed using BUSCO (Simão et al. 2015) and was at 91.8%. This number is lower than the scores found for the previously annotated S. lycopersicum and S. pennellii genomes (Table S3), which is an expected difference between genome assemblies generated from the highly heterozygous individuals of self-incompatible species and inbred individuals of selfing species.
Synteny analyses using both iADHORE and DAGchainer showed conserved gene order between the genomes of the three tomato species: S. chilense (this study), S. lycopersicum (NCBI genome annotation release 102, ITAG2.4) and S. pennellii (NCBI genome annotation release 100, v2). We found that our S. chilense gene models (hc and lc) show homology to respectively 24,651 S. lycopersicum and 25,695 S. pennellii genes. By different estimates, from 2,364 to 3,216 (iADHoRe and DAGchainer, respectively) syntenic blocks containing total from 12,984 to 19,090 unique gene pairs were formed between the S. chilense and S. pennellii genomes (Table S4). Comparison with the S. lycopersicum genome output similar results: from 2,535 to 3,225 syntenic blocks containing from 14,013 to 19,114 gene pairs, respectively (Table S5). To compare, 977 syntenic gene blocks were detected between S. lycopersicum and S. pennellii genomes using the same i-ADHoRe parameters consisting of 18,064 and 17,904 gene models, respectively (Table S6). According to the results of the DAGchainer analysis, which has a higher block selection stringency relative to i-ADHoRe, syntenic blocks between S. chilense and both S. pennellii and S. lycopersicum contain at average 5.9 gene pairs; over 69% S. chilense scaffolds are represented by a single syntenic block containing at average 8.5 genes (maximum 136 genes; for both comparisons). Results of these analyses show preservation of positional association between genes among the three Solanum genomes. However, relatively high n■ fragmentation of the S. chilense genome assembly does not allow us to assess large chromosomal re-arrangements in this species relative to S. pennellii and S. lycopersicum.
NLR annotation and comparison
In total we found 236 putative NLRs, of which 139 are CNLs and 35 TNLs. Sixty two NLRs cannot be assigned to either class. Most CDS were supported by all three measures used for the annotation. The total number of NLRs identified in S. chilense the S. chilense genome is lower than in cultivated tomato (355) and more similar to S. pennellii (216), (Stam et al. 2016). The syntenic blocks identified between the S. chilense and the S. lycopersicum and S. pennellii genomes include 69 and 50 NLR genes, respectively, and show that NLRs are distributed across all 12 chromosomes (Supplementary Material). Except for several short tandems of identical or nearly identical gene copies, NLRs do not tend to form any positional clusters in tomato genomes. Only 30% of Figure 3 Maximum Likelihood (ML) phylogenetic tree of the NLR genes identified in S. chilense. The tree was made as described in Stam et al. 2016. Clades with high (.80%) bootstrap values are collapsed. Most previously described clades can be identified and are indicated as such. The TNL family is highlighted in yellow. Several previously identified NLR genes from different species are included for comparison and Apaf1.1 and Ced4 are used as an outgroup, similar as in Andolfo et al. (2014) and Stam et al. (2016). A list of these genes and their species of origin can be found in Table S8. Clades marked with an asterisk are NRC-dependent. NLR with orthologs (based on reciprocal best blast hits) in S. pennellii are in bold. The branch length is shown as expected number of substitutions per site. Clades CNL20 and CNL21 are new for S. chilense.
S. chilense NLRs belong to syntenic gene blocks (compared to S. lycopersicum and S. pennellii) showing the fast evolution and genomic organization of this gene family at the phylogenetic time scale (over millions of years).
To further confirm the relative completeness of the NLR set in S. chilense, we reconstructed a phylogeny for the gene family based on the NBS protein sequences of the NLRs. All major NLR clades found in S. lycopersium and S. pennellii are present in the S. chilense genome (Figure 3). There are some small but interesting differences with the other tomato species. The CNL-4 and CNL-15 clades contained four or five members in S. lycopersicum, yet in S. chilense each had only one member. In addition, we identified two new clades: CNL20 and CNL21. A direct comparison shows that some clades have more members in S. pennellii, while others have more members in S. chilense ( Figure S3). Similar differences can be seen between S. pennellii and S. lycopersicum (Stam et al. 2016) Using the definitions of Michelmore and Meyers (1998), our data suggest the birth and death of NLR genes between tomato species.
CONCLUSIONS
We present the first draft genome sequence assembly and de novo transcriptome assemblies of the wild tomato species S. chilense. Using several complementary methods, including comparative analyses for a large and complex gene family such as the NLRfamily, we show that quality of this genome assembly and annotation satisfy requirements for a reference genome for comparative genomics studies.
ACKNOWLEDGMENTS
RS was supported by the Alexander von Humboldt foundation. S. chilense genome sequencing was funded by DFG grant TE 809/7-1 to AT. Generating and sequencing of the S. chilense RNA-Seq data were supported by the DFG grant STE 325/15 to WS. We thank the TGRC at UC Davis (USA) for providing the plant material. | 6,406.4 | 2019-04-26T00:00:00.000 | [
"Biology"
] |
Biomass Energy : An Overview of Biomass Sources , Energy Potential , and Management in Southeast Asian Countries
Potential depletion of fossil fuel and climate change have globally accelerated the demand in renewable and alternative energy. Most of the Southeast Asian countries have an abundance of biomass sources for the energy sector due to their agriculture-based economy and enormous forest resources. Therefore, the study aimed at highlighting an overview of biomass energy in the Southeast Asia countries to convey the environmental and economic benefits from the available biomass sources in the region. In order to achieve the aim, the study synthesized and evaluated the biomass sources, energy potential, utilization, and management in the region, based on the published research papers, review papers, and country reports. It was found that the major biomass sources in this region were fuelwood, wood residues, rice husk, rice straw, sugarcane residues, oil palm residues, and coconut residues. The total annual quantity of the biomass potential from agriculture and forest sector in the region was estimated at more than 500 million tons per year and equal to over 8000 million gigajoules of total energy potential. In order to implement the sustainable utilization of biomass sources, the study specified the barriers and challenges of biomass utilization in these countries and proposed a sustainable approach of biomass energy, by comparing the way of traditional biomass utilization.
Introduction
Booming economies have greatly accelerated energy consumption in the Southeast Asian countries.The energy consumption is projected to grow 2.6 times during 2005-2030 [1] and the energy demand will probably rise by almost two-thirds in 2040, representing one-tenth of the rise in global demand [2].Meanwhile, the energy-related environmental pollutions caused vastly by greenhouse gas emissions from the energy sector will rise regionally and globally, as well.Due to the impact of climate change, the Southeast Asian countries, especially Indonesia, Philippines, Thailand, and Vietnam, need to begin rapidly investing in renewable forms of electricity supply [3,4].
Biomass energy is by far the largest renewable energy sources, representing 10.4% of the world's total primary energy supply or 77.4% of global renewable energy supply [5].Asia is a key supplier of biomass feedstock to markets such as Europe or the United States but within the region, new opportunities and investments in biomass are emerging, particularly in Southeast Asia [6].Southeast Asia, with its abundant bioenergy resources, holds a strategic position in the global biomass energy atlas [7].It is also a big producer of agricultural and wood products, and according to conservative estimates, the amount of biomass residues generated from sugar, rice, and palm oil mills is more than 200-230 million tons per year, which corresponds to cogeneration potential of 16-19 gigawatts (GW) [7].
Nowadays, Southeast Asia is fast becoming an attractive market for developing biomass as an energy source [6] and biomass energy could provide 26% of total primary energy supply, equal to 87% of the renewable energy supply [5].Many Southeast Asian countries are among the top producers of agricultural commodities such as rice, sugar, cane, palm oil, coconut, and rubber, and the most promising residues are rice husk, sugarcane bagasse, oil palm residue, and wood residues [5].
The average annual energy consumption in the Southeast Asian countries is estimated at approximately 3.9% and the average carbon emission has been increased by over 5% due to the fast economic growth in the region [8].Bakhtyar et al. [8] state that increasing purchasing power parity leads to an increase in per capita electricity consumption, hence increasing per capita carbon dioxide (CO 2 ) emission.Figure 1 shows a relationship between per capita electricity consumption, purchasing power parity, and CO 2 emission.Although carbon dioxide is the largest source of global greenhouse gas emissions that come greatly from energy sector, it is not the case for some of the Southeast Asian countries, where forestry and agriculture are the major sources of emissions [9].Some of the Southeast Asian countries such as Singapore, Brunei Darussalam, Malaysia, and Thailand have already accessed 100% of electricity (Figure 2).Meanwhile, other countries are expected to reach 100% access to electricity by 2030.Biomass energy is by far the largest renewable energy sources, representing 10.4% of the world's total primary energy supply or 77.4% of global renewable energy supply [5].Asia is a key supplier of biomass feedstock to markets such as Europe or the United States but within the region, new opportunities and investments in biomass are emerging, particularly in Southeast Asia [6].Southeast Asia, with its abundant bioenergy resources, holds a strategic position in the global biomass energy atlas [7].It is also a big producer of agricultural and wood products, and according to conservative estimates, the amount of biomass residues generated from sugar, rice, and palm oil mills is more than 200-230 million tons per year, which corresponds to cogeneration potential of 16-19 gigawatts (GW) [7].
Nowadays, Southeast Asia is fast becoming an attractive market for developing biomass as an energy source [6] and biomass energy could provide 26% of total primary energy supply, equal to 87% of the renewable energy supply [5].Many Southeast Asian countries are among the top producers of agricultural commodities such as rice, sugar, cane, palm oil, coconut, and rubber, and the most promising residues are rice husk, sugarcane bagasse, oil palm residue, and wood residues [5].
The average annual energy consumption in the Southeast Asian countries is estimated at approximately 3.9% and the average carbon emission has been increased by over 5% due to the fast economic growth in the region [8].Bakhtyar et al. [8] state that increasing purchasing power parity leads to an increase in per capita electricity consumption, hence increasing per capita carbon dioxide (CO2) emission.Figure 1 shows a relationship between per capita electricity consumption, purchasing power parity, and CO2 emission.Although carbon dioxide is the largest source of global greenhouse gas emissions that come greatly from energy sector, it is not the case for some of the Southeast Asian countries, where forestry and agriculture are the major sources of emissions [9].Some of the Southeast Asian countries such as Singapore, Brunei Darussalam, Malaysia, and Thailand have already accessed 100% of electricity (Figure 2).Meanwhile, other countries are expected to reach 100% access to electricity by 2030. Figure 3 shows the share of renewable energy to the total electricity generation.The total electricity generation from the renewable and non-renewable generation amounted to approximately 856 Terawatt-hours (TWh).Out of this, 20% came from renewable energy, accounting approximately for hydropower (74.1%), biofuels (12.6%), geothermal (11.5%), solar phtovoltaic (PV) (1.2%), and wind (0.6%).The potential share of renewable energy in total primary energy supply in the Southeast Asian countries is presented in Figure 4. On a country level, the renewable energy share in total primary energy supply seems to increase significantly, especially in the countries that completely phase out traditional uses of bioenergy, such as Cambodia, Lao PDR, Indonesia, and Myanmar [9].In Lao PDR, the potential share of biomass energy in total primary energy supply is likely to reach over 50% of the total primary energy supply by 2025. Figure 3 shows the share of renewable energy to the total electricity generation.The total electricity generation from the renewable and non-renewable generation amounted to approximately 856 Terawatt-hours (TWh).Out of this, 20% came from renewable energy, accounting approximately for hydropower (74.1%), biofuels (12.6%), geothermal (11.5%), solar phtovoltaic (PV) (1.2%), and wind (0.6%). Figure 3 shows the share of renewable energy to the total electricity generation.The total electricity generation from the renewable and non-renewable generation amounted to approximately 856 Terawatt-hours (TWh).Out of this, 20% came from renewable energy, accounting approximately for hydropower (74.1%), biofuels (12.6%), geothermal (11.5%), solar phtovoltaic (PV) (1.2%), and wind (0.6%).The potential share of renewable energy in total primary energy supply in the Southeast Asian countries is presented in Figure 4. On a country level, the renewable energy share in total primary energy supply seems to increase significantly, especially in the countries that completely phase out traditional uses of bioenergy, such as Cambodia, Lao PDR, Indonesia, and Myanmar [9].In Lao PDR, the potential share of biomass energy in total primary energy supply is likely to reach over 50% of the total primary energy supply by 2025.The potential share of renewable energy in total primary energy supply in the Southeast Asian countries is presented in Figure 4. On a country level, the renewable energy share in total primary energy supply seems to increase significantly, especially in the countries that completely phase out traditional uses of bioenergy, such as Cambodia, Lao PDR, Indonesia, and Myanmar [9].In Lao PDR, the potential share of biomass energy in total primary energy supply is likely to reach over 50% of the total primary energy supply by 2025.
Several studies have focused on the renewable energy, biomass energy, renewable energy sources, energy utilization, policy, and emission factors in Asia [2,8,9,[15][16][17][18][19] but mostly in specific countries such as Indonesia, Malaysia, Cambodia, Lao PDR, Brunei Darussalam, Philippines, etc. [20][21][22][23][24]. Therefore, the study highlighted the biomass sources, energy potential, and management in Southeast Asian countries to ensure the biomass sources and their energy utilization be applicable to the policy makers, researchers, and non-government organizations for outlooking biomass energy as an important portion of the future renewable energy sector in the region.
Methodology
Since most Southeast Asian countries are developing countries, the country-specific data related to biomass sources, energy potential, and utilization in some countries including Myanmar, Cambodia, and Lao PDR have not been sufficiently accessible during recent years.Therefore, the data were collated to a feasible extent from the peer-reviewed research papers, reviewed papers, policy reports by the organizations such as Asian Development Bank, the World Bank, United Nations Food and Agriculture Organization, International Energy Agency, International Renewable Energy Agency, and reports by non-government organizations.Then, the study synthesized and evaluated the biomass sources, energy potential, utilization, and management in the Southeast Asian countries to highlight the potential utilization of the available biomass sources in the region.Additionally, the barriers and challenges of biomass utilization in these countries were also described.Finally, the study proposed a sustainable approach of biomass energy by comparing the way of traditional biomass utilization.
Biomass Sources and Utilization in the Southeast Asian Countries
The region is situated in a tropical zone and has the capacity to produce the large quantities of biomass all the year round, out of which woody biomass from forests constitutes a particularly valuable source of energy in the form of domestic fuel for local residents [16].Additionally, the majority of the countries have an abundance of agriculture residues for biomass energy sources, due to their agriculture-based economy.For instance, with 45% of forest cover and agriculture-based economy, Myanmar has gained the biomass resources from the forest sector and agricultural sector.Source: [9]; https://www.irena.org/publications/2017/Mar/Renewable-Energy-Prospects-Indonesia.
Several studies have focused on the renewable energy, biomass energy, renewable energy sources, energy utilization, policy, and emission factors in Asia [2,8,9,[15][16][17][18][19] but mostly in specific countries such as Indonesia, Malaysia, Cambodia, Lao PDR, Brunei Darussalam, Philippines, etc. [20][21][22][23][24]. Therefore, the study highlighted the biomass sources, energy potential, and management in Southeast Asian countries to ensure the biomass sources and their energy utilization be applicable to the policy makers, researchers, and non-government organizations for outlooking biomass energy as an important portion of the future renewable energy sector in the region.
Methodology
Since most Southeast Asian countries are developing countries, the country-specific data related to biomass sources, energy potential, and utilization in some countries including Myanmar, Cambodia, and Lao PDR have not been sufficiently accessible during recent years.Therefore, the data were collated to a feasible extent from the peer-reviewed research papers, reviewed papers, policy reports by the organizations such as Asian Development Bank, the World Bank, United Nations Food and Agriculture Organization, International Energy Agency, International Renewable Energy Agency, and reports by non-government organizations.Then, the study synthesized and evaluated the biomass sources, energy potential, utilization, and management in the Southeast Asian countries to highlight the potential utilization of the available biomass sources in the region.Additionally, the barriers and challenges of biomass utilization in these countries were also described.Finally, the study proposed a sustainable approach of biomass energy by comparing the way of traditional biomass utilization.
Biomass Sources and Utilization in the Southeast Asian Countries
The region is situated in a tropical zone and has the capacity to produce the large quantities of biomass all the year round, out of which woody biomass from forests constitutes a particularly valuable source of energy in the form of domestic fuel for local residents [16].Additionally, the majority of the countries have an abundance of agriculture residues for biomass energy sources, due to their agriculture-based economy.For instance, with 45% of forest cover and agriculture-based economy, Myanmar has gained the biomass resources from the forest sector and agricultural sector.Therefore, the major biomass sources in the country include wood residues, rice husk and rice stalks, sugarcane residues, oil palm residues and other agricultural resides (Figure 5).The forest and agriculture resources for biomass sources in the Southeast Asian countries are presented in Table 1.
Resources 2019, 8, 81 5 of 19 Therefore, the major biomass sources in the country include wood residues, rice husk and rice stalks, sugarcane residues, oil palm residues and other agricultural resides (Figure 5).The forest and agriculture resources for biomass sources in the Southeast Asian countries are presented in Table 1. 2 presents biomass sources and their energy potential in the Southeast Asian countries while Table 3 describes the utilization of biomass energy in the region.It is found that the total quantity of the residues from the agriculture and forest sector is estimated at over 500 million tons per year.Additionally, the total biomass energy potential in the countries has over 8000 million gigajoules.Based on Tables 2 and 3, biomass sources and biomass energy utilization in each of the Southeast Asian countries are briefly described as follows: (a) Cambodia Cambodia has 10,094,000 hectares of forest area, having 57% of the total area of the country.Therefore, wood and wood charcoal account for approximately 80% of the total energy consumption in Cambodia.Approximately 80% in urban and 94% in rural areas are used for cooking [26].The other major biomass sources come from agricultural residues including rice husk, rice straw, corn cob, cassava stalk, bagasse, groundnut shell and husk, and coconut shell and front.Currently, the total installed capacity from biomass is about 23 MW.Cambodia is planning to produce 73 MW of installed capacity from biomass by 2030.
(b) Myanmar
Myanmar is an agriculture country, covering 45% of the area with forest.Myanmar produces over 20 million tons of paddy annually.Therefore, the major biomass sources of the country are obtained largely from the forest and agriculture sector.Since 70% of the population resides in rural areas, they are mostly dependant on solid biomass fuels.Approximately 65% of the total energy consumption of the country comes from biomass sources [28].The total capacity potential from biomass and biogas is estimated at 6899 MW and 4741 MW, respectively [29].Out of this, the total installed capacity has reached 115 MW.
(c) Lao PDR
With 68% of the forest cover, Lao PDR has an abundance of biomass resources from the forest sector.Since the majority of the population live in the rural areas, 80% of the households rely on fire wood and charcoal, having 68% of its primary energy supplies [26,30].In addition to the forest sector, the agriculture could provide a wealth of biomass resources due to its agriculture economy.The installed capacity of biomass energy is about 40 MW and is being planned to achieve 58 MW by 2025.
(d) Vietnam
Being an agricultural country, Vietnam has an abundance of biomass energy sources, with over 300 GW of theoretical capacity potential [31].Biomass is mainly used in households (76%), and the rest (24%) is used in small industrial boilers and combined heat and power (CHP) plants in sugar mills [32].The major biomass sources include forest residues, rice husk, rice straw, bagasse, cane trash, maize trash, cassava stem, peanut shell, coffee husk, and coconut shell.The main energy consumption potential in Vietnam is aimed at municipal and industrial co-generation power plants [32].Vietnam has set a target of having a combined capacity of 500 MW of biomass power by 2020, which is raised to 2000 MW in 2030 [33].
(e) Philippines
As the energy needs of the Philippines rely predominantly on the imports of fossil fuels, the government have looked at renewable energy for possible alternatives [34].Among the alternatives, biomass energy is crucial to the country and nearly 30% of the energy for the 100 million people living in the Philippines come from biomass and are mainly used for household cooking by the rural population [27,35].Additionally, biomass industry is rapidly advancing, with 276.7 MW of a total installed capacity around the country [36].Biomass energy application accounts for around 15% of the primary energy use in the Philippines [35].
(f) Indonesia
Among the Southeast Asian countries, Indonesia has an abundant growing stock in forests due to its most extensive forest area, having 94,432,000 hectares [16].Besides, in Indonesia economies, important biomass fuels are derived from agriculture residues and used in both traditional and modern applications [21].The major agriculture biomass sources are oil palm residues, sugarcane residues, rice husk and rice straw, and corn cob.It is estimated that Indonesia produces 146.7 million tons of biomass per year, equivalent to about 470 million gigajoules (GJ) per year [37].The total estimated capacity potential from biomass accounts for approximately 50,000 MW, with 312 MW of installed capacity.
(g) Thailand
Thailand is an agricultural country, with a huge biomass energy potential for fulfilling additional energy requirements of the country.Biomass sources could cover up to 15% of the energy demand of the country [38].The capacity potential from utilization of biomass and biogas is estimated at 7000 MW and 190 MW, respectively [8,39].Most of the biomass-fired industrial facilities are large-scale, centralized plants operating at economies of scale [40].The installed capacity from biomass and biogas accounts for 1610 MW and 46 MW, respectively, with 3.630 GW of installed capacity for a project target by 2021 [8,39].Thailand's board of investment (BOI) promotes the production of electricity or steam from renewable energy, such as biomass by an eight-year tax holiday, exemption of import duty on machinery, raw, or essential materials used in manufacturing export products [40].
(h) Malaysia
Malaysia has a huge forest area, with around 62% of the total land area.Agriculture also covers approximately 4,890,000 hectares of the whole country.Therefore, Malaysia has the numerous biomass resources such as oil palm residues, sugarcane residues, and coconut resides.The palm oil industry alone contributes to about 8% or over RM 80 billion to the country's gross national income (GNI), making it by far the largest contributor within the agricultural sector, naturally generating the largest amount of biomass [6].Industry figures put this amount at 83 million dry tons in 2012 and this is likely to increase to 100 million dry tons by 2020 [6].The total installed capacity potential from biomass is estimated at 29,000 MW, with 211 MW of the installed capacity [8].
(i) Brunei Darussalam
With plentiful oil and gas resources, Brunei Darussalam relies majorly on fossil fuel not only for its national energy security and booming economy [23,41].For this reason, it had minimal interest in the use of renewable energies, but due to mounting worldwide interest in this and in order to diversify its energy sources and bolster its energy security, it set out a goal of adopting 10% electricity from renewable energies in 2035 [41].Biomass sources in the country account for coconut shell, coconut fiber, corn fiber, rice husk, and saw dust, with approximately 8.773 kilo GJ of the annual biomass energy potential.
(j) Singapore
Being composed of 63 islands, Singapore has a total area of 722.5 square kilometers and approximately two hectares of forest area.In 2007, Singapore identified clean technology as a key driver of economic growth, allocating S$700 million to fund research and development (R&D), innovation, and manpower development in the sector [6].Singapore has gained a reputation as a clean, green "garden city" [42].Utilization of horticultural and wood wastes processed by ecoWise could produce approximately 0.9 MW of electricity and 5.4 MW of heat for co-generation plant [6].The total biomass energy potential from biomass accounts for approximately 2.901 million GJ [43] and the installed capacity from biomass sources accounts for 220 MW [8].Nowadays, there already exists several applicable technologies for biomass energy utilization in the Southeast Asian region.These technologies include direct combustion and cofiring of biomass products for heat and electricity, anaerobic digestion of animal wastes for methane-rich gas, pyrolysis of biomass products for bio-char, gas, and oil, gasification of agricultural waste such as rice husk and others, wood chips, sawdust, forest residues, product waste, etc.In Thailand, the combustion of agriculture residues for power generation can be widely seen around the country.Meanwhile, in Myanmar, power generation from biomass gasification has been conducted by the government institutions and private sectors.Upon the different fuel alternatives and local supply demand, various ranges of generating capacities for the gasification plant can be found; especially rice husk biomass gasification shares the most due to that the staple food is rice in Myanmar agricultural system.Additionally, small villages within 100-200 households could be provided electricity for lighting with 10 kW power generation capacity via 25 hp gas engine, which was operated by biogas produced from 50 m 3 fixed-dome type biogas plant using the cow dung waste from the household.A comparison between theoretical biomass energy potential and installed capacity with project targets in the Southeast Asian countries is presented in Table 3.By far, the total installed capacity in the Southeast Asian countries accounts for approximately 3 GW from biomass and around 330 megawatts (MW) from biogas.It was observed that the applied technologies for the installed capacity of biomass energy included gasification, co-firing, and direction combustion while the installed capacity of biogas power plants was majorly gained from anaerobic digestion.Table 3.A comparison between theoretical biomass energy potential and installed capacity with project targets [6,8,24,27,29,31,33,36,39,[46][47][48][49].As a major source of biomass fuels, fuelwood plays a key role for cooking and heating in the rural areas of most Southeast Asian countries.However, due to deforestation and logging (including illegal logging), the projected annual woody biomass production in natural forests declined from 815.9 million tons (16.3 EJ) in 1990 to 359.3 million tons (7.2 EJ) in 2020 [50].Hence, average annual woody biomass production in all forests in Southeast Asia between 1990 and 2020 was estimated at 563.4 million tons (11.3 EJ) per year declining about 1.5% per year [50].In addition to deforestation, the development of renewable energy sector has largely affected the fuelwood consumption in the Southeast Asian region.Therefore, it could be seen that there is a decline in the projected annual consumption of fuelwood in Southeast Asia after 1990, trending from 222 million cubic meters in 1990 to 122 million cubic meters in 2020 (Figure 6a).Additionally, beyond 2020, it might potentially be seen that there could also be a substantial decline in annual fuelwood consumption in the Southeast Asian countries due to not only deforestation and logging [50] but also the strategic plans and implementations of the ASEAN (Association of Southeast Asian Nations) community related to the promotion of the renewable energy sector development (majorly in hydropower, biomass energy, geothermal energy, solar, and wind energy).In the ASEAN community, it is found that the share of the renewable energy has been set a target from 15% for the total ASEAN installed power capacity by 2015 to 23% for the total ASEAN energy mix by 2023 [18].
Biomass
However, the annual charcoal consumption in the Southeast Asian region seems to remain nearly stable from 2005 (Figure 6b).This situation could probably highlight that since some of the Southeast Asian countries, especially Myanmar, Lao PDR, and Cambodia, are trying to provide 100% access to the electricity nationwide by 2030 [2,14], the people in rural and urban areas are still relying on charcoal consumption for cooking and heating in case of the electrical power outage and electricity shortage, despite the reduction in avoidance of direct consumption of fuelwood.
geothermal energy, solar, and wind energy).In the ASEAN community, it is found that the share of the renewable energy has been set a target from 15% for the total ASEAN installed power capacity by 2015 to 23% for the total ASEAN energy mix by 2023 [18].
However, the annual charcoal consumption in the Southeast Asian region seems to remain nearly stable from 2005 (Figure 6b).This situation could probably highlight that since some of the Southeast Asian countries, especially Myanmar, Lao PDR, and Cambodia, are trying to provide 100% access to the electricity nationwide by 2030 [2,14], the people in rural and urban areas are still relying on charcoal consumption for cooking and heating in case of the electrical power outage and electricity shortage, despite the reduction in avoidance of direct consumption of fuelwood.Figure 7 shows the ratio of bioenergy demand and supply in selected Southeast Asian countries in 2025.Among the selected countries, the ratio of bioenergy demand and supply in Myanmar is likely to be the lowest, with 20% in low estimate and over 30% in high estimate, due to its major focus on hydropower and solar power utilization.On the other hand, Thailand seems to have the highest ratios in both low and high estimate in 2025, along with the quality improvement of biomass fuels, technology advancements, and market opportunities.Table 4 show the methods of biomass energy utilization in the Southeast Asian countries.Since most of the countries have a higher rural population, the traditional ways of biomass energy utilization such as traditional consumptions for cooking and heating, animal feeds, dumping, and open burning are significantly practiced.Due to the high capital cost of technologies, lack of skilled personnel, and uncertainty of economic benefits, most developing countries could not afford to apply the technologies related to refuse-derived fuel (RDF), pyrolysis, and liquefaction.For instance, the actual status for RDF application in Myanmar could be hardly seen.However, some demonstrated facilities for biomass briquettes, especially for rice husk, donated from the foreign countries could be seen in the country.Therefore, the technologies related to biomass energy have been well applied only by a few countries such as Singapore, Thailand, and Malaysia in the region.Figure 7 shows the ratio of bioenergy demand and supply in selected Southeast Asian countries in 2025.Among the selected countries, the ratio of bioenergy demand and supply in Myanmar is likely to be the lowest, with 20% in low estimate and over 30% in high estimate, due to its major focus on hydropower and solar power utilization.On the other hand, Thailand seems to have the highest ratios in both low and high estimate in 2025, along with the quality improvement of biomass fuels, technology advancements, and market opportunities.Table 4 show the methods of biomass energy utilization in the Southeast Asian countries.Since most of the countries have a higher rural population, the traditional ways of biomass energy utilization such as traditional consumptions for cooking and heating, animal feeds, dumping, and open burning are significantly practiced.Due to the high capital cost of technologies, lack of skilled personnel, and uncertainty of economic benefits, most developing countries could not afford to apply the technologies related to refuse-derived fuel (RDF), pyrolysis, and liquefaction.For instance, the actual status for RDF application in Myanmar could be hardly seen.However, some demonstrated facilities for biomass briquettes, especially for rice husk, donated from the foreign countries could be seen in the country.Therefore, the technologies related to biomass energy have been well applied only by a few countries such as Singapore, Thailand, and Malaysia in the region.[6,8,9,15,18,27,29,31,33,36,46,48,52].
Barriers and Challenges for Utilization of Biomass
Scaling up sustainable, modern forms of bioenergy will be crucial both to address the energy access challenge, and to increase renewable energy use in both industry and transport [9].Table 5 presents the barriers and challenges for utilization of biomass.Policy and institutional aspects are crucial to development of biomass energy sector.However, specific goals and targets on the biomass energy development could not clearly seen in most of the countries yet.Meanwhile, as driven by the low economy growth of the countries, lack of sufficient funding for research and development and purchase of technologies is one of the biggest challenges in the development of biomass energy sector in most of the Southeast Asian countries such as Myanmar, Lao PDR, and Cambodia.Likewise, public and private sector involvement is still uncertain owing to the uncertain profits and risks of utilization of biomass energy, since utilization of biomass sources concerns with low energy contents, bulky volume of biomass sources, need for large storage systems and high transportation costs, data reliability issues, underdeveloped biomass industries, and lack of local skilled personnel.Additionally, some of the useful and important information about biomass sources are not widespread among the local people thorough education and training programs.Consequently, the cooperation of the local people in the development of the bioenergy sector remains weak.As one of the most crucial things, market development still seems slow because of lack of sufficient funding, research and development, and weakness of all stakeholder involvement.Table 5. Barriers and challenges for utilization of biomass [6,9,15,18,19,29,30,[53][54][55][56].
Traditional Approach and Sustainable Approach to Biomass Energy
Nowadays, due to the climate change, fast growing populations, and economic growth in the region, the Southeast Asian countries have outlooked the renewable and alternative energies to reduce the greenhouse gas emissions and other environmental impacts from the energy sectors.Out of them, utilization of biomass energy derived from the enormous biomass sources from agriculture and forest residues has become a crucial factor of meeting the future energy needs.In addition to environmental and energy benefits, the economic benefits from utilization of biomass energy could also be gained largely from the production of value-added biomass fuel and agriculture nutrients, fewer imports of fossil fuels and agricultural nutrients from other foreign countries, reduced cost of waste disposal, and local job opportunities that could increase the household incomes of local people.
For the efficient utilization of biomass sources, the countries will need to develop the way forward from traditional management to sustainable one, as described in Figure 8.As the traditional management of biomass sources in most of the Southeast Asian countries, it is observed that firstly, the management process generally seems to go through harvesting and storage, then traditional consumption patterns follow-animal feed, traditional consumption for cooking and heating, open burning and dumping, and traditional agriculture nutrients.However, if a sustainable approach is considered, the aspects about policy and institutions, targets and goals, funding, public-private partnership, stakeholder involvements, research and development, and public awareness and educational trainings will become crucial.Based on policy and goals, research and development would need to be promoted from the growing stages of biomass resources to market development.
To ensure the higher quality of the biomass fuels for energy utilization, Koppejan and van Loo [57] suggest that the quality of the raw biomass could be improved by two stages-growing stage, and harvest and storage stage.During the growing stages, based on soil type, the chemical characteristics of biofuels and the desired yield such as type of species, agricultural and silvicultural practice, fertilization, and harvesting date should be influenced.Likewise, in the harvest and storage stage, the physical characteristics of biomass fuels can be improved by harvesting methods, transshipment, drying, sanitation, upgrading, and storage.Biomass fuel quality and utilization can be finally upgraded by fuel processing such as the improvement of calorific value, and technological conversions such as pyrolysis, combustion, gasification, fermentation, and anaerobic digestion.In addition, co-firing of biomass with coal and hybrid system could also be incorporated.To ensure the higher quality of the biomass fuels for energy utilization, Koppejan and van Loo [57] suggest that the quality of the raw biomass could be improved by two stages-growing stage, and harvest and storage stage.During the growing stages, based on soil type, the chemical characteristics of biofuels and the desired yield such as type of species, agricultural and silvicultural practice, fertilization, and harvesting date should be influenced.Likewise, in the harvest and storage stage, the physical characteristics of biomass fuels can be improved by harvesting methods, transshipment, drying, sanitation, upgrading, and storage.Biomass fuel quality and utilization can be finally upgraded by fuel processing such as the improvement of calorific value, and technological conversions such as pyrolysis, combustion, gasification, fermentation, and anaerobic digestion.In addition, co-firing of biomass with coal and hybrid system could also be incorporated.
However, one of the most crucial factors that need to be considered for the estimation of available energy potential from biomass resources is the amount of energy that would be necessarily involved in the plantation of biomass crops and trees, harvesting and transporting of them, and valorization and conversion of the biomass sources into energy or agricultural nutrients.This amount of energy that must be consumed to supply the biomass energy to the society might depend upon several factors such as climate, strategic plans, and applied technologies; hence, it might contribute a substantial decrease in the amount of potential biomass energy from available biomass sources.
To achieve the sustainability and the efficient utilization of biomass as domestic solutions, financing and micro-financing could enable households and communities to purchase energy equipment through loans and other financing packages [53].Besides, local governments and concerned authorities should implement education and awareness campaigns, public-private partnerships, creation of national technology standards, establishment of maintenance and training centers, international cooperation, technology, and intellectual property transfer [53].In some Southeast Asia countries, the governments have already provided the project developers with investment incentives, guaranteed minimum prices, power purchase agreements with the utility grid, and exemptions pertaining to the import of equipment and certain tax credits [6].As a result, the development of biomass energy from the locally accessible biomass sources could be systemically made in a long run.Therefore, looking forward from policy and institutions to all stakeholder involvements, a holistic approach to biomass energy sector will certainly play a key role in efficient utilization of biomass sources as a renewable and sustainable energy in the Southeast Asian countries.However, one of the most crucial factors that need to be considered for the estimation of available energy potential from biomass resources is the amount of energy that would be necessarily involved in the plantation of biomass crops and trees, harvesting and transporting of them, and valorization and conversion of the biomass sources into energy or agricultural nutrients.This amount of energy that must be consumed to supply the biomass energy to the society might depend upon several factors such as climate, strategic plans, and applied technologies; hence, it might contribute a substantial decrease in the amount of potential biomass energy from available biomass sources.
Conclusion
To achieve the sustainability and the efficient utilization of biomass as domestic solutions, financing and micro-financing could enable households and communities to purchase energy equipment through loans and other financing packages [53].Besides, local governments and concerned authorities should implement education and awareness campaigns, public-private partnerships, creation of national technology standards, establishment of maintenance and training centers, international cooperation, technology, and intellectual property transfer [53].In some Southeast Asia countries, the governments have already provided the project developers with investment incentives, guaranteed minimum prices, power purchase agreements with the utility grid, and exemptions pertaining to the import of equipment and certain tax credits [6].As a result, the development of biomass energy from the locally accessible biomass sources could be systemically made in a long run.Therefore, looking forward from policy and institutions to all stakeholder involvements, a holistic approach to biomass energy sector will certainly play a key role in efficient utilization of biomass sources as a renewable and sustainable energy in the Southeast Asian countries.
Conclusions
Due to potential depletion of fossil fuel and climate change, the Southeast Asian countries have outlooked the renewable and alternative energies to reduce the greenhouse gas emissions and other environmental impacts from the energy sector.As most Southeast Asian countries have an agriculture-based economy and a large area of forest cover, biomass has become one of the most interesting energy sources to fulfill the primary and additional energy needs of the countries.The total annual quantity of the residues from agriculture and forest sector in this region is estimated at more than 500 million tons per year, equal to over 8000 million gigajoules of total biomass energy potential.Additionally, the total installed capacity in the region accounts for approximately 3 GW from biomass and around 330 Megawatts (MW) from biogas.Currently, biomass energy utilization and market development in the region seems progressive.Some of the Southeast Asian countries such as Thailand and Malaysia have effectively developed more innovative solutions to biomass energy utilization despite the barriers and challenges.Therefore, along with the advancements of technologies, research and development, growing energy markets, and knowledge and technology transfer from the other developed countries, biomass energy could be crucial in offering the environmental and economic benefits in the near future of the energy sector in the region.
Figure 3 .
Figure 3. Share of renewable energy to total electricity generation in Southeast Asian countries (2014) [9].
Figure 3 .
Figure 3. Share of renewable energy to total electricity generation in Southeast Asian countries (2014) [9].
Figure 3 .
Figure 3. Share of renewable energy to total electricity generation in Southeast Asian countries (2014) [9].
Figure 7 .
Figure 7. Ratio of bioenergy demand and supply in Southeast Asia countries in 2025 [9].
Resources 2019, 8 , 81 15 of 19 Figure 8 .
Figure 8. Flow diagram of traditional approach and sustainable approach to biomass utilization.
Figure 8 .
Figure 8. Flow diagram of traditional approach and sustainable approach to biomass utilization.
Forest Growing Land Area (1000 × hectares/year) Percent of Land Area (%) Annual Production/ Volume of Stock (million tons/year) Year Remarks Cambodia
-Vietnam produces 10-13 tons of bamboo per ha.
year) Percent of Land Area (%) Annual Production/ Volume of Stock (million tons/year) Year Remarks Cambodia
Forest 10,094.00057.000 -2010 Forest sector could produce 959 Mm 3 of stock per year. | 8,748.6 | 2019-04-25T00:00:00.000 | [
"Environmental Science",
"Economics"
] |
Birth of String Theory
This is a brief summary of an introductory lecture for students and scholars in general given by the author at Nambu Memorial Symposium which was held at Osaka City University on September 29, 2015. We review the invention of string theory by Professor Yoichiro Nambu following the discovery of the Veneziano amplitude. We also discuss Professor Nambu's proposal on string theory in the Schild gauge in 1976 which is related to the matrix model of Yang-Mills type.
Introduction
In 1949, Professor Yoichiro Nambu started his career at Osaka City University where this memorial symposium was held.The idea of this symposium was to deliver the remarkable scientific achievements and originality of Professor Nambu throughout his life as much as possible to younger generations and scholars in general, so that some of what Nambu accomplished become more tangible.On September 29, 2015, ten speakers contributed to the idea of the symposium.The role of the author was to review the birth of string theory, which is a wellknown unpublished (not contradictory) work [1] of Nambu.For a pedagogical reason as well as for the sake of presentation, the developments based on the path integral method before and after his work were included.In the latter part of the talk, a less well-known proposal of Nambu in the quantization and discretization of the string theory in the Schild gauge in [3] was brought to the audience.This, in fact, testified for Nambu as a foreteller of modern physics.
In order to set a current context of that proposal, we include a general discussion of matrix models.
Veneziano amplitude and Koba-Nielsen form
To begin, let us consider the 4-point scattering of scalar mesons.The Mandelstam variables are defined by (2.1) where p µ I are the momenta and the symbol • denotes the Lorentz invariant inner product in the Minkowski space.From experiments, the following facts were known: • Contribution of many particles (poles) in the t channel is evident.
• It suggests the structure of (mass) 2 proportional to spin.
• The behavior in the region s ≫ t is correlated with that in the region s ≪ t.
Figure 2:
The idealization that one can take is that there exists an infinite number of such particles (mass) 2 ∝ spin, by setting N 0 → ∞ in Fig. 3.
Figure 3:
The amplitude was empirically known to satisfy the relation f exp (s, t) = f exp (t, s), which is denoted by = .Therefore the behavior in the region where the first variable ≫ the second variable determines that in the region where the first variable ≪ the second variable.
The sum of exchange of the resonance in the t-channel is equivalent to the sum of the resonance in the s-channel.
Veneziano [4] wrote down the amplitude satisfying these assumptions and we will present the answer in a different way from his route.We will also review the developments where the solution was represented in such a way to be directly generalizable into 4 → n.
Here, we have introduced the factor N 0 ! to render the N 0 → ∞ limit finite.Taking this limit, we obtain1 (2.6) Figure 5: The reduction of the number of integration variables from 4 → 1 variable x, is understood as the Möbius invariance acting on the unit circle in Fig. 5.The cross ratio, defined by and we regard z 2 , z 3 , z 4 to be fixed by the Möbius group rotations.After some manipulations, we obtain where . (2.9) In this form, we can readily generalize the four point amplitude to the n point just by changing 4 → n in the product.This is the Koba-Nielsen form [5].
Next, let us rewrite the last expression (2.8), using the knowledge of two-dimensional electrostatics.Let us note that and that is the Neumann function in the unit disk D. We can rewrite the exponent of the factor (2.10) as where and z I 's are located on the boundary of the unit disk.It looks likes the (quantum)-oscillations of d scalar fields X µ (z, z), µ = 0, 1, • • • , d − 1 on D in two Euclidean dimensions with such scalar fields path-integrated [6].The action, which is a weight upon the path integrations, is identified as Undesirable states, however, appear in the canonical quantization.An infinite number of constraints called Virasoro constraints [7] must be imposed.
Discovery of Nambu-Goto string
According to author's (certainly incomplete) search of references, several people other than the authors of [6] at that time worked out the harmonic oscillator formalism to analyze the factorization and other properties of the Veneziano amplitude and reached the quadratic form of the action (2.14).Most notably, the picture of rubber band was developed by Susskind [8,9,10,11].For contributions on these points from other people, including ones by unpublished reports, the author simply has no choice but to direct the readers to the references of the old review article [12] as well as those of the book [13].
Nambu [1] and Goto [14] adopted the area of the surface Σ swept by a string in d dimensional Minkowski spacetime as the action.The d scalar fields introduced in eq.(2.14) play the role of the embedding function: where z = ξ 1 + iξ 2 = e i(σ+τ M ) .The action is given by where γ ab ≡ ∂ a X • ∂ b X is the induced metric.Since this action has the reparametrization invariance, the following two constraints can be imposed: where Ẋ ≡ ∂X dτ M , X ′ ≡ ∂X ∂σ .These are the Virasoro constraints.The action eq.(2.14) is reproduced, using these.
The next stage of the developments took place more than ten years later.It came from our improved understanding of the quantization procedure based on an auxiliary field (two dimensional metric) g ab (ξ).The Nambu-Goto action is further rewritten in terms of intrinsic quantities of the two dimensional surface swept by a string: ) This form is suited for the study of quantum anomaly [15,16,17].Let us note that the action S P eq.(3.4) does not contain derivatives of g ab .Equation of motion for X µ is the two dimensional Laplace equation or the wave equation, while eq. of motion for g ab is the Virasoro constraints or the energy-momentum tensor = 0 on the two-dimensional background metric.The action 2) is reproduced from S P by eliminating g ab .
There is another way pursued on the quantization of the Nambu-Goto string in the so called Schild gauge: where α and β are constants and is the Poisson bracket.When eliminating √ −g by eq. of motion obtained from the variation δ √ −g, the action "S Schild " becomes that proportional to S N G .
Path integral quantization of string
Let us recall the bottom line of the path integral.The transition amplitude for one-particle quantum mechanics is given by lim where S is the action functional.This is essentially infinite dimensional multiple integrals.
The path integral representation for the correlation function can be Wick rotated into which is the same as the sum over all configurations with Boltzmann weights in statistical mechanics.
The Möbius invariant n-point scattering amplitude can be written as The general variation of g µν is given by δg ab = (P 1 δv) ab + δρg ab +(the variations not generated by the these two).(4.4) The first one is the diffeomorphism with tracelessness condition imposed.The second term is the local Weyl transformation.These are the two local symmetries of the action (3.4).The third term should be written as ker P † 1 and corresponds to the degree of freedom called moduli of the surface deformation.Let us recall and indicate very briefly how we introduce the notion of integration in finite dimensional Riemannian space with its metric given by We need to work out the infinite dimensional analog of this problem.Therefore, we have to estimate the Jacobian associated with the change of variables (4.4) [18,19].
Skipping the remaining procedure, let us give the master formula for string perturbation theory for the case of a bosonic string.Here, we will consider the zero-point amplitude, namely, the partition function of a closed string only.The coupling constant of string theory is denoted by κ and is introduced through where Φ is the condensate of dilaton.The order of string perturbation theory is determined by the Euler number χ(h, b, c) of the surface (h, b and c are the number of holes, boundaries and cross caps, respectively) and string perturbation theory is, therefore, the genus expansion.
The formula for the partition function reads For the detail of the notation, we refer the reader to [18,19].The critical dimension d = 26 is selected by demanding the decoupling of the Liouville degrees of freedom.
In the case of superstring perturbation theory, we first need to introduce fermions on the world-sheet [20,21,22] but we need to work out a lot more to construct the perturbative series.The critical dimension is d = 10.Maximal spacetime supersymmetry is accomplished by the GSO projection [23] and the generalized GSO projection [24,25,26] or orbifolding [27] must be made in order to construct more realistic models having non-maximal supersymmetry.
Eventually, spacetime supersymmetry must be broken and currently there is a revived interest (see, for instance, [28]) in the old work [29,30,31].Turning to the more mathematical aspects, the construction of super Riemann surfaces (see, for instance, [32,33,34,35,36]) as well as that of the super moduli has been major unfinished parts.See, for instance, [37] for recent progress.These are just finite dimensional multiple integrals.There are two types: 1) the one matrix model and its extension to a chain of matrices.2) the Yang-Mills type.
The Haar measure of an N × N Hermitian matrix M is given by where M = U † ΛU and dΩ = dUU † .The factor i>j (λ i − λ j ) 2 works as a repulsive force between the eigenvalues in providing the effective action of the model given.The eigenvalue distribution is expected to become continuous in the limit N → ∞ and it can be regarded as a system of complex planes cut and glued, namely, the Riemann surface.
In the case of the one-matrix model, the simplest model of type 1), equation of motion for the correlation functions (the Schwinger-Dyson equation) takes the form of the Virasoro constraints [38,39,40,41].For more general chain models, they typically obey W n type constraints [42].
The models of type 1) reduce to eigenvalue models as the angular integrations simply factor out.
There are several physical contexts where the models of type 1) are relevant: 1.The string theory where the Liouville factor g a a = 2e φ cannot be factorized [38,43] (string theory in non-critical dimensions).Furthermore, in the case of d ≤ 1, one can sum the perturbative series to treat some non-perturbative effect [44,45,46].
2.
Choosing a multi-log potential and an appropriate integration region (Selberg-type matrix model), and introducing the parameter β to modify the exponent of the measure factor (β-ensemble), the instanton sum has been generated (AGT relation [47]) [48,49].
4. Actions of d = 3 and d = 4 supersymmetric gauge theories often reduce to matrix integrals (localization).(See, for example, [52]).This has led to the study of instanton gas of various kind.(See, for example, [53]).
With regard to the matrix models of type 2), Professor Nambu made a remarkable proposal already in 1977 in [2] in string theory in the Schild gauge.In fact, equation of motion for X µ obtained from "S Schild " in eq.The IIB matrix model [54] was proposed in order to provide a complete treatment of superstrings that includes non-perturbative effects.The action is given by (5.7) The bosonic part takes the same form as that proposed by Nambu.The many-body problem of strings can be treated by integrating out the off-diagonal blocks after dividing each of the original matrices into blocks.It appears, however, that there is no evidence that the gauge volume of the local Weyl symmetry is factored out, which is requisite for (perturbative) string theory in the critical dimension that ensures masslessness of graviton in flat spacetime.
Figure 4 :
Figure 4: ψ I (z I ) O I (z I )|0 in = sum over all surfaces with weights .(4.3) Let us now turn to the path integral quantization of a string.The path integrals over X µ are essentially infinite-dimensional multiple integrals each of which is a gaussian.The question arises on how to treat the path integrals for g ab .Note that in computing configuration • • • e −S E , the sum should be taken over the gauge inequivalent configurations alone.The idea of the computation is that we first carry out the summation, ignoring this double counting problem and then divide the answer by "the number of multiplicities", namely, the volume of the gauge orbit. | 2,983.4 | 2016-04-13T00:00:00.000 | [
"Physics"
] |
The application of volume texture extraction to three-dimensional seismic data – lithofacies structures exploration within the Miocene deposits of the Carpathian Foredeep
There are numerous conventional fields of natural gas in the Carpathian Foredeep, and there is also evidence to suggest that unconventional gas accumulations may occur in this region. The different seismic signatures of these geological forms, the small scale of amplitude variation, and the large amount of data make the process of geological interpretation extremely time consuming. Moreover, the dispersed nature of information in a large block of seismic data increasingly requires automatic, self-learning cognitive processes. Recent developments with Machine Learning have added new capabilities to seismic interpretation, especially to multi-attribute seismic analysis. Each case requires a proper selection of attributes. In this paper, the Grey Level Co-occurrence Matrix method is presented and its two texture attributes: Energy and Entropy. Haralick’s two texture parameters were applied to an advanced interpretation of the interval of Miocene deposits in order to discover the subtle geological features hidden between the seismic traces. As a result, a submarine-slope channel system was delineated leading to the discovery of unknown earlier relationships between gas boreholes and the geological environment. The Miocene deposits filling the Carpathian Foredeep, due to their lithological and facies diversity, provide excellent conditions for testing and implementing Machine Learning techniques. The presented texture attributes are the desired input components for self-learning systems for seismic facies classification.
INTRODUCTION
Modern, high-resolution 3D seismic volumes make a significant contribution to the quality of subsurface geological imaging and are widely used in the oil industry for hydrocarbon exploration. However, due to the huge amount of data obtained by the method of three-dimensional seismic surveying, the effective interpretation of seismic volumes increasingly requires the automation of cognitive processes through the use of the technique of self-learning systems. Recent developments with Machine Learning (ML) have added new capabilities to seismic interpretation, especially to multi-attribute seismic analysis. Moreover, at present ML is perceived as a method that will undoubtedly affect the interpretation of seismic data in the future (Wrona et al. 2018). These processes can proceed in a supervised and unsupervised form, and the key to both cases is the correct selection of seismic attributes (Marfurt 2018).
The results of the latest research prove that instead of the full range of available seismic attributes, only the selection of those attributes which most distinguish elements from the seismic data should be used in the process of correlation with identified seismic facies (Roden et al. 2015, Infante-Paez & Marfurt 2019. The application of texture attributes for seismic facies classification using ML techniques can provide seismic facies information that is not provided by any conventional seismic approach (Marfurt & Chopra 2007). Hence, in this paper two texture attributes: Energy and Entropy will be presented. Both were derived by the use of the Grey Level Co-occurrence Matrix (GLCM) method, which emphasize (in a special way) the continuity of the identified seismic reflection patterns.
The seismic data used in the research comes from a modern 3D survey located in the NE part of the Carpathian Foredeep Basin, which belongs to the foreland basin system that surrounds the Carpathian orogenic belt (Fig. 1). The 3D seismic survey was acquired in order to develop the stratigraphic model that would match the production history as well as being consistent with the available well control.
The study area is located within the northern, outer part of the basin which is filled with thick pelagic and turbidite formations (Wysocka 2006). The main objective of the research was a fragment of sedimentation profile referred to as the Machów Formation (Myśliwiec 2004). The sedimentation process of this Late-Badenian and Sarmatian clastic succession was influenced by its close proximity to the Roztocze Hills ( Fig. 1), forming part of the Carpathian forebulge zone (Wysocka 2016). The results of the seismic data interpretation confirmed the significant tectonic activity in the Miocene basement, highlighted by the high variability of sedimentation environments during the temporal -spatial evolution of a basin fill. All of the above information makes the study area extremely interesting for testing modern tools and unconventional methods to optimally understand the variability of environments and to estimate the exploration potential of structures within the basin. There are numerous conventional fields of natural gas in the Carpathian Foredeep and there is also evidence to suggest that unconventional gas accumulations, related to non-structural types of traps, may occur in this region (Pietsch et al. 2010). Such exploration objects are, in particular, the external and internal elements of submarine channels and fans. The different seismic signatures of these geological forms and the small scale of amplitude variation and limited visibility, along with the large amount of data, make the process of geological interpretation extremely time consuming. The key stage of the interpretation workflow with the use of self-learning techniques is the selection of seismic attributes that are highly sensitive to the presence of the objects sought. They include, among others, amplitude attributes (the most common one), frequency, geometric or those calculated on the basis of seismic texture. The latter, describing the spatial relationships of seismic facies, are the subject of this research. GLCM attributes in the interpretation of seismic data, in addition to frequency analysis, have a significant impact on the understanding of the geology of the area under study, both at the early stage of geological reconnaissance across the seismic volumes and in the later, advanced detection of selected prospecting objects. These cognitive processes can take place in a traditional way, through the conventional work of the interpreter, or in an automated manner by the use of ML techniques which are supervised or not.
ATTRIBUTE ANALYSIS METHODOLOGY
It has been almost 50 years since Haralick and his co-authors published a series of articles covering ways to use the statistical Grey-Level Co-occurrence Matrix method (Haralick et al. 1973, Haralick 1979. His work was based on the results of previous mathematical research (authors quoted by Kupidura et al. 2015, Hall-Beyer 2017, however Haralick was the first to propose the use of texture attributes in the image classification process. The GLCM attributes can be divided into three groups (Hall-Beyer 2017): -contrast (contrast, homogeneity, dissimilarity), -orderliness (entropy, angular second moment, energy), -statistics (mean, variance, correlation).
The GLCM is a square matrix and its size depends on the number of grey levels Ng in the analyzed image. Neighborhood relationship analysis is performed for each pixel in the texel, a defined area (x, y) of the image (Fig. 2). These relations are usually determined for four directions (angles α: 0°, 45°, 90° and 135°) and for a specific distance d between the analyzed pixels (Haralick et al. 1973, Hall-Beyer 2017. Typically, the distance d between the reference pixel and the adjacent pixel is 1, but other values can also be used for calculations.
Fig. 2. Texel (x, y) and defined four directions of neighborhood analysis between pixels at a distance d
As already mentioned, the GLCM method was originally dedicated to texture analysis of digital two-dimensional images. Texture refers to the characteristic patterns in an image, defined by the value and variability of samples/pixels at a given location. In such an approach, the 2D seismic section can also be considered as a texture image (Fig. 3A). Then we are dealing with seismic textures formed by the set of seismic reflections, and the pixel values are determined by the size and variability of seismic samples located along the seismic trace (Gao 1999(Gao , 2002(Gao , 2003. Hence the concept of a seismic texel (Fig. 3B), within which the texture parameters (attributes) are calculated for each seismic sample by analyzing the arrangement of adjacent reflections ( Fig. 3C-F). The values of the GLCM matrix are defined by the frequency of coexistence of a reference pixel of a certain grey level i with an adjacent pixel of a different grey level j. The calculation process is schematically represented in Figure 3C, D by means of green and orange rectangles and squares. There is one coexistence of pixels with values 2 and 1 (green color) and two pixel neighborhoods with the values 3 and 4 (orange color). The GLCM matrix is the basis for further statistical analyzes, but before the texture parameters are determined, it should be normalized (Hall-Beyer 2017) (Fig. 3E). Normalization gives the matrix a probability distribution, and it is obtained by dividing the value of each of its elements (i, j) by the sum of all elements (Badurska, 2007).
At this point, it is worth emphasizing the increased informativeness of the presented vertical seismic section with the textural attribute ( Fig. 3F), where it is much easier to see channel-like objects than in the classic amplitude image (Fig. 3A).
In the literature of the subject, several previous articles can be found on the use of the GLCM method for the interpretation and visualization of 2D seismic data (Zhang & Simaan 1989, Vinther et al. 1996, Gao 1999, 2002. In later years, attempts were made to modify the GLCM method in order to determine the possibility of describing seismic structures within 3D seismic volumes. Two interesting papers presenting the results of research on the characteristics of seismic textures based on 3D volumes were published by Gao (2003) and Eichkitz et al. (2013). In this article, the assumptions of the Gao method will be presented, as his work, along with Haralick's, formed the basis for the development of an interpretative tool that was used by the author to study the GLCM attributes: Energy and Entropy.
The geometry of the 3D seismic volume is based on the perpendicular system of inlines (IL) and xlines (XL), in a defined vertical space (Z) (Fig. 4A). A similar geometry has a three-dimensional texel, a mini-cube composed of N IL × N XL × N Z volume picture elements (voxels) (Fig. 4B). The size of the mini-cube is usually adapted to the characteristics of the search objects, however, the optimal number of voxels in the N IL and N XL domains ranges from 3 to 9, while in the N Z domain ranges from 7 to 21 (Gao 2003). In some cases, the size of one of the 3D texel domains may be neglected comparing to the other two. We use this possibility, for example, to capture the horizontal variability of seismic amplitudes in the analyzed interval of the seismic volume, then N IL = N XL >> N Z .
To perform statistical analysis based on 3D texel, equivalent to the GLCM method used in the texture analysis of 2D images, Gao proposed the use of the Voxel Co-occurrence Matrix (VCM) (Gao 1999(Gao , 2003. The VCM is a statistical representation of the set of seismic reflections in a 3D texel, presented in tabular form. Following the Gao's concept, the VCM matrix is calculated per texel for each analyzed sample in the seismic volume. A square, symmetric matrix is constructed of N g × N g elements, where N g is the number of grey levels in the analyzed 3D seismic data. In the VCM matrix, each element E (i, j, α, β) determines the frequency with which, in a given 3D texel, the voxel of amplitude i (<N g ) is neighbored to the voxel of amplitude j (<N g ) in the direction specified by the angles α and β. The layered pattern of reflections in the seismic image makes the VCM different for each of the three perpendicular directions, determined by the domains: N IL (α = 0°), β = 0°), N XL (α = 90°, β = 0°) and N Z (β = 90°). For example, the VCM matrix for the domain N IL (α = 0°, β = 0°) takes the following form of a mathematical expression (Reed & Hussong 1989, modified by Gao 2003: where (x, y, z) represents the size of the 3D texel, S expresses the frequency of the co-occurrence relationship between voxels specified in curly braces, g(m, n, o) and g(p, q, r) correspond to the values of two voxels with the location (m, n, o) and (p, q, r), respectively.
In the presented research, the Petrel E&P software platform was used, which is applied to generate a number of seismic attributes (volume attributes) what also provides the GLCM method. The platform is dedicated here to the analysis of 3D seismic volumes and is used in the detection of such geological elements as mass transport deposits, channels, dewatering structures, salt forms and other structures separating from the seismic background. In the calculation of GLCM attributes, the application uses the VCM method described above, therefore the elements of the matrix are counts of the frequency which voxels with specific values (corresponding to seismic amplitudes) co-occur in the analyzed 3D texel. The variation of grey levels for each sample (voxel) in a 3D volume is calculated for three basic, perpendicular directions, corresponding to the geometry of inlines, xlines and vertically. In order to use the GLCM method, the interpreter defines four parameters necessary to build the matrix: the number of grey levels of the input volume (quantization level), the size of the 3D texel (here a moving window), the distance between the reference and the adjacent voxel and the type of texture attribute to perform statistics. There are two attributes to be chosen: Energy, which is used to determine texture homogeneity, and Entropy, which measures the amount of disorder between samples/voxels. As a result, for each of the calculated texture attributes, three seismic volumes are generated (one in each considered direction along the inline (IL), xline (XL) and vertically (Z); GLCM_IL, GLCM_XL and GLCM_Z) (Fig. 4C, D, E). The first two volumes are characterized by lateral variation in the amplitude values, from seismic trace to trace (intertrace), while the third volume relates to vertical changes within the seismic trace (intratrace).
In the last stage of the GLCM analysis, the obtained attribute volumes are subject to the interpretation process. It can run both with the use of classic vertical and horizontal sections, especially when the purpose of the texture attribute is to emphasize the continuity of seismic reflections or to emphasize structural objects from the seismic image. However, the most effective analysis of GLCM attribute volumes assumes the use of interactive interpretation tools, like RGB blending within a box probe (Fig. 5). Then, apart from interesting texture objects highlighted from the seismic background, the variability of textures within the analyzed element may reflect, for example, changes in lithology or thickness.
THE RESULTS OF ATTRIBUTE ANALYSIS
The analysis was conducted on one of the most interesting Miocene intervals, with a time thickness of 200 ms. Its upper limit was determined by the reference seismic horizon H, close to the gas-bearing level identified in several production wells. GLCM analyses were performed on the volume of 3D seismic data in the processing version with preserved real amplitude relations. As the GLCM method used for the analysis of seismic data uses the seismic amplitude as a sample, this volume choice should ensure appropriate geometric imaging in the results obtained for objects with similar acoustic parameters. During its geological history, the studied area underwent a continuous structural evolution. As a result of tectonic activity and compaction, the initial structural system of the Miocene deposits was distorted. Therefore, horizon flattening along the selected horizon H was applied to the volume of 3D seismic data, during the data preconditioning stage. Thanks to this transformation, in the course of further cognitive processes (using a box probe or RGB blending), genetically related structural elements from different sedimentary environments could be tracked.
Three seismic volumes were generated for each of the directions analyzed by the GLCM method, i.e. two horizontal components and one vertical component. During careful skimming of the composites of the three obtained volumes, for both the Energy and Entropy attributes, several interesting texture objects were noticed (Figs. 6, 7). The presented images come from the upper part of the analyzed interval, located 10 ms below the seismic horizon H (Fig. 8). The similarity of the results of using both attributes, Energy and Entropy, indicates a high degree of their correlation, as they belong to the same group of ordering attributes (Hall--Beyer 2017). However, in both cases, there is a perfect definition of a few anomalous textural features that stand out from the seismic background. Several exploration wells are located in their vicinity, four of which are important due to the existing production tests in the analyzed interval below the seismic horizon H. Well O-6 is negative, no gas flow was recorded as a result of the tests. On the other hand, O-7, O-12 and O-3 are gas production wells with very good reservoir parameters. The texture attributes indicate areas which calibrate well with above exploration wells. In the remaining boreholes, those located in the immediate vicinity of the obtained texture objects, no production tests were carried out for the analyzed interval. Fig. 7. A blended image using RGB color model. GLCM Entropy. Box probe (15 ms high) located 10 ms below the reference seismic horizon H. An arbitrary section I-I' location (see Fig. 8) Fig. 6. A blended image using RGB color model. GLCM Energy. Box probe (15 ms high) located 10 ms below the reference seismic horizon H. An arbitrary section I-I' location (see Fig. 8)
DISCUSSION AND CONCLUSIONS
The legacy 2D seismic data available so far in the study area, apart from the lack of coherence of the seismic image, has at most provided indications of the presence of a potential gas-saturated zone in the form of an amplitude anomaly. Hypotheses of sedimentation environments based on borehole data, even with a large number of wells, are still characterized by the point character of the information and also do not allow the reconstruction of the trap geometry. This modern 3D seismic survey, supplemented by carefully chosen attributes, allowed us to create a stratigraphic model consistent with the borehole data. It replaced the ambiguous results obtained from several older 2D seismic surveys. The aim of the interpreter's work has now become the search for specific shapes and then their identification. As a result, it is possible to diagnose the geological form of a clear genesis and, consequently, to identify potential reservoirs. The texture attributes are a quantitative suite that aids the interpreter in recognizing and detecting those objects more effectively than from the seismic amplitude volume. The conducted research on the selected interval of the Sarmatian sediments brought a lot of relevant information related to this gas-bearing formation.
The results of the work can be summarized in the following conclusions: 1. Contemporary methods of 3D seismic data acquisition and processing provide a huge amount of information about subsurface geology in the form of multi-variant seismic data volumes. For their effective use, it is necessary to apply advanced interpretation tools, which, based on seismic attributes, provide the interpreter with a number of clues in the process of detecting potential prospecting objects. The use of the GLCM method texture attributes in the described case was one of the important elements of the preliminary exploration phase of the seismic data interpretation work. This mainly concerned the stage of the time-consuming analysis of seismic volumes, aimed at detecting potential unconventional reservoirs. 2. The resulting texture images were the starting point for further, now object-oriented, interpretation within a specific seismic layer, a target zone, covering only an interval of about 10-12 m thick. The details of the analyzed deposition environment are interestingly presented by the Entropy attribute of the GLCM_Z volume, calculated along the seismic trace. In Figure 9 geobodies are presented that have been interpreted within the chosen interval, using a box probe with manipulated transparency. For comparative purposes, the results of two other interpretation tools have also been posted for the same seismic layer. The first one (Fig. 10) is the popular attribute of the distribution of mean square RMS amplitude values. The second one (Fig. 11) is a composite image of iso-frequencies 38, 44 and 48 Hz using cyan, magenta and yellow blending (CMY). The texture attribute carries a lot of information about the complexity of the channel system present here. The observed texture changes (in the form of changing colors) most likely reflect the lithological variability of the studied complex. The application of volume texture extraction to three-dimensional seismic data -lithofacies structures exploration... 3. The indicated position within the seismic volume allowed for a quantitative interpretation of the discovered elements of submarine channels. Figure 12A presents the extraction of real seismic amplitudes performed along an offset horizon H', located 5 ms below the seismic horizon H. This map is presented using a dedicated color palette whose task is to show the geometry of the channels, probably crevasse splays and fans visible here. In the presented interpretation, the area of the color zone reflects potential gas-saturated zones. It is an interpreter's subjective assessment, based on information obtained from gas tests result of the analyzed level in boreholes. The information about the negative gas test result in the O-6 well was of key importance for limiting the potential area. The result of the interpretation provides an explanation of the field condition presented here -its genesis and geometry. It also indicates potential areas where the gas field may continue. This is an example of the presence of a lithofacial gas object in the Miocene formations, the geometry of which is not determined by the structural arrangement of the layers. Figure 12B shows an arbitrary seismic section I-I' (same seismic data volume) through the negative and positive wells associated with the channel system under test.
The Miocene deposits filling the Carpathian
Foredeep, due to their lithological and facies diversity, provide excellent conditions for testing and implementing self-learning systems, referred to in the literature as Machine Learning. The presented texture attributes are the desired input components for ML techniques for seismic facies classification. In the case under consideration, the Energy and Entropy attributes show a very high correlation with each other, at the level of 0.9. Therefore, to reduce the attribute space, only one of them will be used in further interpretation studies using ML. Undoubtedly, a helpful tool in the process of selecting attributes will be Principal Component Analysis.
The author wishes to thank PGNiG SA for its permission to publish this paper. He is also indebted to Paweł Pomianowski and Anna Świerczewska, as well as to the anonymous reviewers for their constructive comments which helped greatly to improve the manuscript. | 5,233.2 | 2021-01-26T00:00:00.000 | [
"Geology",
"Environmental Science"
] |
A Computing Offloading Game for Mobile Devices and Edge Cloud Servers
Computing offloading of mobile devices (MDs) through cloud is a greatly effective way to solve the problem of local resource constraints. However, cloud servers are usually located far away fromMDs leading to a long response time. To this end, edge cloud servers (ECSs) provide a shorter response time due to being closer to MDs. In this paper, we propose a computing offloading game forMDs and ECSs.We prove the existence of a Stackelberg equilibrium in the game. In addition, we propose two algorithms, F-SGA and C-SGA, for delay-sensitive and compute-intensive applications, respectively.Moreover, the response time is reduced by F-SGA, whichmakes decisions quickly. An optimal decision is obtained by C-SGA, which achieves the equilibrium. Both algorithms above proposed can adjust the computing resource and utility of system users according to parameters control in computing offloading. The simulation results show that the game significantly saves the computing resources and response time of both the MD and the ECSs during the computing offloading process.
Introduction
The popularity of the Internet of Things (IoT) allows people to enjoy the convenience of the Internet in most scenarios of daily life.Especially for mobile devices (MDs), network services provide convenience and functional possibilities.However, functional and computationally intensive applications consume a large amount of energy and computing time on MDs, such as augmented reality [1] and face recognition [2].Moreover, the MD is characterized by its mobility and portability with the poor CPU performance and limited battery power.To this end, the mobile cloud computing (MCC) is seen as an effective way to solve the problem of a shortage of local resources by offloading the computations to cloud infrastructure with remarkable computational power [3][4][5].The popular approach is for offloading computing tasks to the public clouds such as Windows Azure and Amazon EC2.Although MCC provides considerable cloud resources, it cannot guarantee a low response time.Furthermore, the user experience is reduced due to the delay.
Edge cloud computing (ECC) is promising for mobile computing offloading, which also considers a promoter of 5G mobile networks because they are located near the edge of the network [6,7], and has been extensively studied in recent years [8,9].As illustrated in Figure 1, edge cloud servers (ECSs) are closer to users, which greatly reduces the time for data transmission.Therefore, offloading computations to less resource ECSs is considered a more advantageous solution.Some previous works on ECC focus on reducing energy consumption such as [10,11].Although [12] considers the energy consumption of MDs and cloud servers in computing offloading, it does not analyze the computing performance of MDs and cloud servers.Refs.[13,14] focus on computing performance enhancement.However, ECSs usually leased in real life scenarios rarely attract attention of researchers.
In this paper, we consider the equilibrium problem during the computing offloading process, which not only considers the needs of MDs, but also considers the maximum benefits of service providers.For this reason, we propose a strategy for computing offloading by computing the equilibrium between a MD and ECSs.Liu et al. [15] considered the computing offloading process between a remote cloud server and several ECSs, which concerned the benefits of different levels of service providers.However, they did not pay attention to the needs of mobile users, which also should be taken seriously because of its mobility and portability with limited resource [3].Ref. [16] considered the mobile user that maximized their performance by choosing of the wireless access points for computing offloading.But they did not consider the benefit of mobile users.In this paper, we mainly focus on the features of mobile users, which concludes the issues of mobility, cost, and so on.We designed an efficient computing offloading strategy considering the scenario that a MD executes computing offloading through ECSs.Suppose a MD needs to offload its computing tasks to one of the sets of ECSs.The MD needs to negotiate an offloading policy with the ESCs to optimize the offloading efficiency of both the MD and the ECSs.For this reason, we propose a strategy among a MD and ECSs.Furthermore, we formulate the computing offloading process among the MD and the ECSs as a Stackelberg game.In particular, the MD increases computing efficiency by offloading complicated computation to the ECSs, and the ECSs obtain certain revenue by performing the computations which are offloaded by the MD.An equilibrium between the benefits of the MD and the ECSs is achieved through our proposed strategy.We make three important contributions in this paper.
(i) Realistically considering the real offloading scenario, we formulate the interaction of the MD and the ECSs during the computing offloading process as a Stackelberg game.(ii) We prove the existence of equilibrium in the Stackelberg game.Furthermore, we propose the C-SGA for computing the equilibrium.And we also design the F-SGA for delay-sensitive applications, which greatly reduces response time.(iii) We verify the performance of the proposed algorithms via the simulation experiments.The results show that the proposed algorithms increase the efficiency of computing offloading.In addition, we performed a detailed analysis of the performance of the strategy for the changes in the values of the different parameters.
The rest of the paper is organized as follows.We present the related work in Section 2. We present our system model and formulate the problem in Section 3. We analyze the Stackelberg game of our model in Section 4. We present our algorithms in Section 5. Performance evaluation is provided in Section 6.We conclude this paper in Section 7.
Related Work
Most previous works have been done on computing offloading [17][18][19].The emergence of computing offloading techniques can be traced back to the concept of Cyber Foraging [20], which reduces the computation, storage, and energy of MDs by offloading tasks of MDs to nearby servers with sufficient resources.The main goal of computing offloading includes expanding CPU capacity, saving energy consumption of MDs, reducing service delays, and saving computational cost.Most of the early computing offloading techniques used static partitioning schemes, relying on programmers to statically divide the application into two parts: one part is executed on the MD; the other part is executed on the server.Li et al. [21] proposed a partitioning approach based on energy consumption.The communication energy consumption depends on the size of the transmitted data and the network bandwidth.The computational energy consumption depends on the number of instructions of the program.They obtain optimized program partitioning based on the consumption of computation and communication.Yang et al. [22] proposed a comprehensive consideration of the use of multiple resources, including CPU, memory, and communication costs.They offloaded some tasks on the MD to a nearby laptop with adequate resources.
Proposition of MAUI [23] is to provide a common dynamic computing offloading solution and minimize the burden on developers.The programmer only needs to divide the application into local methods and remote methods without having to make an offloading decision set for each program.In order to solve the problem of excessive transmission delay in wide area network (WAN), researchers have considered offloading tasks of MDs to infrastructure that are closer to the information source.Then, Satyanarayanan et al. [24] first proposed the concept of Cloudlet, which is defined as a trusted, resource-rich computing device or a group of computing devices to provide computing to nearby mobile terminals.Patel et al. [25] proposed the concept of MEC, which provides powerful computing capability in the wireless access network close to mobile users.MEC runs at the edge of the network and is logically independent of the rest of the network, which is important for applications with high security requirements [26,27].In addition, ECSs are particularly suited for dealing with massive analyses and mass data.At the same time, since the ECSs are geographically close to users, the delay of the network responding to the user request is greatly reduced, and the possibility of network congestion in the transmission network and the core network portion is also reduced [28].There have been some previous studies on computing offloading using ECSs [29][30][31].Wang et al. [32] propose a MEC-WPT design for computing offloading by considering multiuser mobile edge cloud system.Ref. [33] explored how infrastructure of edge computing can improve latency and energy consumption relative to the cloud by analyzing multiple types of mobile applications.They demonstrate that the use of edge computing platforms in WIFI and LTE networks can significantly improve the latency of interactive and intensive computing applications.Sardellitti et al. [34] proposed a QoS-based incentive mechanism for mobile data offloading.The incentive mechanism is used in the quality-aware system to stimulate the users' participation and enhance the robustness of the system [35].Neto et al. [36] designed a mobile offloading framework with an original decision engine, which can significantly reduce energy consumption.Some of previous work conducted extensive research on game theory.There has been some research on the game that can be used in computing offloading [37,38].Chen et al. [39] proposed an approach for computing offloading for mobile cloud computing.In addition, they designed a computation offloading mechanism to achieve a Nash equilibrium of the game.Wang et al. [40] proposed an analysis framework based on evolutionary game theory.Xu et al. [41] designed a security-aware incentive mechanism for computation offloading by using game theory and epidemic theory.
System Model
As the primary deployment method for MEC [25], we consider the edge system in this paper consisting of a set of ECSs and several MDs.We assume that a MD decides to offload its computations to a set S = {1, 2, . . ., } of ECSs. denotes the total computation of ECS for all ∀ ∈ S. denotes the computation offloaded from the MD to ECS , ∈ [0, ].
Mobile Device.
We assume that computation offloaded profile is x = ( 1 , . . ., ); given x, the local remaining unoffloaded computation is given by and computations performed locally completely without offloading is given by The cost of local computing for the mobile device is given by where is the modeling parameter.The payment profile is m = ( 1 , . . ., ).Given m, the payment for offloading is given by where the payment is determined by offloading unit price and computation amount , i.e., We consider the consumption of performing computing offloading time as part of the offloading cost, which includes the time to compute local remaining computations and the time to transfer the data needed by computing offloading. denotes the computational capability of the MD, and denotes the transmission capacity of the MD.The total consumption of performing offloading time is given by where represents the time of computing local remaining computations and is given by where represents the complexity of the computation.
𝑜𝑓𝑓 𝑖
represents the time taken to transfer the data needed by computing offloading and is given by where represents the coefficient of the amount of data required by transferring computations.Therefore, the cost of the MD for performing computing offloading is determined by the computing time, the transmission time, and the payment for the ECSs, i.e., We define the local utility Γ as the cost reduction from performing offloading, i.e., Γ = (0) − (x) = (0) − (x) − (x) − (x) .(10)
Edge Servers.
ECSs usually have their own computations to compute as shown in Figure 1.When the ECSs decide whether to perform the computing offloading for the MD, they must take their own computations into account. denotes the revenue for one unit of ECS to perform its own computations, and the computational capability of the ECS .Similar to previous work [42], we ignore the time for transmitting the computation results.
The profit of the ECS is given by where − is the computation for its own users, and denotes the cost of computing .The utility of each ECS , which is the profit improvement by performing computing offloading, is defined as 3.3.Problem Formulation.The strategy among the MD and the ECSs is formulated as a Stackelberg game.Our strategy has two steps as shown in Figure 2. In the first step, the MD proposes a payment profile, denoted by p = ( 1 , . . ., ).
We assume that the MD gives a first initial payment; then the optimal decision of each ECS is obtained by solving the following optimization problem: Next, we obtain the optimal strategy by maximizing the utility of the MD after receiving the decision of the ECS, i.e., max Γ (x, p) where Γ(x, p) is the utility of the MD in (10).
Stackelberg Game Analysis
As discussed above, the MD determines the payment profile of computation offloading to the ECSs, while the ECSs provide corresponding amount of computation.We model the problem as a two-step Stackelberg game among the MD and the ECSs based on the noncooperative game theory.Explicitly, as shown in Figure 2, the MD acts as a leader proposing the payment profile.As followers of the MD, the ECSs can adjust the corresponding decisions.
Stackelberg Game Design.
In this work, we denote by ⋆ the optimal strategy of the ECS , which is the optimal problem of (13), and x ⋆ the optimal strategy profile.In addition, ⋆ denotes the optimal payment for the ECS .A Nash equilibrium of the Stackelberg game is defined as (x ⋆ , p ⋆ ), in which none of the ECSs can further improve its profit by changing strategy.Definition 1.A Nash equilibrium of the Stackelberg game is a strategy profile (x ⋆ , p ⋆ ), if the strategy satisfies the following conditions: where p is the upper bound of the payment , and p is the lower bound.
Nash Equilibrium Analysis.
In this part, we will analyze the equilibrium in the Stackelberg game that we proposed and prove the existence of Nash equilibrium in the Stackelberg game.In order to confirm the existence of Nash equilibrium in our Stackelberg game, we have made the following proofs.We first discuss the existence and uniqueness of Nash equilibrium of the Stackelberg game.
Lemma 2. The strategy profile set of the ECSs is nonempty, convex, and compact.
Proof.First, according to the characteristics of ECSs, we calculate the first-order derivative of Ψ to that is According to the first-order derivative, we calculate the second-order derivative of Ψ to i that is We can obtain the optimal strategy of ECS by taking (16) to zero Then we can obtain the payment's lower bound of ECS by taking to zero, and we can obtain the payment's upper bound of ECS by taking to , Therefore, Lemma 2 is proved completely.
Lemma 3.
The ECS has a unique optimal strategy after receiving the mobile's strategy.
Proof.Obviously, if the MD gives a that > p , the ECS will perform all of its computation for the MD.However, if < p , the ECS does not perform the offloading.When p < < p , the expression of the strategy is given by ( 18), and we have Evidently, the relation (21) implies that ⋆ is an increasing function of , which means that the higher payment the MD offers, the more computation the ECS provides.Equation (22) implies that ⋆ is a concave function of .Since ∈ [0, ], Ψ ( ) is strictly concave in x ⋆ , and thus the strategy is unique and optimal.Lemma 3 is proved.
Lemma 4. For the optimal strategies of ECSs, the MD has a unique optimal strategy.
Proof.The first-order partial derivative of Γ to is The second-order partial derivative of Γ to is We define two auxiliary matrices as follows, and thus, the Hessian matrix of Γ(x ⋆ , p ⋆ ) is given by Furthermore, for any nonzero column vector z, we have From ( 23), we have Thus, we obtain From the inequality (32), Γ(x, p) is strictly concave, and then ( 15) is a convex optimization problem.Since is strictly negative, p ⋆ is unique, which is the optimal strategy of MD.Lemma 4 is proved.
With Lemmas 2, 3, and 4 in place, we prove the following theorem.
Algorithm Design
In this section, the process of strategy is shown in Figure 3.We propose two algorithms, F-SGA and C-SGA, for delay-sensitive services and compute-intensive services, respectively.Generally, delay-sensitive services require strict response time, which requires the system to make decisions quickly.Compute-intensive services require a large amount of computing by the servers.F-SGA, a fast Stackelberg game algorithm, can make decisions quickly due to its simple decision mechanism.C-SGA, a complex Stackelberg game algorithm, is slower than F-SGA in decision making speed, but it provided more accurate price and computation to maximize the benefit of MD and ECSs.F-SGA and C-SGA are described in detail as follows.Let = /3 + 2 /3; 4: Let = ( + )/2; 5: else 6: Let = ( + )/2; 7: end if 8: for all such that ∈ do 9: Calculate ( ) according to (18); 10: end for 11: Calculate Γ(x, p) according to (10); Algorithm 1: F-SGA.
F-SGA.
We propose F-SGA to quickly achieve equilibrium as shown in Algorithm 1.Because the algorithm can quickly obtain the optimal objective for the MD and the ECSs, it is suitable for computing offloading of latency-sensitives applications.
As discussed before, we set two points, denoted as and .Initially, we set = 0, = max ∈ p .Then we describe F-SGA in detail.The ECSs first send their payment to the MD.After receiving the payment of ECSs, F-SGA proceeds to the next step by comparing the difference between and .It means that when the difference of payment from the ECSs is small, we simply compromise the payment of computing offloading.But when the different of payment is large, F-SGA will also quickly determine the payment of computing offloading, but more detailed.
C-SGA.
The algorithm proposed in Algorithm 1 needs less time and has a faster response speed, but it directly determines the payment, which leads to an increase in the cost of computing offloading.We next propose C-SGA, which for all such that ∈ do 5: Calculate ( ) according to (18); 6: end for 7: Calculate Γ(x, p ) according to (10); 8: for all such that ∈ do 9: Calculate ( ) according to (18); 10: end for 11: Calculate Γ(x, p ) according to (10); 12: if Γ(x, p ) < Γ(x, p ) then 13: Let = ; 14: else 15: Let = ; 16: end if 17: end while 18: Let = ; 19: for all such that ∈ do 20: Calculate ( ) according to ( 18 uses the fine iteration to obtain the optimal strategy.C-SGA are shown in Algorithm 2.
In contrast, C-SGA only needs the ECSs to compare the the bound of payment, which not only greatly reduces the computation of the ECSs, but also obtains more optimized payment.Therefore, C-SGA is suitable for situations where the ECSs have less computation resources.The process of C-SGA is summarized as follows.
(1) The MD first sends the initial value of payment.With the strategy (x ⋆ , p ⋆ ), the ECSs compute the optimal computation for offloading based on (18) and send the computing results to the MD.
(2) After receiving the results, the MD calculates the utility function Γ(x, p d ) and Γ(x, p ) of the strategy.Then we compare Γ(x, p ) and Γ(x, p ).If Γ(x, p ) < Γ(x, p ), this implies that the optimal value must be located between and , and thus we set = , = .
(3) Then the MD and the ECSs continue to perform procedures (1) and (2) until − < , where is supposed to make our algorithm more accurate.
Theorem 6.The proposed Algorithm 2 can reach a unique Nash equilibrium.
Proof.Since Γ is strict convex, the optimal strategy p ⋆ is unique.We can obtain p ⋆ by Algorithm 2 to maximize Γ.Then, ECS can determine corresponding x ⋆ to maximize its utility.Consequently, the MD can also obtain a definitive optimal utility with p ⋆ .Therefore, Algorithm 2 can reach a unique Nash equilibrium.
Performance Evaluation
We use extensive simulations to verify our proposed strategy and algorithms.We set up 3 ECSs as the initial default settings for our simulations.The total computation of ECSs is 100.We consider that the MD and the ECSs are placed over a 1 × 1 region.The ECSs are located at grid points in the region, while the MDs are placed uniformly at random.In the simulations, we set the modeling parameter = 1.5 and the computation complexity parameter = 1.
The Utility of the Mobile Device.
In this part, we analyze the changes in the utility of MD as a function of different conditions.First we analyze the relationship between the utility of a MD and the revenue of the ECSs. Figure 4 shows the utility of the MD by varying the value of revenue of the ECSs from their own users.As shown in the figure, regardless of the parameter being 0.4, 0.6, or 0.8, with the increase of the unit revenue, the ECSs prefer providing the computation to their own users.As a result, the amount of computation provided to computing offloading is reduced.Therefore, the utility of the MD decreases.
Then we analyze how the payment of a MD affects the utility of the MD. Figure 5 shows the correlation between the payment form the MD and the utility of the MD under different value of parameter .With the increase of the payment from the MD, the utility of it increases at first.But after reaching a peak, the utility of the MD has dropped.This is because as the payment increases, the ECS provides more computation.However, the payment continues to increase, resulting in an increase in the cost of MD, so the utility is reduced.The high utility of ECSs is attributed to the fact that ECSs are willing to provide computation to their own users, leading to efficient computation offloading.Interestingly, the ECSs achieve less utility when the revenue is large enough.As we know, ECSs are profit driven to provide computation for their users.However, large unit revenue is a double-edged sword for ECSs.Although edge servers are more willing to serve their users, it may result in fewer computing offloading.
The Utility of the Edge Servers.
Figure 7 shows the trend of ESCs' utility as a function of payment for a MD.We set = 0.4, = 0.6, and = 0.8, respectively.As the figure shows, the utility of ECSs begins to increase as the payment of the MD increases, and the utility of ECSs begins to decrease after reaching a peak.At the beginning, due to the increase in the payment, the utility of ECSs increases, but this will increase the cost of the MD, so it will not continue to increase.
Offloading Computations.
In order to evaluate how the unit revenue impacts computation for offloading, we set three different unit revenues for simulation.We set = 0.2, = 0.4, and = 0.6, respectively.As can be seen from Figure 8, the trends of different are similar, and their computation for offloading increases as the payment increases.In other words, in the case of the above three unit revenues, the computation increases as the payment from the MD increases.Note that when the unit revenue is greater than the MD's given payment, the ECSs will not perform any offloading.
Figure 9 shows the relationship between the computation of offloading and the utility of MD.It also shows the relationship between the computation and the utility of ECSs.Through the simulation results, we see that, within a certain range, the greater the computation of offloading, the higher the utility of the MD.At the same time, the utility of ECSs increases.It is well understood that, due to the strategy, when the computation of offloading increases, the utility of the MD will increase accordingly.Of course ECSs will also benefit.We can say with certainty that, within a certain range bound, the more computation performed, the more beneficial to both sides.6.4.The Impact of the Utility and Response Time.We are interested in the impact of that represents the value of accuracy for the proposed strategy.So we set a series of values in the range of 0.2 to 1.5.Figure 10 shows the simulation results.As the value of increases, the accuracy of our strategy increases, and the utility of MD and the profit of ECSs increase.It will be more beneficial to both the MD and the ECSs to calculate the benefits of offloading.
Figure 11 shows the response time of F-SGA and C-SGA using the same conditions during the computing offloading.As can be seen from the figure, as the parameter increases, the response time of C-SGA decreases.However, the response time of the F-SGA remains the same and has been at a low level.This is because as the parameter increases, the C-SGA needs to make more rounds of judgment and iteration, resulting in an increase in response time.But F-SGA can always make decisions quickly, regardless of the value of the parameter .
Conclusion
In this paper, we proposed a game for the computing offloading between a MD and ECSs.We provided a Stackelberg game theoretic analysis and proved the existence of the equilibrium in the Stackelberg game.Furthermore, we proposed two algorithms for different scenarios and provided the upper and lower boundary of the payment.Moreover, multiple optimization results were obtained by regulating model parameters.The simulation results showed that the game is effective in improving the utility of both the MD and the ECSs.
Figure 3 :
Figure 3: The game process of our Stackelberg game.
Figure 4 :
Figure 4: The utility of the MD with different unit reward.
Figure 6 shows the average utility of the ECSs by varying the unit revenue.With the increase of the unit revenue, the utility of the ECSs increases.
Figure 5 :Figure 6 :
Figure 5: The utility of the MD with different payment.
Figure 7 :Figure 8 :
Figure 7: The utility of the ECSs with different revenue.
Figure 11 :
Figure 11: Response time of F-SGA and C-SGA. | 5,966.8 | 2018-12-02T00:00:00.000 | [
"Computer Science"
] |
Design of Low Phase Noise SIPC based Complementary LC-QVCO for IEEE 802.11a Application
: The paper presents the design of a source injection parallel coupled (SIPC) quadrature voltage controlled oscillator (QVCO), realized in a complementary architecture, which is usually preferred in low-power applications as it exploits » 50% bias current reduction with double efficiency compared to the structure with single coupled, when operating in the current-limited regime. A stacked spiral inductor exhibiting a Q factor of 5.8, with pMOS based depletion mode varactor of 32% in tuning range, corresponding to 3.2-3.6GHz of tuning frequency, is implemented in 0.18 m m CMOS technology. The phase noise of the SIPC QVCO architecture simulated at 1MHz of offset frequency is indicated to be -114.3dBc/Hz, while dissipating 11.0mW of core circuit power.
INTRODUCTION
Increasing demand for higher capacity in the growing LAN (WLAN) market has led to the introduction of a new generation of WLAN standards using more spectrally efficient modulation techniques. The 802.11a standards are based on orthogonal frequency division multiplexing (OFDM) modulation, where 52 uniformly spaced carriers are independently modulated with PSK or QAM, hence requires circuit architecture with low amplitude, high linearity and low phase mismatch, thus improved Error Vector Magnitude (EVM) performance. The standard supports data rates from 6 to 54Mbps in the 5GHz unlicensed national information infrastructure (UNII) band (5.15-5.35 GHz) [1].
In the transmitter the PA (Power Amplifier) output contains large spectral components in the vicinity of LO f , leaking through the package and the substrate to the VCO and causing pulling. This effect is known as injection pulling [2]. To alleviate this effect proper frequency planning is utilized in the two-step upconversion mixing action of the RF transmitter [3].
The accuracy in reported QVCO architecture designed utilizing a RC-CR polyphase filter is strongly dependent on the on-chip component matching, whereas the usage of frequency divider in realizing the QVCO topology increases the power consumption and results in quadrature inaccuracy due to any asymmetry in the duty cycle of the master-slave D-flip flop based frequency divider [4]. A cross coupled QVCO topology is exploited to enhance the phase accuracy. In this paper a SIPC based QVCO topology is adapted [5]. By alleviating the noise current flow through the switching transistor from the coupling transistor the up conversion of the 1 f , flicker noise is relaxed.
A stacked spiral inductor with comparable Qfactor and self resonant frequency is designed [6] and integrated into the QVCO architecture to provide frequency tuning via the LC tank configuration. A metal6-metal4 stacked rectangular spiral inductor which provides self shielding effect is implemented and extracted utilizing ASITIC (Analysis and Simulation of Inductors and Transformer for IC's) tool.
A pMOS based capacitor with drain, source and bulk (D,S,B) connected together [7], realizes the frequency tuning of the LC tank. Both in accumulation and inversion region of operation the MOS capacitor exhibit a maximum of oxide capacitance, C ox. This paper is organized as follows. The frequency planning scheme description for IEEE 802.11a application is followed by the review on the design of the stacked spiral inductor, subsequently by the utilized pMOS based capacitor and the description of the integrated complementary based SIPC-QVCO architecture. Simulation results on the realized SIPC based QVCO in 0.18µm CMOS technology is reported prior to the presented conclusion. Figure 1 reports an LO generation scheme utilized in realizing two step up-conversion transmitter in compliance with IEEE 802.11a application. The voltage controlled oscillator (VCO) operates at two thirds of the LO frequency and a divide by 2 circuit produces quadrature outputs at one third of LO frequency. As the VCO operates at two thirds of the LO frequency, this scheme effectively suppresses the injection pulling effect and LO-RF interaction by subsequent stage of PA. The generated LO signal has a cleaner frequency content at the LO frequency, minimizing the adverse effect of the unwanted sideband [8].
ARCHITECTURE AND CIRCUIT IMPLEMENTATION
Stacked Spiral Inductor: Figure 2 illustrates the vertical cross section of the realized stacked inductor, with the indication of substrate and oxide thickness. where L DC+Eddy current , is the equivalent inductance due to the dc self inductance and mutual coupling inductance, R Metal and R Eddy current , denotes the dc metal line and reverse eddy current induction losses, respectively, C S is the series capacitance due to the effect of interwinding and overlapping capacitance effect, whereas C p and R shld are the shield parasitics.
pMOS Varactor
The gate of the device is defined as anode v + , while the source, drain and bulk are tied together, forming the cathode, v -, of the device as described in Figure 4. The varactor gate sided tuning is used to alleviate leakage. Inversion channel with mobile holes builds up for V BG >|V T |, where |V T | is the threshold voltage of the transistor, resulting in an equivalent capacitance, C ox [7]: where A and t ox are the transistor channel area and oxide thickness, respectively. The depletion mode with very few mobile charge carriers, results in a decrease of the equivalent capacitance to C ox +C d , where C d is the series depletion mode capacitance. The varactor Q is defined by [7]: where R V is the series parasitic resistance including the channel resistance and gate resistance, which is reduced utilizing minimal length double sided tapped gate MOS varactor with multi finger realization. C V describes the varactor capacitance, where C V =C ox .W.L.nf, in which W, L and nf corresponds to the width(µm), length(µm) and number of fingers of the varactor, respectively. Figure 5 shows the schematic of the complementary based SIPC-QVCO topology. In contrary to the conventional QVCO architecture, the drain node A of the coupling transistor, M C1 -M C4 are connected directly to the ground (GND) terminal. The quadrature generation is obtained through coupling of two identical oscillators in such a way that forces their outputs to oscillate 90° out of phase, with a tradeoff of two times in area and power utilization of a single LC oscillator [4]. Figure 6 illustrates the inductance and quality factor variation of the designed stacked spiral inductor extracted utilizing ASITIC tool. The designed inductor consumes an area of 100x100µm 2 with 3.25 number of spiral turns. From Figure 6 it is evident that the inductance variation is somewhat constant with frequency. At frequency well below the peak in the inductor Q, the shunt parasitic of the spiral inductor has little effect and consequently the inductive reactance and Q factor increases with frequency. However as the operating frequency continues to rise, the energy dissipation in the semiconducting substrate and the ac resistance of the metallization begins to increase faster than the inductive reactance, thus the Q factor peaks and then decreases. Figure 7 describes the tuning characteristic of the designed pMOS based capacitor. From Figure 7, when the diffusion voltage is constant and the dc voltage applied at the gate V CTRL , is increased the MOS capacitor varies from the inversion region to the accumulation region of operation. The simulated varactor consists of 130 segments with a total gate dimension of 650µm x 0.18µm. The size of each segment is 5µm x 0.18µm. Figure 8 describes the pre-layout phase noise performance of the designed pMOS based SIPC-QVCO in comparison with conventional LC-QVCO topology. It is observed that the SIPC-QVCO has superior close in phase noise suppression. Figure 9 describes the prelayout tuning characteristic of the designed QVCO. The tuning frequency ranges from approximately 3.2-3.6GHz.
CONCLUSION
A low phase noise differential complementary based SIPC QVCO in comparison of the conventional LC-QVCO architecture is presented in compliance with IEEE 802.11a two step up-conversion outlines. An investigation of the stacked spiral inductor and pMOS varactor is performed in optimizing the design of the realized QVCO architecture. | 1,821.4 | 2008-02-28T00:00:00.000 | [
"Physics",
"Engineering"
] |
Search for long-lived heavy neutral leptons with lepton flavour conserving or violating decays to a jet and a charged lepton
A search for long-lived heavy neutral leptons (HNLs) is presented, which considers the hadronic final state and coupling scenarios involving all three lepton generations in the 2-20 GeV HNL mass range for the first time. Events comprising two leptons (electrons or muons) and jets are analyzed in a data sample of proton-proton collisions, recorded with the CMS experiment at the CERN LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. A novel jet tagger, based on a deep neural network, has been developed to identify jets from an HNL decay using various features of the jet and its constituent particles. The network output can be used as a powerful discriminating tool to probe a broad range of HNL lifetimes and masses. Contributions from background processes are determined from data. No excess of events in data over the expected background is observed. Upper limits on the HNL production cross section are derived as functions of the HNL mass and the three coupling strengths $V_{\ell\mathrm{N}}$ to each lepton generation $\ell$ and presented as exclusion limits in the coupling-mass plane, as lower limits on the HNL lifetime, and on the HNL mass. In this search, the most stringent limit on the coupling strength is obtained for pure muon coupling scenarios; values of $\lvert V_{\mu\mathrm{N}}\rvert^{2}$ $\gt $ 5 (4) $\times$ 10$^{-7}$ are excluded for Dirac (Majorana) HNLs with a mass of 10 GeV at a confidence level of 95% that correspond to proper decay lengths of 17 (10) mm.
Introduction
The observation of neutrino oscillations [1][2][3], a mechanism by which neutrinos can change their flavour, implies that at least two of the standard model (SM) neutrinos must have a nonzero mass and that neutral lepton flavour number is not a conserved quantity.Upper limits on the sum of all neutrino masses have been derived from cosmological considerations, whereas the study of particle decays via charged currents (e.g.β-decay of tritium [4]) has allowed upper limits to be set on the mass per lepton generation [5].The smallness of the neutrino masses compared to those of the other SM particles and to the vacuum expectation value of the Higgs potential suggests that there might exist another mechanism, beyond the SM, to explain the fundamental nature of neutrinos.
In this context, a minimal extension to the SM is given by a "seesaw" mechanism [6][7][8][9][10][11], which postulates additional neutral leptons that are singlets with respect to the SM gauge groups and hence can possess an arbitrary mass.Through coupling to the Higgs field, these new particles mix with the SM neutrinos after electroweak symmetry breaking.The resulting mass eigenstates correspond to the three SM neutrinos with small masses and to three nearly sterile heavy neutral leptons (HNLs) that couple to the W and Z bosons in a similar way as the SM neutrinos.However, their coupling strengths are suppressed because of small mixing angles.An overview of the phenomenology of HNLs at the GeV mass scale can be found in Ref. [12].
A common model that incorporates HNLs via the seesaw mechanism is the neutrino minimal standard model [13,14].Models incorporating HNLs are further motivated since, beside neutrino oscillations, they can explain additional phenomena that are not described by the SM: the baryonic asymmetry of the universe and the nature of dark matter [15,16].Phenomenologically, an HNL can be either a Dirac or Majorana particle, N, that is characterized by its mass m N and coupling strengths V eN , V µN , and V τN to electrons, muons, and tau leptons, respectively.The HNL can be long-lived for sufficiently low coupling strengths since its partial three-body decay widths are proportional to m 5 N |V ℓN | 2 , where ℓ ∈ {e, µ, τ} [12].In general, lepton flavour number is not a conserved quantity in HNL interactions.It is only conserved in the special case where only one V ℓN coupling is nonzero.
Searches for HNLs are pursued at various experiments covering a wide range of masses from a few keV up to several TeV [17,18].At the CERN LHC, searches for HNLs are performed employing their production in the decay of mesons or through on-shell W or Z bosons, where the most stringent limits on V eN and V µN can be derived starting at the GeV mass scale.Corresponding analyses have been conducted by the ATLAS, CMS, and LHCb Collaborations [19][20][21][22][23][24][25][26][27][28][29][30][31][32], which mainly target signatures arising from the production of HNLs and their prompt decay to only one lepton generation (e or µ), whereas long-lived HNLs and the possibility of cross-generation lepton couplings are only recently being explored.Various of these experimental results have been statistically combined using the GAMBIT tool [33].
The two most common three-body decay modes of HNLs involve a virtual W boson and result in final states comprising two leptons and a neutrino or one lepton and two quarks with branching fractions of approximately 25 and 50% for m N > 5 GeV, respectively.A signature considered in this search is depicted in Fig. 1, which shows the Feynman diagram for Dirac HNL production at the LHC via an on-shell W boson for m N < m W , and the subsequent HNL decay to a lepton and two quarks.Alternatively, HNLs can also be produced in decays of b hadrons for m N < m b at the LHC, which is not considered in this search.For long-lived HNLs, the decay products are spatially separated (i.e.displaced) from the point where the HNL is produced.Thus, the process depicted in Fig. 1 results in a signature comprising one prompt lepton ℓ 1 , a displaced lepton ℓ 2 , and at least one displaced jet j ⋆ , a collimated set of particles originating from the hadronization of the two quarks.If the HNL is highly Lorentz-boosted, a single jet can also be formed encapsulating all displaced decay products from the HNL, a case that is also considered in this analysis.For Dirac HNLs, the final-state leptons have opposite electrical charges, while for Majorana HNLs they can have either the same or opposite electrical charges with equal probability.
Figure 1: Born-level Feynman diagram for Dirac HNL production and decay via a chargedcurrent interaction.Corresponding diagrams exist also for Dirac anti-HNL and Majorana HNL production and decay.In this search, the HNL decay products, encapsulated by the boxes, can be found collimated within a single jet j ⋆ .
In this paper, a search for long-lived Dirac and Majorana HNLs is performed without assuming that their coupling is exclusive to only one lepton generation.Instead, HNL production is investigated in the full coupling space spanned by V eN , V µN , and V τN for 2 < m N < 20 GeV, where an HNL proper lifetime τ 0 of up to cτ 0 = 10 4 mm can be probed.A data set of protonproton (pp) collisions recorded by the CMS detector at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb −1 is analyzed.Events containing two leptons (e or µ) and jets are selected to target the hadronic HNL decay channel.Several event categories are defined to provide sensitivity to Dirac and Majorana HNL signals, both prompt and displaced, while contributions from background processes are estimated from data.A central feature of the analysis is the identification of displaced jets (with or without an overlapping displaced lepton) using a deep neural network (DNN) that does not explicitly require the reconstruction of displaced vertices.The DNN uses a domain adaptation technique to ensure accurate performance of the resulting classifier in data.The presented search explores an orthogonal phase space compared to Ref. [28], where similar parameter ranges in m N and cτ 0 are probed but events with three leptons and no jets have been investigated instead.
An outline of the paper is as follows: a brief description of the CMS detector and the reconstruction of events is given in Section 2. The real and simulated data sets are detailed in Section 3, followed by a description of the event selection and categorization in Section 4. In Section 5, details of the identification of displaced jets based on a DNN are presented including its architecture and training setup.The determination of the number of events from background processes is described in Section 6.A list of the sources of systematic uncertainties affecting the expected number of signal and background events can be found in Section 7. The results are presented in Section 8, followed by a summary in Section 9.
Tabulated results are provided in the HEPData record for this analysis [34].
The CMS detector and event reconstruction
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintilla-tor hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.Forward calorimeters extend the pseudorapidity η coverage provided by the barrel and endcap detectors.Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [35].
The particle-flow (PF) algorithm [36] aims to reconstruct and identify each individual particle in an event, with an optimized combination of information from the various elements of the CMS detector.The energy of photons is obtained from the ECAL measurement.The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track.The energy of muons is obtained from the curvature of the corresponding track.The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the response function of the calorimeters to hadronic showers.Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.The PF algorithm is able to reconstruct electrons and muons with efficiencies of about 80 and 95%, respectively, for transverse displacements of less than 1 cm.At larger displacements, the efficiencies gradually reduce and approach zero at 40 cm and 1 m, respectively, as determined from simulation.
The missing transverse momentum vector ⃗ p miss T is defined as the projection onto the plane perpendicular to the beams of the negative vector momentum sum of all PF candidates in an event.Its magnitude is referred to as p miss T .Jets are reconstructed from PF candidates and clustered by applying the anti-k T algorithm [37] with a distance parameter of 0.4.The reconstruction of jets is fully efficient with transverse displacements up to the edge of the inner tracking volume.After this, the reconstruction efficiency degrades as displaced charged particles can only be identified through their calorimetric energy deposits.
The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [38].
Events with spuriously high p miss T , originating from a variety of reconstruction failures, detector malfunctions, or noncollision backgrounds, are vetoed by event filters with negligible impact on events with genuine p miss T [39].
Events of interest are selected using a two-tiered trigger system.The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a fixed latency of 4 µs [40].The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage [41].
Data set and simulated samples
The analyzed sample of pp collision data was recorded at √ s = 13 TeV with the CMS detector during 2016, 2017, and 2018.The subsamples by year correspond to integrated luminosities of 36.3, 41.5, and 59.7 fb −1 , respectively.The 2016, 2017, and 2018 data sets are analyzed independently and only combined for the final result to account for differences related to the data-taking conditions and to apply proper corrections and calibrations per year.Events were triggered by requiring at least one electron or muon candidate within |η| < 2.4.Electron candidates must have a transverse momentum p T of at least 27 (32) GeV in 2016 (2017, 2018), and pass additional identification requirements [42].Muon candidates have to fulfil p T > 24 GeV (2016, 2018) or p T > 27 GeV (2017), and have to be isolated from other activity in the event [43].
Samples of simulated signal events are used to evaluate the detector resolution, efficiency, and acceptance for HNL production processes.Additionally, samples of simulated background events are used for understanding the composition of the data and to optimize the analysis strategy.Samples of simulated events are furthermore used to train machine learning algorithms.However, the final results are obtained by determining the contribution from background processes using data in sideband regions.
Samples of HNL production with various values of m N ranging from 2 to 20 GeV, and with 10 −5 < cτ 0 < 10 4 mm, are generated in the five-flavour scheme at leading order (LO) accuracy (i.e.tree-level) using the MADGRAPH5 aMC@NLO v2.6.5 event generator [44].The parton distribution function (PDF) set used is NNPDFv3.1 [45].Parton showering is performed with PYTHIA 8.230 [46] using the underlying event tunes CUETP8M1 [47] (2016) or CP5 [48] (2017, 2018).Each sample is generated assuming an equal coupling strength for the three lepton generations, V eN = V µN = V τN .The resulting events are reweighted to also probe different combinations of coupling strengths.For these, the HNL displacement, determined by the total HNL decay width Γ N , has to be kept constant such that the subsequent detector simulation and event reconstruction do not need to be rerun.The HNL decay width can be written as where the factors A ℓ , calculated by MADGRAPH5 aMC@NLO, describe the dependence of the partial widths per lepton flavour Γ ℓ on m N .Equation (1) describes an ellipsoid spanned by V eN , V µN , and V τN for a given Γ N and m N .Thus, the generated events of a particular sample can be reweighted to any coupling combination on the ellipsoid surface.The barycentric coordinates f e , f µ , and f τ with ∑ f ℓ = 1 are introduced, which denote the relative ratios between the coupling strengths squared |V eN | 2 : |V µN | 2 : |V τN | 2 ≡ f e : f µ : f τ .In total, 66 equidistant weights in f ℓ space are used, which have been calculated by the event generator at the matrix element level [49].The modelling of low-p T jets originating from HNL decays has been validated by using the average charged particle multiplicity and comparing it to previous measurements in e + e − annihilation [50].The HNL production cross sections are calculated at next-to-leading order (NLO) in the strong coupling constant, using the same generator settings, and are found to be approximately 10% higher than the cross sections calculated at tree level for all samples.
Further details on the HNL Lagrangian and the implementation of models for both Dirac and Majorana HNLs can be found in Refs.[51][52][53][54].
The major background processes are the production of vector bosons in association with jets (W+jets, Z/γ * +jets, and Vγ * +jets, where V ∈ {W, Z}), top quark production (tt, single t), and multijet events consisting of jets produced through the strong interaction.Samples of simulated background events are generated at NLO accuracy using the MADGRAPH5 aMC@NLO or POWHEG [55][56][57] 2.0 event generators with the exception of multijet events that are generated at LO with PYTHIA.The NNPDFv3.1 set is used and parton showering is performed by PYTHIA with the same underlying event tunes as used for the signal samples.
The simulated events are overlaid with additional simulated minimum bias collisions ("pileup") according to the distributions inferred from the data per year.All generated events un-dergo a full GEANT4 [58] simulation of the detector response and are subjected to the same event reconstruction as the data.
Event selection and categorization
Events containing two leptons (ℓ ∈ {e, µ}) and at least one jet are analyzed.This signature targets the production and decay of HNLs via charged currents, pp → ℓ 1 N, N → ℓ 2 qq ′ .The first lepton ℓ 1 is expected to originate from the production vertex, while the second lepton ℓ 2 and the jet(s) from the hadronization of the two quarks can be displaced with respect to the PV.The hadronic HNL decay channel targeted by this analysis has a branching fraction of about 50% for m N > 5 GeV, which is approximately twice as large compared to the leptonic decay channel, N → ℓ ± ℓ ∓ ν.Other decay channels occur via neutral currents and result in νqq or ννν final states.Decays to other BSM particles, e.g.lighter HNLs, are not considered in the model used for generating the signal samples.In scenarios where m N ≲ 8 GeV, the HNL is found to be sufficiently Lorentz-boosted with respect to the laboratory frame such that its decay products are collimated inside a single jet.The selected events also include leptonic τ decays to e or µ.Tau lepton decays to hadrons are not considered in this analysis because efficient event trigger strategies with sufficiently low p T thresholds on τ candidates were not available.In the following, the selection criteria for the physics objects are described.
Physics object selection
Two types of candidates are defined for electrons and muons depending on whether they are considered for ℓ 1 or ℓ 2 .The former is used to trigger the event and thus has to fulfil more stringent, tight identification criteria, while the latter is required to pass only relaxed, loose identification criteria instead.This increases the signal selection efficiency in cases when ℓ 2 is displaced and/or clustered inside a jet.
Tight electron candidates are required to have a p T of at least 29 (34) GeV and be within |η| < 2.4 for the 2016 (2017, 2018) data-taking periods.A boosted decision tree (BDT) discriminant is used to identify genuine electrons with an efficiency of ≈90% as measured in Drell-Yan events [42].This BDT is trained using several features of the electron track and of the associated energy deposits in the ECAL, including the relative isolation parameter I rel (e).This parameter is defined as the scalar p T sum of the charged and neutral PF candidates within a cone of radius ∆R = √ (∆η) 2 + (∆ϕ) 2 = 0.3 around the electron candidate, excluding the candidate itself, divided by the electron p T .Here, ∆η and ∆ϕ are, respectively, the pseudorapidity and azimuthal angle measured in radians and relative to the electron direction.The relative contribution from pileup is estimated as A eff ρ and subtracted from the isolation parameter, where A eff denotes an η-dependent effective area, and ρ is the median of the transverse energy density in a δη-δϕ region calculated using the charged particle tracks associated with the pileup vertices.Furthermore, the electron candidate has to originate from the vicinity of the PV by requiring a transverse and longitudinal impact parameter of |d xy | < 0.05 (0.10) cm and |d z | < 0.1 (0.2) cm, respectively, in the ECAL barrel (endcap) region.
Loose electron candidates need to fulfil p T > 5 GeV, |η| < 2.4, and pass a series of loose selection criteria that have been optimized to enhance the acceptance for displaced electrons that can also be clustered within nearby jets, as defined below.The criteria are a modified version of the standard identification requirements [42] but allow for any number of missing electron track hits in the inner tracker.Furthermore, no requirements on the compatibility with the PV or on I rel (e) are imposed.
Tight muon candidates must be within |η| < 2.4, have a p T of at least 26, 29, 26 GeV for the 2016, 2017, 2018 data-taking periods, respectively, and fulfil additional identification requirements optimized for the selection of genuine muons that result in efficiencies of >96% as determined from a data sample of Drell-Yan events [59].In particular, muon candidates are required to be within |d xy | < 0.01 cm and |d z | < 0.05 cm of the PV.Furthermore, the candidates must be isolated with a relative isolation parameter I rel (µ) < 15%, which is defined as the scalar p T sum of PF photons and charged and neutral PF hadrons within a cone of radius of ∆R = 0.4, divided by the muon p T .Contributions from pileup are estimated from the energy deposited by charged hadrons within the isolation cone that are associated with pileup vertices and subtracted from the isolation parameter.
Loose muon candidates are required to pass p T > 3 GeV, |η| < 2.4, and fulfil only minimal requirements necessary for being reconstructed by the PF algorithm [59].Similar to loose electron candidates, loose muon candidates are allowed to be inside jets and do not have to be compatible with the PV.
Events with exactly two leptons of any charge and flavour combination are considered for further analysis, where at least one needs to fulfil the tight candidate requirements.This results in event categories, denoted "ℓ 1 ℓ 2 ", where the first lepton is the tight candidate that is also matched to a corresponding event trigger and has to have p T (ℓ 1 ) > p T (ℓ 2 ) to avoid the double counting of events where both leptons are responsible for a positive decision by the trigger system.
The momentum of each jet is defined as the vectorial momentum sum over all its constituent PF candidates.To mitigate the contribution of additional tracks and calorimetric energy depositions from pileup interactions, PF candidates identified as originating from pileup vertices are discarded and an offset correction is applied to account for remaining contributions [60].Jet energy corrections are derived from simulation so that their average measured energy becomes identical to that of particle level jets.In situ measurements of the momentum balance in dijet, photon+jet, Z+jet, and multijet events are used to determine any residual differences between the jet energy scale in data and in simulation, and appropriate corrections are made.The corrections are propagated to the measured ⃗ p miss T .
The analysis considers jets within |η| < 2.4 with a calibrated p T greater than 20 GeV.Jets that overlap with ℓ 1 within ∆R < 0.4 are ignored, whereas the jet p T needs to be at least 30 GeV if ℓ 2 is within ∆R < 0.4 from the jet.Jets close to ℓ 2 are also ignored if I rel (ℓ 2 ) < 15% to reject jets that are primarily clustered from isolated leptons.The jet that is the closest in ∆R to ℓ 2 is interpreted as the jet from the (displaced) HNL decay and is hereafter referred to as j ⋆ .In simulation this procedure assigns a reconstructed jet correctly to the HNL decay with an efficiency of larger than 95%.Events with more than one displaced jet from the HNL decay passing the event selection constitute a negligible fraction and are hence not explicitly targeted by the selection.
Event categories
The invariant mass m ℓℓj ⋆ is calculated from the summed four momenta of the two leptons and j ⋆ .In signal events, m ℓℓj ⋆ approximates the mass of the W boson.The signal region (SR) is defined for selected events with an invariant dilepton mass of 20 < m ℓℓ < 80 GeV, p miss T < 60 GeV, and consisting of 1-4 jets, to reject Z/γ * +jets, W+jets, and high-p T processes (e.g.tt) with many jets that can additionally be produced in association with neutrinos.Additionally, j ⋆ must be within ∆R < 1.3 of ℓ 2 since in signal events both are expected to be spatially close together and even overlap when the HNL is sufficiently boosted.To suppress contributions from low-p T leptons produced during hadronization, which are often found in W+jets and multijet events, the ratio p T (j ⋆ )/p T (ℓ 2 ) must be smaller than 2-4 depending on the data-taking period and category, since the p T threshold for leptons also varies per data-taking period.Additionally, µ ± µ ∓ events must have m ℓℓ < 70 GeV to further reject the overwhelming Z/γ * +jets background in these categories.After applying all object and event selection criteria, the following approximate fractions of signal events remain when summed over all lepton flavour combinations: 2.5% for cτ 0 ≤ 1 mm, 1.5% for cτ 0 = 10 mm, 0.9% for cτ 0 = 100 mm, and less than 0.1% for scenarios with larger cτ 0 values.These low efficiencies are primarily due to HNLs decaying into low-p T leptons that often do not satisfy the p T thresholds applied as part of the event selection.
A control region (CR), enriched in background events (mainly Z/γ * +jets), is obtained by inverting the SR selection on m ℓℓ , i.e. to be larger than 80 GeV.This region is used for validating various aspects of the analysis strategy such as the modelling of the simulation and the displaced jet tagger (Section 5).
Events in the SR are categorized through a series of criteria to be simultaneously sensitive to various HNL mass and coupling scenarios.First, events are separated depending on the lepton flavour combination (ee, eµ, µe, µµ) for probing different coupling scenarios and on the lepton charge combination, i.e. opposite-or same-sign (OS, SS) events, to be sensitive to Dirac and Majorana HNL production, simultaneously.Furthermore, events are classified as either "boosted" if ℓ 2 overlaps with j ⋆ (i.e.∆R < 0.4) or "resolved" otherwise.Finally, events are split into three subcategories depending on the significance of the transverse displacement d Distributions of m ℓℓj ⋆ in the SR are presented in Fig. 2 for events with OS and SS lepton pairs.The data are found to be described well by the prediction from simulation normalized to the integrated luminosity.A representative signal scenario for Majorana HNL production assuming m N = 10 GeV and cτ 0 = 1 mm with V eN = V µN = V τN is overlaid.A resonance is expected in the m ℓℓj ⋆ distribution for signal events at the W boson mass, while a broader spectrum is found for background processes.The background in events with OS lepton pairs consists primarily of Z/γ * +jets and W+jets events, while Vγ * +jets, tt, single top quark, and multijet processes are subdominant.A peak around the Z boson mass is seen in Z/γ * +jets events since m ℓℓj ⋆ is mainly calculated from the two leptons momenta when the hadronic activity in j ⋆ is low.In SS lepton pair events, multijet and W+jets events get selected because of misidentified leptons and compose the majority of the background.The number of multijet events appears to be slightly overestimated by the simulation resulting in an overall mismatch in normalization between data and prediction, which is however found to be covered by uncertainties.For further analysis, only events in the signal-enhanced region, defined by 70 < m ℓℓj ⋆ < 90 GeV, are kept, whereas the sideband region in m ℓℓj ⋆ is used to estimate the background contributions from data (Section 6).Overall, the total background is of comparable size in both categories and since the Majorana and Dirac HNL production cross sections are identical, a similar sensitivity for both HNL types is expected.
Identification of displaced jets
Displaced jets that originate from the HNL decay products are identified using a jet tagger based on a DNN.The tagger is trained using jets originating from HNL decays with a transverse displacement L xy between 100 µm and 1 m, where the lower threshold corresponds to a factor 2-4 times the position resolution of the PV [61].The DNN is trained on various features of the selected jets and parameterized with respect to L xy , resulting in an optimized multiclass classifier that can be applied for a large variety of jets and displacements.The network is based on the developments reported in Ref. [62], but its setup has been extended in several aspects to account for the specific properties of jets from HNL decays, as detailed in the following.
The DNN architecture consists of approximately 330 000 parameters.The set of input features includes global jet features, as well as specific features for each type of jet constituent.The global jet features are the jet p T , |η|, mass, and area; the fraction of energy carried by the constituents within cones of ∆R = 0.1, 0.2, 0.3, 0.4 with respect to the jet axis; the number of constituents carrying 60 or 90% of the jet energy; the charged, electromagnetic, muon, and electron energy fractions; the variables used in the combined secondary vertex b tagging algorithm [63]; the 1-, 2-, and 3-subjettiness variables [64]; and various event shape observables that are calculated from the constituents in the rest frame of the jet to probe its substructure.In total, 47 global jet features are used.
The features per constituent are grouped into blocks according to their type as follows: • Charged PF candidates: These candidates have an associated track and can thus provide information about the potential displacement of the jet within the tracking volume.The features encapsulate various properties of the track, its displacement with respect to the PV, and whether the track is also linked to a secondary vertex or a PF electron or muon.Up to 25 charged PF candidates are considered per jet, which are sorted according to the significance of their displacement in the transverse plane with respect to the PV.In total, 36 features are used per charged PF candidate.
• Neutral PF candidates: Features from up to 25 neutral constituents are used as input, which are important for identifying jets from HNL decays that occur at the outer edge of the tracking volume, where the track reconstruction efficiency is low.
The neutral candidate features include the likelihood that the candidate stems from pileup interactions as calculated by the PUPPI algorithm [65].The candidates are sorted by either their distance in ∆R to a secondary vertex or by their p T in cases where no secondary vertex has been reconstructed.In total, 9 features are used per neutral PF candidate.
• Secondary vertices: Features from up to four secondary vertices, reconstructed with the inclusive secondary vertex finder algorithm [66], that are found within ∆R < 0.4 of the jet axis and use at least one jet constituent in their reconstruction, are provided as input to the DNN as well.They are sorted by the significance of their displacement in the transverse plane with respect to the PV.In total, 14 features are used per secondary vertex.
• PF electrons/muons: If a charged PF candidate is linked to a PF electron or muon, features that are specific to their reconstruction are used as additional inputs.For electrons, the properties of the Gaussian-sum-filter track [67] and matching clusters in the ECAL are used.For muons, the features include details of the global track fit and the hit pattern in the muon chambers.Up to two electrons and muons are considered per jet, which are sorted according to the significance of their displacement in the transverse plane with respect to the PV.In total, 78 (37) features are used per electron (muon) candidate.
In the first stage of the DNN, the various jet constituent features are compressed through a series of one-dimensional convolutions with varying filter sizes using a kernel size of one.The last convolutional layer can be seen as a bottleneck that forces the DNN to extract only the most discriminating information from the larger number of input features, which is then passed on to the next stage.The compressed features of each block are flattened and concatenated with global jet features and L xy , where the latter acts as a parameter of the DNN [68].The result is then passed through two dense layers with 200 nodes.At this stage, the network splits into one branch to predict the jet class and into another branch to predict the jet domain (i.e.simulation or data), where each branch consists of another series of dense layers.The following jet classes are considered: jets from the hadronization of gluons or quarks; jets from pileup interactions; jets clustered primarily from prompt e, µ, photons, or hadronically decaying τ leptons; displaced jets from the HNL decay with or without displaced e, µ, or hadronically decaying τ leptons.
In general, the intricate modelling of displaced signatures is less well studied compared to prompt ones.Hence, features of displaced jets can possess a different trend in data compared to simulation.The distribution of output discrimination scores from a classifier, trained solely on simulated events, can differ significantly when evaluated on simulation or data.In a previous study, differences of up to 50% have been seen between the selection efficiencies of data and simulation [62].In this search, a domain adaptation technique is used to mitigate such differences and effectively calibrate the response of the tagger for simulated events.Technically, a layer is inserted into the domain branch that reverses the gradients of the loss function with respect to the DNN parameters in the preceding layers.During the training, this forces the DNN to retain only discriminating features from the inputs that are domain-invariant [69], i.e. features that are well described by the simulation.The loss function is chosen to approximate the earth mover distance [70], which yields well-defined gradients and thus stabilizes the ad-versarial training.The relative strength of the domain loss is chosen such that a trade-off is achieved between obtaining a discriminant with approximately equal efficiencies in data and simulation while simultaneously retaining high discrimination between the various jet classes.
The class branch is trained using jets from independent samples of simulated events from various processes.The jets are resampled to obtain a balanced set with equal class proportions as a function of the jet p T and η.Random L xy values are assigned to background jets that are sampled from the distribution of L xy values of true HNL jets [68].The domain branch is trained on jets from data and simulated background events in the CR, where the latter are weighted according to the expected cross section per process.
The best discrimination against SM jets is found by calculating the ratios for each displaced jet likelihood over the sum of the SM background likelihoods.The ratios are monotonically mapped to the range 0-1 for simplicity.Per displaced jet, the L xy parameter is chosen in the range 10 −1 -10 3 mm to maximize the resulting score for each class.For true displaced jets, the score will be the largest when L xy matches the displacement of the HNL, whereas it is randomly distributed for SM jets.The resulting scores are used as follows.For resolved events, the score for displaced jets with and without hadronically decaying τ leptons, P q (j ⋆ ), is evaluated.On the other hand, for boosted events the flavour of ℓ 2 determines whether the score for displaced jets with electrons, P e (j ⋆ ), or with muons, P µ (j ⋆ ), is evaluated instead.Distributions of the resulting scores are shown in Fig. 3 for resolved and boosted categories in the CR and SR.In general, the prediction from simulation, normalized to the integrated luminosity, describes the data well in all regions, except for a slight overestimation of multijet events as seen before in Fig. 2. Selections on the resulting displaced-jet tagger score can reduce the SM backgrounds by several orders in magnitude.For example, a selection of P(j ⋆ ) > 0.6 reduces the background yield by a factor of about 3000 (800) while retaining 10 (17%) of signal events for boosted (resolved) events considering the signal scenario in Fig. 3.In the analysis, optimized thresholds on P q,ℓ (j ⋆ ) are applied ranging from 0.2-0.7 depending on the event category to achieve the best sensitivity, as described later in Section 8.
Estimation of background processes
Various background sources contribute to the SR, with different relative fractions depending on the category.A substantial background contribution originates from Z/γ * +jets production in events with two genuine OS leptons of same flavour.In events with either SS leptons or OS leptons of different flavour, the dominant source of background events is misidentified leptons, which primarily originate from W+jets, Vγ * +jets, and multijet production, whereas events from tt production are less prominent.For final states containing electrons, "chargeflip" backgrounds, where the charge of one of the electrons is misidentified, are also possible.
Contributions from background processes are determined from data to accurately account for the reconstruction effects, selection efficiencies, and object calibrations of background events in the final event categories.This procedure has the additional advantage that no large samples of background events have to be simulated and subsequently calibrated for modelling the background contribution in the SR.
The yields in data, n α X , from three background-enriched sideband regions α ∈ {A, B, C} in each of the 48 categories X per data-taking period are used to determine the background contribution, b D X , in a signal-enriched region.The regions are defined by selecting events to be either above or below optimized thresholds on the P q,ℓ (j ⋆ ) score or on the m ℓℓj ⋆ observable, which are found to be independent from studies of simulated events.These selections partition the SR Figure 4: Schematic of the orthogonal regions in the (m ℓℓj ⋆ ,P q,ℓ (j ⋆ )) plane, that are used to determine the background in region D from data through an ABCD method.The threshold P opt.depends on the category.Regions with P q,ℓ (j ⋆ ) < 0.1 (0.2) for resolved (boosted) events are not considered.The three VRs that are subsets of regions A and C are indicated in lighter shades.The figure is not to scale.
A so-called matrix ("ABCD") method is used, where the pass-fail ratio of an event passing the threshold on P q,ℓ (j ⋆ ) is measured in m ℓℓj ⋆ sidebands (50-70 GeV or 90-110 GeV) and then ap- plied to the observed yield found within 70-90 GeV.The yields b D X are determined through a maximum likelihood fit to data using the following model to properly account for non-Gaussian uncertainties in case of small event yields: where n α ijk is the number of events observed in region α with i denoting the data-taking period, j denoting the event topology, and k denoting the subcategory {ee, eµ, µe, µµ} ⊗ {OS,SS} ⊗ {d sig xy (ℓ 2 ) bins}.Nuisance parameters ⃗ θ that control the effects of systematic uncertainties are constrained through prior probability density functions p( ⃗ θ).A possible signal contamination of r s α ijk in the sidebands is explicitly considered, where r modifies the expected signal yields s α ijk from simulation for the given HNL scenario under consideration.
In addition to the signal strength r, fit parameters κ ij are introduced, for which the fitted values will be found to diverge from unity in the presence of a bias from the ABCD method.Separate κ ij parameters are used per data-taking period and per event topology.In summary, the parameters of this fit are r, b α ijk , ⃗ θ, and κ ij .The validity of the background estimation method is tested by predicting the data yields in three background-dominated validation regions (VRs) that are defined as follows.The first two VRs comprise events within m ℓℓj ⋆ ranges of 65-70 GeV or 90-100 GeV together with selections on the P q,ℓ (j ⋆ ) scores.For the third VR, events within a m ℓℓj ⋆ range of 70-90 GeV that are within an interval in the P q,ℓ (j ⋆ ) scores below P opt.are used.The three VRs in the (m ℓℓj ⋆ ,P q,ℓ (j ⋆ )) plane are sketched in Fig. 4. Another test is performed in an additional VR, defined using a narrow m ℓℓj ⋆ window within 5 GeV of region D, comprising subsets of events from both VR1 and VR2, to test the background estimation method close to region D.
Per VR, each κ ij parameter is determined through a simultaneous fit to 24 independent event categories.Overall, the determined event yields agree well with the observations in all VRs and uncertainties of 10-25% are assigned on b D ijk , chosen based on the most significant deviations of κ ij from unity.These uncertainties are implemented in fits of the SR through log-normal priors on the κ ij parameters.
Systematic uncertainties
The expected numbers of signal and background events can be affected by several sources of systematic uncertainties.Their impact is modelled through nuisance parameters that change the expected events yields and are correlated across all categories and years, where applicable.Most uncertainties only impact the signal prediction since it is obtained from simulation, whereas the number of expected background events is determined from data in sideband regions, as detailed in Section 6.
A set of systematic uncertainties related to the selection efficiencies and calibration of leptons, jets, and p miss T is evaluated for simulated events as described below.These are propagated through the displaced jet tagger by recalculating the scores on the modified inputs where applicable.
Systematic uncertainties in the prompt lepton reconstruction, identification, and trigger efficiencies are accounted for by varying p T and η-dependent normalization factors, derived from data-to-simulation ratios, within their uncertainties.Systematic uncertainties in the identification efficiency of the displaced lepton candidates are taken into account by varying additional scale factors within their uncertainties.These have been derived in J/ψ → µµ events and in asymmetric γ → ee conversion events.Furthermore, an uncertainty in the lepton track reconstruction efficiency is considered, derived from tracks in tt-enriched events.
The jet energy scale in simulated events is modified for all jets using the uncertainty associated with the p T and η-dependent scale factors.The resulting differences are propagated to p miss T .The jet energy resolution is modified in simulated events by either increasing or decreasing the difference in p T with respect to the matched jet at the generator level.Random smearing is used when no generator-level jet is found within ∆R < 0.4.The component of p miss T that is not clustered inside jets, and thus remains uncorrected by the jet energy scale, is varied within its uncertainty.
An uncertainty of 5% in the total inelastic cross section [71] is used when calculating the expected distribution of the number of pileup interactions in data.
An uncertainty in the displaced track reconstruction and jet tagging efficiency, which accounts for differences between data and simulation, is determined using tracks matched to secondary vertices in events from a tt-enriched region.These differences are parameterized as a function of the track |d xy |.A correction and the corresponding uncertainty in the displaced jet tagging efficiency is derived by varying the efficiency of the three most significantly displaced tracks within j ⋆ .These are found to be less than 10% for jets with prompt-like tracks (d xy < 0.1 cm) and in the range 10-20% at larger displacements.Uncertainties in the mistagging efficiency for jets from SM backgrounds are accounted for through the uncertainties in the background estimation.
The factorization and renormalization scales are varied by factors of 2 and 0.5 in simulated signal samples using precomputed weights by the event generator [72].Only residual changes after the selection are taken as uncertainties while the overall effect on the normalization is considered part of the theoretical uncertainty instead.Uncertainties due to the PDF choice are determined by reweighting each event according to the prescribed variations of the corresponding PDF set.
The integrated luminosities of the 2016, 2017, and 2018 data-taking periods are individually known with uncertainties in the 1.2-2.5% range [73][74][75], while the total 2016-2018 integrated luminosity has an uncertainty of 1.6%, the improvement in precision reflecting the (uncorrelated) time evolution of some systematic effects.
Uncertainties resulting from the finite size of the simulated samples are incorporated into the likelihood model using the Barlow-Beeston method [76].
The background yields are determined in-situ using the likelihood model defined in Eq. ( 2), which properly accounts for the statistical uncertainties in the data yields in the sidebands.Additional uncertainties in the range of 10-25% in the background yield are considered to account for the difference in the background estimation per data-taking period and for additional differences between resolved and boosted categories.
In summary, the statistical uncertainties from the sideband regions in the background yields are found to have the largest impact on the determined signal yield for the signal+background hypothesis, which can be as large as 10% depending on the category.Smaller impacts originate from the loose muon reconstruction (7%), the jet tagging efficiency (6%), the loose electron reconstruction (4%), and the jet energy scale and resolution (2%).
Results
The thresholds on the P q,ℓ (j ⋆ ) scores are optimized per category to yield the best discovery sensitivity [77] to the various HNL scenarios as follows.The expected yields and uncertainties from background processes are determined from data in sideband regions and the expected signal yields are taken from simulation, such that no bias with respect to the observed data can occur.The optimal thresholds are found to be within the range 0.2-0.7,depending on the event category.The resulting background yields are compared to the observed number of events in Fig. 5.The events in data are found to agree well with the estimated number of background events in each category.
Upper limits on the HNL production cross sections at 95% confidence level (CL) are determined as functions of m N and the absolute values of the couplings strengths squared |V eN | 2 , |V µN | 2 , and |V τN | 2 .A modified frequentist approach is employed, which uses the profile likelihood ratio as the test statistic [78], the CL s criterion [79,80], and the asymptotic formulae [81] to approximate the distributions of the test statistic under the background-only and signal-plusbackground hypotheses.
Two-dimensional exclusion limits on Dirac and Majorana HNL production are shown in Figs. 6, 7, and 8 for scenarios of pure coupling, of mixed coupling, and of democratic couplings to all lepton generations, respectively.A broad parameter space in mass and coupling values is excluded by this search.For m N ≲ 8 GeV, most exclusion limits roughly follow a constant cτ 0
fb
Figure 5: Observed number of events and predicted number of background events per category for (left) resolved and (right) boosted categories.The bin label denotes the flavour of the prompt (ℓ 1 ) and displaced (ℓ 2 ) lepton as ℓ 1 ℓ 2 .Two representative signal scenarios for Majorana HNL production with equal coupling to all lepton generations are overlaid.The lower panels show the ratio of the data to the predicted background.The hatched band shows the total systematic uncertainty in the predicted background.value.At higher masses, the cross section becomes too low and, at the same time, sensitivity to displaced scenarios is lost causing the limit curve to turn.At m N ≳ 14 GeV, the limits have transitioned into a prompt regime and follow a constant cross section value with negligible dependence on m N for m ℓ,q ≪ m N ≪ m W .The sensitivity rapidly deteriorates towards the pure τ lepton coupling scenario since ττ+jets events are only selected in the analysis in the case of leptonic τ decays to e or µ, whereas τ lepton decays to hadrons are not considered.No limits can be derived for scenarios with m N ≲ 3 GeV that are close to the pure τ lepton coupling case, because of the tau mass.For some HNL scenarios, the results are compared to an orthogonal search exploiting N → ℓ ± ℓ ∓ ν decays, where the two leptons form a displaced vertex [28], which prevents sensitivity to prompt scenarios, resulting in a different trend in the limits at high masses.In this search, the sensitivity to prompt scenarios is achieved by the displaced jet tagger, in part due to the absence of any requirement on the presence (or otherwise) of reconstructed secondary vertices.The best limits are obtained for pure muon coupling scenarios due to the excellent muon identification performance.Coupling strength values as low as |V µN | 2 > 5 (4) × 10 −7 are excluded for Dirac (Majorana) HNLs with m N = 10 GeV at 95% CL that correspond to proper decay lengths of 17 (10) mm.Limits on the HNL mass and proper lifetime are presented in Figs. 9 and 10, respectively, as functions of the relative coupling strengths to the three lepton generations, defined as ).The results are obtained by interpolating the logarithmic value of the limits linearly between neighbouring points in f ℓ -space.The most stringent limits are found for pure muon coupling scenarios.
The results obtained from the hadronic HNL decay show a comparable sensitivity as previous HNL searches targeting the orthogonal leptonic final state by the ATLAS, CMS and LHCb Collaborations [20,21,25,26,28,31,32].In particular, the presented results for the pure electron coupling scenario are found to be more stringent for m N ≲ 4 GeV.These are the first results reported that involve a prompt or long-lived Majorana or Dirac HNL that couples to all three lepton generations in the 2-20 GeV mass range.
Summary
A search is presented for long-lived heavy neutral leptons (HNLs), which are predicted in extensions of the standard model of particle physics through a seesaw mechanism.Dirac or Majorana HNLs can mix with the three standard model lepton generations in a nontrivial way, resulting in lepton flavour number violation.Hence, a complete set of coupling scenarios involving all three lepton generations is considered.A novelty of this analysis is the simultaneous sensitivity to prompt and displaced scenarios through the use of a dedicated displaced jet tagger that does not explicitly rely on the presence of secondary vertices.
A data sample of proton-proton collision events recorded with the CMS experiment at the CERN LHC at a centre-of-mass energy of 13 TeV is analyzed, corresponding to an integrated luminosity of 138 fb −1 .Events containing two leptons (electrons or muons) and jets are selected and categorized according to the lepton flavour and electrical charge, the displacement of the lower-momentum lepton, and whether the lepton overlaps with a nearby jet.Jets originating from the decay of a long-lived HNL are identified through a deep neural network using various features of the jet and its constituent particles.The network training relies on simulated event samples that cover a broad range of HNL masses and lifetimes, and acts as a powerful discriminant for jets that are spatially separated from the luminous region, even in the absence of reconstructed secondary vertices.
Contributions from background processes are determined from data in sideband regions.No excess of events in the data over the expected background is observed.Upper limits on the HNL production cross section are determined as functions of the HNL mass and the three coupling strengths to each lepton generation.Exclusion limits are presented in the couplingmass plane, as lower limits on the HNL lifetime, and on the HNL mass.Results are provided for Dirac and Majorana HNL production considering various coupling combinations.The most stringent limit on the coupling strength is obtained for pure muon coupling scenarios, with values of |V µN | 2 > 5 (4) × 10 −7 excluded for Dirac (Majorana) HNLs with a mass of 10 GeV at a confidence level of 95% that correspond to proper decay lengths of 17 (10) mm.This analysis is the first HNL search at the LHC that targets long-lived and hadronically decay- sig xy of ℓ 2 with respect to the PV; d sig xy is defined as d xy /σ xy , where d xy and σ xy are the transverse impact parameter and its uncertainty, respectively, as determined by the lepton track fit.The d xy /σ xy parameter is chosen because potential mismeasurements in d xy and σ xy cancel each other out in the ratio and its distribution in the CR is found to be well described by the simulation.Events are grouped by the d sig xy values into prompt-like (d sig xy < 3), displaced (3 < d sig xy < 10), and very displaced (d sig xy > 10) subcategories that probe a wide range of HNL lifetime scenarios.In total, this results in 48 independent event categories.
Figure 2 :
Figure2: Distributions of m ℓℓj ⋆ for events with (left) OS leptons and (right) SS leptons in the signal region.A representative signal scenario for Majorana HNL production with equal coupling to all lepton generations is overlaid with its expected cross section scaled up as indicated in parentheses.The hatched band shows the total experimental systematic uncertainty in the simulated background prediction including the uncertainty from the finite sample size.The bottom panel shows the ratio of data over the prediction.
Figure 3 :
Figure 3: Distributions of the displaced jet tagging score for (left) resolved and (right) boosted categories: (upper row) control region; (middle row) signal region with OS leptons; (lower row) signal region with SS leptons.A representative signal scenario for Majorana HNL production with equal coupling to all lepton generations is overlaid with its expected cross section scaled up as indicated in parentheses.The hatched band shows the total experimental systematic uncertainty in the simulated background prediction including the uncertainty from the finite sample size.The bottom panel shows the ratio of data over the prediction.
Figure 6 :
Figure 6: Expected and observed 95% CL limits on (left) Majorana and (right) Dirac HNL production as functions of the HNL mass and coupling strengths for (upper row) pure electron, (middle row) pure muon, and (lower row) pure τ lepton coupling scenarios.For the last coupling case no limits are derived for m N ≲ 3 GeV because of the tau mass.The dashed-dotted line shows the result of an orthogonal CMS analysis targeting HNL decays to leptons.
Figure 7 :
Figure 7: Expected and observed 95% CL limits on (left) Majorana and (right) Dirac HNL production for various coupling scenarios as functions of the HNL mass and coupling strengths: (upper row) mixed e-µ couplings; (middle row) mixed e-τ couplings; (lower row) mixed µ-τ couplings.The relative ratios of the coupling per lepton generation are indicated in the plots.
Figure 8 :
Figure 8: Expected and observed 95% CL limits on (left) Majorana and (right) Dirac HNL production for the democratic couplings to all lepton generation scenario as functions of the HNL mass and coupling strengths.
Figure 9 :Figure 10 :
Figure 9: Observed 95% CL lower limits on the (left column) Majorana and (right column) Dirac HNL mass as functions of the relative couplings to the three lepton generations considering a fixed proper decay length of (upper row) 0.1 mm and (lower row) 1 mm.The limits are determined for m N > 3 GeV.ingHNLs in the 2-20 GeV mass range, with inclusive coupling to all three lepton generations.The results show comparable sensitivity to an orthogonal analysis that targets long-lived HNLs decaying to leptons. | 12,887 | 2023-12-12T00:00:00.000 | [
"Physics"
] |
Development of a Method for Detecting and Estimating Moniliophthora roreri Spore Loads Based on Spore Traps and qPCR
Frosty pod rot, caused by Moniliophthora roreri, is the most damaging disease of cacao in Latin America and, to better comprehend its epidemiology, we must understand its dissemination and proliferation. However, we do not know how M. roreri spores loads fluctuate in time and space due to the lack of a reliable technique to quantify M. roreri spores in the fields. Therefore, we developed a method that relies on spore traps and qPCR to detect and quantify M. roreri spore loads. This study demonstrated that the qPCR protocol can detect down to 0.025 ng of M. roreri DNA and quantify between 0.006 ng and 60 ng. Moreover, it demonstrated that qPCR protocol can detect and quantify DNA extracted from spore suspension and spore traps containing at least 2.9 × 104 M. roreri spores. However, the variability of the estimates for spore samples was high. Finally, we described a spore-trap device designed to carry spore traps in the field. The qPCR protocol and spore-trap device here developed will help in the understanding of the M. roreri dissemination patterns since they can be used to assess the environmental loads of M. roreri spore in cacao fields.
Introduction
Frosty pod rot (FPR), caused by the basidiomycete Moniliophthora roreri, is the most prevalent and severe cacao disease in Latin America [1]. This disease causes production losses between 16% and 100% depending on the growing region and agronomic factors [1][2][3]. In Colombia, the production losses derived from FPR are close to 40% but can be 100% in some plantations [4]. FPR exclusively affects the cacao pods, beginning as chlorotic spots on the pod's exterior, which turn dark brown as the disease progress. In severe diseases, brown spots grow and cover the pods' surface. Then, pods turn white and powdery as M. roreri mycelia and spores become visible [2,5]. Spore-covered pods can carry about seven billion spores, each capable of initiating a new infection. Understanding how M. roreri spores disseminate is critical for the pathogen's epidemiology and designing control strategies to mitigate FPR losses [6].
Only a handful of M. roreri studies have evaluated the spore dissemination in the field or the environmental spore loads, and their results are mostly inconclusive [2,[5][6][7][8][9]. Still, we have gained some insights. The literature shows that M. roreri environmental spore loads vary in time and space and that climatic variables influence them at different scales [3,5,6,8]. On a small scale, mist, wind, and rain are critical since they move M. roreri spores away from the inoculum source (i.e., sporulated pod) [10]. Multiple evaluations have shown that FPR incidences and M. roreri spore loads decrease as they move away from the inoculum source until they plateau and remain at low levels [5,7]. These low levels of spore loads are critical for M. roreri disease cycle since they constitute a background inoculum, always present in cacao plantations and ready to initiate an FPR infection [4,5,7]. The distance from the inoculum source at which M. roreri spore loads plateau is unclear. Some studies suggest that spores can travel more than one kilometer without reaching this plateau, while others indicate distances below 375 m [4,5,7]. It is also unknown whether the spore loads will eventually drop to zero at farther distances.
Inconsistencies are also found in studies addressing the M. roreri spore dissemination and environmental spore loads at larger scales. For example, two studies evaluating the daily spore load variation found that the highest concentration of M. roreri spores occurred around noon [5,8], while another found that it occurred at night [11]. On a larger temporal scale, some studies have found that dry months with relatively high temperatures (close to 30 • C) favor the long-distance spread of the pathogen and relate to increased spore loads in the environment [2,5,8,9,11]. However, this association was weak since it was supported by noisy data [5,8].
The inconsistencies in the M. roreri literature regarding spore dissemination and environmental spore loads might come from the use of outdated methods. Half of the evaluations are nearly three decades old [5,7,8], and most used spore traps and microscopy to collect, identify and quantify spores [5,8,11]. This approach might be appropriate for some fungal pathogens [12]. However, M. roreri spores have variable shapes and sizes due to their conidiogenetic process [11,13]. Therefore, using microscopy to identify and quantify them can lead to errors. An alternative to microscopy is to grow spores in spore traps in culture media and quantify colonies [14]. M. roreri colonies can take several weeks to develop and there is no culture media specific to M. roreri. Therefore, growing trapped spores in culture media is also not feasible for M. roreri since it is time consuming and colonies can be overgrown by other fungi in the environmental samples [15].
Quantitative PCR (qPCR) is a fast and reliable alternative to microscopy and colony culture. Several studies have successfully coupled spore traps with qPCR to analyze the environmental spore loads of several plant pathogens [16][17][18][19], but none have used it for M. roreri. This study aimed to develop a technique coupling spore traps with qPCR for detecting and quantifying M. roreri spores. Such a technique could facilitate future studies evaluating the environmental M. roreri spore loads in cacao plantations. During this study, we developed a qPCR protocol specific to M. roreri, which was validated following the MIQE Guidelines [20]. Then, we used this protocol to detect and quantify M. roreri spores in suspensions and spore traps. Finally, we describe a spore trap device designed for carrying the spore traps in the cacao fields. The qPCR protocol and spore trap device here develop are useful for the understanding of the M. roreri epidemiology since they will be used in further evaluations to asses the M. roreri spore loads in cacao plantations with FPR prevalence.
Fungal Strains and Cultures
The M. roreri strains used in this study were isolated from cocoa pods with late FPR symptoms collected from commercial farms in representative cacao-growing regions in Colombia (Table S1). Specifically, we hit the symptomatic pods over ×0.5 potato dextrose agar PDA (OXOID, Cheshire, UK) plates supplemented with kanamycin (Thermo Fisher Scientific, Boston, MA, USA) at 50 µg/mL to release M. roreri spores. Plates were incubated at 30 • C for three days. Single-germinated spores were transferred to plates containing malt extract agar (MEA) (OXOID, Cheshire, UK) using a needle and a stereomicroscope Discovery V12 (Zeiss, Germany). Then, they were incubated at 30 • C for nearly one month (the time required by the colonies to grow and sporulate). Spores were washed off MEA plates with sterile 20% glycerol (Thermo Fisher Scientific, Boston, MA, USA) and stored at −80 • C as 20% glycerol stocks until needed.
We attempted to isolate Moniliophthora perniciosa from cacao branches with witches' broom symptoms and fungal signs without success. Therefore, the M. perniciosa DNA was extracted from a basidiocarp collected from one of the commercial farms sampled for M. roreri isolations (Table S1). The remaining fungal strains used in these evaluations came from the EAFIT University culture collection, where they were also kept at −80 • C as 20% glycerol stocks (Table S1).
Fungal strains were activated at 30 • C in MEA plates and grown in Sabouraud broth cultures (Merck, NJ, USA) for 48 h at 200 rpm and 30 • C to produce mycelia for DNA extractions. The M. roreri MR2 strain was grown at 30 • C in MEA plates until sporulation to obtain M. roreri spores. Spores were washed off the MEA cultures with 0.05% tween 80 (Merk, NJ, USA) and their concentration was adjusted using a Neubauer chamber (Boeco, Germany) as required. The resulting spore suspensions were used for DNA extraction from spore suspensions and to inoculate spore traps.
The identity of the fungal strains and M. perniciosa DNA were confirmed by analysis of partial regions of the internal transcribed spacer (ITS) of the ribosomal DNA. The ITS fragments were PCR amplified with the ITS1 and ITS4 primers [21] (see PCR amplification). The PCR products were Sanger sequenced using the same primers (ITS1 and ITS4). Sequences were processed, and the taxonomic identity was assigned using the Basic Local Alignment Search Tool (BLAST) and the NCBI database in the platform Geneious Prime (version 2020.2.4, New Zealand) (https://www.geneious.com accessed on 1 December 2022).
DNA Extractions
We used two DNA extraction methodologies, one for extracting DNA from mycelia, and the other from spore suspensions, spore traps, and M. perniciosa basidiocarp. For the former, the mycelium was harvested from the Sabouraud broth cultures and homogenized using liquid nitrogen, a mortar, and a pestle. Then, the DNeasy PowerSoil kit (Qiagen, Germany) was used to extract DNA from the homogenized mycelium, following the manufacturer's instructions. For the latter, a modified protocol published elsewhere was implemented [22]. For spores suspensions, 1 mL of M. roreri spore suspension containing 2.9 × 10 6 , 2.9 × 10 5 , or 2.9 × 10 4 spores per ml was placed in 50-mL falcon tubes and centrifugated at 4500 rpm for 10 min to collect the spores. For M. roreri spores in spore traps, 1 mL of the same spore suspension was spread on spore traps, consisting of 2.5 cm × 6.5 cm sections of crystal-clear adhesive tape (Tesa, Switzerland) attached to microscopy slides with the sticky side facing outwards ( Figure S1). Spore traps were air-dried, cut into 0.7 cm × 0.7 cm pieces to facilitate DNA extraction, and placed in 50-mL falcon tubes. For M. perniciosa basidiocarp, 100 mg of fresh-weight tissue was placed in 50 mL falcon tubes. Ballotini beads of 4-and 2-mm diameter (~3 mL) were added to the tubes, and samples were mechanically disrupted six times for 30 s using a vortex (Labnet S0200 Model VX-200 Vortex Mixer) at maximum speed, with submersion in liquid nitrogen between disruption cycles to avoid DNA degradation.
Then, they were resuspended in 50 µL of TE buffer (Bio Basic, Markham, ON, Canada) containing 0.05 mg/mL of RNase A (Thermo Fisher Scientific, Boston, MA, USA) and incubated at 37 • C for 30 min. The RNase A was deactivated at 65 • C for five min, and the DNA suspensions were kept at −20 • C until needed.
The DNA concentration and quality were assessed using a NanoDrop 2000 (Thermo Fisher Scientific spectrophotometer, USA). The DNA integrity was evaluated by electrophoresis using five µL of the extracted DNA in agarose (Amresco, OH, USA) gels at 1%. Gels were run for 90 min at 70 V and visualized using an Enduro GDS gel visualizer (Labnet, NJ, USA). The DNA concentration was adjusted to 3 ng per µL to maintain consistency in the evaluations unless otherwise stated.
PCR Amplification
Primers in these evaluations targeted ITS regions of the ribosomal DNA, including generic ITS1 and ITS4 primers [23] and M. roreri-specific Mr_ITSF and Mr_ITSR primers (Table S2). For designing the Mr_ITSF and Mr_ITSR primers, we identified ITS regions conserved in M. roreri but no other fungi from the GeneBank, including the close relative M. perniciosa (Table S2). The alignment and primer design used the global alignment with free end gaps and the primer design functionalities of the Geneious prime application (version 2020.2.3). For conventional PCR amplification, 2 µL of the extracted DNA were used in 20 µL reactions of EconoTaq PLUS (Lucigen, WI, USA) with the generic (ITS1 and ITS4) or the specific (Mr_ITSF and Mr_ITSR) primers at 0.5 mM. Thirty-four amplification cycles were carried out in a BIO-RAD T100 Thermal Cycler (Bio-Rad, CA, USA) with an annealing temperature of 57 • C and an extension time of 1 min. The remaining conditions followed the manufacturer's specifications. The PCR products were visually inspected by loading five µL of the amplification products into agarose gels at 1.2% that were run and visualized as before.
qPCR Optimization
To establish the best quantitative PCR (qPCR) conditions, we performed two preliminary evaluations, one assessing varying annealing temperatures and another primers concentrations. In these evaluations, the qPCR reactions consisted of 2 µL of the extracted DNA in 10 µL reactions of Universal IT SYBR Green supermix (Bio-Rad, CA, USA) with the Mr_ITSF and Mr_ITSR primers. The evaluations were repeated twice using DNA extracted from the mycelia of M. roreri strains MR1 and MR2 and three technical replicates per sample (Table S1). Three replicates of M. perniciosa basidiocarp DNA and H 2 O were also included as negative and non-template controls.
The primers' concentration was set at 0.25 mM for the first evaluation assessing annealing temperatures. The amplification used the CFX96 real-time system (Bio-Rad, CA, USA) with a PCR program consisting of a denaturing step of 3 min at 98 • C followed by 33 cycles of 30 sec at 98 • C, 30 s at annealing temperatures ranging between 55 • C and 64 • C (Table S3), and 15 sec at 77 • C. The DNA was quantified at the end of each cycle, and dissociation curves followed the last cycle following the manufacturer's specifications. The second evaluation assessing primers concentrations included concentrations between 0.2 mM and 0.4 mM (Table S3). These evaluations used the same qPCR reaction and amplifications program, but the annealing temperature was set at 62 • C, considering the results of the first evaluation.
For both evaluations, the mean and standard deviation (SD) of the cycle thresholds (Ct) were calculated considering the three technical replicates of the two repetitions (n = 6). Differences between Cts means were evaluated using anova followed by a Tukey's range test with the anova and emmeans functions of the R libraries stats (version 4.0.4) and emmeans (version 1.8.0) [24,25]. As for the PCR products, qPCR products were visually inspected in agarose gels at 1.2%. Dissociation curves were also considered. A qPCR reaction was considered only when they had a single band in the gels and single-peak dissociation curves.
qPCR Characterization and Validation
The reactions and amplifications for the qPCR characterization and validation used primer concentrations of 0.3 mM and 37 cycles with an annealing temperature of 62 • C, considering the results of the qPCR optimization. The remaining factors were kept the same unless otherwise stated, including the two repetitions using three technical replicates per evaluation, which were analyzed as before, and including negative (M. perniciosa DNA) and non-template (H 2 O) controls. To assess the specificity of the qPCR, we used 6 ng (2 µL at 3 ng/µL) of DNA extracted from the mycelia of M. roreri and non-M. roreri strains and M. perniciosa basidiocarp (Table S1).
The qPCR efficiency was calculated using a standard-curve analysis [20,26]. Specifically, Ct values were estimated for serial dilutions (×1/10n) of the DNA extracted from the mycelia of M. roreri strain MR2 with concentrations between 0.0003 and 30 ng per µL. A linear model was used to correlate Ct values with the logarithm with base ten (log10) of the DNA concentrations, assuring that the model had no deviation from linearity, homogeneity of variance, or normality by visual inspection. The model estimates were used to determine the qPCR efficiency according to Equation (1).
E denotes the qPCR efficiency, and m is the slope of the linear model [20,26]. These analyses used the function lm of R library stat (version 4.0.4) [23], and the results were visualized using the stat_poly_line and stat_poly_eq functions of the R library ggpmisc (version 0.0.5) and the R library ggplot2 (version 3.3.3) [27]. This evaluation was also repeated twice but used ten technical replicates per sample instead of three. Negative and nontemplate controls were also included in each qPCR. The dilution with 0.0003 ng of DNA per µL was excluded from the analysis since it was below the linear dynamic range of the qPCR [20,26].
The qPCR's 95% detection limit (LOD) was calculated using the logit approach [26]. Specifically, the probability of detecting M. roreri in a sample containing M. roreri DNA, i.e., a true positive, was estimated for the same serial dilutions used for the qPCR efficiency estimation (DNA ng/µL between 0.0003 and 30). For this evaluation, a positive qPCR reaction was defined as a qPCR reaction yielding a Ct of at least 30 cycles since non-template and negative controls had Cts over 33. The probabilities of a true positive were fitted into a general linearized model (GLM) using the Logit link function, the binomial error family, and the log10 of the DNA ng (DNA ng between 0.0006 and 60) as the predictor. The GLM was used to estimate the ng of DNA associated with the probability of obtaining a true result 95% of the time (i.e., 95% LOD). This analysis used the GLM and predict functions of the R library stat (version 4.0.4) and the R library ggplot2 (version 3.3.3) for visualization [24,27].
To assess whether the qPCR could detect and quantify DNA from M. roreri spores, we extracted DNA from spore suspensions and spore traps containing 2.9 × 10 6 , 2.9 × 10 5, and 2.9 × 10 4 spores. The extracted DNA was used in qPCR reactions as before. In this case, the evaluations were repeated two times (i.e., two qPCR runs), including three biological replicates each with two technical replicates per sample (Table S1). These evaluations also included replicates of serial dilutions (×1/10n) of the DNA extracted from the mycelia of M. roreri strain MR2 with concentrations between 30 and 0.003 ng per µL, as standard curve, and replicates of M. perniciosa basidiocarp DNA and H 2 O as negative and non-template controls. The Cts of the serial dilutions of strain MR2 were linearly correlated with the log10 of the DNA concentrations. Then, the resulting linear model was used to estimate the DNA ng in the spore suspension and spore trap samples [28]. Then, DNA ng estimates were used to assess the inter and intra-qPCR run variability. This analysis used the lm and predict functions of the R library stat (version 4.0.4) [24].
Results
The initial step for developing a qPCR protocol specific to M. roreri was to design a pair of M. roreri-specific primers. We decided to focus on the ITS region of the ribosomal DNA, as sequences for this region are the most abundant for M. roreri and closely related fungi. Sequence alignment of fungal ITS revealed potential primer-binding sites that distinguished between M. roreri and other fungi, including the close relative M. perniciosa. Therefore, a pair of primers (Mr_ITSF and Mr_ITSR) was designed to target these regions. Several single-nucleotide polymorphisms (SNPs) were found between M. roreri and fungi from different genera in these primer-binding sites, but only a few between M. roreri and M. perniciosa. Despite their lower SNP number, the Mr_ITSF and Mr_ITSR primers likely distinguished between both Moniliophthora species since SNPs were located towards the primers' 3 -end ( Figure S2). Therefore, we decided to continue with this primers pair.
As expected, Mr_ITSF and Mr_ITSR primers distinguished M. roreri from other fungi, including M. perniciosa, in the conventional PCR assay. While the generic primers (ITS1 and ITS4) amplified nearly 550 bp ITS segments in all evaluated fungi ( Figure S3, lanes 2-10), the Mr_ITSF and Mr_ITSR primers amplified about 120 bp ITS fragments only from M. roreri strains MR1 and MR2 ( Figure S3, lanes 12-20). Therefore, we proceeded with the qPCR evaluations and the optimization of the qPCR conditions. In qPCR, Mr_ITSF and Mr_ITSR primers behaved best at concentrations of 0.3 mM and with an annealing temperature of 62 • C. Among the temperatures and concentrations evaluated, these conditions yielded the lowest Cts for the DNA suspensions of M. roreri strains MR1 and MR2 while yielding Cts above 33 for the non-template and negative controls (Table S2). They also generated a single peak around 80 • C in the dissociation curves ( Figure S4A) and a single band in the agarose gel ( Figure S4B). Considering the above, we decided to characterize and validate the M. roreri qPCR using the Mr_ITSF and Mr_ITSR primers at 0.3 mM, an annealing temperature of 62 • C, and 37 amplification cycles.
Moniliophthora roreri qPCR's Specificity, Efficiency, Limit of Detection, and Presicion
The diversity of M. roreri in Colombia is high, and at least five populations have been identified [29,30]. To evaluate whether the qPCR could differentiate different M. roreri strains from other fungi, we used the DNA of M. roreri isolates from representative cacao-growing regions in Colombia. Ct varied widely between M. roreri isolates (nearly 9 cycles, from 15 to 24 cycles) ( Table 1). This variation was unexpected since the qPCR reactions used comparable DNA amounts (6 ng). Despite the variation, the qPCR differentiated the M. roreri isolates from other fungi since all of them had higher Cts (>32 cycles, p-value < 0.05) ( Table 1). Furthermore, strong 120 bp-bands were evident in the agarose gels only for the qPCR reactions of the M. roreri isolates ( Figure S5). These results indicate that the qPCR can detect M. roreri isolates from several Colombian cacao-growing regions and distinguish them from other fungi, at least among the evaluated fungi. Considering that the sensitivity and accuracy of the qPCR depend on the amount of the target in the qPCR reactions [20], we assessed the qPCR using different amounts of DNA of M. roreri strain MR2. We decided to use strain MR2 since it was among those with the higher Cts in the specificity evaluations ( Table 1). The probability of the qPCR detecting M. roreri DNA (true positive) formed a sigmoid curve against the log10 of DNA ng, with the probability being 1 for over 0.06 ng of M. roreri DNA and closer to 0 as the ng of DNA dropped ( Figure 1A). According to the glm correlating qPCR-detection probability with the log10 of the M. roreri DNA (Table S4), the qPCR's 95% limit of detection (95% LOD) was 0.025 ng of M. roreri DNA (Figure 1 A), indicating that the qPCR should accurately detect M. roreri at least 95% of the time in samples with at least 0.025 ng of M. roreri DNA. The qPCR could detect fewer ng of DNA, but the risk of a false negative increased as the amount of DNA decreased. For example, the qPCR detected M. roreri DNA in 75% of the samples with 0.006 ng of M. roreri DNA. In contrast, it detected M. roreri DNA only in 30% of the samples containing 0.0006 ng of M. roreri DNA. most pronounced at the lower limit of the qPCR linearity range (0.006 ng of DNA). For example, while 0.006 ng of DNA had a mean Ct of 31.1 with a standard deviation (SD) of 1, 0.6 had a mean Ct of 25.6 and an SD of 0.4 ( Figure 1B).
The qPCR properly and consistently estimated the ng of M. roreri DNA in samples with amounts of DNA within the linearity range. The estimates for suspensions containing 6 and 0.6 ng of M. roreri DNA were 6.51 ± 0.27 ng and 0.80 ± 0.11 ng, showing coefficients of variation (CV) between and within qPCR runs below 14% (Table 2). Regarding the accuracy and precision, the qPCR's linearity range was between 0.006 and 60 ng of DNA, as indicated by the correlation between Ct values and the log10 of the serial dilutions of M. roreri DNA (R 2 : 0.98). In the linearity range, the Ct values lowered around 3.3 cycles for each ×10 increase in the DNA load, indicating a qPCR efficiency (E) of 100.9% ( Figure 1B). DNA amounts below this range (0.0006 ng) compromised the lm fitting and the qPCR efficiency (R 2 : 0.96 and E: 115.4%) ( Figure S6), showing that the reliability of the technique drops below this range. Consequently, the Ct variability was most pronounced at the lower limit of the qPCR linearity range (0.006 ng of DNA). For example, while 0.006 ng of DNA had a mean Ct of 31.1 with a standard deviation (SD) of 1, 0.6 had a mean Ct of 25.6 and an SD of 0.4 ( Figure 1B).
The qPCR properly and consistently estimated the ng of M. roreri DNA in samples with amounts of DNA within the linearity range. The estimates for suspensions containing 6 and 0.6 ng of M. roreri DNA were 6.51 ± 0.27 ng and 0.80 ± 0.11 ng, showing coefficients of variation (CV) between and within qPCR runs below 14% (Table 2). Table 2. qPCR estimates and within and between qPCR runs coefficients of variance for the Moniliophthora roreri DNA in suspension and extracted from M. roreri spores in suspension and spore-traps.
Mean and SD, the standard deviation for the estimates of the biological replicates of each qPCR runs (n:3). b CV, Coeficient of variance (SD/mean) for the estimates of the biological replicates of each qPCR runs. c Mean and SD, the standard deviation for the estimates of the qPCR runs (n:2). d CV, Coefficient of variance (SD/mean) for the estimates of the biological replicates of each qPCR runs.
Moniliophthora roreri Spores Quantification
All of the above showed that the qPCR reliably detected at least 0.025 ng M. roreri DNA and could accurately quantify ng of M. roreri DNA between 0.006 and 60 ng. Now, we wondered if the qPCR was sensitive enough to detect and quantify DNA from M. roreri spore samples. For this purpose, we modified a previously published protocol [22] to extract DNA from spore suspension and spore traps containing 2.9 × 10 6 , 2.9 × 10 5, and 2.9 × 10 4 M. roreri spores. Spore suspensions with 2.9 × 10 6 and 2.9 × 10 5 spores yield 7.5 ± 3.9 (CV = 52.0%) and 1.13 ± 0.24 (CV = 21.2%) µg of total DNA. On the other hand, spore traps with 2.9 × 10 6 spores yield 0.13 ± 0.01 ug (CV = 7.7%) of total DNA, nearly ×1/58 lower than that of spore suspensions with the same spore load. The amount of DNA extracted from the remaining samples, including spore suspensions with 2.9 × 10 4 spores, was too low to be quantified by NanoDrop. The results above showed that our protocol successfully extracted DNA from M. roreri spores in suspension and spore traps. However, the extraction was less efficient for spores in the spore traps and the yield was low for the samples with low spore loads.
Regarding the detection and quantification of DNA from M. roreri spore samples, all the estimates were above the 0.025 ng 95% LOD and within the 0.006 ng and 60 ng linear range of the qPCR. The exception was the estimates of spore suspensions with 2.9 × 10 6 spores which were above the linearity range ( Table 2). As expected, the estimated ng of DNA decreased with the spore loads and was higher (nearly ×10) for spore suspension than for spore traps. Overall, the estimates for spore suspensions with 2.9 × 10 6 , 2.9 × 10 5 , and 2.9 × 10 4 spores were 81.83 ± 25.27, 10.9 ± 3.76, 0.56 ± 0.06 ng of estimated DNA compared with 8.36 ± 3.55, 0.35 ± 0.20, 0.07 ± 0.04 ng of estimated DNA for spore traps with the same spore loads (Table 2). Nonetheless, these estimates had a high variability compared with DNA suspensions, with the variation between the biological replicates in the same qPCR run (within-qPCR run CV) being particularly high. While the within-qPCR run CVs varied from 12% to 173% (vs. <13% for the DNA suspension estimates), the between-qPCR runs CVs from 10% to 57% (vs. <14% for the DNA suspension estimates) ( Table 2). Despite this variation, these results showed that the qPCR can detect and quantify DNA from M. roreri spores in suspensions and spore traps. However, its variability must be considered when evaluating the M. roreri spore loads in the cacao fields.
Spore Trap Devices
This study aimed to develop a technique to evaluate the M. roreri spore loads in commercial cacao plantations. Therefore, we developed a homemade-spore-trap device to carry the spore traps for field evaluations. The spore-trap devices consist of an Arduino UNO R3 system with an AVR microcontroller encapsulated in a commercial IP67-ABS box of 18 cm × 8 cm × 7 cm. The Arduino UNO system has an L298N H-bridge motor driver connected to a PWM output, which controls a 12 V DC 60 rpm geared motor moving 20 cm-long blades carrying the spore traps ( Figure S1). The spore-trap devices are powered by a Solar-Powered Systems CN3065 which is connected to a LiPo 3.7 V 6000 mAh battery and a 1 W 5.5 V Seeed monocrystalline solar panel (170 mA). Furthermore, they have a DS3231 real-time clock (RTC) coupled to the Arduino UNO R3 communicating via an I2C bidirectional bus. For collecting environmental data, the devices have SHT31 Sensirion temperature and humidity sensors attached to the I2C bidirectional bus. The data collected are stored in a 32 GB Sandisk memory connected to a DM3AT micro-SD connector and can be downloaded to a computer for its analysis.
The present study did not include the assessment of M. roreri spore loads in the fields. However, the spore-trap device can be used for this purpose since it was custom-made to carry the same spore traps used in the Moniliophthora roreri spores quantification. Further evaluations must validate the spore trap device in the cacao plantations
Discussion
Coupling spore traps with pathogen-specific qPCR is a reliable method for detecting and quantifying spores of fungal plant pathogens in the field [16][17][18][19] and could be useful for assessing the M. roreri spore loads in cacao plantations. Therefore, we developed a qPCR protocol to detect and quantify M. roreri DNA. According to our estimations, this method can distinguish M. roreri from other fungi and detect down to 0.025 ng of M. roreri DNA (95% LOD). It can also reliably quantify between 0.006 ng and 60 ng of M. roreri DNA.
While developing a qPCR protocol for detecting and quantifying spores of fungal plant pathogens, the specificity is crucial since air-born spores of several fungi, including plant pathogenic and non-pathogenic fungi, populate the crops environment [16,26,31,32].
Our qPCR protocol was successful in distinguishing M. roreri from other fungi, including its close relative, M. perniciosa [4]. Distinguishing between the Moniliophthora species is critical since M. perniciosa is also a cacao pathogen responsible for the Witches' broom [33]. In Colombia, Witches' broom (WBD) is a disease secondary to FPR, as its derived losses are lower [4]. However, in other countries such as Brazil, where FPR was only recently introduced, WBD is more relevant than FPR [3]. Failing to distinguish between M. roreri and M. perniciosa can lead to false positives and an overestimation of the M. roreri spore load.
Besides being specific, a method for assessing spore loads of plant pathogenic fungi must be sensitive and precise since spore loads are low in the field, meaning it must have low LOD and CV [26]. The 0.025 ng 95% LOD of our method suggests that it can reliably detect spore loads of at least 1.2 × 10 4 spores, supposing mononucleated spores with a single ITS copy and a genome size close to 50 Mb [31,32]. However, the number of spores is probably lower since fungi have several copies of ribosomal DNA (between 14 and 1442 copies) [34], therefore ITS. The number of ribosomal DNA copies in M. roreri is unknown since, to our knowledge, there are no studies have addressed this issue. However, the LOD of our qPCR protocol is in line with similar evaluations in other systems [32,35].
Regarding the precision, the qPCR protocol yielded consistent estimates from M. roreri DNA suspensions (between and within qPCR runs CV close below 14%). However, the estimates for DNA extracted from M. roreri spores in suspension and spore traps were more variable (CV between 12% and 173%). The higher CVs for spore samples compared with DNA suspension are likely derived from the complexity of the biological sample. Extracting DNA from fungal spores is not trivial, especially from spore traps [26,28]. We used a modified protocol for extracting DNA from M. roreri spore samples trying to overcome some of the difficulties associated with the complexity of the samples [22], and despite being able to extract DNA from the spores, the yields varied from one sample to another and from one experiment to another. Despite the variation, the DNA estimates for most roreri spore samples were above the 95% LOD and within the linear range of the qPCR, meaning that our methods can detect and measure the DNA from spore suspension and spore traps containing at least 2.9 × 10 4 M. roreri spores. Therefore, it could be used to assess the M. roreri spore loads in cacao plantations. However, the variability of the method must be considered and can be reduced by increasing the sample size.
We designed a spore-trap device to carry the spore traps, but this device still requires validation. Therefore, further evaluations must validate the spore trap device and the qPCR protocol in cacao plantations. We expect our method (coupling the spore trap device and the qPCR protocol) to be sensitive enough to assess the M. roreri spore loads in the field since evaluations using similar methods in other systems have reported between 1.0 and 1.0 × 10 5 spores or DNA copies per m 3 of air [18,19,36]. To our knowledge, no comparable analyses have been conducted for M. roreri in cacao fields. However, an older study using passive spore traps and microscopy detected between 30 and 144 M. roreri spores per cm 2 of spore trap in an 8-h evaluation period [5]. These values are lower than those in our evaluations (i.e., 2.9 × 10 4 M. roreri spores), and it is hard to predict if the sensitivity of our method will be enough to detect the M. roreri spore loads in the cacao plantations due to the methodology differences.
Even though our study was limited to laboratory evaluations, we consider that our method has great potential for estimating natural M. roreri spore loads in cacao crops. Following some validation, future work can use the spore-trap device and the M. rorerispecific qPCR protocol to estimate environmental M. roreri spore loads and evaluate how they are affected by the environment since the spore-trap device records climatic variables.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/jof9010047/s1; Figure S1. Spore-trap device developed for assessing the Moniliophthora roreri spore load in cacao plantations. (A) shows a picture of the device with a spore trap by itself and in the blade (detail). (B) is a block diagram showing the main components of the spore-trap device; Figure S2. Sequence alignment of the ITS sequences of the Moniliophthora roreri strains MR2 (OM056946) and MCA2954 (Genbank DQ222927) and Moniliophthora perniciosa strain COAD2616 (Genbank MK785158) and basidiocarp (Genbank OM056947) showing the binding sites of the Mr_ITSF and Mr_ITSR primers; Figure S3. Agarose gel showing the PCR products for the ITS fragments of Moniliophthora roreri and other fungi amplified with the ITS1 and ITSR4 (Lanes: 1-10) and the Mr_ITSF and Mr_ITSR primers (Lanes: [11][12][13][14][15][16][17][18][19][20]. Figure S6. Correlation between the qPCR threshold cycle (Ct) and the logarithm with base 10 (log10) of serial dilutions (×1/10n) of the DNA extracted from the mycelia of M. roreri strain MR2 with concentrations between 30 and 0.0003 ng per µL were evaluated in two separated qPCR, each containing ten technical replicates per dilution. Non-template (H2O) and negative (M. perniciosa basidiocarp DNA) controls were included in every qPCR. A) shows the correlation between the qPCR threshold cycle (Ct) and the log10 of the DNA concentration of the M. roreri serial dilutions. The points (n = 20 per log10 of DNA concentration) represent each sample. The line and the gray area represent the prediction and standard error of the linear model (lm), respectively; Table S1. Fungal strains used in this study; Table S2. Primers and fungal ITS sequences used in this study; Table S3. qPCR results for the evaluations assessing melting different temperatures and primers concentrations; Table S4. Estimates for the general linearized model (glm) with the logit function and the binomial family error correlating thedetection probability of the qPCR with the logarithm with base 10 (log10) of Moniliophthora roreri DNA in serial dilutions. Institutional Review Board Statement: The study was conducted in accordance with the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) o EAFIT University (protocol code 082019 and date of approval of 19 August 2019).
Informed Consent Statement: Not applicable.
Data Availability Statement: The authors declare that the data supporting the findings of this study are available within the article. | 8,540 | 2022-12-28T00:00:00.000 | [
"Environmental Science",
"Biology"
] |
Optimisation of the Green Process of Industrial Hemp—Preparation and Its Extract Characterisation
Natural medicines and products are becoming increasingly important in the pharmaceutical and food industries. The most important step in obtaining a natural remedy is the processing of the natural material. This study offers the separation of the industrial hemp plant into fractions by mechanical treatment, which has a significant impact on the selectivity of the obtained fractions. This study also offers a solution to reduce waste by fractionating industrial hemp, focusing on the fraction with the highest cannabinoid content (49.5% of CBD). The study confirmed the anticancer potential of the extract, which prevents further division of WM-266-4 melanoma cells at a concentration of 10−3 mg/mL. However, application of the extract (c = 10−3 mg/mL) to normal human epidermal melanocytes proved to be insignificant, as the metabolic activity of the cells was the same as in the control cell group.
Introduction
Knowing the phytotomy of the hemp plant and understanding its potential in phytopharmacy can help us to select the proper part of a certain species and obtain a highquality extract or product. Hemp has great added value as each part of the plant represents many potentially valuable resources for quality products. The hemp plant consists of the woody part (44% of the plant weight), fibres (24%), seeds (11%) and other components such as flowers, leaves and dust (21%) [1][2][3]. This diversity of substances means that the potential uses of hemp go far beyond medicinal use, since every part of the hemp plant can be useful. A large part of the plant is made up of the fibres extracted from the stems, which, with low weight and high strength, are an important material for the construction industry and offer good prospects for the automotive industry [4,5]. The seeds can also be used in a variety of applications, such as for the production of cooking oil, which have been shown to have several beneficial effects on the body [6][7][8]. Hemp seeds are also used to make biodiesel through seed pressing. They have been shown to contribute four times more fuel than soybeans, which has led the United States to produce biofuels [9,10].
Hemp has great potential for the sustainable planning of whole plant processing according to the zero waste and green process concept. Since each part of the hemp has its own potential for a certain product, the main thing in planning is the pretreatment of the material (for example, the screening method), which separates plant parts. This pretreatment process allows fragmentation of materials according to their active size and consequently, after extraction, the desired components [11]. The entire concept results in extracts with a high proportion of the desired components and above all, sustainability. One of the most important variables that affects the quality of the product, besides the Plants 2022, 11, 1749 2 of 14 appropriate choice of a plant screening method, is the selection of an extraction method. The choice of extraction solvent is crucial. Studies have already introduced several solvents such as methanol, ethanol, chloroform, butane, hexane, etc. [6,11,12]. However, there are safety reasons regarding their toxicity, thus it is important to comply with the European directive (Directive 2009/32/EC of the European Parliament and of the council of 23 April 2009 on the approximation of the laws of the Member States on extraction solvents used in the production of foodstuffs and food ingredients), which recognises the extraction solvents used in the production of food and food ingredients (such as ethanol and carbon dioxide) [13].
In this study, the investigation into the pretreatment of the material was focused further on the selected segments obtained after processing, which were obtained mainly from hemp flowers and leaves. The female cannabis plants were used as male plants do not produce flowers, and are the main topic of this work. Certain known forms of leaves also constitute a part of the plant and are located above the cola from which the flower emerges [4]. Within the cola area, tiny orange, brown hairs are positioned that sprout from the flower and the small nodules (calyx) from which the flower emerges. The nodules usually have an extensive collection of trichomes, which are glands that secrete cannabinoids [4,14]. Shiny crystals on tiny leaves (also called sugar leaves) are crystallised secretions of terpenes, tetrahydrocannabinol (∆9 THC), cannabidiol (CBD) and other cannabinoids [15][16][17]. Phytocannabinoids represent a group of C21 or C22 terpenophenolic compounds synthesised from fatty acid precursors [18] in the acid (cannabinoid) form (C22). They are decarboxylated to their neutral forms (C21) upon exposure to light [19]. Cannabigerolic acid (CBGA) is a major precursor of tetrahydrocannabinolic acid (∆9-THCA), cannabidiolic acid (CBDA) and cannabichromenic acid (CBCA). Geranyl diphosphate and olivetolic acid are synthesised to CBGA by synthase [20]. CBGA, CBDA and CBCA are formed by various cyclisations and have pentyl side chains (C5-phytocannabinoids). Decarboxylation of these precursors results in ∆9-THC, CBD, CBC and its chemical artifact CBL (cannabicyclol). CBN (cannabinol) is formed by the degradation of THC. On the other hand, cannabigerovaric acid (CBGVA), ∆9-tetrahydrocannabivaric acid (∆9-THCVA), cannabidivaric acid (CBDVA), and cannabichromevarinic acid (CBCVA) are formed from geranyl diphosphate and divaric acid [20]. Nonacidic forms of cannabinoids (CBD, THC, CBG, etc.) are credited with many healing effects on the human body [1,21]. The extraction of raw material results in the acidic form of cannabinoid compounds and decarboxylation is required to obtain nonacidic forms [22].
As mentioned above, in the first step we focused on the research of the pretreatment material (screening) for the separation of plant parts. There has been no such precise separation of dried material described in the literature. The separation (sieving) was used to achieve higher selectivity of the required components (cannabinoids) already in the crude mass. The crude mass was further extracted in two unconventional ways with different solvent polarities (ethanolic ultrasonic extraction and supercritical CO 2 extraction) and the resulting extracts were mixed in a 1:1 ratio. The selected extraction procedure and mixing were explained as the most appropriate in the previous study [23]. The CO 2 solvent was chosen because it isolates nonpolar components, such as cannabinoids in case of hemp extraction. On the other hand, ethanol as a polar solvent isolates other components, as reported by Appendino et al. who studied the isolation of the polar cannabinoid carmagerol [24]. They point out that previous research focused on a specific polarity range, which may have overlooked smaller compounds with higher or lower polarity than the major cannabinoids. However, no co-solvent was added to the supercritical CO 2 , otherwise it could increase its solubility in favour of other polar molecules that are not desired; higher solvent strength could mean lower process selectivity [23,25]. The aim of this study was to demonstrate that appropriate pretreatment affects the better selectivity (purity) of the extract and improves anticancer activity while bioavailability is increased. Therefore, the research was conducted on melanoma cells WM-266-4 and normal human epidermal melanocytes, demonstrating the biocompatibility of the extract.
Materials and Methods
Hemp (Cannabis sativa) was purchased from a local grower in Slovenia (Makoter agricultural estate, Cven, Slovenia, coordinates: 46.5431403, 16.2197896). The used hemp type was Kc Dora with an organic certificate (BV-SVN-EKO-160/20). The material was supplied dried. The screened parts of hemp used in this study were also prepared on the growers' estates.
Pretreatment of Hemp
The dried hemp plant (stems, leaves and flowers) was sieved according to the procedure presented in Figure 1. It represents the output of each sieving unit and the loss of the material during the procedure. Material A (on Figure 1) represents the entire dried plant (stems, leaves and flowers), which goes along the closed conveyor belt (1) to the rotating drum (2). In (2), the stems and seeds in the drum (material F) are separated from the other parts of the hemp. The rest of the material (material B) goes along the conveyor belt (1) to the sieve with a slope (3), under which the collecting vessel (4) is separated into two parts. In the first part, material C is collected, and in the second, material D. The vessel is separated, because more cannabinoids are expected to fall in the first half than in the second. The material remaining on the sieve (3) represents material E. The material F that remains in the rotating drum is transferred along the conveyor belt (1) to the shaker with a sieve (5), where the waste material (material H) is separated from the seeds (material G). Seven material samples (A, B, C, D, E, G, H) were obtained during sieving. Dried hemp (materials A, B, C, D, E, and H) was decarboxylated for 60 min at 140 • C. Extraction was performed for materials A, B, C, D, E, and H. Material F was a collection of seeds and waste material, which was further sieved (5) and only then the resulting hemp seeds (material G) and waste material representing stems (material H) were extracted. Hemp seeds do not contain cannabinoids, but the extraction of this fraction has been performed for comparison.
Extractions
The subsequent extraction procedure was explained and the conditions for the extraction were already established in our previously published article [23]. Supercritical fluid extraction with CO 2 and ultrasonic extraction with EtOH were carried out according to the procedure described by Žitek et al. [23]. However, once both extracts were obtained, they were mixed in a 1:1 ratio. The ultrasonic extraction process was performed at 40 kHz at 25 • C. Solvent (EtOH) was removed at 40 • C under reduced pressure with a rotary evaporator (Büchi Rotavapor R-114, Flawil, Switzerland). On the other hand, the supercritical experiments were performed in an SFE system, shown in Figure 2. Material (10 g) was placed in an autoclave, and extraction was carried out at 350 bar and 60 • C. The solvent to feed ratio was 8.205. Extraction procedures were performed in triplicates. The obtained extracts were stored at −20 • C until analysed with LC-MS/MS.
Determination of Cannabinoids with LC-MS/MS Method
An Agilent 1200 HPLC apparatus coupled with an Agilent 6460 Jet Stream triple quadrupole (QQQ) mass spectrometer was used in this study. Using a chromatographic Agilent Poroshell EC-C18 column with 2.7 µm particles and dimensions of 100 × 2.1 mm ID after an Agilent Poroshell EC-C18 precolumn with 4.6 µm particles, separation of cannabinoids was achieved with a mobile phase of water containing 0.1% formic acid (A) and acetonitrile containing 0.1% formic acid (B). The initial conditions were 34% of B held for 8 min; then, B was increased to 95% over 4 min and maintained for 1 min; then, B was reduced to 34% over 1 min and maintained for 6 min with an additional 3 min post-run. The flow rate was 0.2 mL/min, and the column temperature was maintained at 35 • C. Detection was performed in negative ion mode, and analytes were ionised by electrospray and monitored in multiple reaction monitoring (MRM) mode. Optimised mass spectrometer parameters were: gas temperature 300 • C, gas flow 5 L/min, nebuliser voltage 35 V, sheath gas temperature 250 • C at flow 11 L/min, and capillary and nozzle voltage 4000 V and 500 V, respectively. The MRM transition ions are shown in Table 1.
Metabolic Activity of Metastatic Melanoma Cells WM-266-4 and Normal Human Epidermal Melanocytes upon Application of the Extracts
Different concentrations of the extracts in DMSO (c = 60, 30, 20, 10, 5, 1, 0.5 and 0.1 mg/mL) were applied to melanoma cells WM-266-4. After the initial results, the experiments were repeated in a lower concentration range (with small differences in the concentrations) and the extract was applied to healthy cells, melanocytes.
The Five replicates of each experiment were performed. To measure the metabolic activity of the cells, they were exposed to selected concentrations of extracts and cultured for 24 h. Control cells were cultured for the same time and under the same conditions, but without the addition of extracts. A WST-8 Colorimetric Cell Viability Kit I (PromoKine, PromoCell, Heidelberg, Germany) was used according to the manufacturer's instructions. Absorbance was measured spectrophotometrically at 570 nm (background absorbance at 630 nm) for all samples in pentaplicate. The percentage of metabolic activity of the cells (MA) was calculated according to a procedure described in a previous study [23]. After application of extracts, the cell morphology was observed using an inverted microscope (DM16000B, Leica, Morrisville, NC, USA) with a digital camera (DFC365 FX Leica, Buffalo Grove IL, Leica, Morrisville, NC, USA).
Detection of Cell Apoptosis
To were used. Analysis was performed using a dead cell marker and calcium-dependent phospholipid-binding protein Annexin V and 7-AAD according to the manufacturer's instructions (Muse Annexin V & Dead Cell Kit Catalog No. MCH100105). Briefly, after each experiment, cells were trypsinised and 100 µL of cells suspensions were prepared for analysis. Next, 100 µL of Annexin V & Dead Cell Reagent was added to each sample and mixed. Samples were stained for 20 min in the dark and then analysed with the Muse Cell Analyzer. Each experiment was performed in triplicate and the mean value was determined.
Statistical Analysis
Statistical analysis was performed using R software version 4.1.0. and RStudio Version 1.4.1717 supported by the following packages: rstatix [26], ggplot2 [27] and dplyr [28]. Differences in melanoma cell metabolic activity between extract groups were evaluated, as well as the correlation between extract concentration and cancer cell metabolic activity. The Shapiro-Wilk test for normality of distribution was performed (p = 0.010). As the data were not normally distributed, the Kruskall-Wallis test was selected to evaluate the differences in metabolic activity between extract groups. The Spearman correlation test was performed to evaluate correlation between extract concentration and cancer cell metabolic activity. Numerical variables with abnormal distribution are described by median (interquartile range) [29].
Results and Discussion
This study is oriented towards a sustainable concept of utilisation of the whole hemp plant by integrating a pretreatment process to separate different parts of the hemp plant. This results in the high content of cannabinoids in specific fractions such as fractions B, C and D. This is a prerequisite for a high-quality extract with specific components. Table 2 and Figure 1 show percentages based on the input material (material A), representing 100% of the material. Figure 1 shows that material A, constituting 100% of the weight, was placed in a rotary drum (2). In total, 66.23% of the material was sieved through the sieve (2), and 33% remained in the drum. In the first stage of sowing, 0.77% of the material was lost. The mass that fell through the first sieve (2) was sieved through a second sieve, a sowing disc with slope (3), leaving 61.13% on the sieve (3). In addition, 4.49% of the material fell separately in two parts into the collection container (4). The first part of the collection container (4) contained 3.74% of the material, and the second part contained 0.75% of the material. The loss of material in this stage was 0.61%. In the third screening stage, the material F that remained on the drum when screened through the sieve (2), i.e., 33%, was screened through a closed shaker with a sieve (5). Out of this, 5.3% was sieved and 27% remained on the sieve (seed). In the last stage, 0.7% of the material was lost. It was observed that the loss of material during seeding was relatively low (2.08%). Therefore, by analysing the material loss, it was proved that the process itself is economical in terms of material loss. Table 3 shows yields after extraction. Our assumptions about the maximum content of cannabinoids in the extract, obtained from material C, were confirmed by the LC-MS/MS analysis (Table 4). Despite the process of separation of hemp parts resulting in the lowest amount of fraction C (Table 3; 3.74%), the yield was significantly higher (Table 3); 19%. It was also found that the extracts obtained from material C contained the highest levels of cannabinoids, especially CBD components (EC = 49.5%). Table 4 presents the cannabinoid contents in hemp extracts (percentage of selected cannabinoids (CBD, THC) per gram of extract. The ratios of cannabinoids in the plant and later in the extract depend on the type of plant, harvest, weathering, etc. [30]. Therefore, the results are difficult to compare with other studies because the literature is scarce on studies of the separation of a plant into fractions. Nevertheless, in general, our results can be compared with the literature based on material A and material E. It is reported that the content of CBD in the extracts after decarboxylation is between 30% and 40% [31,32]. In this study, the content of CBD in the hemp extract from material A was EA = 27.1%, whereas the content of CBD in extract from material E was 36.8% (EE). The higher contents were achieved in extracts from materials B, C and D, where almost 50% of the CBD component was measured in the hemp extract from material C (EC).
The increasing need for recycling and supplies from the planet is met by this novel approach, the screening process, which represents the innovativeness of this process. It is essential that a minimum amount of solvent is used in the recovery process and to have as little waste as possible. Therefore, as a solution, we present the process of sieving hemp, where every fraction can be used.
According to the results, the most suitable materials for extraction are material C and material D (for extraction of world-famous hemp resin). Material E would be suitable for use as tea, as it retains enough cannabinoids despite sieving [33]. Hemp oil, which has been known on the market for some time, is obtained from material G [34]. The waste, material H, would be interesting to research further in terms of fibre content. Hemp fibres are used in technical textiles (ropes, nets, tents, sails, carpets, etc.), textiles (clothing, footwear, tablecloths, bedspreads, bedding, etc.), industry and construction (geotextiles, bio composites, nonwovens, pipes, moulding, insulation, etc.) [9,10,35]. Stems can also be used for energy and in the environment (biofuel, ethanol, anti-erosion textiles), paper industry (cardboard, fine/coarse paper, filters), agriculture (mulch, animal litter), etc. [36,37]. In this study, the focus was on the fraction that contained the most cannabinoids (EC). In the future, it would be interesting to study the benefits of other fractions for humans.
Effect of the Extract on Metastatic Skin Cancer Cells and Normal Human Epidermal Melanocytes
The extracts (EA, EB, EC, ED, EE, EG and EH) were applied to WM-266-4 melanoma cells at different concentrations. The minimum concentration at which significant inhibition of cancer cell division or activity occurred was 0.005 mg/mL. The exception was the EC extract, where the required concentration was even lower than in the other cases (0.001 mg/mL). At a concentration of 0.001 mg/mL, the metabolic activity of cancer cells was only 11.74% compared to the control (Figure 4). ED and EB extracts also showed a significant decrease in cancer cell function at a concentration of 0.001 mg/mL (Figure 4), but with slightly higher percentages of cell metabolic activity (approx. MA (ED) = 30% and MA (EB) = 50%) than at higher concentrations (e.g., 0.005 mg/mL). The Kruskall-Wallis test confirmed significant differences between the metabolic activity of cancer cells after application of different extracts (H(6) = 45.264, p < 0.001). Regardless of the added concentration of the extract, the metabolic activities of the cancer cells differed from each other with respect to the added extract, as shown in Figures 4 and A1. The median MAs of the samples EA, EB, EC and ED were below 20% of MA according to control. Cell growth was most inhibited by the EC extract, which had a median of 11.7 (11.7, 11.7)% of MA according to control. The EE extract had a median of 31.1 (30.0, 33.0)% of MA according to control. Least effective were the EH extract with a median of 48.5 (47.8, 50.8)% of MA and EG with a median of 50.0 (50.0, 57.5)% of MA according to control.
The metabolic activity of all tested cells decreased in the concentration range from 0 to 0.01 mg/mL, but at higher concentrations of the extract the metabolic activity stabilised in the median range corresponding to the control, which is also shown on Figure A2. The Spearman correlation test showed a statistically significant, strong, inverse relationship between extract concentration and metabolic activity of cells in the range of 0 to 0.01 mg/mL (r = −0.767, p < 0.001).
To investigate the extent of apoptotic cell death, WM-266-4 cells were treated with EC extract at different concentrations (c1 = 3×10 −3 mg/mL, c2 = 2×10 −3 mg/mL, c3 = 10 −3 mg/mL, c4 = 7×10 −4 mg/mL) and cells were stained with Muse™ Annexin V & Dead Cell Reagent and recorded using the Muse™ Cell Analyzer. Representative results of the assay with untreated WM-266-4 cells are represented in Figure 5e) and WM-266-4 cells treated with EC extract of following concentration are shown: c1 (a), c2 (b), c3 (c) and c4 (d). The graph in Figure 6 shows the percentage of live, early apoptotic, late apoptotic and cellular debris represented by Annexin(−)7-AAD(−), Annexin(+)7-AAD(−), Annexin(+)7-AAD(+) and Annexin(−)7-AAD(+), respectively. Data are presented as mean ± SD of three independent experiments. The most potent hemp extract (EC) was used for measurements at a higher concentration (Figure 7). The EC extract was applied to melanoma cells WM-266-4 and compared with normal human epidermal melanocytes (NHEMs). NHEMs are pigment-producing cells located at the basal level of the epidermis. Their function is to communicate with keratinocytes via cellular processes (dendrites). Melanocytes produce melanin (a pigment), which is transferred to the keratinocytes and stored in melanosomes located around the nucleus for protection against UV radiation [38]. In Figure 7, it can be seen that the metabolic activity of cancer cells (WM-266-4) at an extract concentration of 10 −3 mg/mL is only approximately MA = 11.60%, whereas normal human epidermal melanocytes had a metabolic activity of 97.05% at this concentration. There was no significant difference with the control (MA = 100%). An example of cells morphology (WM-266-4 and NHEMs) using EC extract at 10 −3 mg/mL is shown in Figure 8. Figure 8b,d shows the controls, i.e., the cells in the complete medium. The morphology of NHEMs when the extract is applied at a concentration of 10 −3 mg/mL ( Figure 8a) and that of the control samples are the same. In contrast, there is a significant difference in the morphology of metastatic cells. When the extract was applied to metastatic cells (Figure 8c), they lost their original morphology.
EC extract was confirmed as the best for our work in these studies. The selected screen fraction (material C) of dried industrial hemp was extracted using two methods (by supercritical fluid CO 2 at the 350 bar and 60 • C and by ultrasonic extraction with EtOH); both extracts were mixed in a 1:1 ratio. In the current study, dried hemp was further decarboxylated, which contributed to an even higher cannabinoid content in the extract (e.g., the CBD content was measured at 49.5%).
An anticytotoxic effect was also observed for EC extract. When applied to melanoma cells WM-266-4 and normal human epidermal cells (at a concentration of 0.001 mg/mL), it showed significant inhibition of melanoma (MA = 11.7%) and at the same time no effect on normal cells (MA = 97.1%).
Conclusions
The study was concerned with the determination of optimal procedures for the production and extraction of industrial hemp material. The results show that hemp screening plays a crucial role in obtaining a high-quality extract. Zero waste is achieved with the prescreening process, which is in line with sustainable development. The study confirmed significant differences between extracts of different plant materials against cancer cells (H(6) = 45.264, p < 0.001). For all extracts in the range of 0 to 0.01 mg/mL of the applied extract, a statistically significant, strong, inverse relationship between the extract concentration and the metabolic activity of cells (r = −0.767, p < 0.001) was confirmed. The most pronounced anticancer effect was determined for hemp extract (EC). When applied to WM-266-4 cancer cells (c = 10 −3 ), the EC extract inhibited their activity by 88.3%, which means that there is a possibility that the cells were destroyed. This was also confirmed by the apoptosis results, which showed 97% late apoptosis represented by (+)7-AAD(+) when the extract was applied at a concentration of 10 −3 mg/mL. However, these results are supported by the results obtained in healthy cells (NHEMs), in which the selected extract did not inhibit their activity. In addition to all these results, the screening process showed the possibility of using the entire plant and reducing waste during processing. The process used is novel in hemp processing. It is assumed that the significant inhibition was achieved precisely because of the high content of the CBD, which was measured at 49.5% in the extract mixture. The content of other cannabinoid compounds was much lower (CBC = 1.40%, CBN = 0.15%, THC = 4.47%), but they have many therapeutic effects on the body, such as anticancer and antimicrobial effects [21,23,39,40].
The process is considered as waste-free and consequently economical, as the sieved fractions yield cannabinoid-rich material. Therefore, less solvent is used. Furthermore, the article provides new solutions for the valorisation of the whole plant, waste and byproducts, thus contributing to minimal waste generation or fulfilling the popular "zero waste concept" to meet today's needs and demands of consumers and society. of the project. We thank the owner of the Makoter agricultural estate, I. M., for the donation of the hemp material.
Conflicts of Interest:
The authors declare no conflict of interest. Appendix A Figure A1. Comparison of cancer cell metabolic activity in % according to control between different hemp extracts. Figure A2. Correlation of extract concentration and cancer cell metabolic activity in % according to control of different hemp extracts. | 6,035.4 | 2022-06-30T00:00:00.000 | [
"Environmental Science",
"Medicine",
"Materials Science"
] |
Voyager 1 Electron Densities in the Very Local Interstellar Medium to beyond 160 au
The two Voyager spacecraft have been exploring the interstellar medium beyond the heliopause since 2012 (Voyager 1) and 2018 (Voyager 2). Electron plasma oscillations and a quasi-thermal noise line at the electron plasma frequency have enabled the determination of the electron density in this region, revealing a radial density gradient convolved with shocks and pressure fronts. Voyager 1 has a functioning wideband receiver that provides high-spectral-resolution observations allowing the detection of the quasi-thermal noise line and has now provided electron densities to 161.4 au. Since a pressure pulse observed in 2020 around day 146 at about 149 au, the density has remained relatively constant at 0.147 cm−3 based on the most recent observations from 2023, suggesting that Voyager 1 has reached a broad density peak and possibly a new regime.
Introduction
Voyager 1 crossed the heliopause and entered the very local interstellar medium (VLISM) on 2012 August 25 (Gurnett et al. 2013;Krimigis et al. 2013;Stone et al. 2013) at about 121.6 au.Voyager 2 followed on 2018 November 5 at 119 au (Burlaga et al. 2019;Gurnett & Kurth 2019;Krimigis et al. 2019;Richardson et al. 2019;Stone et al. 2019).These spacecraft have provided the first in situ observations of the magnetic field, energetic charged particles, cosmic rays, and plasma waves in this region.In particular, plasma wave observations have revealed electron plasma oscillations at the local electron plasma frequency f pe (Gurnett et al. 2013;Gurnett & Kurth 2019;Kurth & Gurnett 2020) and, more recently, the detection of a quasithermal noise line at f pe (Burlaga et al. 2021;Gurnett et al. 2021;Ocker et al. 2021;Meyer-Vernet et al. 2022;Kurth et al. 2023;Meyer-Vernet et al. 2023), both of which allow the local electron density to be determined by n f 8980.
where frequency is in Hz and density is in cm −3 .
An overview of the Voyager 1 plasma wave and electron density observations since the heliopause crossing are given in Figure 1.The bottom panel shows the plasma wave spectrum from the Voyager wideband receiver between 1.8 and 4.0 kHz using an extreme stretch of the gray amplitude scale to highlight the narrow line at f pe after about 2017.The result is that intense plasma oscillations (labeled epo) are saturated.The plasma oscillations occur at frequencies as low as about 2.1 kHz in late 2012, which is shortly after the heliopause crossing.These occur approximately annually at increasingly higher frequencies through 2019.The more recent plasma oscillation events are brief and are not clearly visible in this presentation, but are shown more clearly in Figure 3 of Gurnett & Kurth (2019).In that paper, there is a correspondence shown between two of the plasma oscillation events and shocks detected in the magnetometer data.However, Gurnett et al. (2021) argue the other events are likely associated with distant shocks that were too weak to be observed in situ by Voyager 1. Burlaga et al. (2021) show two pressure fronts, pf1 and pf2, as identified in the magnetometer data that are not accompanied by plasma oscillations.It is thought these are pressure waves that have not yet steepened into shocks.Nevertheless, the increase in magnetic field intensity across the pressure front as expressed as B 2 /B 1 is the same as the increase in plasma density as determined by the quasi-thermal line at f pe and expressed as n 2 /n 1 to within the uncertainties.In each case the subscript 2 refers to the parameter measured after the pressure front and 1 to the parameter measured before crossing the front.
The observations presented herein are from the Voyager Plasma Wave Science instrument (Scarf & Gurnett 1977).The instrument detects radio and plasma waves with two receivers.One is a stepped-frequency receiver having 16 log-spaced channels with center frequencies from 10 Hz to 56.2 kHz and ∼15% bandwidth.This spacing gives four channels per decade in frequency.For the Voyager Interstellar Mission, each channel provides an average of four measurements of the electric field acquired every 16 s.The second receiver is a wideband receiver with a bandpass of 50 Hz to ∼12 kHz.The voltage at the input is sampled at a rate of 28,800 s −1 with 4-bit precision.There is an automatic gain control amplifier to keep the signal within an optimum range for the 4-b analog-to-digital converter, but there is no telemetry channel for the gain; hence the wideband data do not have an absolute calibration.The Appendix of Kurth et al. (2023) describes the processing of the wideband data used for the spectrogram in the bottom panel of Figure 1.The Voyager 2 wideband receiver ceased returning usable data in 2002.
The purpose of this paper is to update the Voyager 1 densities through late 2023.We show that the electron density has remained remarkably constant since the pressure front in 2020 and we suggest this represents the end of the heliospheric boundary layer (Pogorelov et al. 2017;Gurnett & Kurth 2019) characterized by a radial gradient in the electron density and the beginning of a broad region of relatively constant density, possibly related to the broad maximum predicted by heliospheric models.Of course, only continued observations of the density by Voyager 1 will be able to identify an actual peak.
New Observations
Figure 2 expands the timescale for the last five years shown in Figure 1.This covers the interval from before pf2 through the most recent data.It should be noted that the digital wideband waveforms are recorded on board Voyager at a rate of 115 kbps whereas the maximum downlink rate from Voyager at its great distance is 1.4 kbps.Hence, extraordinary measures are required to return these data.Only tens of seconds of these data are acquired per week.And, since the data are played back only a few times per year and they are periodically overwritten on the onboard digital tape recorder, gaps can occur if there is a loss of data during downlink due to weather or other issues; this accounts for the gaps in Figures 1 and 2. Furthermore, even using most of the resources at a Deep Space Network complex (i.e., an array of one 70 m and four 34 m antennas) the received signal-to-noise ratio on the ground is minimal, which can translate into bit errors in the telemetry stream.While some despiking can be performed on the received data to minimize the effect of these errors, the resulting spectrogram can have a high noise background such as during mid-2022.
Figure 2 shows that the electron density has been relatively stable since pf2, averaging 0.1484 ± 0.0028 cm −3 .This period includes a modest rise centered on 2021 when Burlaga et al. (2023) reported a "hump" in the magnetic field and a somewhat smaller rise in 2023.After both of these time-limited rises, the density returned to what appears to be a nominal value of ∼0.147 cm −3 .After the hump, from 2022 through the end of the available data, the average density was 0.1469 ±0.0014 cm −3 .The latter is a less than 1% variation.Further, the post-2022 average density is virtually the same as the post-pf2/pre-hump value of 0.147 cm −3 .We have added a dashed red line at a density of 0.147 cm −3 to show that both before and after the two density rises in this time period, the background density seems to return to this value.
The post-2022 average density of 0.1469 cm −3 corresponds to a plasma frequency of 3.44 kHz.Strikingly, this is very close to the maximum frequency of heliospheric radio emissions reported by Kurth et al. (1984Kurth et al. ( , 1987) ) and Gurnett et al. (1993).They suggested the radio emissions were generated in a plasma whose plasma frequency matched the frequency of the radio emissions.Voyager 1 has apparently reached this VLISM density.To avoid confusion, however, given the recent lack of electron plasma oscillations as evidence of shocks, Kurth et al. (2023) suggested that either due to the recent minimum in the solar cycle or the increasing distance of Voyager 1, one might conclude that shocks simply do not propagate beyond about 145 au.And, should very strong shocks associated with the current solar maximum be able to propagate much farther, these would likely not reach Voyager 1 until 2036.Hence, we do not suggest Voyager 1 is currently in the radio emission source region, just that the radio emissions' maximum frequency argue for a VLISM density similar to what Voyager 1 observed in 2023.
Discussion
Voyager 1 has reached a region whose plasma density corresponds to the source of the highest-frequency heliospheric radio emissions observed by the Voyagers in the 1980s and 1990s.However, it remains to be seen whether this is a maximum of the expected VLISM density, prior to the rollover in the density predicted, for example, by simulations such as in Pogorelov et al. (2017) and Sokół et al. (2022).Alternately, this could be a transient feature due to an extended increase in the solar wind dynamic pressure related to a solar cycle effect as described by Burlaga et al. (2023).
Voyager 1 is likely more than several hundred astronomical units from reaching an interstellar medium unaffected by the Sun and its heliosphere (see, Pogorelov et al. 2017).A heliospheric bow shock existing at a distance of order 250 au was discounted by McComas et al. (2012).However, this issue has been reconsidered (Ben-Jaffel et al. 2013;Scherer & Fichtner 2014;Pogorelov et al. 2017;Mostafavi et al. 2022) and may exist as far as 400 au (Zank et al. 2013).And Lyα measurements (see, Linsky & Wood 1996) and simulations have shown a hydrogen wall extending hundreds of astronomical units upstream from the heliosphere (Zank et al. 2013;Figure 3. (Top) Daily averages of the magnetic field magnitude from 2012 through April 2022.Notations sh1, sh2, pf1, and pf2 are shocks and pressure fronts described in (Burlaga et al. 2021).(Bottom) Electron densities from the Voyager 1 plasma wave instrument's observations of electron plasma oscillations (epo) and detection of a quasi-thermal line at the electron plasma frequency f pe .Taken from (Kurth et al. 2023).Pogorelov et al. 2017).Hence, Voyager is still well within the very local interstellar medium defined as being subject to the influence of the Sun and heliosphere.Nevertheless, Voyager 1 has not observed electron plasma oscillations, an indicator of a shock, since 2019 near 145 au (Kurth et al. 2023) and the observations presented herein show a nearly constant plasma density extending for ∼10 au and more than 3 yr since pf2.Such a broad local maximum is given in simulations (see Pogorelov et al. 2017).This appears to be an evolution into a new (for Voyager) region still influenced by the nearby heliosphere, and characterized by minimal density gradients.Burlaga et al. (2023) have shown that since the 2020 pressure front, Voyager 1 has observed generally high magnetic field intensities.This is in contrast to earlier shock and pressure front crossings characterized by jumps in |B| followed by ramps during which the field intensity decreases.These authors point to an ∼2 yr interval between 2015 and 2017 during the declining phase of the solar cycle when the solar wind dynamic pressure was unusually high at 1 au.This high-pressure region, then, would propagate through the heliosphere and result in a pressure wave upon colliding with the heliopause.The pressure wave would eventually arrive at Voyager's location in 2020, about 5 yr after it was observed near Earth.In this regard, the large electron densities observed after pf2 could be considered an aspect of this solar cycle effect.We point out, though, that while the jump in n e matched the jump in B at the second shock and two pressure fronts discussed by Burlaga et al. (2021), the density and |B| follow different general trends between these events.Figure 3 from (Kurth et al. 2023) shows the large-scale variations in |B| and n e .The top panel in Figure 3 makes the point that after the jump in |B| at the two shocks and pf1, there is a downward ramp.This was not the case after pf2, the "hump" feature.The electron densities do not show the jump-ramp variation seen in the magnetic field.In general, there is a general increase in density through about 2018, which is not seen in the field.Only after pf2 do both parameters show a jump and remain high through 2021.That both the density and field strength have remained high since pf2, therefore, stands as a difference with the previous interval.And, recently (Burlaga et al. 2024) reported that the magnetic field in 2022 displays no intermittency, something not observed elsewhere in the VLISM.Data from 2023 were not analyzed in that work.
Conclusion
It is apparent that Voyager 1 has entered a new regime beyond the heliospheric boundary layer in the VLISM.This regime is characterized by sustained high plasma densities of ∼0.147 cm −3 and magnetic fields of ∼0.5 nT (at least through 2022).The plasma densites show very small variations, of the order 0.3% or half that outside of two modest density increases lasting several months to a year.Further, they approximately correspond in plasma frequency to the maximum heliospheric radio emission frequencies observed by the Voyagers in the 1980s and 1990s coming from beyond the heliopause.What is not understood is whether this region is the result of a solar cycle variation in solar wind dynamic pressure (Burlaga et al. 2023), or a more stable region, possibly an indication of a broad density maximum beyond the heliopause as given in a number of models.Continued Voyager observations may resolve this.
Figure 1 .
Figure 1.(Top) Electron densities determined from electron plasma oscillations (in red) and a quasi-thermal line at the electron plasma frequency f pe (in black) shown in the bottom panel.Noted in green are the times of two shocks, sh1 and sh2, and two pressure fronts, pf1 and pf2, reported by Burlaga et al. (2021).(Bottom) A frequency-time spectrogram showing plasma wave phenomena as a function of frequency and time.Noted are electron plasma oscillation events (epo) that are highly saturated due to the extreme grayscale stretch.In the last half of the plotted interval, a thin line at the electron plasma frequency can be seen.
Figure 2 .
Figure 2. Similar in format to Figure 1, this figure focuses on the interval from just before pressure front 2 through the end of available data.The dashed red line at about 0.147 cm −3 represents a recurring density observed in the post-pf2 regime. | 3,326.4 | 2024-02-20T00:00:00.000 | [
"Physics",
"Environmental Science"
] |
Shifting economic activity to services has limited potential to reduce global environmental impacts due to the household consumption of labour
The tertiary (or ‘service’) sector is commonly identified as a relatively clean part of the economy. Accordingly, sustainable development policy routinely invokes ‘tertiarization’—a shift from primary and secondary sectors to the tertiary sector—as a means of decoupling economic growth from environmental damages. However, this argument does not account for environmental impacts related to the household consumption of tertiary sector employees. Here we show using a novel analytical framework that when the household consumption of labour is treated as a necessary and endogenous input to production, the environmental impacts of all sectors converge. This shift in perspective also exacerbates existing disparities in the attribution of environmental impact from economic activity among developed and developing economies. Our findings suggest that decoupling of economic activity from environmental impacts is unlikely to be achieved by transitioning to a service-based economy alone, but rather, that reducing environmental damages from economic activity may require fundamental changes to the scale and composition of consumption across all economic sectors.
Introduction
Human activity is driving a dramatic acceleration of global environmental degradation [1][2][3]. Decoupling economic activity from environmental impacts has been proposed as a solution, mitigating environmental damage while preserving economic growth ('green growth'). There are two fundamental pathways to such decoupling-technological advances that reduce the quantity of resources used or wastes produced per unit of economic output ('dematerialization'), and shifting the composition of economic activity from primary and secondary sectors to the tertiary sector ('tertiarization'). We focus on the second of these pathways and evaluate the potential for structural change in economic activity towards 5 Authors contributed equally to this work. tertiary sectors to alleviate the environmental impacts generated by the global economy.
Tertiarization, or the 'structural change hypothesis' , is a core part of Environmental Kuznets Curve (EKC) theory positing an inverted U-shaped relationship between average income and various measures of environmental quality [4]. This relationship, demonstrated by the experience of the developed nations in their transitions toward post-industrial service economies, is frequently alluded to in the context of sustainable development, offering a model pathway to grow economic prosperity while fostering environmental sustainability at the global level [5][6][7][8][9][10][11][12][13][14][15][16]. Several recent studies attribute various positive environmental trends observed in recent decades, in part, to structural change in the composition of economies and an overall shift toward services [17][18][19][20]. The environmental promise of tertiarization is premised on the ostensibly lower environmental impacts per unit of economic output ('impact intensity') of industries within the tertiary sector, particularly those producing knowledge-intensive services [7,12,21,22]. In contrast, the agricultural and manufacturing industries are frequently identified as the most prominent culprits in the generation of environmental impacts [9,23]. This framing can be understood as part of the broader 'green growth' narrative, influencing goals for sustainable development at the highest level, such as the United Nation's Sustainable Development Goal 8.2, to 'achieve higher levels of economic productivity through diversification, technological upgrading and innovation, including through a focus on high-value added and labour-intensive sectors' [24].
Here, we suggest that this perspective overlooks the role of labour in economic production. Specifically, it neglects how household consumption is a prerequisite to economic production, and hence a relevant driver of the environmental impacts of sectoral output. In practice, tertiarization occurs by increasing the number of people employed in higher wage sectors, alongside increasing consumption with rising income [25]. Both the labour intensity of production and level of household consumption vary considerably from industry to industry, and likewise between sectors of the economy. Therefore, heterogeneity of labour (and wages) should strongly influence the attribution of environmental impacts when consumption by employed persons is included in estimates of sectoral impact.
In this study, we examine the potential for reducing the environmental impacts of economic activity through tertiarization, separate from dematerialization of production or changes in the composition of demand. The inclusion of household consumption in the production supply chain of employing sectors is justified on the basis that the provision of labour is fundamental to production and wages paid to households provide the bulk of household income directed towards consumption. Therefore, labour must be included in intermediate consumption for the attribution of sectoral environmental impacts. We show that when labour is treated as an input to production, distributions of environmental impacts by sector tend to converge. Endogenizing labour as an economic input also reveals consumption in developed countries to be the dominant driver of environmental impacts-to a greater degree than is already revealed by the shift from conventional productionbased accounting to consumption-based accounting [26][27][28]. Implementing this change within environmental impact accounting frameworks provides a more causally accurate representation of economic sectors needed to assess the potential of tertiarization for economy-environment decoupling (see section S1(stacks.iop.org/ERL/15/064019/mmedia) for further discussion).
While we acknowledge the possibility of green growth through dematerialization, it is equally plausible that economic growth will outpace reductions in impact intensity leading to rising aggregate ecological burdens, even allowing for unprecedented technological innovation [29]. Instances of decoupling growth from specific pollutants and resource inputs have been observed in the past, and some aggregate measures such as global land use and biomass consumption have plateaued. However, these achievements are typically mixed successes, for example, the substitution of wood with fossil fuels [30] has alleviated land-use impacts while exacerbating climate impacts from rising greenhouse gas emissions. When measured in terms of total material footprint, the developed world has not decoupled (from 1990 to 2008), although certain industrializing nations have exhibited relative and even absolute decoupling over the same period [31]. This experience suggests that while important uncertainties remain, the feasibility of long-term absolute decoupling of economic activity from environmental impacts cannot be taken for granted. Here, we seek to better characterize the potential for green growth through the tertiarization pathway, while acknowledging important uncertainties in future dematerialization via technological change.
Experimental design
We perform consumption-based accounting (CBA) using the environmentally extended multi-regional input-output (EE-MRIO) model provided by the EXIOBASE 3 project [32,33], modified to treat labour as an endogenous input to production. Labour is represented in terms of household consumption by employed persons. We aggregate 163 industries of the global economy into eight sectors describing consumption categories following Ivanova and colleagues [34], and select three common metrics representing diverse environmental impacts: greenhouse gas (GHG) emissions, water consumption, and land use. This method of 'closing' the input-output (IO) model with respect to labour allocates the environmental impacts associated with household consumption by employed persons to the economic sectors employing them, allowing for a novel accounting of consumption-based environmental impacts across economic sectors [35]. For the purposes of our study, we define tertiarization to be the structural economic change from primary and secondary sectors to the tertiary sector, measurable as an increase in the relative proportion of services to manufacturing, resource extraction, and agricultural industries.
We compare consumption-based accounts (CBA) generated from the standard 'open' (exogenous labour) and our proposed 'closed' (endogenous labour) versions of the detailed multi-region tables with environmental extensions. To close the model, we use a method of endogenizing households into the inter-industry transaction matrix similar to that described by Miller and Blair [36]. Input-output (IO) models incorporating industry-household linkages are known as 'semi-closed' , 'extended' , or 'Type-II' models, and are commonplace in macroeconomic analysis. Our analysis extends this established technique to the allocation of environmental impacts to economic sectors across the global economy.
We use pymrio, an open source code package in Python designed for use with this and other environmentally extended multi-regional input-output (EE-MRIO) databases [37]. We use the industry-byindustry (ixi) classification scheme, which describes the global economy as 163 industries based in 44 countries and five rest of world (RoW) regions, interlinked by industry and location. Temporal analysis is made possible by the recent addition of time series data provided in EXIOBASE 3 for the years 1995-2011. In order to compare output from different years, output in nominal terms was inflation adjusted to real Euros with 2005 as the base year. EXIOBASE 3 contains a multitude of environmental indicators, with resource inputs and waste outputs described as both terms of raw values ('emissions'), as well as characterized measures of impacts. We selected a small representative group of three impacts: (1) aggregate GHG emissions in units of carbon dioxide equivalents (CO 2 e) using the global warming potential method with a 100-year time horizon (GWP 100), (2) total water consumption (blue water, i.e. net water use), and (3) total land use.
We employ the Leontief demand-pull transformation in two ways: open and closed with respect to labour. The first method is identical to that conventionally used to derive CBA, which we refer to as the 'open model' . The second method involves closing the model with respect to labour, which endogenizes wages paid and the household consumption of labour into the transaction matrix (the 'closed model'). Wages paid to employees by industry and location are inserted as rows and household consumption as columns in the global transaction matrix, while simultaneously subtracting this consumption from final demand, leaving only non-household purchases (e.g. government). This modification of conventional IO methodology follows the approach described by [38]. The corresponding closed-CBA results in an attribution of the household consumption by labour to employing industries (equivalent to adding labour as an additional branch to each step of the production supply chain; see section S5 for a more detailed explanation of this process). Impacts are derived using emissions extensions and conversion factors provided in the database.
Note that we do not differentiate between employment skill levels (in practice, employees of differing income levels, e.g. low-vs. high-skilled) within industries or sectors, since it is aggregate wages that correspond with household income that drive impacts. To clarify, when we refer to 'highwage sectors' , we are describing aggregate wages paid to employees of a sector, not what is colloquially understood as high individual wages (i.e. wages per worker). While salary is a reliable proxy of personal impact [39], aggregate wages are the key variable for determining total environmental impacts related to consumption [25], as studied here. It is therefore not strictly necessary to differentiate between skill levels unless one wants to know how much impact is attributable to each labour category. We consider homogenous representation of labour within industries as a valid approximation when income distributions within industries are approximately stable over time. That way, although the proportion of income saved tends to increase with rising wages, impacts per unit growth in economic output should not substantially change for incremental increases.
Industry-level data is aggregated into sectors according to the Consumption Categories outlined in the DEvelopment of a System of Indicators for a Resource efficient Europe (DESIRE) classification scheme (for details, see [40]). Alternative groupings can be used, and results are somewhat sensitive to the choice of grouping. The same analysis presented in the paper's main results performed with the International Standard Industrial Classification (ISIC) scheme can be found in the Supplementary Information (figures S1 and S2). The qualitative findings of the results are largely unchanged, though constituent industries within aggregate groupings sometimes exhibit different behavior from the mean change for the grouping. See section S2 for a discussion of how aggregation classification choice affects results.
We then compare the CBA derived environmental impacts before and after model closure, to examine the change in their global distribution by sector ( We also examine the distributions of sectoral impacts before and after closure with respect to labour when normalized by output ('impact intensity'). Box plots shown in figure 2 The services and construction sectors show the most pronounced increase in absolute terms under closure across all measured impacts, while manufactured products exhibits notable growth in land use and water consumption. Conversely, food, shelter, clothing and mobility sectors show clear decreases in absolute impacts under closure. High wage intensities, particularly where wages comprise more than half of a sector's total output, is a strong indicator that a sector's environmental impact will grow substantially under closure. Relative proportions of impacts remain relatively stable over time, even with growth of overall magnitude of impacts for GHG emissions and water consumption. maximum and minimum values within 1.5 IQR of the 75th and 25th percentiles, respectively. Outliers have been omitted for legibility.
Household consumption and global environmental impacts
The reallocation of household consumption to employing industries reveals increased absolute environmental impacts for the Service, Manufacturing and Construction sectors, with corresponding decreases in the impacts originating from the Food, Clothing, Shelter, and Mobility sectors (figure 1). We find this pattern is time invariant (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) and consistent across all selected indicators: GHG emissions ( figure 1(a)), land use ( figure 1(c)) and water consumption ( figure 1(d)). Changes in absolute impacts from 'open' to 'closed' models are not significantly correlated with wage intensity, however, the sectors where wages exceed a third of final output-Services and Construction have wages per unit production (measured in total output) of 0.36 and 0.33, respectively-exhibit marked increases in allocated impacts ( figure 1(b)). By far, the largest aggregate wages paid occur within Services, which comprise 54% of total global wages annually, followed distantly by Manufactured Products with 15% of global wages (see supplementary data for summary tables of wage intensity and percentages by sector. Wages alone are insufficient predictors of impact when accounting for household consumption by employees. For example, emissions from Manufactured Products remain relatively unchanged ( figure 1(a)), which suggests that increased impacts attributable to household consumption by labour in this sector are offset by impacts embodied in products consumed by labour employed by other sectors. When examining impacts averaged over the most recent five-year period available (2007-2011), the Service and Construction sectors show the largest overall increases after closure, with increases in GHG emissions of 102% and 71%, increased land use of 213% and 203%, and increased water consumption of 208% and 394%, respectively. Impacts associated with the Food sector decrease more than any other sector consistently across all three metrics (GHG: -85%; land use: -85%; water: -90%).
The Service sector occupies the largest proportion of GHG emissions in both the open and closed models, and approximately doubles from 22% to 45% of the global total upon IO model closure. The Service sector also rises to the top position in land use and water consumption from third and second place, respectively, rising from 15% for both to 48% and 46% shares of global totals. The Food sector falls from the top driver of both land use and water consumption in the open model to fifth place for both in the closed model (48%-4% and 68%-1%, respectively). In other words, food production is shown to be much less environmentally burdensome than conventionally thought when it is not attributed with impacts generated by consumption supporting employees working in other sectors.
Specific industries with the largest relative increases (measured in percent change) in impact after model closure are concentrated in the Construction, Manufactured Products, Service, and Shelter sectors. In the Service sector, 'Computer and related activities' increases by the largest amount: by 292%, 680%, and 770% for GHG emissions, land use, and water consumption, respectively. The next largest increases in industrial impacts in Services (in decreasing order) are 'Public administration, defense and compulsory social security' , 'Education' , and 'Research and development' , with increases of approximately 125%-175%, 350%-550%, and 450%-650% in GHG emissions, land use and water consumption, respectively (see supplementary data for full analysis). We find up to 1100% increases in land use for industries in the Construction sector, and up to 1200% increases in water consumption for industries in the Shelter sector. Industries with the largest relative decreases in impacts are overwhelmingly found in the Food sector, along with industries closely related to food production or food services (classified as part of other sectors), and select Clothing and Manufactured Products industries; with some industries specific to food processing and electricity production exhibiting declines of −99.8%, −99.7%, and −99.5% of their original (i.e. open-CBA) values for GHG emissions, land use, and water consumption, respectively. Note that these percent differences are true for absolute impacts as well as impact intensities (section 3.2).
Environmental impact intensities of sectors
We find a dramatic convergence in sectoral impact intensities when household consumption of labour is endogenized ( figure 2). In the open model, differences in environmental impact intensity among sectors are statistically different for all three environmental metrics (Kruskal-Wallis: p = 2e-7 for GHG emissions; p = 7e-10 for land use; p = 3e-10 for water consumption), with the Food, Clothing, Mobility, and Shelter sectors showing statistically higher impact intensity than the Construction, Manufacturing, Service, and Trade sectors (Mann-Whitney pairwise comparison, p < 0.05, figure 2(a)). By contrast, in the closed model, sectoral differences in environmental impact intensity are generally not statistically significant (Kruskal-Wallis: p = 0.3 for GHG emissions; p = 0.7 for land use; p = 0.04 for water consumption), with the exception of water consumption in which the Food sector remained statistically higher per unit economic output than that of Shelter (Mann-Whitney pairwise comparison: p < 0.05, figure 2(b)).
Although the results show that overall, sectors do not differ significantly in their impacts, the aggregated figures mask a wide spread of impact intensities intra-sectorally. Simply said, industries within sectors do not all have the same impact. In Services, due to the heterogeneity of wages within the sector, impacts of employment vary dramatically. Intuitively, industries that employ more low-skilled labour (with correspondingly lower total wages paid) have lower impact per unit production than high-skilled, high-wage industries. For example, within Services, the closed impacts of 'Computer and related activities' (GHG: 0.5 kg CO 2 e € −1 , land use: 0.9 µm 2 € −1 , water: 20 nl € −1 ) are 20 to 25 times larger than that of the 'Hotels and restaurants' industry (0.02 kg CO 2 e € −1 , land use: 0.04 µm 2 € −1 , water: 1 nl € −1 ). A full account of the open and closed impact intensities is presented in the supplementary data.
International distribution of environmental impacts embodied in trade flows
The shift from an open to closed model amplifies the allocation of environmental impacts resulting from final consumption to wealthy countries with a corresponding decrease in allocation to developing countries ( figure 3). Country-level results follow sectoral patterns-countries with a high proportion of service-based industries tend to exhibit increases in impacts, while those with high proportions of primary and secondary production, such as agriculture and manufacturing, show marked decreases in impacts. When compared to the open model (which represents a typical consumption-based accounting of environmental impacts), Scandinavian and Western European countries, Japan, and the United States show prominent increases in impacts associated with economic production, while countries in Africa, Eastern Europe, and South, Central, and Southeast Asia show notable decreases ( figure 3).
In absolute terms, closed-CBA reveals China and India as the largest exporters of GHG emissions embodied in goods and services, while the United States and Japan are the largest importers for all three impacts studied. The largest exporters of embodied land use include Russia and Brazil, and the largest exporters of embodied water consumption are India and China (supplementary data). Note that the rest of world (RoW) regions exhibit declines in impacts on the same scale or higher than individual countries identified; the largest decreases in GHG emissions and land use would be by RoW Asia and Pacific and RoW Africa, respectively, if these regions are compared directly to countries.
When switching from open to closed models, annual international transfers of environmental impacts increase by approximately 3.3 GtCO 2 e for GHG emissions, 8.8 Mkm 2 for land use, and 170 km 3 for water consumption (using mean values for the 2007-2011 period). This represents an additional shift on top of that which occurs when moving from production-to consumption-based accounting of impacts in an open model configuration. For comparison, there are 36 GtCO 2 e of GHG emissions, 65 Mkm 2 of land use, and 1100 km 3 of water consumption embodied in trade from a conventional consumption-based perspective (i.e. when switching from PBA to open-CBA). In percentage terms, the total amount of GHG emissions, land use, and water consumption embodied in trade (when switching from PBA to open-CBA) has been estimated at approximately 27%, 30%, and 28% of global totals for the mean of the 2007-2011 period; consequently, the trade flows in our closed model increase to 36%, 44%, and 43% of global totals (from PBA to closed-CBA; i.e. an increase of 9, 14, and 15 percentage points, respectively, from open-to closed-CBA). Note that most of the shifts in impacts comparing open and closed models are concentrated in a small number of developing and emerging economies, and a larger number of developed ones. This pattern is broadly similar to that of GHG emissions embodied in trade when moving from production-to consumptionbased accounting.
Geographic changes due to model closure are largest for water consumption (changes of up to ±90%) followed by land use (up to ±60%), and GHG emissions (up to ±30%). For example, the largest increases in GHG emissions upon model closure occur in Norway (+30%), Switzerland, Luxembourg, Sweden, and France (each approximately +20%), with 'Education' as the largest single driving industry for all five countries (supplementary data). This predominance of increased impacts in the high-wage service-oriented economies in northern climates is likely due to high net imports of labour-intensive goods in these countries. Over recent decades, more affluent nations have increasingly imported consumption goods from regions where labour costs are lower. Closing the EE-MRIO model with respect to labour thus exacerbates existing disparities in environmental impacts between richer and poorer nations. The shift in environmental impacts among nations that results from changing from productionto consumption-based accounting is therefore likely underestimated in conventional consumption-based accounts [27,41].
Summary of results and comparison with previous literature
After endogenizing labour in global supply chains, we show that industries typically labelled 'dirty' (i.e. high impact per unit value) are not the main drivers of environmental pressures (figure 1), and are also no 'dirtier' than services (figure 2), which are typically thought of as high productivity sectors with low environmental burdens. Instead, we find that all sectors are roughly equivalent in terms of climate, land and water impacts per unit production ( figure 3). In other words, the distributions of sectoral impacts per unit production converge, and in almost all instances, become indistinguishable from one another.
Our findings are consistent with recent research that has highlighted hidden sources of environmental impacts in the ostensibly 'clean' knowledge-based service industries [4,22,42]. This research also supports the argument that the effect of international trade can be to offshore the more impact-intensive components of global supply chains to low-wage developing countries, making the developed economies appear to be getting cleaner [10,28,[43][44][45][46]. We show that a reallocation of impacts to account for labour and household consumption amplifies the effect of offshoring, owing to disparities in income and consumption between developed and developing nations.
We speculate that India and China are still among the largest net exporters of impacts because they are the factories of the world, though their largest workforce does not imply they have the largest purchasing power. Rich countries import more than they export, and this is compounded when labour's upkeep is included. For example, much of the cotton grown in India is woven there or in China but ultimately is bought by affluent people in other countries, and the water embodied in it follows it there.
Assessing potential for green growth via a shift to services
The operation of any economic sector both requires and supports household consumption, which in turn generates environmental impacts. Therefore, we argue that in order to assess the potential for green growth via a shift to services (or any other sector), one must estimate the sector's total impact including the sector's influence on employment and aggregate demand. We demonstrate that when the associated impacts are ascribed to the employing sectors, the scope for absolute economy-environment decoupling is considerably more limited than is typically assumed.
Based on our analysis, we argue that the environmental burden of high-wage, labour-intensive (i.e. tertiary) industries has been significantly understated. Conversely, primary and secondary industries producing significant direct impacts but with lower reliance on high-wage labour have been overemphasized in relation to their environmental impact, since the demand for products from these industries is generated by the household consumption supporting production in other economic sectors, notably in Services. Our results are in line with those of Stern et al [47], Henriques and Kander [48], Parrique et al [49], and Fix [50], all of whom note a relative lack of importance of structural economic changes for environmental outcomes.
Limitations and caveats
Limitations of our study include those inherent to all EE-MRIO analyses. For example, the precision of our estimates is limited by national data quality and inconsistencies when harmonizing data across countries. Industries are approximated as being homogenous in composition (producing a single, aggregate product), while inter-industry transaction coefficients and environmental impact coefficients are treated as constant for each year. Specific to our study, model closure with respect to labour assumes that a static proportion of income is allocated by households to consumption during a given year (i.e. static savings rates). Changes in economic structure associated with tertiarization would in fact likely raise aggregate household consumption through higher wages, but would also raise savings rates, which tend to increase alongside income. As such, aggregate impacts can be expected to grow somewhat more slowly than wages paid as a result of tertiarization. To clarify, we are interested in impacts related to household expenditures, not due to economic activity that is driven by investments (made with household savings). We acknowledge that savings may drive impacts, but we expect them to be less correlated with savings rates. We leave the verification of this hypothesis to future inquiry.
The composition of aggregate household demand can be expected to change in line with tertiarization and increased aggregate wages, with a growing level of demand for services. This change is not modeled explicitly in our closed-EE-MRIO formulation but is unlikely to invalidate our findings, as additional service demand would typically add to, rather than substitute for, absolute demand for primary and secondary goods [49]. Rather, people tend to maintain spending on necessities like food, energy, and shelter, while simultaneously increasing their spending on services (for example, see [51]). We therefore expect that primary and secondary output would increase with a growing tertiary sector. In other words, we expect proximate economic drivers of environmental impacts to be relatively unaffected by tertiarization, barring unprecedented disruptions to trends in technological or behavioural factors in the near term, which we feel to be an acceptable assumption given the evidence provided to date. Furthermore, as our analysis shows similar levels of environmental impact intensity across sectors, the effects of modest changes in demand composition can be safely assumed to have a minor effect. Ultimately, a dynamic closed-EE-MRIO model would be required to assess the effect of more radical long-term changes in demand composition, which we leave for future study.
Possible roles of tertiarization in sustainable development
We show the effect of tertiarization on global environmental impacts to be statistically insignificant, all else being equal. However, this does not imply that tertiarization cannot play a beneficial role in sustainable development. Tertiary industries typically entail higher levels of employment and remuneration, and so we expect that impacts determined via closed-CBA will be more responsive to decreases in impact intensity (through technological improvements) and consumption levels per capita, than open-CBA, since household consumption is a primary driver of environmental impacts. If it were to occur alongside cleaner production and reductions in aggregate demand, tertiarization may augment the mitigation of environmental burdens. Conversely, this greater sensitivity means that tertiarization may exacerbate environmental impacts if household consumption continues to increase in line with historical trends.
It is important to note that dematerialization via technological changes, the first pathway mentioned in the introduction, would reduce total impacts irrespective of structural changes in economic composition. However, we are concerned that dematerialization on the scale required to achieve absolute reductions in environmental impacts may be implausible on relevant timelines [49,52], particularly given that efficiency gains from technological improvements often translate to productivity increases rather than a reduction of the environmental impacts of production [53,54]. As such, our results suggest that tertiarization will not help to reduce global environmental impacts or assist sustainable development without simultaneous reductions in household consumption.
To date, attempts to identify pathways towards sustainability have focused heavily on proximate, rather than structural causes of environmental pressures. The service sectors of developed economies foster higher than average material standards of living, stemming from high wages and consumptionoriented social norms. The patterns of consumption required to maintain the provision of labour, regardless of industry, face the same complex web of economic interdependencies implicated in the generation of environmental impacts. As such, increases in income (and aggregate economic output) cannot easily be reconciled with sustainable development [55][56][57][58]. Rather, our results suggest that, barring unprecedented technological innovation, the patterns of consumption behavior that currently permeate the social fabric of contemporary societies will need to change in order to alleviate the environmental harm caused by economic activity. A broader range of research perspectives should therefore be directed to assess how the United Nations' Sustainable Development Goals (SDGs) can be achieved, and notably to how we can 'create the conditions that allow people to have quality jobs that stimulate the economy while not harming the environment.' (SDG 8) [59]. Closed formulations of EE-MRIO models could also be prioritized in studies of economic change and environmental impact, and be used alongside standard IO analysis for environmental accounting more generally to better inform macroeconomic analysis and decisionmaking. As discussed by Ottelin and colleagues [60], the discussion of appropriate policy instruments in alignment with the broader CBA perspective is lacking. Our findings support this assessmentfuture research should be directed towards exploring appropriate policy instruments for the amelioration of environmental impacts stemming from economic activity while recognizing the limitations of proposed pathways for decoupling of economy and environment. | 7,025.2 | 2020-03-12T00:00:00.000 | [
"Economics"
] |
coatings Microstructure and Corrosion Properties of Laser Cladding Fe-Based Alloy Coating on 27SiMn Steel Surface
: In this paper, the corrosion performance of a laser cladding Fe-based alloy coating on the surface of 27SiMn steel was studied. The Fe-based alloy coating was prepared on a 27SiMn steel surface by high-speed laser cladding. The microstructure, morphological characteristics, element content, and phase composition of the cladding layer were analyzed by an optical microscope (OM), scanning electron microscope (SEM), energy dispersive spectrometer (EDS), and X-ray diffractometer (XRD), respectively. The corrosion resistance of the 27SiMn substrate and Fe-based coating in different corrosive environments was tested through an electrochemical experimental station, a salt spray corrosion test box, and an immersion experiment. The Fe-based alloy cladding layer is mainly composed of a-Fe, M 7 C 3 , M 2 B, and Cr 3 Si. The cladding layer structure forms planar, cellular, dendrite, and equiaxed dendrite during rapid solidification. The corrosion potential of the cladding layer is higher than that of the substrate, and the arc radius of the cladding layer is larger than that of the substrate. After salt spray corrosion, a large number of red and black corrosion products appeared on the surface of the substrate; the surface of the cladding layer sample was still smooth, and the morphology was almost unchanged. The weight loss results of the cladding layer and 27SiMn matrix after 120 h of immersion are 0.0688 and 0.0993 g · cm − 2 , respectively. The weight loss of the cladding layer is 30.7% less than that of the matrix. Conclusion: Laser cladding an Fe-based alloy coating on the surface of 27SiMn has better corrosion resistance than the substrate, which improves the corrosion resistance of hydraulic supports.
Introduction
The 27SiMn hydraulic support is indispensable core support equipment for underground mining. To adapt to the complex environment of coal mines, the support column not only needs to have high enough hardness, wear resistance, impact resistance, and other properties but also needs to have good corrosion resistance. To effectively improve the corrosion resistance of the support column, it can be surface modified to improve its corrosion resistance. Laser cladding technology is a kind of material surface modification technology. Its principle is to melt the metal powder and weld it on the substrate surface with a high-energy laser beam so that the substrate and cladding surface can achieve good metallurgical bonding [1].
In recent years, a large number of scholars have studied laser cladding. Saeedi et al. [2] prepared NiCr-TiC metal matrix composites by laser cladding NiCr-TiC and NiCr-TiC powders on a stainless-steel matrix to improve the hardness and corrosion resistance of AISI420 (Martensitic stainless steel) stainless steel. Farotade et al. [3] studied the microstructural characteristics and surface properties of a Ti-6Al-4V alloy laser cladding nickel-zirconium-boron coating.
For the main material of hydraulic support, the laser cladding of 27SiMn steel, related researchers have also conducted a lot of research. Chai et al. [4] studied the effect of laser power on the laser cladding of iron-based alloys on the surface of 27SiMn steel, and the results showed that the tensile strength and microhardness of the cladding layer prepared under different laser power levels were higher than that of the 27SiMn steel substrate. Yang et al. [5] used JG-2(A specially developed iron-based alloy powder brand) and JG-3(A specially developed iron-based alloy powder brand), two kinds of iron-based alloy cladding powders, for cladding on 27SiMn hydraulic support. By comparing the contents of the two kinds of powder elements, they found that JG-2 alloy powder contained more Cr and Ni elements, was easier to form a passivation film, and could strongly hinder the development of corrosion.
The hydraulic prop is used downhole, and water droplets from the formation are sprayed on it to form a film of water on the surface. The water film on the surface of the hydraulic prop contains strong corrosive anions, causing electrochemical corrosion reactions [6]. The corrosion of metals in the atmosphere is mainly affected by the atmosphere, the corrosion composition, and the corrosion factors of pollutants [7]. The middle and upper parts of the hydraulic support work in the complex environment of the underground coal mines, and the middle and upper parts are mainly corroded by the atmosphere. The lower part of the hydraulic prop is immersed in mine water with weak acid and a large number of anions in the water quality.
In this paper, an Fe-based alloy coating was prepared by high-speed laser cladding on the surface of 27SiMn steel, and the microstructure, phase composition, and element composition of the coating were analyzed. The corrosion resistance of the substrate and coating under different corrosion environments was analyzed by electrochemical corrosion, salt spray corrosion, and immersion corrosion.
Material
The substrate used in this test is a hollow cylindrical 27SiMn material with an outer diameter of 123 mm and a length of 600 mm. Sanding with sandpaper was performed before cladding to remove rust and oil until the surface showed a metallic luster. It was then cleaned with alcohol and dried for use. Its chemical composition is listed in Table 1. The cladding powder used is an Fe-based alloy powder with an average diameter of 38 µm. The spherical shape of the powder can ensure better flow properties. It is composed of Fe, Cr, Ni, Si powder, and other trace element powders. The specific ingredients are shown in Table 2.
Preparation of the Cladding Layer
Use the RFL (Raycus Fiber Laser)-C4000 high-power fiber laser with the DPSF (Dual Package System Framework)-2 powder feeder was used to perform synchronous powder feeding laser cladding on the substrate, and the shielding gas and powder feeding gas were both Ar. The specific cladding process parameters are shown in Table 3.
Method
The sample after laser cladding was cut into multiple pieces of 10 × 10 × 10 mm 3 using a wire-cutting machine. The surface and cross-section of the cladding layer were ground and polished. The metallographic structure of the sample section was observed by a Motic-AE2000MET optical microscope (Motic, Hong Kong, China) after metallographic corrosion. A Zeiss (ZEISS: ΣIGMA300) field emission scanning electron microscope (Carl Zeiss, Jena, Germany) was used to observe the microstructure and morphology of the sample, and the element distribution and content of the coating were detected by an energy spectrometer (EDS, Carl Zeiss, Jena, Germany). An Empyrean X-ray diffractometer (PANalytical, Almelo, The Netherlands) was used to determine the phase of the sample. The test conditions were a Cu target, the diffraction range was 20-80 • , and the diffraction speed was 2 • /min. The diffraction data were analyzed and processed using Jade6.5. A VH-Z100R microscope (KEYENCE, Osaka, Japan) was used to observe the surface corrosion morphology.
Electrochemical experiments were carried out on an electrochemical workstation with an RST5000 three-electrode system (Ceres, Zhengzhou, China). The samples were treated in advance. In the electrochemical corrosion test, 3.5% NaCl solution was used as the electrolyte solution, the sample with the test area of 1 cm 2 was used as the working electrode, the saturated calomel electrode was used as the reference electrode, and the metal platinum sheet was used as the auxiliary electrode. Under the condition of stable open-circuit potential, the test frequency range of the test was set to 10 −2 -10 5 Hz and the AC (Alternating current) amplitude to 10 mV for the impedance test. A scanning rate of 0.5 mV/s was set to conduct the action potential polarization test in the range of −1000-2000 mV.
The LJ-60A salt spray corrosion box continuous spray was used for the salt spray experiment test (simulating atmospheric corrosion). The sample was treated before the salt spray test. The spray pressure was maintained at 1 kg/cm 2 , the temperature in the salt spray box was 35 ± 2 • C, and the corrosive medium was 5 ± 0.5% NaCl aqueous solution. The salt spray experiment lasted for 48 h.
The static corrosion of the cladding layer and substrate was evaluated by an immersion test. The corrosive liquid simulated mine water was mixed with 5% (NaCl, CaSO 4 , FeSO 4 ) in a ratio of 1:1:1, and sulfuric acid was added to mix the corrosive liquid with a pH value of about 3. Before soaking, the sample was pretreated and weighed, and placed into the sample bottle. They were then placed into a corrosive solution for 120 h and removed. After the taken-out sample was cleaned and air-dried, the mass of the sample was weighed with an electronic balance with an accuracy of 0.0001 g.
Results and Discussion
The cross-sectional morphology of the cladding layer is shown in Figure 1. It can be seen that the cladding layer is intact, without pores and cracks. Figure 2 shows the XRD pattern of the laser cladding Fe-based alloy cladding layer. It can be seen from Figure 2 that the Fe-based alloy cladding layer is mainly composed of a-Fe solid solution and intermetallic compounds M 7 C 3 , M 2 B, Cr 3 Si. The lattice parameters of a-Fe in the body-centered cubic structure (bcc) of the cladding layer are a = 0.2886 nm, as measured by the experiment. Compared with the lattice parameter of body-centered cubic a-Fe at room temperature (a = 0.2866 nm) [8], the lattice parameter of a-Fe of the cladding layer increased. With the change in the lattice parameters, the same group of parallel (hkl) crystal planes will be affected, and the interplanar spacing d hkl will also increase. The calculation formula is as follows [9]: The relationship between the distance between crystal planes and its index in the cubic crystal system is:
Phase Analysis
where a is the lattice parameter; h, k, and l are the crystal plane indices; and d is the crystal plane spacing. This is mainly due to the different properties of solute atoms and solvent atoms and different atomic radii. When the solute atoms dissolve into the crystal lattice of the solvent, the lattice parameters of the solid solution will increase. C, B, and Cr in the alloy powder melt into the solvent metal (Fe) crystal lattice to form a solid solution. There is no obvious γ-Fe phase residual in the cladding layer, which is mainly caused by the very high cooling rate during the laser cladding process. Under such a high cooling rate, the austenite enters the martensite transformation region without growing up [10][11][12]. M 7 C 3 and M 2 B are metal interstitial compounds formed by the transition metal M with a larger radius and C and B with a smaller radius in the alloy powder. Cr 3 Si is a metal close-packed phase formed by Cr atoms and Si atoms.
Microstructure Morphology of the Coating
The structure of the cladding layer formed planar crystals, cell crystals, dendrites, and equiaxed dendrites during rapid solidification. It can be seen from Figure 3a that the structure at the bottom of the cladding layer grows in a planar crystal manner and forms a good metallurgical bond with the matrix. As the cladding thickness increases and the cladding process changes, the temperature of the base material is low. The undercooling degree of the structure at the bottom of the cladding layer is small, and the temperature gradient G is large. Due to the existence of a temperature gradient and concentration gradient, although the supersaturation is uniform, the crystal will still grow into a flat crystal plane. This situation is because the growth rate of the entire crystal plane is determined by the supersaturation of the solute concentration at the outcropping point on the crystal plane, which is the core point that plays a dominant role and promotes growth on the crystal plane [13]. At a large temperature gradient G and a small crystal growth rate R, the G/R value is large, so the solidified structure grows in a flat plane at a low speed to form a flat crystal. In the area above the plane crystal, a new interface morphology composed of many convex circular cells similar to the paraboloid of revolution-and network-shaped recessed grooves appears. This morphology is called cellular crystal [14]. This is because the distance between the region and the substrate increases, and the temperature gradient-solidification rate ratio decreases, resulting in the formation of a cellular crystal structure. Bartkowski et al. [15] also came to a similar conclusion. He reported that the temperature gradient-solidification rate ratio decreased, resulting in the formation of the cellular crystal structure. It can be seen from Figure 3b that the middle of the cladding layer is a columnar dendrite structure. The growth direction of cellular crystals is perpendicular to the solid-liquid interface and has nothing to do with crystallographic orientation. The G/R (Temperature gradient G, solidification rate R) ratio decreases, and the solute concentration changes. At this time, the convex unit cell extends farther to the melt, facing the new component undercooling; the original parabolic interface of the cell crystal gradually becomes unstable. The growth direction of the unit cell begins to turn to the preferential crystal growth direction. The lateral direction of the cell crystal will also be affected by crystallographic factors, and a flange structure will appear. When the composition is supercooled and strengthened, a sawtooth structure will appear on the flange (that is, columnar dendrites). It can be seen from Figure 3c that the dendritic structure of the cladding layer is refined in the upper surface area of the cladding layer [16]. The grain size is smaller than the size of the cladding layer at the bottom and the middle. This is because the upper part of the cladding layer is easier to contact with the outside air; the heat loss is accelerated, and the component supercooling zone is widened [17]. The small temperature gradient G and high cooling rate v make new crystal nuclei appear in the liquid at the same time or continuously, prevent the unidirectional extension of dendrites, and promote the formation of small equiaxed branches on the upper part of the cladding layer. Figure 4 shows an EDS diagram of the microstructure in the middle region of the prepared cladding layer. It can be seen that the content of Fe, Cr, and Ni metal elements is consistent with the powder content, indicating that although segregation occurs during the crystallization process of the cladding layer structure, no significant segregation and deposition of metal elements occurs in the cladding layer area. Figure 5 shows an EDS analysis diagram at the interface of the cladding layer. It can be seen that the Fe element content increases from the cladding layer to the substrate, while the Cr and Ni metal element content decreases. This is mainly because the content of the 27SiMn substrate iron element is higher than that of the cladding layer. The Cr and Ni content of the layer is higher than that of the substrate. The results of EDS composition analysis show that the melting of part of the matrix in the transition area will cause the elements in the matrix to enter the molten pool, resulting in the dilution of the elements in the cladding layer, and the closer to the matrix, the more obvious the dilution phenomenon.
Electrochemical Corrosion Performance
The electrochemical impedance spectroscopy (EIS) of the cladding layer and the substrate in 3.5% NaCl solution is shown in Figure 6. It can be seen from Figure 6a that the capacitive arc radius of the cladding layer is larger than that of the substrate, which indicates that the cladding layer has better corrosion resistance. Laser cladding an Fe coating on the surface of 27SiMn can improve the corrosion of hydraulic props. It can be seen from the Bode plot in Figure 6b that the impedance mode |Z| value of the cladding layer in the low-frequency band is greater than that of the 27SiMn matrix. According to Formula (2): where Z is the real part of the impedance, and Z" is the imaginary part of the impedance. The impedance model of the cladding layer is 4.22 × 103 ohm, and the impedance model of 27SiMn is 1.20 × 103 ohm. The impedance modulus value in the low-frequency region represents the degree of penetration of the solution into the sample. The low-frequency impedance modulus value of the cladding layer is significantly greater than that of the substrate, indicating that the solution penetration of the cladding layer is less than the substrate, and the cladding layer is resistant to electrochemical corrosion Ability is better than the matrix. It can be seen from Figure 6c that with the change of frequency, the phase peak of the 27SiMn matrix and the cladding layer is also constantly changing. In the low-frequency and high-frequency phases, the phase peak of the cladding layer is larger than the substrate; at the intermediate frequency phase, the phase peak of the cladding layer is smaller than the substrate. The small phase peak has high capacitance performance, and more charge accumulation is easily generated on the surface, which accelerates the corrosion of the sample [18,19]. Compared with the substrate, the cladding layer corrodes slowly at low and high frequencies and corrodes faster in the middle-frequency region. Figure 7 shows the Tafel polarization curve of the 27SiMn substrate and Fe-based alloy cladding layer in 3.5% NaCl solution. The corrosion potential of the cladding layer is −0.2503 V, and the corrosion potential of the 27SiMn substrate is −0.3479 V. The corrosion potential reflects the difficulty of the material being corroded. The smaller the corrosion potential, the easier it is to be corroded [20]. The cladding layer has a higher corrosion electric potential and is more resistant to corrosion than 27SiMn. Figure 8 shows the electrochemical corrosion morphology of the cladding layer and 27SiMn substrate. It can be observed from the figure that the surface of the cladding layer undergoes pitting corrosion and local corrosion after electrochemical corrosion, and the surface of the substrate undergoes surface corrosion after electrochemical corrosion. The cladding layer and 27SiMn matrix are in NaCl solution, the cathode reaction is a reduction reaction, and the reaction process is as follows: The cladding layer and 27SiMn substrate anode are oxidation reactions, and the reaction process is as follows: Cladding layer: Fe − 2e = Fe 2+ (4) Mo − 3e = Mo 3+ (6) 27SiMn matrix: Fe − 2e = Fe 2+ (7) Mn − 2e = Mn 2+ (8) According to Table 4 [21], it can be seen that the cladding layer is more resistant to corrosion than the substrate. This is mainly because the alloy powder has Ni and Mo elements, which have a higher reduction potential than Fe. Although the equilibrium potential of Cr is much lower than that of iron, Cr is easily passivated. It improves the corrosion potential of the cladding layer. The reduction potential of Mn in the 27SiMn matrix is lower than that of Fe. Figure 9 shows the salt spray corrosion morphology of the cladding layer and 27SiMn substrate. It can be observed that a large number of red and black rusts appear on the surface of the substrate, and the corrosion is more serious. However, the surface of the cladding sample is still flat and smooth, and the morphology is almost unchanged. Macroscopically, it shows that the cladding layer has excellent salt spray corrosion resistance. The relationship between the number of alloying elements and the corrosion rate (v) of steel is as follows [22,23]: Using the relationship between the alloying element content and the corrosion rate in Formula (9), according to the average chemical composition content of Fe alloy powder and 27SiMn, the calculated corrosion rate of the cladding layer is smaller than that of the 27SiMn substrate. This is mainly because the Cr and Si elements of the cladding layer significantly improve the atmospheric corrosion resistance of the cladding layer, while the increase in Mn content has no obvious effect on the atmospheric corrosion resistance of the steel [22][23][24]. The results are similar to the atmospheric corrosion results of 27SiMn reported by Junyan et al. [23]. Cr is very easy to passivate and is very stable under natural conditions and many corrosive media. Cr is not only easy to passivate under conditions containing oxidants and oxygen but can also passivate in water. The dense passivation film of the cladding layer can effectively prevent oxygen in the air from penetrating the cladding layer. At the same time, the passivation film can be repaired by itself after being damaged in the atmospheric environment. Si helps prevent intergranular corrosion while cladding the intermetallic compounds carbides, borides, and Cr3Si formed in the coating layer. It can effectively reduce the penetration channel of the corrosive medium Cl − and prevent the corrosive medium from penetrating the cladding layer. Improve the atmospheric corrosion resistance of the cladding layer. Lin et al. [25] also pointed out that chromium passivation protects the coating and improves its corrosion resistance. Figure 10 shows the immersion corrosion morphology of the cladding layer and 27SiMn substrate in the corrosive solution simulated mine water for 120 h. According to the corrosion morphology, it can be seen that pitting corrosion has occurred in the cladding layer, and uneven ulcer corrosion occurred in the substrate. Groups of pits, which are difficult to count, occurred on the surface of the cladding layer. This is mainly due to the destruction of the passivation film and oxide film formed on the cladding layer under long-term immersion corrosion [26]. The pit-like local corrosion of different sizes and depths appeared on the surface of the substrate. The weight loss of the cladding layer and 27SiMn substrate after 120 h of immersion was, respectively, 0.0688 and 0.0993 g·cm −2 . It can be seen that the weight loss of the cladding layer during immersion corrosion is less than that of the substrate. This is mainly due to the small pitting corrosion of the cladding layer during immersion corrosion and the weight loss caused by countless pitting corrosion. When the cladding layer is immersed, the passivation film must be corroded first, and then micropitting can be carried out. However, the corrosion of the substrate after immersion is mainly local pit-like corrosion, and the size and depth of the corrosion pits are larger, which causes more weight loss.
Conclusions
The Fe-based alloy coating was clad on the surface of 27SiMn by laser cladding technology to prepare a coating with a thickness of about 1.2 mm, complete morphology, a good metallurgical bond between the bottom and the substrate, and no pores or cracks in the layer. The element composition, phase composition, and structural morphology of the cladding layer were explored. Electrochemical, salt spray corrosion, and immersion corrosion studies were carried out on Fe-based alloy coatings and 27SiMn hydraulic props. The conclusions are as follow: (1) The Fe-based alloy cladding layer is mainly composed of a-Fe solid solution, M 7 C 3 , M 2 B, and Cr 3 Si. Planar crystals, cellular crystals, dendrites, and equiaxed dendrites are formed in the cladding layer. (2) The electrochemical corrosion performance test of the cladding layer and 27SiMn substrate shows that the corrosion potential of the cladding layer is larger, and the capacitive arc radius is larger than that of the substrate. This indicates that the cladding layer has better corrosion resistance than 27SiMn. The surface of the cladding layer undergoes pitting and local corrosion after electrochemical corrosion, and the surface of the substrate undergoes surface corrosion after electrochemical corrosion. (3) The cladding layer and 27SiMn matrix were corroded by salt spray for 48 h. It can be observed that the surface of the substrate is corroded seriously, while the surface of the cladding layer sample is still smooth and has almost no change in morphology. After immersion corrosion of the cladding layer and 27SiMn substrate in the mine water simulated by the corrosive solution for 120 h, the weight loss of the cladding layer during immersion corrosion is 0.0305 g·cm −2 , less than that of the substrate. The cladding layer is more resistant to corrosion than the 27SiMn substrate in salt spray corrosion and immersion corrosion. Institutional Review Board Statement: Not applicable. | 5,619.6 | 2021-05-07T00:00:00.000 | [
"Materials Science"
] |
YOLO-v1 to YOLO-v8, the Rise of YOLO and Its Complementary Nature toward Digital Manufacturing and Industrial Defect Detection
: Since its inception in 2015, the YOLO (You Only Look Once) variant of object detectors has rapidly grown, with the latest release of YOLO-v8 in January 2023. YOLO variants are underpinned by the principle of real-time and high-classification performance, based on limited but efficient computational parameters. This principle has been found within the DNA of all YOLO variants with increasing intensity, as the variants evolve addressing the requirements of automated quality inspection within the industrial surface defect detection domain, such as the need for fast detection, high accuracy, and deployment onto constrained edge devices. This paper is the first to provide an in-depth review of the YOLO evolution from the original YOLO to the recent release (YOLO-v8) from the perspective of industrial manufacturing. The review explores the key architectural advancements proposed at each iteration, followed by examples of industrial deployment for surface defect detection endorsing its compatibility with industrial requirements.
Introduction
Humans via the visual cortex, a primary cortical region of the brain responsible for processing visual information [1], are able to observe, recognize [2], and differentiate between objects instantaneously [3]. Studying the inner workings of the visual cortex and the brain in general has paved the way for artificial neural networks (ANNs) [4] along with a myriad of computational architectures residing under the deep learning umbrella. In the last decade, owing to rapid and revolutionary advancements in the field of deep learning [5], researchers have exerted their efforts on providing efficient simulation of the human visual system to computers, i.e., enabling computers to detect objects of interest within static images and video [6], a field known as computer vision (CV) [7]. CV is a prevalent research area for deep learning researchers and practitioners in the present decade. It is composed of subfields consisting of image classification [8], object detection [9], and object segmentation [10]. All three fields share a common architectural theme, namely, manipulation of convolutional neural networks (CNNs) [11]. CNNs are accepted as the de facto when dealing with image data. In comparison with conventional image processing and artificial defection methods, CNNs utilize multiple convolutional layers coupled with aggregation, i.e., pooling structures aiming to unearth deep semantic features hidden away within the pixels of the image [12].
Artificial intelligence (AI) has found opportunities in industries across the spectrum from renewable energy [13,14] and security to healthcare [15] and the education sector. However, one industry that is poised for significant automation through CV is the manufacturing industry. Quality inspection (QI) is an integral part of any manufacturing domain providing integrity and confidence to the clients on the quality of the manufactured products [16]. Manufacturing has wide scope for automation; however, when dealing with surface inspection [17], defects can take sophisticated forms [18], making human-based and ResNet [34]. AlexNet is proposed in 2012 and consists of five convolutional, three pooling, and three fully connected layers primarily utilized for image classification tasks. VGGNet focused on performance enhancement by increasing the internal depth of the architecture, introducing several variants with increased layers, VGG-16/19. GoogleNet introduced the cascading concept by cascading multiple 'inception' modules, whilst Res-Net introduced the concept of skip-connections for preserving information and making it available from the earlier to the later layers of the architecture.
The motive for an object detector is to infer whether the object(s) of interest are residing in the image or present the frame of a video. If the object(s) of interest are present, the detector returns the respective class and locality, i.e., location dimensions of the object(s). Object detection can be further divided into two sub-categories: Two-stage methods and one-stage methods as shown in Figure 1. The former initiates the first stage with the selection of numerous proposals, then in the second stage, performs prediction on the proposed regions. Examples of two-stage detectors include the famous R-CNN [35] variants, such as Fast R-CNN [36] and Faster R-CNN [37], boasting high accuracies but low computational efficiency. The latter transforms the task into a regression problem, eliminating the need for an initial stage dedicated to selecting candidate regions; therefore, the candidate selection and prediction is achieved in a single pass. As a result, architectures falling into this category are computationally less demanding, generating higher FPS and detection speed, but in general the accuracy tends to be inferior with respect to two-stage detectors.
Original YOLO Algorithm
YOLO was introduced to the computer vision community via a paper release in 2015 by Joseph Redmon et al. [29] titled 'You Only Look Once: Unified, Real-Time Object Detection'. The paper reframed object detection, presenting it essentially as a single pass regression problem, initiating with image pixels and moving to bounding box and class probabilities. The proposed approach based on the 'unified' concept enabled the simultaneous prediction of multiple bounding boxes and class probabilities, improving both speed and accuracy.
Since its inception in 2016 until the present year (2023), the YOLO family has continued to evolve at a rapid pace. Although the initial author (Joseph Redmon) halted further work within the computer vision domain at YOLO-v3 [38], the effectiveness and potential of the core 'unified' concept have been further developed by several authors, with the latest addition to the YOLO family coming in the form of YOLO-v8. Figure 2 presents the YOLO evolution timeline.
Original YOLO Algorithm
YOLO was introduced to the computer vision community via a paper release in 2015 by Joseph Redmon et al. [29] titled 'You Only Look Once: Unified, Real-Time Object Detection'. The paper reframed object detection, presenting it essentially as a single pass regression problem, initiating with image pixels and moving to bounding box and class probabilities. The proposed approach based on the 'unified' concept enabled the simultaneous prediction of multiple bounding boxes and class probabilities, improving both speed and accuracy.
Since its inception in 2016 until the present year (2023), the YOLO family has continued to evolve at a rapid pace. Although the initial author (Joseph Redmon) halted further work within the computer vision domain at YOLO-v3 [38], the effectiveness and potential of the core 'unified' concept have been further developed by several authors, with the latest addition to the YOLO family coming in the form of YOLO-v8. Figure 2 presents the YOLO evolution timeline.
Original YOLO
The core principle proposed by YOLO-v1 was the imposing of a grid cell with dimensions of s×s onto the image. In the case of the center of the object of interest falling into one of the grid cells, that particular grid cell would be responsible for the detection of that object. This permitted other cells to disregard that object in the case of multiple appearances.
Original YOLO
The core principle proposed by YOLO-v1 was the imposing of a grid cell with dimensions of s×s onto the image. In the case of the center of the object of interest falling into one of the grid cells, that particular grid cell would be responsible for the detection of that object. This permitted other cells to disregard that object in the case of multiple appearances.
For implementation of object detection, each grid cell would predict B bounding boxes along with the dimensions and confidence scores. The confidence score was indicative of the absence or presence of an object within the bounding box. Therefore, the confidence score can be expressed as Equation (1): where ( ) signified the probability of the object being present, with a range of 0-1 with 0 indicating that the object is not present and represented the intersectionover-union with the predicted bounding box with respect to the ground truth bounding box.
Each bounding box consisted of five components (x, y, w, h, and the confidence score) with the first four components corresponding to center coordinates (x, y, width, and height) of the respective bounding box as shown in Figure 3. For implementation of object detection, each grid cell would predict B bounding boxes along with the dimensions and confidence scores. The confidence score was indicative of the absence or presence of an object within the bounding box. Therefore, the confidence score can be expressed as Equation (1): where p(object) signified the probability of the object being present, with a range of 0-1 with 0 indicating that the object is not present and IoU truth pred represented the intersection-overunion with the predicted bounding box with respect to the ground truth bounding box.
Each bounding box consisted of five components (x, y, w, h, and the confidence score) with the first four components corresponding to center coordinates (x, y, width, and height) of the respective bounding box as shown in Figure 3. As alluded to earlier, the input image is split into s × s grid cells (default = 7 × 7), with each cell predicting B bounding boxes, each containing five parameters and sharing prediction probabilities of classes (C). Therefore, the parameter output would take the following form, expressed in (2): As alluded to earlier, the input image is split into s × s grid cells (default = 7 × 7), with each cell predicting B bounding boxes, each containing five parameters and sharing prediction probabilities of classes (C). Therefore, the parameter output would take the following form, expressed in (2): Considering the example of YOLO network with each cell bounding box prediction set to 2 and evaluating the benchmark COCO dataset consisting of 80 classes, the parameter output would be given as expressed in (3): The fundamental motive of YOLO and object detection in general is the object detection and localization via bounding boxes. Therefore, two sets of bounding box vectors are required, i.e., vector y is the representative of ground truth and vector . y is the predicted vector. To address multiple bounding boxes containing no object or the same object, YOLO opts for non-maximum suppression (NMS). By defining a threshold value for NMS, all overlapping predicted bounding boxes with an IoU lower than the defined NMS value are eliminated.
The original YOLO based on the Darknet framework consisted of two sub-variants. The first architecture comprised of 24 convolutional layers with the final layer providing a connection into the first of the two fully connected layers. Whereas the 'Fast YOLO' variant consisted of only nine convolutional layers hosting fewer filters each. Inspired by the inception module in GoogleNet, a sequence of 1 × 1 convolutional layers was implemented for reducing the resultant feature space from the preceding layers. The preliminary architecture for YOLO-v1 is presented in Figure 3.
To address the issue of multiple bounding boxes for the same object or with a confidence score of zero, i.e., no object, the authors decided to greatly penalize predictions from bounding boxes containing objects (γ coord = 5) and the lowest penalization for prediction containing no object (γ noobj = 0.5). The authors calculated the loss function by taking the sum of all bounding box parameters (x, y, width, height, confidence score, and class probability). As a result, the first part of the equation computes the loss of the bounding box prediction with respect to the ground truth bounding box based on the coordinates x center , y center . As alluded to earlier, the input image is split into s × s grid cells (default = 7 × 7), with each cell predicting B bounding boxes, each containing five parameters and sharing prediction probabilities of classes (C). Therefore, the parameter output would take the following form, expressed in (2): Considering the example of YOLO network with each cell bounding box prediction set to 2 and evaluating the benchmark COCO dataset consisting of 80 classes, the parameter output would be given as expressed in (3): The fundamental motive of YOLO and object detection in general is the object detection and localization via bounding boxes. Therefore, two sets of bounding box vectors are required, i.e., vector y is the representative of ground truth and vector ̇ is the predicted vector. To address multiple bounding boxes containing no object or the same object, YOLO opts for non-maximum suppression (NMS). By defining a threshold value for NMS, all overlapping predicted bounding boxes with an IoU lower than the defined NMS value are eliminated.
The original YOLO based on the Darknet framework consisted of two sub-variants. The first architecture comprised of 24 convolutional layers with the final layer providing a connection into the first of the two fully connected layers. Whereas the 'Fast YOLO' variant consisted of only nine convolutional layers hosting fewer filters each. Inspired by the inception module in GoogleNet, a sequence of 1 × 1 convolutional layers was implemented for reducing the resultant feature space from the preceding layers. The preliminary architecture for YOLO-v1 is presented in Figure 3.
To address the issue of multiple bounding boxes for the same object or with a confidence score of zero, i.e., no object, the authors decided to greatly penalize predictions from bounding boxes containing objects ( = 5) and the lowest penalization for prediction containing no object ( = 0.5). The authors calculated the loss function by taking the sum of all bounding box parameters (x, y, width, height, confidence score, and class probability). As a result, the first part of the equation computes the loss of the bounding box prediction with respect to the ground truth bounding box based on the coordinates , .
is set as 1 in the case of the object residing within ℎ bounding box prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding box would be tasked with predicting an object with the greatest IoU, as expressed in (4): The next component of the loss function computes the prediction error in width and height of the bounding box, similar to the preceding component. However, the scale of error in the large boxes has lesser impact compared to the small boxes. The normalization of width and height between the range 0 and 1 indicates that their square roots increase obj ij is set as 1 in the case of the object residing within j th bounding box prediction in i th cell; otherwise, it is set as 0. The selected, i.e., predicted bounding box would be tasked with predicting an object with the greatest IoU, as expressed in (4): Considering the example of YOLO network with each cell bounding box p set to 2 and evaluating the benchmark COCO dataset consisting of 80 classes, th eter output would be given as expressed in (3): The fundamental motive of YOLO and object detection in general is the obje tion and localization via bounding boxes. Therefore, two sets of bounding box ve required, i.e., vector y is the representative of ground truth and vector ̇ is the p vector. To address multiple bounding boxes containing no object or the sam YOLO opts for non-maximum suppression (NMS). By defining a threshold v NMS, all overlapping predicted bounding boxes with an IoU lower than the defin value are eliminated.
The original YOLO based on the Darknet framework consisted of two sub-The first architecture comprised of 24 convolutional layers with the final layer p a connection into the first of the two fully connected layers. Whereas the 'Fast YO iant consisted of only nine convolutional layers hosting fewer filters each. Inspir inception module in GoogleNet, a sequence of 1 × 1 convolutional layers wa mented for reducing the resultant feature space from the preceding layers. The nary architecture for YOLO-v1 is presented in Figure 3.
To address the issue of multiple bounding boxes for the same object or with dence score of zero, i.e., no object, the authors decided to greatly penalize predicti bounding boxes containing objects ( = 5) and the lowest penalization for p containing no object ( = 0.5). The authors calculated the loss function by ta sum of all bounding box parameters (x, y, width, height, confidence score, and cl ability). As a result, the first part of the equation computes the loss of the boun prediction with respect to the ground truth bounding box based on the coo , .
is set as 1 in the case of the object residing within ℎ boun prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted boun would be tasked with predicting an object with the greatest IoU, as expressed in The next component of the loss function computes the prediction error in w height of the bounding box, similar to the preceding component. However, the error in the large boxes has lesser impact compared to the small boxes. The norm of width and height between the range 0 and 1 indicates that their square roots The next component of the loss function computes the prediction error in width and height of the bounding box, similar to the preceding component. However, the scale of error in the large boxes has lesser impact compared to the small boxes. The normalization of width and height between the range 0 and 1 indicates that their square roots increase the differences for smaller values to a higher degree compared to that of larger values, expressed as (5): As alluded to earlier, the input image is split into s × s grid cells (default = 7 × 7), each cell predicting B bounding boxes, each containing five parameters and sharing diction probabilities of classes (C). Therefore, the parameter output would take the lowing form, expressed in (2): Considering the example of YOLO network with each cell bounding box predi set to 2 and evaluating the benchmark COCO dataset consisting of 80 classes, the pa eter output would be given as expressed in (3): The fundamental motive of YOLO and object detection in general is the object d tion and localization via bounding boxes. Therefore, two sets of bounding box vector required, i.e., vector y is the representative of ground truth and vector ̇ is the pred vector. To address multiple bounding boxes containing no object or the same ob YOLO opts for non-maximum suppression (NMS). By defining a threshold valu NMS, all overlapping predicted bounding boxes with an IoU lower than the defined N value are eliminated.
The original YOLO based on the Darknet framework consisted of two sub-vari The first architecture comprised of 24 convolutional layers with the final layer provi a connection into the first of the two fully connected layers. Whereas the 'Fast YOLO' iant consisted of only nine convolutional layers hosting fewer filters each. Inspired b inception module in GoogleNet, a sequence of 1 × 1 convolutional layers was im mented for reducing the resultant feature space from the preceding layers. The pre nary architecture for YOLO-v1 is presented in Figure 3.
To address the issue of multiple bounding boxes for the same object or with a c dence score of zero, i.e., no object, the authors decided to greatly penalize predictions bounding boxes containing objects ( = 5) and the lowest penalization for predi containing no object ( = 0.5). The authors calculated the loss function by takin sum of all bounding box parameters (x, y, width, height, confidence score, and class p ability). As a result, the first part of the equation computes the loss of the bounding prediction with respect to the ground truth bounding box based on the coordin , .
is set as 1 in the case of the object residing within ℎ bounding prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding would be tasked with predicting an object with the greatest IoU, as expressed in (4): The next component of the loss function computes the prediction error in width height of the bounding box, similar to the preceding component. However, the sca error in the large boxes has lesser impact compared to the small boxes. The normaliza of width and height between the range 0 and 1 indicates that their square roots incr obj ij Next, the loss of the confidence score is computed based on whether the object is present or absent with respect to the bounding box. Penalization of the object confidence error is only executed by the loss function if that predictor was responsible for the ground ability). As a result, the first part of the equation computes the loss of the bounding box prediction with respect to the ground truth bounding box based on the coordinates , .
is set as 1 in the case of the object residing within ℎ bounding box prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding box would be tasked with predicting an object with the greatest IoU, as expressed in (4): The next component of the loss function computes the prediction error in width and height of the bounding box, similar to the preceding component. However, the scale of error in the large boxes has lesser impact compared to the small boxes. The normalization of width and height between the range 0 and 1 indicates that their square roots increase obj ij is set to 1 when the object is present in the cell; otherwise, it is set as 0, whilst of all bounding box parameters (x, y, width, height, confidence score, and class probity). As a result, the first part of the equation computes the loss of the bounding box diction with respect to the ground truth bounding box based on the coordinates , .
is set as 1 in the case of the object residing within ℎ bounding box diction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding box ld be tasked with predicting an object with the greatest IoU, as expressed in (4): (4) The next component of the loss function computes the prediction error in width and ht of the bounding box, similar to the preceding component. However, the scale of r in the large boxes has lesser impact compared to the small boxes. The normalization idth and height between the range 0 and 1 indicates that their square roots increase noobj ij works in the opposite way, as shown in (6): ntaining no object ( = 0.5). The authors calculated the loss function by taking the m of all bounding box parameters (x, y, width, height, confidence score, and class probility). As a result, the first part of the equation computes the loss of the bounding box ediction with respect to the ground truth bounding box based on the coordinates , .
is set as 1 in the case of the object residing within ℎ bounding box ediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding box uld be tasked with predicting an object with the greatest IoU, as expressed in (4): (4) The next component of the loss function computes the prediction error in width and ight of the bounding box, similar to the preceding component. However, the scale of or in the large boxes has lesser impact compared to the small boxes. The normalization width and height between the range 0 and 1 indicates that their square roots increase containing no object ( = 0.5). The authors calculated the loss func sum of all bounding box parameters (x, y, width, height, confidence scor ability). As a result, the first part of the equation computes the loss of prediction with respect to the ground truth bounding box based o , .
is set as 1 in the case of the object residing within prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predic would be tasked with predicting an object with the greatest IoU, as exp The next component of the loss function computes the prediction e height of the bounding box, similar to the preceding component. How error in the large boxes has lesser impact compared to the small boxes. T of width and height between the range 0 and 1 indicates that their squ The last component of the loss function, similar to the normal classification loss, calculates the class (c) probability loss, except for the nary architecture for YOLO-v1 is presented in Figure 3.
To address the issue of multiple bounding boxes for the same object or dence score of zero, i.e., no object, the authors decided to greatly penalize pre bounding boxes containing objects ( = 5) and the lowest penalization f containing no object ( = 0.5). The authors calculated the loss function sum of all bounding box parameters (x, y, width, height, confidence score, an ability). As a result, the first part of the equation computes the loss of the b prediction with respect to the ground truth bounding box based on the , . is set as 1 in the case of the object residing within ℎ b prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted b would be tasked with predicting an object with the greatest IoU, as expresse The next component of the loss function computes the prediction error height of the bounding box, similar to the preceding component. Howeve error in the large boxes has lesser impact compared to the small boxes. The n of width and height between the range 0 and 1 indicates that their square r obj ij part, expressed in (7): To address the issue of multiple bounding boxes for the same object or with a c dence score of zero, i.e., no object, the authors decided to greatly penalize predictions bounding boxes containing objects ( = 5) and the lowest penalization for predi containing no object ( = 0.5). The authors calculated the loss function by takin sum of all bounding box parameters (x, y, width, height, confidence score, and class p ability). As a result, the first part of the equation computes the loss of the bounding prediction with respect to the ground truth bounding box based on the coordi , .
is set as 1 in the case of the object residing within ℎ bounding prediction in ℎ cell; otherwise, it is set as 0. The selected, i.e., predicted bounding would be tasked with predicting an object with the greatest IoU, as expressed in (4): The next component of the loss function computes the prediction error in width height of the bounding box, similar to the preceding component. However, the sca error in the large boxes has lesser impact compared to the small boxes. The normaliz of width and height between the range 0 and 1 indicates that their square roots inc Next, the loss of the confidence score is computed based on whether the object is present or absent with respect to the bounding box. Penalization of the object confidence error is only executed by the loss function if that predictor was responsible for the ground truth bounding box.
is set to 1 when the object is present in the cell; otherwise, it is set as 0, whilst ij noobj works in the opposite way, as shown in (6): The last component of the loss function, similar to the normal classification loss, calculates the class (c) probability loss, except for the part, expressed in (7): ( ) ) 2 (7) Performance wise, the simple YOLO (24 convolutional layers) when trained on the PASCAL VOC dataset (2007 and 2012) [39,40] achieved a mean average precision (referring to cross-class performance) (mAP) of 63.4% at 45 FPS, whilst Fast YOLO achieved 52.7% mAP at an impressive 155 FPS. Although the performance was better than real-time detectors, such as DPM-v5 [41] (33% mAP), it was lower than the state-of-the-art (SOTA) at the time, i.e., Faster R-CNN (71% mAP).
There were some clear loopholes that required attention, such as the architecture having comparatively low recall and higher localization error compared to Faster R-CNN. Additionally, the architecture struggled to detect close proximity objects due to the fact that each grid cell was capped to two bounding box proposals. The loopholes attributed to the original YOLO provided inspiration for the following variants of YOLO.
YOLO-v2/9000
YOLO-v2/9000 was introduced by Joseph Redmon in 2016 [42]. The motive was to remove or at least mitigate the inefficiencies observed with the original YOLO while maintaining the impressive speed factor. Several enhancements were claimed through the implementation of various techniques. Batch normalization [43] was introduced with the internal architecture to improve model convergence, leading to faster training. This introduction eliminated the need for other regularization techniques, such as dropout [44] aimed at reducing overfitting [45]. Its effectiveness can be gauged by the fact that simply introducing batch normalization improved the mAP by 2% compared to the original YOLO.
The original YOLO worked with an input image size of 224 × 224 pixels during the training stage, whilst for the detection phase, input images could be scaled up to 448 × 448 pixels, enforcing the architecture to adjust to the varying image resolution, which in turn decrease the mAP. To address this, the authors trained the architecture on 448 × 448 pixel images for 10 epochs on the ImageNet [46] dataset, providing the architecture with the capacity to adjust the internal filters when dealing with higher resolution images, resulting in an increased mAP of 4%. Whilst architectures, such as Fast and Faster R-CNN predict coordinates directly from the convolutional network, the original YOLO utilized fully (7) Performance wise, the simple YOLO (24 convolutional layers) when trained on the PASCAL VOC dataset (2007 and 2012) [39,40] achieved a mean average precision (referring to cross-class performance) (mAP) of 63.4% at 45 FPS, whilst Fast YOLO achieved 52.7% mAP at an impressive 155 FPS. Although the performance was better than real-time detectors, such as DPM-v5 [41] (33% mAP), it was lower than the state-of-the-art (SOTA) at the time, i.e., Faster R-CNN (71% mAP).
There were some clear loopholes that required attention, such as the architecture having comparatively low recall and higher localization error compared to Faster R-CNN. Additionally, the architecture struggled to detect close proximity objects due to the fact that each grid cell was capped to two bounding box proposals. The loopholes attributed to the original YOLO provided inspiration for the following variants of YOLO.
YOLO-v2/9000
YOLO-v2/9000 was introduced by Joseph Redmon in 2016 [42]. The motive was to remove or at least mitigate the inefficiencies observed with the original YOLO while maintaining the impressive speed factor. Several enhancements were claimed through the implementation of various techniques. Batch normalization [43] was introduced with the internal architecture to improve model convergence, leading to faster training. This introduction eliminated the need for other regularization techniques, such as dropout [44] aimed at reducing overfitting [45]. Its effectiveness can be gauged by the fact that simply introducing batch normalization improved the mAP by 2% compared to the original YOLO.
The original YOLO worked with an input image size of 224 × 224 pixels during the training stage, whilst for the detection phase, input images could be scaled up to 448 × 448 pixels, enforcing the architecture to adjust to the varying image resolution, which in turn decrease the mAP. To address this, the authors trained the architecture on 448 × 448 pixel images for 10 epochs on the ImageNet [46] dataset, providing the architecture with the capacity to adjust the internal filters when dealing with higher resolution images, resulting in an increased mAP of 4%. Whilst architectures, such as Fast and Faster R-CNN predict coordinates directly from the convolutional network, the original YOLO utilized fully connected layers to serve this purpose. YOLO-v2 replaced the fully connected layer responsible for predicting bounding boxes by adding anchor boxes for bounding box predictions. Anchor boxes [47] are essentially a list of predefined dimensions (boxes) aimed at best matching the objects of interest. Rather than manual determination of best-fit anchor boxes, the authors utilized k-means clustering [48] on the training set bounding boxes, inclusive of the ground truth bounding boxes, grouping similar shapes and plotting average IoU with respect to the closest centroid as shown in Figure 4. YOLO-v2 was trained on different architectures, namely, VGG-16 and GoogleNet, in addition to the authors proposing the Darknet-19 [49] architecture due to characteristics, such as reduced processing requirements, i.e., 5 trained on different architectures, namely, VGG-16 and GoogleNet, in addition to the thors proposing the Darknet-19 [49] architecture due to characteristics, such as redu processing requirements, i.e., 5.58 FLOPs compared to 30.69 FLOPs and 8.52 FLOP VGG-16 and GoogleNet, respectively. In terms of performance, YOLO-v2 provided mAP at 67 FPS and 78.6 mAP at 40 FPS. The results demonstrated the architectures' su riority over SOTA architectures of that time, such as SSD and Faster R-CNN. YOLOutilized YOLO-v2 architecture, aimed at real-time detection of more than 9000 diffe objects; however, at a significantly reduced mAP of 19.7%.
YOLO-v3
Architectures, such as VGG, focused their development work around the con that deeper networks, i.e., more internal layers, equated to higher accuracy. YOLO-v2 had higher number of convolutional layers compared to its predecessor.
However, as the image progressed through the network, the progressive down s pling resulted in the loss of fine-grained features; therefore, YOLO-v2 often struggled w detecting smaller objects. At the time research was active in addressing this issue, as dent by the deployment of skip connections [50] embedded within the proposed Res architecture, the focus was on addressing the vanishing gradient issue by facilitating formation propagation via skip connection, as presented in Figure 5.
YOLO-v3
Architectures, such as VGG, focused their development work around the concept that deeper networks, i.e., more internal layers, equated to higher accuracy. YOLO-v2 also had higher number of convolutional layers compared to its predecessor.
However, as the image progressed through the network, the progressive down sampling resulted in the loss of fine-grained features; therefore, YOLO-v2 often struggled with detecting smaller objects. At the time research was active in addressing this issue, as evident by the deployment of skip connections [50] embedded within the proposed ResNet architecture, the focus was on addressing the vanishing gradient issue by facilitating information propagation via skip connection, as presented in Figure 5. YOLO-v3 proposed a hybrid architecture factoring in aspects of YOLO-v2, Dark 53 [51], and the ResNet concept of residual networks. This enabled the preservatio fine-grained features by allowing for the gradient flow from shallow layers to deeper ers.
On top of the existing 53 layers of Darknet-53 for feature extraction, a stack o YOLO-v3 proposed a hybrid architecture factoring in aspects of YOLO-v2, Darknet-53 [51], and the ResNet concept of residual networks. This enabled the preservation of fine-grained features by allowing for the gradient flow from shallow layers to deeper layers.
On top of the existing 53 layers of Darknet-53 for feature extraction, a stack of 53 additional layers was added for the detection head, totaling 106 convolutional layers for the YOLO-v3. Additionally, YOLO-v3 facilitated multi-scale detection, namely, the architecture made predictions at three different scales of granularity for outputting better performance, increasing the probability of small object detection.
YOLO-v4
YOLO-v4 was the first variant of the YOLO family after the original author discontinued further work that was introduced to the computer vision community in April 2020 by Alexey Bochkovsky et al. [52]. YOLO-v4 was essentially the distillation of a large suite of object detection techniques, tested and enhanced for providing a real-time, lightweight object detector.
The backbone of an object detector has a critical role in the quality of features extracted. In-line with the experimental spirit, the authors experimented with three different backbones: CSPResNext-50, CSPDarknet-53, and EfficientNet-B3 [53]. The first was based on DenseNet [54] aimed at alleviating the vanishing gradient problem and bolstering feature propagation and reuse, resulting in reduced number of network parameters. EfficientNet was proposed by Google Brain. The paper posits that an optima selection for parameters when scaling CNNs can be ascertained through a search mechanism. After experimenting with the above feature extractors, the authors based on their intuition and backed by their experimental results selected CSPDarknet-53 as the official backbone for YOLO-v4.
For feature aggregation, the authors experimented with several techniques for integration at the neck level including feature pyramid network (FPN) [55] and path aggregation network (PANet) [56]. Ultimately, the authors opted for PANet as the feature aggregator. The modified PANet, as shown in Figure 6, utilized the concatenation mechanism. PANet can be seen as an advanced version of FPN, namely, PANet proposed a bottom-up augmentation path along with the top-down path (FPN), adding a 'shortcut' connection for linking fine-grained features from high-and low-level layers. Additionally, the authors introduced a SPP [57] block post CSPDarknet-53 aimed at increasing the receptive field and separation of the important features arriving from the backbone. The authors also introduced a bag-of-freebies, presented in Figure 7, primarily con sisting of augmentations, such as Mosaic aimed at improving performance without intro ducing additional baggage onto the inference time. CIoU loss [58] was also introduced a a freebie, focused on the overlap of the predicted and ground truth bounding box. In th case of no overlap, the idea was to observe the closeness of the two boxes and encourag overlap if in close proximity.
In addition to the bag-of-freebies, the authors introduced 'bag-of-specials', with th The authors also introduced a bag-of-freebies, presented in Figure 7, primarily consisting of augmentations, such as Mosaic aimed at improving performance without introducing additional baggage onto the inference time. CIoU loss [58] was also introduced as a freebie, focused on the overlap of the predicted and ground truth bounding box. In the case of no overlap, the idea was to observe the closeness of the two boxes and encourage overlap if in close proximity.
The authors also introduced a bag-of-freebies, presented in Figure 7, primarily consisting of augmentations, such as Mosaic aimed at improving performance without introducing additional baggage onto the inference time. CIoU loss [58] was also introduced as a freebie, focused on the overlap of the predicted and ground truth bounding box. In the case of no overlap, the idea was to observe the closeness of the two boxes and encourage overlap if in close proximity.
In addition to the bag-of-freebies, the authors introduced 'bag-of-specials', with the authors claiming that although this set of optimization techniques presented in Figure 7 would marginally impact the inference time, they would significantly improve the overall performance. One of the components within the 'bag-of-specials' was the Mish [59] activation function aimed at moving feature creations toward their respective optimal points. Cross mini-batch normalization [60] was also presented facilitating the running on any GPU as many batch normalization techniques involve multiple GPUs operating in tandem.
YOLO-v5
The YOLO network in essence consists of three key pillars, namely, backbone for feature extraction, neck focused on feature aggregation, and the head for consuming output In addition to the bag-of-freebies, the authors introduced 'bag-of-specials', with the authors claiming that although this set of optimization techniques presented in Figure 7 would marginally impact the inference time, they would significantly improve the overall performance. One of the components within the 'bag-of-specials' was the Mish [59] activation function aimed at moving feature creations toward their respective optimal points. Cross mini-batch normalization [60] was also presented facilitating the running on any GPU as many batch normalization techniques involve multiple GPUs operating in tandem.
YOLO-v5
The YOLO network in essence consists of three key pillars, namely, backbone for feature extraction, neck focused on feature aggregation, and the head for consuming output features from the neck as input and generating detections. YOLO-v5 [61] similar to YOLO-v4, with respect to contributions, focus on the conglomeration and refinement of various computer vision techniques for enhancing performance. In addition, in less than 2 months after the release of YOLO-v4, Glenn Jocher open-sourced an implementation of YOLO-v5 [61].
A notable mention is that YOLO-v5 was the first native release of architectures belonging to the YOLO clan, to be written in PyTorch [62] rather than Darknet. Although Darknet is considered as a flexible low-level research framework, it was not purpose built for production environments with a significantly smaller number of subscribers due to configurability challenges. PyTorch, on the other hand, provided an established eco-system, with a wider subscription base among the computer vision community and provided the supporting infrastructure for facilitating mobile device deployment.
In addition, another notable proposal was the 'automated anchor box learning' concept. In YOLO-v2, the anchor box mechanism was introduced based on selecting anchor boxes that closely resemble the dimensions of the ground truth boxes in the training set via k-means. The authors select the five close-fit anchor boxes based on the COCO dataset [63] and implement them as default boxes. However, the application of this methodology to a unique dataset with significant object differentials compared to those present in the COCO dataset can quickly expose the inability of the predefined boxes to adapt quickly to the unique dataset. Therefore, authors in YOLO-v5 integrated the anchor box selection process into the YOLO-v5 pipeline. As a result, the network would automatically learn the best-fit anchor boxes for the particular dataset and utilize them during training to accelerate the process. YOLO-v5 comes in several variants with respect to the computational parameters as presented in Table 1. YOLO-v5 comprised of a weight file equating to 27 MB compared to YOLO-v5l at 192 MB. Figure 8 demonstrates the superiority of YOLO-v5 over EfficientDet [64]. [61].
A notable mention is that YOLO-v5 was the first native release of architectures belonging to the YOLO clan, to be written in PyTorch [62] rather than Darknet. Although Darknet is considered as a flexible low-level research framework, it was not purpose built for production environments with a significantly smaller number of subscribers due to configurability challenges. PyTorch, on the other hand, provided an established eco-system, with a wider subscription base among the computer vision community and provided the supporting infrastructure for facilitating mobile device deployment.
In addition, another notable proposal was the 'automated anchor box learning' concept. In YOLO-v2, the anchor box mechanism was introduced based on selecting anchor boxes that closely resemble the dimensions of the ground truth boxes in the training set via k-means. The authors select the five close-fit anchor boxes based on the COCO dataset [63] and implement them as default boxes. However, the application of this methodology to a unique dataset with significant object differentials compared to those present in the COCO dataset can quickly expose the inability of the predefined boxes to adapt quickly to the unique dataset. Therefore, authors in YOLO-v5 integrated the anchor box selection process into the YOLO-v5 pipeline. As a result, the network would automatically learn the best-fit anchor boxes for the particular dataset and utilize them during training to accelerate the process. YOLO-v5 comes in several variants with respect to the computational parameters as presented in Table 1. Figure 8 demonstrates the superiority of YOLO-v5 over EfficientDet [64].
YOLO-v6
The initial codebase for YOLO-v6 [65] was released in June 2022 by the Meituan Technical Team based in China. The authors focused their design strategy on producing an industry-orientated object detector.
To meet industrial application requirements, the architecture would need to be highly performant on a range of hardware options, maintaining high speed and accuracy. To conform with the diverse set of industrial applications, YOLO-v6 comes in several variants starting with YOLO-v6-nano as the fastest with the least number of parameters and reaching YOLO-v6-large with high accuracy at the expense of speed, as shown in Table 2. The impressive performance presented in Table 2 is a result of several innovations integrated into the YOLO-v6 architecture. The key contributions can be summed into four points. First, in contrast to its predecessors, YOLO-v6 opts for an anchor-free approach, making it 51% faster when compared to anchor-based approaches.
Second, the authors introduced a revised reparametrized backbone and neck, proposed as EfficientRep backbone and Rep-PAN neck [66], namely, up to and including YOLO-v5, the regression and classification heads shared the same features. Breaking the convention, YOLO-v6 implements the decoupled head as shown in Figure 9. As a result, the architecture has additional layers separating features from the final head, as empirically shown to improve the performance. Third, YOLO-v6 mandates a two-loss function. Varifocal loss (VFL) [67] is used as the classification loss and distribution focal loss (DFL) [68], along with SIoU/GIoU [69] as regression loss. VFL being a derivative of focal loss, treats positive and negative samples at varying degrees of importance, helping in balancing the learning signals from both sample types. DFL is deployed for box regression in YOLO-v6 medium and large variants, treating the continuous distribution of the box locations as discretized probability distribution, which is shown to be particularly efficient when the ground truth box boundaries are blurred.
To meet industrial application requirements, the architecture would need to be highly performant on a range of hardware options, maintaining high speed and accuracy. To conform with the diverse set of industrial applications, YOLO-v6 comes in several variants starting with YOLO-v6-nano as the fastest with the least number of parameters and reaching YOLO-v6-large with high accuracy at the expense of speed, as shown in Table 2. The impressive performance presented in Table 2 is a result of several innovations integrated into the YOLO-v6 architecture. The key contributions can be summed into four points. First, in contrast to its predecessors, YOLO-v6 opts for an anchor-free approach, making it 51% faster when compared to anchor-based approaches.
Second, the authors introduced a revised reparametrized backbone and neck, proposed as EfficientRep backbone and Rep-PAN neck [66], namely, up to and including YOLO-v5, the regression and classification heads shared the same features. Breaking the convention, YOLO-v6 implements the decoupled head as shown in Figure 9. As a result, the architecture has additional layers separating features from the final head, as empirically shown to improve the performance. Third, YOLO-v6 mandates a two-loss function. Varifocal loss (VFL) [67] is used as the classification loss and distribution focal loss (DFL) [68], along with SIoU/GIoU [69] as regression loss. VFL being a derivative of focal loss, treats positive and negative samples at varying degrees of importance, helping in balancing the learning signals from both sample types. DFL is deployed for box regression in YOLO-v6 medium and large variants, treating the continuous distribution of the box locations as discretized probability distribution, which is shown to be particularly efficient when the ground truth box boundaries are blurred. Additional improvements focused on industrial applications include the use of knowledge distillation [70], involving a teacher model used for training a student model, where the predictions of the teacher are used as soft labels along with the ground truth for training the student. This comes without fueling the computational cost as essentially the aim is to train a smaller (student) model to replicate the high performance of the larger (teacher) model. Comparing the performance of YOLO-v6 with its predecessors, including YOLO-v5 on the benchmark COCO dataset in Figure 10, it is clear that YOLO-v6 achieves a higher mAP at various FPS.
where the predictions of the teacher are used as soft labels along with the ground truth for training the student. This comes without fueling the computational cost as essentially the aim is to train a smaller (student) model to replicate the high performance of the larger (teacher) model. Comparing the performance of YOLO-v6 with its predecessors, including YOLO-v5 on the benchmark COCO dataset in Figure 10, it is clear that YOLO-v6 achieves a higher mAP at various FPS.
YOLO-v7
The following month after the release of YOLO-v6, the YOLO-v7 was released [72]. Although other variants have been released in between, including YOLO-X [73] and YOLO-R [74], these focused more on GPU speed enhancements with respect to inferencing. YOLO-v7 proposes several architectural reforms for improving the accuracy and maintaining high detection speeds. The proposed reforms can be split into two categories: Architectural reforms and Trainable BoF (bag-of-freebies). Architectural reforms included the implementation of the E-ELAN (extended efficient layer aggregation network) [75] in the YOLO-v7 backbone, taking inspiration from research advancements in network efficiency. The design of the E-ELAN was guided by the analysis of factors that impact accuracy and speed, such as memory access cost, input/output channel ratio, and gradient path.
The second architectural reform was presented as compound model scaling, as shown in Figure 11. The aim was to cater for a wider scope of application requirements, i.e., certain applications require accuracy to be prioritized, whilst others may prioritize speed. Although NAS (network architecture search) [76] can be used for parameter-specific scaling to find the best factors, the scaling factors are independent [77]. Whereas the compound-scaling mechanism allows for the width and depth to be scaled in coherence for concatenation-based networks, maintaining optimal network architecture while scaling for different sizes.
YOLO-v7
The following month after the release of YOLO-v6, the YOLO-v7 was released [72]. Although other variants have been released in between, including YOLO-X [73] and YOLO-R [74], these focused more on GPU speed enhancements with respect to inferencing. YOLO-v7 proposes several architectural reforms for improving the accuracy and maintaining high detection speeds. The proposed reforms can be split into two categories: Architectural reforms and Trainable BoF (bag-of-freebies). Architectural reforms included the implementation of the E-ELAN (extended efficient layer aggregation network) [75] in the YOLO-v7 backbone, taking inspiration from research advancements in network efficiency. The design of the E-ELAN was guided by the analysis of factors that impact accuracy and speed, such as memory access cost, input/output channel ratio, and gradient path.
The second architectural reform was presented as compound model scaling, as shown in Figure 11. The aim was to cater for a wider scope of application requirements, i.e., certain applications require accuracy to be prioritized, whilst others may prioritize speed. Although NAS (network architecture search) [76] can be used for parameter-specific scaling to find the best factors, the scaling factors are independent [77]. Whereas the compound-scaling mechanism allows for the width and depth to be scaled in coherence for concatenationbased networks, maintaining optimal network architecture while scaling for different sizes. Re-parameterization planning is based on averaging a set of model weights to obtain a more robust network [78,79]. Expanding further, module level re-parameterization enables segments of the network to regulate their own parameterization strategies. YOLO-v7 utilizes gradient flow propagation paths with the aim to observe which internal network Re-parameterization planning is based on averaging a set of model weights to obtain a more robust network [78,79]. Expanding further, module level re-parameterization enables segments of the network to regulate their own parameterization strategies. YOLO-v7 utilizes gradient flow propagation paths with the aim to observe which internal network modules should deploy re-parameterization strategies.
The auxiliary head coarse-to-fine concept is proposed on the premise that the network head is quite far downstream; therefore, the auxiliary head is deployed at the middle layers to assist in the training process. However, this would not train as efficiently as the lead head, due to the former not having access to the complete network. Figure 12 presents a performance comparison of YOLO-v7 with the preceding YOLO variants on the MS COCO dataset. It is clear from Figure 12 that all YOLO-v7 variants surpassed the compared object detectors in accuracy and speed in the range of 5-160 FPS. It is, however, important to note, as mentioned by the authors of YOLO-v7, that none of the YOLO-v7 variants are designed for CPU-based mobile device deployment. YOLO-v7-tiny/v7/W6 variants are designed for edge GPU, consumer GPU, and cloud GPU, respectively. Whilst YOLO-v7-E6/D6/E6E are designed for high-end cloud GPUs only. Re-parameterization planning is based on averaging a set of model weights to obtain a more robust network [78,79]. Expanding further, module level re-parameterization enables segments of the network to regulate their own parameterization strategies. YOLO-v7 utilizes gradient flow propagation paths with the aim to observe which internal network modules should deploy re-parameterization strategies.
The auxiliary head coarse-to-fine concept is proposed on the premise that the network head is quite far downstream; therefore, the auxiliary head is deployed at the middle layers to assist in the training process. However, this would not train as efficiently as the lead head, due to the former not having access to the complete network. Figure 12 presents a performance comparison of YOLO-v7 with the preceding YOLO variants on the MS COCO dataset. It is clear from Figure 12 that all YOLO-v7 variants surpassed the compared object detectors in accuracy and speed in the range of 5-160 FPS. It is, however, important to note, as mentioned by the authors of YOLO-v7, that none of the YOLO-v7 variants are designed for CPU-based mobile device deployment. YOLO-v7tiny/v7/W6 variants are designed for edge GPU, consumer GPU, and cloud GPU, respectively. Whilst YOLO-v7-E6/D6/E6E are designed for high-end cloud GPUs only. Internal variant comparison of YOLO-v7 is presented in Table 3. As evident, there is a significant performance gap with respect to mAP when comparing YOLO-v7-tiny with the computationally demanding YOLO-v7-D6. However, the latter would not be suitable for edge deployment onto a computationally constrained device.
YOLO-v8
The latest addition to the family of YOLO was confirmed in January 2023 with the release of YOLO-v8 [80] by Ultralytics (also released YOLO-v5). Although a paper release is impending and many features are yet to be added to the YOLO-v8 repository, initial comparisons of the newcomer against its predecessors demonstrate its superiority as the new YOLO state-of-the-art. Figure 13 demonstrates that when comparing YOLO-v8 against YOLO-v5 and YOLO-v6 trained on 640 image resolution, all YOLO-v8 variants output better throughput with a similar number of parameters, indicating toward hardware-efficient, architectural reforms. The fact that YOLO-v8 and YOLO-v5 are presented by Ultralytics with YOLO-v5 providing impressive real-time performance and based on the initial benchmarking results released by Ultralytics, it is strongly assumed that the YOLO-v8 will be focusing on constrained edge device deployment at high-inference speed.
Industrial Defect Detection Via YOLO
The previous section demonstrates the rapid evolution of the YOLO 'clan' of object detectors amongst the computer vision community. This section of the review focuses on the implementation of YOLO variants for the detection of surface defects within the industrial setting. The selection of 'industrial setting' is due to its varying and stringent requirements alternating between accuracy and speed, a theme which is found through DNA of the YOLO variants.
Industrial Fabric Defect Detection
Rui Jin et al. [81] in their premise state the inefficiencies of manual inspection in the textile manufacturing domain as high cost of labor, human-related fatigue, and reduced detection speed (less than 20 m/min). The authors aim to address these inefficiencies by
Industrial Defect Detection via YOLO
The previous section demonstrates the rapid evolution of the YOLO 'clan' of object detectors amongst the computer vision community. This section of the review focuses on the implementation of YOLO variants for the detection of surface defects within the industrial setting. The selection of 'industrial setting' is due to its varying and stringent requirements alternating between accuracy and speed, a theme which is found through DNA of the YOLO variants.
Industrial Fabric Defect Detection
Rui Jin et al. [81] in their premise state the inefficiencies of manual inspection in the textile manufacturing domain as high cost of labor, human-related fatigue, and reduced detection speed (less than 20 m/min). The authors aim to address these inefficiencies by proposing a YOLO-v5-based architecture, coupled with a spatial attention mechanism for accentuation of smaller defective regions. The proposed approach involved a teacher network trained on the fabric dataset. Post training of the teacher network, the learned weights were distilled to the student network, which was compatible for deployment onto a Jetson TX2 [82] via TensorRT [83]. The results presented by the authors show, as expected, that the teacher network reported higher performance with an AUC of 98.1% compared to 95.2% (student network). However, as the student network was computationally smaller, the inference time was significantly less at 16 ms for the student network in contrast to the teacher network at 35 ms on the Jetson TX2. Based on the performance, the authors claim that the proposed solution provides high accuracy and real-time inference speed, making it compatible for deployment via the edge device.
Sifundvoleshile Dlamini et al. [84] propose a production environment fabric defect detection framework focused on real-time detection and accurate classification on-site, as shown in Figure 14. The authors embed conventional image processing at the onset of their data enhancement strategy, i.e., filtering to denoise feature enhancement. Post augmentations and data scaling, the authors train the YOLO-v4 architecture based on pretrained weights. The reported performance was respectable with an F1-score of 93.6%, at an impressive detection speed of 34 fps and prediction speed of 21.4 ms. The authors claim that the performance is evident to the effectiveness of the selected architecture for the given domain. authors claim that the proposed solution provides high accuracy and real-time inference speed, making it compatible for deployment via the edge device. Sifundvoleshile Dlamini et al. [84] propose a production environment fabric defect detection framework focused on real-time detection and accurate classification on-site, as shown in Figure 14. The authors embed conventional image processing at the onset of their data enhancement strategy, i.e., filtering to denoise feature enhancement. Post augmentations and data scaling, the authors train the YOLO-v4 architecture based on pretrained weights. The reported performance was respectable with an F1-score of 93.6%, at an impressive detection speed of 34 fps and prediction speed of 21.4 ms. The authors claim that the performance is evident to the effectiveness of the selected architecture for the given domain. Restricted by the available computing resources for edge deployment, Guijuan Lin et al. [85] state problems with quality inspection in the fabric production domain, including minute scale of defects, extreme unbalance with the aspect ratio of certain defects, and slow defect detection speeds. To address these issues, the authors proposed a sliding-window, self-attention (multihead) mechanism calibrated for small defect targets. Additionally, the Swin Transformer [86] module as depicted in Figure 15 was integrated into the original YOLO-v5 architecture for the extraction of hierarchical features. Furthermore, the generalized focal loss is implemented with the architecture aimed at improving the learning process for positive target instances, whilst lowering the rate of missed detections. The authors report the accuracy of the proposed solution on a real-world fabric dataset, reaching 76.5% mAP at 58.8 FPS, making it compatible with the real-time detection requirements for detection via embedded devices. Restricted by the available computing resources for edge deployment, Guijuan Lin et al. [85] state problems with quality inspection in the fabric production domain, including minute scale of defects, extreme unbalance with the aspect ratio of certain defects, and slow defect detection speeds. To address these issues, the authors proposed a sliding-window, selfattention (multihead) mechanism calibrated for small defect targets. Additionally, the Swin Transformer [86] module as depicted in Figure 15 was integrated into the original YOLO-v5 architecture for the extraction of hierarchical features. Furthermore, the generalized focal loss is implemented with the architecture aimed at improving the learning process for positive target instances, whilst lowering the rate of missed detections. The authors report the accuracy of the proposed solution on a real-world fabric dataset, reaching 76.5% mAP at 58.8 FPS, making it compatible with the real-time detection requirements for detection via embedded devices.
Solar Cell Surface Defect Detection
Setting their premise, the authors [87] state that human-led Photovoltaic (PV) inspec tion has many drawbacks including the requirement of operation and maintenance (O&M) engineers, cell-by-cell inspection, high workload, and reduced efficiency. The au thors propose an improved architecture based on YOLO-v5 for the characterization o complex solar cell surface textures and defective regions. The proposal is based on the integration of deformable convolution within the CSP module with the aim of achieving an adaptive learning scale. Additionally, an attention mechanism is incorporated for en hanced feature extraction. Moreover, the authors optimize the original YOLO-v5 architec ture further via K-means++ clustering for anchor box determination algorithm. Based on the presented results, the improved architecture achieved a respectable mAP of 89.64% on an EL-based solar cell image dataset, 7.85% higher compared to mAP for the original ar chitecture, with detection speed reaching 36.24 FPS, which can be translated as a more accurate detection while remaining compatible with the real-time requirements.
Amran Binomairah et al. [88] highlight two frequent defects encountered during the manufacturing process of crystalline solar cells as dark spot/region and microcracks. The latter can have a detrimental impact on the performance of the module, which is a major cause for PV module failures. The authors subscribe to the YOLO architecture, comparing the performance of their methodology on YOLO-v4 and an improved YOLO-v4-tiny inte grated with a spatial pyramid pooling mechanism. Based on the presented results, YOLO v4 achieved 98.8% mAP at 62.9 ms, whilst the improved YOLO-v4-tiny lagged with 91% mAP at 28.2 ms. The authors claim that although the latter is less accurate, it is notably faster than the former.
Tianyi Sun et al. [89] focus on automated hot-spot detection within PV cells based a modified version of the YOLO-v5 architecture. The first improvement comes in the form of enhanced anchors and detection heads for the respective architecture. To improve the detection precision at varying scales, k-means clustering [48] is deployed for clustering the length-width ratio with respect to the data annotation frame. Additionally, a set of the anchors consisting of smaller values were added to cater for the detection of small defects by optimizing the cluster number. The reported performance of the improved architecture was reported as 87.8% mAP, with the average recall rate of 89.0% and F1-score reaching
Solar Cell Surface Defect Detection
Setting their premise, the authors [87] state that human-led Photovoltaic (PV) inspection has many drawbacks including the requirement of operation and maintenance (O&M) engineers, cell-by-cell inspection, high workload, and reduced efficiency. The authors propose an improved architecture based on YOLO-v5 for the characterization of complex solar cell surface textures and defective regions. The proposal is based on the integration of deformable convolution within the CSP module with the aim of achieving an adaptive learning scale. Additionally, an attention mechanism is incorporated for enhanced feature extraction. Moreover, the authors optimize the original YOLO-v5 architecture further via K-means++ clustering for anchor box determination algorithm. Based on the presented results, the improved architecture achieved a respectable mAP of 89.64% on an EL-based solar cell image dataset, 7.85% higher compared to mAP for the original architecture, with detection speed reaching 36.24 FPS, which can be translated as a more accurate detection while remaining compatible with the real-time requirements.
Amran Binomairah et al. [88] highlight two frequent defects encountered during the manufacturing process of crystalline solar cells as dark spot/region and microcracks. The latter can have a detrimental impact on the performance of the module, which is a major cause for PV module failures. The authors subscribe to the YOLO architecture, comparing the performance of their methodology on YOLO-v4 and an improved YOLO-v4tiny integrated with a spatial pyramid pooling mechanism. Based on the presented results, YOLO-v4 achieved 98.8% mAP at 62.9 ms, whilst the improved YOLO-v4-tiny lagged with 91% mAP at 28.2 ms. The authors claim that although the latter is less accurate, it is notably faster than the former.
Tianyi Sun et al. [89] focus on automated hot-spot detection within PV cells based a modified version of the YOLO-v5 architecture. The first improvement comes in the form of enhanced anchors and detection heads for the respective architecture. To improve the detection precision at varying scales, k-means clustering [48] is deployed for clustering the length-width ratio with respect to the data annotation frame. Additionally, a set of the anchors consisting of smaller values were added to cater for the detection of small defects by optimizing the cluster number. The reported performance of the improved architecture was reported as 87.8% mAP, with the average recall rate of 89.0% and F1-score reaching 88.9%. The reported FPS was impressive reaching 98.6 FPS, with the authors claiming that the proposed solution would provide intelligent monitoring at PV power stations. Inferencing output presented in Figure 16 shows the proposed AP-YOLO-v5 architecture, providing inferences at a higher confidence level compared to the original YOLO-v5.
Steel Surface Defect Detection
Dinming Yang et al. [90] set the premise of their research by stating the importance of steel pipe quality inspection, citing the growing demand in countries, such as China. Although X-ray testing is utilized as one of the key methods for industrial nondestructive testing (NDT), the authors state that it still requires human assistance for the determination, classification, and localization of the defects. The authors propose the implementation of YOLO-v5 for production-based weld steel defect detection based on X-ray images of the weld pipe. The authors claim that the trained YOLO-v5 reached a mAP of 98.7% (IoU-0.5), whilst meeting the real-time detection requirements of steel pipe production with a single image detection rate of 0.12 s.
Zhuxi MA et al. [91] address the issue of large-scale computation and specific hardware requirements for automated defect detection in aluminum strips. The authors select YOLO-v4 as the architecture, whilst the backbone is constructed to make use of depthwise separable convolutions along with a parallel dual attention mechanism for feature enhancement, as shown in Figure 17. The proposed network is tested on real data from a cold-rolling workshop, providing impressive results on real data achieving an mAP of 96.28%. Compared to the original YOLO-v4, the authors claim that the proposed architecture volume is reduced by 83.38%, whilst the inference speed is increased by a factor of three. The increase in performance was partly due to the custom anchor approach, whereby due to the maximum aspect ratio of the custom dataset, the defect was set to 1:20 which is in-line with the defect characteristics, such as scratch marks.
Steel Surface Defect Detection
Dinming Yang et al. [90] set the premise of their research by stating the importance of steel pipe quality inspection, citing the growing demand in countries, such as China. Although X-ray testing is utilized as one of the key methods for industrial nondestructive testing (NDT), the authors state that it still requires human assistance for the determination, classification, and localization of the defects. The authors propose the implementation of YOLO-v5 for production-based weld steel defect detection based on X-ray images of the weld pipe. The authors claim that the trained YOLO-v5 reached a mAP of 98.7% (IoU-0.5), whilst meeting the real-time detection requirements of steel pipe production with a single image detection rate of 0.12 s.
Zhuxi MA et al. [91] address the issue of large-scale computation and specific hardware requirements for automated defect detection in aluminum strips. The authors select YOLO-v4 as the architecture, whilst the backbone is constructed to make use of depthwise separable convolutions along with a parallel dual attention mechanism for feature enhancement, as shown in Figure 17. The proposed network is tested on real data from a cold-rolling workshop, providing impressive results on real data achieving an mAP of 96.28%. Compared to the original YOLO-v4, the authors claim that the proposed architecture volume is reduced by 83.38%, whilst the inference speed is increased by a factor of three. The increase in performance was partly due to the custom anchor approach, whereby due to the maximum aspect ratio of the custom dataset, the defect was set to 1:20 which is in-line with the defect characteristics, such as scratch marks. Jianting Shi et al. [92] cite the manufacturing process of steel production as the reason for various defects originating on the steel surface, such as rolling scale and patches. Th authors state that the small dimensions of the defects as well as the stringent detection requirements make the quality inspection process a challenging task. Therefore, the au thors present an improved version of YOLO-v5 by incorporating an attention mechanism for facilitating the transmission of shallow features from the backbone to the neck, pre serving the defective regions, in addition to k-means clustering of anchor boxes for ad dressing the extreme aspect ratios of defective targets within the dataset. The authors stat that the improved architecture achieved 86.35% mAP reaching 45 FPS detection speed whilst the original architecture achieved 81.78% mAP at 52 FPS.
Pallet Racking Defect Inspection
A promising application with significant deployment scope in the warehousing and general industrial storage centers is automated pallet racking inspection. Warehouses and distribution centers host a critical infrastructure known as racking for stock storage. Un noticed damage to pallet racking can pave the way for significant losses initiated by rack ing collapse leading to wasted/damaged stock, financial implications, operational losses injured employees, and worst-case, loss of lives [93]. Due to the inefficiencies of the con ventional racking inspection mechanisms, such as human-led annual inspection resulting in labor costs, bias, fatigue, and mechanical products, such as rackguards [94] lacking clas sification intelligence, CNN-based automated detection seems to be a promising alterna tive.
Realizing the potential, Hussain et al. [95] inaugurated research into automated palle racking detection via computer vision. After presenting their initial research based on th MobileNet-V2 architecture, the authors recently proposed the implementation of YOLO v7 for automated pallet racking inspection [96]. The selection of the architecture was in line with the stringent requirements of production floor deployment, i.e., edge device de ployment, placed onto an operating forklift, requiring real-time detection as the forklif approaches the racking. Evaluating the performance of the proposed solution on a rea dataset, the authors claimed an impressive performance of 91.1% mAP running at 19 FPS Jianting Shi et al. [92] cite the manufacturing process of steel production as the reason for various defects originating on the steel surface, such as rolling scale and patches. The authors state that the small dimensions of the defects as well as the stringent detection requirements make the quality inspection process a challenging task. Therefore, the authors present an improved version of YOLO-v5 by incorporating an attention mechanism for facilitating the transmission of shallow features from the backbone to the neck, preserving the defective regions, in addition to k-means clustering of anchor boxes for addressing the extreme aspect ratios of defective targets within the dataset. The authors state that the improved architecture achieved 86.35% mAP reaching 45 FPS detection speed, whilst the original architecture achieved 81.78% mAP at 52 FPS.
Pallet Racking Defect Inspection
A promising application with significant deployment scope in the warehousing and general industrial storage centers is automated pallet racking inspection. Warehouses and distribution centers host a critical infrastructure known as racking for stock storage. Unnoticed damage to pallet racking can pave the way for significant losses initiated by racking collapse leading to wasted/damaged stock, financial implications, operational losses, injured employees, and worst-case, loss of lives [93]. Due to the inefficiencies of the conventional racking inspection mechanisms, such as human-led annual inspection resulting in labor costs, bias, fatigue, and mechanical products, such as rackguards [94] lacking classification intelligence, CNN-based automated detection seems to be a promising alternative.
Realizing the potential, Hussain et al. [95] inaugurated research into automated pallet racking detection via computer vision. After presenting their initial research based on the MobileNet-V2 architecture, the authors recently proposed the implementation of YOLO-v7 for automated pallet racking inspection [96]. The selection of the architecture was in-line with the stringent requirements of production floor deployment, i.e., edge device deployment, placed onto an operating forklift, requiring real-time detection as the forklift approaches the racking. Evaluating the performance of the proposed solution on a real dataset, the authors claimed an impressive performance of 91.1% mAP running at 19 FPS. Table 4 presents a comparison of the present research in this emerging field. Although mask R-CNN presents the highest accuracy, which is a derivative of the segmentation family of architectures with significant computational load, this makes it an infeasible option for deployment. Whereas the proposed approach utilizing YOLO-v7 achieved similar accuracy compared to MobileNet-V2, whilst requiring significantly less training data along with inferencing at 19 FPS.
Discussion
The YOLO family of object detectors has had a significant impact on improving the potential of computer vision applications. Right from the onset, i.e., the release of the YOLO-v1 in 2015, significant breakthroughs were introduced. YOLO-v1 became the first architecture combining the two conventionally separate tasks of bounding box prediction and classification into one. YOLO-v2 was released in the following year, introducing architectural improvements and iterative improvements, such as batch normalization, higher resolution, and anchor boxes. In 2018, YOLO-v3 was released, an extension of previous variants with enhancements including the introduction of objectness scores for bounding box predictions added connections for the backbone layers and the ability to generate predictions at three different levels of granularity, leading to improved performance on smaller object targets.
After a short delay, YOLO-v4 was released in April 2020, becoming the first variant of the YOLO family not to be authored by the original author Joseph Redmon. Enhancements included improved feature aggregation, gifting of the 'bag of freebies', and the mish activation. In a matter of months, YOLO-v5 entered the computer vision territory, becoming the first variant to be released without being accompanied by a paper release. YOLO-v5 based on PyTorch, with an active GitHub repo further delineated the implementation process, make it accessible to a wider audience. Focused on internal architectural reforms, YOLO-v6 authors redesigned the backbone (EfficientRep) and neck (Rep-PAN) modules, with an inclination toward hardware efficiency. Additionally, anchor-free and the concept of decoupled head was introduced, implying additional layers for feature separation from the final head, which is empirically shown to improve the overall performance. The authors of YOLO-v7 also focused on architectural reforms, considering the amount of memory required to keep layers within memory and the distance required for gradients to backpropagate, i.e., shorter gradients, resulting in enhanced learning capacity. For the ultimate layer aggregation, the authors implemented E-ELAN, which is an extension of the ELAN computational block. The advent of 2023 introduced the latest version of the YOLO family, YOLO-v8, which was released by Ultralytics. With an impending paper release, initial comparisons of the latest version against predecessors have shown promising performance with respect to throughput when compared to similar computational parameters. Table 5 presents a summary of the reviewed YOLO variants based on the underlying framework, backbone, average-precision (AP), and key contributions. It can be observed from Table 3 that as the variants evolved there was a shift from the conservative Darknet framework to a more accessible one, i.e., PyTorch. The AP presented here is based on COCO-2017 [63] with the exception of YOLO-v1/v2, which are based on VOC-2017 [39]. COCO-2017 [63] consists of over 80 objects designed to represent a vast array of regularly seen object. It contains 121,408 images resulting in 883,331 object annotations with median image ratio of 640 × 480 pixels. It is important to note that the overall accuracy along with inference capacity depends on the deployed design/training strategies, as demonstrated in the industrial surface detection section. Anchor-free reducing the number of prediction boxes whilst speeding up non-maximum suppression. Pending paper for further architectural insights.
Reason for Rising Popularity
The AP metric consists of precision-recall (PR) metrics, defining of a positive prediction using Intersection over Union, and the handling of multiple object categories. AP provides a balanced overview of PR based on the area under the PR curve. IoU facilitates the quantification of similarity between predicted k p and ground truth k g bounding boxes as expressed in (8): The rise of YOLO can be attributed to two factors. First, the fact that the architectural composition of YOLO variants is compatible for one-stage detection and classification makes it computationally lightweight with respect to other detectors. However, we feel that efficient architectural composition by itself did not drive the popularity of the YOLO variants, as other single-stage detectors, such as MobileNets, also serve a similar purpose.
The second reason is the accessibility factor, which was introduced as the YOLO variants progressed, with YOLO-v5 being the turning point. Expanding further on this point, the first two variants were based on the Darknet framework. Although this provided a degree of flexibility, accessibility was limited to a smaller user base due to the required expertise. Ultralytics, introduced YOLO-v5 based on the PyTorch framework, making the architecture available for a wider audience and increasing the potential domain of applications.
As evident from Table 6, the migration to a more accessible framework coupled with architectural reforms for improved real-time performance sky-rocketed. At present, YOLO-v5 has 34.7 k stars, a significant lead compared to its predecessors. From implementation, YOLO-v5 only required the installation of lightweight python libraries. The architectural reforms indicated that the model training time was reduced, which in turn reduced the experimentation cost attributed to the training process, i.e., GPU utilization. For deployment and testing purposes, researchers have several routes, such as individual/batch images, video/webcam feeds, in addition to simple weight conversion to ONXX weights for edge device deployment.
YOLO and Industrial Defect Detection
Manifestations of the fourth industrial revolution can be observed at present in an ad-hoc manner, spanning across various industries. With respect to the manufacturing industry, this revolution can be targeted at the quality inspection processes, which are vital for assuring efficiency and retaining client satisfaction. When focusing on surface defect detection, as alluded to earlier, the inspection requirements can be more stringent as compared to other applications. This is due to many factors, such as the fact that the defects may be extremely small, requiring external spectral imaging to expose defects prior to classification and due to the fact that the operational setting of the production line may only provide a small-time window within which inference must be carried out.
Considering the stringent requirements outlined above and benchmarking against the principles of YOLO family of variants, forms the conclusion that the YOLO variants have the potential to address both real-time, constrained deployment and small-scale defect detection requirements of industrial-based surface defect detection. YOLO variants have proven real-time compliance in several industrial environments as shown in [81,84,85,90,95]. An interesting observation arising from the industrial literature reviewed is the ability for users to modify the internal modules of YOLO variants in order to take care of their specific application needs without compromising on real-time compliance, for example [81,87,91,92], introducing attention-mechanisms for accentuation of defective regions.
An additional factor, found within the later YOLO variants is sub-variants for each base architecture, i.e., for YOLO-v5 variants including YOLO-v5-S/M/L, this corresponds to different computational loads with respect to the number of parameters. This flexibility enables researchers to consider a more flexible approach with the architecture selection criteria based on the industrial requirements, i.e., if real-time inference is required with less emphasis on optimal mAP, a lightweight variant can be selected, such as YOLO-v5-small rather than YOLO-v5-large.
Conclusions
In conclusion, this work is the first of its type focused on documenting and reviewing the evolution of the most prevalent single-stage object detector within the computer vision domain. The review presents the key advancements of each variant, followed by implementation of YOLO architectures within various industrial settings focused on surface automated real-time surface defect detection.
From the review, it is clear as the YOLO variants have progressed, latter versions in particular, YOLO-v5 has focused on constrained edge deployment, a key requirement for many manufacturing applications. Due to the fact that there is no copyright and patent restrictions, research anchored around the YOLO architecture, i.e., real-time, lightweight, accurate detection, can be conducted by any individual or research organization, which has also contributed to the prevalence of this variant.
With YOLO-v8 released in January 2023, showing promising performance with respect to throughput and computational load requirements, it is envisioned that 2023 will see more variants released by previous or new authors focused on improving the deployment capacity of the architectures with respect to constrained deployment environments.
With research organizations, such as Ultralytics and Meituan Technical Team taking a keen interest in the development of YOLO architectures with a focus on edge-friendly deployment, we anticipate further technological advancements in the architectural footprint of YOLO. To cater for constrained deployment, these advancements will need to focus on energy conservation whilst maintaining high inference rates. Furthermore, we envision the proliferation of YOLO architectures into production facilities to help with quality inspection pipelines as well as providing stimulus for innovative products as demonstrated by [96] with an automated pallet racking inspection solution. Along with integration into a diverse set of hardware and IoT devices, YOLO has the potential to tap into new domains where computer vision can assist in enhancing existing processes whilst requiring limited resources. | 18,709.6 | 2023-06-23T00:00:00.000 | [
"Computer Science",
"Engineering",
"Materials Science"
] |
Mechanisms of Consumer Purchase Intent Formation in the Context of Live Streaming E-commerce
: This paper investigates the factors influencing purchase intent in the context of live streaming e-commerce and the variations in their impact among consumers with different levels of digital literacy. By constructing a purchase intent model for live streaming e-commerce, we collected 248 valid survey responses through a questionnaire survey. We employed a structural equation modeling approach to verify the influence of five dimensions of perceived value on purchase intent in live streaming e-commerce and the moderating effect of digital literacy. The results indicate that consumers' perceived value significantly affects their purchase intent through their attitudes toward live streaming e-commerce. The order of the impact of perceived value dimensions on consumer attitudes is as follows: entertainment, supply chain perception, functionality, economy, and host characteristics. Notably, as consumers' digital literacy increases, they tend to focus more on the supply chain perception factor.
Introduction
According to commercial big data, in the first half of 2020, there were over 10 million live streaming e-commerce sessions, with more than 400,000 active hosts and over 50 billion viewers.The number of products available for sale exceeded 20 million [1].In just 26 seconds after the start of the 2020 Double 11 (Singles' Day) shopping festival, the peak order creation rate on Tmall reached 583,000 orders per second.By 24:00 on November 11, 2020, the real-time logistics order volume for the Tmall Double 11 Global Shopping Festival was 2.321 billion, with a transaction volume of 498.2 billion RMB, and JD's live streaming sales reached 271.5 billion RMB [2].
From 2016 to the present, live streaming e-commerce has experienced nearly five years of development, demonstrating a strong growth trend.It has become increasingly integrated into people's daily lives.However, what are the mechanisms that attract consumers to live streaming ecommerce?Why is it favored by consumers?The COVID-19 pandemic in 2020 accelerated the development of live streaming e-commerce, but it also brought about various challenges, such as data fraud and the sale of counterfeit goods.In the post-pandemic era, is live streaming e-commerce a passing trend or a sustainable development?To answer these questions, it is necessary to study the development mechanisms of live streaming e-commerce and propose corresponding strategies.
Literature Review
Currently, in academia, research on consumer purchase intent in traditional shopping scenarios primarily examines consumer attitudes [3], maximizing perceived value [4], and minimizing perceived risk [5].It is widely acknowledged that consumer characteristics, product lines, consumption scenarios, and socioeconomic factors are crucial factors influencing consumer purchase intent [6].The characteristics of online products do share similarities with traditional shopping, but the key difference lies in the fact that online products cannot provide consumers with direct sensory stimulation [7].Instead, consumers can only gain insights through static cues like text and images, lacking the tangible experience of touch.
In the study of consumer online purchase intent, in addition to consumer attitudes, product cues, and perceived risk, scholars have expanded their research from the perspectives of customer trust [8], transaction costs [9], social presence [10], among others.Factors affecting consumer online purchase intent mainly include website environment: webpage design [11], technological maturity, and visual effects [12], website ambiance [13], and more.Kim and others suggest that multidimensional display technologies such as 3D can offer consumers comprehensive product information, enhancing the shopping experience and participation, thereby increasing purchase intent [14].Diao Lei Yu believes that website convenience, aesthetics, and the perceived utility of information have a positive impact on consumer purchase intent [15].Furthermore, many researchers have studied the impact mechanisms of online influencers on consumer purchase intent in live streaming e-commerce.Building on this, subsequent research posits that besides influencer factors, product information, promotional elements, personalized services, and perceived value elements all influence consumer purchase intent [16][17][18][19].
Scholars have conducted considerable research on live streaming e-commerce, providing a valuable foundation for this paper.However, live streaming e-commerce is an emerging phenomenon, distinct from the factors affecting consumer purchase intent in the traditional era of text and images.It exhibits characteristics such as a dynamic, visual, and scenario-driven nature, and should be considered holistically, encompassing the frontend (live streams, hosts, product features, pricing, etc.) and backend (supply chain factors like payment, logistics, after-sales, etc.).In the context of the new digital economy, as consumers' digital literacy gradually improves, how does this variable affect their decision-making?These areas are still ripe for exploration.Therefore, this study aims to address the following research gaps: (1) What are the mechanisms by which live streaming e-commerce attracts consumers to generate purchase intent?(2) How does consumer digital literacy moderate the relationship between perceived value and attitude?Thus, this study attempts to answer these questions by constructing a multi-channel retail system adoption intention model.
Hypothesis Formulation
"Economy" refers to consumers finding products of interest to be cheaper than their expectations [20].The economy of a product can reduce the pain associated with payment [21].Existing research indicates that cost is a significant influencing factor in the adoption behavior of information systems, significantly impacting users' attitudes toward adopting services [22].Consumers compare the purchase costs of live streaming e-commerce and use this as a decision-making factor.The economy of a product implies reduced purchase costs.When consumers perceive that shopping through live streaming e-commerce will save them money, they are more likely to make purchases through this channel.Therefore, the following hypothesis can be proposed: H1: Economy has a positive impact on consumer attitudes.
When the sales theme is clear, the direct presentation of commercial information such as brands, products, prices, and promotional methods during live streams is advantageous in saving consumers time in searching and comparing, thus increasing decision efficiency [23].Hosts rely on their professional skills to demonstrate and introduce products to consumers, providing differentiated and specialized services that facilitate comprehensive understanding of product usage and functionality, making it easier for consumers to make purchase decisions.Based on this, the following hypothesis regarding the impact of functionality on consumer attitudes can be proposed: H2: Functionality has a positive impact on consumer attitudes."Entertainment" refers to "the degree of pleasure obtained when perceiving or enjoying a product or service without the influence of other factors" [24].Wexler pointed out that the perception of entertainment significantly influences computer users' acceptance of new systems.Furthermore, Lee's research showed that the perception of entertainment significantly improves customers' attitudes toward retailers.Therefore, when customers discover that shopping through live streaming ecommerce provides a joyful shopping experience, their attitudes toward using live streaming ecommerce become more positive.Hence, the following hypothesis can be proposed: H3: Entertainment has a positive and stimulating impact on consumer attitudes.Opinion leaders have a more significant and lasting impact on consumer purchase intent than traditional marketing, especially in online virtual communities, where opinion leaders can influence consumer behavioral intentions through their expertise, product involvement, interaction, and consistency.Internet celebrity hosts combine the characteristics of celebrities and opinion leaders, having a large fan base and a certain level of influence.In online communities, they act as opinion leaders, influencing community members through professional knowledge, high-quality speech, and frequent interaction, thus having a significant impact on consumers' purchase intent [17].Therefore, the following hypothesis can be proposed: H4: Host characteristics have a positive and stimulating impact on consumer attitudes.The live streaming industry chain consists of upstream brand companies, midstream operating agencies, and downstream content and e-commerce platforms.The information generated through their cooperation forms the content of live streaming.Part of the live streaming content is directly presented in the live room, using forms such as text, graphics, sound, tone, and other forms to present information-type content and emotional content to consumers.Another part exists covertly in transaction links, payment methods, logistics delivery, after-sales services, and other processes, objectively affecting consumers' rational consumption behavior [23].Based on the differences in supply chain service content in the live streaming backend, the following hypothesis can be proposed: H5: Supply chain perception has a positive and stimulating impact on consumer attitudes."Attitude" refers to an individual's enduring evaluation, feeling, and tendency toward certain individuals or concepts, while "intent" reflects the strength of an individual's intention to perform specific actions [24].The Theory of Reasoned Action (TRA), Theory of Planned Behavior (TPB), and Technology Acceptance Model (TAM) all suggest that users' attitudes toward the use of a new system directly influence their intention to use that system.This viewpoint is supported by numerous empirical studies [27].Therefore, it can be assumed that customers' attitudes toward multi-channel retail systems should directly influence their intention to adopt the system.Thus, the following hypothesis can be proposed: H6: Consumer attitudes have a positive impact on purchase intent.The term "digital literacy" first appeared in 1994 when Israeli scholar Y. Eshet-Alkalai summarized it as the "ability to understand and use a variety of digital resources and information displayed through computers" [28].In 2004, he outlined five aspects of digital literacy: visual literacy, innovation literacy, branch literacy, information literacy, and socio-emotional literacy.Subsequently, Paul Gilster formally introduced the concept of "digital literacy" in his work "Digital Literacy," emphasizing a critical evaluation of online information [29].As one of the eight core literacies emphasized by the European Union, digital literacy has evolved from its initial focus on "information technology" (emphasizing the technology itself) to "information technology skills and usage," "information technology skills" (emphasizing usage skills), and finally "digital literacy" (emphasizing literacy) [30].In 2012, the American Library Association (ALA) Digital Literacy Task Force defined digital literacy as the "ability to use information and communication technologies to find, evaluate, create, and communicate digital information, requiring both cognitive and technical skills" [31].
In the digital age, consumer digital literacy mainly pertains to digital information, emphasizing the development of people's ability to use digital tools, understand multimedia digital information, and foster innovative and critical thinking.Live streaming e-commerce, as an emerging phenomenon of the digital age, is received differently by consumers with varying levels of digital literacy.Hence, the following hypothesis can be proposed: H7: Consumer digital literacy moderates attitudes.
Conceptual Model Construction
Purchase intent refers to the probability of consumers purchasing goods or services, encompassing both positive and negative dimensions.Consumer purchase intent plays a critical predictive role in consumer behavior.According to Fishbein & Ajzen's Theory of Reasoned Action (TRA) [31], an individual's beliefs about the outcomes of a behavior, including their evaluation of the value of those outcomes, influence the individual's attitude towards performing that behavior, subsequently affecting their intent to act.Building upon the Theory of Reasoned Action, Moon & Kim introduced and validated the extended Technology Acceptance Model (TAM) under internet contexts [27].In this model, perceived usefulness, perceived ease of use, and perceived enjoyment are three critical beliefs that affect consumer attitudes and intentions to use.Given that the live streaming e-commerce environment is a technology-driven transaction setting, this study posits that these three beliefs can also influence consumer attitudes towards live streaming e-commerce, thereby affecting their purchase intent.These beliefs include functionality, economy, and entertainment.Furthermore, based on scholars' research, the model incorporates the host characteristics as a frontend factor and the "perceived supply chain" as a backend factor.Based on the above analysis, digital literacy is introduced as a moderating variable into the model, and it is believed that this variable can moderate the relationship between consumer perceived value and attitude towards using live streaming e-commerce.Following the impact process of "customer perceived value (beliefs) -usage attitude -adoption intent."
Research Design
Based on the analysis of consumer perceived value in the express delivery industry, the questionnaire was divided into two parts: the first part collected basic information about the respondents, including gender, age, occupation, educational background, and more.The second part consisted of the Consumer Perceived Value Scale, which was divided into five dimensions (functionality, economy, entertainment, host characteristics, and perceived supply chain).Each dimension had 3-4 questions, as shown in Table 1.The second part of the questionnaire formed the fundamental data for the subsequent analysis.Both qualitative and quantitative questions in the questionnaire used a 5-point Likert scale to ensure the uniformity and consistency of the questionnaire.
Q10
The host's ability to promote products is professional.Zhu Tong (2017), Wu Yuhong (2017) Q11 The host is interesting and has personal charm.
Q12 The host has strong interaction skills with fans.
Perceived Supply Chain
Q13 Live streaming shopping allows secure payments.
Batachij et al. Q14
Live streaming shopping provides worry-free after-sales service.
Q15
I can shop on live streams with complete peace of mind.
Q18
Live streaming e-commerce shopping is very appealing to me.
Q20
When I encounter useful digital information, I have the habit of recording it.
Q21
When I need to buy products online, I know what relevant knowledge I should have.
Q22
When I need to purchase products, I can find live streams independently.I am very satisfied with the services provided by the live streaming e-commerce platform I use.
Q25
The platform's services exceed my expectations, and I will continue to choose this live streaming platform in the future.After the initial questionnaire draft was prepared, the project team submitted the questionnaire to relevant experts at the school for review.Adjustments were made to address vague and inaccurate phrasing and to make certain questions more concise, ensuring greater clarity and reducing the potential for ambiguity.
To ensure the credibility of the questionnaire results, the project team conducted a preliminary test questionnaire.The test questionnaire included 24 questions that assessed the sufficiency of each dimension.In terms of distribution, given the ongoing need for contact reduction due to the normalized pandemic control measures, this study used an online method to distribute the questionnaire.The electronic questionnaire was designed to prevent multiple entries and ensure data quality.The electronic questionnaire was distributed through social networks to students, friends, and others, ensuring the timeliness of questionnaire sources.In the end, a total of 302 experimental questionnaires were distributed, with 249 responses collected, resulting in an effective questionnaire rate of 82.4%..74%From the data in the table, it is evident that the majority of respondents were female, accounting for 61.5% of the sample, indicating a higher level of female participation in live streaming ecommerce.Respondents were primarily between the ages of 18 and 40, representing nearly 97% of the total sample.Among them, the age group of 19-25 years accounted for 63%, suggesting that this age group is the main user base for live streaming e-commerce.Geographically, over 80% of the respondents lived in tier 1 cities.In terms of education, most respondents had at least a university degree, with a significant portion holding postgraduate degrees.
Reliability Test
In this study, as all the variables in the measurement scale were assessed using a 5-point Likert scale, the reliability of the scale was evaluated using Cronbach's α coefficient.It is generally accepted that a higher Cronbach's α coefficient indicates greater internal consistency of the scale.An α value greater than 0.7 suggests relatively high reliability, while values between 0.35 and 0.7 indicate acceptable reliability.Values below 0.35 suggest low reliability and should be rejected.From Table 3, it can be observed that all variables have Cronbach's α coefficients above 0.8, indicating that the questionnaire has good reliability.Furthermore, a Kaiser-Meyer-Olkin (KMO) test and Bartlett's test of sphericity were performed on the questionnaire.The KMO test yielded a coefficient of 0.937, exceeding the recommended threshold of 0.5, and the statistical significance probability (p-value) was less than 0.001, which is lower than the critical p-value of 0.05.This indicates that the structural validity test was passed, allowing for factor analysis to be conducted.889 In this study, structural equation modeling was conducted using AMOS software to verify the relationships between these variables.Based on the hypotheses of this study and the conceptual model presented, a complete structural equation model to be tested was established using AMOS.
Confirmatory Factor Analysis
Confirmatory factor analysis was conducted using AMOS 24.0 and SPSS 26.0 software to validate the factors.The software calculations revealed that the minimum factor loading between the measured variables and latent variables was 0.728, which is greater than 0.6.Therefore, no items needed to be deleted.The composite reliability (CR) and average variance extracted (AVE) for each factor were calculated.The CR values for Functionality, Economic Value, Entertainment, Host Traits, Supply Chain Perception, Consumer Attitude, and Purchase Intention were found to be 0.618, 0.697, 0.813, 0.696, 0.676, 0.599, and 0.626, respectively, all of which exceeded 0.5.The AVE values for these factors were 0.829, 0.872, 0.929, 0.872, 0.86, 0.817, and 0.834, respectively, all exceeding 0.8.This indicates that each factor has good convergent validity, as shown in Table 4. From Table 8, it can be observed that when consumers have lower digital literacy, they are more concerned with the functionality and entertainment value of products in live e-commerce.However, when consumers have higher digital literacy, they pay more attention to the impact of supply chain factors.Additionally, consumers' focus on functionality and entertainment decreases relatively.These findings support H7.
Conclusion
This article explores consumers' purchase intention in the context of live e-commerce from the perspective of perceived value, while also verifying the moderating effect of consumer digital literacy.The following research conclusions are drawn: 1. "Economic value," "entertainment," "functionality," "host traits," and "supply chain perception" significantly influence consumers' attitudes toward live e-commerce."Functionality" indicates that meeting basic usability needs is a crucial motivator for consumer purchase intention.Consumers are more inclined to favor products that are not only functional but also economically advantageous and cost-effective.Furthermore, due to the diverse nature of consumer shopping motivations, in addition to functionality and economic value, more emphasis should be placed on the entertainment factor brought by live e-commerce.Leveraging host traits to enhance consumer attraction is essential.Attention should be given to improving consumers' perception of the supply chain.In other words, a comprehensive understanding of consumer purchase motivations is needed to provide a holistic live e-commerce shopping experience.
2. Consumers' positive attitudes toward live e-commerce significantly affect their purchase intention.This conclusion aligns with the findings of previous scholars and emphasizes that consumer usage attitudes are decisive factors in the adoption of a multi-channel retail system.[27] Therefore, enhancing consumers' perceptions of value to improve their attitudes toward a multi-channel retail system should be a crucial approach for retailers to strengthen consumer adoption intentions.
3. Consumer digital literacy significantly moderates the relationship between perceived value and attitude.For consumers with lower digital literacy, the "entertainment" value of live e-commerce and the functionality of displayed products are the primary factors affecting their attitude.Among these factors, "entertainment" holds the highest weight.In other words, when consumers have lower digital literacy, enhancing the entertainment value of live e-commerce can easily improve their attitudes.For consumers with higher digital literacy, "supply chain perception" has the strongest impact on their attitude toward live e-commerce.Providing higher-quality supply chain services can positively change the attitude of this group toward live e-commerce.
Research Limitations and Prospects
(1) The factors explored in this paper that affect purchase intention in live e-commerce primarily focus on perceived value.Further research could introduce other variables such as "trust" into the model to enhance its explanatory power.
(2) This study only examined the moderating effect of digital literacy.Subsequent research could consider other factors like price sensitivity as moderating variables to understand more factors that affect purchase intention due to differences in consumer characteristics.
(3) This research solely employed a questionnaire survey to gather data.Further studies could design more rigorous experimental procedures to validate the effectiveness of the model proposed in this research.
streaming e-commerce shopping is a clever way to shop.
Table 1 :
Measurement Dimensions and Reference Sources
Table 2 :
Summary of Consumer Demographic Information
Table 3 :
Descriptive Statistics and Reliability Test of the Sample Scale
Table 4 :
Results of Confirmatory Factor Analysis
Table 6 :
Moderation Effects Analysis | 4,484.2 | 2023-10-25T00:00:00.000 | [
"Business",
"Computer Science"
] |