When a hazardous chemical soaks into a porous material such as a concrete floor, it can be difficult to remove. One approach is chemical decontamination, where a cleanser is added to react with and neutralise the contaminating agent. The goal of this paper is to investigate the reaction dynamics and the factors that affect the efficacy of the decontamination procedure. We consider a one-dimensional porous medium initially saturated with an oil-based agent. An aqueous cleanser is applied at the surface, so the two chemicals are immiscible and a boundary forms between them. A neutralising reaction takes place at this boundary in which cleanser and agent are consumed and reaction products are created. This is a Stefan problem, and the boundary between the cleanser and agent moves as the reaction proceeds. Reaction products formed at the interface may dissolve in one or both liquids. This may temporarily prevent cleanser and/or agent from reaching the reaction site, so diffusion of the chemical species, in particular the diffusion of product from the interface, plays a key role. The scenario described above was considered previously by ?? in the limit where the depth of the porous medium is large compared to the length scale over which concentrations vary inside the medium. Here, we present results that are valid for any ratio between these length scales and an analysis of agent removal times for various dimensionless parameter regimes. We also highlight the emergence of a boundary layer associated with diffusion in the oil phase for early times, where the thickness of the boundary layer is directly proportional to the square root of the time variable.
{"title":"Reaction dynamics and early-time behaviour of chemical decontamination","authors":"S Murphy, M Vynnycky, S L Mitchell, D O’Kiely","doi":"10.1093/imamat/hxae001","DOIUrl":"https://doi.org/10.1093/imamat/hxae001","url":null,"abstract":"When a hazardous chemical soaks into a porous material such as a concrete floor, it can be difficult to remove. One approach is chemical decontamination, where a cleanser is added to react with and neutralise the contaminating agent. The goal of this paper is to investigate the reaction dynamics and the factors that affect the efficacy of the decontamination procedure. We consider a one-dimensional porous medium initially saturated with an oil-based agent. An aqueous cleanser is applied at the surface, so the two chemicals are immiscible and a boundary forms between them. A neutralising reaction takes place at this boundary in which cleanser and agent are consumed and reaction products are created. This is a Stefan problem, and the boundary between the cleanser and agent moves as the reaction proceeds. Reaction products formed at the interface may dissolve in one or both liquids. This may temporarily prevent cleanser and/or agent from reaching the reaction site, so diffusion of the chemical species, in particular the diffusion of product from the interface, plays a key role. The scenario described above was considered previously by ?? in the limit where the depth of the porous medium is large compared to the length scale over which concentrations vary inside the medium. Here, we present results that are valid for any ratio between these length scales and an analysis of agent removal times for various dimensionless parameter regimes. We also highlight the emergence of a boundary layer associated with diffusion in the oil phase for early times, where the thickness of the boundary layer is directly proportional to the square root of the time variable.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zilong Song, Robert Eisenberg, Shixin Xu, Huaxiong Huang
Voltage-gated K$_{mathrm{v}}$ channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of K$_{mathrm{v}}$ channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson-Nernst-Planck (PNP) system to capture the key characteristics, particularly the delay in the opening of channels. The coupled PNP system is solved numerically by a finite-difference method and the solution is compared with an analytical approximation. We hypothesize that the stochastic behaviour of the gating phenomenon is due to randomness of the bubble and channel sizes. The predicted ensemble average of the currents under various applied voltage across the channels is consistent with experimental observations, and the Cole-Moore delay is captured by varying the holding potential.
{"title":"A Bubble Model for the Gating of Kv Channels","authors":"Zilong Song, Robert Eisenberg, Shixin Xu, Huaxiong Huang","doi":"10.1093/imamat/hxae002","DOIUrl":"https://doi.org/10.1093/imamat/hxae002","url":null,"abstract":"Voltage-gated K$_{mathrm{v}}$ channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of K$_{mathrm{v}}$ channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson-Nernst-Planck (PNP) system to capture the key characteristics, particularly the delay in the opening of channels. The coupled PNP system is solved numerically by a finite-difference method and the solution is compared with an analytical approximation. We hypothesize that the stochastic behaviour of the gating phenomenon is due to randomness of the bubble and channel sizes. The predicted ensemble average of the currents under various applied voltage across the channels is consistent with experimental observations, and the Cole-Moore delay is captured by varying the holding potential.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"50 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Initial-boundary value problem for a fractional heat equation on an interval","authors":"","doi":"10.1093/imamat/hxad036","DOIUrl":"https://doi.org/10.1093/imamat/hxad036","url":null,"abstract":"","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"71 12","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138606597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters cannot be feasibly computed and approximate strategies are required. We introduce a unified framework for computing hypergradients that generalizes existing methods based on the implicit function theorem and automatic differentiation/backpropagation, showing that these two seemingly disparate approaches are actually tightly connected. Our framework is extremely flexible, allowing its subproblems to be solved with any suitable method, to any degree of accuracy. We derive a priori and computable a posteriori error bounds for all our methods, and numerically show that our a posteriori bounds are usually more accurate. Our numerical results also show that, surprisingly, for efficient bilevel optimization, the choice of hypergradient algorithm is at least as important as the choice of lower-level solver.
{"title":"Analyzing inexact hypergradients for bilevel learning","authors":"Matthias J Ehrhardt, Lindon Roberts","doi":"10.1093/imamat/hxad035","DOIUrl":"https://doi.org/10.1093/imamat/hxad035","url":null,"abstract":"Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters cannot be feasibly computed and approximate strategies are required. We introduce a unified framework for computing hypergradients that generalizes existing methods based on the implicit function theorem and automatic differentiation/backpropagation, showing that these two seemingly disparate approaches are actually tightly connected. Our framework is extremely flexible, allowing its subproblems to be solved with any suitable method, to any degree of accuracy. We derive a priori and computable a posteriori error bounds for all our methods, and numerically show that our a posteriori bounds are usually more accurate. Our numerical results also show that, surprisingly, for efficient bilevel optimization, the choice of hypergradient algorithm is at least as important as the choice of lower-level solver.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the interfacial growth morphologies of crystals growing in contact in crystal mushes, with a specific application to those formed by the solidification of basaltic magma. We focus on the particular case of an augite (pyroxene) crystal growing between two plagioclase crystals. The augite is treated as an equant unfaceted crystal, whereas the plagioclase is faceted, and our treatment applies generally to such combinations. The resulting three-grain junctions in natural rock samples are commonly of two distinct types. In one, the two augite-plagioclase interfaces grow towards each other with opposite curvatures, whereas in the second the curvatures of the interfaces have the same sign, giving a distinctive morphology which we have called an eagle’s beak. The present paper provides a theoretical framework to provide explanations for both of these morphologies, based on the kinetics of interfacial growth.
{"title":"Interfacial growth morphologies in dense eutectic crystal mushes","authors":"A C Fowler, Marian B Holness","doi":"10.1093/imamat/hxad033","DOIUrl":"https://doi.org/10.1093/imamat/hxad033","url":null,"abstract":"We consider the interfacial growth morphologies of crystals growing in contact in crystal mushes, with a specific application to those formed by the solidification of basaltic magma. We focus on the particular case of an augite (pyroxene) crystal growing between two plagioclase crystals. The augite is treated as an equant unfaceted crystal, whereas the plagioclase is faceted, and our treatment applies generally to such combinations. The resulting three-grain junctions in natural rock samples are commonly of two distinct types. In one, the two augite-plagioclase interfaces grow towards each other with opposite curvatures, whereas in the second the curvatures of the interfaces have the same sign, giving a distinctive morphology which we have called an eagle’s beak. The present paper provides a theoretical framework to provide explanations for both of these morphologies, based on the kinetics of interfacial growth.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"73 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.
{"title":"A unified and constructive framework for the universality of neural networks","authors":"Tan Bui-Thanh","doi":"10.1093/imamat/hxad032","DOIUrl":"https://doi.org/10.1093/imamat/hxad032","url":null,"abstract":"Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"7 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.
{"title":"A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms","authors":"Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar","doi":"10.1093/imamat/hxad031","DOIUrl":"https://doi.org/10.1093/imamat/hxad031","url":null,"abstract":"Abstract We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"30 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Y Peña Pérez, J Sánchez Ortíz, F J Ariza Hernández, M P Árciga Alejandre
Abstract In this paper, we study a Dirichlet problem for a fractional heat equation, with spacial fractional derivative in the sense of Riemann–Liouville on a finite interval. The main ideas of Fokas method is employed, where the Lax pairs are used to obtain an integral representation of solutions.
{"title":"Initial-boundary value problem for a fractional heat equation on an interval","authors":"Y Peña Pérez, J Sánchez Ortíz, F J Ariza Hernández, M P Árciga Alejandre","doi":"10.1093/imamat/hxad029","DOIUrl":"https://doi.org/10.1093/imamat/hxad029","url":null,"abstract":"Abstract In this paper, we study a Dirichlet problem for a fractional heat equation, with spacial fractional derivative in the sense of Riemann–Liouville on a finite interval. The main ideas of Fokas method is employed, where the Lax pairs are used to obtain an integral representation of solutions.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135728101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper is concerned with an approach based on the topological sensitivity notion to solve a geometric inverse problem for a linear wave equation. The considered inverse problem is motivated by elastography. More precisely, the modeling of our application system has been aimed toward the detection of a breast tumor, in particular, and to enable the calculation of the tumor size, location, and type. We start our analysis by rephrasing the considered inverse problem as an optimization one minimizing an energy cost functional. We establish an estimation describing the asymptotic behavior of the wave equation solution with respect to the presence of a small tumor in the breast which plays an important role in the derivation of a topological asymptotic formula for the considered cost function. Based on the derived theoretical results, we have developed a numerical algorithm for solving our inverse problem, which requires only one iteration. Some numerical experiments are presented to point out the efficiency and accuracy of the proposed approach.
{"title":"Application of the topological sensitivity method to the detection of Breast cancer","authors":"Sabeur Mansouri, Mohamed BenSalah","doi":"10.1093/imamat/hxad028","DOIUrl":"https://doi.org/10.1093/imamat/hxad028","url":null,"abstract":"Abstract This paper is concerned with an approach based on the topological sensitivity notion to solve a geometric inverse problem for a linear wave equation. The considered inverse problem is motivated by elastography. More precisely, the modeling of our application system has been aimed toward the detection of a breast tumor, in particular, and to enable the calculation of the tumor size, location, and type. We start our analysis by rephrasing the considered inverse problem as an optimization one minimizing an energy cost functional. We establish an estimation describing the asymptotic behavior of the wave equation solution with respect to the presence of a small tumor in the breast which plays an important role in the derivation of a topological asymptotic formula for the considered cost function. Based on the derived theoretical results, we have developed a numerical algorithm for solving our inverse problem, which requires only one iteration. Some numerical experiments are presented to point out the efficiency and accuracy of the proposed approach.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"12 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135367248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ivan Yu. Tyukin, Desmond J. Higham, Eliyas Woldegeorgis, Alexander N. Gorban
Abstract We develop and study new adversarial perturbations that enable an attacker to gain control over decisions in generic Artificial Intelligence (AI) systems including deep learning neural networks. In contrast to adversarial data modification, the attack mechanism we consider here involves alterations to the AI system itself. Such a stealth attack could be conducted by a mischievous, corrupt or disgruntled member of a software development team. It could also be made by those wishing to exploit a “democratization of AI” agenda, where network architectures and trained parameter sets are shared publicly. We develop a range of new implementable attack strategies with accompanying analysis, showing that with high probability a stealth attack can be made transparent, in the sense that system performance is unchanged on a fixed validation set which is unknown to the attacker, while evoking any desired output on a trigger input of interest. The attacker only needs to have estimates of the size of the validation set and the spread of the AI’s relevant latent space. In the case of deep learning neural networks, we show that a one neuron attack is possible—a modification to the weights and bias associated with a single neuron—revealing a vulnerability arising from over-parameterization. We illustrate these concepts using state of the art architectures on two standard image data sets. Guided by the theory and computational results, we also propose strategies to guard against stealth attacks.
{"title":"The feasibility and inevitability of stealth attacks","authors":"Ivan Yu. Tyukin, Desmond J. Higham, Eliyas Woldegeorgis, Alexander N. Gorban","doi":"10.1093/imamat/hxad027","DOIUrl":"https://doi.org/10.1093/imamat/hxad027","url":null,"abstract":"Abstract We develop and study new adversarial perturbations that enable an attacker to gain control over decisions in generic Artificial Intelligence (AI) systems including deep learning neural networks. In contrast to adversarial data modification, the attack mechanism we consider here involves alterations to the AI system itself. Such a stealth attack could be conducted by a mischievous, corrupt or disgruntled member of a software development team. It could also be made by those wishing to exploit a “democratization of AI” agenda, where network architectures and trained parameter sets are shared publicly. We develop a range of new implementable attack strategies with accompanying analysis, showing that with high probability a stealth attack can be made transparent, in the sense that system performance is unchanged on a fixed validation set which is unknown to the attacker, while evoking any desired output on a trigger input of interest. The attacker only needs to have estimates of the size of the validation set and the spread of the AI’s relevant latent space. In the case of deep learning neural networks, we show that a one neuron attack is possible—a modification to the weights and bias associated with a single neuron—revealing a vulnerability arising from over-parameterization. We illustrate these concepts using state of the art architectures on two standard image data sets. Guided by the theory and computational results, we also propose strategies to guard against stealth attacks.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135666553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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