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arXiv 2023年

作者： Sadeghi, Zahra Alizadehsani, Roohallah Cifci, Mehmet Akif Kausar, Samina Rehman, Rizwan Mahanta, Priyakshi Bora, Pranjal Kumar Almasri, Ammar Alkhawaldeh, Rami S. Hussain, Sadiq Alatas, Bilal Shoeibi, Afshin Moosaei, Hossein Hladík, Milan Nahavandi, Saeid Pardalos, Panos M. Institute for Big Data Analytics Faculty of Computer Science Dalhousie University Canada Deakin University Geelong Australia The Institute of Computer Technology Tu Wien University Vienna1040 Austria University of Kotli Azad Jammu and Kashmir Azad Kashmir Kotli Pakistan Centre for Computer Science and Applications Dibrugarh University Assam India Department of Management Information Sys Al-Balqa Applied University Salt19117 Jordan Department of Computer Information Systems The University of Jordan Aqaba77110 Jordan Examination Branch Dibrugarh University Assam Dibrugarh India Department of Software Eng. Firat University Elazig23100 Turkey Data Science and Computational Intelligence Institute University of Granada Spain Department of Informatics Faculty of Science Jan Evangelista Purkyně University in Ústí nad Labem Czech Republic Department of Applied Mathematics School of Computer Science Faculty of Mathematics and Physics Charles University Prague Czech Republic Harvard Paulson School of Engineering and Applied Sciences Harvard University AllstonMA02134 United States Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida Gainesville32611 United States

XAI refers to the techniques and methods for building AI applications which assist end users to interpret output and predictions of AI models. Black box AI applications in high-stakes decision-making situations, such as medical domain have increased the demand for transparency and explainability since wrong predictions may have severe consequences. Model explainability and interpretability are vital successful deployment of AI models in healthcare practices. AI applications' underlying reasoning needs to be transparent to clinicians in order to gain their trust. This paper presents a systematic review of XAI aspects and challenges in the healthcare domain. The primary goals of this study are to review various XAI methods, their challenges, and related machine learning models in healthcare. The methods are discussed under six categories: Features-oriented methods, global methods, concept models, surrogate models, local pixel-based methods, and human-centric methods. Most importantly, the paper explores XAI role in healthcare problems to clarify its necessity in safety-critical applications. The paper intends to establish a comprehensive understanding of XAI-related applications in the healthcare field by reviewing the related experimental results. To facilitate future research for filling research gaps, the importance of XAI models from different viewpoints and their limitations are investigated. © 2023, CC BY-NC-ND.

关键词： Decision making

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An analytical approach to the Mean–Return-Time Phase of isotropic stochastic oscillators

arXiv

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arXiv 2021年

作者： Holzhausen, Konstantin Thomas, Peter J. Lindner, Benjamin Bernstein Center for Computational Neuroscience Berlin Philippstr. 13 Haus 2 Berlin10115 Germany Physics Department of Humboldt University Berlin Newtonstr. 15 Berlin12489 Germany Department of Mathematics Applied Mathematics and Statistics 212 Yost Hall Case Western Reserve University 10900 Euclid Avenue ClevelandOH United States

One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT-isochrons. © 2021, CC BY.

关键词： Stochastic systems

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RESTRICTION ESTIMATES in A CONICAL SINGULAR SPACE: WAVE EQUATION

arXiv

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arXiv 2020年

作者： Gao, Xiaofen Zhang, Junyong Zheng, Jiqiang Department of Mathematics Beijing Institute of Technology Beijing100081 China Beijing Institute of Technology Department of Mathematics Cardiff University 100081 United Kingdom Institute of Applied Physics and Computational Mathematics Beijing100088 China

We study the restriction estimates in a class of conical singular space X = C(Y) = (0, ∞)r × Y with the metric g = dr2 + r2h, where the cross section Y is a compact (n − 1)-dimensional closed Riemannian manifold (Y, h). Let ∆g be the Friedrich extension positive Laplacian on X, and consider the operator LV = ∆g + V with V = V0r−2, where V0(θ) ∈ C∞(Y) is a real function such that the operator ∆h +V0 +(n−2)2/4 is positive. In the present paper, we prove a type of modified restriction estimates for the solutions of wave equation associated with LV . The smallest positive eigenvalue of the operator ∆h + V0 + (n − 2)2/4 plays an important role in the result. As an application, for independent of interests, we prove local energy estimates and Keel-Smith-Sogge estimates for the wave equation in this setting. Copyright © 2020, The Authors. All rights reserved.

关键词： Wave equations

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Local number fluctuations in hyperuniform and nonhyperuniform systems: Higher-order moments and distribution functions

arXiv

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arXiv 2020年

作者： Torquato, Salvatore Kim, Jaeuk Klatt, Michael A. Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The local number variance σ2(R) associated with a spherical sampling window of radius R enables a classification of many-particle systems in d-dimensional Euclidean space Rd according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To more completely characterize density fluctuations, we carry out an extensive study of higher-order moments or cumulants, including the skewness γ1(R), excess kurtosis γ2(R) and the corresponding probability distribution function P[N(R)] of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. To carry out this comprehensive program, we derive new theoretical results that apply to general point processes and conduct high-precision numerical studies. Specifically, we derive explicit closed-form integral expressions for γ1(R) and γ2(R) that encode structural information up to three-body and four-body correlation functions, respectively. We also derive rigorous bounds on γ1(R), γ2(R) and P[N(R)] for general point processes and corresponding exact results for general packings of identical spheres. High-quality simulation data for γ1(R), γ2(R) and P[N(R)] are generated for each model. We also ascertain the proximity of P[N(R)] to the normal distribution via a novel Gaussian "distance" metric l2(R). Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes such that γ1(R) ∼ l2(R) ∼ R-(d+1)/2 and γ2(R) ∼ R-(d+1) for large R. The convergence to a CLT is slower for standard nonhyperuniform models and slowest for the "antihyperuniform" model studied here. We prove that one-dimensional hyperuniform systems of class I or any d-dimensional lattice cannot obey a CLT. Remarkably, we discovered that the gamma distribution provides a good approximation to P[N(R)] for

关键词： Higher order statistics

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Automated Real-Space Lattice Extraction for Atomic Force Microscopy Images

arXiv

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arXiv 2022年

作者： Corrias, Marco Papa, Lorenzo Sokolović, Igor Birschitzky, Viktor Gorfer, Alexander Setvin, Martin Schmid, Michael Diebold, Ulrike Reticcioli, Michele Franchini, Cesare University of Vienna Faculty of Physics Center for Computational Materials Science Kolingasse 14-16 ViennaA-1090 Austria University of Vienna Vienna Doctoral School in Physics Boltzmanngasse 5 Vienna1090 Austria Institute of Applied Physics TU Wien Wiedner Hauptstrasse 8-10/134 ViennaA 1040 Austria Department of Surface and Plasma Science Faculty of Mathematics and Physics Charles University V Holešovičkách 2 Prague 8180 00 Czech Republic Dipartimento di Fisica e Astronomia Università di Bologna Bologna40127 Italy

Analyzing atomically resolved images is a time-consuming process requiring solid experience and substantial human intervention. In addition, the acquired images contain a large amount of information such as crystal structure, presence and distribution of defects, and formation of domains, which need to be resolved to understand a material’s surface structure. Therefore, machine learning techniques have been applied in scanning probe and electron microscopies during the last years, aiming for automatized and efficient image analysis. This work introduces a free and open source tool (AiSurf: Automated Identification of Surface Images) developed to inspect atomically resolved images via Scale-Invariant Feature Transform (SIFT) and Clustering Algorithms (CA). AiSurf extracts primitive lattice vectors, unit cells, and structural distortions from the original image, with no pre-assumption on the lattice and minimal user intervention. The method is applied to various atomically resolved non-contact atomic force microscopy (AFM) images of selected surfaces with different levels of complexity: anatase TiO2(101), oxygen deficient rutile TiO2(110) with and without CO adsorbates, SrTiO3(001) with Sr vacancies and graphene with C vacancies. The code delivers excellent results and has proved to be robust against atom misclassification and noise, thereby facilitating the interpretation scanning probe microscopy images. © 2022, CC BY.

关键词： Titanium dioxide

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Cloaking the underlying long-range order of randomly perturbed lattices

arXiv

引用

arXiv 2020年

作者： Klatt, Michael Andreas Kim, Jaeuk Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then ‘cloaked’ in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked or not as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 106 particles) of disordered hyperuniform point patterns without Bragg peaks. Copyright © 2020, The Authors. All rights reserved.

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A multi-center quadrature scheme for the molecular continuum

arXiv

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arXiv 2021年

作者： Gharibnejad, Heman Douguet, Nicolas Schneider, Barry I. Olsen, Jeppe Argenti, Luca University of Maryland Department of Chemistry and Biochemistry College ParkMD United States Kennesaw State University Department of Physics MariettaGA United States University of Central Florida Department of Physics CREOL OrlandoFL United States National Institute of Standards and Technology Applied and Computational Mathematics Division GaithersburgMD United States Aarhus University Department of Chemistry Aarhus Denmark

A common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme [J. Chem. Phys. 88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron-molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules. © 2021, CC BY.

关键词： Atoms

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Finite-size effects on the convergence time in continuous-opinion dynamics

arXiv

引用

arXiv 2021年

作者： Jo, Hang-Hyun Masuda, Naoki Department of Physics The Catholic University of Korea Bucheon14662 Korea Republic of Department of Mathematics State University of New York at Buffalo 14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo 14260-5030 United States

We study finite-size effects on the convergence time in a continuous-opinion dynamics model. In the model, each individual's opinion is represented by a real number on a finite interval, e.g., [0;1], and a uniformly randomly chosen individual updates its opinion by partially mimicking the opinion of a uniformly randomly chosen neighbor. We numerically find that the characteristic time to the convergence increases as the system size increases according to a particular functional form in the case of lattice networks. In contrast, unless the individuals perfectly copy the opinion of their neighbors in each opinion updating, the convergence time is approximately independent of the system size in the case of regular random graphs, uncorrelated scale-free networks, and complete graphs. We also provide a mean-field analysis of the model to understand the case of the complete graph. Copyright © 2021, The Authors. All rights reserved.

关键词： Graph theory

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Extreme events in a complex network: interplay between degree distribution and repulsive interaction

arXiv

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arXiv 2022年

作者： Ray, Arnob Bröhl, Timo Mishra, Arindam Ghosh, Subrata Ghosh, Dibakar Kapitaniak, Tomasz Dana, Syamal K. Hens, Chittaranjan Physics and Applied Mathematics Unit Indian Statistical Institute Kolkata700108 India Department of Epileptology University Hospital Bonn Venusberg Campus 1 Bonn53127 Germany Helmholtz-Institute for Radiation and Nuclear Physics University of Bonn Nussallee 14-16 Bonn53115 Germany Department of Physics National University of Singapore Singapore117551 Singapore Center for Computational Natural Sciences and Bioinformatics International Institute of Information Technology Gachibowli Hyderabad500032 India Division of Dynamics Lodz University of Technology Lodz90-924 Poland National Institute of Technology Durgapur713209 India

The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and thereby confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator. Copyright © 2022, The Authors. All rights reserved.

关键词： Complex networks

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Modeling the extracellular matrix in cell migration and morphogenesis: A guide for the curious biologist

arXiv

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arXiv 2023年

作者： Crossley, Rebecca M. Johnson, Samuel Tsingos, Erika Bell, Zoe Berardi, Massimiliano Botticelli, Margherita Braat, Quirine J.S. Metzcar, John Ruscone, Marco Yin, Yuan Shuttleworth, Robyn Wolfson Centre for Mathematical Biology Mathematical Institute University of Oxford United Kingdom Computational Developmental Biology Group Institute of Biodynamics and Biocomplexity Utrecht University Utrecht Netherlands Northern Institute for Cancer Research Newcastle University United Kingdom LaserLab department of Physics and Astronomy Vrije Universiteit Amsterdam Amsterdam Netherlands Optics11 life Amsterdam Netherlands Watson School of Mathematics University of Birmingham United Kingdom Department of Applied Physics and Science Education Eindhoven University of Technology Netherlands Department of Intelligent Systems Engineering Indiana University BloomingtonIN United States Department of Informatics Indiana University BloomingtonIN United States Institut Curie Université PSL ParisF-75005 France Altos Labs Redwood CityCA United States

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies. © 2023, CC BY.

关键词： Tissue

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