检索结果-内蒙古大学图书馆

Manifold learning with arbitrary norms

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Kileel, Joe Moscovich, Amit Zelesko, Nathan Singer, Amit Department of Mathematics Oden Institute University of Texas at Austin United States Department of Statistics and Operations Research Tel-Aviv University Israel Department of Mathematics Brown University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex with each data point and a weighted edge with each pair. Existing theory shows that the Laplacian matrix of the graph converges to the Laplace-Beltrami operator of the data manifold, under the assumption that the pairwise affinities are based on the Euclidean norm. In this paper, we determine the limiting differential operator for graph Laplacians constructed using any norm. Our proof involves an interplay between the second fundamental form of the manifold and the convex geometry of the given norm's unit ball. To demonstrate the potential benefits of non-Euclidean norms in manifold learning, we consider the task of mapping the motion of large molecules with continuous variability. In a numerical simulation we show that a modified Laplacian eigenmaps algorithm, based on the Earthmover's distance, outperforms the classic Euclidean Laplacian eigenmaps, both in terms of computational cost and the sample size needed to recover the intrinsic geometry. Copyright © 2020, The Authors. All rights reserved.

关键词： Mathematical operators

Atomistic mechanism of phase transition in shock compressed gold revealed by deep potential

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Chen, Bo Zeng, Qiyu Wang, Han Zhang, Shen Kang, Dongdong Lu, Denghui Dai, Jiayu Department of Physics National University of Defense Technology Changsha410073 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China HEDPS CAPT College of Engineering Peking University Beijing100871 China

A detailed understanding of the material response to rapid compression is challenging and demanding. For instance, the element gold under dynamic compression exhibits complex phase transformations where there exist some large discrepancies between experimental and theoretical studies. Here, we combined large-scale molecular dynamics simulations with a deep potential to elucidate the dynamic compression processes of gold from an atomic level. The potential is constructed by accurately reproducing the free energy surfaces of density-functional-theory calculations for gold, from ambient conditions to 15 500 K and 500 GPa. Within this framework, we extend the simulations up to 200 000 atoms size, and found a much lower pressure threshold for phase transitioning from face-centered cubic (FCC) to body-centered (BCC), as compared to previous calculations. Furthermore, the transition pressure is strongly dependent on the shock direction, namely 159 GPa for orientation and 219 GPa for orientation, respectively. Most importantly, the accurate atomistic perspective presents that the shocked BCC structure contains unique features of medium-range and short-range orders, which is named "disorders" here. We propose a model and demonstrate that the existence of "disorders" significantly reduces the Gibbs free energies of shocked structures, therefore leading to the lowering of the phase transition pressure. The present study provides a new path to understand the structure dynamics under extreme conditions. Copyright © 2020, The Authors. All rights reserved.

关键词： Gibbs free energy

Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows

学校读者我要写书评

暂无评论

Physical Review Letters 2021年第7期127卷 074503-074503页

作者： Shi-Yuan Hu Jun-Jun Chu Michael J. Shelley Jun Zhang Applied Mathematics Lab Courant Institute of Mathematical Sciences New York University New York New York 10012 USA Department of Physics New York University New York New York 10003 USA School of Physics Science and Engineering Tongji University Shanghai 200092 China Center for Computational Biology Flatiron Institute New York New York 10010 USA NYU-ECNU Institute of Physics at NYU Shanghai Shanghai 200062 China

In cellular vortical flows, namely arrays of counterrotating vortices, short but flexible filaments can show simple random walks through their stretch-coil interactions with flow stagnation points. Here, we study the dynamics of semirigid filaments long enough to broadly sample the vortical field. Using simulation, we find a surprising variety of long-time transport behavior—random walks, ballistic transport, and trapping—depending upon the filament’s relative length and effective flexibility. Moreover, we find that filaments execute Lévy walks whose diffusion exponents generally decrease with increasing filament length, until transitioning to Brownian walks. Lyapunov exponents likewise increase with length. Even completely rigid filaments, whose dynamics is finite dimensional, show a surprising variety of transport states and chaos. Fast filament dispersal is related to an underlying geometry of “conveyor belts.” Evidence for these various transport states is found in experiments using arrays of counterrotating rollers, immersed in a fluid and transporting a flexible ribbon.

关键词： Random walks Thin fluid films Transport phenomena Chaotic systems Filaments Viscosity Chaos & nonlinear dynamics Hele-Shaw cell

Phonon dispersions throughout the iron spin crossover in ferropericlase

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Marcondes, Michel L. Zheng, Fawei Wentzcovitch, Renata M. Department of Earth and Environmental Sciences Columbia University Lamont-Doherty Earth Observatory PalisadesNY10964 United States Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States

Ferropericlase (Fp), (Mg1-xFex)O, is the second most abundant phase in the Earth’s lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), S=2, to low spin (LS), S=0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermo-elastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasi-harmonic approximation (QHA). Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin-crossover using ab initio DFT+Usc calculations. We address vibrational modes associated with isolated and (2nd) nearest neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient while optical modes are the most affected. We show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures. Copyright © 2020, The Authors. All rights reserved.

关键词： Iron

A Brief Review of Explainable Artificial Intelligence in Healthcare

学校读者我要写书评

暂无评论

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

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

学校读者我要写书评

暂无评论

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

RESTRICTION ESTIMATES in A CONICAL SINGULAR SPACE: WAVE EQUATION

学校读者我要写书评

暂无评论

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

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

学校读者我要写书评

暂无评论

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

Automated Real-Space Lattice Extraction for Atomic Force Microscopy Images

学校读者我要写书评

暂无评论

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