检索结果-内蒙古大学图书馆

Precise Determination of Pair Interactions from Pair Statistics of Many-Body Systems In and Out of Equilibrium

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Torquato, Salvatore Wang, Haina Department of Chemistry Department of Physics Princeton Institute of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised a novel optimization algorithm to find effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point;(2) liquid under the Dzugutov potential;(3) nonequilibrium random sequential addition packing;and (4) and a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice (URL). We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L2-norm errors

关键词： Statistics

Developing a medical artificial intelligence course for high school students

学校读者我要写书评

暂无评论

Developing a medical artificial intelligence course for high...

International Forum on Medical Imaging in Asia 2021, IFMIA 2021

作者： Huang, Chao-Jung Wu, Tinghui Lu, Jui-Ting Lin, Beatrice Chang, Dawei Wang, Pochuan Wang, Mei-Chi Lee, Peijung Wang, Weichung National Taiwan University-Stanford Joint Program Office of AI in Biotechnology Ministry of Science and Technology Joint Research Center for Artificial Intelligence Technology and All Vista Healthcare Taipei Taiwan Institute of Applied Mathematical Sciences National Taiwan University Taipei Taiwan Department of Mathematics Ecole Normale Supérieure de Lyon Lyon France Department of Computer Science and Information Engineering National Taiwan University Taipei Taiwan Department of Electronic and Computer Engineering National Taiwan University of Science and Technology Taipei Taiwan Department of Mathematics National Taiwan University Taipei Taiwan

ISBN: (数字)9781510644212

ISBN: (纸本)9781510644205

Artificial intelligence (AI) training courses often require prerequisites such as calculus or statistics. It is hence challenging to design and develop an introductory AI course for students of secondary education. This research intends to develop a medical AI course, provide high school students with an overview of deep learning applications in medical image analysis, and inspire them to pursue careers in the field of medical AI. We designed a 20-hour course, including lectures and two hands-on projects based on medical image classification. The proposed courses provided medical AI disciplines and built up their knowledge from basic to advanced levels. During the ten-day online courses, all the students were fully engaged and gave us positive feedback. The students endeavored to complete the experimental study in training, testing, and hypothesis of medical images application in the course. Their performance exceeded all expectations, for they did further analysis by tuning different hyperparameters. We designed a course evaluation form, which suggested that the students found it essential and expected to interact with the instructors. The results indicate that combining lectures with hands-on sessions would lead to evidently better achievement in terms of high school students' medical AI knowledge and positive attitudes while addressing real-world problems in the projects. Through this innovative education model, high school students regained their enthusiasm and were encouraged to cultivate their medical AI skills through self-learning while finishing the project. We conclude that this course could be successfully applied to interdisciplinary education in high school. © 2021 SPIE.

关键词： Students

A general positivity-preserving algorithm for implicit high-order finite volume schemes solving the Euler and Navier-Stokes equations

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Huang, Qian-Min Ren, Yu-Xin Wang, Qian Department of Engineering Mechanics Tsinghua University Beijing100084 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China

This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes solving Euler and Navier-Stokes equations. Previous positivity-preserving algorithms are mainly based on mathematical analyses, being highly dependent on the existence of low-order positivity-preserving numerical schemes for specific governing equations. This dependency poses serious restrictions on extending these algorithms to temporally implicit schemes, since it is difficult to know if a low-order implicit scheme is positivity-preserving. The present positivity-preserving algorithm is based on an asymptotic analysis of the solutions near local vacuum minimum points. The asymptotic analysis shows that the solutions decay exponentially with time to maintain non-negative density and pressure at a local vacuum minimum point. In its neighborhood, the exponential evolution leads to a modification of the linear evolution process, which can be modelled by a direct correction of the linear residual to ensure positivity. This correction however destroys the conservation of the numerical scheme. Therefore, a second correction procedure is proposed to recover conservation. The proposed positivity-preserving algorithm is considerably less restrictive than existing algorithms. It does not rely on the existence of low-order positivity-preserving baseline schemes and the convex decomposition of volume integrals of flow quantities. It does not need to reduce the time step size for maintaining the stability either. Furthermore, it can be implemented iteratively in the implicit dual time-stepping schemes to preserve positivity of the intermediate and converged states of the sub-iterations. It is proved that the present positivity-preserving algorithm is accuracy-preserving. Numerical results demonstrate that the proposed algorithm preserve the positive density and pressure in all test cases, and considerably improve the robustness of the numerical schemes. Copyright © 2023,

关键词： Finite volume method

Heat Transfer Analysis in a Flow Over Concave Wall With Primary and Secondary Instabilities

学校读者我要写书评

暂无评论

Procedia IUTAM 2015年 14卷 487-495页

作者： Vinicius Malatesta Leandro F. Souza Joseph T.C. Liu Markus J. Kloker Mobility Engineering Center Federal University of Santa Catarina Joinville Santa Catarina Brazil Department of Applied Mathematics and Statistics Institute of Mathematics and Computational Sciences University of São Paulo São Carlos São Paulo Brazil School of Engineering and Center for Fluid Mechanics Brown University Providence Rhode Island USA Institute of Aerodynamics and Gasdynamics University of Stuttgart Stuttgart Germany

The centrifugal instability mechanism in boundary layers over concave surfaces is responsible for the development of counter- rotating vortices, aligned in the streamwise direction, known as Görtler vortices. These vortices create two regions in the spanwise direction, the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer towards the wall, increasing the drag coefficient and the heat transfer rate. The upwash region does the opposite. The Görtler vortices distort the streamwise velocity profile in the spanwise and the wall-normal directions. These distortions generate inflections in the distribution of streamwise velocity that are unstable to unsteady disturbances giving rise to secondary instabilities. In these flows the secondary instabilities can be of varicose or sinuous mode. The present paper analyses the heat transfer in a flow over a concave wall subjected to primary and secondary instabilities. The research is carried out by a Spatial Direct Numerical Simulation. The adopted parameters mimic the experimental parameters of Winoto and collaborators 17,18 and the Prandtl number adopted was Pr = 0.72. The results show that the varicose mode is the dominant secondary instability for the adopted parameters and that the spanwise average heat transfer rates can reach higher values than the turbulent ones. The higher heat transfer is caused by the mean flow distortion induced by the vortices, and this is present before high–frequency secondary instability sets in. Hence there is no direct connection to secondary instability. Possibly low–frequency modes undergo instability earlier.

关键词： Centrifugal instability Secondary instability Heat transfer Spatial direct numerical simulation.

Outlier detection using flexible categorisation and interrogative agendas

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Boersma, Marcel Manoorkar, Krishna Palmigiano, Alessandra Panettiere, Mattia Tzimoulis, Apostolos Wijnberg, Nachoem School of Business and Economics Vrije Universiteit Amsterdam Netherlands Department of Mathematics and Applied Mathematics University of Johannesburg South Africa College of Business and Economics University of Johannesburg South Africa Faculty of Economics and Business University of Amsterdam Netherlands Computational Science Lab University of Amsterdam Amsterdam Netherlands KPMG Amstelveen Netherlands

Categorization is one of the basic tasks in machine learning and data analysis. Building on formal concept analysis (FCA), the starting point of the present work is that different ways to categorize a given set of objects exist, which depend on the choice of the sets of features used to classify them, and different such sets of features may yield better or worse categorizations, relative to the task at hand. In their turn, the (a priori) choice of a particular set of features over another might be subjective and express a certain epistemic stance (e.g. interests, relevance, preferences) of an agent or a group of agents, namely, their interrogative agenda. In the present paper, we represent interrogative agendas as sets of features, and explore and compare different ways to categorize objects w.r.t. different sets of features (agendas). We first develop a simple unsupervised FCA-based algorithm for outlier detection which uses categorizations arising from different agendas. We then present a supervised meta-learning algorithm to learn suitable (fuzzy) agendas for categorization as sets of features with different weights or masses. We combine this meta-learning algorithm with the unsupervised outlier detection algorithm to obtain a supervised outlier detection algorithm. We show that these algorithms perform at par with commonly used algorithms for outlier detection on commonly used datasets in outlier detection. These algorithms provide both local and global explanations of their results. © 2023, CC BY.

关键词： Anomaly detection

INTEGRABILITY PROPAGATION FOR A BOLTZMANN SYSTEM DESCRIBING POLYATOMIC GAS MIXTURES

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Alonso, Ricardo Pavić-Čolić, Milana Texas A&M Division of Arts & Sciences Education City Doha Qatar Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad Trg Dositeja Obradovića 4 Novi Sad21000 Serbia Applied and Computational Mathematics RWTH Aachen University Schinkelstr. 2 Aachen52062 Germany

This paper explores the Lp Lebesgue's integrability propagation, p ∈ (1, ∞], of a system of space homogeneous Boltzmann equations modelling a multi-component mixture of polyatomic gases based on the continuous internal energy. For typical collision kernels proposed in the literature, Lp moment-entropy-based estimates for the collision operator gain part and a lower bound for the loss part are performed leading to a vector valued inequality for the collision operator and, consequently, to a differential inequality for the vector valued solutions of the system. This allows to prove the propagation property of the polynomially weighted Lp norms associated to the vector valued solution of the system of Boltzmann equations. The case p = ∞ is found as a limit of the case p MSC Codes 35Q20, 76P05, 82C40 Copyright © 2023, The Authors. All rights reserved.

关键词： Gas mixtures

Electron collisions with the BH2 radical using the R-matrix method

学校读者我要写书评

暂无评论

Physical Review A 2010年第6期82卷 062711-062711页

作者： Song Bin Zhang Jian Guo Wang R. K. Janev Xiang Jun Chen Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 China Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 China Macedonian Academy of Sciences and Arts P. O. Box 428 1000 Skopje Macedonia

Differential, integral, and momentum-transfer cross sections for the rotationally elastic and inelastic scattering of electron by the BH2 radical at low collision energies (0–8 eV) are reported in a 22-state molecular R-matrix method. The excitation cross sections from the ground X 2A1 state to the first two excited states 2B1 and 4A2 are calculated as well, for incident electron energies from the respective thresholds up to 8 eV. Configuration-interaction wave functions are used to represent the target states which account for the correlation effects. Four shape and three Feshbach resonances are detected. The Born-closure approximation is applied for the elastic and dipole-allowed transitions to account for the l>4 partial waves excluded from the R-matrix calculations.

关键词： Wave functions

CP Factor Model for Dynamic Tensors

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Han, Yuefeng Yang, Dan Zhang, Cun-Hui Chen, Rong Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Business School The University of Hong Kong Hong Kong Department of Statistics Rutgers University PiscatawayNJ08854 United States

Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CP decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly different from the existing tensor factor models based on Tucker-type tensor decomposition. The model structure allows for a set of uncorrelated one-dimensional latent dynamic factor processes, making it much more convenient to study the underlying dynamics of the time series. A new high order projection estimator is proposed for such a factor model, utilizing the special structure and the idea of the higher order orthogonal iteration procedures commonly used in Tucker-type tensor factor model and general tensor CP decomposition procedures. Theoretical investigation provides statistical error bounds for the proposed methods, which shows the significant advantage of utilizing the special model structure. Simulation study is conducted to further demonstrate the finite sample properties of the estimators. Real data application is used to illustrate the model and its interpretations. © 2021, CC BY-NC-SA.

关键词： Tensors

AnisoGNN: graph neural networks generalizing to anisotropic properties of polycrystals

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Hu, Guangyu Latypov, Marat I. Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

We present AnisoGNNs - graph neural networks (GNNs) that generalize predictions of anisotropic properties of polycrystals in arbitrary testing directions without the need in excessive training data. To this end, we develop GNNs with a physics-inspired combination of node attributes and aggregation function. We demonstrate the excellent generalization capabilities of AnisoGNNs in predicting anisotropic elastic and inelastic properties of two alloys. © 2024, CC BY.

关键词： Anisotropy