检索结果-内蒙古大学图书馆

Thermally Radiative Casson Fluid Flow over a Cylinder with Newtonian Heating and Heat generation/absorption 1

学校读者我要写书评

暂无评论

Thermally Radiative Casson Fluid Flow over a Cylinder with N...

1st International Conference on Advances in computational science and Engineering, ICACSE 2020

作者： Loganathan, K. Sivakumar, M. Mohanraj, M. Sakthivel, P. Research and Development Wing Live4Research Tamil Nadu Tiruppur638 106 India Department of Applied Mathematics and Computational Science PSG College of Technology Tamil Nadu Coimbatore641 004 India Department of Mechanical Engineering Hindusthan College of Engineering and Technology Tamil Nadu Coimbatore641 032 India Department of Physics Faculty of Engineering Karpagam Academy of Higher Education Tamil Nadu Coimbatore641 021 India

This communication explains the impact of thermally radiative flow of a Casson fluid over a cylinder with velocity slip, suction/injection, and Newtonian heating condition. The governing PDE expressions are remodeled into an ODE expressing by applying suitable variables. The homotopy analysis (HAM) technique was implemented for solving our models. The impact of velocity field, temperature distribution, skin friction coefficient, Nusselt number in terms of diverse physical parameters like Casson parameter, suction/injection parameter, Newtonian heating parameter, radiation parameters, heat generation/absorption, Hartmann number and velocity slip parameter. The Hartmann number leads to slow down the fluid velocity, skin friction coefficient and local Nusselt number. The slip parameter decreases the fluid velocity and enhance the fluid heat transfer gradient. © Published under licence by IOP Publishing Ltd.

关键词： Nusselt number

The Rique-Number of Graphs

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Bekos, Michael A. Felsner, Stefan Kindermann, Philipp Kobourov, Stephen Kratochvíl, Jan Rutter, Ignaz Department of Mathematics University of Ioannina Ioannina Greece Institut für Mathematik Technische Universität Berlin Berlin Germany Fachbereich Iv - Informatikwissenschaften Universität Trier Trier Germany Department of Computer Science University of Arizona TucsonAZ United States Department of Applied Mathematics Charles University Prague Czech Republic Fakultät für Informatik und Mathematik Universität Passau Passau Germany

We continue the study of linear layouts of graphs in relation to known data structures. At a high level, given a data structure, the goal is to find a linear order of the vertices of the graph and a partition of its edges into pages, such that the edges in each page follow the restriction of the given data structure in the underlying order. In this regard, the most notable representatives are the stack and queue layouts, while there exists some work also for deques. In this paper, we study linear layouts of graphs that follow the restriction of a restricted-input queue (rique), in which insertions occur only at the head, and removals occur both at the head and the tail. We characterize the graphs admitting rique layouts with a single page and we use the characterization to derive a corresponding testing algorithm when the input graph is maximal planar. We finally give bounds on the number of needed pages (so-called rique-number) of complete graphs. Copyright © 2022, The Authors. All rights reserved.

关键词： Queueing theory

Beyond fine-tuning: Classifying high resolution mammograms using function-preserving transformations

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Wei, Tao Aviles-Rivero, Angelica I. Wang, Shuo Huang, Yuan Gilbert, Fiona J. Schönlieb, Carola-Bibiane Chen, Chang Wen Department of Computer Science State University of New York at Buffalo NY United States Department of Pure Mathematics and Mathematical Statistics University of Cambridge United Kingdom Data Science Institute Imperial College London United Kingdom Department of Radiology University of Cambridge United Kingdom Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom

The task of classifying mammograms is very challenging because the lesion is usually small in the high resolution image. The current state-of-the-art approaches for medical image classification rely on using the de-facto method for ConvNets - fine-tuning. However, there are fundamental differences between natural images and medical images, which based on existing evidence from the literature, limits the overall performance gain when designed with algorithmic approaches. In this paper, we propose to go beyond fine-tuning by introducing a novel framework called MorphHR, in which we highlight a new transfer learning scheme. The idea behind the proposed framework is to integrate function-preserving transformations, for any continuous non-linear activation neurons, to internally regularise the network for improving mammograms classification. The proposed solution offers two major advantages over the existing techniques. Firstly and unlike fine-tuning, the proposed approach allows for modifying not only the last few layers but also several of the first ones on a deep ConvNet. By doing this, we can design the network front to be suitable for learning domain specific features. Secondly, the proposed scheme is scalable to hardware. Therefore, one can fit high resolution images on standard GPU memory. We show that by using high resolution images, one prevents losing relevant information. We demonstrate, through numerical and visual experiments, that the proposed approach yields to a significant improvement in the classification performance over state-of-the-art techniques, and is indeed on a par with radiology experts. Moreover and for generalisation purposes, we show the effectiveness of the proposed learning scheme on another large dataset, the ChestX-ray14, surpassing current state-of-the-art techniques. Copyright © 2021, The Authors. All rights reserved.

关键词： Mammography

The complexity of nonconvex-strongly-concave minimax optimization

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Zhang, Siqi Yang, Junchi Guzmán, Cristóbal Kiyavash, Negar He, Niao UrbanaIL United States Department of Applied Mathematics University of Twente Netherlands. And Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Chile College of Management of Technology EPFL Switzerland Department of Computer Science ETH Zürich Switzerland

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity bounds of Ω(√κ∆Lǫ−2) and Ω(n + √nκ∆Lǫ−2) for the two settings, respectively, where κ is the condition number, L is the smoothness constant, and ∆ is the initial gap. Our result reveals substantial gaps between these limits and best-known upper bounds in the literature. To close these gaps, we introduce a generic acceleration scheme that deploys existing gradient-based methods to solve a sequence of crafted strongly-convex-strongly-concave subproblems. In the general setting, the complexity of our proposed algorithm nearly matches the lower bound;in particular, it removes an additional poly-logarithmic dependence on accuracy present in previous works. In the averaged smooth finite-sum setting, our proposed algorithm improves over previous algorithms by providing a nearly-tight dependence on the condition number. Copyright © 2021, The Authors. All rights reserved.

关键词： Number theory

Sparse-grid Discontinuous Galerkin Methods for the Vlasov–Poisson–Lenard–Bernstein Model

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Schnake, Stefan Kendrick, Coleman Endeve, Eirik Stoyanov, Miroslav Hahn, Steven Hauck, Cory D. Green, David L. Snyder, Phil Canik, John Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Fusion Energy Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Department of Mathematics University of Tennessee KnoxvilleTN37996 United States Type One Energy Group Oak RidgeTN37830 United States Commonwealth Scientific and Industrial Research Organisation Mayfield WestNSW2304 Australia

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD. Copyright © 2024, The Authors. All rights reserved.

关键词： Integral equations

A Likelihood Approach to Nonparametric Estimation of a Singular Distribution Using Deep Generative Models

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Chae, Minwoo Kim, Dongha Kim, Yongdai Lin, Lizhen Department of Industrial and Management Engineering Pohang University of Science and Technology Gyeongbuk Pohang37673 Korea Republic of School of Mathematics Statistics and Data Science Data Science Center Sungshin Women’s University Seoul02844 Korea Republic of Department of Statistics Seoul National University Seoul08826 Korea Republic of Department of Applied and Computational Mathematics and Statistics University of Notre Dame South BendIN46556 United States

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance *** Codes 62G05 (Primary), 62G20 (Secondary) © 2021, CC BY-NC-SA.

关键词： Perturbation techniques

Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Chen, Yixiao Zhang, Linfeng Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation. Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

Limit Distribution of a Risk Estimate in the Problem of Inverting Linear Homogeneous Operators with a Random Sample Size

学校读者我要写书评

暂无评论

Journal of Mathematical sciences (United States) 2020年第1期248卷 123-128页

作者： Shestakov, O.V. Department of Mathematical Statistics Faculty of Computational Mathematics and Cybernetics M.V. Lomonosov Moscow State University Moscow Russian Federation Institute of Informatics Problems Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russian Federation

Inverse statistical problems associated with the inversion of some linear homogeneous transformation arise in areas such as tomography, plasma physics, optics, etc. As a rule, noise is present in observations, and it is necessary to apply some regularization methods. Recently, methods of threshold processing of wavelet expansion coefficients have become popular. When using threshold processing methods, it is usually assumed that the number of decomposition coefficients is fixed and the noise distribution is Gaussian. This model has been well studied in the literature, and the optimal threshold values have been calculated for different classes of signal functions. However, in some situations, the sample size is not known in advance and has to be modeled by some random variable. In this paper, a model with a random number of observations is considered, and it is shown that the limit distribution of the mean-square risk estimate is a shift-scale mixture of normal laws. © 2020, Springer science+Business Media, LLC, part of Springer Nature.

关键词：

FROBENIUS NONCLASSICAL HYPERSURFACES

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Asgarli, Shamil Duan, Lian Lai, Kuan-Wen Department of Mathematics and Computer Science Santa Clara University Santa ClaraCA95050 United States Institute of Mathematical Sciences ShanghaiTech University No.393 Middle Huaxia Road Pudong New District Shanghai China Department of Smart Computing and Applied Mathematics Tunghai University No. 1727 Sec. 4 Taiwan Blvd. Xitun Dist. Taichung City407224 Taiwan

A smooth hypersurface over a finite field Fq is called Frobenius nonclassical if the image of every geometric point under the q-th Frobenius endomorphism remains in the unique hyperplane tangent to the point. In this paper, we establish sharp lower and upper bounds for the degrees of such hypersurfaces, give characterizations for those achieving the maximal degrees, and prove in the surface case that they are Hermitian when their degrees attain the minimum. We also prove that the set of Fq-rational points on a Frobenius nonclassical hypersurface form a blocking set with respect to lines, which indicates the existence of many Fq-points. Copyright © 2022, The Authors. All rights reserved.

关键词： Geometry