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Global well-posedness and nonlinear stability of a chemotaxis system modeling multiple sclerosis

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arXiv 2020年

作者： Desvillettes, Laurent Giunta, Valeria Morgan, Jeff Tang, Bao Quoc Université de Paris Sorbonne Université CNRS Institut de Mathématiques de Jussieu-Paris Rive Gauche France Department of Engineering University of Palermo Italy Department of Mathematics University of Houston HoustonTX77004 United States Institute of Mathematics and Scientific Computing University of Graz Heinrichstrasse 36 Graz8010 Austria

We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modeling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chemotaxis term is not too big. We also perform numerical simulations to show the appearance of Turing patterns when the chemotaxis term is large. Copyright © 2020, The Authors. All rights reserved.

关键词： Biochemistry

Rational evaluation of various epidemic models based on the COVID-19 data of China

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arXiv 2020年

作者： Yang, Wuyue Zhang, Dongyan Peng, Liangrong Zhuge, Changjing Hong, Liu School of Mathematics Sun Yat-Sen University Guangzhou510275 China Yau Mathematical Sciences Center Tsinghua University Beijing100084 China Beijing Institute for Scientific and Engineering Computing Faculty of Sciences Beijing University of Technology Beijing100124 China College of Mathematics and Data Science Minjiang University Fuzhou350108 China

In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz’s function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases. Copyright © 2020, The Authors. All rights reserved.

关键词： Mean square error

Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics

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arXiv 2021年

作者： Campbell, Kristen M. Dai, Haocheng Su, Zhe Bauer, Martin Fletcher, P. Thomas Joshi, Sarang C. Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States School of Computing University of Utah Salt Lake CityUT United States Department of Neurology University of California Los Angeles Los AngelesCA United States Department of Mathematics Florida State University TallahasseeFL United States Department of Electrical & Computer Engineering University of Virginia CharlottesvilleVA United States Department of Computer Science University of Virginia CharlottesvilleVA United States Department of Bioengineering University of Utah Salt Lake CityUT United States

The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

Improved Fitness Dependent Optimizer for Solving Economic Load Dispatch Problem

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arXiv 2022年

作者： Tahir, Barzan Hussein Rashid, Tarik A. Rauf, Hafiz Tayyab Bacanin, Nebojsa Chhabra, Amit Vimal, S. Yaseen, Zaher Mundher Department of Computer Science and Engineering University of Kurdistan Helwer Erbil Iraq Centre for Smart Systems AI and Cybersecurity Staffordshire University Stoke-on-Trent United Kingdom Singidunum University Danijelova 32 Belgrade11000 Serbia Department of Computer Engineering and Technology Guru Nanak Dev University Amritsar India Department of Artificial Intelligence and Data Science Ramco Institute of Technology North Venganallur Village Virudhunagar District Tamilnadu Rajapalayam626 117 India Department of Earth Sciences and Environment Faculty of Science and Technology Universiti Kebangsaan Malaysia Selangor Bangi43600 Malaysia USQ's Advanced Data Analytics Research Group School of Mathematics Physics and Computing University of Southern Queensland QLD4350 Australia New era and Development in Civil Engineering Research Group Scientific Research Center Al-Ayen University Thi-Qar64001 Iraq

Economic Load Dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to Economic Load Dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness Dependent Optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness Dependent Optimizer (FDO) examines the search spaces based on the searching approach of Particle Swarm Optimization. To calculate the pace, the fitness function is utilized to generate weights that direct the search agents in the phases of exploitation and exploration. In this research, the authors have carried out Fitness Dependent Optimizer to solve the Economic Load Dispatch problem by reducing fuel cost, emission allocation, and transmission loss. Moreover, the authors have enhanced a novel variant of Fitness Dependent Optimizer, which incorporates novel population initialization techniques and dynamically employed sine maps to select the weight factor for Fitness Dependent Optimizer. The enhanced population initialization approach incorporates a quasi-random Sabol sequence to generate the initial solution in the multi-dimensional search space. A standard 24-unit system is employed for experimental evaluation with different power demands. Empirical results obtained using the enhanced variant of the Fitness Dependent Optimizer demonstrate superior performance in terms of low transmission loss, low fuel cost, and low emission allocation compared to the conventional Fitness Dependent Optimizer. The experimental study obtained 7.94E-12, the lowest transmission loss using the enhanced Fitness Dependent Optimizer. Correspondingly, various standard estimations are used to prove the stability

关键词： Decision making

${\sf DeepNC}$DeepNC: Deep Generative Network Completion

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IEEE Transactions on Pattern Analysis and Machine Intelligence 2020年第4期44卷 1837-1852页

作者： Cong Tran Won-Yong Shin Andreas Spitz Michael Gertz Department of Computer Science and Engineering Dankook University Yongin Republic of Korea Machine Intelligence & Data Science Laboratory Yonsei University Seoul Republic of Korea School of Mathematics and Computing (Computational Science and Engineering) Yonsei University Seoul Republic of Korea School of Computer and Communication Sciences École Polytechnique Fédérale de Lausanne Lausanne Switzerland Institute of Computer Science Heidelberg University Heidelberg Germany

Most network data are collected from partially observable networks with both missing nodes and missing edges, for example, due to limited resources and privacy settings specified by users on social media. Thus, it stands to reason that inferring the missing parts of the networks by performing network completion should precede downstream applications. However, despite this need, the recovery of missing nodes and edges in such incomplete networks is an insufficiently explored problem due to the modeling difficulty, which is much more challenging than link prediction that only infers missing edges. In this paper, we present DeepNC, a novel method for inferring the missing parts of a network based on a deep generative model of graphs. Specifically, our method first learns a likelihood over edges via an autoregressive generative model, and then identifies the graph that maximizes the learned likelihood conditioned on the observable graph topology. Moreover, we propose a computationally efficient ${\sf DeepNC}$ algorithm that consecutively finds individual nodes that maximize the probability in each node generation step, as well as an enhanced version using the expectation-maximization algorithm. The runtime complexities of both algorithms are shown to be almost linear in the number of nodes in the network. We empirically demonstrate the superiority of DeepNC over state-of-the-art network completion approaches.

关键词： Matrix decomposition Prediction algorithms Deep learning Pattern analysis Social networking (online) Predictive models

Meson spectroscopy in the Sp(4) gauge theory with three antisymmetric fermions

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Physical Review D 2025年第7期111卷 074511-074511页

作者： Ed Bennett Deog Ki Hong Ho Hsiao Jong-Wan Lee C.-J. David Lin Biagio Lucini Maurizio Piai Davide Vadacchino Swansea Academy of Advanced Computing Swansea University (Bay Campus) Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Pusan National University Busan 46241 Korea Extreme Physics Institute Pusan National University Busan 46241 Korea Center for Computational Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305-8577 Japan Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Particle Theory and Cosmology Group Center for Theoretical Physics of the Universe Institute for Basic Science (IBS) Daejeon 34126 Korea Centre for High Energy Physics Chung-Yuan Christian University Chung-Li 32023 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University (Bay Campus) Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park SA2 8PP Swansea Wales United Kingdom Centre for Mathematical Sciences University of Plymouth Plymouth PL4 8AA United Kingdom

We report the results of an extensive numerical study of the Sp(4) lattice gauge theory coupled to fermion matter content consisting of three (Dirac) flavors, transforming in the two-index antisymmetric representation of the gauge group. In the presence of (degenerate) fermion masses, the theory has an enhanced global SU(6) symmetry, broken explicitly and spontaneously to its SO(6) subgroup. This symmetry breaking pattern makes the theory interesting for applications in the context of composite Higgs models, as well as for the implementation of top partial compositeness. Alternatively, it can also provide a dynamical realization of the strongly interacting massive particle paradigm for the origin of dark matter. We adopt the standard plaquette gauge action, along with the Wilson-Dirac formulation for the fermions, and apply the (rational) hybrid Monte Carlo algorithm in our ensemble generation process. We monitor the autocorrelation and topology of the ensembles. We explore the bare parameter space, and identify the weak and strong coupling regimes, which are separated by a line of first-order bulk phase transitions.

关键词：

On the complexity of an augmented lagrangian method for nonconvex optimization

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arXiv 2019年

作者： Grapiglia, Geovani N. Yuan, Ya-Xiang Departamento de Matemática Universidade Federal do Paraná Centro Politécnico Cx. postal 19.081 Paraná Curitiba81531-980 Brazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Zhong Guan Cun Donglu 55 Beijing100190 China

In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of O(| log(ǫ)|) outer iterations for the referred algorithm to generate an ǫ-approximate KKT point, for ǫ ∈ (0, 1). When the penalty parameters are unbounded, we prove an outer iteration complexity bound of O (ǫ−2/(α−1)), where α > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems, these bounds yield to evaluation complexity bounds of O(| log(ǫ)|2ǫ−2) and O ( ǫ− ( 2(2+ α−1 α) +2 )), respectively, when appropriate first-order methods (p = 1) are used to approximately solve the unconstrained subproblems at each iteration. In the case of problems having only linear equality constraints, the latter bounds are improved to O(| log(ǫ)|2ǫ−(p+1)/p) and O ( ǫ− ( α−4 1 + p+1 p )), respectively, when appropriate p-order methods (p ≥ 2) are used as inner solvers. Copyright © 2019, The Authors. All rights reserved.

关键词： Nonlinear programming

A Full Multigrid Method for Distributed Control Problems Constrained by Stokes Equations

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高等学校计算数学学报（英文版） 2017年第3期10卷 639-655页

作者： M.M.Butt Y.Yuan Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100080 China Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of SciencesBeijing 100080China and Higher Education Department Government of the PunjabLahore 54000Pakistan

A full multigrid method with coarsening by a factor-of-three to distributed control problems constrained by Stokes equations is *** optimal control problem with cost functional of velocity and/or pressure tracking-type is considered with Dirichlet boundary *** optimality system that results from a Lagrange multiplier framework,form a linear system connecting the state,adjoint,and control *** investigate multigrid methods with finite difference discretization on staggered grids.A coarsening by a factor-of-three is used on staggered grids that results nested hierarchy of staggered grids and simplified the inter-grid transfer operators.A distributive-Gauss-Seidel smoothing scheme is employed to update the stateand adjoint-variables and a gradient update step is used to update the control *** experiments are presented to demonstrate the effectiveness and efficiency of the proposed multigrid framework to tracking-type optimal control problems.

关键词： PDE-constrained optimization stokes equations multigrid staggered grids finite difference

An enhanced SDR based global algorithm for nonconvex complex quadratic programs with signal processing applications

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arXiv 2019年

作者： Lu, Cheng Liu, Ya-Feng Zhou, Jing School of Economics and Management North China Electric Power University Beijing102206 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics College of Science Zhejiang University of Technology Hangzhou310023 China

In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first derive a new enhanced semidefinite relaxation (SDR) for problem (CQP). Based on the newly derived SDR, we further propose an efficient branch-and-bound algorithm for solving problem (CQP). Key features of our proposed algorithm are: (1) it is guaranteed to find the global solution of the problem (within any given error tolerance);(2) it is computationally efficient because it carefully utilizes the special structure of the problem. We apply our proposed algorithm to solve the multiinput multi-output (MIMO) detection problem, the unimodular radar code design problem, and the virtual beamforming design problem. Simulation results show that our proposed enhanced SDR, when applied to the above problems, is generally much tighter than the conventional SDR and our proposed global algorithm can efficiently solve these problems. In particular, our proposed algorithm significantly outperforms the state-of-the-art sphere decode algorithm for solving the MIMO detection problem in the hard cases (where the number of inputs and outputs is equal or the SNR is low) and a state-of-the-art general-purpose global optimization solver called Baron for solving the virtual beamforming design problem. Copyright © 2019, The Authors. All rights reserved.

关键词： Beamforming