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Franklin Open 2023年 3卷

作者： Tchoumi, S.Y. Njintang, N.Y. Kamgang, J.C. Tchuenche, J.M. Department of Mathematics and Computer Sciences ENSAI University of NGaoundere P.O. Box 455 Ngaoundere Cameroon Department of Mathematics and Applied Mathematics University of Pretoria South Africa Department of Food Science and Nutrition ENSAI University of NGaoundere P.O. Box 455 Ngaoundere Cameroon Department of Biological Sciences Faculty of Science University of NGaoundere P.O. Box 454 Ngaoundere Cameroon School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa School of Computational and Communication Sciences and Engineering Nelson Mandela African Institution of Science and Technology P.O. Box 447 Arusha Tanzania

Malaria, a vector-borne disease, and malnutrition, an imbalance of essential nutrients, or poor nutrition are two major causes of childhood mortality in malaria endemic regions. Despite their geographical overlap, mathematical investigation of their co-dynamics is lacking. To fill this gap, we formulate a deterministic model of malaria subdividing the children population into two groups;those who are well-nourished and the poorly nourished, in order to investigate the potential effect of malnutrition on malaria dynamics. The proposed model is analyzed, the basic reproduction number is computed, and the local asymptotic stability of the disease-free equilibrium is proven. By applying the Centre Manifold Theory, the endemic equilibrium exists and may not be globally asymptotically stable owing to the system exhibiting the phenomenon of backward bifurcation under certain conditions. Using the chosen model parameter values, numerical simulations are provided. The endemic equilibrium is globally asymptotically stable and this persistence of the disease implies much efforts should be done to mitigate the spread of malaria and malnutrition in the population. With no competitive exclusion, the modification parameter which accounts for the relative infectiousness of children poorly nourished to malaria infection is used to investigate the potential impact of malnutrition on the dynamics of malaria. Our results reveal that to mitigate the spread of malaria in young children, a balanced diet is imperative to reduce morbidity and mortality. © 2023

关键词： Bifurcation Dynamical systems Malaria Malnutrition Reproduction number

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Rough Shadowed Set: Hybridization of Rough Set and Shadowed Set 11th

Rough Shadowed Set: Hybridization of Rough Set and Shadowe...

引用

11th International Joint Conference on Rough Sets, IJCRS 2025

作者： Gao, Man Zhang, Qinghua Jin, Pengren Xia, Deyou Wang, Guoyin School of Computer Science and Technology Chongqing University of Posts and Telecommunications Chongqing400065 China Chongqing Key Laboratory of Computational Intelligence Chongqing University of Posts and Telecommunications Chongqing400065 China Key Laboratory of Cyberspace Big Data Intelligent Security Ministry of Education Chongqing400065 China National Center for Applied Mathematics in Chongqing Chongqing Normal University Chongqing401331 China

ISBN: (纸本)9783031927461

Shadowed set is a mathematical tool that processes uncertain information through three-way approximations, effectively reducing the cost of fuzzy decision-making and computation, and has been widely used in fields such as data mining, pattern recognition, and decision support. However, the existing shadowed set models are mainly based on the consideration of a single fuzzy set, lacking the comprehensive consideration of multiple fuzzy sets (multiple attributes, multiple approximation spaces) and information granules (equivalent classes), which is difficult to effectively achieve the approximate description of complex target concepts. In addition, the issues of "hard computation" and "subjectivity" in traditional rough set models also weaken the effectiveness of the three-way partitioning results. Therefore, Rough Shadowed Set (RSS) is proposed in this paper. First, analyzed the mapping relationship between rough set, shadowed set, and the three-way decision, and divided the results of the approximate partitioning of RSS into two stages. Second, in two stages, rough set is utilized to achieve comprehensive consideration of multiple attributes and information granules, shadowed set is utilized to achieve deblurring of real valued information system, and quadratic analysis and partitioning of uncertainty equivalence classes in the boundary region of rough set. Third, integrating the results of two stages to achieve the combination of the advantages of rough set and shadowed set theory, as well as a more reasonable and effective approximation of complex target concepts. Finally, the framework, definition, decision rules, algorithms, experimental analysis, and future discussions of the model are presented. The experimental results indicate that RSS has better payoff compared to traditional rough set and shadowed set models, namely higher approximate coverage and accuracy, which demonstrates the validity and rationality of RSS. © The Author(s), under exclusive license to

关键词： Equivalence classes

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A robust alternating direction method of multipliers numerical scheme in a shape optimization setting for solving geometric inverse problems

arXiv

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arXiv 2023年

作者： Rabago, Julius Fergy Tiongson Hadri, Aissam Afraites, Lekbir Hendy, Ahmed S. Zaky, Mahmoud A. Faculty of Mathematics and Physics Institute of Science and Engineering Kanazawa University Kanazawa920-1192 Japan Université Ibn Zohr Faculté Polydisciplinaire Ouarzazate Morocco EMI FST Université Sultan Moulay Slimane Béni-Mellal Morocco Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University 19 Mira St. Ekaterinburg620002 Russia Department of Mathematics Faculty of Science Benha University Benha13511 Egypt Department of Mathematics and Statistics College of Science Imam Mohammad Ibn Saud Islamic University Riyadh Saudi Arabia Department of Applied Mathematics National Research Centre Dokki Cairo12622 Egypt

The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and evaluation techniques. The rationale behind this method is to achieve more accurate detection of unknown inclusions with pronounced concavities, emphasizing the aspect of shape optimization. Several numerical results to illustrate the applicability and efficiency of the method are presented for various shape detection problems. These numerical experiments are conducted in both two- and three-dimensional settings, with a focus on cases involving noise-contaminated data. The main finding of the study is that the proposed method significantly outperforms conventional shape optimization methods in reconstructing unknown cavity shapes. © 2023, CC BY.

关键词： Inverse problems

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Dynamic Shifts: The Rise of Unicorns in the AI Ecosystem 9th

Dynamic Shifts: The Rise of Unicorns in the AI Ecosystem

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9th China National Conference on Big Data and Social Computing, BDSC 2024

作者： Liu, Boen Liu, Jiayi Zou, Hui Xu, Kunpeng Qu, Jingjing Governance Research Center Shanghai Artificial Intelligence Laboratory Shanghai200232 China Applied Mathematics and Computational Sciences Duke Kunshan University Suzhou215316 China School of Computer Science and Technology Fudan University Shanghai200433 China Department of Library and Information Shanghai University Shanghai200444 China Center for Internet and Society Fudan University Shanghai200438 China

ISBN: (纸本)9789819758029

In the era of rapidly advancing artificial intelligence (AI), an increasing number of companies are engaging in AI research, spanning domains such as large language models, computer vision, and natural language processing, all vying for prominence in the AI market. Consequently, competition in the market has intensified, with numerous companies entering the fray. Against this backdrop, some established "whale" companies have maintained a stronghold in AI research, holding leading positions, while emerging "unicorn" companies have swiftly risen to prominence, claiming significant footholds in the AI market. Amidst these dynamics, an increasing number of AI companies are opting for collaborative research endeavors. This article delves into the evolution of collaboration in AI research and investigates the types of collaborative modes that yield more influential publications. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： Time series analysis

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Half-metallic porphyrin-based molecular junctions for spintronic applications

引用

Physical Review B 2021年第23期104卷 235435-235435页

作者： Azar Ostovan Nick Papior S. Shahab Naghavi Department of Physical and Computational Chemistry Shahid Beheshti University *** Tehran Iran DTU Computing Center Department of Applied Mathematics and Computer Science Technical University of Denmark DK-2800 Kongens Lyngby Denmark

Single molecular magnets (SMMs) have become promising paradigms to develop novel spintronics for futuristic information technologies such as high-density information and quantum computing. The efficiency and characteristics of SMM devices are determined by the intrinsic nature of the molecular magnets placed in the spin transport pathway. In this work, to understand the role of the central magnetic ion on the performance of SMM devices, we screen the spin-conductance properties of whole 3d and 4d metalloporphyrins using the nonequilibrium Green's function formalism in conjunction with density functional theory. Our results show that the investigated SMMs according to spintronic conductance behavior can be categorized into three groups: type I non-spin-polarized, type II′ minor spin-polarized current, and type II″ major spin-polarized current devices. Type-II′ and type-II″ molecular systems show perfect spin filtering and spin-dependent negative differential resistance. The optimal energy alignment of spin-polarized molecular orbitals with gold electrodes results in one-channel spin transport (minor for type II′ and major for type II″). Thus type-II junctions are half-metal. The type-II″ junctions also show a voltage-induced spin switchability at low bias voltages. In this regard, type-II molecular systems are promising candidates for a low-power consumption spin filter, spin switch, memory, to name just a few. Our results highlight the practical applications of metalloporphyrin for the development of multipurpose miniature spintronic devices.

关键词： Ballistic transport Electrical conductivity Electronic structure Electronic structure of atoms & molecules First-principles calculations Magnetism Molecular magnetism Quantum transport Solid-state chemistry Spintronics Transport phenomena

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Minuscule corrections to near-surface solar internal rotation using mode-coupling

arXiv

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arXiv 2023年

作者： Das, Srijan Bharati Kashyap, Samarth G. Oktay, Deniz Hanasoge, Shravan M. Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ United States Department of Astronomy and Astrophysics Tata Institute of Fundamental Research Mumbai India Department of Computer Science Princeton University PrincetonNJ United States Department of Geosciences and Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode eigenfunctions. Global axisymmertric flow — differential rotation — is a very prominent perturbation. Tightly constrained rotation profiles as a function of latitude and radius are products of established helioseismic pipelines that use observed Dopplergrams to generate frequency-splitting measurements at high precision. However, the inference of rotation using frequency-splittings do not consider the effect of mode-coupling. This approximation worsens for high-angular-degree modes, as they become increasingly proximal in frequency. Since modes with high angular degrees probe the near-surface layers of the Sun, inversions considering coupled modes could potentially lead to more accurate estimates of rotation very close to the surface. In order to investigate if this is indeed the case, we perform inversions for solar differential rotation, considering coupling of modes for angular degrees 160 ≤ ` ≤ 300 in the surface gravity f-branch and first-overtone p modes. In keeping with the character of mode coupling, we carry out a non-linear inversion using an eigenvalue solver. Differences in inverted profiles for frequency splitting measurements from MDI and HMI are compared and discussed. We find that corrections to the near-surface differential rotation profile, when accounting for mode-coupling effects, are smaller than 0.003 nHz and hence are insignificant. These minuscule corrections are found to be correlated with the solar cycle. We also present corrections to even-order splitting coefficients, which could consequently impact inversions for structure and magnetic fields. © 2023, CC BY.

关键词： Rotation

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Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters

arXiv

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arXiv 2023年

作者： An, Dong Childs, Andrew M. Lin, Lin Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Department of Mathematics University of California Berkeley BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Challenge Institute for Quantum Computation University of California Berkeley BerkeleyCA94720 United States

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel

arXiv

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arXiv 2022年

作者： Chen, Hao Zaky, Mahmoud A. Hendy, Ahmed S. Qiu, Wenlin MOE-LCSM School of Mathematics and Statistics Hunan Normal University Hunan Changsha410081 China Department of Applied Mathematics National Research Centre Cairo Dokki12622 Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University 19 Mira St. Yekaterinburg620002 Russia Department of Mathematics Faculty of Science Benha University Benha13511 Egypt

In this paper, a two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with weakly singular kernel is proposed to reduce the computation time and improve the accuracy of the scheme developed by Xu et al. (applied Numerical mathematics 152 (2020) 169-184). The proposed scheme consists of three steps: First, a small nonlinear system is solved on the coarse grid using fix-point iteration. Second, the Lagrange's linear interpolation formula is used to arrive at some auxiliary values for analysis of the fine grid. Finally, a linearized Crank-Nicolson finite difference system is solved on the fine grid. Moreover, the algorithm uses a central difference approximation for the spatial derivatives. In the time direction, the time derivative and integral term are approximated by Crank-Nicolson technique and product integral rule, respectively. With the help of the discrete energy method, the stability and space-time second-order convergence of the proposed approach are obtained in L2-norm. Finally, the numerical results agree with the theoretical analysis and verify the effectiveness of the algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Nonlinear equations

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ON FINITE ANALOGS of SCHMIDT'S PROBLEM and ITS VARIANTS

arXiv

引用

arXiv 2022年

作者： Berkovich, Alexander Uncu, Ali Kemal Department of Mathematics University of Florida 358 Little Hall GainesvilleFL32611 United States University of Bath Faculty of Science Department of Computer Science BathBA2 7AY United Kingdom Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Science Altenbergerstraße 69 LinzA-4040 Austria

We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szego polynomials by Berkovich-Warnaar, and present various Schmidt's problem alike theorems and their refinements. Our new Schmidt type results include the use of even-indexed parts' sums, alternating sum of parts, and hook lengths as well as the odd-indexed parts' sum which appears in the original Schmidt's problem. We also translate some of our Schmidt's problem alike relations to weighted partition counts with multiplicative weights in relation to Rogers-Ramanujan *** Codes 05A15, 05A17, 05A19, 11B34, 11B75, 11P81 Copyright © 2022, The Authors. All rights reserved.

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Differentially Private Generalized Linear Models Revisited

arXiv

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arXiv 2022年

作者： Arora, Raman Bassily, Raef Guzmán, Cristóbal Menart, Michael Ullah, Enayat Department of Computer Science The Johns Hopkins University United States The Ohio State University United States Department of Applied Mathematics University of Twente Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Chile Department of Computer Science & Engineering The Ohio State University United States

We study the problem of (ϵ, δ)-differentially private learning of linear predictors with convex losses. We provide results for two subclasses of loss functions. The first case is when the loss is smooth and non-negative but not necessarily Lipschitz (such as the squared loss). For this case, we establish an upper bound on the excess population risk of e O (kw*√nk + minn w*2 (nϵ)2/3 , √dw*2 nϵ }), where n is the number of samples, d is the dimension of the problem, and w*is the minimizer of the population risk. Apart from the dependence on w*, our bound is essentially tight in all parameters. In particular, we show a lower bound of Ω(1 √n + minn{w*4/3 (nϵ)2/3 , √dw* nϵ }). We also revisit the previously studied case of Lipschitz losses [SSTT20]. For this case, we close the gap in the existing work and show that the optimal rate is (up to log factors) Θ({kw*√nk + min nkw*√nϵk , √rankw* nϵ }), where rank is the rank of the design matrix. This im- proves over existing work in the high privacy regime. Finally, our algorithms involve a private model selection approach that we develop to enable attaining the stated rates without a-priori knowledge of w*. © 2022, CC BY.

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