检索结果-内蒙古大学图书馆

arXiv 2025年

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

Machine learning of microstructure–property relationships from data is an emerging approach in computational materials science. Most existing machine learning efforts focus on the development of task-specific models for each microstructure–property relationship. We propose utilizing pre-trained foundational vision transformers for the extraction of task-agnostic microstructure features and subsequent light-weight machine learning of a microstructure-dependent property. We demonstrate our approach with pre-trained state-of-the-art vision transformers (CLIP, DINOV2, SAM) in two case studies on machine-learning: (i) elastic modulus of two-phase microstructures based on simulations data;and (ii) Vicker’s hardness of Ni-base and Co-base superalloys based on experimental data published in literature. Our results show the potential of foundational vision transformers for robust microstructure representation and efficient machine learning of microstructure–property relationships without the need for expensive task-specific training or fine-tuning of bespoke deep learning models. © 2025, CC BY.

关键词： Elastic moduli

来源：评论

学校读者我要写书评

暂无评论

A simple yet effective approach for predicting disease spread using mathematically-inspired diffusion-informed neural networks

引用

Scientific Reports 2025年第1期15卷 1-14页

作者： Jeong, ByeongChang Lee, Yeon Ju Han, Cheol E. Department of Electronics and Information Engineering Korea University Sejong South Korea Interdisciplinary Graduate Program for Artificial Intelligence Smart Convergence Technology Korea University 2511 Sejong-ro Sejong 30019 South Korea Department of Applied Mathematics Korea University Sejong South Korea

The COVID-19 outbreak has highlighted the importance of mathematical epidemic models like the Susceptible-Infected-Recovered (SIR) model, for understanding disease spread dynamics. However, enhancing their predictive accuracy complicates parameter estimation. To address this, we proposed a novel model that integrates traditional mathematical modeling with deep learning which has shown improved predicted power across diverse fields. The proposed model includes a simple artificial neural network (ANN) for regional disease incidences, and a graph convolutional neural network (GCN) to capture spread to adjacent regions. GCNs are a recent deep learning algorithm designed to learn spatial relationship from graph-structured data. We applied the model to COVID-19 incidences in Spain to evaluate its performance. It achieved a 0.9679 correlation with the test data, outperforming previous models with fewer parameters. By leveraging the efficient training methods of deep learning, the model simplifies parameter estimation while maintaining alignment with the mathematical framework to ensure interpretability. The proposed model may allow the more robust and insightful analyses by leveraging the generalization power of deep learning and theoretical foundations of the mathematical models. © The Author(s) 2025.

关键词： Artificial neural networks COVID-19 Deep learning Graph convolutional neural network

来源：评论

学校读者我要写书评

暂无评论

Fairness Through Matching

arXiv

引用

arXiv 2025年

作者： Kim, Kunwoong Kong, Insung Lee, Jongjin Chae, Minwoo Park, Sangchul Kim, Yongdai Department of Statistics Seoul National University Korea Republic of Department of Applied Mathematics University of Twente Netherlands Samsung Research Korea Republic of School of Law Seoul National University Korea Republic of Department of Statistics Interdisciplinary Program in Artificial Intelligence Seoul National University Korea Republic of Seoul National University Korea Republic of

Group fairness requires that different protected groups, characterized by a given sensitive attribute, receive equal outcomes overall. Typically, the level of group fairness is measured by the statistical gap between predictions from different protected groups. In this study, we reveal an implicit property of existing group fairness measures, which provides an insight into how the group-fair models behave. Then, we develop a new group-fair constraint based on this implicit property to learn group-fair models. To do so, we first introduce a notable theoretical observation: every group-fair model has an implicitly corresponding transport map between the input spaces of each protected group. Based on this observation, we introduce a new group fairness measure termed Matched Demographic Parity (MDP), which quantifies the averaged gap between predictions of two individuals (from different protected groups) matched by a given transport map. Then, we prove that any transport map can be used in MDP to learn group-fair models, and develop a novel algorithm called Fairness Through Matching (FTM)1, which learns a group-fair model using MDP constraint with an user-specified transport map. We specifically propose two favorable types of transport maps for MDP, based on the optimal transport theory, and discuss their advantages. Experiments reveal that FTM successfully trains group-fair models with certain desirable properties by choosing the transport map accordingly. © 2025, CC BY.

关键词：

来源：评论

学校读者我要写书评

暂无评论

A SIZE-STRUCTURED MODEL FOR CANNIBALISM

引用

THEORETICAL POPULATION BIOLOGY 1992年第3期42卷 347-361页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

A size-structured model for the dynamics of a cannibalistic population is derived under the assumption that cannibals (successfully) attack only smaller bodied victims, as is generally the case in the biological world. In addition to the resulting size-dependent death rate, the model incorporates the positive feedback mechanism resulting from the added resource energy obtained by the cannibal from the consumption of the victim. From the nonlinear partial integro-differential equation model, it is shown how to obtain a complete analysis of the global dynamics of the total population biomass. This analysis yields many dynamical features that have been attributed to cannibalism in the literature, including density self-regulation, a “life-boat strategy” phenomenon by which a population avoids extinction by practicing cannibalism under circumstances when it would otherwise go extinct, and multiple stable positive equilibrium states and hysteresis.

关键词：

来源：评论

学校读者我要写书评

暂无评论

A DISCRETE MODEL FOR COMPETING STAGE-STRUCTURED SPECIES

引用

THEORETICAL POPULATION BIOLOGY 1992年第3期41卷 372-387页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts for the dynamics of stage-structured populations under the assumption that individuals in the populations can be placed into well defined descriptive stages. Density feedback is modeled through an assumption that (stage-specific) fertilities and transitions are proportional to a resource uptake functional which is dependent upon a total weighted population size. It is shown how, if stage-specific differences in mortality are insignificant compared to stage-specific differences in fertility and inter-stage transitions, a nonlinear version of the strong ergodic theorem of demography mathematically separates the population level dynamics from the dynamics of the stage distribution vector, which is shown to stabilize independently of the population level dynamics. The nonlinear dynamics at the population level are governed by a key parameter π that encapsulates the stage-specific parameters and thereby affords a means by which population level dynamics can be linked to properties of individual organisms. The method is applied to a community of stagestructured populations competing for a common limiting resource, and it is seen how the parameter π determines the competitively superior species. An example of size structured competitors illustrates how the method can relate the competitive success of a species to such size-specific properties as resource conversion efficiencies and allocation fractions for individual growth and reproduction, largest adult body size, and size at birth and maturation.

关键词：

来源：评论

学校读者我要写书评

暂无评论

THE DYNAMICS OF HIERARCHICAL AGE-STRUCTURED POPULATIONS

引用

JOURNAL OF MATHEMATICAL BIOLOGY 1994年第7期32卷 705-729页

作者： CUSHING, JM 1. Department of Mathematics Interdisciplinary Program on Applied Mathematics Building 89 University of Arizona 85721 Tucson AZ USA

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

关键词： AGE-STRUCTURED POPULATION DYNAMICS MCKENDRICK EQUATIONS HIERARCHICAL MODELS EXISTENCE/UNIQUENESS ASYMPTOTIC DYNAMICS GLOBAL STABILITY INTRA-SPECIFIC COMPETITION CANNIBALISM

来源：评论

学校读者我要写书评

暂无评论

On the relationship between r and R₀ and its role in the bifurcation of stable equilibria of Darwinian matrix models

引用

Journal of Biological Dynamics 2011年第3期5卷 277-297页

作者： Cushing, J.M. Department of Mathematics Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ 85721 United States

If the demographic parameters in a matrix model for the dynamics of a structured population are dependent on a parameter u, then the population growth rate r = r(u) and the net reproductive number R₀ = R₀(u) are functions of u. For a general matrix model, we showthat r and R₀ share critical values and extrema at values u = u^* for which r(u^*) = R₀(u^*) = 1. This allows us to re-interpret, in terms of the more analytically tractable quantity R₀, a fundamental bifurcation theorem for non-linear Darwinian matrix models from the evolutionary game theory that concerns the destabilization of the extinction equilibrium and creation of positive equilibria. Two illustrations are given: a theoretical study of trade-offs between fertility and survivorship in the evolution of an evolutionarily stable strategies and an application to an experimental study of the evolution to a genetic polymorphism. © 2011 Taylor & Francis.

关键词： Bifurcation Darwinian matrix models Equilibria Net reproductive number The evolutionary game theory

来源：评论

学校读者我要写书评

暂无评论

Competitive outcomes changed by evolution

引用

Journal of Biological Dynamics 2011年第3期5卷 227-252页

作者： Rael, R.C. Vincent, T.L. Cushing, J.M. Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States Aerospace and Mechanical Engineering University of Arizona Tucson AZ United States Department of Mathematics and Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States

When evolution plays a role, population dynamic models alone are not sufficient for determining the outcome of multi-species *** an expansion of Maynard Smith's concept of an evolutionarily stable strategy, evolutionary game theory (EGT) combines population and evolutionary dynamics so that natural selection becomes a dynamic game with phenotypic traits as strategies. Using EGT,we showhowevolution can change the outcome of the interaction between two competing *** are particularly interested in situations where the interaction changes from one of competitive exclusion to one of coexistence and where the interaction changes from the exclusion of one species to the exclusion of the other. There are two crucial factors that determine whether or not such events can occur: the rate of evolution (which is proportional to the amount of variability in phenotypic traits within a species) and what we term the boxer effect, a phenomenon that concerns how the intensity of interspecies competition relates to species' trait differences. We apply the theory to data from two historical competition experiments involving species of flour beetle from the genus Tribolium. In both applications, we show how EGT can explain certain seemingly 'anomalous' experimental results. © 2011 Taylor & Francis.

关键词： Competition Competitive coexistence Competitive exclusion Evolutionarily stable strategy Evolutionary game theory

来源：评论

学校读者我要写书评

暂无评论

Truncated Gaussian RBF Differences are Always Inferior to Finite Differences of the Same Stencil Width

引用

Communications in Computational Physics 2009年第1期5卷 42-60页

作者： John P.Boyd Lei Wang Department of Atmospheric Oceanic and Space ScienceUniversity of MichiganAnn Arbor MI 48109USA Department of Mathematics and Program in Applied and Interdisciplinary Mathematics University of MichiganAnn Arbor MI 48109USA

Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ***,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the *** Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is ***,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference *** a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors *** show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil *** error of the infinite series(M=∞)decreases exponentially asα→***,truncated GARBF series have a second error(truncation error)that grows exponentially asα→*** forα∼O(1)where the sum of these two errors is minimized,it is

关键词： Pseudospectral radial basis function high order finite difference nonstandard finite differences spectral differences

来源：评论

学校读者我要写书评

暂无评论

Periodic cycles of nonlinear discrete renewal equations

引用

Journal of Difference Equations and Applications 1996年第2期2卷 117-137页

作者： J. M. Cushing - [a] [a] Department of Mathematics Interdisciplinary Program on Applied Mathematics Tucson AZ

A general class of discrete, nonlinear renewal equations containing a real parameter is studied. Bifurcation theory methods are used to prove the existence of nontrivial periodic solutions and asymptotically periodic solutions. Fundamental to the approach is the “limit equation” whose periodic solutions are shown to be asymptotic limits of solutions of the renewal equation. An application is made to a model of age-structured population dynamics in which the bifurcation of nontrivial equilibria and 2-cycles is shown to occur with increasing inherent net reproductive value.

关键词： 39A10 difference equations renewal equation asymptotic dynamics equilibrium periodic solutions bifurcation

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：