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We consider a model of energy minimization arising in the study of the mechanical behavior caused by cell contraction within a fibrous biological medium. The macroscopic model is based on the theory of non rank-one convex nonlinear…

Numerical Analysis · Mathematics 2021-10-05 Georgios Grekas , Konstantinos Koumatos , Charalambos Makridakis , Phoebus Rosakis

We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J…

Analysis of PDEs · Mathematics 2017-08-22 Michael Goldman , Eris Runa

In this work we establish under certain hypotheses the $N \to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,\Gamma}[V] \, = \, \int_{\Gamma^N} \prod_{ a < b}^{N}(z_a - z_b)^\beta \, \prod_{k=1}^{N} \mathrm{e}^{ - N…

Mathematical Physics · Physics 2024-11-22 Alice Guionnet , Karol Kozlowski , Alex Little

We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…

Numerical Analysis · Mathematics 2021-08-03 D. Belomestny , L. Iosipoi , Q. Paris , N. Zhivotovskiy

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

Optimization and Control · Mathematics 2014-01-13 Bogdan Dumitrescu , Bogdan C. Sicleru , Florin Avram

Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…

Numerical Analysis · Mathematics 2021-06-28 Sören Bartels , Robert Tovey , Friedrich Wassmer

Fast Incremental Expectation Maximization (FIEM) is a version of the EM framework for large datasets. In this paper, we first recast FIEM and other incremental EM type algorithms in the {\em Stochastic Approximation within EM} framework.…

Machine Learning · Computer Science 2021-01-01 Gersende Fort , P. Gach , E. Moulines

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general…

Mathematical Physics · Physics 2019-10-02 Roberto Conti , Gerardo Morsella

We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…

Analysis of PDEs · Mathematics 2012-03-01 Mihai Bostan , J. A. Carrillo

This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…

Optimization and Control · Mathematics 2025-02-10 Livia Betz

We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…

Functional Analysis · Mathematics 2025-12-16 Armen Petrosyan

A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…

Optimization and Control · Mathematics 2019-07-01 Francesco Maddalena , Danilo Percivale , Franco Tomarelli

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Statistics Theory · Mathematics 2025-04-16 Mika Meitz , Alexander Shapiro

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

In this paper we provide a unified treatment of some convex minimization problems, which allows for a better understanding and, in some cases, improvement of results in this direction proved recently in spaces of curvature bounded above.…

Functional Analysis · Mathematics 2014-11-26 David Ariza-Ruiz , Genaro López-Acedo , Adriana Nicolae

Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…

Numerical Analysis · Mathematics 2025-02-19 Martin Alkämper , Stephan Hilb , Andreas Langer

The main drawback for the application of the conforming Argyris FEM is the labourious implementation on the one hand and the low convergence rates on the other. If no appropriate adaptive meshes are utilised, only the convergence rate…

Numerical Analysis · Mathematics 2022-07-21 Benedikt Gräßle

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…

Chemical Physics · Physics 2021-01-27 Kieron Burke

We obtain new asymptotic results about systems of $ N $ particles governed by Riesz interactions involving $ k $-nearest neighbors of each particle as $N\to\infty$. These results include a generalization to weighted Riesz potentials with…

Classical Analysis and ODEs · Mathematics 2023-03-21 Douglas P. Hardin , Edward B. Saff , Oleksandr Vlasiuk

In our previous work,, we studied asymptotic behavior of minimizers of the Landau-de Gennes energy functional on planar domains as the nematic correlation length converges to zero. Here we improve upon those results, in particular by…

Analysis of PDEs · Mathematics 2021-09-27 Dmitry Golovaty , Jose Alberto Montero