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Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…

Machine Learning · Statistics 2011-11-30 Akshay Soni , Jarvis Haupt

Entropic optimal transport -- the optimal transport problem regularized by KL diver\-gence -- is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of…

Statistics Theory · Mathematics 2025-05-09 Alberto González-Sanz , Stephan Eckstein , Marcel Nutz

Compressed Neural Networks have the potential to enable deep learning across new applications and smaller computational environments. However, understanding the range of learning tasks in which such models can succeed is not well studied.…

Machine Learning · Computer Science 2023-08-10 Matt Gorbett , Hossein Shirazi , Indrakshi Ray

We use the alternating direction method to simulate implicit dynamics. ur spatial discretization uses isogeometric analysis. Namely, we simulate a (hyperbolic) wave propagation problem in which we use tensor-product B-splines in space and…

Numerical Analysis · Mathematics 2019-11-20 Marcin Los , Pouria Behnoudfar , Maciej Paszynski , Victor Manuel Calo

In this article, we consider elliptic diffusion problems with an anisotropic random diffusion coefficient. We model the notable direction in terms of a random vector field and derive regularity results for the solution's dependence on the…

Numerical Analysis · Mathematics 2016-07-20 Helmut Harbrecht , Michael Peters , Marc Schmidlin

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

Numerical Analysis · Mathematics 2023-06-12 Olivier Pironneau , Pierre-Henri Tournier

The Stokes system with constant viscosity can be cast into different formulations by exploiting the incompressibility constraint. For instance the strain in the weak formulation can be replaced by the gradient to decouple the velocity…

Numerical Analysis · Mathematics 2016-04-28 Markus Huber , Ulrich Rüde , Christian Waluga , Barbara Wohlmuth

In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…

Mathematical Physics · Physics 2023-09-22 Yuan Hu , Chang Liu , Huayun Shen

We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary…

Disordered Systems and Neural Networks · Physics 2015-09-21 Carlo Baldassi , Alessandro Ingrosso , Carlo Lucibello , Luca Saglietti , Riccardo Zecchina

This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…

Numerical Analysis · Mathematics 2018-11-01 Faraniaina Rasolofoson , Beverley Grieshaber , B. Daya Reddy

A generalized anisotropic-diffusion framework is developed for transport problem in media described by a tensorial scattering coefficient and a scalar Henyey--Greenstein asymmetry factor. In this regime the classical similarity relation…

Optics · Physics 2026-02-24 Ernesto Pini , Michele Giusfredi , Lorenzo Pattelli

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

Numerical Analysis · Mathematics 2021-04-29 Monica Pragliola , Daniela Calvetti , Erkki Somersalo

This work addresses models (e.g. potential models of directed orbital systems- the manganates) in which an effective reduction dimensionality occurs as a result of a new symmetry which is intermediate between that of global and local gauge…

Statistical Mechanics · Physics 2007-05-23 Zohar Nussinov

This paper proposes an original adaptive refinement framework using Radial Basis Functions-generated Finite Differences method. Node distributions are generated with a Poisson Disk Sampling-based algorithm from a given continuous density…

Numerical Analysis · Mathematics 2020-05-12 Jure Slak , Gregor Kosec

Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting. We aim to study stochastic convex minimization problems through the…

Optimization and Control · Mathematics 2025-02-21 Rodrigo Maulen-Soto , Jalal Fadili , Hedy Attouch , Peter Ochs

Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse…

Functional Analysis · Mathematics 2012-06-12 Philipp Grohs , Gitta Kutyniok

Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…

Numerical Analysis · Mathematics 2024-06-05 Silvia Gazzola , Ali Gholami

We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…

Analysis of PDEs · Mathematics 2012-04-16 Christoph Ortner , Endre Suli

In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…

Machine Learning · Computer Science 2015-07-21 Tianbao Yang , Lijun Zhang , Rong Jin , Shenghuo Zhu

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of…

Computational Engineering, Finance, and Science · Computer Science 2020-12-08 Renate Sachse , Manfred Bischoff