Publications associées à Random Finite-Difference Discretizations Of The Ambrosio-Tortorelli Functional With Optimal Mesh-Size

Publications associées (18)

Some Physical Implications Of Absolute Geometries In The Description Of Complex Systems Dynamics

Some implications of absolute geometries in the description of complex systems dynamics, at various scale resolutions are highlighted. In such context, by means of an analytic geometry of 2 x 2 matrices, a generalization of the standard velocities space in ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2023

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

2023

Semiclassical Estimates for Eigenvalue Means of Laplacians on Spheres

Davide Buoso, Joachim Stubbe, Luigi Provenzano

We compute three-term semiclassical asymptotic expansions of counting functions and Riesz-means of the eigenvalues of the Laplacian on spheres and hemispheres, for both Dirichlet and Neumann boundary conditions. Specifically for Riesz-means we prove upper ...

SPRINGER2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Ivana Sain Glibic, Daniel Kressner

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

The N-Clock Model: Variational Analysis for Fast and Slow Divergence Rates of N

Matthias Benjamin Ruf

We study a nearest neighbors ferromagnetic classical spin system on the square lattice in which the spin field is constrained to take values in a discretization of the unit circle consisting of N equi-spaced vectors, also known as the N-clock model. We fin ...

2022

Universal Solution Manifold Networks (USM-Nets): Non-Intrusive Mesh-Free Surrogate Models for Problems in Variable Domains

Alfio Quarteroni

We introduce universal solution manifold network (USM-Net), a novel surrogate model, based on artificial neural networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. We employ a mesh-less arc ...

ASME2022

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

On polyhedral graphs and their complements

Riccardo Walter Maffucci

We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary. ...

2022

Factorial Lower Bounds for (Almost) Random Order Streams

Mikhail Kapralov

In this paper we introduce and study the STREAMINGCYCLES problem, a random order streaming version of the Boolean Hidden Hypermatching problem that has been instrumental in streaming lower bounds over the past decade. In this problem the edges of a graph G ...

IEEE COMPUTER SOC2022

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Raphaël Jean Berthier

Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...

OXFORD UNIV PRESS2022

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

A hybrid collocation-perturbation approach for PDEs with random domains

Fabio Nobile

Consider a linear elliptic PDE defined over a stochastic stochastic geometry a function of N random variables. In many application, quantify the uncertainty propagated to a quantity of interest (QoI) is an important problem. The random domain is split into ...

2021

LENA: Communication-Efficient Distributed Learning with Self-Triggered Gradient Uploads

Martin Jaggi, Sebastian Urban Stich

In distributed optimization, parameter updates from the gradient computing node devices have to be aggregated in every iteration on the orchestrating server. When these updates are sent over an arbitrary commodity network, bandwidth and latency can be limi ...

MICROTOME PUBLISHING2021

Every Elementary Higher Topos Has A Natural Number Object

Nima Rasekh

We prove that every elementary (infinity, 1)-topos has a natural number object. We achieve this by defining the loop space of the circle and showing that we can construct a natural number object out of it. Part of the proof involves showing that various de ...

2021

Faster Parallel Training of Word Embeddings

Martin Jaggi

Word embeddings have gained increasing popularity in the recent years due to the Word2vec library and its extension fastText that uses subword information. In this paper, we aim at improving the execution speed of fastText training on homogeneous multi- an ...

IEEE COMPUTER SOC2021

Augmenting and Tuning Knowledge Graph Embeddings

Farnood Salehi

Knowledge graph embeddings rank among the most successful methods for link prediction in knowledge graphs, i.e., the task of completing an incomplete collection of relational facts. A downside of these models is their strong sensitivity to model hyperparam ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

Integral Convexity And Parabolic Systems

Bernard Dacorogna

In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...

SIAM PUBLICATIONS2020

The Almost-Sure Asymptotic Behavior Of The Solution To The Stochastic Heat Equation With Levy Noise

Carsten Hao Ye Chong

We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a Levy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short tim ...

INST MATHEMATICAL STATISTICS2020