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19972026
most citedOn the Number of Linear Regions of Deep Neural Networks

832 citations

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120 papers · 1 filter

math.AP2025

A variational view on constitutive laws in parabolic problems

Stefan Schiffer, Espen Xylander

We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A…

math.AP2025

Existence of martingale solutions to a stochastic kinetic model of chemotaxis

Benjamin Gess, Sebastian Herr, Anne Niesdroy

We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions…

math.AP2025

Uniqueness of Dirac-harmonic maps from a compact surface with boundary

Jürgen Jost, Jingyong Zhu

As a commutative version of the supersymmetric nonlinear sigma model, Dirac-harmonic maps from Riemann surfaces were introduced fifteen years ago. They are critical points of an un…

math.AP2024

Eyring--Kramers law for the hyperbolic model

Nikolay Barashkov, Petri Laarne

We study the expected transition frequency between the two metastable states of a stochastic wave equation with double-well potential. By transition state theory, the frequency fac…

math.AP2024★ 1 cited

Contact discontinuities for 2-D isentropic Euler are unique in 1-D but wildly non-unique otherwise

Sam G. Krupa, László Székelyhidi

We develop a general framework for studying non-uniqueness of the Riemann problem for the isentropic compressible Euler system in two spatial dimensions, and in this paper we prese…

math.AP2024

An alternative approach to Shnirelman's inequality

Martina Zizza

In this paper we examine the discrete Shnirelman's inequality [Shnirelman A., 1985], which relates the -distance of two discrete configurations of a fluid to the -…