Publications associées à Fonction localement intégrable

Publications associées (16)

Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that fa ...

2022

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 Note on BIBO Stability

Michaël Unser

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

2020

Geometric ergodicity for some space-time max-stable Markov chains

Erwan Fabrice Koch

Max-stable processes are central models for spatial extremes. In this paper, we focus on some space-time max-stable models introduced in Embrechts et al. (2016). The processes considered induce discrete-time Markov chains taking values in the space of cont ...

ELSEVIER SCIENCE BV2019

On two isomorphic Lie algebroids associated with feedback linearization

Philippe Müllhaupt

We present two Lie algebroids linked to the construction of the linearizing output of an input affine nonlinear system. The algorithmic development of the linearizing output proceeds inductively, and each stage has two structures, namely a codimension one ...

ELSEVIER2019

Some regularity results for p-harmonic mappings between Riemannian manifolds

Changyu Guo

Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an eleme ...

2019

On two isomorphic Lie algebroids for Feedback Linearization

Philippe Müllhaupt

Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system.\ The algorithmic construction of the linearizing output proceeds inductively, and each stage has two structures, name ...

2019

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion ...

Univ Washington, Dept Mathematics2015

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Jan Sickmann Hesthaven, Paolo Gatto

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

Springer Verlag2015

Left-inverses of fractional Laplacian and sparse stochastic processes

Michaël Unser

The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...

Springer2012

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

Moyennabilité et courbure : G-espaces boréliens et espaces CAT(0)

Martin Anderegg

As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...

EPFL2010

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010

Inversion de Fourier ponctuelle

Emanuel Enrico Seifert

Let f be an integrable function on RN, a a point in RN and B a complex number. If the mean value of f on the sphere of centre a and radius r tends to B when r tends to 0, we show that the Fourier integral at a of f is summable to B in Cesàro means of order ...

EPFL2007

Quasilinear second order elliptic systems and topological degree

Hicham Georges Gebran

We consider a large class of quasilinear second order elliptic systems of the form - ∑α,β=1N aαβ(x,u(x)),∇u(x))∂2αβu(x) + b(x,u(x),∇u(x)) = 0, where x varies in an unbounded domain Ω of the Euclidean space RN and u = (u1,...,um) is a vector of functi ...

EPFL2005