Publications related to Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

LISA – A Modern Proof System

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and fun ...

2023

LDP and CLT for SPDEs with transport noise

Lucio Galeati

In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...

SPRINGER2023

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

Tobias Johannes Schmid

For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...

AMER MATHEMATICAL SOC2022

Landing Proteins on Graphene Trampoline Preserves Their Gas-Phase Folding on the Surface

Klaus Kern, Stephan Rauschenbach, Sven Alexander Szilagyi, Hannah Julia Ochner

Molecule-surface collisions are known to initiate dynamics that lead to products inaccessible by thermal chemistry. These collision dynamics, however, have mostly been examined on bulk surfaces, leaving vast opportunities unexplored for molecular collision ...

AMER CHEMICAL SOC2022

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

ECOLE POLYTECHNIQUE2022

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Hoài-Minh Nguyên

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Nicolas Henri Bernard Flammarion, Scott William Pesme, Loucas Pillaud-Vivien

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension

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WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

LISA – A Modern Proof System

LDP and CLT for SPDEs with transport noise

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

Landing Proteins on Graphene Trampoline Preserves Their Gas-Phase Folding on the Surface

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

A Continuized View on Nesterov Acceleration

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

LISA – A Modern Proof System

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

LDP and CLT for SPDEs with transport noise

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Landing Proteins on Graphene Trampoline Preserves Their Gas-Phase Folding on the Surface

Energy Bounds For A Fourth-Order Equation In Low Dimensions Related To Wave Maps

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

A dependence of the cost of fast controls for the heat equation on the support of initial datum

A Continuized View on Nesterov Acceleration