Related papers: Characterizing models in regularity structures: a …

We study the stability of quantum motion of classically regular systems in presence of small perturbations. Onthe base of a uniform semiclassical theory we derive the fidelity decay which displays a quite complexbehaviour, from Gaussian to…

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the previous cotangent…

We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…

The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…

We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents

We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…

We study the appearance of large scale mean motion sustained by stochastic forcing on a rotating fluid (in the quasigeostrophic approximation) flowing over topography. As in other noise rectification phenomena, the effect requires…

We study the pattern formation in a lattice of coupled phase oscillators with quenched disorder. In the synchronized regime concentric waves can arise, which are induced and increase in regularity by the disorder of the system. Maximal…

The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…

Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from…

Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…

Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise…

In this article we prove a regularization by noise phenomenon for the energy-critical and mass-critical nonlinear Schr\"odinger equations. We show that for any deterministic data, the probability that the corresponding solution exists…

In this work, we explore the maximum-margin bias of quasi-homogeneous neural networks trained with gradient flow on an exponential loss and past a point of separability. We introduce the class of quasi-homogeneous models, which is…

This article deals with the study of a non-local one-dimensional quasilinear problem with continuous forcing. We use a time-reparameterization to obtain a semilinear problem and study a more general equation using semigroup theory. The…

We introduce a notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance…

We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $\mathbb{R}^n$, $n\ge 2$, for classes of semilinear and quasilinear conductivity equations,…

We prove an embedded local uniformization theroem for a valuation centered on a point of a quasi-excellent scheme of characteristic zero. The proof reduces to valuations of rank 1 and consists in desingularizing the ideal formed by the…

Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance…