Related papers: Characterizing models in regularity structures: a …
We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the…
In this paper, we characterize the topological support in Holder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. This note is a continuation of [9] and [10]. The result is a…
We consider a 2D XY model subjected to time-correlated noise, a model of direct relevance to active crystals, which were shown recently to be able to support very large deformations without melting in the presence of persistent…
Trustworthy machine learning necessitates meticulous regulation of model reliance on non-robust features. We propose a framework to delineate and regulate such features by attributing model predictions to the input. Within our approach,…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results.…
Noise mechanisms in quantum systems can be broadly characterized as either coherent (i.e., unitary) or incoherent. For a given fixed average error rate, coherent noise mechanisms will generally lead to a larger worst-case error than…
We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…
The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional…
We study the smoothness properties of a global and nonautonomous topological conjugacy between a linear system and a quasilinear perturbation. The linear system exhibits a nonuniform exponential dichotomy with a nontrivial projector and…
Quadratically-constrained basis pursuit has become a popular device in sparse regularization; in particular, in the context of compressed sensing. However, the majority of theoretical error estimates for this regularizer assume an a priori…
We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…
These lecture notes are intended as reader's digest of recent work on a diagram-free approach to the renormalized centered model in Hairer's regularity structures. More precisely, it is about the stochastic estimates of the centered model,…
We consider the 2D quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with subcritical or critical indices. The proof of Onsager's conjecture concerning weak…
Robustness is a basic property of any control system. In the context of linear output regulation, it was proved that embedding an internal model of the exogenous signals is necessary and sufficient to achieve tracking of the desired…
Emergence of noise induced regularity or Coherence Resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance ($V_{N}$) of inter spike time intervals, which is a measure of regularity in…
In this paper, we investigate the averaging principle for a class of semilinear slow-fast partial differential equations driven by finite-dimensional rough multiplicative noise. Specifically, the slow component is driven by a general random…
Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasi-stability is a characteristic…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…