相关论文: Small cap decoupling inequalities: Bilinear method…

This paper presents an iterative smoothing technique for polygonal approximation of digital image boundary. The technique starts with finest initial segmentation points of a curve. The contribution of initially segmented points towards…

We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new…

In this note we show that a sharp rigidity estimate and a sharp Korn's inequality for matrix-valued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due…

The purpose of this paper is to present some further applications of the general decoupling theory from [B-D1, 2] to certain diophantine issues. In particular, we concider mean value estimates relevant to the Bombieri-Iwaniec approach to…

By means of the concentrated compactness method of Bahouri-Gerard and Kenig-Merle, we prove global existence and regularity for wave maps with smooth data and large energy from 2+1 dimensions into the hyperbolic plane. The argument yields…

To prove Fourier restriction estimate using polynomial partitioning, Guth introduced the concept of $k$-broad part of regular $L^p$ norm and obtained sharp $k$-broad restriction estimates. To go from $k$-broad estimates to regular $L^p$…

Sup-norm curve estimation is a fundamental statistical problem and, in principle, a premise for the construction of confidence bands for infinite-dimensional parameters. In a Bayesian framework, the issue of whether the…

We prove a small cap decoupling theorem for the parabola over a general non-Archimedean local field for which $2\neq 0$. We obtain polylogarithmic dependence on the scale parameter $R$ and polynomial dependence in the residue prime, except…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities.…

New local smoothing estimates in Besov spaces adapted to the half-wave group are proved via $\ell^2$-decoupling. We apply these estimates to obtain new well-posedness results for the cubic nonlinear wave equation in two dimensions. The…

We study a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction, which depends on a positive parameter. The reaction is assumed to be (p-1)-sublinear near the origin and (p-1)-superlinear at…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…

In a previous work we investigated the existence of Hopf degenerate bifurcation points for a differential delay equation modeling leukemia and we actually found Hopf points of codimension two for the considered problem. If around the…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…

Multilevel methods are among the most efficient numerical methods for solving large-scale linear systems that arise from discretized partial differential equations. The fundamental module of such methods is a two-level procedure, which…

Recovering sharp images from dual-pixel (DP) pairs with disparity-dependent blur is a challenging task.~Existing blur map-based deblurring methods have demonstrated promising results. In this paper, we propose, to the best of our knowledge,…

Let $\Gamma$ be a compact patch of a well-curved $C^{n+1}$ curve in $\mathbb{R}^n$ with induced Lebesgue measure ${\rm d} \lambda$, and let $g \mapsto \widehat{g \,{\rm d}\lambda}$ be the Fourier extension operator for $\Gamma$. Then we…

A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a…