Related papers: Scaling-sharp dispersive estimates for the Kortewe…

We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of…

High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…

We prove a dispersive estimate for periodic discrete Schr\"odinger operators on the line with optimal rate of decay. Additionally, by standard methods, we deduce dispersive estimates for the discrete nonlinear Schr\"odinger equation with…

We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential Korteweg-de Vries equation (pKdV). We show that the mappings corresponding to the…

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

We prove sharp radial estimates using Besov spaces. We also prove the propagation of singularities in Besov spaces.

We study the propagation of narrow solitons through various profiles of dispersive shock waves (DSW) for the generalized Korteweg-de Vries equation. We consider situations in which the soliton passes through the DSW region quickly enough…

We prove sharp estimates for the dilation operator $f(x)\longmapsto f(\lambda x)$, when acting on Wiener amalgam spaces $W(L^p,L^q)$. Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations…

Integral equation of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of…

Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative…

We prove several scattering results for dispersion-managed nonlinear Schr\"odinger equations. In particular, we establish small-data scattering for both `intercritical' and `mass-subcritical' powers by suitable modifications of the standard…

We show sharp square function estimates for curves in the plane whose curvature degenerates at a point and estimates sharp up to endpoints for cones over these curves. To this end, for curves of finite type we extend the classical…

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collocation method. The time integration is performed with an…

We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general…

We present a method to compute dispersive shock wave solutions of the Korteweg-de Vries equation that emerge from initial data with step-like boundary conditions at infinity. We derive two different Riemann-Hilbert problems associated with…

It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear…

We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considered is connected with several equations in Mathematical…

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study…

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…

The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…