Related papers: Generalizing the German Tank Problem
We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…
Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one,…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
We study the energy-critical nonlinear Schr\"{o}dinger equation with randomised initial data in dimensions $d>6$. We prove that the Cauchy problem is almost surely globally well-posed with scattering for randomised super-critical initial…
In this paper we discuss the local discontinuous Galerkin methods coupled with two specific explicit-implicit-null time discretizations for solving one-dimensional nonlinear diffusion problems $U_t=(a(U)U_x)_x$. The basic idea is to add and…
The motion of one-hundred point vortices in a circular cylinder is simulated numerically and compared with theoretical predictions based on statistical mechanics. The novel aspect considered here is that the vortices have greatly different…
This paper provides new insight into the classical problem of determining both the capacity of the discrete-time channel with uniform output quantization and the capacity achieving input distribution. It builds on earlier work by Gallager…
In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides. The statistical focus is estimating the sample size of measures necessary to calculate an…
In this paper, L\"uscher's formula is generalized to the case of two spin-$\frac{1}{2}$ particles in two-channel scattering based on Ref. \cite{Li:2012bi}. This is first done in a non-relativistic quantum mechanics model and then…
After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see [14], leads us to invert a sum of linear operators in a suitable Banach space, see (2) below. The…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…
How condensed-matter simulations depend on the number of molecules being simulated ($N$) is sometimes itself a valuable piece of information. Liquid crystals provide a case in point. Light scattering and $2d$-IR experiments on…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number. In this limit, the concentration of tracers is shown to…
Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but…
We investigate a generalisation of the logistic map as $ x_{n+1}=1-ax_{n}\otimes_{q_{map}} x_{n}$ ($-1 \le x_{n} \le 1$, $0<a\le2$) where $\otimes_q$ stands for a generalisation of the ordinary product, known as $q$-product [Borges, E.P.…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…