Related papers: Moment transference principles and multiplicative …
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
Given a 3D mesh with a UV parameterization, we introduce a novel approach to generating textures from text prompts. While prior work uses optimization from Text-to-Image Diffusion models to generate textures and geometry, this is slow and…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
We study the performance of nonparametric Bayes procedures for one-dimensional diffusions with periodic drift. We improve existing convergence rate results for Gaussian process (GP) priors with fixed hyper parameters. Moreover, we exhibit…
Energy conversion in a physical system requires time-translation invariance breaking according to Noether's theorem. Closely associated with this symmetry-conservation relation, the frequencies of electromagnetic waves are found to be…
We propose a novel macroscopic model for conjugate heat and mass transfer between a \emph{mobile region}, where advective transport is significant, and a set of \emph{immobile regions} where diffusive transport is dominant. Applying a…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
We explain how the Transference Principles from Diophantine approximation can be interpreted in terms of geometry of the locally symmetric spaces $T_n=SO(n) \backslash SL(n,R) /SL(n,Z)$ with $n>1$, and how, via this dictionary, they become…
We study translation minimal hypersurfaces and separable minimal hypersurfaces in the ($n+1$)-space with $2m$-norm.
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
In this work we address the problem of uniform approximation of differential forms starting from weak data defined by integration on rectifiable sets. We study approximation schemes defined by the projection operator L given by either…
The surface roughness correction to the near-field heat transfer between two rough bulk materials is discussed by using second-order perturbation theory. The results allow for estimating the impact of surface roughness to the heat transfer…
In this paper we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold $M \subset \mathbb{R}^n$ is of dimension strictly greater than…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt…
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of…
We analyze diffusion of particles on a two dimensional square lattice. Each lattice site contains an arbitrary number of particles. Interactions affect particles only in the same site, and are macroscopically represented by the excess…
We implement a shape optimization algorithm for body-assisted light-matter interactions described by the formalism of macroscopic quantum electrodynamics. The approach uses the level-set method to represent and incrementally evolve…