相关论文: Convolutional dynamical sampling and some new resu…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
Using the group theoretic approach based on the set of digits, we first investigate a finite collection of functions in $\ell^2 ({\mathbb{Z}}^2_N)$ that satisfies some localization properties in a region of the time-frequency plane. The…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
We report recent results on the extraction of the rapidity evolution kernel for Sudakov processes from experimental measurements of Drell-Yan (DY) transverse momentum distributions. We discuss the role of high-precision Large Hadron…
Direct load control of a heterogeneous cluster of residential demand flexibility sources is a high-dimensional control problem with partial observability. This work proposes a novel approach that uses a convolutional neural network to…
The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh $\Z$ on $\ell^p$ spaces, and its analogies with the continuous-space case. We do a deep study of…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat…
Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
We consider the heat equation associated with a class of second order hypoelliptic H\"{o}rmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a…
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such as subdiffusion or subdiffusive Fokker-Planck equation with…
Space-time covariance modeling under the Lagrangian framework has been especially popular to study atmospheric phenomena in the presence of transport effects, such as prevailing winds or ocean currents, which are incompatible with the…
It is shown that the rich algebraic structure of the standard $d$-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so($d+1$,2) dynamical algebra generators of the…
One of recent trends [30, 31, 14] in network architec- ture design is stacking small filters (e.g., 1x1 or 3x3) in the entire network because the stacked small filters is more ef- ficient than a large kernel, given the same computational…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…