Related papers: Sampling trajectories for the short-time Fourier t…
We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of…
Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose a novel operator learning framework that leverages the…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
Let $\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\Sigma=\{0,1\}^{\mathbb{N}}$ associated with a H\"older potential. The thermodynamic and multifractal properties of $\mu$ are well known to be linked via the…
The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
We introduce conservative curved systems over multiply connected domains and study relationships of such systems with related notions of functional model, characteristic function, and transfer function. In contrast to standard theory for…
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…
The reconstruction of a function from its spectrogram (i.e., the absolute value of its short-time Fourier transform (STFT)) arises as a key problem in several important applications, including coherent diffraction imaging and audio…
The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…
We studied piecewise smooth differential systems of the form $$\dot{z} = Z(z) = \dfrac{1 + \operatorname{sgn}(F)}{2}X(z) + \dfrac{1 - \operatorname{sgn}(F)}{2}Y(z),$$ where $F: \mathbb{R}^{n}\rightarrow \mathbb{R}$ is a smooth map having 0…
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
Rare events in molecular dynamics are often related to noise-induced transitions between different macroscopic states (e.g., in protein folding). A common feature of these rare transitions is that they happen on timescales that are on…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…