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A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
Given an input graph and weights on its vertices, the maximum co-2-plex problem is to find a subset of vertices maximizing the sum of their weights and inducing a graph of degree at most 1. In this article, we analyze polyhedral aspects of…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Orthogonal wavelet transforms are a cornerstone of modern signal and image denoising because they combine multiscale representation, energy preservation, and perfect reconstruction. In this paper, we show that these advantages can be…
The wavelet scattering transform (WST) has recently gained attention in the context of large-scale structure studies, being a possible generator of summary statistics encapsulating non-Gaussianities beyond the reach of the conventional…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…
Let $V$ be a finite dimensional real vector space. In the article we construct an isomorphism between the space of smooth translation invariant valuations on convex subsets of $V$ and the space of such valuations (twisted by densities) on…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces in representation learning,…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling…
The study of Cowen-Douglas operators not only involves traditional operator-theoretic tools but also concepts and results from complex geometry on holomorphic vector bundles. We make use of the ratio of the metric matrices first considered…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…