Related papers: Optimal shift-invariant spaces from uniform measur…

In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions and, more generally, to small diffeomorphisms. Translation invariant representations of signals in…

We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory…

Let $X$ be a compact metric space, $C(X)$ be the space of continuous real-valued functions on $X$, and $A_1$, $A_2$ be two closed subalgebras of $C(X)$ containing constant functions. We consider the problem of approximation of a function…

Let $\{S_i\}_{i\in \Lambda}$ be a finite contracting affine iterated function system (IFS) on ${\Bbb R}^d$. Let $(\Sigma,\sigma)$ denote the two-sided full shift over the alphabet $\Lambda$, and $\pi:\Sigma\to {\Bbb R}^d$ be the coding map…

We present a perfect marginal sampler of the unique Gibbs measure of a spin system on $\mathbb Z^2$. The algorithm is an adaptation of a previous `lazy depth-first' approach by the authors, but relaxes the requirement of strong spatial…

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…

For a second countable locally compact group $G$ and a closed abelian subgroup $H$, we give a range function classification of closed subspaces in $L^2(G)$ invariant under left translation by $H$. For a family $\mathscr{A} \subset L^2(G)$,…

This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers $\mathbb{R}_{\mathcal{F}(A)}$. Recall that…

We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $\mathbb{R}^N$. In particular, inspired by recent work of Brezis and Nguyen on the distributional…

Let $l\geq 6$ be any integer, where $l\equiv 2$ mod $4$. Suppose that $\mu(\tau)d\tau$ is a measure with bounded variation and is supported on a compact subset of the complex plane, where…

Multi-frequency subspace migration imaging technique are usually adopted for the non-iterative imaging of unknown electromagnetic targets such as cracks in the concrete walls or bridges, anti-personnel mines in the ground, etc. in the…

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum…

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this…

This paper presents an explicit solution to decentralized control of a class of spatially invariant systems. The problem of optimal $H_2$ decentralized control for cone causal systems is formulated. Using Parseval's identity, the optimal…

We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null…

We consider the centralized detection of an intruder, whose location is modeled as uniform across a specified set of points, using an optimally placed team of sensors. These sensors make conditionally independent observations. The local…

Animals' internal states reflect variables like their position in space, orientation, decisions, and motor actions -- but how should these internal states be arranged? Internal states which frequently transition between one another should…

One of the basic problems in data analysis lies in choosing the optimal rescaling (change of coordinate system) to study properties of a given data-set $Y$. The classical Mahalanobis approach has its basis in the classical…

In this article, via certain lower bound conditions on the measures under consideration, the authors fully characterize the Sobolev embeddings for the scales of Haj{\l}asz-Triebel-Lizorkin and Haj{\l}asz-Besov spaces in the general context…

This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…