Related papers: Reverse mathematics of regular countable second co…

The topological reconstruction problem asks how much information about a topological space can be recovered from its point-complement subspaces. If the whole space can be recovered in this way, it is called reconstructible. Our main result…

We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $\tau^*$ of the natural topology of the real line $\mathbb{R}$ with properties such…

This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity…

Additive CA on a cylinder of size $n$ can be represented by 01-string $V$ of length $n$ which is its rule. We study a problem: a class $S$ of rules given, for any $V\in S$ describe all sizes $n', n'>n,$ of cylinders such that extension of…

In this paper, some features of countably $\alpha$-compact topological spaces are presented and proven. The connection between countably $\alpha$% -compact, Tychonoff, and $\alpha$-Hausdorff spaces is explained. The space is countably…

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…

We show that the sequential closure of a family of probability measures on the canonical space of c{\`a}dl{\`a}g paths satisfying Stricker's uniform tightness condition is a weak${}^*$ compact set of semimartingale measures in the pairing…

This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem. We examine two statements in graph…

Nested counter systems (NCS) are a generalization of counter systems to higher-order counters. Here, a higher-order counter is allowed to have other (lower-order) counters as elements, instead of just a number. Such systems can be viewed as…

For applications in computing, Bezier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R^3 and yields a smooth polynomial curve C embedded in R^3. It is of interest to understand when L and C have the…

By ECS manifolds one means pseudo-Riemannian manifolds of dimensions $\,n\ge4\,$ which have parallel Weyl tensor, but not for one of the two obvious reasons: conformal flatness or local symmetry. As shown by Roter [10, 2], they exist for…

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same…

Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS…

Under the assumption that a finite signal with different sampling lengths or different sampling frequencies is considered as equivalent, the signal space is considered as the quotient space of $\mathbb{R}^{\infty}$ over equivalence. The…

The measurable Riemann mapping theorem proved by Morrey and in some particular cases by Ahlfors, Lavrentiev and Vekua, says that any measurable almost complex structure on $\rd$ ($S^2$) with bounded dilatation is integrable: there is a…

We provide a machinery for transferring some properties of metrizable $ANR$-spaces to metrizable $LC^n$-spaces. As a result, we show that for complete metrizable spaces the properties $ALC^n$, $LC^n$ and $WLC^n$ coincide to each other. We…

Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning…

Learning scientific document representations can be substantially improved through contrastive learning objectives, where the challenge lies in creating positive and negative training samples that encode the desired similarity semantics.…

A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic…