Related papers: Rectangular shrinking targets for $\mathbb{Z}^m$ a…

We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…

The zeta-function regularization method is used to evaluate the renormalized effective action for massless conformally coupling scalar field propagating in a closed Friedman spacetime perturbed by a small rotation. To the second order of…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…

In this article, we define relative resolutions and coresolutions in extriangulated categories. By studying this relative resolutions and coresolutions, we get a generalization of the Auslander-Buchweitz approximation theory. Finally, we…

We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…

In recommender system or crowdsourcing applications of online learning, a human's preferences or abilities are often a function of the algorithm's recent actions. Motivated by this, a significant line of work has formalized settings where…

Motivated by the notion of K-gentle partition of unity introduced in [12] and the notion of K-Lipschitz retract studied in [17], we study a weaker notion related to the Kantorovich-Rubinstein transport distance, that we call K-random…

I developed an efficient numerical method for obtaining the gravitational potential of razor-thin spiral perturbations and used it to assess the standard tight-winding approximation, which is found to be reasonably accurate for pitch angles…

Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…

We introduce the notion of directed diagrammatic reducibility which is a relative version of diagrammatic reducibility. Directed diagrammatic reducibility has strong group theoretic and topological consequences. A multi-relator version of…

In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to…

This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…

Let $(X,d)$ be a compact metric space and $(X,\mathcal{A},\mu,T)$ a measure preserving dynamical system. Furthermore, given a real, positive function $\psi$, let $W(T, \psi)$ and $ R(T,\psi) $ respectively denote the shrinking target set…

Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address this issue, the largest observations are removed, this…

We study the pointwise convergence of Landau type Schr\"odinger operators within the fractional Sobolev space $W^{s,p}(\mathbb R)$. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531-546, 2013) and Yuan, Zhao…

Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…

This note is devoted to the study of sets of finite perimeter over RCD$(K,N)$ metric measure spaces. Its aim is to complete the picture about the generalization of De Giorgi's theorem within this framework. Starting from the results of [2]…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…