Related papers: Borel-piecewise continuous reducibility for unifor…
In scientific disciplines such as neuroimaging, climatology, and cosmology it is useful to study the uncertainty of excursion sets of imaging data. While the case of imaging data obtained from a single study condition has already been…
We prove a compact embedding theorem in a class of spaces of piecewise H1 functions subordinated to a class of shape regular, but not necessarily quasi-uniform triangulations of a polygonal domain. This result generalizes the…
Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of Brouwer degree theory. Between the…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Lipschitz continuity of algorithms, introduced by Kumabe and Yoshida (FOCS'23), measures the stability of an algorithm against small input perturbations. Algorithms with small Lipschitz continuity are desirable, as they ensure reliable…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
The notion of pointwise differentials for distributions is a way to extract local information of distributions by rescaling the distribution at a point. In this paper, we study the pointwise differentials for distributions corresponding to…
While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…
We study classes of Borel subsets of the real line $\mathbb{R}$ such as levels of the Borel hierarchy and the class of sets that are reducible to the set $\mathbb{Q}$ of rationals, endowed with the Wadge quasi-order of reducibility with…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
The Weihrauch degrees are a tool to gauge the computational difficulty of mathematical problems. Often, what makes these problems hard is their discontinuity. We look at discontinuity in its purest form, that is, at otherwise constant…
We first extend the Peierls algebra of gauge invariant functions from the space ${\cal S}$ of classical solutions to the space ${\cal H}$ of histories used in path integration and some studies of decoherence. We then show that it may be…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…