Related papers: Approximate Fixed Point Properties in Digital Topo…
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…
Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.
We study the local behavior of integral points on log pairs near a fixed rational point in the boundary by means of an integral approximation constant. In light of Siegel's theorem about integral points on curves and McKinnon's conjecture…
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…
For every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field is topologically dense in the set of its points with…
Fixed-Point-Oriented Programming (FPOP) is an emerging paradigm designed to streamline the implementation of problems involving self-referential computations. These include graph algorithms, static analysis, parsing, and distributed…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
Fixed points represent equilibrium states, stability, and solutions to a range of problems. It has been an active field of research. In this paper, we provide an overview of the main branches of fixed point theory. We discuss the key…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
Approximation Fixpoint Theory (AFT) was founded in the early 2000s by Denecker, Marek, and Truszczy\'nski as an abstract algebraic framework to study the semantics of non-monotonic logics. Since its early successes, the potential of AFT as…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
We study some problems in metric Diophantine approximation over local fields of positive characteristic.
In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
In this paper we explore a connection between certain Almost Perfect Nonlinear Functions (APN functions) and relative difference sets. In particular, we show that the image set of certain 2-to-1 APN functions is a relative difference set.…
A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
Federated learning (FL) is a distributed learning paradigm that allows several clients to learn a global model without sharing their private data. In this paper, we generalize a primal dual fixed point (PDFP) \cite{PDFP} method to federated…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…