Related papers: Remarks on Fixed Point Assertions in Digital Topol…
New fixed point results are presented for ${\cal U}_c^{\kappa}(X,X)$ maps in extension type spaces.
In this article, we present some fixed point theorems in partially ordered G-metric space using the concept of $(\psi,\phi)$- weak contraction which extend many existing fixed point theorems in such space. We also give some examples to show…
Many machine learning algorithms rely on iterative updates of uncertainty representations, ranging from variational inference and expectation-maximization, to reinforcement learning, continual learning, and multi-agent learning. In the…
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be…
The reachability problem in vector addition systems is a central question, not only for the static verification of these systems, but also for many inter-reducible decision problems occurring in various fields. The currently best known…
The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…
We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…
A recent Comment [arXiv:0806.2142] has argued that "there is a simple duality between A-site and B-site" R3c ABO$_3$ materials and that our Letter [PRL 100, 167203 (2208)] "breaks this duality by ignoring a non-polar distortion that is…
Modern science increasingly relies on ever-growing observational datasets and automated inference pipelines, under the implicit belief that accumulating more data makes scientific conclusions more reliable. Here we show that this belief can…
We continue the study of freezing sets in digital topology, introduced in [2]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that…
The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Fixed points for scalar theories in $4-\varepsilon$, $6-\varepsilon$ and $3-\varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general…
In section 8.3 of our paper "Duality and Flat Base Change on Formal Schemes" (http://arXiv.org/abs/alg-geom/9708006) some important results concerning localization of, and preservation of coherence by, basic duality functors, were based on…
This note corrects a technical error in the ACM Computing Surveys paper mentioned in the title. The flaw involved constructions for showing that timed automata with urgent locations have the same expressiveness as timed automata that allow…
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…