Related papers: Remarks on Fixed Point Assertions in Digital Topol…

Networked discrete dynamical systems are often used to model the spread of contagions and decision-making by agents in coordination games. Fixed points of such dynamical systems represent configurations to which the system converges. In the…

We give an overview of issues surrounding computer-verified theorem proving in the standard pure-mathematical context. This is based on my talk at the PQR conference (Brussels, June 2003).

We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…

We review some of the problems associated with deriving field theoretic results from nonsupersymmetric AdS, focusing on how to control the behavior of the field theory along the flat directions. We discuss an example in which the origin of…

We show that the traditional criterion for a simplex to belong to the Delaunay triangulation of a point set is equivalent to a criterion which is a priori weaker. The argument is quite general; as well as the classical Euclidean case, it…

In this article we establish some fixed point (known also as critical point, invariant point) theorems in quasi-metric spaces. Our results unify and further extend in some regards the fixed point theorem proposed by Dancs et al. (1983), the…

The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further…

We criticize the article "Quantifying sustainability: Resilience, efficiency and the return of information theory" (Ulanowicz et al., Ecological Complexity, 2009) for its presentation of information theory to an audience of ecologists. We…

In this article, we discuss fixed point results for $(\varepsilon,\lambda)$-uniformly locally contractive self mapping defined on $\varepsilon$-chainable $G$-metric type spaces. In particular, we show that under some more general…

We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…

We derive conditions for the existence of fixed points of cone mappings without assuming scalability of functions. Monotonicity and scalability are often inseparable in the literature in the context of searching for fixed points of…

We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between…

On objects of a triangulated category with a stability condition, we construct a topology.

Artificial intelligence and machine learning algorithms have become ubiquitous. Although they offer a wide range of benefits, their adoption in decision-critical fields is limited by their lack of interpretability, particularly with textual…

This note provides a brief guide to the current state of the literature on Tarski's problems with emphasis on features that distinguish the approach based on combinatorial and algorithmic group theory from the topological approach to…

Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some…

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…

Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…