Related papers: Funny Problems in Intuitive Topology
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…
Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by…
In this short article, we present a solution to one of the probability puzzles that Daniel Litt, a mathematician at the University of Toronto, posted on his X account earlier this year. The main goal of this note is to show how some of the…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
We discuss the objectives of any endeavor in creating artificial intelligence, AI, and provide a possible alternative. Intelligence might be an unintended consequence of curiosity left to roam free, best exemplified by a frolicking infant.…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
We introduce a simple property, affine invariance, which characterizes within the class of fuzzy topological spaces those which are induced from an underlying topology on the space. We illustrate it by considering the simple notions of…
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every…
Position: (1) Partial solutions to machine intelligence can lead to systems which may be useful creating interesting and expressive musical works. (2) An appropriate general goal for this field is augmenting human expression. (3) The study…
The purpose of this paper is twofold: (i) we argue that the structure of commonsense knowledge must be discovered, rather than invented; and (ii) we argue that natural language, which is the best known theory of our (shared) commonsense…
A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…
Given a nonempty set $X$ and a function $f:X \rightarrow X$, three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…