Related papers: Funny Problems in Intuitive Topology
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
Generating diverse questions for given images is an important task for computational education, entertainment and AI assistants. Different from many conventional prediction techniques is the need for algorithms to generate a diverse set of…
This article presents new colored link invariants by introducing the concepts of multi-quandles and topological multi-quandles.
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
Explainable AI (XAI) algorithms aim to help users understand how a machine learning model makes predictions. To this end, many approaches explain which input features are most predictive of a target label. However, such explanations can…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
We cast new light on the existing models of one-way deterministic topological automata by introducing a fresh but general, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
Artificial spin ices provide a controlled platform for investigating diverse physical phenomena, such as geometric frustration, magnetic monopoles, and phase transitions, via deliberate design. Here, we introduce a novel approach by…
While Large Language Models (LLMs) have demonstrated impressive natural language understanding capabilities across various text-based tasks, understanding humor has remained a persistent challenge. Humor is frequently multimodal, relying on…
This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding…
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate…
We observe a subtle and apparently generally unnoticed difficulty with the definition of the relative topology on a subset of a topological space, and with the weak topology defined by a function.