相关论文: Hegel and Modern Topology

Topological photonics is emerging as a new paradigm for the development of both classical and quantum photonic architectures. What makes topological photonics remarkably intriguing is the built-in protection as well as intrinsic…

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…

This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…

The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…

Pathways are integral to systems biology. Their classical representation has proven useful but is inconsistent in the meaning assigned to each arrow (or edge) and inadvertently implies the isolation of one pathway from another. Conversely,…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

In the last years the debate on complexity has been developing and developing in transdisciplinary way to meet the need of explanation for highly organized collective behaviors and sophisticated hierarchical arrangements in physical,…

Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…

We consider the interplay of point counts, singular cohomology, \'etale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked,…

In this paper, the theoretical terms of contemporary cosmology are examined as intellectual artefacts. An ontology and methodology are introduced for this purpose, which includes defining the concept of a hypothetical object. Introducing a…

A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…

Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…

We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…

The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…

The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…

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…

We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…

A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…