Related papers: Topological Surgery in Nature
In this working paper, we present a simple theoretical framework based on network theory to study how speciation, the process by which new species appear, shapes spatial patterns of diversity. We show that this framework can be expanded to…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
Although osmosis is a familiar phenomenon, and of pivotal importance in natural systems, it is seldom explained how it might work on the molecular level (if treated at all in physics text books). The standard treatment of osmosis in…
We propose a definition of phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes all the definitions based on the curvature anomalies of thermodynamical…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this…
The central goal of this thesis is to develop methods to experimentally study topological phases. We do so by applying the powerful toolbox of quantum simulation techniques with cold atoms in optical lattices. To this day, a complete…
Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.
The relation between thermodynamic phase transitions in classical systems and topology changes in their state space is discussed for systems in which equivalence of statistical ensembles does not hold. As an example, the spherical model…
A simple model of the new notion of "Markov up" processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions.
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…
Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…
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…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…