Related papers: Methods of generating soft topologies and soft sep…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
Soft materials, such as colloidal suspensions, polymer solutions, and biological systems, are typically multicomponent mixtures of macromolecules and simpler components (e.g., microions, monomers, solvent) that can assemble into complex…
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological…
We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
Topological pressures of the preimages of $\epsilon$-stable sets and some certain closed subsets of stable sets in positive entropy systems are investigated. It is showed that the topological pressure of any topological system can be…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
In a recent paper, Chiney and Samanta have introduced a new definition of soft topology, using the soft elementary intersection and union. In this paper, basing at this approach, we introduce a definition of soft elementary compact set, and…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
Unlike molecular crystals, soft self-assembled fibres, micelles, vesicles, etc., exhibit a certain order in the arrangement of their constitutive monomers, but also high structural dynamicity and variability. Defects and disordered local…
We present a method for differentiable simulation of soft articulated bodies. Our work enables the integration of differentiable physical dynamics into gradient-based pipelines. We develop a top-down matrix assembly algorithm within…