Related papers: MATRIX MODELS FOR SPACETIME TOPODYNAMICS
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…
The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time. Just as network topology can teach us about the system in question, so can its…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
A brief review is given on the study of the thermodynamic properties of spin models defined on different topologies like small-world, scale-free networks, random graphs and regular and random lattices. Ising, Potts and Blume-Capel models…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a…
We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
Spatial and visual connectivity are important metrics when developing workplace layouts. Calculating those metrics in real-time can be difficult, depending on the size of the floor plan being analysed and the resolution of the analyses.…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…
The accurate, reliable and efficient numerical approximation of multi-physics processes in heterogeneous porous media with varying media coefficients that include fluid flow and structure interactions is of fundamental importance in energy,…
For a pointed topological space $X$, we use an inductive construction of a simplicial resolution of $X$ by wedges of spheres to construct a "higher homotopy structure" for $X$ (in terms of chain complexes of spaces). This structure is then…
We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.