Related papers: Algebraic topology and the quantization of fluctua…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
A short survey on applications of algebraic geometry in topological data analysis.
We study topological properties of the graph topology.
We investigate how the topology of attributed graphs influences the distribution of node attributes. This work offers a novel perspective by treating topology and attributes as structurally distinct but interacting components. We introduce…
Graphical models are a succinct way to represent the structure in probability distributions. This article analyzes the graphical model of nodal voltages in non-radial power distribution grids. Using algebraic and structural properties of…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems,…
Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
A Random Geometric Graph (RGG) ensemble is defined by the disordered distribution of its node locations. We investigate how this randomness drives sample-to-sample fluctuations in the dynamical properties of these graphs. We study the…
Distribution grids represent the final tier in electric networks consisting of medium and low voltage lines that connect the distribution substations to the end-users. Traditionally, distribution networks have been operated in a radial…
We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
Some work in progress is announced, on the use of algebraic geometry, mostly concerning elliptic curve theory, to model turbulence. Attention is given to flows across the scales, on some convenient model space, and some current trials are…
Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume…
Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and non-adiabatic effects. In this…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being…
We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in…