Related papers: Ensemble-based Topological Entropy Calculation (E-…
We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to…
When a granular system is tapped, its volume changes. Here, using a well-defined macroscopic protocol, we prepare an ensemble of granular systems and track the statistics of volume changes as a function of the number of taps. This is in…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov's coordinates on the boundary of Teichm\"uller space, is described. The method is illustrated on two two-parameter families of…
Data stream mining problem has caused widely concerns in the area of machine learning and data mining. In some recent studies, ensemble classification has been widely used in concept drift detection, however, most of them regard…
Time lag between variables is a key characteristics of dynamical systems in different fields and identifying such time lag is an important problem in complex systems with many applications. Transfer Entropy (TE) was proposed as a tool for…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
This work introduces a minimal, information-theoretic dynamical framework for modeling longitudinal cohort data using an entropy-initiated system of coupled-trait ordinary differential equations (ECTO). For each survey wave, item-level…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…
We consider topological dynamical systems given by skew products $S\rtimes_{\tau} T$, where $S\colon Y\to Y$ is a subshift, $\tau\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For…
Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the entanglement entropy may be obtained by…
We review the behavior of the entropy per particle in various two-dimensional electronic systems. The entropy per particle is an important characteristic of any many body system that tells how the entropy of the ensemble of electrons…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…