相关论文: On computing the entropy of braids

We explore a web of connections between quantum entanglement and knot theory by examining how topological entanglement entropy probes the braiding data of quasi-particles in Chern-Simons theory, mainly using $SU(2)$ gauge group as our…

Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…

The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every…

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of…

We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…

In this paper, we study properties of random walks on finite groups and later use them to obtain the limiting braid length expectation and component number of braid closure in a model of random braids, which is constructed by lifting…

The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…

In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.

Given a large real symmetric, positive semidefinite m-by-m matrix, the goal of this paper is to show how a numerical approximation of the entropy, given by the sum of the entropies of the individual eigenvalues, can be computed in an…

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on…

Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…

We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open…

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees.

We consider the problem of coding for computing with maximal distortion, where the sender communicates with a receiver, which has its own private data and wants to compute a function of their combined data with some fidelity constraint…

We estimate from above the set of knots, $\Omega(n,\mu)$, generated by closure of n-string 1+1- and 2+1-dimensional braids of irreducible length $\mu$ ($\mu>>1$) in the limit n>>1.

A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\rho$-th moment of the number of performed…

This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include information, Shannon entropy and Gibbs entropy, the principle of…

The expression for entropy sometimes appears mysterious - as it often is asserted without justification. This short manuscript contains a discussion of the underlying assumptions behind entropy as well as simple derivation of this…