Related papers: Simplicial Complex Entropy
We introduce tropical holonomic sequences of a given order and calculate their entropy in case of the second order.
Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…
We study the connected sum of Hopf links in $S^3$. Particularly, we compute the entanglement entropy (EE) as a function of the number of link components. We find evidence of lower and upper bounds for the entanglement entropy. We show that…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…
This study introduces the syntropy function ($S_N$) and expectancy function ($E_N$), derived from the novel function $\phi$, to provide a refined perspective on complexity, extending beyond conventional entropy analysis. $S_N$ is designed…
The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…
We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
In earlier work the authors obtained integral formulas for probabilities for a single particle in the asymmetric simple exclusion process. Here formulas are obtained for joint probabilities for several particles. In the case of a single…
The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the…
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 introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…