Related papers: Simplicial Complex Entropy
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…
We introduce a novel technique to numerically calculate R\'enyi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are…
In this paper, motivated by symplectic topology, we explore categorical entropy and present two main results. The first result establishes a relation between categorical entropies of functors on a category and its localization.…
In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest…
The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The…
By an appropriate definition, we divide the irregular set into level sets. Then we characterize the multifractal spectrum of these new pieces by calculating their entropies. We also compute the entropies of various intersections of the…
arXiv:1205.2953 defines an entropy for a gaussian scalar field $\phi$ in an arbitrary region of either a causal set or a continuous spacetime, given only the correlator $\langle\phi(x)\phi(y)\rangle$ within the region. As a first…
This paper provides a self-contained exploration of subdivisions of simplicial complexes, with emphasis on barycentric subdivision. We present formal definitions of subdivisions, show how the realization of a complex is preserved under…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…
We introduce "Replicated Entanglement Entropy (REE)" as the entanglement entropy of a subspace in a replicated theory. We calculate this quantity by replicating the original theory in two steps along the same entangling region and taking…
In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…