Related papers: Measures of $\e$-complexity
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Despite the common misconception of nearly static organisms, plants do interact continuously with the environment and with each other. It is fair to assume that during their evolution they developed particular features to overcome problems…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…
In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Within the framework of generalized combinatorial approach, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
At present, there is a great deal of confusion regarding complexity and its measures (reviews on complexity measures are found in, e.g. Lloyd, 2001 and Shalizi, 2006 and more references therein). Moreover, there is also confusion regarding…
We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…