Related papers: Complexity Measures from Interaction Structures
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this…
The intensity matching approach for tractable performance evaluation and optimization of cellular networks is introduced. It assumes that the base stations are modeled as points of a Poisson point process and leverages stochastic geometry…
This paper exhibits a series of semantic characterisations of sublinear nondeterministic complexity classes. These results fall into the general domain of logic-based approaches to complexity theory and so-called implicit computational…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
Nanostructured surfaces usually exhibit complicated morphologies that cannot be described in terms of Euclidean geometry. Simultaneously, they do not constitute fully random noise fields to be characterized by simple stochastics and…
Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…
We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are…
In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex…
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…
This paper formulates and evaluates a series of multi-unit measures of directional association, building on the pairwise {\Delta}P measure, that are able to quantify association in sequences of varying length and type of representation.…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…