Related papers: Entropic descriptor of a complex behaviour
The information processing capacity of a complex dynamical system is reflected in the partitioning of its state space into disjoint basins of attraction, with state trajectories in each basin flowing towards their corresponding attractor.…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
Assessing quantitatively the state and dynamics of a social system is a very difficult problem. It is of great importance for both practical and theoretical reasons such as establishing the efficiency of social action programs, detecting…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible…
Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories.…
Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This…
Networks are a convenient way to represent many interactions among different entities as they provide an efficient and clear methodology to evaluate and organize relevant data. While there are many features for characterizing networks there…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behaviour of different types of systems by observing their outputs. With the aim of measuring the stability…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series of such entropies have been proposed in…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…