Related papers: A statistical theory of complex systems
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
We propose a generalization of classical statistical mechanics which describes the behavior of dissipative systems placed in contact with a heat bath. In contrast to conventional statistical mechanics, which assigns probabilities to the…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
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…
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…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
We describe the fundamental difference between the nature of problems in traditional physics and that of many problems arising today in systems biology and other complex settings. The difference hinges on the much larger number of a priori…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
The development of modern information technologies permits to collect and to analyze huge amounts of statistical data in different spheres of life. The main problem is not to only to collect but to process all relevant information. The…