Related papers: A statistical theory of complex systems
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…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
We show that an arbitrary probability distribution can be represented in exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical…
We discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view. The main characteristics of complex systems and of system approach to complex system study are…
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
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…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
This paper proposes a systems theory approach to the modeling of onset and evolution of criminality in a territory, which aims at capturing the complexity features of social systems. Complexity is related to the fact that individuals have…
Complex risk is a critical factor for both intelligent systems and risk management. In this paper, we consider a special class of risk statistics, named complex risk statistics. Our result provides a new approach for addressing complex…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…