Related papers: On The Complexity Of Statistical Models Admitting …

The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…

Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…

We consider systems under uncertainty whose dynamics are partially unknown. Our aim is to study satisfaction of temporal logic properties by trajectories of such systems. We express these properties as signal temporal logic formulas and…

We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium…

The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…

We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…

In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we…

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled modes interacting with a thermal…

The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…

We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field…

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…

Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…

Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…

The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a…

Modern data sets in various domains often include units that were sampled non-randomly from the population and have a latent correlation structure. Here we investigate a common form of this setting, where every unit is associated with a…

This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with…

In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…

Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…