Related papers: Information and Criticality in Complex Stochastic …
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…
We discuss the relationships between large deviations in stochastic systems, and "effective interactions" that induce particular rare events. We focus on the nature of these effective interactions in physical systems with many interacting…
We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state.…
In this study, we explore the information capacity of open quantum systems, focusing on the effective channels formed by the subsystem of random quantum circuits and quantum Hamiltonian evolution. By analyzing the subsystem information…
Biological neural systems encode and transmit information as patterns of activity tracing complex trajectories in high-dimensional state-spaces, inspiring alternative paradigms of information processing. Heteroclinic networks, naturally…
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…