Related papers: Phase transitions from linear to nonlinear informa…

This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…

Echo state networks are computationally lightweight reservoir models inspired by the random projections observed in cortical circuitry. As interest in reservoir computing has grown, networks have become deeper and more intricate. While…

We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…

An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added…

The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic…

Contemporary technological challenges often involve many degrees of freedom in a distributed or networked setting. Three aspects are notable: the variables are usually associated with the nodes of a graph with limited communication…

This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion…

In this paper we present an analysis of information transfer time based on holomorphism, causality and the classical principle of stationary phase. We also make a preliminary study of the effect of noise on information transfer time, and…

Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…

Lateral predictive coding is a recurrent neural network which creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here we investigate the trade-off between information robustness and…

In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another.…

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks…

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…

It is universally accepted that noise may bring order to complex nonequilibrium systems. Most strikingly, entirely new states not seen in the noiseless system can be induced purely by including multiplicative noise -- an effect known as…

The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…

The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature…

Non-equilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative {reactive} particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…