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Progress in the creation of large scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are non-perturbative. Analysis of multiparticle…
In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We…
We consider a population of agents competing for finite resources using strategies based on two channels of signals. The model is applicable to financial markets, ecosystems and computer networks. We find that the dynamics of the system is…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
The complex interplay between human societies and their environments has long been a subject of fascination for social scientists. Utilizing agent-based modeling, this study delves into the profound implications of seemingly inconsequential…
The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent…
The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor,…
We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite…
In real-world systems, phase transitions often materialize abruptly, making it difficult to design appropriate controls that help uncover underlying processes. Some agent-based computational models display transformations similar to phase…
This paper studies a class of consensus dynamics where the interactions between agents are affected by a time-varying unknown scaling factor. This situation is encountered in the control of robotic fleets over a wireless network or in…
Complex systems universally exhibit emergence, where macroscopic dynamics arise from local interactions, but a predictive law governing this process has been absent. We establish and verify such a law. We define a system's causal power at a…
We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an…
We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
We study the evolution of social clusters, in an analogy with physical spin systems, and in detail show the importance of the concept of the "self" of each agent with quantifiable variable attributes. We investigate the effective influence…