Evolutionary games on graphs

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems In many cases, however, the edges are not continuously active As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts In some cases, edges are active for non-negligible periods of time: eg, the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Temporal Networks

Brownian motors: noisy transport far from equilibrium

[1] The Madden-Julian Oscillation (MJO) is the dominant component of the intraseasonal (30–90 days) variability in the tropical atmosphere. It consists of large-scale coupled patterns in atmospheric circulation and deep convection, with coherent signals in many other variables, all propagating eastward slowly (∼5 m s−1) through the portion of the Indian and Pacific oceans where the sea surface is warm. It constantly interacts with the underlying ocean and influences many weather and climate systems. The past decade has witnessed an expeditious progress in the study of the MJO: Its large-scale and multiscale structures are better described, its scale interaction is recognized, its broad influences on tropical and extratropical weather and climate are increasingly appreciated, and its mechanisms for disturbing the ocean are further comprehended. Yet we are facing great difficulties in accurately simulating and predicting the MJO using sophisticated global weather forecast and climate models, and we are unable to explain such difficulties based on existing theories of the MJO. It is fair to say that the MJO remains an unmet challenge to our understanding of the tropical atmosphere and to our ability to simulate and predict its variability. This review, motivated by both the acceleration and gaps in our knowledge of the MJO, intends to synthesize what we currently know and what we do not know on selected topics: its observed basic characteristics, mechanisms, numerical modeling, air-sea interaction, and influences on the El Nino and Southern Oscillation.

/pdf/madden-julian-oscillation-2f6izjkiaw.pdf

Madden‐Julian Oscillation

Our aim is to propose a theory which goes beyond the classical formulation of thermodynamics. This is achieved by enlarging the space of basic independent variables, through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations. The next step is to find evolution equations for the dissipative fluxes. Whereas the evolution equations for the classical variables are given by the usual balance laws, no general criteria exist concerning the evolution equations of the dissipative fluxes, with the exception of the restrictions imposed on them by the second law of thermodynamics.

https://iopscience.iop.org/article/10.1088/0034-4885/51/8/002/pdf

Extended irreversible thermodynamics

/pdf/analytical-and-numerical-studies-of-multiplicative-noise-54fo293eia.pdf

Analytical and numerical studies of multiplicative noise

We discuss the problem of eliminating the momentum variable in the phase space Langevin equations for a system of Brownian particles in two related situations: (i) position-dependent damping and (ii) existence of hydrodynamic interactions. We discuss the problems associated with the conventional elimination and we develop an alternative elimination procedure, in the Lagevin framework, which leads to the correct Smoluchowski equation. We give a heuristic argument on the basis of stochastic differential equations for the Smoluchowski limit and establish rigorously the limit for the general case of position-dependent friction and diffusion coefficents.

Adiabatic elimination for systems of Brownian particles with nonconstant damping coefficients

We introduce a general methodology of update rules accounting for arbitrary interevent time (IET) distributions in simulations of interacting agents. We consider in particular update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully connected, random, and scale-free networks with an activation probability inversely proportional to the time since the last action, where an action can be an update attempt (an exogenous update) or a change of state (an endogenous update). We find that in the thermodynamic limit, at variance with standard updates and the exogenous update, the system orders slowly for the endogenous update. The approach to the absorbing state is characterized by a power-law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined. The IET distributions resulting from both update schemes show power-law tails.

/pdf/update-rules-and-interevent-time-distributions-slow-ordering-5f7c86qmes.pdf

Update rules and interevent time distributions: slow ordering versus no ordering in the voter model.

We study the noisy voter model using a specific non-linear dependence of the rates that takes into account collective interaction between individuals. The resulting model is solved exactly under the all-to-all coupling configuration and approximately in some random network environments. In the all-to-all setup, we find that the non-linear interactions induce bona fide phase transitions that, contrary to the linear version of the model, survive in the thermodynamic limit. The main effect of the complex network is to shift the transition lines and modify the finite-size dependence, a modification that can be captured with the introduction of an effective system size that decreases with the degree heterogeneity of the network. While a non-trivial finite-size dependence of the moments of the probability distribution is derived from our treatment, mean-field exponents are nevertheless obtained in the thermodynamic limit. These theoretical predictions are well confirmed by numerical simulations of the stochastic process.

/pdf/analytical-and-numerical-study-of-the-non-linear-noisy-voter-33tqb041l4.pdf

Analytical and numerical study of the non-linear noisy voter model on complex networks.

The paper addresses the problem as to whether the microscopic photon polarization entanglement leaves any trace in the regime of high parametric down-conversion efficiency, where the number of down-converted photons can be rather large, and in which form. A local version of Stokes operators is defined and quantum correlation between operators measured from symmetric portions of the far field beam cross-section is studied.

/pdf/multi-photon-multi-mode-polarization-entanglement-in-4ktkrwjcsj.pdf

M. San Miguel

Papers

Analytical and numerical studies of multiplicative noise

Adiabatic elimination for systems of Brownian particles with nonconstant damping coefficients

Update rules and interevent time distributions: slow ordering versus no ordering in the voter model.

Analytical and numerical study of the non-linear noisy voter model on complex networks.

Multi-photon, multi-mode polarization entanglement in parametric down-conversion