Temporal networks are increasingly being used to model the interactions of complex systems. Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis. In this article we describe a static, lossless, and unique representation of a temporal network, the temporal event graph (TEG). The TEG describes the temporal network in terms of both the inter-event time and two-event temporal motif distributions. By considering these distributions in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network. We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.
We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type q1 or q2, or is an inflexible zealot. At each time step, a qi-susceptible voter (i=1,2) consults a group of qi neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever q1≠q2 and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the non-equilibrium stationary state of the system in terms of its probability distribution, non-vanishing currents and unequal-time two-point correlation functions. We also study the switching times properties of the model by exploiting an approximate mapping onto the model of [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and also outline some properties of the model near criticality.
We introduce an heterogeneous nonlinear q-voter model with two types of susceptible voters and zealots, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a susceptible voter of type q1 or q2, or is an inflexible zealot. At each time step, a qi-susceptible voter (i=1,2) consults a group of qi neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. We show that this model violates the detailed balance whenever q1≠q2 and has surprisingly rich properties. Here, we focus on the characterization of the model’s non-equilibrium stationary state (NESS) in terms of its probability distribution and currents in the distinct regimes of low and high density of zealotry. We unveil the NESS properties in each of these phases by computing the opinion distribution and the circulation of probability currents, as well as the two-point correlation functions at unequal times (formally related to a “probability angular momentum”). Our analytical calculations obtained in the realm of a linear Gaussian approximation are compared with numerical results.
We generalize the classical Bass model of innovation diffusion to include a new class of agents --- Luddites --- that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate. In response to the rate of adoption, an ignorant may become a Luddite and permanently reject the innovation. Instead of reaching complete adoption, the final state generally consists of a population of Luddites, ignorants, and adopters. The evolution of this system is investigated analytically and by stochastic simulations. We determine the stationary distribution of adopters, the time needed to reach the final state, and the influence of the network topology on the innovation spread. Our model exhibits an important dichotomy: when the rate of adoption is low, an innovation spreads slowly but widely; in contrast, when the adoption rate is high, the innovation spreads rapidly but the extent of the adoption is severely limited by Luddites.
The program consists of an intensive series of lectures, laboratories, and discussion sessions focusing on foundational ideas, tools, and current topics in complex systems research. These include nonlinear dynamics and pattern formation, scaling theory, information theory and computation theory, adaptation and evolution, network structure and dynamics, adaptive computation techniques, computer modeling tools and specific applications of these core topics to various disciplines.
This workshop explored topics such as recent advances in the extension of the formalism of large deviation theory to describe non-equilibrium fluctuations, anomalous scaling in reaction diffusion systems and stochastic aggregation and nonequilibrium phase transitions such as gelation and out-of-equilibrium condensation. It also included work on systems where rigorous mathematical progress is being made such as in understanding condensation in interacting particle systems for which exact stationary stationary measures are known and the use of fluctuation theorems to characterise non-equilibrium fluctuations.
A three-day workshop at the University of Bath on the analysis of models of collective dynamics and evolutionary networks, and their use across physical, social, financial and biological applications.
This year's Warwick Graduate Summer School in Complexity Science will provide graduate students and researchers in the mathematical sciences with an introduction to modern theoretical and computational tools for tackling the challenges posed by such modeling and optimsation problems.
Major international conference and event in the area of complex systems and interdisciplinary science in general.
The school aims at giving a solid fundamental background to Master and PhD students and young researchers working with or on complex networks, by introducing the main concepts and tools that are useful in this field. The school will introduce the concepts and tools of graph theory, statistical physics, statistical analysis, modeling, and visualization used in the field of complex networks.
The event brings together people in commerce, government and academia, covering technical issues (data, collection, algorithms, high performance computing) and implications for marketing, healthcare, social sciences and the study of human interaction (questions of interest, limitations, pitfalls).