Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies

The well-known Ising model used in statistical physics was adapted to a social dynamics context to simulate the adoption of a technological innovation. The model explicitly combines (a) an individual’s perception of the advantages of an innovation and (b) social influence from members of the decision-maker’s social network. The micro-level adoption dynamics are embedded into an agent-based model that allows exploration of macro-level patterns of technology diffusion throughout systems with different configurations (number and distributions of early adopters, social network topologies). In the present work we carry out many numerical simulations. We find that when the gap between the individual’s perception of the options is high, the adoption speed increases if the dispersion of early adopters grows. Another test was based on changing the network topology by means of stochastic connections to a common opinion reference (hub), which resulted in an increment in the adoption speed. Finally, we performed a simulation of competition between options for both regular and small world networks.     

Green’s function-stochastic methods framework for probing nonlinear evolution problems: Burger’s equation, the nonlinear Schrödinger’s equation, and hydrodynamic organization of near-molecular-scale vorticity

A framework which combines Green’s function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green’s function and stochastic representative solutions of linear drift–diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems – Burgers’ equation and the nonlinear Schrödinger’s equation – are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole–Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger’s vortex sheets. Here, the governing vorticity equation corresponds to the Fokker–Planck equation of an Ornstein–Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion and spread of single, multiple, and continuous sets of Burger’s vortex sheets, evolving within deterministic and random strain rate fields, under both viscous and inviscid conditions, are obtained. In order to promote application to other nonlinear problems, a tutorial development of the framework is presented. Likewise, time-incremental solution approaches and construction of approximate, though otherwise difficult-to-obtain backward-time GF’s (useful in solution of forward-time evolution problems) are discussed.     

Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism

We introduce a stochastic win-stay-lose-shift (WSLS) mechanism into evolutionary Prisoner’s Dilemma on small-world networks. At each time step, after playing with all its immediate neighbors, each individual gets a score to evaluate its performance in the game. The score is a linear combination of an individual’s total payoff (i.e., individual gain from the group) and local contribution to its neighbors (i.e., individual donation to the group). If one’s actual score is not larger than its desired score aspiration, it switches current strategy to the opposite one with the probability depending on the difference between the two scores. Under this stochastic WSLS regime, we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood, and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation. We also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation. Simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score. For much low intensity of deterministic switch, cooperation is to a large extent independent of learning rate, and full cooperation can be reached when relative weight is not less than 0.5. Otherwise, cooperation level is affected by the value of learning rate. Besides, we find that the cooperation level is not sensitive to the topological parameters. To explain these simulation results, we provide corresponding analytical results based on mean-field approximation, and find out that simulation results are in close agreement with the analytical ones. Our work may be helpful in understanding the cooperative behavior in social systems based on this stochastic WSLS mechanism.     

Stochastic climate dynamics: Random attractors and time-dependent invariant measures

This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures.     

Individual’s strategy characterized by local topology conditions in prisoner’s dilemma on scale-free networks

We introduce a “gradient” to find out the defectors, and further a “topology potential” to characterize the individual’s strategy preference in the prisoner’s dilemma on scale-free networks. It is shown that the cooperators typically locate on the nodes with high topology potential and the defectors are mainly found on the nodes with small topology potential. A critical topology potential is found for the nodes where cooperators are nip and tuck with defectors. So the information of node’s degree, gradient and topology potential together can predict individual’s strategy decision in the prisoner’s dilemma on the complex networks.     

Temporal percolation of a susceptible adaptive network

In the past decades, many authors have used the susceptible–infected–recovered model to study the impact of the disease spreading on the evolution of the infected individuals. However, few authors focused on the temporal unfolding of the susceptible individuals. In this paper, we study the dynamic of the susceptible–infected–recovered model in an adaptive network that mimics the transitory deactivation of permanent social contacts, such as friendship and work-ship ties. Using an edge-based compartmental model and percolation theory, we obtain the evolution equations for the fraction susceptible individuals in the susceptible biggest component. In particular, we focus on how the individual’s behavior impacts on the dilution of the susceptible network. We show that, as a consequence, the spreading of the disease slows down, protecting the biggest susceptible cluster by increasing the critical time at which the giant susceptible component is destroyed. Our theoretical results are fully supported by extensive simulations.     

How information influences an individual opinion evolution

We propose an opinion formation model which takes an individual’s opinion transition probability into consideration. In the model, each individual updates his/her opinion based on the probability of reception and acceptance. We describe the process of opinion evolution by using individual’s awareness _Wi$W_i$, message intensity _a0$a_0$ and message credibility _b0$b_0$. Results show that if a message’s view stays below 1 and its credibility takes a value around 2, it can win the trust of individuals with a high value of awareness (_Wi≥1$W_i\ge 1$), leading the public opinion to support the message’s own view within 100 steps and then decide the opinion formation. The final average opinion is closely related to the first message’s credibility and individual’s awareness.     

Rational behavior is a ‘double-edged sword’ when considering voluntary vaccination

Of particular importance for public health is how to understand strategic vaccination behavior in social networks. Social learning is a central aspect of human behavior, and it thus shapes vaccination individuals’ decision-making. Here, we study two simple models to address the impact of the more rational decision-making of individuals on voluntary vaccination. In the first model, individuals are endowed with memory capacity for their past experiences of dealing with vaccination. In addition to their current payoffs, they also take account of the historical payoffs that are discounted by a memory-decaying factor. They use such overall payoffs (weighing the current payoffs and historical payoffs) to reassess their vaccination strategies. Those who have higher overall payoffs are more likely imitated by their social neighbors. In the second model, individuals do not blindly learn the strategies of neighbors; they also combine the fraction of infection in the past epidemic season. If the fraction of infection surpasses the perceived risk threshold, individuals will increase the probability of taking vaccination. Otherwise, they will decrease the probability of taking vaccination. Then we use evolutionary game theory to study the vaccination behavior of people during an epidemiological process. To do this, we propose a two-stage model: individuals make vaccination decisions during a yearly vaccination campaign, followed by an epidemic season. This forms a feedback loop between the vaccination decisions of individuals and their health outcomes, and thus payoffs. We find that the two more rational decision-making models have nontrivial impacts on the vaccination behavior of individuals, and, as a result, on the final fraction of infection. Our results highlight that, from an individual’s viewpoint, the decisions are optimal and more rational. However, from the social viewpoint, the strategies of individuals can give rise to distinct outcomes. Namely, the rational behavior of individuals plays a ‘double-edged-sword’ role on the social effects.     

Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: A brief review

It is explained why the set of the fundamental empirical features of traffic breakdown (a transition from free flow to congested traffic) should be the empirical basis for any traffic and transportation theory that can be reliably used for control and optimization in traffic networks. It is shown that the generally accepted fundamentals and methodologies of the traffic and transportation theory are not consistent with the set of the fundamental empirical features of traffic breakdown at a highway bottleneck. To these fundamentals and methodologies of the traffic and transportation theory belong (i) Lighthill–Whitham–Richards (LWR) theory, (ii) the General Motors (GM) model class (for example, Herman, Gazis et al. GM model, Gipps’s model, Payne’s model, Newell’s optimal velocity (OV) model, Wiedemann’s model, Bando et al. OV model, Treiber’s IDM, Krauß’s model), (iii) the understanding of highway capacity as a particular (fixed or stochastic) value, and (iv) principles for traffic and transportation network optimization and control (for example, Wardrop’s user equilibrium (UE) and system optimum (SO) principles). Alternatively to these generally accepted fundamentals and methodologies of the traffic and transportation theory, we discuss the three-phase traffic theory as the basis for traffic flow modeling as well as briefly consider the network breakdown minimization (BM) principle for the optimization of traffic and transportation networks with road bottlenecks.     

Absortive and dispersive optical properties in molecular systems

Solute-solvent collisions for a two-level molecular system interacting with a four-wave mixing signal are analyzed in the present contribution. The system is described using the optical stochastic Bloch equations (OSBE), where Bohr’s frequency is treated a stochastic variable due to the random collisions with the solvent. The resulting equations for the Fourier components associated to the coherence are averaged over all the realizations of the stochastic variable, using an approximant for the Voigt’s function as a probability distribution. In this model we were able to calculate the optical susceptibilities at different frequencies, depicted as numerical surfaces for the behavior of the optical properties.     

Modeling language evolution: Aromanian,an endangered language in Greece

Time evolution of the relative density of speakers of an endangered language, Aromanian, which is spoken by a bilingual community in North-Western Greece, is approached theoretically by means of a two-state model and a three-state model. The same prestige and volatility parameters are used in these two models. Furthermore, a culture parameter and a second exponent are introduced in the three-state model. The parameters of each model are fitted to the current status of Aromanian, on the basis of field evidence collected by us, and the first findings about the risk of the language’s extinction are presented.     

Evolution of cooperation in lattice population with adaptive interaction intensity

We study the evolutionary Prisoner’s Dilemma game among individuals endowed with adaptively interaction intensity. Individuals adjust their interaction intensity according to the rules “payoff increase-high intensity, payoff decrease-low intensity”: if an individual’s payoff increases compared with that in the previous generation, he raises his interaction intensity; otherwise, he reduces the probability of interaction. We find that if individuals can adjust their interaction intensity with a proper scale, cooperation can be promoted. Interestingly, individuals with low interaction intensity usually hold the boundary of cooperator cluster. Such spatial distribution can alleviate the exploitation from defectors to cooperators since the interaction between cooperators and defectors is weakened. We hope our work can yield some insight into investigation of the evolution of cooperation in structured population.     

Fluctuation,relaxation, and extensivity of macrovariables in nonequilibrium systems

The extensive property of a macrovariable is proved for a quantal system whose Hamiltonian depends on time and for a stochastic system whose temporal evolution operator depends on time. These generalized situations are concerned with bulk-contact open systems. The extensive property, fluctuation, and nonlinear relaxation are investigated explicitly by calculating rigorously generating functions in exactly soluble models such as the linear stochastic model and linearXY model. The relation between the nonlinear critical slowing down and linear critical slowing down is also discussed.     

Resonant phenomena in extended chaotic systems subject to external noise: The Lorenz’96 model case

We have investigated the effects of noise on an extended chaotic system. The chosen model is the Lorenz’96, a type of “toy” model used for climate studies. Through the analysis of the system’s time evolution and its time and space correlations, we have obtained numerical evidence for two distinct stochastic resonance-like behaviors. Such behaviors are seen when both the usual and a generalized signal-to-noise ratio functions are depicted as a function of the external noise intensity, or of the system size. The underlying mechanisms seem to be associated with a noise-induced chaos reduction. The possible relevance of these and other findings for an optimal climate prediction are discussed.     

Estimating parameters in stochastic systems: A variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.     

Socioeconomic Patterns of Twitter User Activity

Stratifying behaviors based on demographics and socioeconomic status is crucial for political and economic planning. Traditional methods to gather income and demographic information, like national censuses, require costly large-scale surveys both in terms of the financial and the organizational resources needed for their successful collection. In this study, we use data from social media to expose how behavioral patterns in different socioeconomic groups can be used to infer an individual’s income. In particular, we look at the way people explore cities and use topics of conversation online as a means of inferring individual socioeconomic status. Privacy is preserved by using anonymized data, and abstracting human mobility and online conversation topics as aggregated high-dimensional vectors. We show that mobility and hashtag activity are good predictors of income and that the highest and lowest socioeconomic quantiles have the most differentiated behavior across groups.     

Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term.     

Sequential reconstruction of driving-forces from nonlinear nonstationary dynamics

This paper describes a functional analysis-based method for the estimation of driving-forces from nonlinear dynamic systems. The driving-forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system. The proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics. We derive the estimator conditioned on the differentiability of the unknown system’s mapping, and smoothness of the driving-force. The proposed algorithm is an adaptive sequential realization of the blind prediction error method, where the basic idea is to predict the observables, and retrieve the driving-force from the prediction error. Our realization of this idea is embodied by predicting the observables one-step into the future using a bank of echo state networks (ESN) in an online fashion, and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages. The adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving-forces accurately, which are illustrated by simulations. Logistic and Moran-Ricker maps are studied in controlled experiments, exemplifying chaotic state and stochastic measurement models. The algorithm is also applied to the estimation of a driving-force from another nonlinear dynamic system that is stochastic in both state and measurement equations. The results are judged by the posterior Cramer-Rao lower bounds. The method is finally put into test on a real-world application; extracting sun’s magnetic flux from the sunspot time series.     

Breakdown of weak-turbulence and nonlinear wave condensation

The formation of a large-scale coherent structure (a condensate) as a result of the long time evolution of the initial value problem of a classical partial differential nonlinear wave equation is considered. We consider the nonintegrable and unforced defocusing NonLinear Schrödinger (NLS) equation as a representative model. In spite of the formal reversibility of the NLS equation, the nonlinear wave exhibits an irreversible evolution towards a thermodynamic equilibrium state. The equilibrium state is characterized by a homogeneous solution (condensate), with small-scale fluctuations superposed (uncondensed particles), which store the information necessary for “time reversal”. We analyze the evolution of the cumulants of the random wave as originally formulated by D.J. Benney and P.G. Saffman [D.J. Benney, P.G. Saffman, Proc. Roy. Soc. London A 289 (1966) 301] and A.C. Newell [A.C. Newell, Rev. Geophys. 6 (1968) 1]. This allows us to provide a self-consistent weak-turbulence theory of the condensation process, in which the nonequilibrium formation of the condensate is a natural consequence of the spontaneous regeneration of a non-vanishing first-order cumulant in the hierarchy of the cumulants’ equations. More precisely, we show that in the presence of a small condensate amplitude, all relevant statistical information is contained in the off-diagonal second order cumulant, as described by the usual weak-turbulence theory. Conversely, in the presence of a high-amplitude condensate, the diagonal second-order cumulants no longer vanish in the long time limit, which signals a breakdown of the weak-turbulence theory. However, we show that an asymptotic closure of the hierarchy of the cumulants’ equations is still possible provided one considers the Bogoliubov’s basis rather than the standard Fourier’s (free particle) basis. The nonequilibrium dynamics turns out to be governed by the Bogoliubov’s off-diagonal second order cumulant, while the corresponding diagonal cumulants, as well as the higher order cumulants, are shown to vanish asymptotically. The numerical discretization of the NLS equation implicitly introduces an ultraviolet frequency cut-off. The simulations are in quantitative agreement with the weak turbulence theory without adjustable parameters, despite the fact that the theory is expected to breakdown nearby the transition to condensation. The fraction of condensed particles vs energy is characterized by two distinct regimes: For small energies (H?H_c) the Bogoliubov’s regime is established, whereas for H?H_c the small-amplitude condensate regime is described by the weak-turbulence theory. In both regimes we derive coupled kinetic equations that describe the coupled evolution of the condensate amplitude and the incoherent field component. The influence of finite size effects and of the dimensionality of the system are also considered. It is shown that, beyond the thermodynamic limit, wave condensation is reestablished in two spatial dimensions, in complete analogy with uniform and ideal 2D Bose gases.