Advances in Complex Systems

Statistical mechanics points out as fluctuations have a relevant role for systems near critical points. We study the effect of traffic fluctuations and the transition to congested states for a stochastic dynamical model of traffic on a road network. The model simulates a finite population that moves from one road to another according to random transition probabilities. In such a way, we mimic the traffic fluctuations due to the granular feature of traffic and the dynamics at the crossing points. Then the amplitude of traffic flow fluctuations is proportional to the average flow as suggested by empirical observations. Assuming a parabolic shaped flow-density relation, there exists an unstable critical point for the road dynamics and the system can perform a phase transition to a congested state, where some roads reach their maximal capacity. We apply a statistical physics approach to study the onset congestion and we characterize analytically the relation between the fluctuations amplitude and the appearance of congested nodes. We verify the results by means of numerical simulations on a Manhattan-like road network. Moreover we point out the existence of oscillating regimes, where traffic oscillations back propagate on the road network, whose onset depend sensitively from the traffic fluctuations and that have a strong influence on the hysteresis cycles of the systems when the traffic load is modulated. The comparison between the numerical simulations and the empirical traffic data recorded by an inductive-loop traffic detector system (MTS system) on the county roads of the Emilia Romagna region in Italy is shortly discussed.

For Agent-based models, in particular the Voter Model (VM), a general framework of aggregation is developed which exploits the symmetries of the agent network G. Depending on the symmetry group Aut_ω(N) of the weighted agent network, certain ensembles of agent configurations can be interchanged without affecting the dynamical properties of the VM. These configurations can be aggregated into the same macro state and the dynamical process projected onto these states is, contrary to the general case, still a Markov chain. The method facilitates the analysis of the relation between microscopic processes and a their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations. In some cases the macro chain is solvable.

Semidefinite integer programming model is an accurate tool for the structural design of networks. In this paper, we propose a semidefinite integer programming model with the constraints of spectral distributions and node degree distributions for the simulation of complex networks. Also, the feasible solutions and branch-and-bound solving algorithms of the model are designed. Based on eight metrics (e.g., spectral distribution, node degree distribution, clustering coefficients, etc.), the validity and practicability of the proposed method are illustrated.

Results from two studies on longitudinal friendship networks are presented, exploring the impact of a gratitude intervention on positive and negative affect dynamics in a social network. The gratitude intervention had been previously shown to increase positive affect and decrease negative affect in an individual but dynamic group effects have not been considered. In the first study, the intervention was administered to the whole network. In the second study, two social networks are considered and in each only a subset of individuals, initially low/high in negative affect respectively received the intervention as "agents of change". Data was analyzed using stochastic actor-based modeling techniques to identify resulting network changes, impact on positive and negative affect and potential contagion of mood within the group. The first study found a group level increase in positive and a decrease in negative affect. Homophily was detected with regard to positive and negative affect but no evidence of contagion was found. The network itself became more volatile along with a fall in rate of change of negative affect. Centrality measures indicated that the best broadcasters were the individuals with the least negative affect levels at the beginning of the study. In the second study, the positive and negative affect levels for the whole group depended on the initial levels of negative affect of the intervention recipients. There was evidence of positive affect contagion in the group where intervention recipients had low initial level of negative affect and contagion in negative affect for the group where recipients had initially high level of negative affect.