Connectivity and Wiener Index of Fuzzy Incidence Graphs

Connectivity is a key theory in fuzzy incidence graphs FIGs . In this paper, we introduced connectivity index CI , average connectivity index ACI , and Wiener index WI of FIGs . Three types of nodes including fuzzy incidence connectivity enhancing node FICEN , fuzzy incidence connectivity reducing node FICRN , and fuzzy incidence connectivity neutral node FICNN are also discussed in this paper. A correspondence between WI and CI of a FIG is also computed.

TURNOUT INTENTION AND RANDOM SOCIAL NETWORKS

How can networking affect the turnout in an election? We present a simple model to explain turnout as a result of a dynamic process of formation of the intention to vote within Erdös–Rényi networks. Citizens have fixed preferences for one of two parties and are embedded in a social network. They decide whether or not to vote on the basis of the attitude of their immediate contacts. They may simply follow the behavior of the majority (followers) or make an adaptive local calculus of voting (calculators). So they have the intention of voting either when the majority of their neighbors are willing to vote too, or when they perceive in their social neighborhood that elections are "close". We study the long-run average intention to vote, interpreted as the actual turnout observed in an election. Depending on the values of the average connectivity and the probability of behaving as a follower/calculator, the system exhibits monostability (zero turnout), bistability (zero and moderate/high turnout) or tristability (zero, moderate and high turnout). By obtaining realistic turnout rates for a wide range of values of both parameters, our model suggests a mechanism behind the observed relevance of social networks in recent elections.

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems , their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network , and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.