Diffusion limited aggregation, resetting and large deviations of Brownian motion

Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and its generalisations, the fractal dimension is sensitive to the nature of the stochastic motion of the particles. Here, we study the structures formed by finite-lived Brownian particles, i.e., particles constrained to find the aggregate within a prescribed time, and which are removed otherwise. This motion can be modelled by diffusion with stochastic resetting, a class of processes which has been widely studied in recent years. In the short lifetime limit, a very small fraction of the particles manage to reach the aggregate. Hence, growth is controlled by atypical Brownian trajectories, that move nearly in straight line according to a large deviation principle. In $d$ dimensions, the resulting fractal dimension of the aggregate decreases from the DLA value and tends to 1, instead of increasing to $d$ as expected from ballistic aggregation. In the zero lifetime limit one recovers the non-trivial model of "aggregation by the tips" proposed long ago by R. Jullien [J. Phys. A: Math. Gen. 19, 2129 (1986)].Comment: 13 pages, 5 figure

Strength of minority ties: the role of homophily and group composition in a weighted social network

Homophily describes a fundamental tie-formation mechanism in social networks in which connections between similar nodes occur at a higher rate than among dissimilar ones. In this article, we present an extension of the weighted social network (WSN) model that, under an explicit homophily principle, quantifies the emergence of attribute-dependent properties of a social system. To test our model, we make use of empirical association data of a group of free-ranging spider monkeys in Yucatan, Mexico. Our homophilic WSN model reproduces many of the properties of the empirical association network with statistical significance, specifically, the average weight of sex-dependent interactions (female-female, female-male, male-male), the weight distribution function, as well as many weighted macro properties (node strength, weighted clustering, and weighted number of modules), even for different age group combinations (adults, subadults, and juveniles). Furthermore, by performing simulations with fitted parameters, we show that one of the main features of a spider monkey social system, namely, stronger male-male interactions over female-female or female-male ones, can be accounted for by an asymmetry in the node-type composition of a bipartisan network, independently of group size. The reinforcement of connections among members of minority groups could be a general structuring mechanism in homophilic social networks