Cascading failures constitute an important vulnerability of interconnected systems. Here we focus on the study of such failures on networks in which the connectivity of nodes is constrained by geographical distance. Specifically, we use random geomet
ric graphs as representative examples of such spatial networks, and study the properties of cascading failures on them in the presence of distributed flow. The key finding of this study is that the process of cascading failures is non-self-averaging on spatial networks, and thus, aggregate inferences made from analyzing an ensemble of such networks lead to incorrect conclusions when applied to a single network, no matter how large the network is. We demonstrate that this lack of self-averaging disappears with the introduction of a small fraction of long-range links into the network. We simulate the well studied preemptive node removal strategy for cascade mitigation and show that it is largely ineffective in the case of spatial networks. We introduce an altruistic strategy designed to limit the loss of network nodes in the event of a cascade triggering failure and show that it performs better than the preemptive strategy. Finally, we consider a real-world spatial network viz. a European power transmission network and validate that our findings from the study of random geometric graphs are also borne out by simulations of cascading failures on the empirical network.
The generation of novelty is central to any creative endeavor. Novelty generation and the relationship between novelty and individual hedonic value have long been subjects of study in social psychology. However, few studies have utilized large-scale
datasets to quantitatively investigate these issues. Here we consider the domain of American cinema and explore these questions using a database of films spanning a 70 year period. We use crowdsourced keywords from the Internet Movie Database as a window into the contents of films, and prescribe novelty scores for each film based on occurrence probabilities of individual keywords and keyword-pairs. These scores provide revealing insights into the dynamics of novelty in cinema. We investigate how novelty influences the revenue generated by a film, and find a relationship that resembles the Wundt-Berlyne curve. We also study the statistics of keyword occurrence and the aggregate distribution of keywords over a 100 year period.
Public opinion is often affected by the presence of committed groups of individuals dedicated to competing points of view. Using a model of pairwise social influence, we study how the presence of such groups within social networks affects the outcome
and the speed of evolution of the overall opinion on the network. Earlier work indicated that a single committed group within a dense social network can cause the entire network to quickly adopt the groups opinion (in times scaling logarithmically with the network size), so long as the committed group constitutes more than about 10% of the population (with the findings being qualitatively similar for sparse networks as well). Here we study the more general case of opinion evolution when two groups committed to distinct, competing opinions $A$ and $B$, and constituting fractions $p_A$ and $p_B$ of the total population respectively, are present in the network. We show for stylized social networks (including ErdH{o}s-Renyi random graphs and Barabasi-Albert scale-free networks) that the phase diagram of this system in parameter space $(p_A,p_B)$ consists of two regions, one where two stable steady-states coexist, and the remaining where only a single stable steady-state exists. These two regions are separated by two fold-bifurcation (spinodal) lines which meet tangentially and terminate at a cusp (critical point). We provide further insights to the phase diagram and to the nature of the underlying phase transitions by investigating the model on infinite (mean-field limit), finite complete graphs and finite sparse networks. For the latter case, we also derive the scaling exponent associated with the exponential growth of switching times as a function of the distance from the critical point.
Social networks are not static but rather constantly evolve in time. One of the elements thought to drive the evolution of social network structure is homophily - the need for individuals to connect with others who are similar to them. In this paper,
we study how the spread of a new opinion, idea, or behavior on such a homophily-driven social network is affected by the changing network structure. In particular, using simulations, we study a variant of the Axelrod model on a network with a homophilic rewiring rule imposed. First, we find that the presence of homophilic rewiring within the network, in general, impedes the reaching of consensus in opinion, as the time to reach consensus diverges exponentially with network size $N$. We then investigate whether the introduction of committed individuals who are rigid in their opinion on a particular issue, can speed up the convergence to consensus on that issue. We demonstrate that as committed agents are added, beyond a critical value of the committed fraction, the consensus time growth becomes logarithmic in network size $N$. Furthermore, we show that slight changes in the interaction rule can produce strikingly different results in the scaling behavior of $T_c$. However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider.
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show th
at when the committed fraction grows beyond a critical value p_c approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c sim exp(alpha(p)N), while for p > p_c, T_c sim ln N. We conclude with simulation results for ErdH{o}s-Renyi random graphs and scale-free networks which show qualitatively similar behavior.
