Influence Maximization for Fixed Heterogeneous Thresholds.

Influence Maximization is a NP-hard problem of selecting the optimal set of influencers in a network. Here, we propose two new approaches to influence maximization based on two very different metrics. The first metric, termed Balanced Index (BI), is fast to compute and assigns top values to two kinds of nodes: those with high resistance to adoption, and those with large out-degree. This is done by linearly combining three properties of a node: its degree, susceptibility to new opinions, and the impact its activation will have on its neighborhood. Controlling the weights between those three terms has a huge impact on performance. The second metric, termed Group Performance Index (GPI), measures performance of each node as an initiator when it is a part of randomly selected initiator set. In each such selection, the score assigned to each teammate is inversely proportional to the number of initiators causing the desired spread. These two metrics are applicable to various cascade models; here we test them on the Linear Threshold Model with fixed and known thresholds. Furthermore, we study the impact of network degree assortativity and threshold distribution on the cascade size for metrics including ours. The results demonstrate our two metrics deliver strong performance for influence maximization.

Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows.

Cascading failures are a critical vulnerability of complex information or infrastructure networks. Here we investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures, and propose mitigation strategies to reduce the severity of damages caused by such failures. We introduce a stochastic method for optimal heterogeneous distribution of resources (node capacities) subject to a fixed total cost. Additionally, we design and compare the performance of networks with N-stable and (N-1)-stable network-capacity allocations by triggering cascades using various real-world node-attack and node-failure scenarios. We show that failure mitigation through increased node protection can be effectively achieved against single-node failures. However, mitigating against multiple node failures is much more difficult due to the combinatorial increase in possible sets of initially failing nodes. We analyze the robustness of the system with increasing protection, and find that a critical tolerance exists at which the system undergoes a phase transition, and above which the network almost completely survives an attack. Moreover, we show that cascade-size distributions measured in this region exhibit a power-law decay. Finally, we find a strong correlation between cascade sizes induced by individual nodes and sets of nodes. We also show that network topology alone is a weak predictor in determining the progression of cascading failures.

Effects of communication burstiness on consensus formation and tipping points in social dynamics.

Current models for opinion dynamics typically utilize a Poisson process for speaker selection, making the waiting time between events exponentially distributed. Human interaction tends to be bursty though, having higher probabilities of either extremely short waiting times or long periods of silence. To quantify the burstiness effects on the dynamics of social models, we place in competition two groups exhibiting different speakers' waiting-time distributions. These competitions are implemented in the binary naming game and show that the relevant aspect of the waiting-time distribution is the density of the head rather than that of the tail. We show that even with identical mean waiting times, a group with a higher density of short waiting times is favored in competition over the other group. This effect remains in the presence of nodes holding a single opinion that never changes, as the fraction of such committed individuals necessary for achieving consensus decreases dramatically when they have a higher head density than the holders of the competing opinion. Finally, to quantify differences in burstiness, we introduce the expected number of small-time activations and use it to characterize the early-time regime of the system.

Assortative Mating: Encounter-Network Topology and the Evolution of Attractiveness.

We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node's attractiveness. The developed model reveals that increasing either the network's mean degree or the "choosiness" exercised during pair formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair formation. By iterating over the model's mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.

Competing effects of social balance and influence.

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field p_{c} such that for a weak external field (pp_{c}), there is only one (stable) fixed point, which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasistationary distribution and is found to be in agreement with the results obtained by numerical simulations.

Building damage-resilient dominating sets in complex networks against random and targeted attacks.

We study the vulnerability of dominating sets against random and targeted node removals in complex networks. While small, cost-efficient dominating sets play a significant role in controllability and observability of these networks, a fixed and intact network structure is always implicitly assumed. We find that cost-efficiency of dominating sets optimized for small size alone comes at a price of being vulnerable to damage; domination in the remaining network can be severely disrupted, even if a small fraction of dominator nodes are lost. We develop two new methods for finding flexible dominating sets, allowing either adjustable overall resilience, or dominating set size, while maximizing the dominated fraction of the remaining network after the attack. We analyze the efficiency of each method on synthetic scale-free networks, as well as real complex networks.

Extreme fluctuations in stochastic network coordination with time delays.

We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.

Dominating scale-free networks using generalized probabilistic methods.

We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for applications. We propose two novel probabilistic dominating set selection strategies that are applicable to heterogeneous networks. One of them obtains the smallest probabilistic dominating set and also outperforms the deterministic degree-ranked method. We show that a degree-dependent probabilistic selection method becomes optimal in its deterministic limit. In addition, we also find the precise limit where selecting high-degree nodes exclusively becomes inefficient for network domination. We validate our results on several real-world networks, and provide highly accurate analytical estimates for our methods.

Threshold-limited spreading in social networks with multiple initiators.

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple initiators trigger the cascade, and where all nodes possess the same adoption threshold ϕ. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction p. We find that even for arbitrarily high value of ϕ, there exists a critical initiator fraction pc(ϕ) beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.

Network coordination and synchronization in a noisy environment with time delays.

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.

Accelerating consensus on coevolving networks: the effect of committed individuals.

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 homophily-driven rewiring rule imposed. First, we find that the presence of 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 consensus time, T(c). However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider.

Analytic treatment of tipping points for social consensus in large random networks.

We introduce a homogeneous pair approximation to the naming game (NG) model by deriving a six-dimensional Open Dynamics Engine (ODE) for the two-word naming game. Our ODE reveals the change in dynamical behavior of the naming game as a function of the average degree {k} of an uncorrelated network. This result is in good agreement with the numerical results. We also analyze the extended NG model that allows for presence of committed nodes and show that there is a shift of the tipping point for social consensus in sparse networks.

Scanning magneto-optical Kerr microscope with auto-balanced detection scheme.

We have developed a scanning magneto-optical Kerr microscope dedicated to localization and measurement of the in-plane magnetization of ultra-thin layered magnetic nanostructures with high sensitivity and signal-to-noise ratio. The novel light detection scheme is based on a differential photodetector with automatic common mode noise rejection system with a high noise suppression up to 50 dB. The sensitivity of the developed detection scheme was tested by measurement of a single Co layer and a giant magnetoresistance (GMR) multilayer stack. The spatial resolution of the Kerr microscope was demonstrated by mapping an isolated 5×5 µm spin-valve pillar.

Social consensus through the influence of committed minorities.

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 that when the committed fraction grows beyond a critical value p(c) ≈ 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 < pc, T(c) ~ exp [α(p)N], whereas for p>p(c), T(c) ~ ln N. We conclude with simulation results for Erdos-Rényi random graphs and scale-free networks which show qualitatively similar behavior.

Social influencing and associated random walk models: Asymptotic consensus times on the complete graph.

We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.

Domain-wall movement control in Co/Au multilayers by He(+)-ion-bombardment-induced lateral coercivity gradients.

Defined perpendicular anisotropy gradients in the Co sublayers of a [Co(0.6 nm)/Au(2 nm)](3) sputter-deposited multilayer have been introduced by light ion bombardment through a wedged Au stopper layer. Within such a layer system, domain walls between up- and down-magnetized areas are controllably movable by an external perpendicular homogeneous magnetic field. This method and layer system is very promising for a controlled magnetic particle transport within the stray fields of the moving domain walls.

Network synchronization in a noisy environment with time delays: fundamental limits and trade-offs.

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the synchronizability threshold for an arbitrary network. Further, by constructing the scaling theory of the underlying fluctuations, we establish the absolute limit of synchronization efficiency in a noisy environment with uniform time delays, i.e., the minimum attainable value of the width of the synchronization landscape. Our results also have strong implications for optimization and trade-offs in network synchronization with delays.

Naming games in two-dimensional and small-world-connected random geometric networks.

We investigate a prototypical agent-based model, the naming game, on two-dimensional random geometric networks. The naming game [Baronchelli, J. Stat. Mech.: Theory Exp. (2006) P06014] is a minimal model, employing local communications that captures the emergence of shared communication schemes (languages) in a population of autonomous semiotic agents. Implementing the naming games with local broadcasts on random geometric graphs, serves as a model for agreement dynamics in large-scale, autonomously operating wireless sensor networks. Further, it captures essential features of the scaling properties of the agreement process for spatially embedded autonomous agents. Among the relevant observables capturing the temporal properties of the agreement process, we investigate the cluster-size distribution and the distribution of the agreement times, both exhibiting dynamic scaling. We also present results for the case when a small density of long-range communication links are added on top of the random geometric graph, resulting in a "small-world"-like network and yielding a significantly reduced time to reach global agreement. We construct a finite-size scaling analysis for the agreement times in this case.

Lyme disease in New York State: spatial pattern at a regional scale.

Lyme disease occurs commonly in New York State, but its geographic distribution is heterogeneous. Over each of nine consecutive years, incidence rates from 57 New York State counties were subjected to spatial autocorrelation analysis. Although the epidemic advanced during the study period, the analyses reveal a consistent pattern of spatial dependence. The correlation distance, the distance over which incidence rates covary positively, remained near 120 km over the nine years. A local spatial analysis around Westchester County, a major disease focus, indicated that the global correlation distance matched the extent of the most intense local clustering; statistically weaker clustering extended to 200 km from Westchester. Analyzing the spatial character of the epidemic may reveal the epizootic processes underlying patterns in human infection, and may help identify a spatial scale for regional control of disease.

Host spatial heterogeneity and the spread of vector-borne infection.

We analyze how spatial heterogeneity in host density affects the advance of vector-borne disease. Infection requires vector infestation. The vector spreads only between hosts occupying the same neighborhood, and the number of hosts varies randomly among neighborhoods. Simulation of a spatially detailed model shows that increasing heterogeneity in host abundance reduces pathogen prevalence. Clumping of hosts can limit the advance of the vector, which inhibits the spread of infection indirectly. Clumping can also increase the chance that the pathogen and vector become physically separated during the initial phase of the epidemic process. The latter limitation on the pathogen's spread, in our simulations, is restricted to small interaction neighborhoods. A mean-field model, which does not maintain spatial correlations between sites, approximates simulation results when hosts are arrayed uniformly, but overestimates infection prevalence when hosts are aggregated. A pair approximation, which includes some of the simulation model's spatial correlations, better describes the vector infestation frequencies across host spatial dispersions.