“Small steps to better understanding”

December 10, 2019

Concurrency and reachability in treelike temporal networks

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of accessibility, whether there is a temporally consistent path from one node to another, and reachability, the density of the corresponding accessibility graph representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean-field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.

November 04, 2019

Exploring Concurrency and Reachability in the Presence of High Temporal Resolution

Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where nodes and links appear and disappear. We review previous studies on the effects of temporal connectivity for understanding the spreading rate and outbreak size of model infection processes. We focus on the effects of “accessibility”, whether there is a temporally consistent path from one node to another, and “reachability”, the density of the corresponding “accessibility graph” representation of the temporal network. We study reachability in terms of the overall level of temporal concurrency between edges, quantifying the overlap of edges in time. We explore the role of temporal resolution of contacts by calculating reachability with the full temporal information as well as with a simplified interval representation approximation that demands less computation. We demonstrate the extent to which the computed reachability changes due to this simplified interval representation. 

July 22, 2019

Homophily and minority size explain perception biases in social networks

People's perceptions about the size of minority groups in social networks can
be biased, often showing systematic over- or underestimation. These social
perception biases are often attributed to biased cognitive or motivational
processes. Here we show that both over- and underestimation of the size of a
minority group can emerge solely from structural properties of social networks.
Using a generative network model, we show analytically that these biases depend
on the level of homophily and its asymmetric nature, as well as on the size of
the minority group. Our model predictions correspond well with empirical data
from a cross-cultural survey and with numerical calculations on six real-world
networks. We also show under what circumstances individuals can reduce their
biases by relying on perceptions of their neighbors. This work advances our
understanding of the impact of network structure on social perception biases
and offers a quantitative approach for addressing related issues in society.

May 10, 2019

Impact of perception models on friendship paradox and opinion formation

Topological heterogeneities of social networks have a strong impact on the individuals embedded in those networks. One of the interesting phenomena driven by such heterogeneities is the friendship paradox (FP), stating that the mean degree of one's neighbors is larger than the degree of oneself. Alternatively, one can use the median degree of neighbors as well as the fraction of neighbors having a higher degree than oneself. Each of these reflects on how people perceive their neighborhoods, i.e., their perception models, hence how they feel peer pressure. In our paper, we study the impact of perception models on the FP by comparing three versions of the perception model in networks generated with a given degree distribution and a tunable degree-degree correlation or assortativity. The increasing assortativity is expected to decrease network-level peer pressure, while we find a nontrivial behavior only for the mean-based perception model. By simulating opinion formation, in which the opinion adoption probability of an individual is given as a function of individual peer pressure, we find that it takes the longest time to reach consensus when individuals adopt the median-based perception model compared to other versions. Our findings suggest that one needs to consider the proper perception model for better modeling human behaviors and social dynamics.

July 17, 2017

We investigate opinion spreading by a threshold model in a situation in which the influence of people is heterogeneously distributed. We assume that there is a coupling between the influence of an individual (measured by the out-degree) and the threshold for accepting a new opinion or habit. We find that if the coupling is strongly positive, the final state of the system will be a mix of different opinions. Otherwise, it will converge to a consensus state. This phenomenon cannot simply be explained as a phase transition, but it is a combined effect of mechanisms and their relative dominance in different regions of parameter space.

April 24, 2017

We investigate the formation of opinion against authority in an authoritarian society composed of agents with different levels of authority. We explore a ‘‘dissenting’’ opinion, held by lower-ranking, obedient, or less authoritative people, spreading in an environment of an ‘‘affirmative’’ opinion held by authoritative leaders. A real-world example would be a corrupt society where people revolt against such leaders, but it can be applied to more general situations. In our model, agents can change their opinion depending on their au- thority relative to their neighbors and their own confidence level. In addition, with a certain probability, agents can override the affirmative opinion to take the dissenting opinion of a neighbor. Based on analytic derivation and numerical simulations, we observe that both the network structure and heterogeneity in authority, and their correlation, significantly affect the possibility of the dissenting opinion to spread through the population. In particular, the dissenting opinion is suppressed when the authority distribution is very heterogeneous and there exists a positive correlation between the authority and the number of neighbors of people (degree). Except for such an extreme case, though, spreading of the dissenting opinion takes place when people have the tendency to override the authority to hold the dissenting opinion, but the dissenting opinion can take a long time to spread to the entire society, depending on the model parameters. We argue that the internal social structure of agents sets the scale of the time to reach consensus, based on the analysis of the underlying structural properties of opinion spreading.

February 05, 2016

In ad hoc wireless networking, units are connected to each other rather than to a central, fixed, infrastructure. Constructing and maintaining such networks create several trade-off problems between robustness, communication speed, power consumption, etc., that bridges engineering, computer science and the physics of complex systems. In this work, we address the role of mobility patterns of the agents on the optimal tuning of a small-world type network construction method. By this method, the network is updated periodically and held static between the updates. We investigate the optimal updating times for different scenarios of the movement of agents (modeling, for example, the fat-tailed trip distances, and periodicities, of human travel). We find that these mobility patterns affect the power consumption in non-trivial ways and discuss how these effects can best be handled.

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