Speakers:
- János Török (10am-11pm). Associate professor at Budapest University of Technology, Department of Theoretical Physics.
- János Kertész (11am-12pm). Professor & Director of the Institute of Physics, Budapest University of Technology and Economics
Multi-level, multi-channel, multi-agent modeling of social interactions (János Török)
Abstract: We present a model of society. Human relations are strengthened by communication and eroded by time. Communication is, in general, related to some social activity (work, friendship, hobby) or social context. Therefore we postulate that individuals having different social needs participate in a number of social contexts (family, workplace etc.) – which may also evolve in time – and communicate with other members of the contexts using different communication channels (face to face, phone, email, etc.) for different purposes and with different impact on their relationship. We show that using realistic input data from surveys and statistical data one can reproduce important features of real society like Dunbar’s numbers and their meaning.
Spreading on temporal networks: Results from empirical analysis, model calculations and simulation (János Kertész)
Abstract: Spreading phenomena typically take place on temporal networks, where connections between the nodes are only occasionally and for limited time present. Such events can be, e.g., encounters of people, which are important for contagion or opening a communication channel needed for information transmission. We studied a mobile call network from this point of view: Having the time stamped records of the calls we played a ‘susceptible-infected’ game by infecting one node at random and assuming transmission at every possible event. We introduced different reference systems by appropriate shuffling of the data and identified this way the contributions of the different types of correlations to the speed of spreading. We concluded that there is a considerable slowing down as compared to the random models, mainly due to the correlations between the link weights and the topology and the inhomogeneous, bursty character of the events. We have also shown that the temporal inhomogeneity cannot be characterized by the inter-event time distribution (IETD) alone as there are strong dependencies between the events. In order to understand better the role of the different components we investigated models of temporal networks. In the analytically solvable infinite complete graph we showed that burstiness, i.e., power law IETD distribution always accelerates the process provided the clocks are positioned on the nodes. For the complementary case of link related burstiness we considered a number of models, like the analytically tractable Cayley tree, BA trees and networks. We show that if the stationary bursty process is governed by power-law IETD, the spreading can be slowed down or accelerated as compared to a Poisson process; the speed is determined by the short time behavior, which in our model is controlled by the exponent. We demonstrate that finite, so called “locally tree-like” networks, like the Barabási-Albert networks behave very differently from real tree graphs if the IETD is strongly fat-tailed, as the lack or presence of rare alternative paths modifies the spreading. A further important result is that the non-stationarity of the dynamics has a significant effect on the spreading speed for strongly fat-tailed power-law IETDs, thus bursty processes characterized by small power-law exponents can cause slow spreading in the stationary state but also very rapid spreading heavily depending on the age of the processes.
References:
1. M. Karsai, M. Kivelä, R. K. Pan, K. Kaski, J. Kertész, A.-L. Barabási, J. Saramäki: Small But Slow World: How Network Topology and Burstiness Slow Down Spreading, Phys. Rev. E 83, 025102 (2011)
2. Márton Karsai, Kimmo Kaski, Albert-László Barabási, János Kertész: Universal features of correlated bursty behavior, Scientific Reports 2, Article number 397 (2012)
3. Márton Karsai, Kimmo Kaski, János Kertész: Correlated dynamics in egocentric communication networks, PLoS ONE 7(7) e40612 (2012)
4. Hang-Hyun Jo, Márton Karsai, János Kertész, Kimmo Kaski: Circadian pattern and burstiness in human communication activity, New J. Phys. 14 013055 (2012)
5. Szabolcs Vajna, Bálint Tóth, János Kertész: Modelling power-law distributed interevent times, New J. Phys.15, article 103023 (2013)
6. Hang-Hyun Jo, Juan I. Perotti, Kimmo Kaski, János Kertész: Enhanced Spreading Dynamics by Non-Poissonian Processes, Physical Review X 4, 011041 (2014)
7. Dávid X. Horváth, János Kertész: Spreading dynamics on networks: the role of burstiness, topology and non-stationarity, New Journal of Physics 16 (7), 073037