Sobehart, Lucas A. (2023) Procesos estocásticos sobre una red aleatoria de cliques / Stochastic processes on a random network of cliques. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo se propone una clase de redes aleatorias que puede ser aplicada a una amplia variedad de sistemas complejos en donde los agentes interactuantes se dividen en comunidades y, a su vez, cada uno puede interactuar con algún otro agente que no se encuentre en su comunidad. Usando el formalismo de redes aleatorias con distribuciones de grado genéricas para redes de gran tamaño, se estudió la estructura de la red en forma analítica y se validaron los resultados analíticos mediante simulaciones numéricas. Se analizaron la distribución de grado, el tamaño de la componente gigante, los coeficientes de clustering medio y global, la homofilia y la distancia media. Además, se estudiaron las mismas magnitudes estructurales para la componente gigante. Se obtuvo un buen acuerdo entre los resultados analíticos y numéricos corroborando así un modelo que permite construir redes con valores prefijados para cada magnitud. Dicho modelo fue utilizado para estudiar numéricamente dos procesos estocásticos orientados a entender la influencia de una topología de red en forma de grupos interconectados en procesos sociales y económicos. Por un lado, se evidenció la aparición de una transición crítica en la propagación de un rumor a lo largo de la red. Se vio que existen dos regímenes determinados por los parámetros estructurales de la misma. En el primero, el rumor no se propaga más allá de un vecindario reducido respecto a su condición inicial y, en el segundo, el rumor llega a ser escuchado por una fracción finita de la red en redes de tamaño infinito. A partir del método de escaleo finito se determinaron valores para el exponente crítico en distintos sistemas. Por otro lado, se estudió la distribución estacionaria de recursos para una dinámica multiplicativa, redistributiva y con reseteo estocástico. A partir de dicho análisis se concluyó que la estructura en forma de comunidades interconectadas produce un mayor acoplamiento entre individuos mientras mayor sea el tamaño de cada comunidad. Además, bajo la dinámica estudiada, cada grupo de individuos se ve principalmente afectado por los individuos de su mismo grupo.
Resumen en inglés
A new class of random networks which can be applied to a wide range of complex systems where interacting agents are divided into communities and each agent can interact with another one from a different community is proposed. The structure of the network was analytically studied using the formalism of random networks with generic degree distributions, obtaining closed expressions for its degree distribution, its clustering coefficients, its assortativity coefficient, its mean distance and the size of its giant component. In addition, the analytical results were verified through numerical simulations and all the mentioned structural properties were numerically studied for the giant component too. All numerical simulations were in good agreement with the analytical results, thus ratifying a model that allows for the generation of networks with predefined values for each parameter. The model was used to computationally study two stochastic processes with the intention of understanding the influence of a network topology shaped as interconnected groups in social and economic systems. The first of them showed the appearance of a critical transition on the propagation of rumors throughout the network. The transition is comprised of two regimes determined by the network’s structure. Within the first regime, the rumor does not propagate any further than a reduced neighborhood near the initial condition. On the contrary, the rumor reaches a finite fraction of the random network in infinite-sized systems within the second regime. Values for the critical exponent were determined using the finite-size scaling method on networks with different structures. Finally, the study of the stationary resource distribution of a multiplicative and redistributive process with stochastic resetting allowed to conclude that the interconnected community structure of the network produces a greater coupling between individuals when the size of each community increases. Moreover, under this redistributive process each agent is mainly affected by the other individuals in its same community.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
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| Palabras Clave: | [Complex network; Red compleja; Clique; Clique; Giant component; Componente gigante; Socioeconic systems; Sistemas Socioeconómicos; Critical transition; Transición crítica; Stochastic resetting; Reseteo estocástico] |
| Referencias: | [1] Barabasi, A.-L., Posfai, M. Network science. Cambridge: Cambridge University Press, 2016. URL http://barabasi.com/networksciencebook/. 1 [2] Newman, M. Networks: An Introduction. Oxford University Press, 2012. URL https://doi.org/10.1093/oso/9780198805090.001.0001. 1 [3] Newman, M., Barabasi, A., Watts, D. The Structure and Dynamics of Networks:. Princeton Studies in Complexity. Princeton University Press, 2006. URL https://books.google.com.ar/books?id=6LvQIIP0TQ8C. 1 [4] Small, M., Hou, L., Zhang, L. Random complex networks. National Science Review, 1 (3), 357–367, 07 2014. URL https://doi.org/10.1093/nsr/nwu021. 1 [5] Erdos, P., Renyi, A., et al. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci, 5 (1), 17–60, 1960. 1 [6] Newman, M. E. J., Strogatz, S. H., Watts, D. J. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E, 64, 026118, Jul 2001. URL https://link.aps.org/doi/10.1103/PhysRevE.64.026118. 2, 8 [7] Zanette, D. H. Statistical properties of model kinship networks. Journal of Statistical Mechanics: Theory and Experiment, 2019 (9), 094008, sep 2019. URL https://dx.doi.org/10.1088/1742-5468/ab3720. 2 [8] Bellomo, N., Marsan, G. A., Tosin, A. Complex Systems and Society: Modeling and Simulation. Springer New York, 2013. 3 [9] Hagberg, A. A., Schult, D. A., Swart, P. J. Exploring network structure, dynamics, and function using networkx. En: G. Varoquaux, T. Vaught, J. Millman (eds.) Proceedings of the 7th Python in Science Conference, p´ags. 11 – 15. Pasadena, CA USA, 2008. 3, 63 [10] Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., et al. Array programming with NumPy. Nature, 585 (7825), 357–362, sep. 2020. URL https://doi.org/10.1038/s41586-020-2649-2. 4, 63 [11] Dorogovtsev, S. N. Lectures on Complex Networks. Oxford University Press, 2010. 8 [12] Tishby, I., Biham, O., Katzav, E., K¨uhn, R. Revealing the microstructure of the giant component in random graph ensembles. Phys. Rev. E, 97, 042318, Apr 2018. URL https://link.aps.org/doi/10.1103/PhysRevE.97.042318. 8 [13] Watts, D. J., Strogatz, S. H. Collective dynamics of ‘small-world’networks. nature, 393 (6684), 440–442, 1998. 10 [14] Newman, M. E. J., Watts, D. J., Strogatz, S. H. Random graph models of social networks. Proceedings of the National Academy of Sciences, 99 (suppl 1), 2566–2572, 2002. URL https://www.pnas.org/doi/abs/10.1073/pnas.012582999. 10 [15] Kaiser, M. Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. New Journal of Physics, 10 (8), 083042, aug 2008. URL https://dx.doi.org/10.1088/1367-2630/10/8/083042. 10 [16] Barrenas, F., Chavali, S., Holme, P., Mobini, R., Benson, M. Network properties of complex human disease genes identified through genome-wide association studies. PLOS ONE, 4 (11), 1–6, 11 2009. URL https://doi.org/10.1371/journal.pone.0008090. 12 [17] Fronczak, A., Fronczak, P., Ho lyst, J. A. Average path length in random networks. Physical Review E, 70 (5), nov 2004. 14 [18] Schank, T.,Wagner, D. Approximating clustering coefficient and transitivity. Journal of Graph Algorithms and Applications, 9 (2), 265–275, 2005. 26 [19] Barrat, A., Barthelemy, M., Vespignani, A. Dynamical Processes on Complex Networks. Cambridge University Press, 2008. 35 [20] María Jose Muñoz Torrecillas, R. Y., McKelvey, B. Identifying the transition from efficient-market to herding behavior: Using a method from econophysics. Journal of Behavioral Finance, 17 (2), 157–182, 2016. 35 [21] Bossomaier, T., Barnett, L., Harre, M. Information and phase transitions in socioeconomic systems. Complex Adaptive Systems Modeling, 1 (1), 2013. 35 [22] Deb, S., Bhandary, S., Sinha, S. K., Jolly, M. K., Dutta, P. S. Identifying critical transitions in complex diseases. Journal of Biosciences, 47 (2), 2022. 35 [23] Jurczyk, J., Rehberg, T., Eckrot, A., Morgenstern, I. Measuring critical transitions in financial markets. Scientific Reports, 7 (1), 2017. 35 [24] Zanette, D. H. Critical behavior of propagation on small-world networks. Phys. Rev. E, 64, 050901, Oct 2001. URL https://link.aps.org/doi/10.1103/PhysRevE.64.050901. 35 [25] Zanette, D. H. Dynamics of rumor propagation on small-world networks. Phys. Rev. E, 65, 041908, Mar 2002. URL https://link.aps.org/doi/10.1103/PhysRevE.65.041908. 35 [26] Newman, M. E. J., Barkema, G. T. Monte Carlo methods in statistical physics. Oxford, England: Clarendon Press, 1998. 41 [27] Fisher, M. E., Barber, M. N. Scaling theory for finite-size effects in the critical region. Phys. Rev. Lett., 28, 1516–1519, Jun 1972. URL https://link.aps.org/doi/10.1103/PhysRevLett.28.1516. 41 [28] Binder, K., Heermann, D. W. Monte Carlo Simulation in statistical physics an introduction. Springer, 1992. 41 [29] Zanette, D. H., Manrubia, S. Fat tails and black swans: Exact results for multiplicative processes with resets. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30 (3), 033104, 03 2020. URL https://doi.org/10.1063/1.5141837. 45 [30] Garay, I. T. G., Zanette, D. H. Collective behavior of coupled multiplicative processes with stochastic resetting. Journal of Physics: Complexity, 2 (3), 035020, sep 2021. URL https://dx.doi.org/10.1088/2632-072X/ac2070. [31] Gómez Garay, I. T., Zanette, D. H. Resource concentration and clustering in replicator dynamics with stochastic reset events. Entropy, 25 (1), 2023. URL https://www.mdpi.com/1099-4300/25/1/99. 45 |
| Materias: | Física > Física estadística |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Física estadística interdisciplinaria |
| Código ID: | 1248 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 12 Sep 2024 14:50 |
| Última Modificación: | 12 Sep 2024 14:50 |
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