Probabilidad

Resetting a stochastic process from time to time to its initial state can represent an efficient way of finding hidden targets. This property has been applied in statistical physics and computer science, and also allows to understand biological processes such as enzymatic reactions or search strategies adopted by foraging animals. Random walks on general networks and subject to resetting have been very little studied, despite their relevance to epidemic spreading, searching on the web or human mobility. We develop here an extension to an arbitrary network topology of the diffusion problem with stochastic resetting. Our formalism applies to finite undirected networks and is implemented from the spectral properties of the random walk without resetting. We show that resetting can allow a faster exploration of many network architectures such as rings, Cayley trees, random networks and complex networks, highlighting the importance of the choice of the starting/resetting node. The small-world effect and the presence of communities, two properties of many real world networks, strongly affects exploration strategies based on resetting.

Fecha	Expositor	Lugar	Título (haga click para ver el abstract)
29 de enero	Lizbeth Peñaloza Velasco IIMAS UNAM	Salón S-104 Departamento de Matemáticas Facultad de Ciencias	La forma del coalescente seed bank El coalescente seed bank es un modelo genealógico estructurado que aparece en modelos evolutivos para poblaciones de plantas (con bancos de semillas) y también poblaciones de continentes/islas. Los linajes de este coalescente pueden ser activos (plantas) o inactivos (semillas). En esta plática ofrecemos una imagen completa de la forma de este árbol de coalescencia, definiendo tiempos de paro que dividen al árbol en sus diferentes dinámicas. Esta división nos ayudó a demostrar que la longitud total está localizada en la parte inferior del árbol. Finalmente obtuvimos una fórmula de muestreo del estilo de Ewens, dando lugar a algunas herramientas estadísticas para aplicaciones genéticas. Proyecto en conjunto con Adrián González Casanova y Arno Siri-Jégousse.
12 de febrero	Denis Boyer Departamento de Sistemas Complejos Instituto de Física UNAM	Salón 201 IIMAS	Caminatas aleatorias en redes con reinicio estocástico Resetting a stochastic process from time to time to its initial state can represent an efficient way of finding hidden targets. This property has been applied in statistical physics and computer science, and also allows to understand biological processes such as enzymatic reactions or search strategies adopted by foraging animals. Random walks on general networks and subject to resetting have been very little studied, despite their relevance to epidemic spreading, searching on the web or human mobility. We develop here an extension to an arbitrary network topology of the diffusion problem with stochastic resetting. Our formalism applies to finite undirected networks and is implemented from the spectral properties of the random walk without resetting. We show that resetting can allow a faster exploration of many network architectures such as rings, Cayley trees, random networks and complex networks, highlighting the importance of the choice of the starting/resetting node. The small-world effect and the presence of communities, two properties of many real world networks, strongly affects exploration strategies based on resetting.