Título: Time averages of a metastable system of spiking neurons
Palestrante: Morgan André (IME-USP)
Data: 13/12/2021
Horário: 15hrs
Local: Transmissão online
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Resumo: We study a stochastic system of spiking neurons in which the spikes of the neurons are represented by a family of interacting point processes on the positive real line. The model depends on a parameter gamma, representing the intensity of the natural leakage of the neurons. This model has already been proven to exhibit several interesting behaviors. Firstly it undergoes phase transition with respect to the parameter gamma. Moreover the time of extinction of finite versions of the system have been proven to be asymptotically memory-less for small gamma, a characteristic property of metastable systems. Here we show that this last result actually holds in the whole subcritical region and that previous to extinction the finite versions of the system are in a regime which in some sense resemble stationarity. This is the second characteristic property of metastable dynamics. The main idea is to use a bypass through the theory of "Interacting particles systems".
All the talks are held in English.
The videos of the online seminars are available:
For the second semester, a few days after each meeting the video should be available HERE.
Título: Interacting cluster point process model for epidermal nerve fibers (ENF)
Palestrante: Nancy Lopes Garcia (IME-Unicamp)
Data: 06/12/2021
Horário: 15hrs
Local: Transmissão online
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Resumo: We propose an interacting cluster model for the spatial distribution of epidermal nerve fibers (ENF). The model consists of a spatial process of parent points modeling the base points of nerve fiber bundles. To each base point there is an offspring point process of fibers end points associated. The parent process is, possibly, inhibited by fiber endings that belong to different base bundles. The fibers themselves have random length and spatial orientation. We consider a non-orphan process where we can connect each offspring to a parent. Cluster processes with repulsion are rare in the literature. In this work we propose a model based on birth and death processes for which we can approximate the likelihood function. Coefficient estimation can be performed under the Bayesian paradigm via Markov chain Monte Carlo methods.
Joint work with Peter Guttorp and Guilherme Ludwig.
All the talks are held in English.
The videos of the online seminars are available:
For the second semester, a few days after each meeting the video should be available HERE.
Título: Fast Consensus and Metastability in a Highly Polarized Social Network
Palestrante: Antonio Galves (IME-USP and NeuroMat)
Data: 22/11/2021
Horário: 15hrs
Local: Transmissão online
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Resumo: Discrepancy between the results of electoral intentions carried out a few days before the actual voting and the electoral poll results during the first round of the 2018 presidential elections in Brazil was striking. At the time, it was conjectured that this discrepancy was the result of social-media campaigning days before the elections. The question remains: is social-media campaigning enough to change the voting intention of a significant portion of voters? To provide an answer to this question was the initial motivation for this work. The model we consider is a system with a large number of interacting marked point processes with memory of variable length. Each point process indicates the successive times in which a social actor expresses a "favorable'' (+1) or "contrary'' (-1) opinion on a certain subject. The social pressure on an actor determines the orientation and the rate at which he expresses opinions. When an actor expresses their opinion, social pressure on them is reset to 0, and simultaneously social pressure on the other actors is changed by one unit in the direction of the opinion that was just expressed. The network has a polarization coefficient that indicates the tendency of social actors to express an opinion in the same direction of the social pressure exerted on them. We show that when the polarization coefficient diverges consensus is reached almost instantaneously. Moreover, in a highly polarized network, consensus has a metastable behavior and changes its direction after a long and unpredictable random time. This is a joint work and a joint talk with Kádmo de Souza Laxa.
All the talks are held in English.
The videos of the online seminars are available:
For the second semester, a few days after each meeting the video should be available HERE.
Título: Models selection procedures for random objects driven by context tree models
Palestrante: Aline Duarte (IME-USP)
Data: 29/11/2021
Horário: 15hrs
Local: Transmissão online
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Resumo: In several research problems we deal with stochastic sequences of inputs from which a volunteer generates a corresponding sequence of responses and it is of interest to model the relation between them. A new class of stochastic processes, namely sequences of random objects driven by context tree models, has been introduced to model this relation. In the talk I will formalize this class of stochastic processes and present model selection procedures to make inference on it.
All the talks are held in English.
The videos of the online seminars are available:
For the second semester, a few days after each meeting the video should be available HERE.
Título: Random Walks on Random Cayley Graph
Palestrante: Sam Olesker-Taylor, University of Bath
Data: 10/11/2021
Horário: 13:00hrs
Local: Transmissão online
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ID da reunião: 958 0581 3232
Resumo: We investigate mixing properties of RWs on random Cayley graphs of a finite group G with k ≫ 1 independent, uniformly random generators. Denote this Gₖ. Assume that 1 ≪ log k ≪ log |G|. Aldous and Diaconis (1985) conjectured that the RW exhibits cutoff for any group G whenever k ≫ log |G| and further that the time depends only on k and |G|. This was verified for Abelian groups by Dou and Hildebrand (1994, 1996). Their upper bound holds for all groups. We establish cutoff for the RW on Gₖ for all Abelian groups when 1 ≪ k ≲ log |G|, subject to some 'almost necessary' conditions. We also exhibit a non-Abelian matrix group which contradicts the second part of the AD conjecture. Lastly, we upper bound the mixing time of a RW on a nilpotent group by that of the RW on a corresponding Abelian group.
