Talks 2014

Organizers: Pablo Rodriguez and Francisco Rodrigues.

Abstracts

Atividade espontânea e avalanches em dinâmica neural

Speaker: Leonardo Maia (IFSC-USP)
Date: 24/10/2014 • Time: 16h00 • Room: 4-111

Abstract: Os progressos tecnológicos em computação e instrumentação científica nas duas últimas décadas abriram importantes linhas de pesquisa em Neurociência. O notável aumento na capacidade de aquisição e processamento de sinais eletrofisiológicos tem levado a um "dilúvio de dados" cuja interpretação é desafiadora e exige abordagens teórico/computacionais. Neste seminário, vou discutir algumas investigações que vêm sendo desenvolvidas nesse contexto, enfatizando em particular algumas abordagens que sugerem (i) que conceitos de criticalidade da física estatística podem ser relevantes na análise de "avalanches" de atividade neural e (ii) que, em algumas situações, os padrões estatísticos de respostas estimuladas de redes neurais podem ser praticamente independentes da natureza dos estímulos, de modo que a atividade espontânea desses redes (determinada por sua topologia) pode ser preditiva para algumas de suas propriedades funcionais (sob estímulo).

Backbends in oriented percolation

Speaker: Rahul Roy (Indian Statistical Institute)
Date: 30/10/2014 • Time: 10h00 • Room: 4-111

Abstract: When percolation occurs in a bond percolation process, any path to infinity will zigzag along the lattice. Backbends are the parts of these zigzags which go against the direction in an oriented percolation setup. In the regime where bond percolation occurs but oriented percolation does not, is it possible to find paths with restricted backbends (i.e. restricted zigzags) along which percolation occurs? We discuss this question and other questions connected with backbend percolation.

Um Sistema de Partículas 'Diferente': Teoria Quântica dos Campos (em Poucos Minutos...)

Speaker: Paulo Afonso Faria da Veiga (ICMC-USP)
Date: 17/10/2014 • Time: 16h00 • Room: 4-111

Abstract: Para fixar as bases para um futuro seminário envolvendo EDPs Estocásticas, pretendemos apresentar o que é uma teoria quântica de campos, na formulação da integral funcional no espaço-tempo Euclideano. Para tal, iniciaremos com uma discussão da fórmula de Feynman-Kac num contexto da mecânica quântica. Apresentaremos os principais problemas matemáticos envolvidos e percorreremos historicamente como estes problemas foram atacados e resolvidos em alguns casos. Tocaremos nas questões da existência do limite termodinâmico, da renormalização perturbativa e da renormalização não perturbativa. Para esta última, apresentaremos como métodos de análise multi-escala vem ao nosso socorro (grupo de renormalização), o que faz contato com o universo dos sistemas dinâmicos. Claramente, não temos a possibilidade de percorrer todos esses temas com detalhes e rigor satisfatórios. Nossa meta é apresentar o quadro geral. Depois, caso haja interesse e com mais tempo, podermos aprofundar na discussão.

The weighted Gibbs inequality and its consequences

Speaker: Salimeh Yasaei Sekeh (UFScar)
Date: 03/10/2014 • Time: 16h00 • Room: 4-111

Abstract: In various applications of Information Theory, different events/outcomes may depend upon experiments goal or be influenced by some qualitative characteristics of the physical system which should be taken into account. That is, they may have different utilities (or weights). Belis and Guiasu (1968) introduced weighted uncertainty by ascribing to each out-come a non-negative weight which measures its importance.

The purpose of this talk is to extend the well-known Gibbs inequality to the case of weighted entropies with weighted function φ. A number of inequalities for weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. This is a joint work with Yuri Suhov, Department of Mathematics, Penn State University, USA; DPMMS, University of Cambridge, UK
Keywords: weighted entropy, weighted conditional entropy, weighted relative entropy, weighted mutual entropy, weighted Gibbs inequality, convexity, concavity.

Matrizes aleatórias: alguns fundamentos e algumas aplicações

Speaker: Marcel Novaes (UFU)
Date: 22/09/2014 • Time: 16h00 • Room: TBA

Abstract: Faremos um passeio pelos fundamentos da Teoria de Matrizes Aleatórias, apresentando os conceitos básicos e alguns resultados importantes. Depois, discutiremos brevemente algumas aplicações. O nível do seminário será bastante acessível

Ornstein and Weiss theorem for entrance time

Speaker: Alejandra Rada (IME-USP)
Date: 19/09/2014 • Time: 17h10 • Room: 4-111

Abstract: For ergodic systems with generating partitions, the well known result of Ornstein and Weiss shows that the exponential growth rate of the recurrence time is almost surely equal to the metric entropy. Here we look at the exponential growth rate of entrance times, and show that it equals the entropy, where the convergence is in probability in the product measure. This is however under the assumptions that the limiting entrance times distribution exists almost surely.

Critical line for a Potts model coupled to causal triangulations

Speaker: José Javier Cerda Hernández (IME-USP)
Date: 19/09/2014 • Time: 16h00 • Room: 4-111

Abstract: We present a new approach for identifying a region of location of the critical curve for the Potts model coupled to two-dimensional causal triangulations (CT's). The approach is based on the relation between the free energy of the Potts model coupled to two-dimensional causal triangulations (CT's), and its dual. The provided relation is derived by implementation the duality of graph technique on a torus, and is based on the FK representation for the Potts model. Having obtained the duality relation, we propose to utilize it together with the FK representation and the high-temperature expansion in order to determine a region in the quadrant of parameters where the critical curve for the Potts model coupled to CT's can be located. This can be carried out by outlining a region where the infinite-volume Gibbs measure exists and is unique, and a region where the finite-volume Gibbs measure does not have a weak limit (intrinsically, does not exist if the volume is large enough).

Sincronização de Osciladores de Kuramoto em Redes Complexas

Speaker: Thomas Kauê Dal Maso Peron (IFSC-USP)
Date: 16/09/2014 • Time: 17h00 • Room: 4-111

Abstract: Diversos tipos de sistemas complexos podem ser descritos em termos de redes complexas, como por exemplo, redes de distribuição de energia, redes metabólicas, Internet e redes sociais. O conceito matemático de redes tornou-se recentemente uma importante ferramenta na descrição destes sistemas, onde a principal característica á a presença de um grande número de unidades dinâmicas discretas acopladas entre si atravás de estruturas heterogêneas e não-triviais. A teoria de redes complexas tem como objetivo explicar a estrutura das interações entre as subunidades destes sistemas de modo a compreender o seu funcionamento bem como processos dinâmicos que ocorrem nestas topologias. Esforços neste quesito concentram-se em compreender, por exemplo, como a estrutura de redes sociais afeta a propagação de informação e doenças infecciosas ou atá mesmo como os padrões de conexões da World Wide Web influenciam mecanismos de busca. Neste trabalho, estudamos como a topologia influencia a emergência de comportamento coletivo em uma população de osciladores. Mais precisamente, analisamos processos de sincronização em redes complexas cuja topologia local apresenta ciclos de ordem 3, utilizando generalizações recentemente propostas para o modelo configuracional de geração de redes. Desenvolvendo aproximações de campo mádio nessas redes, mostramos que tais ciclos pouco influenciam a sincronizabilidade de redes, podendo esta ser descrita por aproximações de campo mádio para redes com estrutura local semelhante a grafos de tipo árvore. Ademais, generalizamos o modelo de Kuramoto de segunda-ordem para redes complexas sem correlação de grau, resultado inátido atá então na literatura, verificando que osciladores aderem ao componente síncrono em grupos de nós de mesma conectividade, fenômeno o qual denominamos cluster explosive synchronization.

A Fintite-Element-Method model to assess the shape variance in neuronal spike signals

Speaker: Robert Bestel (University of Applied Sciences Aschaffenburg)
Date: 12/09/2014 • Time: 17h00 • Room: 4-111

Abstract: To study the electrophysiological properties of neuronal networks, in vitro studies based on microelectrode arrays (MEA) have become one of the most used approaches. Yet, a detailed analysis of the measured signals still remains one of the most challenging tasks in this context. The main reason for this is an observable inconsistency in the electrical signals, which can be derived from an individual neuron. Hence it is quite complex to define the actual activity of a specific neuron and its influence on the whole network, since the measured in vitro signals cannot be assigned easily. Furthermore the actual processes behind this signal fluctuation have not been clearly determined or their influence assessed yet, making the issue even more complicated. In order to address this lack of a priori knowledge we propose a FEM simulation approach, that models the electrical processes of a distinct neuron accurately in a three-dimensional in vitro environment. The described modelling approach covers not only an electrical active neuron based on the Hodgkin-Huxley equation system, but also addresses the effects of the different compartments in the physical neuron structure (e.g. dendrites, soma, axon-hillock, axon). Furthermore the effects of the derived in vitro signal with respect to the spatial geometry and morphology of the neuron-electrode coupling are discussed and analysed, in order to define a set of possible sources or origins that can be made accountable for the observable variance in measured neuron signals.

Constrained information transmission on Erdös-Rényi graphs

Speaker: Christophe Gallesco (IMECC-UNICAMP)
Date: 05/09/2014 • Time: 16h00 • Room: 4-111

Abstract: We model the transmission of information of a message on the Erdös-Rényi random graph with parameters $(n,p)$ and limited resources. The vertices of the graph represent servers that may broadcast a message at random. Each server has a random emission capital that decreases by one at each emission. We examine two natural dynamics: in the first dynamics, an informed server performs its attempts, then checks at each of them if the corresponding edge is open or not; in the second dynamics the informed server knows a priori who are its neighbors, and it performs all its attempts on its actual neighbors in the graph. In each case, we obtain first and second order asymptotics (law of large numbers and central limit theorem), when $n\to \infty$ and $p$ is fixed, for the final proportion of informed servers.

Relationship between the Fundamental Theorem of Probability and de Finetti's Representation Theorem

Speaker: Márcio Diniz (UFSCar)
Date: 22/08/2014 • Time: 16h00 • Room: 4-111

Abstract: Nesta palestra pretendo mostrar como o teorema da representação pode ser visto como um caso particular do teorema fundamental da probabilidade. Tal relação foi demonstrada primeiramente por Marcel Riesz: em sua demonstração Riesz se valeu (de uma versão preliminar) do teorema de Hahn-Banach para demonstrar o teorema dos momentos de Hausdorff, equivalente ao teorema da representação de de Finetti. Todos esses resultados foram de fundamental importância para o desenvolvimento das teorias de análise funcional e cálculo de probabilidades ao longo do século XX.

Uso de redes complexas para classificação em textos

Speaker: Diego Raphael Amancio (ICMC-USP)
Date: 27/06/2014 • Time: 16h00 • Room: 4-111

Abstract: A classificação automática de textos em categorias pré-estabelecidas tem atraído um crescente interesse na comunidade científica devido à necessidade de organização do grande número de documentos disponíveis eletronicamente. Como alternativa à estratégia tradicional baseada na análise de conteúdo textual, será apresentada uma abordagem topológica para análise de estilo usando a modelagem de redes complexas (RC), onde vértices representam as palavras e arestas representam as relações de adjacência. Um estudo das medidas será apresentado a fim de classificar as propriedades das medidas no cenário da modelagem de textos e na análise do famoso manuscrito Voynich. Com relação ao uso de RC em cenários práticos, serão apresentados estudos demonstrando a capacidade das RC em tarefas de reconhecimento de autoria, estilo, complexidade e sentidos. Finalmente, a utilidade das medidas topológicas para problemas de classificação será ilustrada através da definição de um classificador híbrido.

The Widom--Rowlinson model and the allelopathy phenomenon

Speaker: Yuri Suhov (University of Cambridge/ICMC-USP)
Date: 05/06/2014 • Time: 15h10 • Room: 4-003

Abstract: The phenomenon of allelopathy is observed when a biological species prevents other species from sharing space (algae, rhododendrons, walnut trees). An opposite development occurs with some types of tumors when abnormal cells overcome allelopathic resistance of healthy cells and grow uncontrollably. The Widom--Rowlinson model proposed in the 1970 in chemistry may be useful for modeling such phenomena. I will discuss some new results about this model, both analytic and numerical.

Optimal stopping for partially observed piecewise-deterministic Markov processes

Speaker: Benoite de Saporta (Inria Bordeaux Sud Ouest, Equipe CQFD)
Date: 29/05/2014 • Time: 17h30 • Room: 3-009

Abstract: This talk deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes (PDMPs). PDMPs have been introduced by Davis in the literature as a general class of stochastic models. They form a family of Markov processes involving deterministic motion punctuated by random jumps. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an epsilon-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence. This is a joint work with Adrien Brandejsky and François Dufour.

Non-singularity of symmetric random matrices

Speaker: Rahul Roy (Indian Statistical Institute)
Date: 29/05/2014 • Time: 16h10 • Room: 3-009

Abstract: We obtain the almost sure non-singularity of general Wigner ensembles of random matrices when the distribution of the entries are independent but not necessarily identically distributed and may depend on the size of the matrix. These models include adjacency matrices of random graphs and also sparse, generalized, universal and banded random matrices. We find universal rates of convergence and precise estimates for the probability of singularity which depend only on the size of the biggest jump of the distribution functions governing the entries of the matrix. Our proofs are based on a concentration function inequality due to Kesten and allows us to improve the known rates of convergence for the Wigner case when the distribution of the entries do not depend on the size of the matrix. This is joint work with Paulo Manrique and Victor Pérez-Abreu.

Asymptotic properties of the softest return path in stochastic processes

Speaker: Miguel Abadi (IME-USP)
Date: 16/05/2014 • Time: 16h00 • Room: 4-111

Abstract: We consider stationary stochastic processes. We consider a sequence of refined partitions of the phase space. For each one of this states, we consider the shortest (topological) that starts and ends on that state. We present theorems that shows its concentration and fluctuation and its relation with the entropy of the process.

Explosive synchronization in complex networks

Speaker: Francisco Rodrigues (ICMC-USP)
Date: 25/04/2014 • Time: 16h00 • Room: 4-111

Abstract: Synchronization is a ubiquitous phenomenon in both the natural world and in technology. Kuramoto oscillators display a second-order phase transition to the synchronous state with a critical coupling strength that depends on the network topology. Recently, it has been observed that a first-order synchronization transition can be observed in complex networks when there is a positive correlation between the heterogeneity of the connections and the natural frequencies of the oscillators. This phenomenon is called explosive synchronization. In this presentation, we consider mean-field approximations to determine the critical coupling of explosive synchronization in complex networks. We demonstrate that the equation obtained for the critical coupling has an inverse dependence on the network average degree. Moreover, we show that the inclusion of time-delay enhances the level of synchronization. Finally, we demonstrate that the nodes in a second-order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

References:
  1. Peng Ji, Thomas K.D. M. Peron, Peter J. Menck, Francisco A. Rodrigues and Jürgen Kurths, Cluster Explosive Synchronization in complex networks, Physical Review Letters, 110, 218701 (2013).
  2. Thomas K. D. M. Peron and Francisco A. Rodrigues, Determining the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations, Physical Review E, vol. 86, issue 5, 056108, (2012).
  3. Thomas K. D. M. Peron and Francisco A. Rodrigues, Explosive synchronization enhanced by time-delayed coupling, Physical Review E, vol. 86, issue 1, 016102 (2012).

Synchronization in clustered random networks

Speaker: Thomas Kauê Dal Maso Peron (IFSC-USP)
Date: 11/04/2014 • Time: 16h00 • Room: 3-009

Abstract: We study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order three does not play an important role on network synchronization, showing that the synchronization of random clustered networks can be described by tree-based theories, even for high values of clustering. In order to support our findings, we provide numerical simulations considering clustered and non-clustered networks, which are in good agreement with our theoretical results.

Reference:
  1. Physical Review E, 87, 032807 (2013)
    http://arxiv.org/abs/1310.3389

Rumor Processes on N and Discrete Renewal Processes

Speaker: Sandro Gallo (Universidade Federal do Rio de Janeiro)
Date: 04/04/2014 •Time: 16h00 • Room: 3-009

Abstract: We study two rumor processes on N, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site 0 and ignorants at all the other sites of N, but differ by the transmission mechanism. In one model, the spreaders transmit the information within a random distance on their right, and in the other the ignorants take the information from a spreader within a random distance on their left. We obtain the probability of survival, information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders. The key step of our proofs is to show that, in each model, the position of the spreaders on N can be related to a suitably chosen discrete renewal process.

Absence of Percolation in Doubling Graphs

Speaker: Cristian Coletti (Universidade Federal do ABC)
Date: 21/03/2014 • Time: 16h00 • Room: 3-009

Abstract: Let \Gamma = (V, E) be a graph satisfying the doubling metric condition. We study sufficient conditions on the distribution of the radius of the balls placed at the points of a point process defined on the graph \Gamma for the absence of percolation, provided that the intensity of the point process is small enough. Joint work with Sebastian P. Grynberg - FIUBA and Daniel Miranda M. - UFABC.