09h30-10h: Registration (and payment of the fee) in front of Auditório 2 with Prof. Sandro Gallo.

10h-10h50: Frédéric Paccaut (U. Picardie Jules Verne)
A model for invasive dynamics in a stochastic environment
Abstract: We build a model to describe the invasive dynamics of Prunus Serotina Ehrh. in Europe. This model is spatially explicit and deals with stage-structured populations in a stochastic environement. The mathematical tools involved are markov chains and random products of matrices.

11h-11h50: Arnaud Le Ny (U. Paris-Est)
On the mathematical consequences of binning spike trains in neuroscience
Abstract: In this talk, we shall investigate the Markov and Gibbs properties inherited from the Binning procedure used in neurobiology the analyse the so-called spike-trains of the neuronal activities in the brain. We shall relate this technical binning procedure to scaling or renormalizing transformations in mathematical statistical mechanics and theoretical physics and investigate the conservation or loss of the Markovian property -- of measures invariant under one-sided (past) conditional probabilities -- and compare it to the Gibbsian one -- of measures invariant under two-sided (past and future) conditional probabilities --. Joint work with B. Cessac (Nice) and E. Löcherbach (Cergy).

12h-14h: Lunch

14h-14h50: Julio Singer (IME-USP)
n=?
Abstract: Perguntas sobre qual o tamanho da amostra necessário para a “validade” ou “representatividade” de estudos provenientes das mais diferentes áreas são frequentes na prática estatística. Embora este seja um problema bastante estudado e amplamente difundido na literatura pertinente, sua solução em casos concretos nem sempre pode seguir as receitas básicas, pois usualmente envolve características do planejamento do estudo em questão e não raramente, o desconhecimento de aspectos fundamentais do método estatístico por parte dos investigadores responsáveis. Por essa razão, geralmente exige que a informação essencial para esse propósito seja extraída a fórceps. Por meio de exemplos práticos, mostraremos como as soluções comummente apresentadas para alguns casos básicos podem ser adaptadas para situações mais complexas. Em particular, discutiremos a necessidade de utilização de triplicatas, uma prática bastante adotada em experimentos da área de Farmácia, Nutrição, etc.

15h-15h50: Giulio Iacobelli (COPPE-UFRJ)
Growing Networks with Random Walks
Abstract: The growth and evolution of real networks is a fundamental theme in Network Science. Prominent examples of growing networks are the Web, where new web pages and hyperlinks are constantly added, and social networks such as Facebook, where new user accounts and new friendship relations are continuously created. Explaining how and why different real networks grow and evolve the way they do has kept researchers busy for the past decades. Not surprisingly, various mathematical models for network growth have been proposed in the literature. A celebrated network growth model is the Barabási-Albert (BA) model which embodies the principle of preferential attachment, also known as rich-get-richer phenomenon. A recognized drawback of most proposed network growth models is the assumption of global information about the network. For example, the BA model requires the knowledge of the degree of every node in the network to randomly choose where a new node will be connected. In an attempt to better describe reality, more recent network growth models embody local rules of attachment, however they still require some kind of global knowledge about the network(for example, the size of the network).
In this work we propose and explore a network growth model that is purely local. The model is based on a continuously moving random walk that after s steps connects a new node to its current location. Through extensive simulations and theoretical arguments, we analyze the behavior of the model finding a fundamental dependency on the parity of s, where networks with either exponential or heavy-tailed degree distribution can emerge. As s increases, parity dependency diminishes and the model recovers the degree distribution of BA preferential attachment model. The proposed purely local model indicates that networks can grow to exhibit interesting properties even in the absence of any global information.
Joint work with Bernardo Amorim, Daniel Figueiredo, and Giovanni Neglia.

16h-16h30: Coffee Break

16h30-17h30: Nancy L. Garcia (IMECC-UNICAMP)
Interacting cluster point process model for epidermal nerve fibers
Abstract: Epidermal nerve bers (ENFs) are sensory fibers that originate in the dermis and terminate in the epidermis, the outermost layer of the skin. The data consist of the location of the origin of a nerve fiber bundle as well as the final location of each ENF. The original data are three-dimensional and come in voxels of base 330 432 microns, with depth varying between 20 and 50 microns. Like the other studies mentioned above, we will consider this as a planar process. We will focus on a data set obtained from the thigh of a healthy patient.The central idea of this work is to obtain a repulsive cluster point process that models the ENF's. The process will be obtained as the invariant measures of birth and death cluster processes.