Conferencias

TBA

Stochastic chains with variable length memory define an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called "context", is enough to predict the next symbol. The set of contexts can be represented by a rooted tree with finite labeled branches. The law of the chain is characterized by its tree of contexts and by an associated family of transition probabilities indexed by the tree.
In my talk I will present a recent result which says that even in the unbounded case, these chains have a "visible" regenerative scheme. As an application I will show how to make a perfect simulation of a chain with unbounded context tree. This is a joint work with A. Gallo and D. Maia.

In this talk i will present a joint work with Anis Ben Ishak. In statistical learning we model the relation between an output variable and a set of explanatory variables using data. In multiclass classification the output variable is discrete with more than two levels. As usual we wish to learn the model generating the data, with the constraint that the sample size is too small relatively to the number of explanatory variables. We will show how we can select the most important variables within the learning task, using multiclass support vector machines.

This talk describes a new paradigm we propose to analyze the performance of nodes in a communication network. Assume the following textbook situation: variable-size packets arrive at an output link of a node according to a Poisson process (of course, unrealistic) with rate r in pps (packets per sec). The buffer associated with the link is large enough, so we neglect losses. The link speed is constant and equal to c bps (bits per sec). The packets have a very variable length in bits, and we decide to represent it by an exponential random variable with mean B in bits. The question is: how much memory is occupied in the buffer, on the average, if the system is stable and in equilibrium? The standard answer is: at the packet level, this is an M/M/1 model with arrival rate r pps and service rate c/B pps. The system is stable iff r < c/B and, in that case, the average occupied memory is B rho /(1 - rho) bits, where rho = r/(c/B) < 1 is the load of the system.

We claim that this answer misrepresents the dynamics of the system, without any change in the assumptions above. This happens because of the implicit assumptions about the way memory is used hidden in the standard answer, and, in particular, the way memory is freed. We provide an alternative analysis taking into account the usual way memory is managed in a communication node. The analysis is done in the more general M/G/1 setting, leading to a new Pollaczec-Khintchine-like formula. We also provide some supplementary results in other situations, all illustrating the same phenomenon, together with material concerning the joint distribution of all packets’ lengths in the queue in the M/M/1 case.

The talk is based on an joint work with V. Beffara and V. Sidoravicius. We study a variant of poly-nuclear growth where the level boundaries perform continuous-time, discrete-space random walks, and study how its asymptotic behavior is affected by the presence of a columnar defect on the line. We show that there is a non-trivial phase transition in the strength of the perturbation, above which the law of large numbers for the height function is modified.

TBA