Georgia Institute of Technology College of Sciences

We consider weighted random ball model driven by a Poisson random measure on \Bbb{R}^d\times \Bbb{R}^+\times \Bbb{R} with product heavy tailed intensity and we are interested in the functional describing the contribution of the model in some configurations of \Bbb{R}^d. The fluctuations of such functionals are investigated under different types of scaling and the talk will discuss the possible limits. Such models arise in communication network to represent the transmission of information emitted by stations distributed according to the Poisson measure.

We study four discrete time stochastic systems on $\bbN$ modelingprocesses of rumour spreading. The involved individuals can eitherhave an active ora passive role, speaking up or asking for the rumour. The appetite inspreading or hearing the rumour is represented by a set of randomvariables whose distributionsmay depend on the individuals. Our goal is to understand - based on those randomvariables distribution - whether the probability of having an infiniteset of individuals knowing the rumour is positive or not.

Semimartingales constitute the larges class of "good integrators" for which Ito integral could reasonably be defined and the stochastic analysis machinery applied. In this talk we identify semimartingales within certain infinitely divisible processes. Examples include stationary (but not independent) increment processes, such as fractional and moving average processes, as well as their mixtures. Such processes are non-Markovian, often possess long range memory, and are of interest as stochastic integrators. The talk is based on a joint work with Andreas Basse-O'Connor.

 Let (X,Y) be a random couple with unknown distribution P, X being an observation and Y - a binary label to be predicted. In practice, distribution P remains unknown but the learning algorithm has access to the training data - the sample from P. It often happens that the cost of obtaining the training data is associated with labeling the observations while the pool of observations itself is almost unlimited. This suggests to measure the performance of a learning algorithm in terms of its label complexity, the number of labels required to obtain a classifier with the desired accuracy. Active Learning theory explores the possible advantages of this modified framework.We will present a new active learning algorithm based on nonparametric estimators of the regression function and explain main improvements over the previous work.Our investigation provides upper and lower bounds for the performance of proposed method over a broad class of underlying distributions.