A class on statistical regularities and statistical model selection. Lecturer: Prof. Antonio Galves, NeuroMat principal investigator and professor at the University of São Paulo's Institute of Mathematics and Statistics.

Introductory class on techniques and tools to manage scientific data, focusing on sources of information and data analysis. Lecturer: Prof. Kelly Rosa Braghetto, a NeuroMat associate investigator and a professor at the University of São Paulo's Department of Computer Science.

*P. Allen, Y. Kohayakawa, G. O. Mota, R. F. Parente*

Let H⃗ be an orientation of a graph H. Alon and Yuster proposed the problem of determining or estimating D(n,m,H⃗), the maximum number of H⃗-free orientations a graph with n vertices and m edges may have. We consider the maximum number of H⃗-free orientations of typical graphs G(n,m) with *n* vertices and *m* edges. Suppose H⃗ =C↻ℓ is the directed cycle of length ℓ≥3. We show that if m≫n^(1+1/(ℓ−1)), then this maximum is 2^o(m), while if m≪n^(1+1/(ℓ−1)), then it is 2^(1−o(1))m.

*Allen, P.; Böttcher, J.; Kohayakawa, Y. and Person Y.*

We give an algorithmic proof for the existence of tight Hamilton cycles in a random r-uniform hypergraph with edge probability p=n^{-1+eps} for every eps>0. This partly answers a question of Dudek and Frieze [Random Structures Algorithms], who used a second moment method to show that tight Hamilton cycles exist even for p=omega(n)/n (r>2) where omega(n) tends to infinity arbitrary slowly, and for p=(e+o(1))/n (r>3). The method we develop for proving our result applies to related problems as well.

NeuroMat released at the end of September the First Report of Activities. This document is required by the São Paulo Research Foundation (FAPESP), the funding entity of the Research, Innovation and Dissemination Center for Neuromathematics (CEPID NeuroMat), and presented detailed accounts of scientific, dissemination and technology-transfer activities.