The Research, Innovation and Dissemination Center for Neuromathematics (NeuroMat), hosted by the University of Sao Paulo, Brazil, and funded by FAPESP (São Paulo Research Foundation), is offering several postdoctoral fellowships for recent PhDs with outstanding research potential.

Alfredo N. Iusem, Alejandro Jofré, Roberto I. Oliveira, and Philip Thompson

In this paper, we propose dynamic sampled stochastic approximated (DS-SA) extragradient methods for stochastic variational inequalities (SVIs) that are *robust* with respect to an unknown Lipschitz constant $L$. We propose, to the best of our knowledge, the first provably convergent *robust* SA *method with variance reduction*, either for SVIs or stochastic optimization, assuming just an unbiased stochastic oracle within a large sample regime. This widens the applicability and improves, up to constants, the desired efficient acceleration of previous variance reduction methods, all of which still assume knowledge of $L$ (and, hence, are not robust against its estimate). Precisely, compared to the iteration and oracle complexities of $\mathcal{O}(\epsilon^{-2})$ of previous robust methods with a small stepsize policy, our robust method uses a DS-SA line search scheme obtaining the faster iteration complexity of $\mathcal{O}(\epsilon^{-1})$ with oracle complexity of $(\ln L)\mathcal{O}(d\epsilon^{-2})$ (up to log factors on $\epsilon^{-1}$) for a $d$-dimensional space. This matches, up to constants, the sample complexity of the sample average approximation estimator which does not assume additional problem information (such as $L$). Differently from previous robust methods for ill-conditioned problems, we allow an unbounded feasible set and an oracle with *multiplicative noise* (MN) whose variance is not necessarily uniformly bounded. These properties are appreciated in our complexity estimates which depend only on $L$ and *local* variances or fourth moments at solutions. The robustness and variance reduction properties of our DS-SA line search scheme come at the expense of *nonmartingale-like dependencies* (NMDs) due to the needed inner statistical estimation of a lower bound for $L$. In order to handle an NMD and an MN, our proofs rely on a novel *iterative localization* argument based on empirical process theory.

The whole paper is available here.

Leonardo Dalla Porta and Mauro Copelli

We revisit the CROS (“CRitical OScillations”) model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.

The RIDC NeuroMat research team has put forward a rigorous mathematical model for short-term plasticity. This type of plasticity has been the object of studies since at least the mid 90s, and a recent paper by Antonio Galves, Eva Löcherbach, Christophe Pouzat and Errico Presutti has now proposed a simple probabilistic model describing this phenomenon within a large network of neurons.

Carlos Hoppen, Roberto F. Parente and Cristiane M. Sato

We study the problem of packing arborescences in the random digraph D(n, p), where each possible arc is included uniformly at random with probability p = p(n). Let λ(D(n, p)) denote the largest integer λ ≥ 0 such that, for all 0 ≤ ≤ λ, we have −1 i=0 ( − i)|{v : din(v) = i}| ≤ . We show that the maximum number of arc-disjoint arborescences in D(n, p) is λ(D(n, p)) a.a.s. We also give tight estimates for λ(D(n, p)) depending on the range of p. Keywords: random graph, random digraph, edge-disjoint spanning tree, spanning tree, packing arborescence.

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