### Stochastic chains with unbounded memory applied in neuroscience

Ricardo Felipe Ferreira is a mathematician who, during his doctoral research, was guided by the RIDC NeuroMat associated investigator Alexsandro Giacomo Grimbert Gallo (UFSCar). During the first semester of 2019, Ferreira defended his doctoral thesis, in which NeuroMat research is a highlight.

### Positions for Postdoctoral Researchers

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.

### Variance-Based Extragradient Methods with Line Search for Stochastic Variational Inequalities

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.

### Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic M/EEG results

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.

### A mathematical model for short-term plasticity

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 recent paper by Antonio Galves, Eva Löcherbach, Christophe Pouzat and has now proposed a simple probabilistic model describing this phenomenon within a large network of neurons.

NeuroCineMat
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