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 (Sao Paulo Research Foundation), is offering several postdoctoral fellowships for recent PhDs with outstanding research potential.

The lower tail of random quadratic forms, with applications to ordinary least squares and restricted eigenvalue properties

Roberto Imbuzeiro Oliveira

Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the one-dimensional marginals of the random vectors. A similar result holds for more general sums of random positive semidefinite matrices, and the (relatively simple) proof uses a variant of the so-called PAC-Bayesian method for bounding empirical processes.
We give two applications of the main result. In the first one we obtain a new finite-sample bound for ordinary least squares estimator in linear regression with random design. Our result is model-free, requires fairly weak moment assumptions and is almost optimal. Our second application is to bounding restricted eigenvalue constants of certain random ensembles with "heavy tails". These constants are important in the analysis of problems in Compressed Sensing and High Dimensional Statistics, where one recovers a sparse vector from a small umber of linear measurements. Our result implies that heavy tails still allow for the fast recovery rates found in efficient methods such as the LASSO and the Dantzig selector. Along the way we strengthen, with a fairly short argument, a recent result of Rudelson and Zhou on the restricted eigenvalue property.

Synaptic Homeostasis and Restructuring across the Sleep-Wake Cycle

Wilfredo Blanco ,Catia M. Pereira ,Vinicius R. Cota ,Annie C. Souza ,César Rennó-Costa,Sharlene Santos,Gabriella Dias,Ana M. G. Guerreiro,Adriano B. L. Tort,Adrião D. Neto,Sidarta Ribeiro

Sleep is critical for hippocampus-dependent memory consolidation. However, the underlying mechanisms of synaptic plasticity are poorly understood. The central controversy is on whether long-term potentiation (LTP) takes a role during sleep and which would be its specific effect on memory. To address this question, we used immunohistochemistry to measure phosphorylation of Ca^2+/calmodulin-dependent protein kinase II (pCaMKIIα) in the rat hippocampus immediately after specific sleep-wake states were interrupted. Control animals not exposed to novel objects during waking (WK) showed stable pCaMKIIα levels across the sleep-wake cycle, but animals exposed to novel objects showed a decrease during subsequent slow-wave sleep (SWS) followed by a rebound during rapid-eye-movement sleep (REM). The levels of pCaMKIIα during REM were proportional to cortical spindles near SWS/REM transitions. Based on these results, we modeled sleep-dependent LTP on a network of fully connected excitatory neurons fed with spikes recorded from the rat hippocampus across WK, SWS and REM. Sleep without LTP orderly rescaled synaptic weights to a narrow range of intermediate values. In contrast, LTP triggered near the SWS/REM transition led to marked swaps in synaptic weight ranking. To better understand the interaction between rescaling and restructuring during sleep, we implemented synaptic homeostasis and embossing in a detailed hippocampal-cortical model with both excitatory and inhibitory neurons. Synaptic homeostasis was implemented by weakening potentiation and strengthening depression, while synaptic embossing was simulated by evoking LTP on selected synapses. We observed that synaptic homeostasis facilitates controlled synaptic restructuring. The results imply a mechanism for a cognitive synergy between SWS and REM, and suggest that LTP at the SWS/REM transition critically influences the effect of sleep: Its lack determines synaptic homeostasis, its presence causes synaptic restructuring.

Experiment sheds new light to learning processes

The time that each of us takes to make a decision increases proportionally to the number of alternatives available to us. How so? This is actually just partially true, according to results from an experiment led by André Helene , professor of the Institute of Biosciences (IB) of USP and researcher at the Research, Innovation and Dissemination Center for Neuromathematics (NeuroMat). Report by Tabita Said, Jornal da USP, 6/6/2016. (In Portuguese.)

Neuromathematics Research Center works with Wikipedia to boost science diffusion

Wikipedia, the open-content, online encyclopedia produced by the collaborative efforts of a worldwide community, is one of the most frequently visited websites, yet some say that many of its entries lack a sound scientific basis. To improve the platform’s content in its particular knowledge area, the Research, Innovation and Dissemination Center for Neuromathematics (RDIC-NeuroMat), one of the RIDCs funded by FAPESP, has set up a task force of journalists and scientists to edit Wikipedia entries and to add new information. Report by Diego Freire, Agência FAPESP, 5/25/2016.




The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).


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