Publications

The Shortest Possible Return Time of β-Mixing Processes

Miguel Abadi; Sandro Gallo and Erika Alejandra Rada-Mora

We consider a stochastic process and a givenn-string. We study the shortestpossiblereturn time (or shortest return path) of the string over all the realizations of process starting from this string. For aβ-mixing process having complete grammar, and for each sizenof the strings, we approximate the distribution of this short return (properly re-scaled) by a non-degenerated distribution. Under mild conditions on theβcoefficients, we prove the existence of the limit of this distribution to a non-degenerated distribution. We also prove that ergodicity is not enough to guaranty this convergence. Finally, we present a connection between the shortest return and the Shannon entropy, showing that maximum of the re-scaled variables grow as the matching function of Wyner and Ziv.

Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noise: Spontaneous activity in networks with synaptic noise.

Pena RFO, Zaks MA and Roque AC.

Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.

Physiology and assessment as low-hanging fruit for education overhaul

Sidarta Ribeiro, Natália Bezerra Mota, Valter da Rocha Fernandes, Andrea Camaz Deslandes, Guilherme Brockington and Mauro Copelli

Physiology and assessment constitute major bottlenecks of school learning among students with low socioeconomic status. The limited resources and household overcrowding typical of poverty produce deficits in nutrition, sleep, and exercise that strongly hinder physiology and hence learning. Likewise, overcrowded classrooms hamper the assessment of individual learning with enough temporal resolution to make individual interventions effective. Computational measurements of learning offer hope for low-cost, fast, scalable, and yet personalized academic evaluation. Improvement of school schedules by reducing lecture time in favor of naps, exercise, meals, and frequent automated assessments of individual performance is an easily achievable goal for education.

Discrepancy and eigenvalues of Cayley graphs

Yoshiharu Kohayakawa, Vojtěch Röd and Mathias Schacht

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.

Large Deviations for Cascades of Diffusions Arising in Oscillating Systems of Interacting Hawkes Processes

E. Löcherbach

We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Löcherbach (Stoch Process Appl 2017, http://arxiv.org/abs/1512.00265) to model multi-class systems of interacting neurons together with the diffusion approximations of their intensity processes. This diffusion, which incorporates the memory terms defining the dynamics of the Hawkes process, is hypo-elliptic. It is given by a high-dimensional chain of differential equations driven by 2-dimensional Brownian motion. We study the large population, i.e., small noise limit of its invariant measure for which we establish a large deviation result in the spirit of Freidlin and Wentzell.

Chromatic thresholds in dense random graphs

Peter Allen, Julia Böttcher, Simon Griffiths, Yoshiharu Kohayakawa and Robert Morris

The chromatic threshold δχ(H, p) of a graph H with respect to the random graphG(n, p) is the infimum over d > 0 such that the following holds with high probability: the familyof H-free graphs G ⊆ G(n, p) with minimum degree δ(G) ≥ dpn has bounded chromatic number.The study of the parameter δχ(H) := δχ(H,1) was initiated in 1973 by Erd˝os and Simonovits, andwas recently determined for all graphs H. In this paper we show that δχ(H, p) = δχ(H) for all fixedp ∈ (0, 1), but that typically δχ(H, p) ≠ δχ(H) if p = o(1). We also make significant progress towardsdetermining δχ(H, p) for all graphs H in the range p = n−o(1). In sparser random graphs the problem issomewhat more complicated, and is studied in a separate paper.

Estimating the distance to a hereditary graph property

Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann and Henrique Stagni

Given a family of graphs "F", we prove that the distance to being induced "F"-free is estimable with a query complexity that depends only on the bounds of the Frieze-Kannan Regularity Lemma and a Removal Lemma for "F".

Dopamine Modulates Delta-Gamma Phase-Amplitude Coupling in the Prefrontal Cortex of Behaving Rats

Victoria Andino-Pavlovsky, Annie C. Souza, Robson Scheffer-Teixeira, Adriano B. L. Tort, Roberto Etchenique and Sidarta Ribeiro

Dopamine release and phase-amplitude cross-frequency coupling (CFC) have independently been implicated in prefrontal cortex (PFC) functioning. To causally investigate whether dopamine release affects phase-amplitude comodulation between different frequencies in local field potentials (LFP) recorded from the medial PFC (mPFC) of behaving rats, we used RuBiDopa, a light-sensitive caged compound that releases the neurotransmitter dopamine when irradiated with visible light. LFP power did not change in any frequency band after the application of light-uncaged dopamine, but significantly strengthened phase-amplitude comodulation between delta and gamma oscillations. Saline did not exert significant changes, while injections of dopamine and RuBiDopa produced a slow increase in comodulation for several minutes after the injection. The results show that dopamine release in the medial PFC shifts phase-amplitude comodulation from theta-gamma to delta-gamma. Although being preliminary results due to the limitation of the low number of animals present in this study, our findings suggest that dopamine-mediated modification of the frequencies involved in comodulation could be a mechanism by which this neurotransmitter regulates functioning in mPFC.

On the estimation of the mean of a random vector

Emilien Joly, Gábor Lugosi and Roberto Imbuzeiro Oliveira

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.

Densities in large permutations and parameter testing

Roman Glebov, Carlos Hoppen, Tereza Klimošová, Yoshiharu Kohayakawa, Daniel Král’ and Hong Liu.

A classical theorem of Erdős, Lovász and Spencer asserts that the densities of connected subgraphs in large graphs are independent. We prove an analogue of this theorem for permutations and we then apply the methods used in the proof to give an example of a finitely approximable permutation parameter that is not finitely forcible. The latter answers a question posed by two of the authors and Moreira and Sampaio.

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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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