Publicações

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.

Packing arborescences in random digraphs

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≤ℓ≤λ, we have ∑i=0ℓ−1(ℓ−i)|{v:din(v)=i}|≤ℓ. 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.

Thought disorder measured as random speech structure classifies negative symptoms and schizophrenia diagnosis 6 months in advance

Natália B. Mota, Mauro Copelli and Sidarta Ribeiro

In chronic psychotic patients, word graph analysis shows potential as complementary psychiatric assessment. This analysis relies mostly on connectedness, a structural feature of speech that is anti-correlated with negative symptoms. Here we aimed to verify whether speech disorganization during the first clinical contact, as measured by graph connectedness, can correctly classify negative symptoms and the schizophrenia diagnosis 6 months in advance. Positive and negative syndrome scale scores and memory reports were collected from 21 patients undergoing first clinical contact for recent-onset psychosis, followed for 6 months to establish diagnosis, and compared to 21 well-matched healthy subjects. Each report was represented as a word-trajectory graph. Connectedness was measured by number of edges, number of nodes in the largest connected component and number of nodes in the largest strongly connected component. Similarities to random graphs were estimated. All connectedness attributes were combined into a single Disorganization Index weighted by the correlation with the positive and negative syndrome scale negative subscale, and used for classifications. Random-like connectedness was more prevalent among schizophrenia patients (64 × 5% in Control group, p = 0.0002). Connectedness from two kinds of memory reports (dream and negative image) explained 88% of negative symptoms variance (p  <  0.0001). The Disorganization Index classified low vs. high severity of negative symptoms with 100% accuracy (area under the receiver operating characteristic curve = 1), and schizophrenia diagnosis with 91.67% accuracy (area under the receiver operating characteristic curve = 0.85). The index was validated in an independent cohort of chronic psychotic patients and controls (N = 60) (85% accuracy). Thus, speech disorganization during the first clinical contact correlates tightly with negative symptoms, and is quite discriminative of the schizophrenia diagnosis.

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O Centro de Pesquisa, Inovação e Difusão em Neuromatemática está sediado na Universidade de São Paulo e é financiado pela FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo).

 

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