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, 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.

The role of negative conductances in neuronal subthreshold properties and synaptic integration

Cesar C. Ceballos, Antonio C. Roque and Ricardo M. Leão

Based on passive cable theory, an increase in membrane conductance produces a decrease in the membrane time constant and input resistance. Unlike the classical leak currents, voltage-dependent currents have a nonlinear behavior which can create regions of negative conductance, despite the increase in membrane conductance (permeability). This negative conductance opposes the effects of the passive membrane conductance on the membrane input resistance and time constant, increasing their values and thereby substantially affecting the amplitude and time course of postsynaptic potentials at the voltage range of the negative conductance. This paradoxical effect has been described for three types of voltage-dependent inward currents: persistent sodium currents, L- and T-type calcium currents and ligand-gated glutamatergic N-methyl-D-aspartate currents. In this review, we describe the impact of the creation of a negative conductance region by these currents on neuronal membrane properties and synaptic integration. We also discuss recent contributions of the quasi-active cable approximation, an extension of the passive cable theory that includes voltage-dependent currents, and its effects on neuronal subthreshold properties.

Variability in functional brain networks predicts expertise during action observation

Amoruso L, Ibáñez A, Fonseca B, Gadea S, Sedeño L, Sigman M, García AM, Fraiman R, Fraiman D.

Observing an action performed by another individual activates, in the observer, similar circuits as those involved in the actual execution of that action. This activation is modulated by prior experience; indeed, sustained training in a particular motor domain leads to structural and functional changes in critical brain areas. Here, we capitalized on a novel graph-theory approach to electroencephalographic data (Fraiman et al., 2016) to test whether variability in functional brain networks implicated in Tango observation can discriminate between groups differing in their level of expertise. We found that experts and beginners significantly differed in the functional organization of task-relevant networks. Specifically, networks in expert Tango dancers exhibited less variability and a more robust functional architecture. Notably, these expertise-dependent effects were captured within networks derived from electrophysiological brain activity recorded in a very short time window (2s). In brief, variability in the organization of task-related networks seems to be a highly sensitive indicator of long-lasting training effects. This finding opens new methodological and theoretical windows to explore the impact of domain-specific expertise on brain plasticity, while highlighting variability as a fruitful measure in neuroimaging research.




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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