An investigation of Hebbian phase sequences as assembly graphs

Daniel G. Almeida-Filho, Vitor Lopes-dos-Santos, Nivaldo A. P. Vasconcelos, José G. V. Miranda, Adriano B. L. Tort, Sidarta Ribeiro

Hebb proposed that synapses between neurons that fire synchronously are strengthened, forming cell assemblies and phase sequences. The former, on a shorter scale, are ensembles of synchronized cells that function transiently as a closed processing system; the latter, on a larger scale, correspond to the sequential activation of cell assemblies able to represent percepts and behaviors. Nowadays, the recording of large neuronal populations allows for the detection of multiple cell assemblies. Within Hebb's theory, the next logical step is the analysis of phase sequences. Here we detected phase sequences as consecutive assembly activation patterns, and then analyzed their graph attributes in relation to behavior.

Primary Motor Cortex Representation of Handgrip Muscles in Patients with Leprosy

Vagner Wilian Batista e Sá, Maria Katia Gomes, Maria Luíza Sales Rangel, Tiago Arruda Sanchez, Filipe Azaline Moreira, Sebastian Hoefle, Inaiacy Bittencourt Souto, Antônio José Ledo Alves da Cunha, Ana Paula Fontana, Claudia Domingues Vargas

Leprosy is an endemic infectious disease caused by Mycobacterium leprae that predominantly attacks the skin and peripheral nerves, leading to progressive impairment of motor, sensory and autonomic function. Little is known about how this peripheral neuropathy affects corticospinal excitability of handgrip muscles. Our purpose was to explore the motor cortex organization after progressive peripheral nerve injury and upper-limb dysfunction induced by leprosy using noninvasive transcranial magnetic stimulation (TMS).

Sleep Deprivation and Gene Expression

Annie da Costa Souza, Sidarta Ribeiro

Sleep occurs in a wide range of animal species as a vital process for the maintenance of homeostasis, metabolic restoration, physiological regulation, and adaptive cognitive functions in the central nervous system. Long-term perturbations induced by the lack of sleep are mostly mediated by changes at the level of transcription and translation. This chapter reviews studies in humans, rodents, and flies to address the various ways by which sleep deprivation affects gene expression in the nervous system, with a focus on genes related to neuronal plasticity, brain function, and cognition.

Rényi Entropies and Large Deviations for the First Match Function

Miguel Natalio Abadi, Liliam Cardeño

We define the first match function Tn : C^n → {1, ... , n} where C is a finite alphabet. For two copies of x1^n ∈ C^n, this function gives the minimum number of steps one has to slide one copy of x1^n to get a match with the other one. For ergodic positive entropy processes, Saussol and coauthors proved the almost sure convergence of Tn/n. We compute the large deviation properties of this function. We prove that this limit is related to the Rényi entropy function, which is also proved to exist.

Hawkes processes with variable length memory and an infinite number of components

Pierre Hodara, Eva Löcherbach

In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components. We propose a graphical construction of the process and we build, by means of a perfect simulation algorithm, a stationary version of the process. To carry out this algorithm, we make use of a Kalikow-type decomposition technique.

A test of hypotheses for random graph distributions built from EEG data

Andressa Cerqueira, Daniel Fraiman, Claudia D. Vargas, Florencia Leonardi

The theory of random graphs is being applied in recent years to model neural interactions in the brain. While the probabilistic properties of random graphs has been extensively studied in the literature, the development of statistical inference methods for this class of objects has received less attention. In this work we propose a non-parametric test of hypotheses to test if two samples of random graphs were originated from the same probability distribution.

Minimum number of edges in a hypergraph guaranteeing a perfect fractional matching and the MMS conjecture

Vladimir Blinovsky

In this paper we prove the Ahlswede-Khachatrian conjecture [1] up to a finite number of cases, which can be checked using modern computers. This conjecture implies the conjecture from [2] and the Manickam-Miklós-Singhi conjecture.

The whole paper is available here.

Modeling networks of spiking neurons as interacting processes with memory of variable length

Antonio Galves, Eva Löcherbach

We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given time. The system evolves as follows. For each component, the rate (in continuous time) or the probability (in discrete time) of having a spike depends on the entire time evolution of the system since the last spike time of the component.

Identifying interacting pairs of sites in Ising models on a countable set

Antonio Galves, Enza Orlandi and Daniel Yasumasa Takahashi

This paper addresses the problem of identifying pairs of interacting sites from a finite sample of independent realizations of the Ising model. We consider Ising models in a infinite countable set of sites under Dobrushin uniqueness condition. The observed sample contains only the values assigned by the Ising model to a finite set of sites. Our main result is an upper bound for the probability of misidentification of the pairs of interacting sites in this finite set.

Stochastically Perturbed Chains of Variable Memory

Garcia, N. L. and Moreira, L. - In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider a chain of variable memory on a finite alphabet containing zero, at each instant of time an independent coin is flipped and if it turns head a contamination occurs.




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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