Publications

Effect of synaptic plasticity on functional connectivity and global activity of a neocortical network model

Renan O. Shimoura, Rodrigo F.O. Pena and Antonio C. Roque

Neocortex plays key role in diverse brain functions. Understanding this role involves the study of collective neural activity patterns under different situations, and how these patterns relate to the structural and functional organization of neocortex. Here we study the effect of synaptic plasticity on neural spiking activity patterns in a neocortical network model. We measure changes in neural spiking patterns due to changes in the strengths of the synapses connecting neurons and relate them to changes in the functional connectivity of the network as disclosed by graph-theoretic measures.

Our neocortical network model was composed of excitatory and inhibitory neurons in the proportion of four excitatory cells for each inhibitory cell. Neurons were described by the Izhikevich model [1]. The parameters of the model were adjusted so that excitatory neurons were of the regular spiking (RS) type and inhibitory neurons were all of either the fast spiking (FS) or the low-threshold spiking (LTS) type. Synapses were modeled as event-based, and two types of synaptic dynamics were considered: one without synaptic plasticity in which the synaptic weight received a fixed increment after the pre-synaptic event and decayed exponentially after that, and one with synaptic plasticity in which the synapse obeyed an asymmetric spike-timing dependent plasticity (STDP) rule described by [2]. Neurons were organized into four layers (2/3, 4, 5 and 6) with layer- and cell-specific statistical connectivity rules based on [3]. The total number of neurons in the model was about 4,000. Two experiments were done: one with all synapses described by the model without synaptic plasticity, and the other with synapses between excitatory neurons described by the STDP rule while the remaining synapses were described by the model without synaptic plasticity. In both cases, the model was stimulated by a current injection of random amplitude applied to neurons of layer 4 (L4), which is the main input layer of the cortex. The spiking activity of the network was evaluated by measures extracted from the raster plot of the spikes produced by the neurons, e.g. layer-specific and network mean and time-dependent firing rates. The structural and functional connectivities of the network were represented by the respective structural and functional adjacency matrices. The functional adjacency matrix was constructed by taking in consideration neuron pairs with strength of their synaptic coupling above a specific threshold. The topology of the adjacency matrices was characterized by graph-theoretic measures, e.g. clustering coefficient.

We determined a set of parameters for which the spiking activity generated in L4 by the external input propagated to the entire network. This network-wide activity was oscillatory, and we found that its mean frequency was higher for the network version with synaptic plasticity than for the version without synaptic plasticity. We also found that the formation of clusters of synchronous neural activity was facilitated in the case with LTS cells as inhibitory neurons. Our results suggest that synaptic plasticity may induce changes in the functional connectivity of the neocortical network with impact on its global activity.

A Naturalistic Assessment of the Organization of Children’s Memories Predicts Cognitive Functioning and Reading Ability

Natália Bezerra Mota, Janaína Weissheimer, Beatriz Madruga, Nery Adamy, Silvia A. Bunge, Mauro Copelli and Sidarta Ribeiro

To explore the relationship between memory and early school performance, we used graph theory to investigate memory reports from 76 children aged 6–8 years. The reports comprised autobiographical memories of events days to years past, and memories of novel images reported immediately after encoding. We also measured intelligence quotient (IQ) and theory of mind (ToM). Reading and Mathematics were assessed before classes began (December 2013), around the time of report collection (June 2014), and at the end of the academic year (December 2014). IQ and ToM correlated positively with word diversity and word-to-word connectivity, and negatively with word recurrence. Connectivity correlated positively with Reading in June 2014 as well as December 2014, even after adjusting for IQ and ToM. To our knowledge, this is the first study demonstrating a link between the structure of children's memories and their cognitive or academic performance.

Cerebral Dynamics during the Observation of Point-Light Displays Depicting Postural Adjustments

Eduardo F. Martins, Thiago Lemos, Ghislain Saunier, Thierry Pozzo, Daniel Fraiman and Claudia D. Vargas

Objective: As highly social creatures, human beings rely part of their skills of identifying, interpreting, and predicting the actions of others on the ability of perceiving biological motion. In the present study, we aim to investigate the electroencephalographic (EEG) cerebral dynamics involved in the coding of postural control and examine whether upright stance would be codified through the activation of the temporal-parietal cortical network classically enrolled in the coding of biological motion.

Design: We registered the EEG activity of 12 volunteers while they passively watched point light displays (PLD) depicting quiet stable (QB) and an unstable (UB) postural situations and their respective scrambled controls (QS and US). In a pretest, 13 volunteers evaluated the level of stability of our two biological stimuli through a stability scale.

Results: Contrasting QB vs. QS revealed a typical ERP difference in the right temporal-parietal region at an early 200–300 ms time window. Furthermore, when contrasting the two biological postural conditions, UB vs. QB, we found a higher positivity in the 400–600 ms time window for the UB condition in central-parietal electrodes, lateralized to the right hemisphere.

Conclusions: These results suggest that PLDs depicting postural adjustments are coded in the brain as biological motion, and that their viewing recruit similar networks with those engaged in postural stability control. Additionally, higher order cognitive processes appear to be engaged in the identification of the postural instability level. Disentangling the EEG dynamics during the observation of postural adjustments could be very useful for further understanding the neural mechanisms underlying postural control.

Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

João Guilherme Ferreira Campos, Ariadne de Andrade Costa, Mauro Copelli and Osame Kinouchi

In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the so-called annealed dynamics). Calculations agree with simulations of the annealed version, showing that the nominal branching ratio σ converges to unity in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to the biological case where only the synapses of firing neurons are depressed (the so-called quenched dynamics). We show that simulations of the quenched model yield significant deviations from σ = 1 due to spatial correlations. However, the model is shown to be critical, as the largest eigenvalue of the synaptic matrix approaches unity in the thermodynamic limit, that is, λc = 1. We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.

A Test of Hypotheses for Random Graph Distributions Built From EEG Data

Andressa Cerqueira; Daniel Fraiman; Claudia D. Vargas and Florencia Leonardi

The theory of random graphs has been applied in recent years to model neural interactions in the brain. While the probabilistic properties of random graphs has been extensively studied, 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 a sample of random graphs was generated by a given probability distribution (one-sample test) or if two samples of random graphs were originated from the same probability distribution (two-sample test). We prove a Central Limit Theorem providing the asymptotic distribution of the test statistics and we propose a method to compute the quantiles of the finite sample distributions by simulation. The test makes no assumption on the specific form of the distributions and it is consistent against any alternative hypothesis that differs from the sample distribution on at least one edge-marginal. Moreover, we show that the test is a Kolmogorov-Smirnov type test, for a given distance between graphs, and we study its performance on simulated data. We apply it to compare graphs of brain functional network interactions built from electroencephalographic (EEG) data collected during the visualization of point light displays depicting human locomotion.

Stochastic Processes With Random Contexts: A Characterization and Adaptive Estimators for the Transition Probabilities

Roberto Imbuzeiro Oliveira

This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (also known as variable length Markov chains), and are proved to coincide with processes whose transition probabilities are almost surely continuous functions of the (infinite) past. This is similar to a classical result by Kalikow about continuous transition probabilities. Existence and uniqueness of a minimal random context representation are shown, in the sense that there exists a unique representation that looks into the past as little as possible in order to determine the next symbol. Both this representation and the transition probabilities can be consistently estimated from data, and some finite sample adaptivity properties are also obtained (including an oracle inequality). In particular, the estimator achieves minimax performance, up to logarithmic factors, for the class of binary renewal processes whose arrival distributions have bounded moments of order 2 + γ.

Inhibitory loop robustly induces anticipated synchronization in neuronal microcircuits

Fernanda S. Matias, Leonardo L. Gollo, Pedro V. Carelli, Claudio R. Mirasso and Mauro Copelli

We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamic inhibition together with noise independently applied to each neuron provide phase diversity in the dynamics of the neuronal motif. We show that the interplay between the coupling strengths and the external noise controls the phase relations between the neurons in a counterintuitive way. For a master-slave configuration (unidirectional coupling) we find that the slave can anticipate the master, on average, if the slave is subject to the inhibitory feedback. In this nonusual regime, called anticipated synchronization (AS), the phase of the postsynaptic neuron is advanced with respect to that of the presynaptic neuron. We also show that the AS regime survives even in the presence of unbalanced bidirectional excitatory coupling. Moreover, for the symmetric mutually coupled situation, the neuron that is subject to the inhibitory loop leads in phase.

Potential Well Spectrum and Hitting Time in Renewal Processes

Miguel Abadi, Liliam Cardeño and Sandro Gallo

The potential well of a state can be interpreted physically as the energy that a stationary process needs to leave the state. We prove that for discrete time renewal processes, the potential well is the right scaling for the hitting and return time distributions of the state. We further detail the potential well spectrum of these processes by giving a complete classification of the states according to their potential well.

Estimating Parameters Associated with Monotone Properties

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

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real function defined on the set of finite graphs, by sampling a randomly chosen substructure whose size is independent of the size of the input. Graph parameters that may be successfully estimated in this way are said to be testable or estimable, and the sample complexity qz = qz(ε) of an estimable parameter z is the size of the random sample required to ensure that the value of z(G) may be estimated within error ε with probability at least 2/3. In this paper, we study the sample complexity of estimating two graph parameters associated with a monotone graph property, improving previously known results. To obtain our results, we prove that the vertex set of any graph that satisfies a monotone property P may be partitioned equitably into a constant number of classes in such a way that the cluster graph induced by the partition is not far from satisfying a natural weighted graph generalization of P. Properties for which this holds are said to be recoverable, and the study of recoverable properties may be of independent interest

On the Number of Bh-Sets

Domingos Dellamonica, Yoshiharu Kohayakawa, Sang June Lee, Vojtěch Rödl and Wojciech Samotij

A set A of positive integers is a Bh-set if all sums of the form a1 + ··· + ah, with a1,...,ah ∈ A and a1 ··· ah, are distinct. We provide asymptotic bounds for the number of Bh-sets of a given cardinality contained in the interval [n] = {1,...,n}. As a consequence of our results, we address a problem of Cameron and Erd˝os (1990) in the context of Bh-sets.
We also use these results to estimate the maximum size of a Bh-set contained in a typical (random) subset of [n] with a given cardinality.

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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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