Ariadne de Andrade Costa

Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function Φ(V) of the membrane potential V, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function Φ. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains – a form of short-term plasticity probably located at the axon initial segment (AIS) – instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.

Can dynamical synapses produce true self-organized criticality?

Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The model exhibits a very similar to conservative self-organized criticality (SOC) models behavior even with dissipative bulk dynamics. This occurs because in the stationary regime the model is conservative on average, and, in the thermodynamic limit, the probability distribution for the global branching ratio converges to a delta-function centered at its critical value. So, this non-conservative model pertain to the same universality class of conservative SOC models and contrasts with other dynamical synapses models that present only self-organized quasi-criticality (SOqC). Analytical results show very good agreement with simulations of the model and enable us to study the emergence of SOC as a function of the parametric derivatives of the stationary branching ratio.

A computational model for exploratory activity of rats with different anxiety levels in elevated plus-maze

The elevated plus-maze is an apparatus widely used to study the level of anxiety in rodents. The maze is plus-shaped, with two enclosed arms and two open arms, and elevated 50cm from the floor. During a test, which usually lasts for 5min, the animal is initially put at the center and is free to move and explore the entire maze. The level of anxiety is measured by variables such as the percentage of time spent and the number of entries in the enclosed arms. High percentage of time spent at and number of entries in the enclosed arms indicate anxiety. Here we propose a computational model of rat behavior in the elevated plus-maze based on an artificial neural network trained by a genetic algorithm. The fitness function of the genetic algorithm is composed of reward (positive) and punishment (negative) terms, which are incremented as the computational agent (virtual rat) moves in the maze. The punishment term is modulated by a parameter that simulates the effects of different drugs. Unlike other computational models, the virtual rat is built independently of prior known experimental data. The exploratory behaviors generated by the model for different simulated pharmacological conditions are in good agreement with data from real rats.

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

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, λ_{c}=1. We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.

Using explicit averaging fitness for studying the behaviour of rats in a maze

In this paper we study the performance of different evolutionary strategies based on explicit averaging. On a previous study, (Costa et al., 2012) proposed a probabilistic fitness function for an agent model based on neural networks and genetic algorithms employed to investigate the behaviour of rats in an elevated plus-maze (EPM). Differently from other computational models, the virtual rat proposed in (Costa et al., 2012) is not built based on experimental data comparisons with real rats, but, instead, is based on a behavioural model exploring the conflict between fear and anxiety. Despite the good results of the proposed agent, the effects of the uncertain fitness functions in the evolutionary learning process were not studied in the previous study. In our experiments we found significant differences in the performance of the genetic algorithm when the fitness of the individuals is sampled different times thus enabling us to define the best strategy for the studied problem. Genetic algorithm, Uncertainty, Explicit averaging fitness, Elevated plus-maze, Rat

A model based on genetic algorithm for investigation of the behavior of rats in the elevated plus-maze

In this paper we propose the use of an artificial neural network associated to a genetic algorithm to develop a behavioral model of rats in elevated plus-maze. The main novelty is the fitness function used, which is independent of prior known experimental data. Our results agree with experimental tests, demonstrating that open arms exploration evoke greater avoidance. The perspective of the results are increased by analyzing Markov chains obtained by experiments with real rats and by computational simulations, suggesting that the general fitness function proposed summarizes the main relevant characteristics for the study of the rats behavior in the elevated plus-maze.

Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons

Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by computational simulations. The neurons have dynamic gains that enable the network to converge to a stationary slightly supercritical state (self-organized supercriticality or SOSC) in the presence of the continuous transition. We show that SOSC, which presents power laws for neuronal avalanches plus some large events, is robust as a function of the main parameter of the neuronal gain dynamics. We discuss the possible applications of the idea of SOSC to biological phenomena like epilepsy and dragon king avalanches. We also find that neuronal gains can produce collective oscillations that coexists with neuronal avalanches, with frequencies compatible with characteristic brain rhythms.

An Evolving Artificial Neural Network for the Investigation of Rat Exploratory Behavior

The elevated plus-maze is widely used as a tool for neurobiological studies of anxiety and defense in rodents. In a previous work, an artificial neural network (ANN) with weights adjusted by a genetic algorithm (GA) was used to investigate the behaviour of rats in an elevated plus-maze. The study of the ANNs architecture, which was fixed in the previous work, can provide insights about the role of sensory inputs and memory in models employed to investigate the behaviour of rats. In this paper, we propose an evolving ANN for this problem. The architecture of the recurrent ANN is evolved by the GA together with its weights. The experiments indicate that the evolving ANN produces better results than the fixed architecture previously investigated. Besides, the experiments indicate that only three of the six sensory units and only two of the four hidden units are used in the evolved ANN. This result is useful to understand how the rat uses the sensory information and memory while navigating in the elevated plus-maze.

Investigation of rat exploratory behavior via evolving artificial neural networks

BACKGROUND Neuroevolution comprises the use of evolutionary computation to define the architecture and/or to train artificial neural networks (ANNs). This strategy has been employed to investigate the behavior of rats in the elevated plus-maze, which is a widely used tool for studying anxiety in mice and rats. NEW METHOD Here we propose a neuroevolutionary model, in which both the weights and the architecture of artificial neural networks (our virtual rats) are evolved by a genetic algorithm. COMPARISON WITH EXISTING METHOD(S) This model is an improvement of a previous model that involves the evolution of just the weights of the ANN by the genetic algorithm. In order to compare both models, we analyzed traditional measures of anxiety behavior, like the time spent and the number of entries in both open and closed arms of the maze. RESULTS When compared to real rat data, our findings suggest that the results from the model introduced here are statistically better than those from other models in the literature. CONCLUSIONS In this way, the neuroevolution of architecture is clearly important for the development of the virtual rats. Moreover, this technique allowed the comprehension of the importance of different sensory units and different number of hidden neurons (performing as memory) in the ANNs (virtual rats).