arXiv subjects

O. Kinouchi

Publications and source records attributed to O. Kinouchi.

7 recordsLinked to original sources

arXiv2018

Stochastic oscillations produce dragon king avalanches in self-organized quasi-critical systems

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. This phenomenology has been called self-organized quasi-criticality (SOqC). Here we make a linear stability analysis of the mean field fixed points of two SOqC systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.

nlin.AO↗

arXiv2016

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 in 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.

nlin.AO↗

arXiv2013

A Brief History of Excitable Map-Based Neurons and Neural Networks

This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003). We also review map-based schemes for electrical and chemical synapses and some recent findings as critical avalanches in map-based neural networks. We conclude with suggestions for further work in this area like more efficient maps, compartmental modeling and close dynamical comparison with conductance-based models.

q-bio.NC↗

arXiv2004

Stability diagrams for bursting neurons modeled by three-variable maps

We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present bursts and other interesting biological behaviors. Bifurcation lines which locate the excitability region are obtained for different planes in parameter space.

q-bio.NC↗

arXiv2002

Deterministic walks in random networks: an application to thesaurus graphs

In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last τsteps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period p. The tourist walk presents universal aspects with respect to τand can be done in a wide range of networks that can be viewed as ordinal neighborhood graphs. As an example, we show that graphs defined by thesaurus dictionaries share some of the statistical properties of low dimensional (d=2) Euclidean graphs and are easily distinguished from random graphs. This approach furnishes complementary information to the usual clustering coefficient and mean minimum separation length.

cond-mat.dis-nn↗

arXiv1997

Absence of self-organized criticality in a random-neighbor version of the OFC stick-slip model

We report some numerical simulations to investigate the existence of a self-organized critical (SOC) state in a random-neighbor version of the OFC model for a range of parameters corresponding to a non-conservative case. In contrast to a recent work, we do not find any evidence of SOC. We use a more realistic distribution of energy among sites to perform some analytical calculations that agree with our numerical conclusions.

adap-org↗

arXiv1997

Time ordering in the evolution of information processing and modulation systems

The ideas of optimization of learning algorithms in Artificial Neural Networks are reviewed emphasizing generic properties and the online implementations are interpreted from a biological perspective. A simple model of the relevant subsidiary variables needed to improve learning in artificial feedforward networks and the `time ordering' of the appearance of the respective information processing systems is proposed. We discuss the possibility that these results might be relevant in other contexts, not being restricted to the simple models from which they stem. The analysis of a few examples, which range from the lowest cellular scale to the macroscopic level, suggests that similar ideas could be applied to biological systems.

cond-mat.dis-nn↗