arXiv subjects

Mauro Copelli

Publications and source records attributed to Mauro Copelli.

44 records · Page 3Linked to original sources

arXiv2007

Scaling law for the transient behavior of type-II neuron models

We study the transient regime of type-II biophysical neuron models and determine the scaling behavior of relaxation times $τ$ near but below the repetitive firing critical current, $τ\simeq C (I_c-I)^{-Δ}$. For both the Hodgkin-Huxley and Morris-Lecar models we find that the critical exponent is independent of the numerical integration time step and that both systems belong to the same universality class, with $Δ= 1/2$. For appropriately chosen parameters, the FitzHugh-Nagumo model presents the same generic transient behavior, but the critical region is significantly smaller. We propose an experiment that may reveal nontrivial critical exponents in the squid axon.

q-bio.NC↗

arXiv2006

Physics of Psychophysics: it is critical to sense

It has been known for about a century that psychophysical response curves (perception of a given physical stimulus vs. stimulus intensity) have a large dynamic range: many decades of stimulus intensity can be appropriately discriminated before saturation. This is in stark contrast with the response curves of sensory neurons, whose dynamic range is small, usually covering only about one decade. We claim that this paradox can be solved by means of a collective phenomenon. By coupling excitable elements with small dynamic range, the {\em collective} response function shows a much larger dynamic range, due to the amplification mediated by excitable waves. Moreover, the dynamic range is optimal at the phase transition where self-sustained activity becomes stable, providing a clear example of a biologically relevant quantity being optimized at criticality. We present a pedagogical account of these ideas, which are illustrated with a simple mean field model.

q-bio.NC↗

arXiv2005

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $α=1$, while for deterministic spike propagation we obtain $α=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.

q-bio.NC↗

arXiv2004

Physics of Psychophysics: Stevens and Weber-Fechner laws are transfer functions of excitable media

Sensory arrays made of coupled excitable elements can improve both their input sensitivity and dynamic range due to collective non-linear wave properties. This mechanism is studied in a neural network of electrically coupled (e.g. via gap junctions) elements subject to a Poisson signal process. The network response interpolates between a Weber-Fechner logarithmic law and a Stevens power law depending on the relative refractory period of the cell. Therefore, these non-linear transformations of the input level could be performed in the sensory periphery simply due to a basic property: the transfer function of excitable media.

cond-mat.dis-nn↗

arXiv2004

Intensity Coding in Two-Dimensional Excitable Neural Networks

In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.

q-bio.NC↗

arXiv2003

Long Term and Short Term Effects of Perturbations in a Immune Network Model

In this paper we review the trajectory of a model proposed by Stauffer and Weisbuch in 1992 to describe the evolution of the immune repertoire and present new results about its dynamical behavior. Ten years later this model, which is based on the ideas of the immune network as proposed by Jerne, has been able to describe a multi-connected network and could be used to reproduce immunization and aging experiments performed with mice. Besides its biological implications, the physical aspects of the complex dynamics of this network is very interesting {\it per se}. The immunization protocol is simulated by introducing small and large perturbations (damages), and in this work we discuss the role of both. In a very recent paper we studied the aging effects by using auto-correlation functions, and the results obtained apparently indicated that the small perturbations would be more important than the large ones, since their cumulative effects may change the attractor of the dynamics. However our new results indicate that both types of perturbations are important. It is the cooperative effects between both that lead to the complex behavior which allows to reproduce experimental results.

cond-mat.stat-mech↗

arXiv2003

On the Aging Dynamics in an Immune Network Model

Recently we have used a cellular automata model which describes the dynamics of a multi-connected network to reproduce the refractory behavior and aging effects obtained in immunization experiments performed with mice when subjected to multiple perturbations. In this paper we investigate the similarities between the aging dynamics observed in this multi-connected network and the one observed in glassy systems, by using the usual tools applied to analyze the latter. An interesting feature we show here is that the model reproduces the biological aspects observed in the experiments during the long transient time it takes to reach the stationary state. Depending on the initial conditions, and without any perturbation, the system may reach one of a family of long-period attractors. The pertrubations may drive the system from its natural attractor to other attractors of the same family. We discuss the different roles played by the small random perturbations (noise) and by the large periodic perturbations (immunizations).

cond-mat.stat-mech↗

arXiv2000

Phase-Induced (In)-Stability in Coupled Parametric Oscillators

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $θ$. Being to a large extent analytically solvable, the model reveals a rich $θ$ dependence of the regions of parametric resonance. In particular, the intuitive notion that anti-phase modulations are less prone to parametric resonance is confirmed for sufficiently large coupling and damping. We also compare our results to a recently reported mean field model of collective parametric instability, showing that the two-oscillator model can capture much of the qualitative behavior of the infinite system.

cond-mat.stat-mech↗