arXiv subjects

Mauro Copelli

Publications and source records attributed to Mauro Copelli.

At least 37 records · Page 2Linked to original sources

arXiv2016

Inhibitory loop robustly induces anticipated synchronization in neuronal microcircuits

We investigate the synchronization properties between two excitatory coupled neurons in the presence of an inhibitory loop mediated by an interneuron. Dynamical 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 external noise controls the phase relations between the neurons in a counter-intuitive 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 non-usual regime, called anticipated synchronization (AS), the phase of the post-synaptic neuron is advanced with respect to that of the pre-synaptic 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.

q-bio.NC↗

arXiv2016

Emotional Intensity analysis in Bipolar subjects

The massive availability of digital repositories of human thought opens radical novel way of studying the human mind. Natural language processing tools and computational models have evolved such that many mental conditions are predicted by analysing speech. Transcription of interviews and discourses are analyzed using syntactic, grammatical or sentiment analysis to infer the mental state. Here we set to investigate if classification of Bipolar and control subjects is possible. We develop the Emotion Intensity Index based on the Dictionary of Affect, and find that subjects categories are distinguishable. Using classical classification techniques we get more than 75\% of labeling performance. These results sumed to previous studies show that current automated speech analysis is capable of identifying altered mental states towards a quantitative psychiatry.

cs.AI↗

arXiv2015

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.

nlin.AO↗

arXiv2015

Diversity improves performance in excitable networks

As few real systems comprise indistinguishable units, diversity is a hallmark of nature. Diversity among interacting units shapes properties of collective behavior such as synchronization and information transmission. However, the benefits of diversity on information processing at the edge of a phase transition, ordinarily assumed to emerge from identical elements, remain largely unexplored. Analyzing a general model of excitable systems with heterogeneous excitability, we find that diversity can greatly enhance optimal performance (by two orders of magnitude) when distinguishing incoming inputs. Heterogeneous systems possess a subset of specialized elements whose capability greatly exceeds that of the nonspecialized elements. Nonetheless, the behavior of the whole network can outperform all subgroups. We also find that diversity can yield multiple percolation, with performance optimized at tricriticality. Our results are robust in specific and more realistic neuronal systems comprising a combination of excitatory and inhibitory units, and indicate that diversity-induced amplification can be harnessed by neuronal systems for evaluating stimulus intensities.

q-bio.NC↗

arXiv2013

Single-Neuron Criticality Optimizes Analog Dendritic Computation

Neurons are thought of as the building blocks of excitable brain tissue. However, at the single neuron level, the neuronal membrane, the dendritic arbor and the axonal projections can also be considered an extended active medium. Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions, despite several proposals, remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. By using a probabilistic cellular automaton approach, we model the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes. We find that, if dendritic spikes have a non-deterministic duration, the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near a phase transition to take advantage of specific properties of the critical state, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.

q-bio.NC↗

arXiv2012

Collective behavior of coupled nonuniform stochastic oscillators

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [Phys. Rev. Lett. 96}, 145701 (2006)], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter $0\leq α\leq 1$, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for $α\leq α^\prime < 1$. At $α=1$ the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.

physics.data-an↗

arXiv2012

Statistical Physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a non-equilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5(6) e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

q-bio.NC↗

arXiv2011

An excitable electronic circuit as a sensory neuron model

An electronic circuit device, inspired on the FitzHugh-Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of the electronics quantitatively reproduces the experimental observations on the circuit, including the Hopf bifurcation at the onset of tonic spiking. Moreover, we have implemented an analog noise generator as a source to study the variability of the spike trains. When the circuit is in the excitable regime, coherence resonance is observed. At sufficiently low noise intensity the spike trains have Poisson statistics, as in many biological neurons. The transfer function of the stochastic spike trains has a dynamic range of 6 dB, close to experimental values for real olfactory receptor neurons.

physics.bio-ph↗

arXiv2011

An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations

A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value of the coupling parameter, leading to stable global oscillations. We show that, in the complete graph version of the model, upon further increase in the coupling, the average frequency of collective oscillations decreases until an infinite-period (IP) phase transition occurs, at which point collective oscillations cease. Above this second critical point, a macroscopic fraction of the oscillators spend most of the time in one of the three states, yielding a prototypical nonequilibrium example (without an equilibrium counterpart) in which discrete rotational (C_3) symmetry is spontaneously broken, in the absence of any absorbing state. Simulation results and nucleation arguments strongly suggest that the IP phase transition does not occur on finite-dimensional lattices with short-range interactions.

physics.bio-ph↗

arXiv2011

Anticipated Synchronization in a Biologically Plausible Model of Neuronal Motifs

Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of simplified neuron models, requiring the coupling of the neuronal membrane potential with its delayed value. However, this coupling has no obvious biological correlate. Here we propose a canonical neuronal microcircuit with standard chemical synapses, where the delayed inhibition is provided by an interneuron. In this biologically plausible scenario, a smooth transition from delayed synchronization (DS) to AS typically occurs when the inhibitory synaptic conductance is increased. The phenomenon is shown to be robust when model parameters are varied within physiological range. Since the DS-AS transition amounts to an inversion in the timing of the pre- and post-synaptic spikes, our results could have a bearing on spike-timing-dependent-plasticity models.

q-bio.NC↗

arXiv2011

Collective oscillations of excitable elements: order parameters, bistability and the role of stochasticity

We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with stable collective oscillations exists even with non-deterministic refractory periods. Moreover, further increasing the coupling strength leads to a reentrant transition, where the synchronized phase loses stability. In an intermediate regime, we also observe bistability (and consequently hysteresis) between a synchronized phase and an active but incoherent phase without oscillations. The onset of the oscillations appears in the mean-field equations as a Neimark-Sacker bifurcation, the nature of which (i.e. super- or subcritical) is determined by the first Lyapunov coefficient. This allows us to determine the borders of the oscillating and of the bistable regions. The mean-field prediction thus obtained agrees quantitatively with simulations of complete graphs and, for random graphs, qualitatively predicts the overall structure of the phase diagram. The latter can be obtained from simulations by defining an order parameter q suited for detecting collective oscillations of excitable elements. We briefly review other commonly used order parameters and show (via data collapse) that q satisfies the expected finite size scaling relations.

q-bio.NC↗

arXiv2011

Spike Avalanches Exhibit Universal Dynamics across the Sleep-Wake Cycle

Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function. To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of spikes from the cerebral cortex (V1 and S1) and hippocampus (HP) of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from V1, S1 and HP. Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

q-bio.NC↗

arXiv2009

Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model

We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1). For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, such as in the usual stochastic SIRS model [Joo and Lebowitz, Phys. Rev. E 70, 036114 (2004)]. However, for strong nonlinearity, the nonequilibrium transition between the two phases can be discontinuous for d>=2, which is confirmed by well-characterized hysteresis cycles and bistability. Analytical mean-field results correctly predict the overall structure of the phase diagram. Furthermore, contrary to what was observed in a model of phase-coupled stochastic oscillators with a similar nonlinearity in the coupling [Wood et al., Phys. Rev. Lett. 96, 145701 (2006)], we did not find a transition to a stable (partially) synchronized state in our nonlinearly pulse-coupled excitable elements. For long enough refractory times and high enough nonlinearity, however, the system can exhibit collective excitability and unstable stochastic oscillations.

nlin.CG↗

arXiv2009

Active dendrites enhance neuronal dynamic range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the last decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of active dendritic trees is a highly non-linear function of their afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease of dynamic range.

q-bio.NC↗

arXiv2008

Deterministic excitable media under Poisson drive: power law responses, spiral waves and dynamic range

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h, the interplay between creation and annihilation of excitable waves leads to an average activity F. It has recently been suggested that in the low-stimulus regime (h ~ 0) the response function F(h) of hypercubic deterministic systems behaves as a power law, F ~ h^m. Moreover the response exponent m has been predicted to depend only on the dimensionality d of the lattice, m = 1/(1+d) [T. Ohta and T. Yoshimura, Physica D 205, 189 (2005)]. In order to test this prediction, we study the response function of excitable lattices modeled by either coupled Morris-Lecar equations or Greenberg-Hastings cellular automata. We show that the prediction is verified in our model systems for d = 1, 2, and 3, provided that a minimum set of conditions is satisfied. Under these conditions, the dynamic range - which measures the range of stimulus intensities that can be coded by the network activity - increases with the dimensionality d of the network. The power law scenario breaks down, however, if the system can exhibit self-sustained activity (spiral waves). In this case, we recover a scenario that is common to probabilistic excitable media: as a function of the conductance coupling G among the excitable elements, the dynamic range is maximized precisely at the critical value G_c above which self-sustained activity becomes stable. We discuss the implications of these results in the context of neural coding.

q-bio.NC↗

arXiv2008

Dynamic range of hypercubic stochastic excitable media

We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active sites rho versus h) is obtained via simulations (for d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels (for all d). In any dimension, the dynamic range of the response function is maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d.

q-bio.NC↗

arXiv2007

Optimal Dynamical Range of Excitable Networks at Criticality

A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard and biologically relevant quantity is optimized at criticality. Here we give a clear example of such a phenomenon: a network of excitable elements has its sensitivity and dynamic range maximized at the critical point of a non-equilibrium phase transition. Our results are compatible with the essential role of gap junctions in olfactory glomeruli and retinal ganglionar cell output. Synchronization and global oscillations also appear in the network dynamics. We propose that the main functional role of electrical coupling is to provide an enhancement of dynamic range, therefore allowing the coding of information spanning several orders of magnitude. The mechanism could provide a microscopic neural basis for psychophysical laws.

q-bio.NC↗

arXiv2007

Excitable Scale Free Networks

When a simple excitable system is continuously stimulated by a Poissonian external source, the response function (mean activity versus stimulus rate) generally shows a linear saturating shape. This is experimentally verified in some classes of sensory neurons, which accordingly present a small dynamic range (defined as the interval of stimulus intensity which can be appropriately coded by the mean activity of the excitable element), usually about one or two decades only. The brain, on the other hand, can handle a significantly broader range of stimulus intensity, and a collective phenomenon involving the interaction among excitable neurons has been suggested to account for the enhancement of the dynamic range. Since the role of the pattern of such interactions is still unclear, here we investigate the performance of a scale-free (SF) network topology in this dynamic range problem. Specifically, we study the transfer function of disordered SF networks of excitable Greenberg-Hastings cellular automata. We observe that the dynamic range is maximum when the coupling among the elements is critical, corroborating a general reasoning recently proposed. Although the maximum dynamic range yielded by general SF networks is slightly worse than that of random networks, for special SF networks which lack loops the enhancement of the dynamic range can be dramatic, reaching nearly five decades. In order to understand the role of loops on the transfer function we propose a simple model in which the density of loops in the network can be gradually increased, and show that this is accompanied by a gradual decrease of dynamic range.

q-bio.NC↗