Antonio de Candia

Neural Avalanches at the Critical Point between Replay and Non-Replay of Spatiotemporal Patterns

We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between the activity of the network and the stored patterns. We find that, depending on the excitability of the network, different working regimes are possible. For high excitability, the dynamical attractors are stable, and a collective activity that replays one of the stored patterns emerges spontaneously, while for low excitability, no replay is induced. Between these two regimes, there is a critical region in which the dynamical attractors are unstable, and intermittent short replays are induced by noise. At the critical spiking threshold, the order parameter goes from zero to one, and its fluctuations are maximized, as expected for a phase transition (and as observed in recent experimental results in the brain). Notably, in this critical region, the avalanche size and duration distributions follow power laws. Critical exponents are consistent with a scaling relationship observed recently in neural avalanches measurements. In conclusion, our simple model suggests that avalanche power laws in cortical spontaneous activity may be the effect of a network at the critical point between the replay and non-replay of spatio-temporal patterns.

Storage of Phase-Coded Patterns via STDP in Fully-Connected and Sparse Network: A Study of the Network Capacity

We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate and fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre and postsynaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully connected networks, we study sparse networks, where each neuron is connected only to a small number z ≪ N of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry.

Alternation of up and down states at a dynamical phase-transition of a neural network with spatiotemporal attractors

Complex collective activity emerges spontaneously in cortical circuits in vivo and in vitro, such as alternation of up and down states, precise spatiotemporal patterns replay, and power law scaling of neural avalanches. We focus on such critical features observed in cortical slices. We study spontaneous dynamics emerging in noisy recurrent networks of spiking neurons with sparse structured connectivity. The emerging spontaneous dynamics is studied, in presence of noise, with fixed connections. Note that no short-term synaptic depression is used. Two different regimes of spontaneous activity emerge changing the connection strength or noise intensity: a low activity regime, characterized by a nearly exponential distribution of firing rates with a maximum at rate zero, and a high activity regime, characterized by a nearly Gaussian distribution peaked at a high rate for high activity, with long-lasting replay of stored patterns. Between this two regimes, a transition region is observed, where firing rates show a bimodal distribution, with alternation of up and down states. In this region, one observes neuronal avalanches exhibiting power laws in size and duration, and a waiting time distribution between successive avalanches which shows a non-monotonic behavior. During periods of high activity (up states) consecutive avalanches are correlated, since they are part of a short transient replay initiated by noise focusing, and waiting times show a power law distribution. One can think at this critical dynamics as a reservoire of dynamical patterns for memory functions.

Percolation transition and the onset of nonexponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ‘‘large scale’’ effects of frustration, present below the percolation threshold. Moreover, these results are consistent with the picture suggested by Campbell et al. @J. Phys. C 20, L47 ~1987!# in the space of configurations. @S1063-651X~98!07412-1#

Glass transition in the quenched and annealed version of the frustrated lattice gas model

In this paper we study the three-dimensional frustrated lattice gas model in the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint. Although the model does not exhibit any thermodynamic transition it shows a diverging peak at some characteristic time in the dynamical nonlinear susceptibility, similar to the results on the p-spin model in mean field and the Lennard-Jones mixture recently found by Donati et al. (e-print cond-mat/9905433). Comparing these results to those obtained in the model with quenched interactions, we conclude that the critical behavior of the dynamical susceptibility is reminiscent of the thermodynamic transition present in the quenched model, and signaled by the divergence of the static nonlinear susceptibility, suggesting therefore a similar mechanism also in supercooled glass-forming liquids.

Clusters in colloidal systems.

We study the dynamical properties of a model for charged colloidal particles, performing molecular dynamics simulations and observing the behavior of bond persistence functions, self-intermediate scattering functions at different wave vectors, and mean-square displacements of the particles, in three different regimes of the volume fraction. At the lowest volume fraction the system displays properties very similar to those of a gelling system, which can be interpreted in terms of the distribution of cluster sizes, with a peak in the dynamical susceptibility at the lowest wave vector. At the highest volume fraction, a percolating network of bonds is always present, and the system is strongly reminiscent of strong glasses, with the maximum in the dynamical susceptibility increasing when the temperature is lowered, and an Arrhenius dependence of the relaxation times. At intermediate volume fractions, a complex behavior is found, where both the distribution of cluster sizes and the intercluster correlations due to crowding are important.

Spin and density overlaps in the frustrated Ising lattice gas

We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the corresponding nonlinear susceptibilities, as a function of the chemical potential. We then evaluate the relaxation functions of the spin and density self-overlap, and study the behavior of the relaxation times. The results suggest that the spin variables undergo a transition very similar to the one of the Ising spin glass, while the density variables do not show any sign of transition at the same chemical potential. It may be that the density variables undergo a transition at a higher chemical potential, inside the phase where the spins are frozen.

Scaling and universality in glass transition

Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator 〈q(t)〉 and the dynamical susceptibility 〈q2(t)〉 − 〈q(t)〉2. Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al. (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension dc = 8.

A simulation environment for directional sensing as a phase separation process

The ability of eukaryotic cells to navigate along spatial gradients of extracellular guidance cues is crucial for embryonic development, tissue regeneration, and cancer progression. One proposed model for chemotaxis is a phosphoinositide-based phase separation process, which takes place at the plasma membrane upon chemoattractant stimulation and triggers directional motility of eukaryotic cells. Here, we make available virtual-cell software that allows the execution and spatiotemporal analysis of in silico chemotaxis experiments, in which the user can control physical and chemical parameters as well as the number and position of chemoattractant sources.

NONEXPONENTIAL RELAXATION IN FULLY FRUSTRATED MODELS

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to nonexponential relaxation dynamics. Nevertheless, we find numerically that the model exhibits a stretched exponential behavior below a temperature