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 post-synaptic 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

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

Thermal Operators in Ising Percolation

We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model, obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to get new exact relations on the topological structure of FK clusters of the Ising model defined on an arbitrary graph.Comment: 17 pages, 2 figures. Improved version. Major changes in the text and in the notations. A missing term added in the specific heat representatio

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 and the dynamical susceptibility -^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 d_c=8.Comment: 16 pages, 9 figure

Glassy behavior of the site frustrated percolation model

The dynamical properties of the site frustrated percolation model are investigated and compared with those of glass forming liquids. When the density of the particles on the lattice becomes high enough, the dynamics of the model becomes very slow, due to geometrical constraints, and rearrangement on large scales is needed to allow relaxation. The autocorrelation functions, the specific volume for different cooling rates, and the mean square displacement are evaluated, and are found to exhibit glassy behavior.Comment: 8 pages, RevTeX, 11 fig

Disordered jammed packings of frictionless spheres

At low volume fraction, disordered arrangements of frictionless spheres are found in un--jammed states unable to support applied stresses, while at high volume fraction they are found in jammed states with mechanical strength. Here we show, focusing on the hard sphere zero pressure limit, that the transition between un-jammed and jammed states does not occur at a single value of the volume fraction, but in a whole volume fraction range. This result is obtained via the direct numerical construction of disordered jammed states with a volume fraction varying between two limits, $0.636$ and $0.646$. We identify these limits with the random loose packing volume fraction \rl and the random close packing volume fraction \rc of frictionless spheres, respectively

Off equilibrium response function in the one dimensional random field Ising model

A thorough numerical investigation of the slow dynamics in the d=1 random field Ising model in the limit of an infinite ferromagnetic coupling is presented. Crossovers from the preasymptotic pure regime to the asymptotic Sinai regime are investigated for the average domain size, the autocorrelation function and staggered magnetization. By switching on an additional small random field at the time tw the linear off equilibrium response function is obtained, which displays as well the crossover from the nontrivial behavior of the d=1 pure Ising model to the asymptotic behavior where it vanishes identically.Comment: 12 pages, 10 figure

Crossover properties from random percolation to frustrated percolation

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents nu, gamma and beta of the percolation transition of the model, for various values of the density of antiferromagnetic interactions pi in the range 0<pi<0.5. Our data are consistent with the existence of a crossover from random percolation behavior for pi=0, to frustrated percolation behavior, characterized by the critical exponents of the ferromagnetic 1/2-state Potts model, as soon as pi>0.Comment: 5 pages, 7 figs, RevTe

Relationship between cigarette smoking and body mass index in the Italian population

Objective: Tobacco smoke, as numerous studies have established, is due to some diseases related to the respiratory, cardio - circulatory and gastrointestinal systems. In addition, tobacco consumption is often associated with a decrease in weight, while former smokers often experience an increase in BMI. The purpose of this research is to test the behavior of body mass index in relation to a representative sample of the Italian population, covering the period 2004-2005. Design: Calculations were made using SPSS software. The data were stratified by age and gender, using odds ratio (OR) to determine the significance of smoking in relation to BMI. The OR was calculated both in a timely manner, both considering a confidence interval of 95%. Material and methods: In this research, we will analyze the variable BMIâ€, in relation to the variable tobacco smokeâ€, derived from the multipurpose ISTAT called Condizione di salute e ricorso ai servizi sanitari. The sample was stratified by age, 18 years and over, and gender. Results: The analysis shows that in 2005, 10% of the Italian population results in overweight, while 22% said they smoke; 23% of female smokers claiming to be underweight, while for the former smokers the value drops to 10%. For males, the difference in BMI between smokers and former smokers is minimal. The OR shows that weight gain among former smokers and smokers is actually due to custom/cessation from tobacco smoke. Conclusion: The structure of BMI in relation to smoking has confirmed the existence emerged in the literature, so that those who quit smoking reflects an increase in weight. However, the results highlighted by some foreign studies, which propose an increase in obesity among former smokers, is not confirmed in the Italian population.Keywords: body mass index; smoking; odds ratio