211 research outputs found
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
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
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, and . We identify these
limits with the random loose packing volume fraction \rl and the random close
packing volume fraction \rc of frictionless spheres, respectively
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
Cage-jump motion reveals universal dynamics and non-universal structural features in glass forming liquids
The sluggish and heterogeneous dynamics of glass forming liquids is
frequently associated to the transient coexistence of two phases of particles,
respectively with an high and low mobility. In the absence of a dynamical order
parameter that acquires a transient bimodal shape, these phases are commonly
identified empirically, which makes difficult investigating their relation with
the structural properties of the system. Here we show that the distribution of
single particle diffusivities can be accessed within a Continuous Time Random
Walk description of the intermittent motion, and that this distribution
acquires a transient bimodal shape in the deeply supercooled regime, thus
allowing for a clear identification of the two coexisting phase. In a simple
two-dimensional glass forming model, the dynamic phase coexistence is
accompanied by a striking structural counterpart: the distribution of the
crystalline-like order parameter becomes also bimodal on cooling, with
increasing overlap between ordered and immobile particles. This simple
structural signature is absent in other models, such as the three-dimesional
Kob-Andersen Lennard-Jones mixture, where more sophisticated order parameters
might be relevant. In this perspective, the identification of the two dynamical
coexisting phases opens the way to deeper investigations of structure-dynamics
correlations.Comment: Published in the J. Stat. Mech. Special Issue "The Role of Structure
in Glassy and Jammed Systems
Dynamical arrest: interplay of the glass and of the gel transitions
The structural arrest of a polymeric suspension might be driven by an
increase of the cross--linker concentration, that drives the gel transition, as
well as by an increase of the polymer density, that induces a glass transition.
These dynamical continuous (gel) and discontinuous (glass) transitions might
interfere, since the glass transition might occur within the gel phase, and the
gel transition might be induced in a polymer suspension with glassy features.
Here we study the interplay of these transitions by investigating via
event--driven molecular dynamics simulation the relaxation dynamics of a
polymeric suspension as a function of the cross--linker concentration and the
monomer volume fraction. We show that the slow dynamics within the gel phase is
characterized by a long sub-diffusive regime, which is due both to the crowding
as well as to the presence of a percolating cluster. In this regime, the
transition of structural arrest is found to occur either along the gel or along
the glass line, depending on the length scale at which the dynamics is probed.
Where the two line meet there is no apparent sign of higher order dynamical
singularity. Logarithmic behavior typical of singularity appear inside
the gel phase along the glass transition line. These findings seem to be
related to the results of the mode coupling theory for the schematic
model
Dynamical Correlation Length and Relaxation Processes in a Glass Former
We investigate the relaxation process and the dynamical heterogeneities of
the kinetically constrained Kob--Anderson lattice glass model, and show that
these are characterized by different timescales. The dynamics is well described
within the diffusing defect paradigm, which suggest to relate the relaxation
process to a reverse--percolation transition. This allows for a geometrical
interpretation of the relaxation process, and of the different timescales
Recurrence of spatio-temporal patterns of spikes and neural avalanches at the critical point of a non-equilibrium phase transition
Recently, many experimental results have supported the idea that the brain operates near a critical point [1-5], as reflected by the power laws of avalanche size distributions and maximization of fluctuations. Several models have been proposed as explanations for the power law distributions that emerge in spontaneous cortical activity [6,5]. Models based on branching processes and on self-organized criticality are the most relevant. However, there are additional features of neuronal avalanches that are not captured in these models, such as the stable recurrence of particular spatiotemporal patterns and the conditions under which these precise and diverse patterns can be retrieved [4]. Indeed, neuronal avalanches are highly repeatable and can be clustered into statistically significant families of activity patterns that satisfy several requirements of a memory substrate. In many areas of the brain having different brain functionality, repeatable precise spatiotemporal patterns of spikes seem to play a crucial role in the coding and storage of information. Many in vitro and in vivo studies have demonstrated that cortical spontaneous activity occurs in precise spatiotemporal patterns, which often reflect the activity produced by external or sensory inputs. The temporally structured replay of spatiotemporal patterns has been observed to occur, both in the cortex and hippocampus, during sleep and in the awake state, and it has been hypothesized that this replay may subserve memory consolidation. Previous studies have separately addressed the topics of phase-coded memory storage and neuronal avalanches, but our work is the first to show how these ideas converge in a single cortical model. We study a network of leaky integrate- and-fire (LIF) neurons, whose synaptic connections are designed with a rule based on spike-timing dependent plasticity (STDP). The network works as an associative memory of phase-coded spatiotemporal patterns, whose storage capacity has been studied in [7]. In this paper, we study the spontaneous dynamics when the excitability of the model is tuned to be at the critical point of a phase transition, between the successful persistent replay and non-replay of encoded patterns. 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 [5]). Notably, in this critical region, the avalanche size and duration distributions follow power laws
Role of topology in the spontaneous cortical activity
Scarpetta et al. BMC Neuroscience 2015, 16(Suppl 1):P6
http://www.biomedcentral.com/1471-2202/16/S1/P
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