162 research outputs found
Methods for a quantitative evaluation of odd-even staggering effects
Odd-even effects, also known as "staggering" effects, are a common feature
observed in the yield distributions of fragments produced in different types of
nuclear reactions. We review old methods, and we propose new ones, for a
quantitative estimation of these effects as a function of proton or neutron
number of the reaction products. All methods are compared on the basis of Monte
Carlo simulations. We find that some are not well suited for the task, the most
reliable ones being those based either on a non-linear fit with a properly
oscillating function or on a third (or fourth) finite difference approach. In
any case, high statistic is of paramount importance to avoid that spurious
structures appear just because of statistical fluctuations in the data and of
strong correlations among the yields of neighboring fragments.Comment: 16 pages, 9 figures - Revised version, mainly with an expanded sect.
2 about smoothing methods (three more methods are presented and an appendix
on relevant aspects of the finite-differences formalism is added); results
are shown also for the simulations with the three additional methods. Some
more references are added. Conclusions are unchange
Chimera states in pulse coupled neural networks: the influence of dilution and noise
We analyse the possible dynamical states emerging for two symmetrically pulse
coupled populations of leaky integrate-and-fire neurons. In particular, we
observe broken symmetry states in this set-up: namely, breathing chimeras,
where one population is fully synchronized and the other is in a state of
partial synchronization (PS) as well as generalized chimera states, where both
populations are in PS, but with different levels of synchronization. Symmetric
macroscopic states are also present, ranging from quasi-periodic motions, to
collective chaos, from splay states to population anti-phase partial
synchronization. We then investigate the influence disorder, random link
removal or noise, on the dynamics of collective solutions in this model. As a
result, we observe that broken symmetry chimera-like states, with both
populations partially synchronized, persist up to 80 \% of broken links and up
to noise amplitudes 8 \% of threshold-reset distance. Furthermore, the
introduction of disorder on symmetric chaotic state has a constructive effect,
namely to induce the emergence of chimera-like states at intermediate dilution
or noise level.Comment: 15 pages, 7 figure, contribution for the Workshop "Nonlinear Dynamics
in Computational Neuroscience: from Physics and Biology to ICT" held in Turin
(Italy) in September 201
Coherent periodic activity in excitatory Erdos-Renyi neural networks:The role of network connectivity
We consider an excitatory random network of leaky integrate-and-fire pulse
coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph
with average connectivity scaling as a power law with the number of
neurons in the network. The scaling is controlled by a parameter ,
which allows to pass from massively connected to sparse networks and therefore
to modify the topology of the system. At a macroscopic level we observe two
distinct dynamical phases: an Asynchronous State (AS) corresponding to a
desynchronized dynamics of the neurons and a Partial Synchronization (PS)
regime associated with a coherent periodic activity of the network. At low
connectivity the system is in an AS, while PS emerges above a certain critical
average connectivity . For sufficiently large networks,
saturates to a constant value suggesting that a minimal average connectivity is
sufficient to observe coherent activity in systems of any size irrespectively
of the kind of considered network: sparse or massively connected. However, this
value depends on the nature of the synapses: reliable or unreliable. For
unreliable synapses the critical value required to observe the onset of
macroscopic behaviors is noticeably smaller than for reliable synaptic
transmission. Due to the disorder present in the system, for finite number of
neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form
of chaos, which vanishes in the thermodynamic limit. In such a limit the
disordered systems exhibit regular (non chaotic) dynamics and their properties
correspond to that of a homogeneous fully connected network for any
-value. Apart for the peculiar exception of sparse networks, which
remain intrinsically inhomogeneous at any system size.Comment: 7 pages, 11 figures, submitted to Chao
Linear stability in networks of pulse-coupled neurons
In a first step towards the comprehension of neural activity, one should
focus on the stability of the various dynamical states. Even the
characterization of idealized regimes, such as a perfectly periodic spiking
activity, reveals unexpected difficulties. In this paper we discuss a general
approach to linear stability of pulse-coupled neural networks for generic
phase-response curves and post-synaptic response functions. In particular, we
present: (i) a mean-field approach developed under the hypothesis of an
infinite network and small synaptic conductances; (ii) a "microscopic" approach
which applies to finite but large networks. As a result, we find that no matter
how large is a neural network, its response to most of the perturbations
depends on the system size. There exists, however, also a second class of
perturbations, whose evolution typically covers an increasingly wide range of
time scales. The analysis of perfectly regular, asynchronous, states reveals
that their stability depends crucially on the smoothness of both the
phase-response curve and the transmitted post-synaptic pulse. The general
validity of this scenarion is confirmed by numerical simulations of systems
that are not amenable to a perturbative approach.Comment: 13 pages, 7 figures, submitted to Frontiers in Computational
Neuroscienc
Stability of the splay state in networks of pulse-coupled neurons
We analytically investigate the stability of {\it splay states} in networks
of pulse-coupled phase-like models of neurons. By developing a perturbative
technique, we find that, in the limit of large , the Floquet spectrum scales
as for generic discontinuous velocity fields. Moreover, the stability
of the so-called short-wavelength component is determined by the sign of the
jump at the discontinuity. Altogether, the form of the spectrum depends on the
pulse shape but is independent of the velocity field.Comment: 22 pages, no figures and 120 equation
Recommended from our members
Chimera states in pulse coupled neural networks: The influence of dilution and noise
We analyse the possible dynamical states emerging for two symmetrically
pulse coupled populations of leaky integrate-and-fire neurons. In particular,
we observe broken symmetry states in this set-up: namely, breathing chimeras,
where one population is fully synchronized and the other is in a state of
partial synchronization (PS) as well as generalized chimera states, where
both populations are in PS, but with different levels of synchronization.
Symmetric macroscopic states are also present, ranging from quasi-periodic
motions, to collective chaos, from splay states to population anti-phase
partial synchronization. We then investigate the influence disorder, random
link removal or noise, on the dynamics of collective solutions in this model.
As a result, we observe that broken symmetry chimeralike states, with both
populations partially synchronized, persist up to 80% of broken links and up
to noise ︠amplitude
Intermittent chaotic chimeras for coupled rotators
Two symmetrically coupled populations of N oscillators with inertia
display chaotic solutions with broken symmetry similar to experimental
observations with mechanical pendula. In particular, we report the first
evidence of intermittent chaotic chimeras, where one population is synchronized
and the other jumps erratically between laminar and turbulent phases. These
states have finite life-times diverging as a power-law with N and m. Lyapunov
analyses reveal chaotic properties in quantitative agreement with theoretical
predictions for globally coupled dissipative systems.Comment: 6 pages, 5 figures SUbmitted to Physical Review E, as Rapid
Communicatio
Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory
instantaneous post-synaptic potentials. In particular, we report exact results
for the firing rate, the coefficient of variation and the spike train spectrum
for various synaptic weight distributions. Our results are not limited to
stimulations of infinitesimal amplitude, but they apply as well to finite
amplitude post-synaptic potentials, thus being able to capture the effect of
rare and large spikes. The developed methods are able to reproduce also the
average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report
Death and rebirth of neural activity in sparse inhibitory networks
In this paper, we clarify the mechanisms underlying a general phenomenon
present in pulse-coupled heterogeneous inhibitory networks: inhibition can
induce not only suppression of the neural activity, as expected, but it can
also promote neural reactivation. In particular, for globally coupled systems,
the number of firing neurons monotonically reduces upon increasing the strength
of inhibition (neurons' death). However, the random pruning of the connections
is able to reverse the action of inhibition, i.e. in a sparse network a
sufficiently strong synaptic strength can surprisingly promote, rather than
depress, the activity of the neurons (neurons' rebirth). Thus the number of
firing neurons reveals a minimum at some intermediate synaptic strength. We
show that this minimum signals a transition from a regime dominated by the
neurons with higher firing activity to a phase where all neurons are
effectively sub-threshold and their irregular firing is driven by current
fluctuations. We explain the origin of the transition by deriving an analytic
mean field formulation of the problem able to provide the fraction of active
neurons as well as the first two moments of their firing statistics. The
introduction of a synaptic time scale does not modify the main aspects of the
reported phenomenon. However, for sufficiently slow synapses the transition
becomes dramatic, the system passes from a perfectly regular evolution to an
irregular bursting dynamics. In this latter regime the model provides
predictions consistent with experimental findings for a specific class of
neurons, namely the medium spiny neurons in the striatum.Comment: 19 pages, 10 figures, submitted to NJ
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