1,312 research outputs found
Noise-induced behaviors in neural mean field dynamics
The collective behavior of cortical neurons is strongly affected by the
presence of noise at the level of individual cells. In order to study these
phenomena in large-scale assemblies of neurons, we consider networks of
firing-rate neurons with linear intrinsic dynamics and nonlinear coupling,
belonging to a few types of cell populations and receiving noisy currents.
Asymptotic equations as the number of neurons tends to infinity (mean field
equations) are rigorously derived based on a probabilistic approach. These
equations are implicit on the probability distribution of the solutions which
generally makes their direct analysis difficult. However, in our case, the
solutions are Gaussian, and their moments satisfy a closed system of nonlinear
ordinary differential equations (ODEs), which are much easier to study than the
original stochastic network equations, and the statistics of the empirical
process uniformly converge towards the solutions of these ODEs. Based on this
description, we analytically and numerically study the influence of noise on
the collective behaviors, and compare these asymptotic regimes to simulations
of the network. We observe that the mean field equations provide an accurate
description of the solutions of the network equations for network sizes as
small as a few hundreds of neurons. In particular, we observe that the level of
noise in the system qualitatively modifies its collective behavior, producing
for instance synchronized oscillations of the whole network, desynchronization
of oscillating regimes, and stabilization or destabilization of stationary
solutions. These results shed a new light on the role of noise in shaping
collective dynamics of neurons, and gives us clues for understanding similar
phenomena observed in biological networks
A Markovian event-based framework for stochastic spiking neural networks
In spiking neural networks, the information is conveyed by the spike times,
that depend on the intrinsic dynamics of each neuron, the input they receive
and on the connections between neurons. In this article we study the Markovian
nature of the sequence of spike times in stochastic neural networks, and in
particular the ability to deduce from a spike train the next spike time, and
therefore produce a description of the network activity only based on the spike
times regardless of the membrane potential process.
To study this question in a rigorous manner, we introduce and study an
event-based description of networks of noisy integrate-and-fire neurons, i.e.
that is based on the computation of the spike times. We show that the firing
times of the neurons in the networks constitute a Markov chain, whose
transition probability is related to the probability distribution of the
interspike interval of the neurons in the network. In the cases where the
Markovian model can be developed, the transition probability is explicitly
derived in such classical cases of neural networks as the linear
integrate-and-fire neuron models with excitatory and inhibitory interactions,
for different types of synapses, possibly featuring noisy synaptic integration,
transmission delays and absolute and relative refractory period. This covers
most of the cases that have been investigated in the event-based description of
spiking deterministic neural networks
Finite-size and correlation-induced effects in Mean-field Dynamics
The brain's activity is characterized by the interaction of a very large
number of neurons that are strongly affected by noise. However, signals often
arise at macroscopic scales integrating the effect of many neurons into a
reliable pattern of activity. In order to study such large neuronal assemblies,
one is often led to derive mean-field limits summarizing the effect of the
interaction of a large number of neurons into an effective signal. Classical
mean-field approaches consider the evolution of a deterministic variable, the
mean activity, thus neglecting the stochastic nature of neural behavior. In
this article, we build upon two recent approaches that include correlations and
higher order moments in mean-field equations, and study how these stochastic
effects influence the solutions of the mean-field equations, both in the limit
of an infinite number of neurons and for large yet finite networks. We
introduce a new model, the infinite model, which arises from both equations by
a rescaling of the variables and, which is invertible for finite-size networks,
and hence, provides equivalent equations to those previously derived models.
The study of this model allows us to understand qualitative behavior of such
large-scale networks. We show that, though the solutions of the deterministic
mean-field equation constitute uncorrelated solutions of the new mean-field
equations, the stability properties of limit cycles are modified by the
presence of correlations, and additional non-trivial behaviors including
periodic orbits appear when there were none in the mean field. The origin of
all these behaviors is then explored in finite-size networks where interesting
mesoscopic scale effects appear. This study leads us to show that the
infinite-size system appears as a singular limit of the network equations, and
for any finite network, the system will differ from the infinite system
Correlation between Progetto Cuore risk score and early cardiovascular damage in never treated subjects
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens
Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
Realistic networks display heterogeneous transmission delays. We analyze here
the limits of large stochastic multi-populations networks with stochastic
coupling and random interconnection delays. We show that depending on the
nature of the delays distributions, a quenched or averaged propagation of chaos
takes place in these networks, and that the network equations converge towards
a delayed McKean-Vlasov equation with distributed delays. Our approach is
mostly fitted to neuroscience applications. We instantiate in particular a
classical neuronal model, the Wilson and Cowan system, and show that the
obtained limit equations have Gaussian solutions whose mean and standard
deviation satisfy a closed set of coupled delay differential equations in which
the distribution of delays and the noise levels appear as parameters. This
allows to uncover precisely the effects of noise, delays and coupling on the
dynamics of such heterogeneous networks, in particular their role in the
emergence of synchronized oscillations. We show in several examples that not
only the averaged delay, but also the dispersion, govern the dynamics of such
networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and
clarified a regularity hypothesis (remark 1
How to Deal with Weak Interactions in Noncovalent Complexes Analyzed by Electrospray Mass Spectrometry: Cyclopeptidic Inhibitors of the Nuclear Receptor Coactivator 1-STAT6
Mass spectrometry, and especially electrospray ionization, is now an efficient tool to study noncovalent interactions between proteins and inhibitors. It is used here to study the interaction of some weak inhibitors with the NCoA-1/STAT6 protein with KD values in the μM range. High signal intensities corresponding to some nonspecific electrostatic interactions between NCoA-1 and the oppositely charged inhibitors were observed by nanoelectrospray mass spectrometry, due to the use of high ligand concentrations. Diverse strategies have already been developed to deal with nonspecific interactions, such as controlled dissociation in the gas phase, mathematical modeling, or the use of a reference protein to monitor the appearance of nonspecific complexes. We demonstrate here that this last methodology, validated only in the case of neutral sugar–protein interactions, i.e., where dipole–dipole interactions are crucial, is not relevant in the case of strong electrostatic interactions. Thus, we developed a novel strategy based on half-maximal inhibitory concentration (IC50) measurements in a competitive assay with readout by nanoelectrospray mass spectrometry. IC50 values determined by MS were finally converted into dissociation constants that showed very good agreement with values determined in the liquid phase using a fluorescence polarization assay
Runaway dilaton and equivalence principle violations
In a recently proposed scenario, where the dilaton decouples while
cosmologically attracted towards infinite bare string coupling, its residual
interactions can be related to the amplitude of density fluctuations generated
during inflation, and are large enough to be detectable through a modest
improvement on present tests of free-fall universality. Provided it has
significant couplings to either dark matter or dark energy, a runaway dilaton
can also induce time-variations of the natural "constants" within the reach of
near-future experiments.Comment: 4 pages, minor change
In search of late-stage planetary building blocks
Genetic contributions to the final stages of planetary growth, including materials associated with the giant Moon forming
impact, late accretion, and late heavy bombardment are examined using siderophile elements. Isotopic similarities
between the Earth and Moon for both lithophile and siderophile elements collectively lead to the suggestion
that the genetics of the building blocks for Earth, and the impactor involved in the Moon-forming event were broadly
similar, and shared some strong genetic affinities with enstatite chondrites. The bulk genetic fingerprint of materials
subsequently added to Earth by late accretion, defined as the addition of ~0.5 wt.% of Earth's mass to the mantle,
following cessation of core formation, was characterized by 187Os/188Os and Pd/Ir ratios that were also similar to
those in some enstatite chondrites. However, the integrated fingerprint of late accreted matter differs from enstatite
chondrites in terms of the relative abundances of certain other HSE, most notably Ru/Ir. The final ≤0.05 wt.% addition
of material to the Earth and Moon, believed by some to be part of a late heavy bombardment, included a component
with much more fractionated relative HSE abundances than evidenced in the average late accretionary component.
Heterogeneous 182W/184Wisotopic compositions of some ancient terrestrial rocks suggest that some very early formed
mantle domains remained chemically distinct for long periods of time following primary planetary accretion.
This evidence for sluggish mixing of the early mantle suggests that if late accretionary contributions to the
mantle were genetically diverse, it may be possible to isotopically identify the disparate primordial components
in the terrestrial rock record using the siderophile element tracers Ru and Mo.NASA grants NNX13AF83G and NNA14AB07A
NSF-CSEDI grants EAR1160728 and EAR1265169
Matter-gravity couplings and Lorentz violation
The gravitational couplings of matter are studied in the presence of Lorentz
and CPT violation. At leading order in the coefficients for Lorentz violation,
the relativistic quantum hamiltonian is derived from the gravitationally
coupled minimal Standard-Model Extension. For spin-independent effects, the
nonrelativistic quantum hamiltonian and the classical dynamics for test and
source bodies are obtained. A systematic perturbative method is developed to
treat small metric and coefficient fluctuations about a Lorentz-violating and
Minkowski background. The post-newtonian metric and the trajectory of a test
body freely falling under gravity in the presence of Lorentz violation are
established. An illustrative example is presented for a bumblebee model. The
general methodology is used to identify observable signals of Lorentz and CPT
violation in a variety of gravitational experiments and observations, including
gravimeter measurements, laboratory and satellite tests of the weak equivalence
principle, antimatter studies, solar-system observations, and investigations of
the gravitational properties of light. Numerous sensitivities to coefficients
for Lorentz violation can be achieved in existing or near-future experiments at
the level of parts in 10^3 down to parts in 10^{15}. Certain coefficients are
uniquely detectable in gravitational searches and remain unmeasured to date.Comment: 59 pages two-column REVTe
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