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

Improved model for air pressure due to wind on 2D freak waves in finite depth

This paper presents an improved model for evaluating air pressure acting on 2D freak waves in a finite depth due to the presence of winds. This pressure model is developed by analysing the pressure distribution over freak waves using the QALE-FEM/StarCD approach, which combines the quasi arbitrary Lagrangian-Eulerian finite element method (QALE-FEM) with the commercial software package StarCD and has been proven to be sufficiently accurate for such cases according to our previous publication Yan and Ma (2010) [8]. In this model for air pressure, the pressure is decomposed into the components related to the local wave profiles and others. By coupling with the QALE-FEM, the accuracy of the pressure model is tested using various cases. The results show that the pressure distribution estimated using this model is close to that computed by using the QALE-FEM/StarCD approach when there is no significant vortex shedding and wave breaking. The accuracy investigation in predicting the freak wave heights and elevations demonstrates that this pressure model is much better than others in the literature so far used for modelling wind effects on freak waves in finite depth

On the simulation of nonlinear bidimensional spiking neuron models

Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. Spikes are emitted when the membrane potential blows up or reaches a cutoff value. The precise simulation of the spike times and of the adaptation variable is critical for it governs the spike pattern produced, and is hard to compute accurately because of the exploding nature of the system at the spike times. We thoroughly study the precision of fixed time-step integration schemes for this type of models and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time. Precise evaluation of these quantities therefore involve very small time steps and long simulation times. In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time-step Euler scheme and other more accurate simulation algorithms

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

OPTIS - a satellite-based test of Special and General Relativity

A new satellite based test of Special and General Relativity is proposed. For the Michelson-Morley experiment we expect an improvement of at least three orders of magnitude, and for the Kennedy-Thorndike experiment an improvement of more than one order of magnitude. Furthermore, an improvement by two orders of the test of the universality of the gravitational red shift by comparison of an atomic clock with an optical clock is projected. The tests are based on ultrastable optical cavities, an atomic clock and a comb generator.Comment: To appear in Class. Quantum Gra

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

Insights into early Earth from the Pt-Re-Os isotope and highly siderophile element abundance systematics of Barberton komatiites

Highly siderophile element (HSE: Os, Ir, Ru, Pt, Pd, and Re) abundance and Pt-Re-Os isotopic data are reported for well-preserved komatiites from the Komati and Weltevreden Formations of the Barberton Greenstone Belt in South Africa. The Re-Os data for whole-rock samples and olivine and chromite separates define isochrons with ages of 3484 +/- 38 and 3263 +/- 12 Ma for the Komati and Weltevreden systems, respectively. The respective initial Os-187/Os-188 = 0.10335 +/- 15 (gamma Os-187 = +0.34 +/- 0.15) and 0.10442 +/- 4 (gamma Os-187 = -0.14 +/- 0.04) are well within the range defined by chondritic meteorites. When considered together with the Re-Os data for late Archean komatiite systems, these data indicate that the mantle sources of most Archean komatiites evolved with essentially uniform long-term Re/Os that is well within the chondritic range. By contrast, the initial Os-186/Os-188 = 0.1198283 +/- 9 (epsilon Os-186 = -0.12 +/- 0.08) and 0.1198330 +/- 8 (epsilon Os-186 = +0.22 +/- 0.07) for the Komati and Weltevreden systems, respectively, are outside of known chondritic evolution paths, indicating that the mantle sources of these two komatiite systems evolved with fractionated time-integrated Pt/Os. The new 186,187 Os isotopic data for these early Archean komatiite systems, combined with published Nd-142,Nd-143 and Hf-176 isotopic data for these systems, are consistent with formation and long-term isolation of deep-seated mantle domains with fractionated time-integrated Sm/Nd, Lu/Hf, and Pt/Os ratios, at ca. 4400 Ma. These domains may have been generated as a result of late-stage crystallization of a primordial magma ocean involving Mg-perovskite, Ca-perovskite and Pt-alloys acting as the fractionating phases. The inferred fractionated mantle domains were sampled by the early Archean komatiites, but were largely mixed away by 2.7 Ga, as evidenced by uniform time-integrated Sm/Nd, Lu/Hf, and Pt/Os ratios inferred for the sources of most late Archean komatiite systems. The calculated total Pt + Pd abundances present in the sources of the early Archean komatiite systems fall only 7-14% short of those present in estimates for the modern primitive mantle. These are also within the range of the total Pt + Pd abundances present in the sources of late Archean komatiite systems, indicating little change in the HSE abundances in the Archean mantle between 3.5 and 2.7 Ga. The new HSE data for the early Archean komatiite systems may implicate late accretion of HSE to the mantle prior to completion of crystallization of a final terrestrial magma ocean, followed by sluggish mixing of diverse, post-magma ocean domains characterized by variably fractionated lithophile element and HSE abundances. (C) 2013 Elsevier Ltd. All rights reserved

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