Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

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

Head-on collision of two solitary waves and residual falling jet formation

The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value

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

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

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

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

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