1,327 research outputs found
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 . 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.
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
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
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
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
New Nd-142 Evidence for a Non-Chondritic Composition of the Moon
The coupled Sm-147,146-Nd-143,142 systematics of lunar samples has been extensively studied for estimating the timescale of lunar differentiation. The published datasets yield consistent ages for Nd isotopic closure within the lunar mantle of approx.200 Myr after CAI formation. Although this time constraint is consistent with estimates derived from Hf-W chronometry of the Moon (>60 Myr after CAI formation), there is debate as to whether this age has chronological significance. Furthermore, there are discrepancies regarding the Nd isotope composition of the bulk Moon. Rankenburg et al. obtained a epsilon Nd-142 vs. Sm-147/Nd-144 correlation for lunar samples passing though the chondritic reference value (Sm-147/Nd-144 = 0.1967, epsilon Nd-142 = -0.21), suggesting that the Moon has a chondritic bulk composition. In contrast, the other datasets define a correlation line that passes approx.10-20 ppm above, suggesting that the Moon has a superchondritic Sm-147/Nd-144 (approx.0.206), close to that of the early depleted Earth (EDM). We present new Sm-Nd data for a high-Ti mare basalt (70135), two low-Ti mare basalt (LAP 02205 and MIL 05035) and a KREEPy low-Ti mare basalt (NWA 2977). These data are used to evaluate the significance of the Sm-Nd systematics for constraining the timescale of lunar differentiation and the bulk Nd isotope composition of the Moon
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
On the equivalence principle and gravitational and inertial mass relation of classical charged particles
We show that the locally constant force necessary to get a stable hyperbolic
motion regime for classical charged point particles, actually, is a combination
of an applied external force and of the electromagnetic radiation reaction
force. It implies, as the strong Equivalence Principle is valid, that the
passive gravitational mass of a charged point particle should be slight greater
than its inertial mass. An interesting new feature that emerges from the
unexpected behavior of the gravitational and inertial mass relation, for
classical charged particles, at very strong gravitational field, is the
existence of a critical, particle dependent, gravitational field value that
signs the validity domain of the strong Equivalence Principle. For electron and
proton, these critical field values are
and , respectively
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