44,571 research outputs found
Estimating Parameters of Partial Differential Equations with Gradient Matching
Parameter inference in partial differential equations (PDEs) is a problem that many researchers are interested in. The conventional methods suffer from severe computational costs because these method require to solve the PDEs repeatedly by numerical integration. The concept of gradient matching have been proposed in order to reduce the computational complexity, which consists of two steps. First, the data are interpolated with certain smoothing methods. Then, the partial derivatives of the interpolants are calculated and the parameters are optimized to minimize the distance (measured by loss functions) between partial derivatives of interpolants and the PDE systems. In this article, we first studied the parameter inference accuracy of gradient matching based on two simple PDE models. Then the method of gradient matching was used to infer the parameters of PDE models describing cell movement and select the most appropriate model
On estimating extremal dependence structures by parametric spectral measures
Estimation of extreme value copulas is often required in situations where
available data are sparse. Parametric methods may then be the preferred
approach. A possible way of defining parametric families that are simple and,
at the same time, cover a large variety of multivariate extremal dependence
structures is to build models based on spectral measures. This approach is
considered here. Parametric families of spectral measures are defined as convex
hulls of suitable basis elements, and parameters are estimated by projecting an
initial nonparametric estimator on these finite-dimensional spaces. Asymptotic
distributions are derived for the estimated parameters and the resulting
estimates of the spectral measure and the extreme value copula. Finite sample
properties are illustrated by a simulation study
Pareto Smoothed Importance Sampling
Importance weighting is a general way to adjust Monte Carlo integration to
account for draws from the wrong distribution, but the resulting estimate can
be noisy when the importance ratios have a heavy right tail. This routinely
occurs when there are aspects of the target distribution that are not well
captured by the approximating distribution, in which case more stable estimates
can be obtained by modifying extreme importance ratios. We present a new method
for stabilizing importance weights using a generalized Pareto distribution fit
to the upper tail of the distribution of the simulated importance ratios. The
method, which empirically performs better than existing methods for stabilizing
importance sampling estimates, includes stabilized effective sample size
estimates, Monte Carlo error estimates and convergence diagnostics.Comment: Major revision: 1) proofs for consistency, finite variance, and
asymptotic normality, 2) justification of k<0.7 with theoretical
computational complexity analysis, 3) major rewrit
Classical-to-critical crossovers from field theory
We extent the previous determinations of nonasymptotic critical behavior of
Phys. Rev B32, 7209 (1985) and B35, 3585 (1987) to accurate expressions of the
complete classical-to-critical crossover (in the 3-d field theory) in terms of
the temperature-like scaling field (i.e., along the critical isochore) for : 1)
the correlation length, the susceptibility and the specific heat in the
homogeneous phase for the n-vector model (n=1 to 3) and 2) for the spontaneous
magnetization (coexistence curve), the susceptibility and the specific heat in
the inhomogeneous phase for the Ising model (n=1). The present calculations
include the seventh loop order of Murray and Nickel (1991) and closely account
for the up-to-date estimates of universal asymptotic critical quantities
(exponents and amplitude combinations) provided by Guida and Zinn-Justin [J.
Phys. A31, 8103 (1998)].Comment: 4 figs, 4 program documents in appendix, some corrections adde
Decline of long-range temporal correlations in the human brain during sustained wakefulness
Sleep is crucial for daytime functioning, cognitive performance and general
well-being. These aspects of daily life are known to be impaired after extended
wake, yet, the underlying neuronal correlates have been difficult to identify.
Accumulating evidence suggests that normal functioning of the brain is
characterized by long-range temporal correlations (LRTCs) in cortex, which are
supportive for decision-making and working memory tasks.
Here we assess LRTCs in resting state human EEG data during a 40-hour sleep
deprivation experiment by evaluating the decay in autocorrelation and the
scaling exponent of the detrended fluctuation analysis from EEG amplitude
fluctuations. We find with both measures that LRTCs decline as sleep
deprivation progresses. This decline becomes evident when taking changes in
signal power into appropriate consideration.
Our results demonstrate the importance of sleep to maintain LRTCs in the
human brain. In complex networks, LRTCs naturally emerge in the vicinity of a
critical state. The observation of declining LRTCs during wake thus provides
additional support for our hypothesis that sleep reorganizes cortical networks
towards critical dynamics for optimal functioning
Fitting Linear Mixed-Effects Models using lme4
Maximum likelihood or restricted maximum likelihood (REML) estimates of the
parameters in linear mixed-effects models can be determined using the lmer
function in the lme4 package for R. As for most model-fitting functions in R,
the model is described in an lmer call by a formula, in this case including
both fixed- and random-effects terms. The formula and data together determine a
numerical representation of the model from which the profiled deviance or the
profiled REML criterion can be evaluated as a function of some of the model
parameters. The appropriate criterion is optimized, using one of the
constrained optimization functions in R, to provide the parameter estimates. We
describe the structure of the model, the steps in evaluating the profiled
deviance or REML criterion, and the structure of classes or types that
represents such a model. Sufficient detail is included to allow specialization
of these structures by users who wish to write functions to fit specialized
linear mixed models, such as models incorporating pedigrees or smoothing
splines, that are not easily expressible in the formula language used by lmer.Comment: 51 pages, including R code, and an appendi
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