582 research outputs found
Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood
Recent likelihood theory produces -values that have remarkable accuracy
and wide applicability. The calculations use familiar tools such as maximum
likelihood values (MLEs), observed information and parameter rescaling. The
usual evaluation of such -values is by simulations, and such simulations do
verify that the global distribution of the -values is uniform(0, 1), to high
accuracy in repeated sampling. The derivation of the -values, however,
asserts a stronger statement, that they have a uniform(0, 1) distribution
conditionally, given identified precision information provided by the data. We
take a simple regression example that involves exact precision information and
use large sample techniques to extract highly accurate information as to the
statistical position of the data point with respect to the parameter:
specifically, we examine various -values and Bayesian posterior survivor
-values for validity. With observed data we numerically evaluate the various
-values and -values, and we also record the related general formulas. We
then assess the numerical values for accuracy using Markov chain Monte Carlo
(McMC) methods. We also propose some third-order likelihood-based procedures
for obtaining means and variances of Bayesian posterior distributions, again
followed by McMC assessment. Finally we propose some adaptive McMC methods to
improve the simulation acceptance rates. All these methods are based on
asymptotic analysis that derives from the effect of additional data. And the
methods use simple calculations based on familiar maximizing values and related
informations. The example illustrates the general formulas and the ease of
calculations, while the McMC assessments demonstrate the numerical validity of
the -values as percentage position of a data point. The example, however, is
very simple and transparent, and thus gives little indication that in a wide
generality of models the formulas do accurately separate information for almost
any parameter of interest, and then do give accurate -value determinations
from that information. As illustration an enigmatic problem in the literature
is discussed and simulations are recorded; various examples in the literature
are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Dual phase-shift Bragg grating silicon photonic modulator operating up to 60 Gb/s
We demonstrate PAM-4 and OOK operation of a novel silicon photonic modulator. The modulator design is based on two phase-shifts in a Bragg Grating structure driven in a push pull configuration. Back-to-back PAM-4 modulation is demonstrated below the FEC threshold at up to 60 Gb/s. OOK modulation is also shown up to 55 Gb/s with MMSE equalization and up to 50 Gb/s without equalization. Eye diagrams and BER curves at different bit rates are provided for both PAM-4 and OOK modulations. To our knowledge, this structure is the fastest silicon photonic modulator based on Bragg gratings, reaching modulation speed comparable to the fastest Mach-Zehnder modulators and micro-ring modulators
Model of Low-pass Filtering of Local Field Potentials in Brain Tissue
Local field potentials (LFPs) are routinely measured experimentally in brain
tissue, and exhibit strong low-pass frequency filtering properties, with high
frequencies (such as action potentials) being visible only at very short
distances (10~) from the recording electrode. Understanding
this filtering is crucial to relate LFP signals with neuronal activity, but not
much is known about the exact mechanisms underlying this low-pass filtering. In
this paper, we investigate a possible biophysical mechanism for the low-pass
filtering properties of LFPs. We investigate the propagation of electric fields
and its frequency dependence close to the current source, i.e. at length scales
in the order of average interneuronal distance. We take into account the
presence of a high density of cellular membranes around current sources, such
as glial cells. By considering them as passive cells, we show that under the
influence of the electric source field, they respond by polarisation, i.e.,
creation of an induced field. Because of the finite velocity of ionic charge
movement, this polarization will not be instantaneous. Consequently, the
induced electric field will be frequency-dependent, and much reduced for high
frequencies. Our model establishes that with respect to frequency attenuation
properties, this situation is analogous to an equivalent RC-circuit, or better
a system of coupled RC-circuits. We present a number of numerical simulations
of induced electric field for biologically realistic values of parameters, and
show this frequency filtering effect as well as the attenuation of
extracellular potentials with distance. We suggest that induced electric fields
in passive cells surrounding neurons is the physical origin of frequency
filtering properties of LFPs.Comment: 10 figs, revised tex file and revised fig
A generalized theory for current-source density analysis in brain tissue
The current-source density (CSD) analysis is a widely used method in brain
electrophysiology, but this method rests on a series of assumptions, namely
that the surrounding extracellular medium is resistive and uniform, and in some
versions of the theory, that the current sources are exclusively made by
dipoles. Because of these assumptions, this standard model does not correctly
describe the contributions of monopolar sources or of non-resistive aspects of
the extracellular medium. We propose here a general framework to model electric
fields and potentials resulting from current source densities, without relying
on the above assumptions. We develop a mean-field formalism which is a
generalization of the standard model, and which can directly incorporate
non-resistive (non-ohmic) properties of the extracellular medium, such as ionic
diffusion effects. This formalism recovers the classic results of the standard
model such as the CSD analysis, but in addition, we provide expressions to
generalize the CSD approach to situations with non-resistive media and
arbitrarily complex multipolar configurations of current sources. We found that
the power spectrum of the signal contains the signature of the nature of
current sources and extracellular medium, which provides a direct way to
estimate those properties from experimental data, and in particular, estimate
the possible contribution of electric monopoles.Comment: Physical Review E, in press, 201
On the flexibility of the design of Multiple Try Metropolis schemes
The Multiple Try Metropolis (MTM) method is a generalization of the classical
Metropolis-Hastings algorithm in which the next state of the chain is chosen
among a set of samples, according to normalized weights. In the literature,
several extensions have been proposed. In this work, we show and remark upon
the flexibility of the design of MTM-type methods, fulfilling the detailed
balance condition. We discuss several possibilities and show different
numerical results
Diffusion of hydrogen in crystalline silicon
The coefficient of diffusion of hydrogen in crystalline silicon is calculated
using tight-binding molecular dynamics. Our results are in good quantitative
agreement with an earlier study by Panzarini and Colombo [Phys. Rev. Lett. 73,
1636 (1994)]. However, while our calculations indicate that long jumps dominate
over single hops at high temperatures, no abrupt change in the diffusion
coefficient can be observed with decreasing temperature. The (classical)
Arrhenius diffusion parameters, as a consequence, should extrapolate to low
temperatures.Comment: 4 pages, including 5 postscript figures; submitted to Phys. Rev. B
Brief Repor
Evolutionary Trajectories are Contingent on Mitonuclear Interactions
Critical mitochondrial functions, including cellular respiration, rely on frequently interacting components expressed from both the mitochondrial and nuclear genomes. The fitness of eukaryotic organisms depends on a tight collaboration between both genomes. In the face of an elevated rate of evolution in mtDNA, current models predict that the maintenance of mitonuclear compatibility relies on compensatory evolution of the nuclear genome. Mitonuclear interactions would therefore exert an influence on evolutionary trajectories. One prediction from this model is that the same nuclear genome evolving with different mitochondrial haplotypes would follow distinct molecular paths toward higher fitness. To test this prediction, we submitted 1,344 populations derived from 7 mitonuclear genotypes of Saccharomyces cerevisiae to >300 generations of experimental evolution in conditions that either select for a mitochondrial function or do not strictly require respiration for survival. Performing high-throughput phenotyping and whole-genome sequencing on independently evolved individuals, we identified numerous examples of gene-level evolutionary convergence among populations with the same mitonuclear background. Phenotypic and genotypic data on strains derived from this evolution experiment identify the nuclear genome and the environment as the main determinants of evolutionary divergence, but also show a modulating role for the mitochondrial genome exerted both directly and via interactions with the two other components. We finally recapitulated a subset of prominent loss-of-function alleles in the ancestral backgrounds and confirmed a generalized pattern of mitonuclear-specific and highly epistatic fitness effects. Together, these results demonstrate how mitonuclear interactions can dictate evolutionary divergence of populations with identical starting nuclear genotypes
On Second-Order Monadic Monoidal and Groupoidal Quantifiers
We study logics defined in terms of second-order monadic monoidal and
groupoidal quantifiers. These are generalized quantifiers defined by monoid and
groupoid word-problems, equivalently, by regular and context-free languages. We
give a computational classification of the expressive power of these logics
over strings with varying built-in predicates. In particular, we show that
ATIME(n) can be logically characterized in terms of second-order monadic
monoidal quantifiers
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