849 research outputs found
Maximum Fidelity
The most fundamental problem in statistics is the inference of an unknown
probability distribution from a finite number of samples. For a specific
observed data set, answers to the following questions would be desirable: (1)
Estimation: Which candidate distribution provides the best fit to the observed
data?, (2) Goodness-of-fit: How concordant is this distribution with the
observed data?, and (3) Uncertainty: How concordant are other candidate
distributions with the observed data? A simple unified approach for univariate
data that addresses these traditionally distinct statistical notions is
presented called "maximum fidelity". Maximum fidelity is a strict frequentist
approach that is fundamentally based on model concordance with the observed
data. The fidelity statistic is a general information measure based on the
coordinate-independent cumulative distribution and critical yet previously
neglected symmetry considerations. An approximation for the null distribution
of the fidelity allows its direct conversion to absolute model concordance (p
value). Fidelity maximization allows identification of the most concordant
model distribution, generating a method for parameter estimation, with
neighboring, less concordant distributions providing the "uncertainty" in this
estimate. Maximum fidelity provides an optimal approach for parameter
estimation (superior to maximum likelihood) and a generally optimal approach
for goodness-of-fit assessment of arbitrary models applied to univariate data.
Extensions to binary data, binned data, multidimensional data, and classical
parametric and nonparametric statistical tests are described. Maximum fidelity
provides a philosophically consistent, robust, and seemingly optimal foundation
for statistical inference. All findings are presented in an elementary way to
be immediately accessible to all researchers utilizing statistical analysis.Comment: 66 pages, 32 figures, 7 tables, submitte
Efficient algorithm for current spectral density calculation in single-electron tunneling and hopping
This write-up describes an efficient numerical method for the Monte Carlo
calculation of the spectral density of current in the multi-junction
single-electron devices and hopping structures. In future we plan to expand
this write-up into a full-size paper.Comment: 4 page
Multifrequency Observations of Giant Radio Pulses from the Millisecond Pulsar B1937+21
Giant pulses are short, intense outbursts of radio emission with a power-law
intensity distribution that have been observed from the Crab Pulsar and PSR
B1937+21. We have undertaken a systematic study of giant pulses from PSR
B1937+21 using the Arecibo telescope at 430, 1420, and 2380 MHz. At 430 MHz,
interstellar scattering broadens giant pulses to durations of secs,
but at higher frequencies the pulses are very short, typically lasting only
-secs. At each frequency, giant pulses are emitted only in narrow
(\lsim10 \mus) windows of pulse phase located -sec after the
main and interpulse peaks. Although some pulse-to-pulse jitter in arrival times
is observed, the mean arrival phase appears stable; a timing analysis of the
giant pulses yields precision competitive with the best average profile timing
studies. We have measured the intensity distribution of the giant pulses,
confirming a roughly power-law distribution with approximate index of -1.8,
contributing \gsim0.1% to the total flux at each frequency. We also find that
the intensity of giant pulses falls off with a slightly steeper power of
frequency than the ordinary radio emission.Comment: 21 pages, 10 Postscript figures; LaTeX with aaspp4.sty and epsf.tex;
submitted to Ap
Sub-electron Charge Relaxation via 2D Hopping Conductors
We have extended Monte Carlo simulations of hopping transport in completely
disordered 2D conductors to the process of external charge relaxation. In this
situation, a conductor of area shunts an external capacitor
with initial charge . At low temperatures, the charge relaxation process
stops at some "residual" charge value corresponding to the effective threshold
of the Coulomb blockade of hopping. We have calculated the r.m.s value
of the residual charge for a statistical ensemble of capacitor-shunting
conductors with random distribution of localized sites in space and energy and
random , as a function of macroscopic parameters of the system. Rather
unexpectedly, has turned out to depend only on some parameter
combination: for negligible Coulomb interaction
and for substantial interaction. (Here
is the seed density of localized states, while is the
dielectric constant.) For sufficiently large conductors, both functions
follow the power law , but with different
exponents: for negligible and
for significant Coulomb interaction. We have been able to derive this law
analytically for the former (most practical) case, and also explain the scaling
(but not the exact value of the exponent) for the latter case. In conclusion,
we discuss possible applications of the sub-electron charge transfer for
"grounding" random background charge in single-electron devices.Comment: 12 pages, 5 figures. In addition to fixing minor typos and updating
references, the discussion has been changed and expande
Analytical model for macromolecular partitioning during yeast cell division
Background: Asymmetric cell division, whereby a parent cell generates two sibling cells with unequal content and thereby distinct fates, is central to cell differentiation, organism development and ageing. Unequal partitioning of the macromolecular content of the parent cell — which includes proteins, DNA, RNA, large proteinaceous assemblies and organelles — can be achieved by both passive (e.g. diffusion, localized retention sites) and active (e.g. motor-driven transport) processes operating in the presence of external polarity cues, internal asymmetries, spontaneous symmetry breaking, or stochastic effects. However, the quantitative contribution of different processes to the partitioning of macromolecular content is difficult to evaluate. Results: Here we developed an analytical model that allows rapid quantitative assessment of partitioning as a function of various parameters in the budding yeast Saccharomyces cerevisiae. This model exposes quantitative degeneracies among the physical parameters that govern macromolecular partitioning, and reveals regions of the solution space where diffusion is sufficient to drive asymmetric partitioning and regions where asymmetric partitioning can only be achieved through additional processes such as motor-driven transport. Application of the model to different macromolecular assemblies suggests that partitioning of protein aggregates and episomes, but not prions, is diffusion-limited in yeast, consistent with previous reports. Conclusions: In contrast to computationally intensive stochastic simulations of particular scenarios, our analytical model provides an efficient and comprehensive overview of partitioning as a function of global and macromolecule-specific parameters. Identification of quantitative degeneracies among these parameters highlights the importance of their careful measurement for a given macromolecular species in order to understand the dominant processes responsible for its observed partitioning
A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport
We have extended our supercomputer-enabled Monte Carlo simulations of hopping
transport in completely disordered 2D conductors to the case of substantial
electron-electron Coulomb interaction. Such interaction may not only suppress
the average value of hopping current, but also affect its fluctuations rather
substantially. In particular, the spectral density of current
fluctuations exhibits, at sufficiently low frequencies, a -like increase
which approximately follows the Hooge scaling, even at vanishing temperature.
At higher , there is a crossover to a broad range of frequencies in which
is nearly constant, hence allowing characterization of the current
noise by the effective Fano factor F\equiv S_I(f)/2e \left. For
sufficiently large conductor samples and low temperatures, the Fano factor is
suppressed below the Schottky value (F=1), scaling with the length of the
conductor as . The exponent is significantly
affected by the Coulomb interaction effects, changing from when such effects are negligible to virtually unity when they are
substantial. The scaling parameter , interpreted as the average
percolation cluster length along the electric field direction, scales as when Coulomb interaction effects are negligible
and when such effects are substantial, in
good agreement with estimates based on the theory of directed percolation.Comment: 19 pages, 7 figures. Fixed minor typos and updated reference
An axisymmetric hydrodynamical model for the torus wind in AGN. III: Spectra from 3D radiation transfer calculations
We calculate a series of synthetic X-ray spectra from outflows originating
from the obscuring torus in active galactic nuclei (AGN). Such modeling
includes 2.5D hydrodynamical simulations of an X-ray excited torus wind,
including the effects of X-ray heating, ionization, and radiation pressure. 3D
radiation transfer calculations are performed in the 3D Sobolev approximation.
Synthetic X-ray line spectra and individual profiles of several strong lines
are shown at different inclination angles, observing times, and for different
characteristics of the torus.
Our calculations show that rich synthetic warm absorber spectra from 3D
modeling are typically observed at a larger range of inclinations than was
previously inferred from simple analysis of the transmitted spectra. In
general, our results are supportive of warm absorber models based on the
hypothesis of an "X-ray excited funnel flow" and are consistent with
characteristics of such flows inferred from observations of warm absorbers from
Seyfert 1 galaxies.Comment: 31 pages, 10 figure
A Numerical Study of Transport and Shot Noise at 2D Hopping
We have used modern supercomputer facilities to carry out extensive Monte
Carlo simulations of 2D hopping (at negligible Coulomb interaction) in
conductors with the completely random distribution of localized sites in both
space and energy, within a broad range of the applied electric field and
temperature , both within and beyond the variable-range hopping region. The
calculated properties include not only dc current and statistics of localized
site occupation and hop lengths, but also the current fluctuation spectrum.
Within the calculation accuracy, the model does not exhibit noise, so
that the low-frequency noise at low temperatures may be characterized by the
Fano factor . For sufficiently large samples, scales with conductor
length as , where , and
parameter is interpreted as the average percolation cluster length. At
relatively low , the electric field dependence of parameter is
compatible with the law which follows from directed
percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference
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