9,396 research outputs found
A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation
Approximate Bayesian computation (ABC) methods make use of comparisons
between simulated and observed summary statistics to overcome the problem of
computationally intractable likelihood functions. As the practical
implementation of ABC requires computations based on vectors of summary
statistics, rather than full data sets, a central question is how to derive
low-dimensional summary statistics from the observed data with minimal loss of
information. In this article we provide a comprehensive review and comparison
of the performance of the principal methods of dimension reduction proposed in
the ABC literature. The methods are split into three nonmutually exclusive
classes consisting of best subset selection methods, projection techniques and
regularization. In addition, we introduce two new methods of dimension
reduction. The first is a best subset selection method based on Akaike and
Bayesian information criteria, and the second uses ridge regression as a
regularization procedure. We illustrate the performance of these dimension
reduction techniques through the analysis of three challenging models and data
sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
End states, ladder compounds, and domain wall fermions
A magnetic field applied to a cross linked ladder compound can generate
isolated electronic states bound to the ends of the chain. After exploring the
interference phenomena responsible, I discuss a connection to the domain wall
approach to chiral fermions in lattice gauge theory. The robust nature of the
states under small variations of the bond strengths is tied to chiral symmetry
and the multiplicative renormalization of fermion masses.Comment: 10 pages, 4 figures; final version for Phys. Rev. Let
Polarization and angular distribution of the radiation emitted in laser-assisted recombination
The effect of an intense external linear polarized radiation field on the
angular distributions and polarization states of the photons emitted during the
radiative recombination is investigated. It is predicted, on symmetry grounds,
and corroborated by numerical calculations of approximate recombination rates,
that emission of elliptically polarized photons occurs when the momentum of the
electron beam is not aligned to the direction of the oscillating field.
Moreover, strong modifications to the angular distributions of the emitted
photons are induced by the external radiation field.Comment: 5 pages, 3 figure
HIV with contact-tracing: a case study in Approximate Bayesian Computation
Missing data is a recurrent issue in epidemiology where the infection process
may be partially observed. Approximate Bayesian Computation, an alternative to
data imputation methods such as Markov Chain Monte Carlo integration, is
proposed for making inference in epidemiological models. It is a
likelihood-free method that relies exclusively on numerical simulations. ABC
consists in computing a distance between simulated and observed summary
statistics and weighting the simulations according to this distance. We propose
an original extension of ABC to path-valued summary statistics, corresponding
to the cumulated number of detections as a function of time. For a standard
compartmental model with Suceptible, Infectious and Recovered individuals
(SIR), we show that the posterior distributions obtained with ABC and MCMC are
similar. In a refined SIR model well-suited to the HIV contact-tracing data in
Cuba, we perform a comparison between ABC with full and binned detection times.
For the Cuban data, we evaluate the efficiency of the detection system and
predict the evolution of the HIV-AIDS disease. In particular, the percentage of
undetected infectious individuals is found to be of the order of 40%
Scaling in Complex Systems: Analytical Theory of Charged Pores
In this paper we find an analytical solution of the equilibrium ion
distribution for a toroidal model of a ionic channel, using the Perfect
Screening Theorem (PST). The ions are charged hard spheres, and are treated
using a variational Mean Spherical Approximation (VMSA) .
Understanding ion channels is still a very open problem, because of the many
exquisite tuning details of real life channels. It is clear that the electric
field plays a major role in the channel behaviour, and for that reason there
has been a lot of work on simple models that are able to provide workable
theories. Recently a number of interesting papers have appeared that discuss
models in which the effect of the geometry, excluded volume and non-linear
behaviour is considered.
We present here a 3D model of ionic channels which consists of a charged,
deformable torus with a circular or elliptical cross section, which can be flat
or vertical (close to a cylinder). Extensive comparisons to MC simulations were
performed.
The new solution opens new possibilities, such as studying flexible pores,
and water phase transformations inside the pores using an approach similar to
that used on flat crystal surfaces
Quantum dynamics of the avian compass
The ability of migratory birds to orient relative to the Earth's magnetic
field is believed to involve a coherent superposition of two spin states of a
radical electron pair. However, the mechanism by which this coherence can be
maintained in the face of strong interactions with the cellular environment has
remained unclear. This Letter addresses the problem of decoherence between two
electron spins due to hyperfine interaction with a bath of spin 1/2 nuclei.
Dynamics of the radical pair density matrix are derived and shown to yield a
simple mechanism for sensing magnetic field orientation. Rates of dephasing and
decoherence are calculated ab initio and found to yield millisecond coherence
times, consistent with behavioral experiments
A corresponding states approach to Small-Angle-Scattering for polydisperse ionic colloidal fluids
Approximate scattering functions for polydisperse ionic colloidal fluids are
obtained by a corresponding states approach. This assumes that all pair
correlation functions of a polydisperse fluid are
conformal to those of an appropriate monodisperse binary fluid (reference
system) and can be generated from them by scaling transformations. The
correspondence law extends to ionic fluids a {\it scaling approximation} (SA)
successfully proposed for nonionic colloids in a recent paper. For the
primitive model of charged hard spheres in a continuum solvent, the partial
structure factors of the monodisperse binary reference system are evaluated by
solving the Orstein-Zernike (OZ) integral equations coupled with an approximate
closure. The SA is first tested within the mean spherical approximation (MSA)
closure, which allows analytical solutions. The results are found in good
overall agreement with exact MSA predictions up to relevant polidispersity. The
SA is shown to be an improvement over the ``decoupling approximation'' extended
to the ionic case. The simplicity of the SA scheme allows its application also
when the OZ equations can be solved only numerically. An example is then given
by using the hypernetted chain (HNC) closure. Shortcomings of the SA approach,
its possible use in the analysis of experimental scattering data and other
related points are also briefly addressed.Comment: 29 pages, 7 postscript figures (included), Latex 3.0, uses aps.sty,
to appear in Phys. Rev. E (1999
Flavor-Symmetry Restoration and Symanzik Improvement for Staggered Quarks
We resolve contradictions in the literature concerning the origins and size
of unphysical flavor-changing strong interactions generated by the
staggered-quark discretization of QCD. We show that the leading contributions
are tree-level in \order(a^2) and that they can be removed by adding three
correction terms to the link operator in the standard action. These corrections
are part of the systematic Symanzik improvement of the staggered-quark action.
We present a new improved action for staggered quarks that is accurate up to
errors of \order(a^4,a^2\alpha_s) --- more accurate than most, if not all,
other discretizations of light-quark dynamics.Comment: 7 page
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