2,472 research outputs found
From Random Matrices to Stochastic Operators
We propose that classical random matrix models are properly viewed as finite
difference schemes for stochastic differential operators. Three particular
stochastic operators commonly arise, each associated with a familiar class of
local eigenvalue behavior. The stochastic Airy operator displays soft edge
behavior, associated with the Airy kernel. The stochastic Bessel operator
displays hard edge behavior, associated with the Bessel kernel. The article
concludes with suggestions for a stochastic sine operator, which would display
bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics.
Changes in this revision: recomputed Monte Carlo simulations, added reference
[19], fit into margins, performed minor editin
Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
We derive expansions of the resolvent
Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the
edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the
finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we
give another proof of the derivation of an Edgeworth type theorem for the
largest eigenvalue distribution function of GUEn. We conclude with a brief
discussion on the derivation of the probability distribution function of the
corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and
Gaussian Symplectic Ensembles (GSEn)
CMB Constraints on WIMP Annihilation: Energy Absorption During the Recombination Epoch
We compute in detail the rate at which energy injected by dark matter
annihilation heats and ionizes the photon-baryon plasma at z ~ 1000, and
provide accurate fitting functions over the relevant redshift range for a broad
array of annihilation channels and DM masses. The resulting perturbations to
the ionization history can be constrained by measurements of the CMB
temperature and polarization angular power spectra. We show that models which
fit recently measured excesses in 10-1000 GeV electron and positron cosmic rays
are already close to the 95% confidence limits from WMAP. The recently launched
Planck satellite will be capable of ruling out a wide range of DM explanations
for these excesses. In models of dark matter with Sommerfeld-enhanced
annihilation, where sigma v rises with decreasing WIMP velocity until some
saturation point, the WMAP5 constraints imply that the enhancement must be
close to saturation in the neighborhood of the Earth.Comment: 17 pages, 6 figures, v2 extends discussion of constraints on
Sommerfeld-enhanced model
Two ways to solve ASEP
The purpose of this article is to describe the two approaches to compute
exact formulas (which are amenable to asymptotic analysis) for the probability
distribution of the current of particles past a given site in the asymmetric
simple exclusion process (ASEP) with step initial data. The first approach is
via a variant of the coordinate Bethe ansatz and was developed in work of Tracy
and Widom in 2008-2009, while the second approach is via a rigorous version of
the replica trick and was developed in work of Borodin, Sasamoto and the author
in 2012.Comment: 10 pages, Chapter in "Topics in percolative and disordered systems
Universal gap fluctuations in the superconductor proximity effect
Random-matrix theory is used to study the mesoscopic fluctuations of the
excitation gap in a metal grain or quantum dot induced by the proximity to a
superconductor. We propose that the probability distribution of the gap is a
universal function in rescaled units. Our analytical prediction for the gap
distribution agrees well with exact diagonalization of a model Hamiltonian
The Photophysics of the Carrier of Extended Red Emission
Interstellar dust contains a component which reveals its presence by emitting
a broad, unstructured band of light in the 540 to 950 nm wavelength range,
referred to as Extended Red Emission (ERE). The presence of interstellar dust
and ultraviolet photons are two necessary conditions for ERE to occur. This is
the basis for suggestions which attribute ERE to an interstellar dust component
capable of photoluminescence. In this study, we have collected all published
ERE observations with absolute-calibrated spectra for interstellar
environments, where the density of ultraviolet photons can be estimated
reliably. In each case, we determined the band-integrated ERE intensity, the
wavelength of peak emission in the ERE band, and the efficiency with which
absorbed ultraviolet photons are contributing to the ERE. The data show that
radiation is not only driving the ERE, as expected for a photoluminescence
process, but is modifying the ERE carrier as manifested by a systematic
increase in the ERE band's peak wavelength and a general decrease in the photon
conversion efficiency with increasing densities of the prevailing exciting
radiation. The overall spectral characteristics of the ERE and the observed
high quantum efficiency of the ERE process are currently best matched by the
recently proposed silicon nanoparticle (SNP) model. Using the experimentally
established fact that ionization of semiconductor nanoparticles quenches their
photoluminescence, we proceeded to test the SNP model by developing a
quantitative model for the excitation and ionization equilibrium of SNPs under
interstellar conditions for a wide range of radiation field densities.Comment: 42 p., incl. 8 fig. Accepted for publication by Ap
Dietary Methionine Restriction Regulates Liver Protein Synthesis and Gene Expression Independently of Eukaryotic Initiation Factor 2 Phosphorylation in Mice
Background: The phosphorylation of eukaryotic initiation factor 2 (p-eIF2) during dietary amino acid insufficiency reduces protein synthesis and alters gene expression via the integrated stress response (ISR).Objective: We explored whether a Met-restricted (MR) diet activates the ISR to reduce body fat and regulate protein balance.Methods: Male and female mice aged 3-6 mo with either whole-body deletion of general control nonderepressible 2 (Gcn2) or liver-specific deletion of protein kinase R-like endoplasmic reticulum kinase (Perk) alongside wild-type or floxed control mice were fed an obesogenic diet sufficient in Met (0.86%) or an MR (0.12% Met) diet for ≤5 wk. Ala enrichment with deuterium was measured to calculate protein synthesis rates. The guanine nucleotide exchange factor activity of eIF2B was measured alongside p-eIF2 and hepatic mRNA expression levels at 2 d and 5 wk. Metabolic phenotyping was conducted at 4 wk, and body composition was measured throughout. Results were evaluated with the use of ANOVA (P < 0.05).Results: Feeding an MR diet for 2 d did not increase hepatic p-eIF2 or reduce eIF2B activity in wild-type or Gcn2-/- mice, yet many genes transcriptionally regulated by the ISR were altered in both strains in the same direction and amplitude. Feeding an MR diet for 5 wk increased p-eIF2 and reduced eIF2B activity in wild-type but not Gcn2-/- mice, yet ISR-regulated genes altered in both strains similarly. Furthermore, the MR diet reduced mixed and cytosolic but not mitochondrial protein synthesis in both the liver and skeletal muscle regardless of Gcn2 status. Despite the similarities between strains, the MR diet did not increase energy expenditure or reduce body fat in Gcn2-/- mice. Finally, feeding the MR diet to mice with Perk deleted in the liver increased hepatic p-eIF2 and altered body composition similar to floxed controls.Conclusions: Hepatic activation of the ISR resulting from an MR diet does not require p-eIF2. Gcn2 status influences body fat loss but not protein balance when Met is restricted
Muscle strengthening intervention for boys with haemophilia: Developing and evaluating a best-practice exercise programme with boys, families and health-care professionals
Background:
Muscle strengthening exercises have the potential to improve outcomes for boys with haemophilia, but it is unclear what types of exercise might be of benefit. We elicited the views of health-care professionals, boys and their families to create and assess a home-based muscle strengthening programme.
Objective:
To design and develop a muscle strengthening programme with health-care professionals aimed at improving musculoskeletal health, and refine the intervention by engaging boys with haemophilia and their families (Study 1). Following delivery, qualitatively evaluate the feasibility and acceptability of the exercise programme with the boys and the study's physiotherapists (Study 2).
Design:
A person-based approach was used for planning and designing the exercise programme, and evaluating it post-delivery. The following methods were utilized: modified nominal group technique (NGT) with health-care professionals; focus group with families; exit interviews with boys; and interviews with the study's physiotherapists.
Results:
Themes identified to design and develop the intervention included exercises to lower limb and foot, dosage, age accommodating, location, supervision and monitoring and incentivization. Programme refinements were carried out following engagement with the boys and families who commented on: dosage, location, supervision and incentivization. Following delivery, the boys and physiotherapists commented on progression and adaptation, physiotherapist contact, goal-setting, creating routines and identifying suitable timeframes, and a repeated theme of incentivization.
Conclusions:
An exercise intervention was designed and refined through engagement with boys and their families. Boys and physiotherapists involved in the intervention's delivery were consulted who found the exercises to be generally acceptable with some minor refinements necessary
Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
Our interest is in the cumulative probabilities Pr(L(t) \le l) for the
maximum length of increasing subsequences in Poissonized ensembles of random
permutations, random fixed point free involutions and reversed random fixed
point free involutions. It is shown that these probabilities are equal to the
hard edge gap probability for matrix ensembles with unitary, orthogonal and
symplectic symmetry respectively. The gap probabilities can be written as a sum
over correlations for certain determinantal point processes. From these
expressions a proof can be given that the limiting form of Pr(L(t) \le l) in
the three cases is equal to the soft edge gap probability for matrix ensembles
with unitary, orthogonal and symplectic symmetry respectively, thereby
reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page
Random matrix ensembles with an effective extensive external charge
Recent theoretical studies of chaotic scattering have encounted ensembles of
random matrices in which the eigenvalue probability density function contains a
one-body factor with an exponent proportional to the number of eigenvalues. Two
such ensembles have been encounted: an ensemble of unitary matrices specified
by the so-called Poisson kernel, and the Laguerre ensemble of positive definite
matrices. Here we consider various properties of these ensembles. Jack
polynomial theory is used to prove a reproducing property of the Poisson
kernel, and a certain unimodular mapping is used to demonstrate that the
variance of a linear statistic is the same as in the Dyson circular ensemble.
For the Laguerre ensemble, the scaled global density is calculated exactly for
all even values of the parameter , while for (random
matrices with unitary symmetry), the neighbourhood of the smallest eigenvalue
is shown to be in the soft edge universality class.Comment: LaTeX209, 17 page
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