Hubble parameter reconstruction from a principal component analysis: minimizing the bias

Aims. A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Methods. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. Results. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.

Quantum statistical correlations in thermal field theories: Boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field phi(c), and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrodinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field phi(c), a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

Precise measurements of direct CP violation, CPT symmetry, and other parameters in the neutral kaon system

We present precise tests of CP and CPT symmetry based on the full data set of K -> pi pi decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This data set contains 16 x 10(6) K -> pi(0)pi(0) and 69 x 10(6) K -> pi(+)pi(-) decays. We measure the direct CP violation parameter Re(epsilon'/epsilon) = (19.2 +/- 2.1) x 10(-4). We find the K(L) -> K(S) mass difference Delta m = (5270 +/- 12) x 10(6) (h) over tilde s(-1) and the K(S) lifetime tau(S) = (89.62 +/- 0.05) x 10(-12) s. We also measure several parameters that test CPT invariance. We find the difference between the phase of the indirect CP violation parameter epsilon and the superweak phase: phi(epsilon) - phi(SW) =(0.40 +/- 0.56)degrees. We measure the difference of the relative phases between the CP violating and CP conserving decay amplitudes for K -> pi(+)pi(-) (phi(+-)) and for K -> pi(0)pi(0) (phi(00)): Delta phi = (0.30 +/- 0.35)degrees. From these phase measurements, we place a limit on the mass difference between K(0) and (K) over bar (0): Delta M < 4.8 x 10(-19) GeV/c(2) at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and CPT symmetry.

Measurement of neutral mesons in p plus p collisions at root s=200 GeV and scaling properties of hadron production

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the invariant differential cross section for production of K(S)(0), omega, eta', and phi mesons in p + p collisions at root s 200 GeV. Measurements of omega and phi production in different decay channels give consistent results. New results for the omega are in agreement with previously published data and extend the measured p(T) coverage. The spectral shapes of all hadron transverse momentum distributions measured by PHENIX are well described by a Tsallis distribution functional form with only two parameters, n and T, determining the high-p(T) and characterizing the low-p(T) regions of the spectra, respectively. The values of these parameters are very similar for all analyzed meson spectra, but with a lower parameter T extracted for protons. The integrated invariant cross sections calculated from the fitted distributions are found to be consistent with existing measurements and with statistical model predictions.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rodlike and disklike molecules. A quenched distribution of shapes leads to a phase diagram with two uniaxial and a biaxial nematic structure. A thermalized distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.

Quantitative constraints on the transport properties of hot partonic matter from semi-inclusive single high transverse momentum pion suppression in Au plus Au collisions at root S(NN)=200 GeV

The PHENIX experiment has measured the suppression of semi-inclusive single high-transverse-momentum pi(0)'s in Au+Au collisions at root s(NN) = 200 GeV. The present understanding of this suppression is in terms of energy loss of the parent (fragmenting) parton in a dense color-charge medium. We have performed a quantitative comparison between various parton energy-loss models and our experimental data. The statistical point-to-point uncorrelated as well as correlated systematic uncertainties are taken into account in the comparison. We detail this methodology and the resulting constraint on the model parameters, such as the initial color-charge density dN(g)/dy, the medium transport coefficient <(q) over cap >, or the initial energy-loss parameter epsilon(0). We find that high-transverse-momentum pi(0) suppression in Au+Au collisions has sufficient precision to constrain these model-dependent parameters at the +/- 20-25% (one standard deviation) level. These constraints include only the experimental uncertainties, and further studies are needed to compute the corresponding theoretical uncertainties.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Zero-phonon emission and magnetic polaron parameters in EuTe

A phonon structure in the photoluminescence of EuTe was discovered, with a well-defined zero-phonon emission line (ZPL). The ZPL redshifts linearly with the intensity of applied magnetic field, indicating spin relaxation of the photoexcited electron, and saturates at a lower magnetic field than the optical absorption bandgap, which is attributed to formation of magnetic polarons. From the difference in these saturation fields, the zero-field polaron binding energy and radius are estimated to be 43 meV and 3.2 (in units of the EuTe lattice parameter), respectively. (C) 2011 American Institute of Physics. [doi:10.1063/1.3634030]

Scaling properties at freeze-out in relativistic heavy-ion collisions

Identified charged pion, kaon, and proton spectra are used to explore the system size dependence of bulk freeze-out properties in Cu + Cu collisions at root s(NN) = 200 and 62.4 GeV. The data are studied with hydrodynamically motivated blast-wave and statistical model frameworks in order to characterize the freeze-out properties of the system. The dependence of freeze-out parameters on beam energy and collision centrality is discussed. Using the existing results from Au + Au and pp collisions, the dependence of freeze-out parameters on the system size is also explored. This multidimensional systematic study furthers our understanding of the QCD phase diagram revealing the importance of the initial geometrical overlap of the colliding ions. The analysis of Cu + Cu collisions expands the system size dependence studies from Au + Au data with detailed measurements in the smaller system. The systematic trends of the bulk freeze-out properties of charged particles is studied with respect to the total charged particle multiplicity at midrapidity, exploring the influence of initial state effects.

INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Estimation of the thickness and the optical parameters of several stacked thin films using optimization

The reverse engineering problem addressed in the present research consists of estimating the thicknesses and the optical constants of two thin films deposited on a transparent substrate using only transmittance data through the whole stack. No functional dispersion relation assumptions are made on the complex refractive index. Instead, minimal physical constraints are employed, as in previous works of some of the authors where only one film was considered in the retrieval algorithm. To our knowledge this is the first report on the retrieval of the optical constants and the thickness of multiple film structures using only transmittance data that does not make use of dispersion relations. The same methodology may be used if the available data correspond to normal reflectance. The software used in this work is freely available through the PUMA Project web page (http://www.ime.usp.br/similar to egbirgin/puma/). (C) 2008 Optical Society of America

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Source populations in coastal crabs: parameters affecting egg production

Benthic marine invertebrates may form metapopulations connected via propagule dispersal. Conservation efforts often target potential source coastlines to indirectly benefit areas depending on allochthonous offspring production. Besides population density, adult size structure, sex ratio, brooding frequency and the proportion of breeding individuals may significantly influence the reproductive output of benthic populations, but these effects have seldom been tested. We used rocky shore crabs to assess the spatial variability of such parameters at relevant scales for conservation purposes and to test their consistency over 2 consecutive years; we then used the data to address whether bottom-up processes or biological interactions might explain the patterns observed. We decomposed egg production rates into their components for the 2 most abundant brachyuran species inhabiting the intertidal rocky habitat. Adult density and brooding frequency varied consistently among shores for both species and largely explained the overall spatial trends of egg production. Temporally consistent patterns also included among-shore differences in the size of ovigerous females of the grapsid Pachygrapsus transversus and between-bay differences in the fecundity of the spider crab Epialtus brasiliensis. Sex ratio was remarkably constant in both. We found no positive or negative correlations between adult density and brooding frequency to support either the existence of a component Allee effect (lack of mate encounters) or an effect of intra-specific competition. Likewise, shore-specific potential growth in P. transversus does not negatively correlate with frequency of ovigerous individuals, as would be expected under a critical balance between these 2 processes. The patterns observed suggest that bottom-up drivers may best explain spatial trends in the reproductive output of these species.

Anthelmintic effects of condensed tannins on Trichostrongylus colubriformis in experimentally infected sheep

Recent surveys have identified anthelmintic effects from many bioactive substances particularly from condensed tannin (CT) sources. The aims of the present study were to investigate the potential anthelmintic effects of condensed tannins (CT) on Trichostrongylus colubriformis in experimentally infected sheep and the nutritional consequences on animals. Twenty helminth-free lambs were divided into five groups of four animals. Groups I to IV were artificially infected with 6,000 third stage larvae (L3) of T. colubriformis. Group I was the infected control and group V was the uninfected control. Twenty-eight days post-infection (p.i.) lambs from GII were supplemented with tanniniferous sorghum (350 g/animal/day, during seven days); GIII were drenched with Acacia mearnsii extract (15% CT) for just one day and GIV during two days (1.6 g extract/kg BW). At day 36 p.i., animals from infected group (GI to GIV) were slaughtered. Faecal egg counts (FEC) values present a reduction on GII when compared with GI at day 29 p.i. (P < 0.05) and between GIII and GI at day 35 and 36 p.i. (P < 0.05). The values of egg hatchability and number of L3 recovered from the faeces were not statistical analyzed (there was no duplicate data), however there was a considerable reduction between the values from treated and control group. The use of CT on diet did not cause significant difference on blood parameters, body-weight and carcass-weight (P > 0.05). No difference was related on total worm burden between treatments; however, GIV presented lower number of females than GI (P < 0.05). The use of CT could be a promising alternative source to reduce the pasture contamination and to control T. colubriformis infection in sheep.