Localization of a polymer in random media: Relation to the localization of a quantum particle

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be {\it localized} inside a low minimum of the potential. We show how the end-to-end distance of a polymer which is free to move can be obtained from the density of states of the quantum particle using extreme value statistics. We give a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729 (2000)) in terms of the statistics of localized tail states. Numerical solutions of the variational equations for chains of different length are performed and compared with quenched averages computed directly by using the eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle in a one-dimensional random potential. The quantities investigated are the radius of gyration of a free gaussian chain, its mean square distance from the origin and the end-to-end distance of a tethered chain. The probability distribution for the position of the chain is also investigated. The glassiness of the system is explained and is estimated from the variance of the measured quantities.Comment: RevTex, 44 pages, 13 figure

Solving Tolman-Oppenheimer-Volkoff equations in f(T) gravity: a novel approach applied to some realistic equations of state

There are many ways to probe alternative theories of gravity, namely, via: experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In the present paper we consider a model of gravity with torsion $f(T)$ applied to compact objects such as neutron stars (NSs) for a couple of realistic equations of state (EOS). To do so we follow our previous articles, in which we show how to model compact stars in this $f(T)$ gravity by obtaining its corresponding Tolman-Oppenheimer-Volkof equations and applying this prescription to model polytropic compact stars. In these modelling of NS in $f(T)$ gravity presented here, we calculate, among other things, the maximum mass allowed for a given realistic EOS, which would also allow us to evaluate which models are in accordance with observations. The results already known to General Relativity must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses for NSs than Relativity itself, which could explain, for example, the secondary component of the event GW190814, if this star is a massive NS

Statistical innovations for estimating shape characteristics of biological macromolecules in solution using small-angle x-ray scattering data

2016 Spring.Includes bibliographical references.Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution images of biological macromolecules by exposing a solution containing the molecule to a powerful X-ray beam. The beam scatters when it interacts with the molecule. The intensity of the scattered beam is recorded on a detector plate at various scattering angles, and contains information on structural characteristics of the molecule in solution. In particular, the radius of gyration (Rg) for a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data using a regression technique known as Guinier analysis. The analysis requires specification of a range or “window” of scattering angles over which the regression relationship holds. We have thus developed methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the radius of gyration, and estimation of its variance. The theory and methodology are developed using a local polynomial model with autoregressive errors. Simulation studies confirm the quality of the asymptotic approximations and the superior performance of the proposed methodology relative to the accepted standard. We show that the algorithm is applicable to data acquired from proteins, nucleic acids and their complexes, and we demonstrate with examples that the algorithm improves the ability to test biological hypotheses. The radius of gyration is a normalized second moment of the pairwise distance distribution p(r), which describes the relative frequency of inter-atomic distances in the structure of the molecule. By extending the theory to fourth moments, we show that a new parameter ψ can be calculated theoretically from p(r) and estimated from experimental SAXS data, using a method that extends Guinier's Rg estimation procedure. This new parameter yields an enhanced ability to use intensity data to distinguish between two molecules with different but similar Rg values. Analysis of existing structures in the protein data bank (PDB) shows that the theoretical ψ values relate closely to the aspect ratio of a molecular structure. The combined values for Rg and ψ acquired from experimental data provide estimates for the dimensions and associated uncertainties for a standard geometric shape, representing the particle in solution. We have chosen the cylinder as the standard shape and show that a simple, automated procedure gives a cylindrical estimate of a particle of interest. The cylindrical estimate in turn yields a good first approximation to the maximum inter-atomic distance in a molecule, Dmax, an important parameter in shape reconstruction. As with estimation of Rg, estimation of ψ requires specification of a window of angles over which to conduct the higher-order Guinier analysis. We again employ a local polynomial model with autoregressive errors to derive methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the aspect ratio, and estimation of its variance. Recent advances in SAXS data collection and more comprehensive data comparisons have resulted in a great need for automated scripts that analyze SAXS data. Our procedures to estimate Rg and ψ can be automated easily and can thus be used for large suites of SAXS data under various experimental conditions, in an objective and reproducible manner. The new methods are applied to 357 SAXS intensity curves arising from a study on the wild type nucleosome core particle and its mutants and their behavior under different experimental conditions. The resulting Rg2 values constitute a dataset which is then analyzed to account for the complex dependence structure induced by the experimental protocols. The analysis yields powerful scientific inferences and insight into better design of SAXS experiments. Finally, we consider a measurement error problem relevant to the estimation of the radius of gyration. In a SAXS experiment, it is standard to obtain intensity curves at different concentrations of the molecule in solution. Concentration-by-angle interactions may be present in such data, and analysis is complicated by the fact that actual concentration levels are unknown, but are measured with some error. We therefore propose a model and estimation procedure that allows estimation of true concentration ratios and concentration-by-angle interactions, without requiring any information about concentration other than that contained in the SAXS data

Quaternionic K\"ahler metrics associated with special K\"ahler manifolds

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic K\"ahler. A similar explicit formula is given for the analogous (K/K) correspondence between K\"ahler manifolds endowed with a Hamiltonian Killing vector field. As an example, we apply this formula in the case of an arbitrary conical K\"ahler manifold.Comment: 30 pages, appendix extended, final version published in JG

Spatio-temporal correlations in Wigner molecules

The dynamical response of Coulomb-interacting particles in nano-clusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap-symmetry, both the spatial and temporal correlations undergo slow, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Our results indicate that the distinction between the `solid' and `liquid' is soft: While particles in a `solid' flow producing dynamic heterogeneities, motion in `liquid' yields unusually long tail in the distribution of particle-displacements. A phenomenological model captures much of the subtleties of our numerical simulations.Comment: 5 pages, 4 figures, includes supplementary material

Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces

We present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified, associated with the complex volume form of the Calabi-Yau metric cone. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.Comment: 10 pages; improved versio

Strategies for implementing genomic selection in family-based aquaculture breeding schemes: double haploid sib test populations

<p>Abstract</p> <p>Background</p> <p>Simulation studies have shown that accuracy and genetic gain are increased in genomic selection schemes compared to traditional aquaculture sib-based schemes. In genomic selection, accuracy of selection can be maximized by increasing the precision of the estimation of SNP effects and by maximizing the relationships between test sibs and candidate sibs. Another means of increasing the accuracy of the estimation of SNP effects is to create individuals in the test population with extreme genotypes. The latter approach was studied here with creation of double haploids and use of non-random mating designs.</p> <p>Methods</p> <p>Six alternative breeding schemes were simulated in which the design of the test population was varied: test sibs inherited maternal (<it>Mat</it>), paternal (<it>Pat</it>) or a mixture of maternal and paternal (<it>MatPat</it>) double haploid genomes or test sibs were obtained by maximum coancestry mating (<it>MaxC</it>), minimum coancestry mating (<it>MinC</it>), or random (<it>RAND</it>) mating. Three thousand test sibs and 3000 candidate sibs were genotyped. The test sibs were recorded for a trait that could not be measured on the candidates and were used to estimate SNP effects. Selection was done by truncation on genome-wide estimated breeding values and 100 individuals were selected as parents each generation, equally divided between both sexes.</p> <p>Results</p> <p>Results showed a 7 to 19% increase in selection accuracy and a 6 to 22% increase in genetic gain in the <it>MatPat</it> scheme compared to the <it>RAND</it> scheme. These increases were greater with lower heritabilities. Among all other scenarios, i.e. <it>Mat, Pat, MaxC</it>, and <it>MinC</it>, no substantial differences in selection accuracy and genetic gain were observed.</p> <p>Conclusions</p> <p>In conclusion, a test population designed with a mixture of paternal and maternal double haploids, i.e. the <it>MatPat</it> scheme, increases substantially the accuracy of selection and genetic gain. This will be particularly interesting for traits that cannot be recorded on the selection candidates and require the use of sib tests, such as disease resistance and meat quality.</p