Is cosmology compatible with sterile neutrinos?

By combining data from cosmic microwave background experiments (including the recent WMAP third year results), large scale structure, and Lyman-alpha forest observations, we constrain the hypothesis of a fourth, sterile, massive neutrino. For the 3 massless+1 massive neutrino case, we bound the mass of the sterile neutrino to ms<0.26 eV (0.44 eV) at 95% (99.9%) C.L., which excludes at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We generalize the analysis to account for active neutrino masses and the possibility that the sterile abundance is not thermal. In the latter case, the contraints in the plane are nontrivial. For a mass of >1 or <0.05 eV, the cosmological energy density in sterile neutrinos is always constrained to be omeganu<0.003 at 95% C.L., but for a mass of approximately 0.25 eV, omeganu can be as large as 0.01.     

Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation

We consider the coarsening dynamics of multiscale solutions to a dissipative singularly perturbed partial differential equation which models the evolution of a thermodynamically unstable crystalline surface. The late-time leading-order behavior of solutions is identified, through the asymptotic expansion of a maximal-dissipation principle, with a completely faceted surface governed by an intrinsic dynamical system. The properties of the resulting piecewise-affine dynamic surface predict the scaling law L(Mu) approximately t(1/3), for the growth in time of a characteristic morphological length scale L(Mu). A novel computational geometry tool which directly simulates a million-facet piecewise-affine dynamic surface is also introduced. Our computed data are consistent with the dynamic scaling hypothesis, and we report a variety of associated morphometric scaling functions.     

A modern Bayesian look at the multi‐armed bandit

A multi‐armed bandit is an experiment with the goal of accumulating rewards from a payoff distribution with unknown parameters that are to be learned sequentially. This article describes a heuristic for managing multi‐armed bandits called randomized probability matching, which randomly allocates observations to arms according the Bayesian posterior probability that each arm is optimal. Advances in Bayesian computation have made randomized probability matching easy to apply to virtually any payoff distribution. This flexibility frees the experimenter to work with payoff distributions that correspond to certain classical experimental designs that have the potential to outperform methods that are ‘optimal’ in simpler contexts. I summarize the relationships between randomized probability matching and several related heuristics that have been used in the reinforcement learning literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type _n

In this paper we show that the leading coeficient μ(y,w) of some Kazhdan-Lusztig polynomials Py,w with y,w in an affine Weyl group of type n is n + 2.This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.     

Sample path Large Deviations and optimal importance sampling for stochastic volatility models

Sample path Large Deviation Principles (LDP) of the Freidlin–Wentzell type are derived for a class of diffusions, which govern the price dynamics in common stochastic volatility models from Mathematical Finance. LDP are obtained by relaxing the non-degeneracy requirement on the diffusion matrix in the standard theory of Freidlin and Wentzell. As an application, a sample path LDP is proved for the price process in the Heston stochastic volatility model.     

NMR Studies of (TMTSF)2PF6

Abstract

Pulsed NMR determinations of the relaxation times T₂, T₂* and T₁, as a function of temperature and field, for the methyl group protons in (TMTSF)₂PF₆ are reported. Below the metal-insulator transition (T_MI)T₂* shortens while T₂ increases, indicating a line which is inhomogeneously broadened due to the onset of a SDW. The SDW also contributes to the spin-lattice relaxation rate, T₁ ^?1, in the neighborhood of T_MI. A frequency dependent maximum in T₁ ^?1 is observed near 20K and is attributed to methyl group rotation. A frequency independent maximum at 58K suggests a structural phase transition involving rearrangement of the methyl and PF₆ groups.     

Surface Chemistry of Polyacetylene: Adhesion to Silica,Derivatization With Nickel And Catalytic Activity

Adhesion of (CH)_x film prepared by the Luttinger method to glass can be improved by silylation in order to more closely match dispersive surface energies. Treatment of n-type (CH) films with NiBr₂/HMPA/THF affords (CH)_x -supported N° which shows selectivity in hydrogenation of phenyl acetylene.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.     

White matter maturation in the brains of Long Evans shaker myelin mutant rats by ex-vivo QSI and DTI

The brains of Long Evans shaker (les) rats, a model of dysmyelination, and their age- matched controls were studied by ex-vivo q-space diffusion imaging (QSI) and diffusion tensor imaging (DTI). The QSI and DTI indices were computed from the same acquisition. The les and the control brains were studied at different stages of maturation and disease progression. The mean displacement, the probability for zero displacement and kurtosis were computed from QSI data while the fractional anisotropy (FA) and the eigenvalues were computed from DTI. It was found that all QSI indices detect the les pathology, at all stages of maturation, while only some of the DTI indices could detect the les pathology. The QSI mean displacement was larger in the les group as compared with their age-matched controls while the probability for zero displacement and the kurtosis were both lower all indicating higher degree of restriction in the control brains. Since all the DTI eigenvalues were higher in the les brains as compared to controls, the less efficient DTI measure for discerning the les pathology was found to be the FA. Clearly, the most sensitive DTI parameter to the les pathology is λ₃, i.e. the minimal diffusivity. Since the QSI and DTI data were obtained from the same acquisition, despite the somewhat higher SNR of the QSI data compared to the DTI data, it seems that the higher diagnostic capacity of the QSI data in this experimental model of dysmyelination, originates mainly from the higher diffusing weighting of the QSI data.     

Coupled spring equations

Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project.