Asymptotics of the mean-field Heisenberg model

We consider the mean-field classical Heisenberg model and obtain detailed information about the total spin of the system by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cramer- and Sanov-type large deviations principles for the total spin and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the total spin throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.Comment: 44 page

Numerical study of scars in a chaotic billiard

We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1 millionth state. We have analyzed the integrated probability density along the periodic orbit. The numerical results confirm that the average intensity of certain types of scars is independent of $\hbar$ rather than scales with $\sqrt{\hbar}$. Our findings confirm the theoretical predictions of Robnik (1989).Comment: 7 pages in Revtex 3.1, 5 PS figures available upon request. To appear in Phys. Rev. E, Vol. 55, No. 5, 199

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

Leading and higher twists in the proton polarized structure function at large Bjorken x

A phenomenological parameterization of the proton polarized structure function has been developed for x > 0.02 using deep inelastic data up to ~ 50 (GeV/c)**2 as well as available experimental results on both photo- and electro-production of proton resonances. According to the new parameterization the generalized Drell-Hearn-Gerasimov sum rule is predicted to have a zero-crossing point at Q**2 = 0.16 +/- 0.04 (GeV/c)**2. Then, low-order polarized Nachtmann moments have been estimated and their Q**2-behavior has been investigated in terms of leading and higher twists for Q**2 > 1 (GeV/c)**2. The leading twist has been treated at NLO in the strong coupling constant and the effects of higher orders of the perturbative series have been estimated using soft-gluon resummation techniques. In case of the first moment higher-twist effects are found to be quite small for Q**2 > 1 (GeV/c)**2, and the singlet axial charge has been determined to be a0[10 (GeV/c)**2] = 0.16 +/- 0.09. In case of higher order moments, which are sensitive to the large-x region, higher-twist effects are significantly reduced by the introduction of soft gluon contributions, but they are still relevant at Q**2 ~ few (GeV/c)**2 at variance with the case of the unpolarized transverse structure function of the proton. Our finding suggests that spin-dependent correlations among partons may have more impact than spin-independent ones. As a byproduct, it is also shown that the Bloom-Gilman local duality is strongly violated in the region of polarized electroproduction of the Delta(1232) resonance.Comment: revised version to appear in Phys. Rev. D; extended discussion on the generalized DHG sum rul

A review of techniques for parameter sensitivity analysis of environmental models

Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42691/1/10661_2004_Article_BF00547132.pd

A Method for Assaying Deubiquitinating Enzymes

A general method for the assay of deubiquitinating enzymes was described in detail using (125)I-labeled ubiquitin-fused αNH-MHISPPEPESEEEEEHYC (referred to as Ub-PESTc) as a substrate. Since the tyrosine residue in the PESTc portion of the fusion protein was almost exclusively radioiodinated under a mild labeling condition, such as using IODO-BEADS, the enzymes could be assayed directly by simple measurement of the radioactivity released into acid soluble products. Using this assay protocol, we could purify six deubiquitinating enzymes from chick skeletal muscle and yeast and compare their specific activities. Since the extracts of E. coli showed little or no activity against the substrate, the assay protocol should be useful for identification and purification of eukaryotic deubiquitinating enzymes cloned and expressed in the cells

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

SPIN-DEPENDENT NUCLEAR STRUCTURE FUNCTIONS: GENERAL APPROACH WITH APPLICATION TO THE DEUTERON

We study deep-inelastic scattering from polarized nuclei within a covariant framework. A clear connection is established between relativistic and non-relativistic limits, which enables a rigorous derivation of convolution formulae for the spin-dependent nuclear structure functions g_1^A and g_2^A in terms of off-mass-shell extrapolations of polarized nucleon structure functions, g_1^N and g_2^N. Approximate expressions for g_{1,2}^A are obtained by expanding the off-shell g_{1,2}^N about their on-shell limits. As an application of the formalism we consider nuclear effects in the deuteron, knowledge of which is necessary to obtain accurate information on the spin-dependent structure functions of the neutron.Comment: 26 pages RevTeX, 9 figures available upon reques