Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.Comment: 25 pages, 4 figure

Design of a 3rd harmonic electron cyclotron emission diagnostic for ballooning mode fluctuations in PBX-M

A third harmonic electron cyclotron emission diagnostic using ultrawide bandwidth ( = 40 GHz) heterodyne receivers centered on 120 GHz with 14 channels per radial view is describecj for localized, long wavelength (5 % X s 50 cm), fast time response ( = 1 ps) fluctuation studies in the PBX-M tokamak. The optically gray emission signal will have a y ie/ne + (3/0)Te/Te dependence on temperature and density fluctuations where y S 1 and 1 _ P: 3 depending on local optical depth. Electron temperature fluctuation sensitivity is estimated to be 0.2 % se ' Te/Te s 2.9 % depending on local optical depth and fluctuation frequency in the 0.1-1 MHz range. Spatial resolution of approximately 3 cm radially and 5 cm vertically are estimated for 2 keV plasmas with low suprathermal electron emission

Spreading lengths of Hermite polynomials

The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These information-theoretic measures of the associated Rakhmanov probability density, which are direct measures of the polynomial spreading in the sense of having the same units as the variable, share interesting properties: invariance under translations and reflections, linear scaling and vanishing in the limit that the variable tends towards a given definite value. The expressions of the Renyi and Fisher lengths for the Hermite polynomials are computed in terms of the polynomial degree. The combinatorial multivariable Bell polynomials, which are shown to characterize the finite power of an arbitrary polynomial, play a relevant role for the computation of these information-theoretic lengths. Indeed these polynomials allow us to design an error-free computing approach for the entropic moments (weighted L^q-norms) of Hermite polynomials and subsequently for the Renyi and Tsallis entropies, as well as for the Renyi spreading lengths. Sharp bounds for the Shannon length of these polynomials are also given by means of an information-theoretic-based optimization procedure. Moreover, it is computationally proved the existence of a linear correlation between the Shannon length (as well as the second-order Renyi length) and the standard deviation. Finally, the application to the most popular quantum-mechanical prototype system, the harmonic oscillator, is discussed and some relevant asymptotical open issues related to the entropic moments mentioned previously are posed.Comment: 16 pages, 4 figures. Journal of Computational and Applied Mathematics (2009), doi:10.1016/j.cam.2009.09.04

Anisotropic phonon conduction and lattice distortions in CMR-type bilayer manganite (La1−z_{1-z}Prz_{z})1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7} (z=0,0.2,0.4 and 0.6) single crystals

We have undertaken a systematic study of thermal conductivity as a function of temperature and magnetic field of single crystals of the compound (La$_{1-z}$Pr$_{z}$)$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ for $z$(Pr) =0.2,0.4. and 0.6. The lattice distortion due to Pr-substitution and anisotropic thermal conductivity in bilayer manganites are discussed on the basis of different relaxation models of local lattice distortions in metal and insulating states proposed by Maderda et al. The giant magnetothermal effect is scaled as a function of magnetization and discussed on the basis of a systematic variation of the occupation of the $e_g$-electron orbital states due to Pr-substitution.Comment: 7 pages, 6 figures, in press in Phys.Rev.

Similarities and differences in lipidomics profiles among healthy monozygotic twin pairs.

Differences in genetic background and/or environmental exposure among individuals are expected to give rise to differences in measurable characteristics, or phenotypes. Consequently, genetic resemblance and similarities in environment should manifest as similarities in phenotypes. The metabolome reflects many of the system properties, and is therefore an important part of the phenotype. Nevertheless, it has not yet been examined to what extent individuals sharing part of their genome and/or environment indeed have similar metabolomes. Here we present the results of hierarchical clustering of blood plasma lipid profile data obtained by liquid chromatographymass spectrometry from 23 healthy, 18-year-old twin pairs, of which 21 pairs were monozygotic, and 8 of their siblings. For 13 monozygotic twin pairs, within-pair similarities in relative concentrations of the detected lipids were indeed larger than the similarities with any other study participant. We demonstrate such high coclustering to be unexpected on basis of chance. The similarities between dizygotic twins and between nontwin siblings, as well as between nonfamilial participants, were less pronounced. In a number of twin pairs, within-pair dissimilarity of lipid profiles positively correlated with increased blood plasma concentrations of C-reactive protein in one twin. In conclusion, this study demonstrates that in healthy individuals, the individual genetic background contributes to the blood plasma lipid profile. Furthermore, lipid profiling may prove useful in monitoring health status, for example, in the context of personalized medicine. © 2008 Mary Ann Liebert, Inc. Chemicals / CAS: C-Reactive Protein, 9007-41-4; Lipid

Is Quantum Mechanics Incompatible with Newton's First Law

Quantum mechanics (QM) clearly violates Newton's First Law of Motion (NFLM) in the quantum domain for one of the simplest problems, yielding an effect in a force-free region much like the Aharonov-Bohm effect. In addition, there is an incompatibility between the predictions of QM in the classical limit, and that of classical mechanics (CM) with respect to NFLM. A general argument is made that such a disparity may be found commonly for a wide variety of quantum predictions in the classical limit. Alternatives to the Schrodinger equation are considered that might avoid this problem. The meaning of the classical limit is examined. Critical views regarding QM by Schrodinger, Bohm, Bell, Clauser, and others are presented to provide a more complete perspective.Comment: Paper has been revised to conform to published versio