Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Efficiency and Stability Issues in the Numerical Computation of Fourier Transforms and Convolutions on the 2-Sphere

Earlier work by Driscoll and Healy has produced an efficient algorithm for computing the Fourier transform of band-limited functions on the sphere. In this paper we present a greatly improved inverse transform, and consequent improved convolution algorithm for such functions. We also discuss implementational considerations and give heuristics for allowing reliable floating point implementations of a slightly modified algorithm at little cost in either theoretical or actual performance. This discussion is supplemented with numerical experiments from our implementation in C on a DecStation 5000. These results give strong indications that the algorithm is both reliable and efficient for a large range of useful problem sizes

On Quantum State Observability and Measurement

We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence the dynamics by generating all the unitary evolutions in a Lie group. We investigate to what extent, by an appropriate sequence of evolutions and measurements, we can obtain information on the initial state of the system. We present a system theoretic viewpoint of this problem in that we study the {\it observability} of the system. In this context, we characterize the equivalence classes of indistinguishable states and propose algorithms for state identification

TGF-beta 1 induces human alveolar epithelial to mesenchymal cell transition (EMT)

Background: Fibroblastic foci are characteristic features in lung parenchyma of patients with idiopathic pulmonary fibrosis (IPF). They comprise aggregates of mesenchymal cells which underlie sites of unresolved epithelial injury and are associated with progression of fibrosis. However, the cellular origins of these mesenchymal phenotypes remain unclear. We examined whether the potent fibrogenic cytokine TGF-β1 could induce epithelial mesenchymal transition (EMT) in the human alveolar epithelial cell line, A549, and investigated the signaling pathway of TGF-β1-mediated EMT. Methods: A549 cells were examined for evidence of EMT after treatment with TGF-β1. EMT was assessed by: morphology under phase-contrast microscopy; Western analysis of cell lysates for expression of mesenchymal phenotypic markers including fibronectin EDA (Fn-EDA), and expression of epithelial phenotypic markers including E-cadherin (E-cad). Markers of fibrogenesis, including collagens and connective tissue growth factor (CTGF) were also evaluated by measuring mRNA level using RT-PCR, and protein by immunofluorescence or Western blotting. Signaling pathways for EMT were characterized by Western analysis of cell lysates using monoclonal antibodies to detect phosphorylated Erk1/2 and Smad2 after TGF-β1 treatment in the presence or absence of MEK inhibitors. The role of Smad2 in TGF-β1-mediated EMT was investigated using siRNA. Results: The data showed that TGF-β1, but not TNF-α or IL-1β, induced A549 cells with an alveolar epithelial type II cell phenotype to undergo EMT in a time-and concentration-dependent manner. The process of EMT was accompanied by morphological alteration and expression of the fibroblast phenotypic markers Fn-EDA and vimentin, concomitant with a downregulation of the epithelial phenotype marker E-cad. Furthermore, cells that had undergone EMT showed enhanced expression of markers of fibrogenesis including collagens type I and III and CTGF. MMP-2 expression was also evidenced. TGF-β1-induced EMT occurred through phosphorylation of Smad2 and was inhibited by Smad2 gene silencing; MEK inhibitors failed to attenuate either EMT-associated Smad2 phosphorylation or the observed phenotypic changes. Conclusion: Our study shows that TGF-β1 induces A549 alveolar epithelial cells to undergo EMT via Smad2 activation. Our data support the concept of EMT in lung epithelial cells, and suggest the need for further studies to investigate the phenomenon

Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized traciality condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.Comment: REVTeX, 18 pages, no figure

Reliability and validity of three questionnaires measuring context-specific sedentary behaviour and associated correlates in adolescents, adults and older adults

BACKGROUND: Reliable and valid measures of total sedentary time, context-specific sedentary behaviour (SB) and its potential correlates are useful for the development of future interventions. The purpose was to examine test-retest reliability and criterion validity of three newly developed questionnaires on total sedentary time, context-specific SB and its potential correlates in adolescents, adults and older adults. METHODS: Reliability and validity was tested in six different samples of Flemish (Belgium) residents. For the reliability study, 20 adolescents, 22 adults and 20 older adults filled out the age-specific SB questionnaire twice. Test-retest reliability was analysed using Kappa coefficients, Intraclass Correlation Coefficients and/or percentage agreement, separately for the three age groups. For the validity study, data were retrieved from 62 adolescents, 33 adults and 33 older adults, with activPAL as criterion measure. Spearman correlations and Bland-Altman plots (or non-parametric approach) were used to analyse criterion validity, separately for the three age groups and for weekday, weekend day and average day. RESULTS: The test-retest reliability for self-reported total sedentary time indicated following values: ICC = 0.37-0.67 in adolescents; ICC = 0.73-0.77 in adults; ICC = 0.68-0.80 in older adults. Item-specific reliability results (e.g. context-specific SB and its potential correlates) showed good-to-excellent reliability in 67.94%, 68.90% and 66.38% of the items in adolescents, adults and older adults respectively. All items belonging to sedentary-related equipment and simultaneous SB showed good reliability. The sections of the questionnaire with lowest reliability were: context-specific SB (adolescents), potential correlates of computer use (adults) and potential correlates of motorized transport (older adults). Spearman correlations between self-reported total sedentary time and the activPAL were different for each age group: rho = 0.02-0.42 (adolescents), rho = 0.06-0.52 (adults), rho = 0.38-0.50 (older adults). Participants over-reported total sedentary time (except for weekend day in older adults) compared to the activPAL, for weekday, weekend day and average day respectively by +57.05%, +46.29%, +53.34% in adolescents; +40.40%, +19.15%, +32.89% in adults; +10.10%, -6.24%, +4.11% in older adults. CONCLUSIONS: The questionnaires showed acceptable test-retest reliability and criterion validity. However, over-reporting of total SB was noticeable in adolescents and adults. Nevertheless, these questionnaires will be useful in getting context-specific information on SB

Perspectives: Quantum Mechanics on Phase Space

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum Structures Association; Denver, Colorado; 17-22 July, 200

Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter

Data collected by the Pierre Auger Observatory through 31 August 2007 showed evidence for anisotropy in the arrival directions of cosmic rays above the Greisen-Zatsepin-Kuz'min energy threshold, \nobreak{$6\times 10^{19}$eV}. The anisotropy was measured by the fraction of arrival directions that are less than $3.1^\circ$ from the position of an active galactic nucleus within 75 Mpc (using the V\'eron-Cetty and V\'eron $12^{\rm th}$ catalog). An updated measurement of this fraction is reported here using the arrival directions of cosmic rays recorded above the same energy threshold through 31 December 2009. The number of arrival directions has increased from 27 to 69, allowing a more precise measurement. The correlating fraction is $(38^{+7}_{-6})$, compared with $21$ expected for isotropic cosmic rays. This is down from the early estimate of $(69^{+11}_{-13})$. The enlarged set of arrival directions is examined also in relation to other populations of nearby extragalactic objects: galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in hard X-rays by the Swift Burst Alert Telescope. A celestial region around the position of the radiogalaxy Cen A has the largest excess of arrival directions relative to isotropic expectations. The 2-point autocorrelation function is shown for the enlarged set of arrival directions and compared to the isotropic expectation.Comment: Accepted for publication in Astroparticle Physics on 31 August 201

Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.Comment: 31 pages, 21 figures, 1 table; references updated (v2,v3); Fig.19 updated & minor changes in text (v3); final version (v4); J. Stat. Phys. Online First (2012