Wavelets and Quantum Algebras

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding non-linear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.Comment: 27 pages Latex, 3 figure p

Differences in receptivity to gastrointestinal infections with nematodes in dairy ewes: Influence of age and of the level of milk production

Resistance to anthelmintics in populations of gastrointestinal nematodes is a major concern in small ruminants. One solution to limit the spread of anthelmintic resistance is to apply treatments selectively by targeting the most susceptible animals within a flock. In dairy goats, previous studies have shown that, within a flock, goats in first lactation and those with high level of milk production were highly receptive to nematode infections. These results provided the rationale for targeted treatments. In dairy ewes, such epidemiological information on possible factors modulating the susceptibility to parasitism were still lacking. The objective of the current study was therefore to examine differences in the level of parasite infection and in the pathophysiological consequences in dairy ewes, depending on the age or on the level of milk production. In three farms, parasite egg excretion, and the serum concentrations of pepsinogen and inorganic phosphate were compared on one hand between primiparous and multiparous ewes; on the other hand, between ewes with the highest and the lowest level of milk production, within a cohort of 3–5-year old animals. Overall, the results did not indicate significant differences for both either the parasitological or pathophysiological measurements depending on the level of milk production. In contrast, significant differences were found according to age, indicating higher levels of infections in the primiparous ewes than in the multiparous ones and suggesting that this category of animals represents a particular parasitic risk within a flock

Fast Numerical simulations of 2D turbulence using a dynamic model for Subgrid Motions

We present numerical simulation of 2D turbulent flow using a new model for the subgrid scales which are computed using a dynamic equation linking the subgrid scales with the resolved velocity. This equation is not postulated, but derived from the constitutive equations under the assumption that the non-linear interactions of subgrid scales between themselves are equivalent to a turbulent viscosity.The performances of our model are compared with Direct Numerical Simulations of decaying and forced turbulence. For a same resolution, numerical simulations using our model allow for a significant reduction of the computational time (of the order of 100 in the case we consider), and allow the achievement of significantly larger Reynolds number than the direct method.Comment: 35 pages, 9 figure

Structures in the RM sky

Coherent structures in the distribution of the Faraday rotation measure of extragalactic radio sources are isolated using wavelet transformation technique. Signatures of the magnetic fields in the local (Orion) spiral arm, the Sagittarius and Carina arms, the synchrotron Loop I and, possibly, the Perseus arm have been revealed using the RM catalogues of Simard-Normandin et al. (1981, 551 source)and Broten et al. (1988, 663 sources). Unlike earlier analyses of the RM sky, our approach has allowed us to assess the stability of the results with respect to modifications of the data sample. We estimate the mean magnetic field strength in the Orion arm as 1.4\pm0.3 mkGauss and find clear indication of a magnetic field reversal at a distance of 0.6-1 kpc towards the Galactic centre. Our analysis has revealed for the first time the extension of the reversal in the Carina arm. The direction of magnetic field in the Perseus arm is reversed with respect to that in the Orion arm. The average pitch angle of magnetic field in the nearby spiral arms is 15^\circ, and the mean field strength in the Sagittarius-Carina and Perseus arms is 1.7\pm0.3 mkGauss and 1.4\pm1.2 mkGauss, respectively. The line-of-sight magnetic field in Loop I is estimated as 0.9\pm0.3 mkGauss. We find firm evidence of a dominant even symmetry of the local mean field with respect to the galactic equator.Comment: 16 pages (LaTEX), 11 figures (eps), accepted for publication in MNRAS (uses mn.sty

First radius measurements of very low mass stars with the VLTI

e present 4 very low mass stars radii measured with the VLTI using the 2.2 microns VINCI test instrument. The observations were carried out during the commissioning of the 104-meter-baseline with two 8-meter-telescopes. We measure angular diameters of 0.7-1.5 mas with accuracies of 0.04-0.11 mas, and for spectral type ranging from M0V to M5.5V. We determine an empirical mass-radius relation for M dwarfs based on all available radius measurements. The observed relation agrees well with theoretical models at the present accuracy level, with possible discrepancy around 0.5-0.8 Msolar that needs to be confirmed. In the near future, dozens of M dwarfs radii will be measured with 0.1-1% accuracy, with the VLTI, thanks to the improvements expected from the near infrared instrument AMBER. This will bring strong observational constraints on both atmosphere and interior physics.Comment: Accepted for publication in Astronomy and Astrophysics Letters, 4 pages, 3 figure

Cumulants as non-Gaussian qualifiers

We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favours quantities defined in Fourier space. Bearing this in mind we decide to be eclectic and define two new sets of statistics to quantify the level of non-Gaussianity. Both sets make use of the concept of cumulants of a distribution. However, one set is defined in real space, with reference to the wavelet transform, whereas the other is defined in Fourier space. We derive a series of properties concerning these statistics for a Gaussian random field and show how one can relate these quantities to the higher order moments of temperature maps. Although our frameworks lead to an infinite hierarchy of quantities we show how cosmic variance and experimental constraints give a natural truncation of this hierarchy. We then focus on the real space statistics and analyse the non-Gaussian signal generated by points sources obscured by large scale Gaussian fluctuations. We conclude by discussing the practical implementations of these techniques

Data reduction methods for single-mode optical interferometry - Application to the VLTI two-telescopes beam combiner VINCI

The interferometric data processing methods that we describe in this paper use a number of innovative techniques. In particular, the implementation of the wavelet transform allows us to obtain a good immunity of the fringe processing to false detections and large amplitude perturbations by the atmospheric piston effect, through a careful, automated selection of the interferograms. To demonstrate the data reduction procedure, we describe the processing and calibration of a sample of stellar data from the VINCI beam combiner. Starting from the raw data, we derive the angular diameter of the dwarf star Alpha Cen A. Although these methods have been developed specifically for VINCI, they are easily applicable to other single-mode beam combiners, and to spectrally dispersed fringes.Comment: Accepted for publication in Astronomy & Astrophysics, 17 pages, 19 figure

Characterizing Multi-Scale Self-Similar Behavior and Non-Statistical Properties of Financial Time Series

We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scales. The fact that, the wavelets belonging to the Daubechies' (Db) basis enables one to isolate local polynomial trends of different degrees, plays the key role in isolating fluctuations at different scales. One of the primary motivations of this work is to study the emergence of the $k^{-3}$ behavior \cite{hes5} of the fluctuations starting with high frequency fluctuations. We make use of Db4 and Db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series. The fluctuations reveal fat tail non-Gaussian behavior, unstable periodic modulations, at finer scales, from which the characteristic $k^{-3}$ power law behavior emerges at sufficiently large scales. We further identify stable periodic behavior through the continuous Morlet wavelet.Comment: 11 pages, 8 figures, bibliography updated, conclusion added, minor changes in the manuscrip

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p

Individual quality assessment of autografting by probability estimation for clinical endpoints: a prospective validation study from the European group for blood and marrow transplantation.

The aim of supportive autografting is to reduce the side effects from stem cell transplantation and avoid procedure-related health disadvantages for patients at the lowest possible cost and resource expenditure. Economic evaluation of health care is becoming increasingly important. We report clinical and laboratory data collected from 397 consecutive adult patients (173 non-Hodgkin lymphoma, 30 Hodgkin lymphoma, 160 multiple myeloma, 7 autoimmune diseases, and 28 acute leukemia) who underwent their first autologous peripheral blood stem cell transplantation (PBSCT). We considered primary endpoints evaluating health economic efficacy (eg, antibiotic administration, transfusion of blood components, and time in hospital), secondary endpoints evaluating toxicity (in accordance with Common Toxicity Criteria), and tertiary endpoints evaluating safety (ie, the risk of regimen-related death or disease progression within the first year after PBSCT). A time-dependent grading of efficacy is proposed with day 21 for multiple myeloma and day 25 for the other disease categories (depending on the length of the conditioning regimen) as the acceptable maximum time in hospital, which together with antibiotics, antifungal, or transfusion therapy delineates four groups: favorable (≤7 days on antibiotics and no transfusions; ≤21 [25] days in hospital), intermediate (from 7 to 10 days on antibiotics and 7 days on antibiotics, >3 but 30/34 days in hospital after transplantation), and very unfavorable (>10 days on antibiotics, >6 transfusions; >30 to 34 days in hospital). The multivariate analysis showed that (1) PBSC harvests of ≥4 × 106/kg CD34 + cells in 1 apheresis procedure were associated with a favorable outcome in all patient categories except acute myelogenous leukemia and acute lymphoblastic leukemia (P = .001), (2) ≥5 × 106/kg CD34 + cells infused predicted better transplantation outcome in all patient categories (P 500 mL) (P = .002), and (5) patients with a central venous catheter during both collection and infusion of PBSC had a more favorable outcome post-PBSCT than peripheral access (P = .007). The type of mobilization regimen did not affect the outcome of auto-PBSCT. The present study identified predictive variables, which may be useful in future individual pretransplantation probability evaluations with the goal to improve supportive care