Exhaustive weakly wandering sequences

AbstractA sequence of integers {ni : i = 0, 1…} is an exhaustive weakly wandering sequence for a transformation T if for some measurable set W, X=⋃∞i=0TniW(disj. We introduce a hereditary Property (H) for a sequence of integers associated with an infinite ergodic transformation T, and show that it is a sufficient condition for the sequence to be an exhaustive weakly wandering sequence for T. We then show that every infinite ergodic transformation admits sequences that possess Property (H), and observe that Property (H) is inherited by all subsequences of a sequence that possess it. As a corollary, we obtain an application to tiling the set of integers ℤ with infinite subsets

Dramatic presentations with adjusted materials for heterogeneous grouping,

Thesis (M.A.)--Boston Universit

Unveiling Hidden Patterns in CMB Anisotropy Maps

Bianchi VII_h models have been recently proposed to explain potential anomalies in the CMB anisotropy as observed by WMAP. We investigate the violation of statistical isotropy due to an embedded Bianchi VII_h templates in the CMB anisotropy maps to determine whether the existence of a hidden Bianchi template in the WMAP data is consistent with the previous null detection of the bipolar power spectrum in the WMAP first year maps. We argue that although correcting the WMAP maps for the Bianchi template may explain some features in the WMAP data it may cause other anomalies such as preferred directions leading to detectable levels of violation of statistical isotropy in the Bianchi corrected maps. We compute the bipolar power spectrum for the low density Bianchi VII_h models embedded in the background CMB anisotropy maps with the power spectrum that have been shown in recent literature to best fit the first year WMAP data. By examining statistical isotropy of these maps, we put a limit of {\sigma/H}_0 < 2.77E-10 (99% CL) on the shear parameter in Bianchi VII_h models.Comment: Matches version accepted to Phys Rev D. Results unchanged. Paper shortened, sharpened, typos fixed. See earlier version for a review of CMB anisotropy patterns in Bianchi universe model

Observational Study of the Multistructured Planetary Nebula NGC 7354

We present an observational study of the planetary nebula (PN) NGC 7354 consisting of narrowband Halpha and [NII]6584 imaging as well as low- and high-dispersion long-slit spectroscopy and VLA-D radio continuum. According to our imaging and spectroscopic data, NGC 7354 has four main structures: a quite round outer shell and an elliptical inner shell, a collection of low-excitation bright knots roughly concentrated on the equatorial region of the nebula, and two symmetrical jet-like features, not aligned either with the shells' axes, or with each other. We have obtained physical parameters like electron temperature and electron density as well as ionic and elemental abundances for these different structures. Electron temperature and electron density slightly vary throughout the nebula. The local extinction coefficient c_Hbeta shows an increasing gradient from south to north and a decreasing gradient from east to west consistent with the number of equatorial bright knots present in each direction. Abundance values show slight internal variations but most of them are within the estimated uncertainties. In general, abundance values are in good agreement with the ones expected for PNe. Radio continuum data are consistent with optically thin thermal emission. We have used the interactive three-dimensional modeling tool SHAPE to reproduce the observed morphokinematic structures in NGC 7354 with different geometrical components. Our SHAPE model is in very good agreement with our imaging and spectroscopic observations. Finally, after modeling NGC 7354 with SHAPE, we suggest a possible scenario for the formation of the nebula.Comment: Accepted for publication in AJ, 12 pages, 8 figure

The association of fasting blood glucose (FBG) and waist circumference in northern adults in Iran: A population based study

Objectives: The aim of this study was to evaluate the association between Fasting Blood Glucose (FBG) level and Waist Circumference (WC) in men and women among 25-65 years old people in the north of Iran.Material and methods: This was a cross-sectional and analytical research gender that carried out on the 1797 subjects (941 males and 856 females) between 25-65 years old using multistage cluster sampling technique. FBG was measured in the morning after a 12-hour fast and was determined by using laboratory kits (enzymatic methods) and spectrophotometry technique. Central obesity was defined based on World Health Organization criteria: waist circumference ≥102 cm and ≥88 cm in men and women, respectively. The SPSS.16 software was used for statistical analysis.Results: As whole, the mean of FBG in women (98.3 ± 40.1 mg/dl) was higher than in men (94.6 ± 32.2 mg/dl). Also, the mean of WC in men 4.5 cm was lower than in women. In men, the mean of FBG statistically differs between normal and central obese subjects both in 35-45 year-age group (P = 0.001) and in 45-55 year-age group (P = 0.042). As whole, in men, the FBG level increased up 2.82 mg/dl in each 10 cm of WC with the highest rate in 35-45 year-age group. In totally, in women, the FBG level increased up 3.48 mg/dl in each 10 cm of WC and in 25-35 year-age group and it was higher than in other age groups. In men, the regression coefficients were constant with age increasing while in women it was decreased. Constant trend in men and decreasing trend in women with age was shown between FBG and WC. The cut-off point of WC for detecting of diabetes obtained 89 cm and 107 cm in men and women, respectively.Conclusion: The positive correlation was seen between WC and FBG level and it was declined with age in women. Cut-off point for detecting of diabetes in men was less than in women. WC is useable as a predictor of type 2 diabetes mellitus risk among adults in the north of Iran. © 2014 Veghari et al.; licensee BioMed Central Ltd

Stellar Astrophysics with a Dispersed Fourier Transform Spectrograph. II. Orbits of Double-lined Spectroscopic Binaries

We present orbital parameters for six double-lined spectroscopic binaries (iota Pegasi, omega Draconis, 12 Bootis, V1143 Cygni, beta Aurigae, and Mizar A) and two double-lined triple star systems (kappa Pegasi and eta Virginis). The orbital fits are based upon high-precision radial velocity observations made with a dispersed Fourier Transform Spectrograph, or dFTS, a new instrument which combines interferometric and dispersive elements. For some of the double-lined binaries with known inclination angles, the quality of our RV data permits us to determine the masses M_1 and M_2 of the stellar components with relative errors as small as 0.2%.Comment: 41 pages, 8 figures, accepted by A

CMB power spectrum estimation with non-circular beam and incomplete sky coverage

Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high resolution, `full' sky measurements from different CMB experiments pose a stiff challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but, the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the final precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using Pseudo-C_l unavoidable for high resolution data. We provide a (semi)analytic framework to estimate bias in the power spectrum due to the effect of beam non-circularity and non-uniform sky coverage including incomplete/masked sky maps and scan strategy. The approach is perturbative in the distortion of the beam from non-circularity, allowing for rapid computations when the beam is mildly non-circular. We advocate that it is computationally advantageous to employ `soft' azimuthally apodized masks whose spherical harmonic transform die down fast with m. We numerically implement our method for non-rotating beams. We present preliminary estimates of the computational cost to evaluate the bias for the upcoming CMB anisotropy probes l_max~3000, with angular resolution comparable to the Planck surveyor mission. We further show that this implementation and estimate is applicable for rotating beams on equal declination scans and possibly can be extended to simple approximations to other scan strategies.Comment: 22 pages, 7 figures. Revised presentation to highlight significance of extended results. Matches version accepted to the MNRA

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar ($l$) and angular ($\ell$) scales $(l,\ell)=(2,5),(4,7),$ and $(6,8)$, which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales $(l,\ell)=(10,8)$ and $(2,9)$ in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale $(l,\ell)=(10,5)$, which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole ($\ell=2$), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy's plane, which may be an indication of residual contaminations in the full- and cut-sky maps.Comment: 15 pages with pdf figure

On black hole temperature in Horndeski gravity

It has been observed that for black holes in certain family of Horndeski gravity theories Wald's entropy formula does not lead to the correct first law for black hole thermodynamics. For this family of Horndeski theories speeds of propagation of gravitons and photons are in general different and gravitons move on an effective metric different than the one seen by photons. We show that the temperature of the black hole should be modified from surface gravity over 2\u3c0 to include effects of this effective metric. The modified temperature, with the entropy unambiguously computed by the solution phase space method, yields the correct first law. Our results have far reaching implications for the Hawking radiation and species problem, going beyond the Horndeski theories

Efficient Cosmological Parameter Estimation with Hamiltonian Monte Carlo

Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 and boosts up the efficiency by at least a factor of D in a D-dimensional parameter space. Therefor shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation