Abstract:
We use the direct Fourier method to calculate the redshift-space power spectrum of the maxBCG cluster catalog -- currently by far the largest existing galaxy cluster sample. The total number of clusters used in our analysis is 12,616. After accounting for the radial smearing effect caused by photometric redshift errors and also introducing a simple treatment for the nonlinear effects, we show that currently favored low matter density "concordance" LCDM cosmology provides a very good fit to the estimated power. Thanks to the large volume (~0.4 h^{-3}Gpc^{3}), high clustering amplitude (linear effective bias parameter b_{eff} ~3x(0.85/sigma_8)), and sufficiently high sampling density (~3x10^{-5} h^{3}Mpc^{-3}) the recovered power spectrum has high enough signal to noise to allow us to find evidence (~2 sigma CL) for the baryonic acoustic oscillations (BAO). In case the clusters are additionally weighted by their richness the resulting power spectrum has slightly higher large-scale amplitude and smaller damping on small scales. As a result the confidence level for the BAO detection is somewhat increased: ~2.5 sigma. The ability to detect BAO with relatively small number of clusters is encouraging in the light of several proposed large cluster surveys.

Abstract:
The PAMELA, Fermi and HESS experiments (PFH) have shown anomalous excesses in the cosmic positron and electron fluxes. A very exciting possibility is that those excesses are due to annihilating dark matter (DM). In this paper we calculate constraints on leptonically annihilating DM using observational data on diffuse extragalactic gamma-ray background and measurements of the optical depth to the last-scattering surface, and compare those with the PFH favored region in the m_{DM} - <\sigma_A v> plane. Having specified the detailed form of the energy input with PYTHIA Monte Carlo tools we solve the radiative transfer equation which allows us to determine the amount of energy being absorbed by the cosmic medium and also the amount left over for the diffuse gamma background. We find that the constraints from the optical depth measurements are able to rule out the PFH favored region fully for the \tau^{-}+\tau^{+} annihilation channel and almost fully for the \mu^{-}+\mu^{+} annihilation channel. It turns out that those constraints are quite robust with almost no dependence on low redshift clustering boost. The constraints from the gamma-ray background are sensitive to the assumed halo concentration model and, for the power law model, rule out the PFH favored region for all leptonic annihilation channels. We also find that it is possible to have models that fully ionize the Universe at low redshifts. However, those models produce too large free electron fractions at z > ~100 and are in conflict with the optical depth measurements. Also, the magnitude of the annihilation cross-section in those cases is larger than suggested by the PFH data.

Abstract:
We develop a new method for deconvolving the smearing effect of the survey window in the analysis of the galaxy multipole power spectra from a redshift survey. This method is based on the deconvolution theorem, and is compatible with the use of the fast Fourier transform. It is possible to measure the multipole power spectra deconvolved from the window effect efficiently. Applying this method to the luminous red galaxy sample of the Sloan Digital Sky Survey data release 7 as well as mock catalogues, we demonstrate how the method works properly. Using this deconvolution technique, the amplitude of the multipole power spectrum is corrected. Besides, the covariance matrices of the deconvolved power spectra get quite close to the diagonal form. This is also advantageous in the study of the BAO signature.

Abstract:
A constraint on the viable f(R) model is investigated by confronting theoretical predictions with the multipole power spectrum of the luminous red galaxy sample of the Sloan Digital Sky survey data release 7. We obtain a constraint on the Compton wavelength parameter of the f(R) model on the scales of cosmological large-scale structure. A prospect of constraining the Compton wavelength parameter with a future redshift survey is also investigated. The usefulness of the redshift-space distortion for testing the gravity theory on cosmological scales is demonstrated.

Abstract:
We investigate the damping of the baryon acoustic oscillations in the matter power spectrum due to the quasinonlinear clustering and redshift-space distortions by confronting the models with the observations of the Sloan Digital Sky Survey luminous red galaxy sample. The chi-squared test suggests that the observed power spectrum is better matched by models with the damping of the baryon acoustic oscillations rather than the ones without the damping.

Abstract:
We determine a constraint on the growth factor by measuring the damping of the baryon acoustic oscillations in the matter power spectrum using the Sloan Digital Sky Survey luminous red galaxy sample. The damping of the BAO is detected at the one sigma level. We obtain \sigma_8D_1(z=0.3) = 0.42^{+0.34}_{-0.28} at the 1\sigma statistical level, where \sigma_8 is the root mean square overdensity in a sphere of radius 8h^{-1}Mpc and D_1(z) is the growth factor at redshift z. The above result assumes that other parameters are fixed and the cosmology is taken to be a spatially flat cold dark matter universe with the cosmological constant.

Abstract:
We present the clustering of galaxy clusters as a useful addition to the common set of cosmological observables. The clustering of clusters probes the large-scale structure of the Universe, extending galaxy clustering analysis to the high-peak, high-bias regime. Clustering of galaxy clusters complements the traditional cluster number counts and observable-mass relation analyses, significantly improving their constraining power by breaking existing calibration degeneracies. We use the maxBCG galaxy clusters catalogue to constrain cosmological parameters and cross-calibrate the mass-observable relation, using cluster abundances in richness bins and weak-lensing mass estimates. We then add the redshift-space power spectrum of the sample, including an effective modelling of the weakly non-linear contribution and allowing for an arbitrary photometric redshift smoothing. The inclusion of the power spectrum data allows for an improved self-calibration of the scaling relation. We find that the inclusion of the power spectrum typically brings a $\sim 50$ per cent improvement in the errors on the fluctuation amplitude $\sigma_8$ and the matter density $\Omega_{\mathrm{m}}$. Finally, we apply this method to constrain models of the early universe through the amount of primordial non-Gaussianity of the local type, using both the variation in the halo mass function and the variation in the cluster bias. We find a constraint on the amount of skewness $f_{\mathrm{NL}} = 12 \pm 157 $ ($1\sigma$) from the cluster data alone.

Abstract:
Glucosamine sulfate is a natural constituent of cartilage and is used in the treatment of knee osteoarthritis. The aim of this study is to provide a short but comprehensive pharmacotherapeutic update on treating knee osteoarthritis with glucosamine sulfate. A literature search was conducted of PubMed, Centre for Reviews and Dissemination databases, Cochrane Reviews and EconLit up to January 2010. The literature review indicated that the mechanism of action of glucosamine sulfate is based on hypothesis, but its treatment effects in knee osteoarthritis are symptomatic. With steady-state peak concentrations at the 1,500 mg dosage in the range of 10 µM, it is estimated that only 2% of glucosamine is incorporated in the cartilage. A once-daily dosage of 1,500 mg of glucosamine sulfate is licensed for the treatment of symptomatic osteoarthritis and has been shown to reduce pain, improve function and exhibit similar safety to placebo. Glucosamine sulfate is likely to be a cost-effective treatment of knee osteoarthritis. In conclusion, a once-daily dosage of 1,500 mg of glucosamine sulfate is likely to be a safe, effective and cost-effective treatment of knee osteoarthritis as compared to placebo.

Abstract:
Ascoli theorems characterize precompact subsets of the set of morphisms between two objects of a category in terms of equicontinuity and pointwise precompactness, with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem in the context of C*-algebras.

Abstract:
Random time changes (RTCs) are right-continuous and non-decreasing random functions passing the zero-level at 0. The behavior of such systems can be studied from a randomly chosen time-point and from a randomly chosen level. From the first point of view, the probability characteristics are described by the time-stationary distribution P. From the second point of view, the detailed Palm distribution (DPD) is the ruling probability mechanism. The main topic of the present paper is a relationship between P and its DPD. Under P, the origin falls in a continuous part of the graph. Under the DPD, there are two typical situations: the origin lies in a jump-part of the extended graph or it lies in a continuous part. These observations lead to two conditional DPDs. We derive two-step procedures, which bridge the gaps between the several distributions. One step concerns the application of a shift, the second is just a change of measure arranged by a weight-function. The procedures are used to derive local characterization results for the distributions of Palm type. We also consider simulation applications. For instance, a procedure is mentioned to generate a simulation of the RTC as seen from a randomly chosen level in a jump-part when starting with simulations from a randomly chosen time-point. The point process with batch-arrivals is often used as an application.