The recursive scheme of clustering

The problem of data clustering is one of the most important in data analysis. It can be problematic when dealing with experimental data characterized by measurement uncertainties and errors. Our paper proposes a recursive scheme for clustering data obtained in geographical (climatological) experiments. The discussion of results obtained by k-means and SOM methods with the developed recursive procedure is presented. We show that the clustering using the new approach gives more acceptable results when compared to experts assessments

Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys

We show that the measurement of the baryonic acoustic oscillations in large high redshift galaxy surveys offers a precision route to the measurement of dark energy. The cosmic microwave background provides the scale of the oscillations as a standard ruler that can be measured in the clustering of galaxies, thereby yielding the Hubble parameter and angular diameter distance as a function of redshift. This, in turn, enables one to probe dark energy. We use a Fisher matrix formalism to study the statistical errors for redshift surveys up to z=3 and report errors on cosmography while marginalizing over a large number of cosmological parameters including a time-dependent equation of state. With redshifts surveys combined with cosmic microwave background satellite data, we achieve errors of 0.037 on Omega_x, 0.10 on w(z=0.8), and 0.28 on dw(z)/dz for cosmological constant model. Models with less negative w(z) permit tighter constraints. We test and discuss the dependence of performance on redshift, survey conditions, and fiducial model. We find results that are competitive with the performance of future supernovae Ia surveys. We conclude that redshift surveys offer a promising independent route to the measurement of dark energy.Comment: submitted to ApJ, 24 pages, LaTe

The 3D soft X-ray cluster-AGN cross-correlation function in the ROSAT NEP survey

X-ray surveys facilitate investigations of the environment of AGNs. Deep Chandra observations revealed that the AGNs source surface density rises near clusters of galaxies. The natural extension of these works is the measurement of spatial clustering of AGNs around clusters and the investigation of relative biasing between active galactic nuclei and galaxies near clusters.The major aims of this work are to obtain a measurement of the correlation length of AGNs around clusters and a measure of the averaged clustering properties of a complete sample of AGNs in dense environments. We present the first measurement of the soft X-ray cluster-AGN cross-correlation function in redshift space using the data of the ROSAT-NEP survey. The survey covers 9x9 deg^2 around the North Ecliptic Pole where 442 X-ray sources were detected and almost completely spectroscopically identified. We detected a >3sigma significant clustering signal on scales s<50 h70^-1 Mpc. We performed a classical maximum-likelihood power-law fit to the data and obtained a correlation length s_0=8.7+1.2-0.3 h_70-1 Mpc and a slope gamma=1.7$^+0.2_-0.7 (1sigma errors). This is a strong evidence that AGNs are good tracers of the large scale structure of the Universe. Our data were compared to the results obtained by cross-correlating X-ray clusters and galaxies. We observe, with a large uncertainty, that the bias factor of AGN is similar to that of galaxies.Comment: 4 pages, 2 figure, proceedings of the Conference "At the edge of the Universe", Sintra Portugal, October 2006. To be published on the Astronomical Society of the Pacific Conference Series (ASPCS

A Comparative Study of Dark Energy Constraints from Current Observational Data

We examine how dark energy constraints from current observational data depend on the analysis methods used: the analysis of Type Ia supernovae (SNe Ia), and that of galaxy clustering data. We generalize the flux-averaging analysis method of SNe Ia to allow correlated errors of SNe Ia, in order to reduce the systematic bias due to weak lensing of SNe Ia. We find that flux-averaging leads to larger errors on dark energy and cosmological parameters if only SN Ia data are used. When SN Ia data (the latest compilation by the SNLS team) are combined with WMAP 7 year results (in terms of our Gaussian fits to the probability distributions of the CMB shift parameters), the latest Hubble constant (H_0) measurement using the Hubble Space Telescope (HST), and gamma ray burst (GRB) data, flux-averaging of SNe Ia increases the concordance with other data, and leads to significantly tighter constraints on the dark energy density at z=1, and the cosmic curvature \Omega_k. The galaxy clustering measurements of H(z=0.35)r_s(z_d) and r_s(z_d)/D_A(z=0.35) (where H(z) is the Hubble parameter, D_A(z) is the angular diameter distance, and r_s(z_d) is the sound horizon at the drag epoch) by Chuang & Wang (2011) are consistent with SN Ia data, given the same pirors (CMB+H_0+GRB), and lead to significantly improved dark energy constraints when combined. Current data are fully consistent with a cosmological constant and a flat universe.Comment: 11 pages, 9 figures. Slightly revised version, to appear in PRD. Supernova flux-averaging code available at http://www.nhn.ou.edu/~wang/SNcode

Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera

Thermal errors are often quoted as being the largest contributor to CNC machine tool errors, but they can be effectively reduced using error compensation. The performance of a thermal error compensation system depends on the accuracy and robustness of the thermal error model and the quality of the inputs to the model. The location of temperature measurement must provide a representative measurement of the change in temperature that will affect the machine structure. The number of sensors and their locations are not always intuitive and the time required to identify the optimal locations is often prohibitive, resulting in compromise and poor results. In this paper, a new intelligent compensation system for reducing thermal errors of machine tools using data obtained from a thermal imaging camera is introduced. Different groups of key temperature points were identified from thermal images using a novel schema based on a Grey model GM (0, N) and Fuzzy c-means (FCM) clustering method. An Adaptive Neuro-Fuzzy Inference System with Fuzzy c-means clustering (FCM-ANFIS) was employed to design the thermal prediction model. In order to optimise the approach, a parametric study was carried out by changing the number of inputs and number of membership functions to the FCM-ANFIS model, and comparing the relative robustness of the designs. According to the results, the FCM-ANFIS model with four inputs and six membership functions achieves the best performance in terms of the accuracy of its predictive ability. The residual value of the model is smaller than ± 2 μm, which represents a 95% reduction in the thermally-induced error on the machine. Finally, the proposed method is shown to compare favourably against an Artificial Neural Network (ANN) model

The clustering of intermediate redshift quasars as measured by the Baryon Oscillation Spectroscopic Survey

We measure the quasar two-point correlation function over the redshift range 2.2<z<2.8 using data from the Baryon Oscillation Spectroscopic Survey. We use a homogeneous subset of the data consisting of 27,129 quasars with spectroscopic redshifts---by far the largest such sample used for clustering measurements at these redshifts to date. The sample covers 3,600 square degrees, corresponding to a comoving volume of 9.7(Gpc/h)^3 assuming a fiducial LambdaCDM cosmology, and it has a median absolute i-band magnitude of -26, k-corrected to z=2. After accounting for redshift errors we find that the redshift space correlation function is fit well by a power-law of slope -2 and amplitude s_0=(9.7\pm 0.5)Mpc/h over the range 3<s<25Mpc/h. The projected correlation function, which integrates out the effects of peculiar velocities and redshift errors, is fit well by a power-law of slope -1 and r_0=(8.4\pm 0.6)Mpc/h over the range 4<R<16Mpc/h. There is no evidence for strong luminosity or redshift dependence to the clustering amplitude, in part because of the limited dynamic range in our sample. Our results are consistent with, but more precise than, previous measurements at similar redshifts. Our measurement of the quasar clustering amplitude implies a bias factor of b~3.5 for our quasar sample. We compare the data to models to constrain the manner in which quasars occupy dark matter halos at z~2.4 and infer that such quasars inhabit halos with a characteristic mass of ~10^{12}Msun/h with a duty cycle for the quasar activity of 1 per cent.Comment: 20 pages, 18 figures. Minor modifications to match version accepted by journa

Clustering and descendants of MUSYC galaxies at z<1.5

We measure the evolution of galaxy clustering out to a redshift of z~1.5 using data from two MUSYC fields, the Extended Hubble Deep Field South (EHDF-S) and the Extended Chandra Deep Field South (ECDF-S). We use photometric redshift information to calculate the projected-angular correlation function, omega(sigma), from which we infer the projected correlation function Xi(sigma). We demonstrate that this technique delivers accurate measurements of clustering even when large redshift measurement errors affect the data. To this aim we use two mock MUSYC fields extracted from a LambdaCDM simulation populated with GALFORM semi-analytic galaxies which allow us to assess the degree of accuracy of our estimates of Xi(sigma) and to identify and correct for systematic effects in our measurements. We study the evolution of clustering for volume limited subsamples of galaxies selected using their photometric redshifts and rest-frame r-band absolute magnitudes. We find that the real-space correlation length r_0 of bright galaxies, M_r<-21 (rest-frame) can be accurately recovered out to z~1.5, particularly for ECDF-S given its near-infrared photometric coverage. There is mild evidence for a luminosity dependent clustering in both fields at the low redshift samples (up to =0.57), where the correlation length is higher for brighter galaxies by up to 1Mpc/h between median rest-frame r-band absolute magnitudes of -18 to -21.5. As a result of the photometric redshift measurement, each galaxy is assigned a best-fit template; we restrict to E and E+20%Sbc types to construct subsamples of early type galaxies (ETGs). Our ETG samples show a strong increase in r_0 as the redshift increases, making it unlikely (95% level) that ETGs at median redshift z_med=1.15 are the direct progenitors of ETGs at z_med=0.37 with equivalent passively evolved luminosities. (ABRIDGED)Comment: 16 pages, 12 figures, 2 tables, accepted for publication in MNRA