Series expansions for finite-state Markov chains

This article provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm. © 2007 Cambridge University Press

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KiDS-i-800: Comparing weak gravitational lensing measurements in same-sky surveys

We present a weak gravitational lensing analysis of 815 square degree of $i$-band imaging from the Kilo-Degree Survey (KiDS-$i$-800). In contrast to the deep $r$-band observations, which take priority during excellent seeing conditions and form the primary KiDS dataset (KiDS-$r$-450), the complementary yet shallower KiDS-$i$-800 spans a wide range of observing conditions. The overlapping KiDS-$i$-800 and KiDS-$r$-450 imaging therefore provides a unique opportunity to assess the robustness of weak lensing measurements. In our analysis, we introduce two new `null' tests. The `nulled' two-point shear correlation function uses a matched catalogue to show that the calibrated KiDS-$i$-800 and KiDS-$r$-450 shear measurements agree at the level of $1 \pm 4$\%. We use five galaxy lens samples to determine a `nulled' galaxy-galaxy lensing signal from the full KiDS-$i$-800 and KiDS-$r$-450 surveys and find that the measurements agree to $7 \pm 5$\% when the KiDS-$i$-800 source redshift distribution is calibrated using either spectroscopic redshifts, or the 30-band photometric redshifts from the COSMOS survey.Comment: 24 pages, 20 figures. Submitted to MNRAS. Comments welcom

The galaxy-halo connection from a joint lensing, clustering and abundance analysis in the CFHTLenS/VIPERS field

We present new constraints on the relationship between galaxies and their host dark matter halos, measured from the location of the peak of the stellar-to-halo mass ratio (SHMR), up to the most massive galaxy clusters at redshift $z\sim0.8$ and over a volume of nearly 0.1~Gpc$^3$. We use a unique combination of deep observations in the CFHTLenS/VIPERS field from the near-UV to the near-IR, supplemented by $\sim60\,000$ secure spectroscopic redshifts, analysing galaxy clustering, galaxy-galaxy lensing and the stellar mass function. We interpret our measurements within the halo occupation distribution (HOD) framework, separating the contributions from central and satellite galaxies. We find that the SHMR for the central galaxies peaks at $M_{\rm h, peak} = 1.9^{+0.2}_{-0.1}\times10^{12} M_{\odot}$ with an amplitude of $0.025$, which decreases to $\sim0.001$ for massive halos ($M_{\rm h} > 10^{14} M_{\odot}$). Compared to central galaxies only, the total SHMR (including satellites) is boosted by a factor 10 in the high-mass regime (cluster-size halos), a result consistent with cluster analyses from the literature based on fully independent methods. After properly accounting for differences in modelling, we have compared our results with a large number of results from the literature up to $z=1$: we find good general agreement, independently of the method used, within the typical stellar-mass systematic errors at low to intermediate mass (${M}_{\star} < 10^{11} M_{\odot}$) and the statistical errors above. We have also compared our SHMR results to semi-analytic simulations and found that the SHMR is tilted compared to our measurements in such a way that they over- (under-) predict star formation efficiency in central (satellite) galaxies.Comment: 31 pages, 18 figures, 4 table. Accepted for publication in MNRAS. Online material available at http://www.cfhtlens.or

Meta-Analysis of Placental Transcriptome Data Identifies a Novel Molecular Pathway Related to Preeclampsia

Studies using the placental transcriptome to identify key molecules relevant for preeclampsia are hampered by a relatively small sample size. In addition, they use a variety of bioinformatics and statistical methods, making comparison of findings challenging. To generate a more robust preeclampsia gene expression signature, we performed a meta-analysis on the original data of 11 placenta RNA microarray experiments, representing 139 normotensive and 116 preeclamptic pregnancies. Microarray data were pre-processed and analyzed using standardized bioinformatics and statistical procedures and the effect sizes were combined using an inverse-variance random-effects model. Interactions between genes in the resulting gene expression signature were identified by pathway analysis (Ingenuity Pathway Analysis, Gene Set Enrichment Analysis, Graphite) and protein-protein associations (STRING). This approach has resulted in a comprehensive list of differentially expressed genes that led to a 388-gene meta-signature of preeclamptic placenta. Pathway analysis highlights the involvement of the previously identified hypoxia/HIF1A pathway in the establishment of the preeclamptic gene expression profile, while analysis of protein interaction networks indicates CREBBP/EP300 as a novel element central to the preeclamptic placental transcriptome. In addition, there is an apparent high incidence of preeclampsia in women carrying a child with a mutation in CREBBP/EP300 (Rubinstein-Taybi Syndrome). The 388-gene preeclampsia meta-signature offers a vital starting point for further studies into the relevance of these genes (in particular CREBBP/EP300) and their concomitant pathways as biomarkers or functional molecules in preeclampsia. This will result in a better understanding of the molecular basis of this disease and opens up the opportunity to develop rational therapies targeting the placental dysfunction causal to preeclampsia.Peer reviewe

Multiwavelength scaling relations in galaxy groups: a detailed comparison of GAMA and KiDS observations to BAHAMAS simulations

We study the scaling relations between the baryonic content and total mass of groups of galaxies, as these systems provide a unique way to examine the role of non-gravitational processes in structure formation. Using Planck and ROSAT data, we conduct detailed comparisons of the stacked thermal Sunyaev-Zel’dovich (tSZ) and X-ray scaling relations of galaxy groups found in the Galaxy And Mass Assembly (GAMA) survey and the BAHAMAS hydrodynamical simulation. We use weak gravitational lensing data from the Kilo Degree Survey to determine the average halo mass of the studied systems. We analyse the simulation in the same way, using realistic weak lensing, X-ray, and tSZ synthetic observations. Furthermore, to keep selection biases under control, we employ exactly the same galaxy selection and group identification procedures to the observations and simulation. Applying this comparison, we find that the simulations reproduce the richness, size, and stellar mass functions of GAMA groups, as well as the stacked weak lensing and tSZ signals in bins of group stellar mass. However, the simulations predict X-ray luminosities that are higher than observed for this optically selected group sample. As the same simulations were previously shown to match the luminosities of X-ray-selected groups, this suggests that X-ray-selected systems may form a biased subset. Finally, we demonstrate that our observational processing of the X-ray and tSZ signals is free of significant biases. We find that our optical group selection procedure has, however, some room for improvement

Tightening weak lensing constraints on the ellipticity of galaxy-scale dark matter haloes

Cosmological simulations predict that galaxies are embedded into triaxial dark matter haloes, which appear approximately elliptical in projection. Weak gravitational lensing allows us to constrain these halo shapes and thereby test the nature of dark matter. Weak lensing has already provided robust detections of the signature of halo flattening at the mass scales of groups and clusters, whereas results for galaxies have been somewhat inconclusive. Here we combine data from five weak lensing surveys (NGVSLenS, KiDS/KV450, CFHTLenS, CS82, and RCSLenS, listed in order of most to least constraining) in order to tighten observational constraints on galaxy-scale halo ellipticity for photometrically selected lens samples. We constrain fh, the average ratio between the aligned component of the halo ellipticity and the ellipticity of the light distribution, finding fh = 0.303-0.079+0.080 for red lens galaxies and fh = 0.217-0.159+0.160 for blue lens galaxies when assuming elliptical Navarro-Frenk-White density profiles and a linear scaling between halo ellipticity and galaxy ellipticity. Our constraints for red galaxies constitute the currently most significant (3.8σ) systematics-corrected detection of the signature of halo flattening at the mass scale of galaxies. Our results are in good agreement with expectations from the Millennium Simulation that apply the same analysis scheme and incorporate models for galaxy-halo misalignment. Assuming these misalignment models and the analysis assumptions stated above are correct, our measurements imply an average dark matter halo ellipticity for the studied red galaxy samples of |e h| = 0.174 ± 0.046, where |e h| = (1 - q)/(1 + q) relates to the ratio q = b/a of the minor and major axes of the projected mass distribution. Similar measurements based on larger upcoming weak lensing data sets can help to calibrate models for intrinsic galaxy alignments, which constitute an important source of systematic uncertainty in cosmological weak lensing studies

KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing

We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ∼450 deg2 of imaging data from the Kilo Degree Survey (KiDS). For a flat Λ cold dark matter (ΛCDM) cosmology with a prior on H0 that encompasses the most recent direct measurements, we find S8≡σ8Ωm/0.3−−−−−−√=0.745±0.039⁠. This result is in good agreement with other low-redshift probes of large-scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A 2.3σ tension in S8 and ‘substantial discordance’ in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved ‘self-calibrating’ version of lensFIT validated using an extensive suite of image simulations. Four-band ugri photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov chains are available at http://kids.strw.leidenuniv.nl