Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

Entropy and Poincar\'e recurrence from a geometrical viewpoint

We study Poincar\'e recurrence from a purely geometrical viewpoint. We prove that the metric entropy is given by the exponential growth rate of return times to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss theorem. Moreover, we show that minimal return times to dynamical balls grow linearly with respect to its length. Finally, some interesting relations between recurrence, dimension, entropy and Lyapunov exponents of ergodic measures are given.Comment: 11 pages, revised versio

Steps toward the power spectrum of matter. II. The biasing correction with sigma_8 normalization

A new method to determine the bias parameter of galaxies relative to matter is suggested. The method is based on the assumption that gravity is the dominating force which determines the formation of the structure in the Universe. Due to gravitational instability the galaxy formation is a threshold process: in low-density environments galaxies do not form and matter remains in primordial form. We investigate the influence of the presence of void and clustered populations to the power spectrum of matter and galaxies. The power spectrum of galaxies is similar to the power spectrum of matter; the fraction of total matter in the clustered population determines the difference between amplitudes of fluctuations of matter and galaxies, i.e. the bias factor. To determine the fraction of matter in voids and clustered population we perform numerical simulations. The fraction of matter in galaxies at the present epoch is found using a calibration through the sigma_8 parameter.Comment: LaTex (sty files added), 31 pages, 4 PostScript figures embedded, Astrophysical Journal (accepted

Cosmological parameter determination from Planck and SDSS data in LambdaCHDM cosmologies

We study the complementarity between the cosmological information obtainable with the Planck surveyour and the large scale structure (LSS) redshift surveys in LambdaCHDM cosmologies. We compute the initial full phase-space neutrino distribution function for LambdaCHDM models by using numerical simulations. As initial condition we adopt the HDM density fluctuation power spectrum normalized on the basis of the analysis of the local cluster X-ray temperature function and derive the initial neutrino phase-space distribution at each spatial wave number k by using the Zel'dovich approximation. These initial neutrino phase-space distributions are implemented in the CMBFAST code for the integration of the coupled linearized Einstein, Boltzmann and fluid equations in k-space. We find that the relative bias between the CMB temperature fluctuations and the underlying matter density fluctuation power spectrum in COBE/DMR normalization is given by the CDM component normalized accordingly to the abundance of rich clusters at the present time. We use the Fisher information matrix approximation to constrain a multi-dimensional parametrization of the LambdaCHDM model, by jointly considering CMB and large scale structure data according to the Planck and the SDSS experimental specifications and by taking into account redshift distortions and nonlinear effects on the matter power spectrum. We found that, although the CMB anisotropy and polarization measurements tend to dominate the constraints on most of the cosmological parameters, the additional small scale LSS data help to break the parameter degeneracies. This work has been done in the framework of the Planck LFI activities.Comment: 36 pages and 8 figures in AAS LATEX macros v5.0 (submitted to ApJ

A Critical Test of Topological Defect Models: Spatial Clustering of Clusters of Galaxies

Gaussian cosmological models, typified by the inflationary cold dark matter models, and non-Gaussian topological defect based cosmological models, such as the texture seeded model, differ in the origin of large-scale cosmic structures. In the former it is believed that peaks at appropriate scales in the initial high density field are the sites onto which matter accretes and collapses to form the present galaxies and clusters of galaxies, whereas in the latter these structures can form around the density perturbation seeds (which are textures in the texture model). Textures initially are randomly distributed on scales larger than their size, in sharp contrast to the initial high density peaks in the Gaussian models which are already strongly clustered before any gravitational evolution has occured. One thus expects that the resultant correlation of large cosmic objects such as clusters of galaxies in the texture model should be significantly weaker than its Gaussian counterpart. We show that an $\Omega_0=1$ biased $b=2$ (as required by cluster abundance observations) texture model (or any random seed model) predicts a two-point correlation length of $\le 6.0h^{-1}$Mpc for rich clusters, independent of richness. On the other hand, the observed correlation length for rich clusters is $\ge 10.0h^{-1}$Mpc at an approximately $2\sigma$ confidence level. It thus appears that the global texture cosmological model or any random seed cosmological models of this sort are ruled out at a very high confidence ($>3\sigma$).Comment: ApJ in press, 17 tex pages and 1 figur

COBE-DMR-Normalized Open CDM Cosmogonies

Cut-sky orthogonal mode analyses of the COBE-DMR 53 and 90 GHz sky maps are used to determine the normalization of a variety of open cosmogonical models based on the cold dark matter scenario. To constrain the allowed cosmological-parameter range for these open cosmogonies, the predictions of the DMR-normalized models are compared to various observational measures of cosmography and large-scale structure, viz.: the age of the universe; small-scale dynamical estimates of the clustered-mass density parameter (Omega_0); constraints on the Hubble parameter (h), the X-ray cluster baryonic-mass fraction (Omega_B/Omega_0), and the matter power spectrum shape parameter; estimates of the mass perturbation amplitude; and constraints on the large-scale peculiar velocity field. The open-bubble inflation model is consistent with current determinations of the 95% confidence level range of these observational constraints.Comment: 49 pages, uses aaspp4.sty; 2 Postscript files of tables; uuencoded format. Complete paper including text, tables and 24 figures available at ftp://ftp.mpa-garching.mpg.de/incoming/banday/open4.u

Evolution of structure in cold dark matter universes

We present an analysis of the clustering evolution of dark matter in four cold dark matter (CDM) cosmologies. We use a suite of high resolution, 17-million particle, N-body simulations which sample volumes large enough to give clustering statistics with unprecedented accuracy. We investigate both a flat and an open model with Omega_0=0.3, and two models with Omega=1, one with the standard CDM power spectrum and the other with the same power spectrum as the Omega_0=0.3 models. The amplitude of primordial fluctuations is set so that the models reproduce the observed abundance of rich galaxy clusters by the present day. The mass 2-point correlation function and power spectrum of all the simulations differ significantly from those of the observed galaxy distribution, in both shape and amplitude. Thus, for any of these models to provide an acceptable representation of reality, the distribution of galaxies must be biased relative to the mass in a non-trivial, scale-dependent, fashion. In the Omega=1 models the required bias is always greater than unity, but in the Omega_0=0.3 models an "antibias" is required on scales smaller than \sim 5\hmpc. The mass correlation functions in the simulations are well fit by recently published analytic models. The velocity fields are remarkably similar in all the models, whether they be characterised as bulk flows, 1-particle or pairwise velocity dispersions. This similarity is a direct consequence of our adopted normalisation. The small-scale pairwise velocity dispersion of the dark matter is somewhat larger than recent determinations from galaxy redshift surveys, but the bulk-flows predicted by our models are broadly in agreement with most available data.Comment: 46 pages Accepted for publication in the Ap.J, May 20th, Vol. 499, Part I. Minor changes: addition of a table summarising results, section 3.1 on simulation details expanded, three new references added. TeX. Figures 4-11 included. The colour figures 1-3 are available as gif files from: http://star-www.dur.ac.uk:80/~arj/plates.htm

Methylation QTLs in the developing brain and their enrichment in schizophrenia risk loci

We characterized DNA methylation quantitative trait loci (mQTLs) in a large collection (n = 166) of human fetal brain samples spanning 56-166 d post-conception, identifying >16,000 fetal brain mQTLs. Fetal brain mQTLs were primarily cis-acting, enriched in regulatory chromatin domains and transcription factor binding sites, and showed substantial overlap with genetic variants that were also associated with gene expression in the brain. Using tissue from three distinct regions of the adult brain (prefrontal cortex, striatum and cerebellum), we found that most fetal brain mQTLs were developmentally stable, although a subset was characterized by fetal-specific effects. Fetal brain mQTLs were enriched amongst risk loci identified in a recent large-scale genome-wide association study (GWAS) of schizophrenia, a severe psychiatric disorder with a hypothesized neurodevelopmental component. Finally, we found that mQTLs can be used to refine GWAS loci through the identification of discrete sites of variable fetal brain methylation associated with schizophrenia risk variants

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Contributions of mean and shape of blood pressure distribution to worldwide trends and variations in raised blood pressure: A pooled analysis of 1018 population-based measurement studies with 88.6 million participants

© The Author(s) 2018. Background: Change in the prevalence of raised blood pressure could be due to both shifts in the entire distribution of blood pressure (representing the combined effects of public health interventions and secular trends) and changes in its high-blood-pressure tail (representing successful clinical interventions to control blood pressure in the hypertensive population). Our aim was to quantify the contributions of these two phenomena to the worldwide trends in the prevalence of raised blood pressure. Methods: We pooled 1018 population-based studies with blood pressure measurements on 88.6 million participants from 1985 to 2016. We first calculated mean systolic blood pressure (SBP), mean diastolic blood pressure (DBP) and prevalence of raised blood pressure by sex and 10-year age group from 20-29 years to 70-79 years in each study, taking into account complex survey design and survey sample weights, where relevant. We used a linear mixed effect model to quantify the association between (probittransformed) prevalence of raised blood pressure and age-group- and sex-specific mean blood pressure. We calculated the contributions of change in mean SBP and DBP, and of change in the prevalence-mean association, to the change in prevalence of raised blood pressure. Results: In 2005-16, at the same level of population mean SBP and DBP, men and women in South Asia and in Central Asia, the Middle East and North Africa would have the highest prevalence of raised blood pressure, and men and women in the highincome Asia Pacific and high-income Western regions would have the lowest. In most region-sex-age groups where the prevalence of raised blood pressure declined, one half or more of the decline was due to the decline in mean blood pressure. Where prevalence of raised blood pressure has increased, the change was entirely driven by increasing mean blood pressure, offset partly by the change in the prevalence-mean association. Conclusions: Change in mean blood pressure is the main driver of the worldwide change in the prevalence of raised blood pressure, but change in the high-blood-pressure tail of the distribution has also contributed to the change in prevalence, especially in older age groups