Low redshift quasars in the SDSS Stripe 82. Host galaxy colors and close environment

We present a photometrical and morphological multicolor study of the properties of low redshift (z<0.3) quasar hosts based on a large and homogeneous dataset of quasars derived from the Sloan Digital Sky Survey (DR7). We used quasars that were imaged in the SDSS Stripe82 that is up to 2 mag deeper than standard Sloan images. This sample is part of a larger dataset of ~400 quasars at z<0.5 for which both the host galaxies and their galaxy environments were studied (Falomo et al. 2014,Karhunen et al. 2014). For 52 quasars we undertake a study of the color of the host galaxies and of their close environments in u,g,r,i and z bands. We are able to resolve almost all the quasars in the sample in the filters g,r,i and z and also in $u$ for about 50% of the targets. We found that the mean colors of the QSO host galaxy (g-i=0.82+-0.26; r-i=0.26+-0.16 and u-g=1.32+-0.25) are very similar to the values of a sample of inactive galaxies matched in terms of redshift and galaxy luminosity with the quasar sample. There is a suggestion that the most massive QSO hosts have bluer colors.Both quasar hosts and the comparison sample of inactive galaxies have candidates of close ($<$ 50 kpc) companion galaxies for ~30% of the sources with no significant difference between active and inactive galaxies. We do not find significant correlation between the central black hole (BH) mass and the quasar host luminosity that appears to be extra luminous at a given BH mass with respect to the local relation (M_BH -- M_host) for inactive galaxies. This confirms previous suggestion that a substantial disc component, not correlated to the BH mass, is present in the galaxies hosting low z quasars. These results support a scenario where the activation of the nucleus has negligible effects on the global structural and photometrical properties of the hosting galaxies.Comment: Accepted for publication in MNRAS, 13 page

Decomposing data sets into skewness modes

We derive the nonlinear equations satisfied by the coefficients of linear combinations that maximize their skewness when their variance is constrained to take a specific value. In order to numerically solve these nonlinear equations we develop a gradient-type flow that preserves the constraint. In combination with the Karhunen-Lo\`eve decomposition this leads to a set of orthogonal modes with maximal skewness. For illustration purposes we apply these techniques to atmospheric data; in this case the maximal-skewness modes correspond to strongly localized atmospheric flows. We show how these ideas can be extended, for example to maximal-flatness modes.Comment: Submitted for publication, 12 pages, 4 figure

Principal manifolds and graphs in practice: from molecular biology to dynamical systems

We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.Comment: 12 pages, 9 figure

Determining the Spectral Signature of Spatial Coherent Structures

We applied to an open flow a proper orthogonal decomposition (pod) technique, on 2D snapshots of the instantaneous velocity field, to reveal the spatial coherent structures responsible of the self-sustained oscillations observed in the spectral distribution of time series. We applied the technique to 2D planes out of 3D direct numerical simulations on an open cavity flow. The process can easily be implemented on usual personal computers, and might bring deep insights on the relation between spatial events and temporal signature in (both numerical or experimental) open flows.Comment: 4 page

An extension of Wiener integration with the use of operator theory

With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.Comment: 13 page

On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Genetic evidence implicating natriuretic peptide receptor-3 in cardiovascular disease risk: a Mendelian randomization study

Background: C-type natriuretic peptide (CNP) is a known target for promoting growth and has been implicated as a therapeutic opportunity for the prevention and treatment of cardiovascular disease (CVD). This study aimed to explore the effect of CNP on CVD risk using the Mendelian randomization (MR) framework. Methods Instrumental variables mimicking the effects of pharmacological intervention on CNP were identified as uncorrelated genetic variants located in the genes coding for its primary receptors, natriuretic peptide receptors-2 and 3 (NPR2 and NPR3), that associated with height. We performed MR and colocalization analyses to investigate the effects of NPR2 signalling and NPR3 function on CVD outcomes and risk factors. MR estimates were compared to those obtained when considering height variants from throughout the genome. Results: Genetically-proxied reduced NPR3 function was associated with a lower risk of CVD, with odds ratio (OR) 0.74 per standard deviation (SD) higher NPR3-predicted height, and 95% confidence interval (95% CI) 0.64–0.86. This effect was greater in magnitude than observed when considering height variants from throughout the genome. For CVD subtypes, similar MR associations for NPR3-predicted height were observed when considering the outcomes of coronary artery disease (0.75, 95% CI 0.60–0.92), stroke (0.69, 95% CI 0.50–0.95) and heart failure (0.77, 95% CI 0.58–1.02). Consideration of CVD risk factors identified systolic blood pressure (SBP) as a potential mediator of the NPR3-related CVD risk lowering. For stroke, we found that the MR estimate for NPR3 was greater in magnitude than could be explained by a genetically predicted SBP effect alone. Colocalization results largely supported the MR findings, with no evidence of results being driven by effects due to variants in linkage disequilibrium. There was no MR evidence supporting effects of NPR2 on CVD risk, although this null finding could be attributable to fewer genetic variants being identified to instrument this target. Conclusions: This genetic analysis supports the cardioprotective effects of pharmacologically inhibiting NPR3 receptor function, which is only partly mediated by an effect on blood pressure. There was unlikely sufficient statistical power to investigate the cardioprotective effects of NPR2 signalling