Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Order statistics of the early-type galaxy luminosity function

We apply order statistics (OS) to the bright end ($M_r < -22$) of the luminosity distribution of early-type galaxies spectroscopically identified in the SDSS DR7 catalog. We calculate the typical OS quantities of this distribution numerically, measuring the expectation value and variance of the $k^{th}$ most luminous galaxy in a sample with cardinality $N$ over a large ensemble of such samples. From these statistical quantities we explain why and in what limit the $k^{th}$ most luminous galaxies can be used as standard candles for cosmological studies. Since our sample contains all bright galaxies including the brightest cluster galaxies (BCG), based on OS we argue that BCGs can be considered as statistical extremes of a well-established Schechter luminosity distribution when galaxies are binned by redshift and not cluster-by-cluster. We presume that the reason behind this might be that luminous red ellipticals in galaxy clusters are \em not random \em samples of an overall luminosity distribution but biased by the fact that they are in a cluster containing the BCG. We show that a simple statistical toy model can reproduce the well-known magnitude gap between the BCG and the second brightest galaxy of the clusters

The r'-band luminosity function of Abell1367: a comparison with Coma

We made a large (approximately 1degr x 1degr) r'-band imaging survey of the central regions of the two nearby clusters of galaxies, Abell1367 and Coma. The data, presented as a catalog, are used to construct the r'-band luminosity function (LF) of galaxies in these two clusters, by subtracting the Yasuda et al. (2001) galaxy counts from our cluster counts. Our Coma luminosity function is consistent with previous determinations, i.e. providing a faint end slope alpha = -1.47_-0.09^+0.08, significantly steeper than the one we find for Abell1367 (alpha = -1.07_-0.16^+0.20). The counts in Abell1367 show a relative minimum at r' ~ 19, followed by a steep increase faintward. The difference between the two clusters appears significant, given the consistency of the experimental conditions in the two clusters. Whereas for Coma we find a significant increase of the slope of the LF outwards, no such effect is found for Abell1367.Comment: 12 pages, 8 figures, accepted for publication in A&

The Kinematics of Intracluster Planetary Nebulae and the On-Going Subcluster Merger in the Coma Cluster Core

The Coma cluster is the richest and most compact of the nearby clusters, yet there is growing evidence that its formation is still on-going. With a new multi-slit imaging spectroscopy technique pioneered at the 8.2 m Subaru telescope and FOCAS, we have detected and measured the line-of-sight velocities of 37 intracluster planetary nebulae associated with the diffuse stellar population of stars in the Coma cluster core, at 100 Mpc distance. We detect clear velocity substructures within a 6 arcmin diameter field. A substructure is present at ~5000 km/s, probably from in-fall of a galaxy group, while the main intracluster stellar component is centered around ~6500 km/s, ~700 km/s offset from the nearby cD galaxy NGC 4874. The kinematics and morphology of the intracluster stars show that the cluster core is in a highly dynamically evolving state. In combination with galaxy redshift and X-ray data this argues strongly that the cluster is currently in the midst of a subcluster merger, where the NGC 4874 subcluster core may still be self-bound, while the NGC 4889 subcluster core has probably dissolved. The NGC 4889 subcluster is likely to have fallen into Coma from the eastern A2199 filament, in a direction nearly in the plane of the sky, meeting the NGC 4874 subcluster arriving from the west. The two inner subcluster cores are presently beyond their first and second close passage, during which the elongated distribution of diffuse light has been created. We predict the kinematic signature expected in this scenario, and argue that the extended western X-ray arc recently discovered traces the arc shock generated by the collision between the two subcluster gas halos. Any preexisting cooling core region would have been heated by the subcluster collision.Comment: Astronomy & Astrophysics, in press, 9 pages, 5 figure

Galaxy-Mass Correlations on 10 Mpc Scales in the Deep Lens Survey

We examine the projected correlation of galaxies with mass from small scales (<few hundred kpc) where individual dark matter halos dominate, out to 15 Mpc where correlated large-scale structure dominates. We investigate these profiles as a function of galaxy luminosity and redshift. Selecting 0.8 million galaxies in the Deep Lens Survey, we use photometric redshifts and stacked weak gravitational lensing shear tomography out to radial scales of 1 degree from the centers of foreground galaxies. We detect correlated mass density from multiple halos and large-scale structure at radii larger than the virial radius, and find the first observational evidence for growth in the galaxy-mass correlation on 10 Mpc scales with decreasing redshift and fixed range of luminosity. For a fixed range of redshift, we find a scaling of projected halo mass with rest-frame luminosity similar to previous studies at lower redshift. We control systematic errors in shape measurement and photometric redshift, enforce volume completeness through absolute magnitude cuts, and explore residual sample selection effects via simulations.Comment: 13 pages, 9 figures, re-submitted to ApJ after addressing referee comment

U, B and r band luminosity functions of galaxies in the Coma cluster

We present a deep multi-colour CCD mosaic of the Coma cluster (Abell 1656), covering 5.2 deg^2 in the B and r bands, and 1.3 deg^2 in the U band. This large, homogeneous data set provides a valuable low redshift comparison sample for studies of galaxies in distant clusters. In this paper we present our survey, and study the dependence of the galaxy luminosity function (LF) on passband and radial distance from the cluster centre. The U, B and r band LFs of the complete sample cannot be represented by single Schechter functions. For the central area, r<245 h_{100}^{-1} kpc, we find best-fitting Schechter parameters of M^{*}_U=-18.60^{+0.13}_{-0.18} and \alpha_U=-1.32^{+0.018}_{-0.028}, M^{*}_B=-19.79^{+0.18}_{-0.17} and \alpha_B=-1.37^{+0.024}_{-0.016} and M^{*}_r=-20.87^{+0.12}_{-0.17} and \alpha_r=-1.16^{+0.012}_{-0.019}. The LF becomes steeper at larger radial distance from the cluster centre. The effect is most pronounced in the U band. This result is consistent with the presence of a star forming dwarf population at large distance from the cluster centre, which may be in the process of being accreted by the cluster. The shapes of the LFs of the NGC 4839 group support a scenario in which the group has already passed through the centre.Comment: Accepted for publication in MNRA

Are Child and Adolescent Responses to Placebo Higher in Major Depression than in Anxiety Disorders? A Systematic Review of Placebo-Controlled Trials

BACKGROUND: In a previous report, we hypothesized that responses to placebo were high in child and adolescent depression because of specific psychopathological factors associated with youth major depression. The purpose of this study was to compare the placebo response rates in pharmacological trials for major depressive disorder (MDD), obsessive compulsive disorder (OCD) and other anxiety disorders (AD-non-OCD). METHODOLOGY AND PRINCIPAL FINDINGS: We reviewed the literature relevant to the use of psychotropic medication in children and adolescents with internalized disorders, restricting our review to double-blind studies including a placebo arm. Placebo response rates were pooled and compared according to diagnosis (MDD vs. OCD vs. AD-non-OCD), age (adolescent vs. child), and date of publication. From 1972 to 2007, we found 23 trials that evaluated the efficacy of psychotropic medication (mainly non-tricyclic antidepressants) involving youth with MDD, 7 pertaining to youth with OCD, and 10 pertaining to youth with other anxiety disorders (N = 2533 patients in placebo arms). As hypothesized, the placebo response rate was significantly higher in studies on MDD, than in those examining OCD and AD-non-OCD (49.6% [range: 17-90%] vs. 31% [range: 4-41%] vs. 39.6% [range: 9-53], respectively, ANOVA F = 7.1, p = 0.002). Children showed a higher stable placebo response within all three diagnoses than adolescents, though this difference was not significant. Finally, no significant effects were found with respect to the year of publication. CONCLUSION: MDD in children and adolescents appears to be more responsive to placebo than other internalized conditions, which highlights differential psychopathology

Star formation, starbursts and quenching across the Coma supercluster

We analyse Spitzer MIPS 24micron observations, and SDSS (DR7) optical broadband photometry and spectra, to investigate the star formation (SF) properties of galaxies residing in the Coma supercluster region. We find that SF in dwarf galaxies is quenched only in the high density environment at the centre of clusters and groups, but passively-evolving massive galaxies are found in all environments, indicating that massive galaxies can become passive via internal processes. We find AGN activity is suppressed in the cluster cores. We present evidence for a strong dependence of the mechanism(s) responsible for quenching SF in dwarf galaxies on the cluster potential. We find a significant increase in the mean EW of Halpha among star-forming dwarf galaxies in the infall regions of the Coma cluster and the core of Abell 1367 with respect to the overall supercluster population, indicative of the infalling dwarf galaxies undergoing a starburst phase. We identify these starburst galaxies as the precursors of the post-starburst k+A galaxies. We find that 11.4% of all dwarf (z mag > 15) galaxies in the Coma cluster and 4.8% in the Abell 1367 have k+A like spectra, while this fraction is just 2.1% when averaged over the entire supercluster region. We show that in the centre of the Coma cluster, the (24-z) colour of galaxies is correlated with their optical (g-r) colour and Halpha emission. By analysing the projected phase space distribution of galaxies detected at 24micron in Coma, we find that the (optically) red 24 micron detected galaxies follow the general distribution of `all' the spectroscopic members, but their (optically) blue counterparts show interesting features, indicative of recent infall.Comment: 17 pages, 14 figures, accepted for publicaton in MNRA

Shear-Selected Clusters From the Deep Lens Survey III: Masses from Weak Lensing

We present weak lensing mass estimates of seven shear-selected galaxy cluster candidates from the Deep Lens Survey. The clusters were previously identified as mass peaks in convergence maps of 8.6 sq. deg of R band imaging, and followed up with X-ray and spectroscopic confirmation, spanning a redshift range 0.19 - 0.68. Most clusters contained multiple X-ray peaks, yielding 17 total mass concentrations. In this paper, we constrain the masses of these X-ray sources with weak lensing, using photometric redshifts from the full set of BVRz' imaging to properly weight background galaxies according to their lensing distance ratios. We fit both NFW and singular isothermal sphere profiles, and find that the results are insensitive to the assumed profile. We also show that the results do not depend significantly on the assumed prior on the position of the mass peak, but that this may become an issue in future larger samples. The inferred velocity dispersions for the extended X-ray sources range from 250-800 km/s, with the exception of one source for which no lensing signal was found. This work further establishes shear selection as a viable technique for finding clusters, but also highlights some unresolved issues such as determination of the mass profile center without biasing the mass estimate, and fully accounting for line-of-sight projections. A follow-up paper will examine the mass-X-ray scaling relations of these clusters.Comment: Accepted for publication in ApJ, 27 pages, 4 figures. Some discussion and clarification added. Cluster centre offset added to Table

Clinical Management of Pediatric Acute-Onset Neuropsychiatric Syndrome: Part I—Psychiatric and Behavioral Interventions

Abstract Objective: This article outlines the consensus guidelines for symptomatic treatment for children with Pediatric Acute-Onset Neuropsychiatric Syndrome (PANS) and Pediatric Autoimmune Neuropsychiatric Syndrome Associated with Streptococcal Infection (PANDAS). Methods: Extant literature on behavioral, psychotherapeutic, and psychopharmacologic treatments for PANS and PANDAS was reviewed. Members of the PANS Research Consortium pooled their clinical experiences to find agreement on treatment of PANS and PANDAS symptoms. Results: Current guidelines result from consensus among the Consortium members. Conclusion: While underlying infectious and inflammatory processes in PANS and PANDAS patients are treated, psychiatric and behavioral symptoms need simultaneous treatment to decrease suffering and improve adherence to therapeutic intervention. Psychological, behavioral, and psychopharmacologic interventions tailored to each child's presentation can provide symptom improvement and improve functioning during both the acute and chronic stages of illness. In general, typical evidence-based interventions are appropriate for the varied symptoms of PANS and PANDAS. Individual differences in expected response to psychotropic medication may require marked reduction of initial treatment dose. Antimicrobials and immunomodulatory therapies may be indicated, as discussed in Parts 2 and 3 of this guideline series