Regression Depth and Center Points

We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

Half-Megasecond Chandra Spectral Imaging of the Hot Circumgalactic Nebula around Quasar Mrk 231

A deep 400-ksec ACIS-S observation of the nearest quasar known, Mrk 231, is combined with archival 120-ksec data obtained with the same instrument and setup to carry out the first ever spatially resolved spectral analysis of a hot X-ray emitting circumgalactic nebula around a quasar. The 65 x 50 kpc X-ray nebula shares no resemblance with the tidal debris seen at optical wavelengths. One notable exception is the small tidal arc 3.5 kpc south of the nucleus where excess soft X-ray continuum emission and Si XIII 1.8 keV line emission are detected, consistent with star formation and its associated alpha-element enhancement, respectively. An X-ray shadow is also detected at the location of the 15-kpc northern tidal tail. The hard X-ray continuum emission within 6 kpc of the center is consistent with being due entirely to the bright central AGN. The soft X-ray spectrum of the outer (>6 kpc) portion of the nebula is best described as the sum of two thermal components with T~3 and ~8 million K and spatially uniform super-solar alpha element abundances, relative to iron. This result implies enhanced star formation activity over ~10^8 yrs accompanied with redistribution of the metals on large scale. The low-temperature thermal component is not present within 6 kpc of the nucleus, suggesting extra heating in this region from the circumnuclear starburst, the central quasar, or the wide-angle quasar-driven outflow identified from optical IFU spectroscopy on a scale of >3 kpc. Significant azimuthal variations in the soft X-ray intensity are detected in the inner region where the outflow is present. The soft X-ray emission is weaker in the western quadrant, coincident with a deficit of Halpha and some of the largest columns of neutral gas outflowing from the nucleus. Shocks created by the interaction of the wind with the ambient ISM may heat the gas to high temperatures at this location. (abridged)Comment: 43 pages, 11 figures, accepted for publication in the Astrophysical Journa

A Chandra X-Ray Survey of Ultraluminous Infrared Galaxies

We present results from Chandra observations of 14 ultraluminous infrared galaxies (ULIRGs; log(L_IR/L_Sun) >= 12) with redshifts between 0.04 and 0.16. The goals of the observations were to investigate any correlation between infrared color or luminosity and the properties of the X-ray emission and to attempt to determine whether these objects are powered by starbursts or active galactic nuclei (AGNs). The sample contains approximately the same number of high and low luminosity objects and ``warm'' and ``cool'' ULIRGs. All 14 galaxies were detected by Chandra. Our analysis shows that the X-ray emission of the two Seyfert 1 galaxies in our sample are dominated by AGN. The remaining 12 sources are too faint for conventional spectral fitting to be applicable. Hardness ratios were used to estimate the spectral properties of these faint sources. The photon indices for our sample plus the Chandra-observed sample from Ptak et al.(2003) peak in the range of 1.0-1.5, consistent with expectations for X-ray binaries in a starburst, an absorbed AGN, or hot bremsstrahlung from a starburst or AGN. The values of photon index for the objects in our sample classified as Seyferts (type 1 or 2) are larger than 2, while those classified as HII regions or LINERs tend to be less than 2. The hard X-ray to far-infrared ratios for the 12 weak sources are similar to those of starbursts, but we cannot rule out the possibility of absorbed, possibly Compton-thick, AGNs in some of these objects. Two of these faint sources were found to have X-ray counterparts to their double optical and infrared nuclei.Comment: 40 pages, 5 tables, 14 figures, accepted by Ap

Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of volume at most $2k^{1+\epsilon}$ and bipartiteness ratio at most $4\sqrt{\theta/\epsilon}$. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time $O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k)$, independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the $k$th \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

Quantitative assessment of nocturnal neural respiratory drive in children with and without obstructive sleep apnoea using surface EMG

New Findings: What is the central question of this study? Recent studies have suggested potential utility of non-normalized respiratory muscle EMG as an index of neural respiratory drive (NRD). Whether NRD measured using non-normalized surface EMG of the lateral chest wall overlying the diaphragm (sEMGcw) recorded during nocturnal clinical polysomnography can differentiate children with and without obstructive sleep apnoea (OSA) is not known. What is the main finding and its importance? Non-normalized sEMGcw was increased in children with OSA and an additional group of snoring children without OSA but subjectively increased respiratory effort compared with primary snorers. The sEMGcw has potential clinical utility in evaluation of children with sleep-disordered breathing as an objective, non-invasive, non-volitional marker of NRD. Abstract: Our aim was to investigate whether neural respiratory drive measured by non-normalized surface EMG recorded from the chest wall overlying the diaphragm (sEMGcw) differentiates children with and without obstructive sleep apnoea (OSA). Polysomnography data of children aged 0–18 years were divided into the following three groups: (i) primary snorers (PS); (ii) snoring children without OSA but with increased work of breathing (incWOB; subjective physician report of increased respiratory effort during sleep); and (iii) children with OSA [obstructive apnoea–hypopnoea index (OAHI) >1 h−1]. Excerpts of sEMGcw obtained during tidal unobstructed breathing from light, deep and rapid eye movement sleep were exported for quantitative analysis. Overnight polysomnography data from 45 PS [median age 4.4 years (interquartile range 3.0–7.7 years), OAHI 0 h−1 (0.0–0.2 h−1)], 19 children with incWOB [age 2.8 years (2.4–5.7 years), OAHI 0.1 h−1 (0.0–0.4 h−1)] and 27 children with OSA [age 3.6 years (2.6–6.2 years), OAHI 3.7 h−1 (2.3–6.9 h−1)] were analysed. The sEMGcw was higher in those with OSA [8.47 μV (5.98–13.07 μV); P < 0.0001] and incWOB [8.97 μV (5.94–13.43 μV); P < 0.001] compared with PS [4.633 μV (2.98–6.76 μV)]. There was no significant difference in the sEMGcw between children with incWOB and OSA (P = 0.78). Log sEMGcw remained greater in children with OSA and incWOB compared with PS after age, body mass index centiles, sleep stages and sleep positions were included in the mixed linear models (P < 0.0001). The correlation between sEMGcw and OAHI in children without OSA was small (rs = 0.254, P = 0.04). The sEMGcw is increased in children with OSA and incWOB compared with PS

Chandra Observations of Galaxy Zoo Mergers: Frequency of Binary Active Nuclei in Massive Mergers

We present the results from a Chandra pilot study of 12 massive galaxy mergers selected from Galaxy Zoo. The sample includes major mergers down to a host galaxy mass of 10$^{11}$ $M_\odot$ that already have optical AGN signatures in at least one of the progenitors. We find that the coincidences of optically selected active nuclei with mildly obscured ($N_H \lesssim 1.1 \times 10^{22}$ cm$^{-2}$) X-ray nuclei are relatively common (8/12), but the detections are too faint ($< 40$ counts per nucleus; $f_{2-10 keV} \lesssim 1.2 \times 10^{-13}$ erg s$^{-1}$ cm$^{-2}$) to reliably separate starburst and nuclear activity as the origin of the X-ray emission. Only one merger is found to have confirmed binary X-ray nuclei, though the X-ray emission from its southern nucleus could be due solely to star formation. Thus, the occurrences of binary AGN in these mergers are rare (0-8%), unless most merger-induced active nuclei are very heavily obscured or Compton thick.Comment: 8 pages, including 5 figures and 1 table. Accepted by Ap

Search for Intrinsic Excitations in 152Sm

The 685 keV excitation energy of the first excited 0+ state in 152Sm makes it an attractive candidate to explore expected two-phonon excitations at low energy. Multiple-step Coulomb excitation and inelastic neutron scattering studies of 152Sm are used to probe the E2 collectivity of excited 0+ states in this "soft" nucleus and the results are compared with model predictions. No candidates for two-phonon K=0+ quadrupole vibrational states are found. A 2+, K=2 state with strong E2 decay to the first excited K=0+ band and a probable 3+ band member are established.Comment: 4 pages, 6 figures, accepted for publication as a Rapid Communication in Physical Review

Quantitative localized proton-promoted dissolution kinetics of calcite using scanning electrochemical microscopy (SECM)

Scanning electrochemical microscopy (SECM) has been used to determine quantitatively the kinetics of proton-promoted dissolution of the calcite (101̅4) cleavage surface (from natural “Iceland Spar”) at the microscopic scale. By working under conditions where the probe size is much less than the characteristic dislocation spacing (as revealed from etching), it has been possible to measure kinetics mainly in regions of the surface which are free from dislocations, for the first time. To clearly reveal the locations of measurements, studies focused on cleaved “mirror” surfaces, where one of the two faces produced by cleavage was etched freely to reveal defects intersecting the surface, while the other (mirror) face was etched locally (and quantitatively) using SECM to generate high proton fluxes with a 25 μm diameter Pt disk ultramicroelectrode (UME) positioned at a defined (known) distance from a crystal surface. The etch pits formed at various etch times were measured using white light interferometry to ascertain pit dimensions. To determine quantitative dissolution kinetics, a moving boundary finite element model was formulated in which experimental time-dependent pit expansion data formed the input for simulations, from which solution and interfacial concentrations of key chemical species, and interfacial fluxes, could then be determined and visualized. This novel analysis allowed the rate constant for proton attack on calcite, and the order of the reaction with respect to the interfacial proton concentration, to be determined unambiguously. The process was found to be first order in terms of interfacial proton concentration with a rate constant k = 6.3 (± 1.3) × 10–4 m s–1. Significantly, this value is similar to previous macroscopic rate measurements of calcite dissolution which averaged over large areas and many dislocation sites, and where such sites provided a continuous source of steps for dissolution. Since the local measurements reported herein are mainly made in regions without dislocations, this study demonstrates that dislocations and steps that arise from such sites are not needed for fast proton-promoted calcite dissolution. Other sites, such as point defects, which are naturally abundant in calcite, are likely to be key reaction sites