Centers of probability measures without the mean

In the recent years, the notion of mixability has been developed with applications to operations research, optimal transportation, and quantitative finance. An n-tuple of distributions is said to be jointly mixable if there exist n random variables following these distributions and adding up to a constant, called center, with probability one. When the n distributions are identical, we speak of complete mixability. If each distribution has finite mean, the center is obviously the sum of the means. In this paper, we investigate the set of centers of completely and jointly mixable distributions not having a finite mean. In addition to several results, we show the (possibly counterintuitive) fact that, for each (Formula presented.), there exist n standard Cauchy random variables adding up to a constant C if and only if (Formula presented.

The Nustar Extragalactic Surveys: Overview and Catalog from the Cosmos Field

To provide the census of the sources contributing to the X-ray background peak above 10 keV, NuSTAR is performing extragalactic surveys using a three-tier wedding cake approach. We present the NuSTAR survey of the COSMOS field, the medium sensitivity and medium area tier, covering 1.7 deg2 and overlapping with both Chandra and XMM-Newton data. This survey consists of 121 observations for a total exposure of ~3 Ms. To fully exploit these data, we developed a new detection strategy, carefully tested through extensive simulations. The survey sensitivity at 20% completeness is 5.9, 2.9 and 6.4 x 10^-14 erg/cm2/s in the 3-24 keV, 3-8 keV and 8-24 keV bands, respectively. By combining detections in 3 bands, we have a sample of 91 NuSTAR sources with 10^42 -10^45.5 erg/s luminosities and redshift z=0.04-2.5. Thirty two sources are detected in the 8-24 keV band with fluxes ~100 times fainter than sources detected by Swift-BAT. Of the 91 detections, all but four are associated with a Chandra and/or XMM-Newton point-like counterpart. One source is associated with an extended lower energy X-ray source. We present the X-ray (hardness ratio and luminosity) and optical-to-X-ray properties. The observed fraction of candidate Compton-thick AGN measured from the hardness ratio is between 13-20%. We discuss the spectral properties of NuSTAR J100259+0220.6 (ID 330) at z=0.044, with the highest hardness ratio in the entire sample. The measured column density exceeds 10^24 /cm2, implying the source is Compton-thick. This source was not previously recognized as such without the \u3e10 keV data

Extremal Dependence Concepts

The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent devel- opments in extremal dependence concepts have drawn a lot of attention to probability and its applications in several disciplines. The aim of this paper is to review various concepts of extremal positive and negative dependence, including several recently established results, reconstruct their history, link them to probabilistic optimization problems, and provide a list of open ques- tions in this area. While the concept of extremal positive dependence is agreed upon for random vectors of arbitrary dimensions, various notions of extremal negative dependence arise when more than two random variables are involved. We review existing popular concepts of extremal negative de- pendence given in literature and introduce a novel notion, which in a gen- eral sense includes the existing ones as particular cases. Even if much of the literature on dependence is focused on positive dependence, we show that negative dependence plays an equally important role in the solution of many optimization problems. While the most popular tool used nowadays to model dependence is that of a copula function, in this paper we use the equivalent concept of a set of rearrangements. This is not only for historical reasons. Re- arrangement functions describe the relationship between random variables in a completely deterministic way, allow a deeper understanding of dependence itself, and have several advantages on the approximation of solutions in a broad class of optimization problems

The multi-phase winds of Markarian 231: from the hot, nuclear, ultra-fast wind to the galaxy-scale, molecular outflow

We present the best sensitivity and angular resolution maps of the molecular disk and outflow of Mrk 231, as traced by CO observations obtained with IRAM/PdBI, and we analyze archival Chandra and NuSTAR observations. We constrain the physical properties of both the molecular disk and outflow, the presence of a highly-ionized ultra-fast nuclear wind, and their connection. The molecular outflow has a size of ~1 kpc, and extends in all directions around the nucleus, being more prominent along the south-west to north-east direction, suggesting a wide-angle biconical geometry. The maximum projected velocity of the outflow is nearly constant out to ~1 kpc, thus implying that the density of the outflowing material decreases from the nucleus outwards as $r^{-2}$. This suggests that either a large part of the gas leaves the flow during its expansion or that the bulk of the outflow has not yet reached out to ~1 kpc, thus implying a limit on its age of ~1 Myr. We find $\dot M_{OF}=[ 500-1000]~ M_{\odot}~yr^{-1}$ and $\dot E_{kin,OF}=[7-10]\times 10^{43}$ erg s$^{-1}$. Remarkably, our analysis of the X-ray data reveals a nuclear ultra-fast outflow (UFO) with velocity -20000 km s$^{-1}$, $\dot M_{UFO}=[0.3- 2.1] ~M_\odot yr^{-1}$, and momentum load $\dot P_{UFO}/\dot P_{rad}=[0.2-1.6]$.We find $\dot E_{kin,UFO}\sim \dot E_{kin,OF}$ as predicted for outflows undergoing an energy conserving expansion. This suggests that most of the UFO kinetic energy is transferred to mechanical energy of the kpc-scale outflow, strongly supporting that the energy released during accretion of matter onto super-massive black holes is the ultimate driver of giant massive outflows. We estimate a momentum boost $\dot P_{OF}/\dot P_{UFO}\approx [30-60]$. The ratios $\dot E_{kin, UFO}/L_{bol,AGN} =[ 1-5]\%$ and $\dot E_{kin,OF}/L_{bol,AGN} = [1-3]\%$ agree with the requirements of the most popular models of AGN feedback.Comment: 16 pages, 17 figures. Accepted for publication in A&

Preclinical discovery and development of fingolimod for the treatment of multiple sclerosis

ABSTRACTIntroduction: Fingolimod, the first oral disease-modifying treatment (DMT) in multiple sclerosis (MS), is a sphingosine 1-phosphate receptor (S1PR) ligand. Approved in 2010, fingolimod has ..

The HELLAS2XMM survey. IX. Spectroscopic identification of super-EROs hosting AGNs

We present VLT near-IR spectroscopic observations of three X-ray sources characterized by extremely high X-ray-to-optical ratios (X/O>40), extremely red colors (6.3<R-K<7.4, i.e. EROs) and bright infrared magnitudes (17.6<K<18.3). These objects are very faint in the optical, making their spectroscopic identification extremely challenging. Instead, our near-IR spectroscopic observations have been successful in identifying the redshift of two of them (z=2.08 and z=1.35), and tentatively even of the third one (z=2.13). When combined with the X-ray properties, our results clearly indicate that all these objects host obscured QSOs (4e44 < L(2-10keV) < 1.5e45 erg/s, 2e22 < N_H < 4e23 cm-2) at high redshift. The only object with unresolved morphology in the K band shows broad Halpha emission, but not broad Hbeta, implying a type 1.9 AGN classification. The other two objects are resolved and dominated by the host galaxy light in the K band, and appear relatively quiescent: one of them has a LINER-like emission line spectrum and the other presents only a single, weak emission line which we tentatively identify with Halpha. The galaxy luminosities for the latter two objects are an order of magnitude brighter than typical local L* galaxies and the derived stellar masses are well in excess of 10^11 Msun. For these objects we estimate black hole masses higher than 10^9 Msun and we infer that they are radiating at Eddington ratios L/L_Edd < 0.1. We discuss the implications of these findings for the coevolution of galaxies and black hole growth. Our results provide further support that X-ray sources with high X/O ratios and very red colors tend to host obscured QSO in very massive galaxies at high redshift.Comment: 7 pages, 5 figures, accepted for publication in A&

Detailed Shape and Evolutionary Behavior of the X-ray Luminosity Function of Active Galactic Nuclei

We construct the rest-frame 2--10 keV intrinsic X-ray luminosity function of Active Galactic Nuclei (AGNs) from a combination of X-ray surveys from the all-sky Swift BAT survey to the Chandra Deep Field-South. We use ~3200 AGNs in our analysis, which covers six orders of magnitude in flux. The inclusion of the XMM and Chandra COSMOS data has allowed us to investigate the detailed behavior of the XLF and evolution. In deriving our XLF, we take into account realistic AGN spectrum templates, absorption corrections, and probability density distributions in photometric redshift. We present an analytical expression for the overall behavior of the XLF in terms of the luminosity-dependent density evolution, smoothed two power-law expressions in 11 redshift shells, three-segment power-law expression of the number density evolution in four luminosity classes, and binned XLF. We observe a sudden flattening of the low luminosity end slope of the XLF slope at z>~0.6. Detailed structures of the AGN downsizing have been also revealed, where the number density curves have two clear breaks at all luminosity classes above log LX>43. The two break structure is suggestive of two-phase AGN evolution, consisting of major merger triggering and secular processes.Comment: 39 Pages, 9 figures. ApJ in pres

VaR bounds for joint portfolios with dependence constraints

Based on a novel extension of classical Hoe ding-Fr\ue9chet bounds, we provide an upper VaR bound for joint risk portfolios with xed marginal distributions and positive dependence information. The positive dependence information can be assumed to hold in the tails, in some central part, or on a general subset of the domain of the distribution function of a risk portfolio. The newly provided VaR bound can be interpreted as a comonotonic VaR computed at a distorted con dence level and its quality is illustrated in a series of examples of practical interest

Broadband Observations of the Compton-thick Nucleus of NGC 3393

We present new NuSTAR and Chandra observations of NGC 3393, a galaxy reported to host the smallest separation dual AGN resolved in the X-rays. While past results suggested a 150 pc separation dual AGN, three times deeper Chandra imaging, combined with adaptive optics and radio imaging suggest a single, heavily obscured, radio-bright AGN. Using VLA and VLBA data, we find an AGN with a two-sided jet rather than a dual AGN and that the hard X-ray, UV, optical, NIR, and radio emission are all from a single point source with a radius <0.2". We find that the previously reported dual AGN is most likely a spurious detection resulting from the low number of X-ray counts (<160) at 6-7 keV and Gaussian smoothing of the data on scales much smaller than the PSF (0.25" vs. 0.80" FWHM). We show that statistical noise in a single Chandra PSF generates spurious dual peaks of the same separation (0.55$\pm$0.07" vs. 0.6") and flux ratio (39$\pm$9% vs. 32% of counts) as the purported dual AGN. With NuSTAR, we measure a Compton-thick source (NH=$2.2\pm0.4\times10^{24}$ cm$^{-2}$) with a large torus half-opening angle, {\theta}=79 which we postulate results from feedback from strong radio jets. This AGN shows a 2-10 keV intrinsic to observed flux ratio of 150. Using simulations, we find that even the deepest Chandra observations would severely underestimate the intrinsic luminosity of NGC 3393 above z>0.2, but would detect an unobscured AGN of this luminosity out to high redshift (z=5).Comment: Accepted for publication in ApJ. 15 Figures and 4 table