Generalizations of the Familywise Error Rate

Consider the problem of simultaneously testing null hypotheses H_1,...,H_s. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which we call the k-FWER. We derive both single-step and stepdown procedures that control the k-FWER, without making any assumptions concerning the dependence structure of the p-values of the individual tests. In particular, we derive a stepdown procedure that is quite simple to apply, and prove that it cannot be improved without violation of control of the k-FWER. We also consider the false discovery proportion (FDP) defined by the number of false rejections divided by the total number of rejections (defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300] controls E(FDP). Here, we construct methods such that, for any \gamma and \alpha, P{FDP>\gamma}\le\alpha. Two stepdown methods are proposed. The first holds under mild conditions on the dependence structure of p-values, while the second is more conservative but holds without any dependence assumptions.Comment: Published at http://dx.doi.org/10.1214/009053605000000084 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The effect of stellar migration on Galactic chemical evolution: a heuristic approach

In the last years, stellar migration in galactic discs has been the subject of several investigations. However, its impact on the chemical evolution of the Milky Way still needs to be fully quantified. In this paper, we aim at imposing some constraints on the significance of this phenomenon by considering its influence on the chemical evolution of the Milky Way thin disc. We do not investigate the physical mechanisms underlying the migration of stars. Rather, we introduce a simple, heuristic treatment of stellar migration in a detailed chemical evolution model for the thin disc of the Milky Way, which already includes radial gas flows and reproduces several observational constraints for the solar vicinity and the whole Galactic disc. When stellar migration is implemented according to the results of chemo-dynamical simulations by Minchev et. al. (2013) and finite stellar velocities of 1 km s$^{-1}$ are taken into account, the high-metallicity tail of the metallicity distribution function of long-lived thin-disc stars is well reproduced. By exploring the velocity space, we find that the migrating stars must travel with velocities in the range 0.5 -2 km s$^{-1}$ to properly reproduce the high-metallicity tail of the metallicity distribution. We confirm previous findings by other authors that the observed spread in the age-metallicity relation of solar neighbourhood stars can be explained by the presence of stars which originated at different Galactocentric distances, and we conclude that the chemical properties of stars currently observed in the solar vicinity do suggest that stellar migration is present to some extent.Comment: Accepted for publication by Ap

On Optimality of Stepdown and Stepup Multiple Test Procedures

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition. Under these assumptions, we prove certain maximin optimality results for some well-known stepdown and stepup procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000066 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A new method of measuring center-of-mass velocities of radially pulsating stars from high-resolution spectroscopy

We present a radial velocity analysis of 20 solar neighborhood RR Lyrae and 3 Population II Cepheids variables. We obtained high-resolution, moderate-to-high signal-to-noise ratio spectra for most stars and obtained spectra were covering different pulsation phases for each star. To estimate the gamma (center-of-mass) velocities of the program stars, we use two independent methods. The first, `classic' method is based on RR Lyrae radial velocity curve templates. The second method is based on the analysis of absorption line profile asymmetry to determine both the pulsational and the gamma velocities. This second method is based on the Least Squares Deconvolution (LSD) technique applied to analyze the line asymmetry that occurs in the spectra. We obtain measurements of the pulsation component of the radial velocity with an accuracy of $\pm$ 3.5 km s$^{-1}$. The gamma velocity was determined with an accuracy $\pm$ 10 km s$^{-1}$, even for those stars having a small number of spectra. The main advantage of this method is the possibility to get the estimation of gamma velocity even from one spectroscopic observation with uncertain pulsation phase. A detailed investigation of the LSD profile asymmetry shows that the projection factor $p$ varies as a function of the pulsation phase -- this is a key parameter which converts observed spectral line radial velocity variations into photospheric pulsation velocities. As a byproduct of our study, we present 41 densely-spaced synthetic grids of LSD profile bisectors that are based on atmospheric models of RR Lyr covering all pulsation phases.Comment: 17 pages, 16 figures, accepted for publication in MNRAS; doi:10.1093/mnras/stx294

The accretion environment of Supergiant Fast X-ray Transients probed with XMM-Newton

Supergiant fast X-ray transients (SFXTs) are characterized by a remarkable variability in the X-ray domain, widely ascribed to the accretion from a clumpy stellar wind. In this paper we performed a systematic and homogeneous analysis of sufficiently bright X-ray flares from the SFXTs observed with XMM-Newton to probe spectral variations on timescales as short as a few hundred of seconds. Our ultimate goal is to investigate if SFXT flares and outbursts are triggered by the presence of clumps and eventually reveal whether strongly or mildly dense clumps are required. For all sources, we employ a technique developed by our group, making use of an adaptive rebinned hardness ratio to optimally select the time intervals for the spectral extraction. A total of twelve observations performed in the direction of five SFXTs are reported. We show that both strongly and mildly dense clumps can trigger these events. In the former case, the local absorption column density may increase by a factor of >>3, while in the latter case, the increase is only by a factor of 2-3 (or lower). Overall, there seems to be no obvious correlation between the dynamic ranges in the X-ray fluxes and absorption column densities in SFXTs, with an indication that lower densities are recorded at the highest fluxes. This can be explained by the presence of accretion inhibition mechanism(s). We propose a classification of the flares/outbursts from these sources to drive future observational investigations. We suggest that the difference between the classes of flares/outbursts is related to the fact that the mechanism(s) inhibiting accretion can be overcome more easily in some sources compared to others. We also investigate the possibility that different stellar wind structures, rather than clumps, could provide the means to temporarily overcome the inhibition of accretion in SFXTs.Comment: Accepted for publication on A&

Soft X-ray characterisation of the long term properties of Supergiant Fast X-ray Transients

We perform the first high-sensitivity soft X-ray long-term monitoring with Swift/XRT of three relatively unexplored Supergiant Fast X-ray Transients (SFXTs), IGR J08408-4503, IGR J16328-4726, and IGR J16465-4507, whose hard X-ray duty cycles are the lowest measured among the SFXT sample, and compare their properties with those of the prototypical SFXTs. The behaviour of J08408 and J16328 resembles that of other SFXTs, and it is characterized by a relatively high inactivity duty cycle (IDC) and pronounced dynamic range (DR) in the X-ray luminosity. Like the SFXT prototypes, J08408 shows two distinct populations of flares, the first one associated with the brightest outbursts ($L_{\rm X}\gtrsim 10^{35-36}$ erg s$^{-1}$), the second one comprising less bright events with $L_{\rm X}\lesssim$10$^{35}$ erg s$^{-1}$. This double-peaked distribution seems to be a ubiquitous feature of the extreme SFXTs. The lower DR of J16328 suggests it is an intermediate SFXT. We find J16465 is characterized by IDC$\sim$5% and DR$\sim$40, reminiscent of classical supergiant HMXBs. The duty cycles measured with XRT are found to be comparable with those reported previously by BAT and INTEGRAL, when the higher limiting sensitivities of these instruments are taken into account and sufficiently long observational campaigns are available. We prove that no clear correlation exists between the duty cycles of the SFXTs and their orbital periods, which makes it difficult to interpret the SFXT peculiar variability by only using arguments related to the properties of supergiant star winds. Our findings favour the idea that a correct interpretation of the SFXT phenomenology requires a mechanism to strongly reduce the mass accretion rate onto the compact object during most of its orbit around the companion, as proposed in a number of theoretical works. [Abridged]Comment: Accepted for publication in Astronomy and Astrophysics. 18 pages, 8 figures, 8 table

Two years of monitoring Supergiant Fast X-ray Transients with Swift

We present two years of intense Swift monitoring of three SFXTs, IGR J16479-4514, XTE J1739-302, and IGR J17544-2619 (since October 2007). Out-of-outburst intensity-based X-ray (0.3-10keV) spectroscopy yields absorbed power laws with by hard photon indices (G~1-2). Their outburst broad-band (0.3-150 keV) spectra can be fit well with models typically used to describe the X-ray emission from accreting NSs in HMXBs. We assess how long each source spends in each state using a systematic monitoring with a sensitive instrument. These sources spend 3-5% of the total in bright outbursts. The most probable flux is 1-2E-11 erg cm^{-2} s^{-1} (2-10 keV, unabsorbed), corresponding to luminosities in the order of a few 10^{33} to 10^{34} erg s^{-1} (two orders of magnitude lower than the bright outbursts). The duty-cycle of inactivity is 19, 39, 55%, for IGR J16479-4514, XTE J1739-302, and IGR J17544-2619, respectively. We present a complete list of BAT on-board detections further confirming the continued activity of these sources. This demonstrates that true quiescence is a rare state, and that these transients accrete matter throughout their life at different rates. X-ray variability is observed at all timescales and intensities we can probe. Superimposed on the day-to-day variability is intra-day flaring which involves variations up to one order of magnitude that can occur down to timescales as short as ~1ks, and whichcan be explained by the accretion of single clumps composing the donor wind with masses M_cl~0.3-2x10^{19} g. (Abridged)Comment: Accepted for publication in MNRAS. 17 pages, 11 figures, 8 table

Benthic Foraminifera as Environmental Indicators in Mediterranean Marine Caves: A Review

Marine caves are characterized by wide environmental variability for the interaction between marine and continental processes. Their conditions may be defined as extreme for inhabiting organisms due to the enclosed morphology, lack of light, and scarcity of nutrients. Therefore, it is necessary to identify reliable ecological indicators for describing and assessing environmental conditions in these habitats even more than elsewhere. This review aims to provide the state of art related to the application of benthic foraminifera as proxies in the (paleo)ecological characterization of different habitats of marine caves. Special attention was addressed to a research project focused on Mediterranean marine caves with different characteristics, such as extent, morphology, freshwater influence, salinity, sediment type, oxygenation, and organic matter supply. This review aims to illustrate the reliability of foraminifera as an ecological and paleoecological indicator in these habitats. They respond to various environmental conditions with different assemblages corresponding to a very detailed habitat partitioning. Because marine caves may be considered natural laboratories for environmental variability, the results of these studies may be interpreted in the perspective of the global variability to understand the environmental drivers of future changes in marine systems