Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

Individual-level determinants of depressive symptoms and associated diseases history in Turkish persons aged 15 years and older: A population-based study

BackgroundDepressive symptoms are associated with both long-lasting and short-term repetitive mood disorders and affect a person's ability to function and lead a rewarding life. In addition to predisposing genetic causes, other factors such as socioeconomic and demographic factors, and chronic diseases have also been reported to associate with depression. In this study, we analyzed the association between history of chronic diseases and presentation of depressive symptoms amongst Turkish individuals. MethodsWe employed the 2019 Turkey health survey to analyze data of 11,993 individuals aged 15+ years. Depressive symptoms were assessed using the eight-item Patient Health Questionnaire (PHQ-8) coded with a binary measure, a score of 10 as moderate-severely depressed. A number of sociodemographic characteristics were adjusted for in the analyses. Logistic regression models were used to test the association between chronic diseases and depressive symptoms in the study sample. ResultsOur analysis revealed that 6.24% of the 11,993 participants had reported an episode of depressive symptoms. The prevalence of depressive symptoms in men was 1.85% and in women, it was 2.34 times higher. Participants who had previously reported experiencing coronary heart diseases (AOR = 7.79, 95% CI [4.96-12.23]), urinary incontinences (AOR = 7.90, 95% CI [4.93-12.66]), and liver cirrhosis (AOR = 7.50, 95% CI [4.90-10.42]) were approximately eight times likely to have depressive symptoms. Similarly, participants with Alzheimer's disease (AOR = 6.83, 95% CI [5.11-8.42]), kidney problems (AOR = 6.63, 95% CI [4.05-10.85]), and history of allergies (AOR = 6.35, 95% CI [4.28-9.23]) had approximately seven-fold odds of reporting episodes of depressive symptoms. The odds of presenting with depressive symptoms amongst participants aged >= 50 were higher than in individuals aged <= 49 years. ConclusionAt individual level, gender and general health status were associated with increased odds of depression. Furthermore, a history of any of the chronic diseases, irrespective of age, was a positive predictor of depression in our study population. Our findings could help to serve as a reference for monitoring depression amongst individuals with chronic conditions, planning health resources and developing preventive and screening strategies targeting those exposed to predisposing factors

Spectra disentangling applied to the Hyades binary Theta^2 Tau AB: new orbit, orbital parallax and component properties

Theta^2 Tauri is a detached and single-lined interferometric-spectroscopic binary as well as the most massive binary system of the Hyades cluster. The system revolves in an eccentric orbit with a periodicity of 140.7 days. The secondary has a similar temperature but is less evolved and fainter than the primary. It is also rotating more rapidly. Since the composite spectra are heavily blended, the direct extraction of radial velocities over the orbit of component B was hitherto unsuccessful. Using high-resolution spectroscopic data recently obtained with the Elodie (OHP, France) and Hermes (ORM, La Palma, Spain) spectrographs, and applying a spectra disentangling algorithm to three independent data sets including spectra from the Oak Ridge Observatory (USA), we derived an improved spectroscopic orbit and refined the solution by performing a combined astrometric-spectroscopic analysis based on the new spectroscopy and the long-baseline data from the Mark III optical interferometer. As a result, the velocity amplitude of the fainter component is obtained in a direct and objective way. Major progress based on this new determination includes an improved computation of the orbital parallax. Our mass ratio is in good agreement with the older estimates of Peterson et al. (1991, 1993), but the mass of the primary is 15-25% higher than the more recent estimates by Torres et al. (1997) and Armstrong et al. (2006). Due to the strategic position of the components in the turnoff region of the cluster, these new determinations imply stricter constraints for the age and the metallicity of the Hyades cluster. The location of component B can be explained by current evolutionary models, but the location of the more evolved component A is not trivially explained and requires a detailed abundance analysis of its disentangled spectrum.Comment: in press, 13 pages, 10 Postscript figures, 5 tables. Table~4 is available as online material. Keywords: astrometry - techniques: high angular resolution - stars: binaries: visual - stars: binaries: spectroscopic - stars: fundamental parameter

Uncertainties in models of stellar structure and evolution

Numerous physical aspects of stellar physics have been presented in Ses- sion 2 and the underlying uncertainties have been tentatively assessed. We try here to highlight some specific points raised after the talks and during the general discus- sion at the end of the session and eventually at the end of the workshop. A table of model uncertainties is then drawn with the help of the participants in order to give the state of the art in stellar modeling uncertainties as of July 2013.Comment: Proc. of the workshop "Asteroseismology of stellar populations in the Milky Way" (Sesto, 22-26 July 2013), Astrophysics and Space Science Proceedings, (eds. A. Miglio, L. Girardi, P. Eggenberger, J. Montalban

Orthogonal schedules in single round robin tournaments

A measure for the flexibility of a Home-Away Pattern set (HAP-set) is the width. The width of a HAP-set equals the size of the largest set of schedules compatible with the HAP-set, for which no match is scheduled in the same round in any two schedules. We prove lower and upper bounds on the width, and identify HAP-sets with largest possible width when the number of teams is a power of 2

Fundamental properties of the Population II fiducial stars HD 122563 and Gmb 1830 from CHARA interferometric observations

We have determined the angular diameters of two metal-poor stars, HD 122563 and Gmb 1830, using CHARA and Palomar Testbed Interferometer observations. For the giant star HD 122563, we derive an angular diameter theta_3D = 0.940 +- 0.011 milliarcseconds (mas) using limb-darkening from 3D convection simulations and for the dwarf star Gmb 1830 (HD 103095) we obtain a 1D limb-darkened angular diameter theta_1D = 0.679 +- 0.007 mas. Coupling the angular diameters with photometry yields effective temperatures with precisions better than 55 K (Teff = 4598 +- 41 K and 4818 +- 54 K --- for the giant and the dwarf star, respectively). Including their distances results in very well-determined luminosities and radii (L = 230 +- 6 L_sun, R = 23.9 +- 1.9 R_sun and L = 0.213 +- 0.002 L_sun, R = 0.664 +- 0.015 R_sun, respectively). We used the CESAM2k stellar structure and evolution code in order to produce models that fit the observational data. We found values of the mixing-length parameter alpha (which describes 1D convection) that depend on the mass of the star. The masses were determined from the models with precisions of <3% and with the well-measured radii excellent constraints on the surface gravity are obtained (log g = 1.60 +- 0.04, 4.59 +- 0.02, respectively). The very small errors on both log g and Teff provide stringent constraints for spectroscopic analyses given the sensitivity of abundances to both of these values. The precise determination of Teff for the two stars brings into question the photometric scales for metal-poor stars.Comment: accepted A&A, 8 dbl-column pages, incl. 7 tables and 4 figure

Water in low-mass star-forming regions with Herschel: HIFI spectroscopy of NGC1333

'Water In Star-forming regions with Herschel' (WISH) is a key programme dedicated to studying the role of water and related species during the star-formation process and constraining the physical and chemical properties of young stellar objects. The Heterodyne Instrument for the Far-Infrared (HIFI) on the Herschel Space Observatory observed three deeply embedded protostars in the low-mass star-forming region NGC1333 in several H2-16O, H2-18O, and CO transitions. Line profiles are resolved for five H16O transitions in each source, revealing them to be surprisingly complex. The line profiles are decomposed into broad (>20 km/s), medium-broad (~5-10 km/s), and narrow (<5 km/s) components. The H2-18O emission is only detected in broad 1_10-1_01 lines (>20 km/s), indicating that its physical origin is the same as for the broad H2-16O component. In one of the sources, IRAS4A, an inverse P Cygni profile is observed, a clear sign of infall in the envelope. From the line profiles alone, it is clear that the bulk of emission arises from shocks, both on small (<1000 AU) and large scales along the outflow cavity walls (~10 000 AU). The H2O line profiles are compared to CO line profiles to constrain the H2O abundance as a function of velocity within these shocked regions. The H2O/CO abundance ratios are measured to be in the range of ~0.1-1, corresponding to H2O abundances of ~10-5-10-4 with respect to H2. Approximately 5-10% of the gas is hot enough for all oxygen to be driven into water in warm post-shock gas, mostly at high velocities.Comment: Accepted for publication in the A&A HIFI special issu

Herschel-HIFI observations of high-J CO lines in the NGC 1333 low-mass star-forming region

Herschel-HIFI observations of high-J lines (up to J_u=10) of 12CO, 13CO and C18O are presented toward three deeply embedded low-mass protostars, NGC 1333 IRAS 2A, IRAS 4A, and IRAS 4B, obtained as part of the Water In Star-forming regions with Herschel (WISH) key program. The spectrally-resolved HIFI data are complemented by ground-based observations of lower-J CO and isotopologue lines. The 12CO 10-9 profiles are dominated by broad (FWHM 25-30 km s^-1) emission. Radiative transfer models are used to constrain the temperature of this shocked gas to 100-200 K. Several CO and 13CO line profiles also reveal a medium-broad component (FWHM 5-10 km s^-1), seen prominently in H2O lines. Column densities for both components are presented, providing a reference for determining abundances of other molecules in the same gas. The narrow C18O 9-8 lines probe the warmer part of the quiescent envelope. Their intensities require a jump in the CO abundance at an evaporation temperature around 25 K, thus providing new direct evidence for a CO ice evaporation zone around low-mass protostars.Comment: 8 pages, 9 figure

Structure and stability in TMC-1: Analysis of NH3molecular line andHerschelcontinuum data

Aims. We examined the velocity, density, and temperature structure of Taurus molecular cloud-1 (TMC-1), a filamentary cloud in a nearby quiescent star forming area, to understand its morphology and evolution. Methods. We observed high signal-to-noise (S/N), high velocity resolution NH3(1,1), and (2, 2) emission on an extended map. By fitting multiple hyperfine-split line profiles to the NH3(1, 1) spectra, we derived the velocity distribution of the line components and calculated gas parameters on several positions. Herschel SPIRE far-infrared continuum observations were reduced and used to calculate the physical parameters of the Planck Galactic Cold Clumps (PGCCs) in the region, including the two in TMC-1. The morphology of TMC-1 was investigated with several types of clustering methods in the parameter space consisting of position, velocity, and column density. Results. Our Herschel-based column density map shows a main ridge with two local maxima and a separated peak to the south-west. The H2 column densities and dust colour temperatures are in the range of 0.5−3.3 × 1022 cm−2 and 10.5−12 K, respectively. The NH3 column densities and H2 volume densities are in the range of 2.8−14.2 × 1014 cm−2 and 0.4−2.8 × 104 cm−3. Kinetic temperatures are typically very low with a minimum of 9 K at the maximum NH3 and H2 column density region. The kinetic temperature maximum was found at the protostar IRAS 04381+2540 with a value of 13.7 K. The kinetic temperatures vary similarly to the colour temperatures in spite of the fact that densities are lower than the critical density for coupling between the gas and dust phase. The k-means clustering method separated four sub-filaments in TMC-1 with masses of 32.5, 19.6, 28.9, and 45.9 Mo and low turbulent velocity dispersion in the range of 0.13−0.2 km s−1. Conclusions. The main ridge of TMC-1 is composed of four sub-filaments that are close to gravitational equilibrium. We label these TMC-1F1 through F4. The sub-filaments TMC-1F1, TMC-1F2, and TMC-1F4 are very elongated, dense, and cold. TMC-1F3 is a little less elongated and somewhat warmer, and probably heated by the Class I protostar, IRAS 04381+2540, which is embedded in it. TMC-1F3 is approximately 0.1 pc behind TMC1-F1. Because of its structure, TMC-1 is a good target to test filament evolution scenarios

Assessment of intellectual impairment, health-related quality of life, and behavioral phenotype in patients with neurotransmitter related disorders: data from the iNTD registry

Inherited disorders of neurotransmitter metabolism are a group of rare diseases, which are caused by impaired synthesis, transport or degradation of neurotransmitters or co-factors and result in various degrees of delayed or impaired psychomotor development. To assess the effect of neurotransmitter deficiencies on intelligence, quality of life, and behavior, the data of 148 patients in the registry of the International Working Group on Neurotransmitter Related Disorders (iNTD) was evaluated using results from standardized age-adjusted tests and questionnaires. Patients with a primary disorder of monoamine metabolism had lower IQ scores (mean IQ 58, range 40-100) within the range of cognitive impairment (<70) compared to patients with a BH4 deficiency (mean IQ 84, range 40-129). Short attention span and distractibility were most frequently mentioned by parents, while patients reported most frequently anxiety and distractibility when asked for behavioral traits. In individuals with succinic semialdehyde dehydrogenase deficiency, self-stimulatory behaviors were commonly reported by parents, whereas in patients with dopamine transporter (DAT) deficiency, DNAJC12 deficiency, and monoamine oxidase A deficiency, self-injurious or mutilating behaviors have commonly been observed. Phobic fears were increased in patients with 6-pyruvoyltetrahydropterin synthase deficiency while individuals with sepiapterin reductase deficiency frequently experienced communication and sleep difficulties. Patients with BH4 deficiencies achieved significantly higher quality of life as compared to other groups. This analysis of the iNTD registry data highlights: a) difference in IQ and subdomains of quality of life between BH4 deficiencies and primary neurotransmitter-related disorders, and b) previously underreported behavioral traits