A structural approach to matching problems with preferences

This thesis is a study of a number of matching problems that seek to match together pairs or groups of agents subject to the preferences of some or all of the agents. We present a number of new algorithmic results for five specific problem domains. Each of these results is derived with the aid of some structural properties implicitly embedded in the problem. We begin by describing an approximation algorithm for the problem of finding a maximum stable matching for an instance of the stable marriage problem with ties and incomplete lists (MAX-SMTI). Our polynomial time approximation algorithm provides a performance guarantee of 3/2 for the general version of MAX-SMTI, improving upon the previous best approximation algorithm, which gave a performance guarantee of 5/3. Next, we study the sex-equal stable marriage problem (SESM). We show that SESM is W[1]-hard, even if the men's and women's preference lists are both of length at most three. This improves upon the previously known hardness results. We contrast this with an exact, low-order exponential time algorithm. This is the first non-trivial exponential time algorithm known for this problem, or indeed for any hard stable matching problem. Turning our attention to the hospitals / residents problem with couples (HRC), we show that HRC is NP-complete, even if very severe restrictions are placed on the input. By contrast, we give a linear-time algorithm to find a stable matching with couples (or report that none exists) when stability is defined in terms of the classical Gale-Shapley concept. This result represents the most general polynomial time solvable restriction of HRC that we are aware of. We then explore the three dimensional stable matching problem (3DSM), in which we seek to find stable matchings across three sets of agents, rather than two (as in the classical case). We show that under two natural definitions of stability, finding a stable matching for a 3DSM instance is NP-complete. These hardness results resolve some open questions in the literature. Finally, we study the popular matching problem (POP-M) in the context of matching a set of applicants to a set of posts. We provide a characterization of the set of popular matchings for an arbitrary POP-M instance in terms of a new structure called the switching graph exploited to yield efficient algorithms for a range of associated problems, extending and improving upon the previously best-known results for this problem

A systematic variation of the stellar initial mass function in early-type galaxies

Much of our knowledge of galaxies comes from analysing the radiation emitted by their stars. It depends on the stellar initial mass function (IMF) describing the distribution of stellar masses when the population formed. Consequently knowledge of the IMF is critical to virtually every aspect of galaxy evolution. More than half a century after the first IMF determination, no consensus has emerged on whether it is universal in different galaxies. Previous studies indicated that the IMF and the dark matter fraction in galaxy centres cannot be both universal, but they could not break the degeneracy between the two effects. Only recently indications were found that massive elliptical galaxies may not have the same IMF as our Milky Way. Here we report unambiguous evidence for a strong systematic variation of the IMF in early-type galaxies as a function of their stellar mass-to-light ratio, producing differences up to a factor of three in mass. This was inferred from detailed dynamical models of the two-dimensional stellar kinematics for the large Atlas3D representative sample of nearby early-type galaxies spanning two orders of magnitude in stellar mass. Our finding indicates that the IMF depends intimately on a galaxy's formation history.Comment: 4 pages, 2 figures, LaTeX. Accepted for publication as a Nature Letter. More information about our Atlas3D project is available at http://purl.org/atlas3

The Fourteenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the extended Baryon Oscillation Spectroscopic Survey and from the second phase of the Apache Point Observatory Galactic Evolution Experiment

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V.Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected

Personality and Temperament Correlates of Pain Catastrophizing in Young Adolescents

Pain catastrophizing is generally viewed as an important cognitive factor underlying chronic pain. The present study examined personality and temperament correlates of pain catastrophizing in a sample of young adolescents (N = 132). Participants completed the Pain Catastrophizing Scale for Children, as well as scales for measuring sensitivity of the behavioral inhibition and behavioral activation systems (BIS-BAS), and various reactive and regulative temperament traits. Results demonstrated that BIS, reactive temperament traits (fear and anger-frustration), and perceptual sensitivity were positively related to pain catastrophizing, whereas regulative traits (attention control, inhibitory control) were negatively associated with this cognitive factor. Further, regression analyses demonstrated that only BIS and the temperamental traits of fear and perceptual sensitivity accounted for a unique proportion of the variance in adolescents’ pain catastrophizing scores

Overview of the SDSS-IV MaNGA survey: mapping nearby galaxies at Apache Point Observatory

We present an overview of a new integral field spectroscopic survey called MaNGA (Mapping Nearby Galaxies at Apache Point Observatory), one of three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV) that began on 2014 July 1. MaNGA will investigate the internal kinematic structure and composition of gas and stars in an unprecedented sample of 10,000 nearby galaxies. We summarize essential characteristics of the instrument and survey design in the context of MaNGA's key science goals and present prototype observations to demonstrate MaNGA's scientific potential. MaNGA employs dithered observations with 17 fiber-bundle integral field units that vary in diameter from 12'' (19 fibers) to 32'' (127 fibers). Two dual-channel spectrographs provide simultaneous wavelength coverage over 3600-10300 Å at R ~ 2000. With a typical integration time of 3 hr, MaNGA reaches a target r-band signal-to-noise ratio of 4-8 (Å–1 per 2'' fiber) at 23 AB mag arcsec–2, which is typical for the outskirts of MaNGA galaxies. Targets are selected with M * 109 M ☉ using SDSS-I redshifts and i-band luminosity to achieve uniform radial coverage in terms of the effective radius, an approximately flat distribution in stellar mass, and a sample spanning a wide range of environments. Analysis of our prototype observations demonstrates MaNGA's ability to probe gas ionization, shed light on recent star formation and quenching, enable dynamical modeling, decompose constituent components, and map the composition of stellar populations. MaNGA's spatially resolved spectra will enable an unprecedented study of the astrophysics of nearby galaxies in the coming 6 yr

Sloan Digital Sky Survey IV: Mapping the Milky Way, Nearby Galaxies, and the Distant Universe

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratios in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially resolved spectroscopy for thousands of nearby galaxies (median $z\sim 0.03$). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between $z\sim 0.6$ and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGNs and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5 m Sloan Foundation Telescope at the Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5 m du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in 2016 July

The Fourteenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the Extended Baryon Oscillation Spectroscopic Survey and from the Second Phase of the Apache Point Observatory Galactic Evolution Experiment

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since 2014 July. This paper describes the second data release from this phase, and the 14th from SDSS overall (making this Data Release Fourteen or DR14). This release makes the data taken by SDSS-IV in its first two years of operation (2014–2016 July) public. Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey; the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data-driven machine-learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from the SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS web site (www.sdss.org) has been updated for this release and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020 and will be followed by SDSS-V

Sloan Digital Sky Survey IV: mapping the Milky Way, nearby galaxies, and the distant universe

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratios in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially resolved spectroscopy for thousands of nearby galaxies (median ). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGNs and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5 m Sloan Foundation Telescope at the Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5 m du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in 2016 July