Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Spectroscopy of an extreme [OIII] emitting active galactic nucleus at z = 3.212: implications for the reionisation era

Reionization-era galaxies often display intense nebular emission lines, both in rest-frame optical ([O III] + H β) and ultraviolet (UV; C III], C IV). How such strong nebular emission is powered remains unclear, with both active galactic nuclei (AGNs) and hot stars considered equally viable. The UV continuum slopes of these early systems tend to be very blue (β −1) than typical star-forming systems in the reionization era. To investigate the properties of AGNs in the reionization era, we have conducted a search for potential examples of rare analogues with blue continua at intermediate redshift (⁠z ∼ 2−3). Our goals are to determine whether AGNs with intense line emission and blue continua exist and thereby to establish the range of rest-frame UV and optical line ratios in this population. In this paper, we report the detection of an X-ray luminous AGN at z = 3.21 (UDS-24561) with extreme [O III] + H β line emission (equivalent width = 1300 Å) and a blue UV continuum slope (β = −2.34). MMT/Binospec and Keck/MOSFIRE spectra indicate rest-frame UV line ratios consistent with AGN photoionization models and rest-frame optical lines with both a narrow component [full width at half-maximum (FWHM) =154kms−1] and extended broad wings (FWHM =977kms−1⁠), consistent with outflowing gas. We describe how such objects can be identified in future James Webb Space Telescope emission line surveys in the reionization era, thereby providing a valuable census of AGN activity at z > 6 and understanding their contribution to cosmic reionization

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to

The MOSDEF Survey: The Metallicity Dependence of X-Ray Binary Populations at z ∼ 2

Population synthesis models predict that high-mass X-ray binary (HMXB) populations produced in low-metallicity environments should be more X-ray luminous, a trend supported by studies of nearby galaxies. This trend may be responsible for the observed increase of the X-ray luminosity (L X) per star formation rate (SFR) with redshift due to the decrease of metallicity (Z) at fixed stellar mass as a function of redshift. To test this hypothesis, we use a sample of 79 z ∼ 2 star-forming galaxies with oxygen abundance measurements from the MOSDEF survey, which obtained rest-frame optical spectra for ∼1500 galaxies in the CANDELS fields at 1.37 < z < 3.80. Using Chandra data from the Chandra AEGIS-X Deep, Chandra Deep Field North, and Chandra Deep Field South surveys, we stack the X-ray data at the galaxy locations in bins of redshift and Z because the galaxies are too faint to be individually detected. In agreement with previous studies, the average L X/SFR of our z ∼ 2 galaxy sample is enhanced by ≈0.4-0.8 dex relative to local HMXB L X-SFR scaling relations. Splitting our sample by Z, we find that L X/SFR and Z are anticorrelated with 97% confidence. This observed Z dependence for HMXB-dominated galaxies is consistent with both the local L X-SFR-Z relation and a subset of population synthesis models. Although the statistical significance of the observed trends is weak owing to the low X-ray statistics, these results constitute the first direct evidence connecting the redshift evolution of L X/SFR and the Z dependence of HMXBs

Type IIn supernovae at z ~ 2 from archival data

Supernovae have been confirmed to redshift z ~ 1.7 for type Ia (thermonuclear detonation of a white dwarf) and to z ~ 0.7 for type II (collapse of the core of the star). The subclass type IIn supernovae are luminous core-collapse explosions of massive stars and, unlike other types, are very bright in the ultraviolet, which should enable them to be found optically at redshifts z ~ 2 and higher. In addition, the interaction of the ejecta with circumstellar material creates strong, long-lived emission lines that allow spectroscopic confirmation of many events of this type at z ~ 2 for 3 - 5 years after explosion. Here we report three spectroscopically confirmed type IIn supernovae, at redshifts z = 0.808, 2.013 and 2.357, detected in archival data using a method designed to exploit these properties at z ~ 2. Type IIn supernovae directly probe the formation of massive stars at high redshift. The number found to date is consistent with the expectations of a locally measured stellar initial mass function, but not with an evolving initial mass function proposed to explain independent observations at low and high redshift.Comment: 8 pages, 2 figures, includes supplementary informatio

The Interstellar Medium In Galaxies Seen A Billion Years After The Big Bang

Evolution in the measured rest frame ultraviolet spectral slope and ultraviolet to optical flux ratios indicate a rapid evolution in the dust obscuration of galaxies during the first 3 billion years of cosmic time (z>4). This evolution implies a change in the average interstellar medium properties, but the measurements are systematically uncertain due to untested assumptions, and the inability to measure heavily obscured regions of the galaxies. Previous attempts to directly measure the interstellar medium in normal galaxies at these redshifts have failed for a number of reasons with one notable exception. Here we report measurements of the [CII] gas and dust emission in 9 typical (~1-4L*) star-forming galaxies ~1 billon years after the big bang (z~5-6). We find these galaxies have >12x less thermal emission compared with similar systems ~2 billion years later, and enhanced [CII] emission relative to the far-infrared continuum, confirming a strong evolution in the interstellar medium properties in the early universe. The gas is distributed over scales of 1-8 kpc, and shows diverse dynamics within the sample. These results are consistent with early galaxies having significantly less dust than typical galaxies seen at z<3 and being comparable to local low-metallicity systems.Comment: Submitted to Nature, under review after referee report. 22 pages, 4 figures, 4 Extended Data Figures, 5 Extended Data table

The NIRVANDELS Survey: A robust detection of α-enhancement in star-forming galaxies at z ≃3.4

We present results from the NIRVANDELS survey on the gas-phase metallicity (Zg, tracing O/H) and stellar metallicity (Z∗, tracing Fe/H) of 33 star-forming galaxies at redshifts 2.95 3, finding (O/Fe) = 2.54 ± 0.38 × (O/Fe)⊙, with no clear dependence on M∗

Significant primordial star formation at redshifts z ~ 3-4

Four recent observational results have challenged our understanding of high--redshift galaxies, as they require the presence of far more ultraviolet photons than should be emitted by normal stellar populations. First, there is significant ultraviolet emission from Lyman Break Galaxies (LBGs) at wavelenghts shorter than 912\AA. Second, there is strong Lyman alpha emission from extended ``blobs'' with little or no associated apparent ionizing continuum. Third, there is a population of galaxies with unusually strong Lyman-alpha emission lines. And fourth, there is a strong HeII (1640 \AA) emission line in a composite of LBGs. The proposed explanations for the first three observations are internally inconsistent, and the fourth puzzle has remained hitherto unexplained. Here we show that all four problems are resolved simultaneously if 10-30 percent of the stars in many galaxies at z ~ 3-4 are mainly primordial - unenriched by elements heavier than helium ('metals'). Most models of hierarchical galaxy formation assume efficient intra--galactic metal mixing, and therefore do not predict metal-free star formation at redshifts significantly below z ~5. Our results imply that micro-mixing of metals within galaxies is inefficient on a ~ Gyr time-scale, a conclusion that can be verified with higher resolution simulations, and future observations of the HeII emission line.Comment: Nature in press, March 23rd issue. Under Nature embargo. Reference and acknowledgement adde

The evolution of galaxies from primeval irregulars to present-day ellipticals

The current understanding of galaxy formation is that it proceeds in a 'bottom up' way, with the formation of small clumps of gas and stars that merge hierarchically until giant galaxies are built up. The baryonic gas loses the thermal energy by radiative cooling and falls towards the centres of the new galaxies, while supernovae (SNe) blow gas out. Any realistic model therefore requires a proper treatment of these processes, but hitherto this has been far from satisfactory. Here we report an ultra-high-resolution simulation that follows evolution from the earliest stages of galaxy formation through the period of dynamical relaxation. The bubble structures of gas revealed in our simulation ($< 3\times10^8$ years) resemble closely the high-redshift Lyman $\alpha$ emitters (LAEs). After $10^9$ years these bodies are dominated by stellar continuum radiation and look like the Lyman break galaxies (LBGs) known as the high-redshift star-forming galaxies at which point the abundance of elements heavier than helium ("metallicity") appears to be solar. After $1.3\times10^{10}$ years, these galaxies resemble present-day ellipticals.Comment: 27 pages and 4 figures, Supplementary Information included, movie available on http://www.isc.senshu-u.ac.jp/~thj0613/natur

Kiadói és nyomdai tevékenység a szerbek körében a középkor végén és az újkor hajnalán

We study the properties of 30 spectroscopically identified pairs of galaxies observed during the peak epoch of star formation in the universe. These systems are drawn from the MOSFIRE Deep Evolution Field (MOSDEF) Survey at 1.4 ≤ z ≤ 3.8, and are interpreted as early-stage galaxy mergers. Galaxy pairs in our sample are identified as two objects whose spectra were collected on the same Keck/MOSFIRE spectroscopic slit. Accordingly, all pairs in the sample have projected separations R proj ≤ 60 kpc. The velocity separation for pairs was required to be Δv ≤ 500 km s -1 , which is a standard threshold for defining interacting galaxy pairs at low redshift. Stellar mass ratios in our sample range from 1.1 to 550, with 12 ratios closer than or equal to 3:1, the common definition of a "major merger." Studies of merging pairs in the local universe indicate an enhancement in star formation activity and deficit in gas-phase oxygen abundance relative to isolated galaxies of the same mass. We compare the MOSDEF pairs sample to a control sample of isolated galaxies at the same redshift, finding no measurable SFR enhancement or metallicity deficit at fixed stellar mass for the pairs sample. The lack of significant difference between the average properties of pairs and control samples appears in contrast to results from low-redshift studies, although the small sample size and lower signal-to-noise of the high-redshift data limit definitive conclusions on redshift evolution. These results are consistent with some theoretical works, suggesting a reduced differential effect of precoalescence mergers on galaxy properties at high redshift - specifically that precoalescence mergers do not drive strong starbursts