An analogue of Ryser's Theorem for partial Sudoku squares

In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition could be reformulated in terms of Hall's Condition for partial latin squares. Thus Ryser's Theorem can be interpreted as saying that any partial latin rectangle $R$ can be completed if and only if $R$ satisfies Hall's Condition for partial latin squares. We define Hall's Condition for partial Sudoku squares and show that Hall's Condition for partial Sudoku squares gives a criterion for the completion of partial Sudoku rectangles that is both necessary and sufficient. In the particular case where $n=pq$, $p|r$, $q|s$, the result is especially simple, as we show that any $r \times s$ partial $(p,q)$-Sudoku rectangle can be completed (no further condition being necessary).Comment: 19 pages, 10 figure

Undamped nonequilibrium dynamics of a nondegenerate Bose gas in a 3D isotropic trap

We investigate anomalous damping of the monopole mode of a non-degenerate 3D Bose gas under isotropic harmonic confinement as recently reported by the JILA TOP trap experiment [D. S. Lob- ser, A. E. S. Barentine, E. A. Cornell, and H. J. Lewandowski (in preparation)]. Given a realistic confining potential, we develop a model for studying collective modes that includes the effects of anharmonic corrections to a harmonic potential. By studying the influence of these trap anharmonicities throughout a range of temperatures and collisional regimes, we find that the damping is caused by the joint mechanisms of dephasing and collisional relaxation. Furthermore, the model is complimented by Monte Carlo simulations which are in fair agreement with data from the JILA experiment.Comment: 11 pages, 6 figure

Production of carbon clusters C3\text{C}_3 to C12\text{C}_{12} with a cryogenic buffer-gas beam source

Cryogenic buffer-gas beam sources are capable of producing intense beams of a wide variety of molecules, and have a number of advantages over traditional supersonic expansion sources. In this work, we report on a neon matrix isolation study of carbon clusters produced with a cryogenic buffer-gas beam source. Carbon clusters created by laser ablation of graphite are trapped in a neon matrix and detected with a Fourier transform infrared spectrometer in the spectral range $4000-1000~\text{cm}^{-1}$. Through a study of carbon cluster production as a function of various system parameters, we characterize the behavior of the buffer-gas beam source and find that approximately $10^{11}-10^{12}$ of each cluster is produced with each pulse of the ablation laser. These measurements demonstrate the usefulness of cryogenic buffer-gas beam sources for producing molecular beams of clusters.Comment: 7 pages, 4 figure

Conditional variances in UK regional house prices

The returns of house price indices for the 13 UK regions are modelled using time series processes, including conditional variances. The first conclusion is that the UK follows the USA, with some regions displaying time-varying variances and others with constant variances. Secondly, there is limited evidence of an asymmetric component in six of the seven regions displaying autoregressive conditional heteroskedasticity. Thirdly, the results suggest that there are three distinct housing markets in the UK, based on common structures within their mean and variance processes, and that South West England is the region driving the other time-varying variances. Variances conditionnelles dans les prix regionaux de l'immobilier au Royaume-Uni Resume Les resultats de l'indice des prix de l'immobilier pour les 13 regions du Royaume-Uni sont modelises ici au moyen de procedes de series chronologiques, y compris des variances conditionnelles. La premiere conclusion est que le Royaume-Uni suit les Etats-Unis, certaines regions presentant des variances temporelles, d'autres des variances constantes. Deuxiemement, on releve peu de traces d'un composant asymetrique dans six des sept regions presentant une heteroscedasticite conditionnelle autoregressive. Troisiemement, les resultats indiquent qu'il y aurait trois marches de l'immobilier distincts au Royaume-Uni, sur la base de structures communes dans le cadre de leurs procedes moyens et de variance, et que le sud-ouest de l'Angleterre est la region qui dynamise les autres variances temporelles. Varianzas condicionales en los precios regionales de la vivienda en el Reino Unido Extracto Las cifras de los indices de precios de la vivienda en 13 regiones del Reino Unido se modelan utilizando procesos de series temporales, incluyendo varianzas condicionales. La primera conclusion es que el Reino Unido sigue a los EE UU, con varias regiones que muestran varianzas fluctuantes con el tiempo y otras con varianzas constantes. En segundo lugar, existe evidencia limitada de un componente asimetrico en seis de las siete regiones que muestran una heteroesquedacidad condicional autorregresiva. En tercer lugar, los resultados sugieren que existen tres mercados distintivos de la vivienda en el Reino Unido, basados en estructuras comunes dentro de sus procesos de media y varianza, y que el sudoeste de Inglaterra es la region que dirige las otras varianzas fluctuantes con el tiemp

Using gamma regression for photometric redshifts of survey galaxies

Machine learning techniques offer a plethora of opportunities in tackling big data within the astronomical community. We present the set of Generalized Linear Models as a fast alternative for determining photometric redshifts of galaxies, a set of tools not commonly applied within astronomy, despite being widely used in other professions. With this technique, we achieve catastrophic outlier rates of the order of ~1%, that can be achieved in a matter of seconds on large datasets of size ~1,000,000. To make these techniques easily accessible to the astronomical community, we developed a set of libraries and tools that are publicly available.Comment: Refereed Proceeding of "The Universe of Digital Sky Surveys" conference held at the INAF - Observatory of Capodimonte, Naples, on 25th-28th November 2014, to be published in the Astrophysics and Space Science Proceedings, edited by Longo, Napolitano, Marconi, Paolillo, Iodice, 6 pages, and 1 figur

Transport dynamics of ultracold atoms in a triple-well transistor-like potential

The transport of atoms is experimentally studied in a transistor-like triple-well potential consisting of a narrow gate well surrounded by source and drain wells. Atoms are initially loaded into the source well with pre-determined temperature and chemical potential. Energetic atoms flow from the source, across the gate, and into the drain where they are removed using a resonant light beam. The manifestation of atom-atom interactions and dissipation is evidenced by a rapid population growth in the initially vacant gate well. The transport dynamics are shown to depend strongly on a feedback parameter determined by the relative heights of the two barriers forming the gate region. For a range of feedback parameter values, experiments establish that the gate atoms develop a larger chemical potential and lower temperature than those in the source.Comment: 13 pages, 5 figures, accepted for publication in NJ

A stellar census of the nearby, young 32 Orionis group

The 32 Orionis group was discovered almost a decade ago and despite the fact that it represents the first northern, young (age ~ 25 Myr) stellar aggregate within 100 pc of the Sun ($d \simeq 93$ pc), a comprehensive survey for members and detailed characterisation of the group has yet to be performed. We present the first large-scale spectroscopic survey for new (predominantly M-type) members of the group after combining kinematic and photometric data to select candidates with Galactic space motion and positions in colour-magnitude space consistent with membership. We identify 30 new members, increasing the number of known 32 Ori group members by a factor of three and bringing the total number of identified members to 46, spanning spectral types B5 to L1. We also identify the lithium depletion boundary (LDB) of the group, i.e. the luminosity at which lithium remains unburnt in a coeval population. We estimate the age of the 32 Ori group independently using both isochronal fitting and LDB analyses and find it is essentially coeval with the {\beta} Pictoris moving group, with an age of $24\pm4$ Myr. Finally, we have also searched for circumstellar disc hosts utilising the AllWISE catalogue. Although we find no evidence for warm, dusty discs, we identify several stars with excess emission in the WISE W4-band at 22 {\mu}m. Based on the limited number of W4 detections we estimate a debris disc fraction of $32^{+12}_{-8}$ per cent for the 32 Ori group.Comment: Accepted for publication in MNRAS; 24 pages, 17 figures and 10 table