Asymptotic enumeration of incidence matrices

We discuss the problem of counting {\em incidence matrices}, i.e. zero-one matrices with no zero rows or columns. Using different approaches we give three different proofs for the leading asymptotics for the number of matrices with $n$ ones as $n\to\infty$. We also give refined results for the asymptotic number of $i\times j$ incidence matrices with $n$ ones.Comment: jpconf style files. Presented at the conference "Counting Complexity: An international workshop on statistical mechanics and combinatorics." In celebration of Prof. Tony Guttmann's 60th birthda

Detecting a rotation in the epsilon Eridani debris disc

The evidence for a rotation of the epsilon Eridani debris disc is examined. Data at 850 micron wavelength were previously obtained using the Submillimetre Common User Bolometer Array (SCUBA) over periods in 1997-1998 and 2000-2002. By chi-square fitting after shift and rotation operations, images from these two epochs were compared to recover proper motion and orbital motion of the disc. The same procedures were then performed on simulated images to estimate the accuracy of the results. Minima in the chi-square plots indicate a motion of the disc of approximately 0.6'' per year in the direction of the star's proper motion. This underestimates the true value of 1'' per year, implying that some of the structure in the disc region is not associated with epsilon Eridani, originating instead from background galaxies. From the chi-square fitting for orbital motion, a counterclockwise rotation rate of ~2.75 degrees per year is deduced. Comparisons with simulated data in which the disc is not rotating show that noise and background galaxies result in approximately Gaussian fluctuations with a standard deviation +/-1.5 degrees per year. Thus counterclockwise rotation of disc features is supported at approximately a 2-sigma level, after a 4-year time difference. This rate is faster than the Keplerian rate of 0.65 degrees per year for features at ~65 AU from the star, suggesting their motion is tracking a planet inside the dust ring. Future observations with SCUBA-2 can rule out no rotation of the epsilon Eridani dust clumps with ~4-sigma confidence. Assuming a rate of about 2.75 degrees per year, the rotation of the features after a 10-year period could be shown to be >1 degree per year at the 3-sigma level.Comment: 8 pages, 6 figure

Rotation in the Orion Nebula Cluster

Eighteen fields in the Orion Nebula Cluster (ONC) have been monitored for one or more observing seasons from 1990-99 with a 0.6-m telescope at Wesleyan University. Photometric data were obtained in Cousins I on 25-40 nights per season. Results from the first 3 years of monitoring were analyzed by Choi & Herbst (1996; CH). Here we provide an update based on 6 more years of observation and the extensive optical and IR study of the ONC by Hillenbrand (1997) and Hillenbrand et al. (1998). Rotation periods are now available for 134 ONC members. Of these, 67 were detected at multiple epochs with identical periods by us and 15 more were confirmed by Stassun et al. (1999) in their study of Ori OBIc/d. The bimodal period distribution for the ONC is confirmed, but we also find a clear dependence of rotation period on mass. This can be understood as an effect of deuterium burning, which temporarily slows the contraction and thus spin-up of stars with M <0.25 solar masses and ages of ~1 My. Stars with M <0.25 solar masses have not had time to bridge the gap in the period distribution at ~4 days. Excess H-K and I-K emission, as well as CaII infrared triplet equivalent widths (Hillenbrand et al. 1998), show weak but significant correlations with rotation period among stars with M >0.25 solar masses. Our results provide new observational support for the importance of disks in the early rotational evolution of low mass stars. [abridged]Comment: 18 pages of text, 17 figures, and 4 tables; accepted for publication in The Astronomical Journa

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

Temporal fluctuations in the differential rotation of cool active stars

This paper reports positive detections of surface differential rotation on two rapidly rotating cool stars at several epochs, by using stellar surface features (both cool spots and magnetic regions) as tracers of the large scale latitudinal shear that distorts the convective envelope in this type of stars. We also report definite evidence that this differential rotation is different when estimated from cool spots or magnetic regions, and that it undergoes temporal fluctuations of potentially large amplitude on a time scale of a few years. We consider these results as further evidence that the dynamo processes operating in these stars are distributed throughout the convective zone rather than being confined at its base as in the Sun. By comparing our observations with two very simple models of the differential rotation within the convective zone, we obtain evidence that the internal rotation velocity field of the stars we investigated is not like that of the Sun, and may resemble that we expect for rapid rotators. We speculate that the changes in differential rotation result from the dynamo processes (and from the underlying magnetic cycle) that periodically converts magnetic energy into kinetic energy and vice versa. We emphasise that the technique outlined in this paper corresponds to the first practical method for investigating the large scale rotation velocity field within convective zones of cool active stars, and offers several advantages over asteroseismology for this particular purpose and this specific stellar class.Comment: 14 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

Magnetic activity on AB Doradus: Temporal evolution of starspots and differential rotation from 1988 to 1994

Surface brightness maps for the young K0 dwarf AB Doradus are reconstructed from archival data sets for epochs spanning 1988 to 1994. By using the signal-to-noise enhancement technique of Least-Squares Deconvolution, our results show a greatly increased resolution of spot features than obtained in previously published surface brightness reconstructions. These images show that for the exception of epoch 1988.96, the starspot distributions are dominated by a long-lived polar cap, and short-lived low to high latitude features. The fragmented polar cap at epoch 1988.96 could indicate a change in the nature of the dynamo in the star. For the first time we measure differential rotation for epochs with sufficient phase coverage (1992.05, 1993.89, 1994.87). These measurements show variations on a timescale of at least one year, with the strongest surface differential rotation ever measured for AB Dor occurring in 1994.86. In conjunction with previous investigations, our results represent the first long-term analysis of the temporal evolution of differential rotation on active stars.Comment: accepted by MNRAS 18 pages 18 figure