Parity of transversals of Latin squares

We introduce a notion of parity for transversals, and use it to show that in Latin squares of order $2 \bmod 4$, the number of transversals is a multiple of 4. We also demonstrate a number of relationships (mostly congruences modulo 4) involving $E_1,\dots, E_n$, where $E_i$ is the number of diagonals of a given Latin square that contain exactly $i$ different symbols. Let $A(i\mid j)$ denote the matrix obtained by deleting row $i$ and column $j$ from a parent matrix $A$. Define $t_{ij}$ to be the number of transversals in $L(i\mid j)$, for some fixed Latin square $L$. We show that $t_{ab}\equiv t_{cd}\bmod2$ for all $a,b,c,d$ and $L$. Also, if $L$ has odd order then the number of transversals of $L$ equals $t_{ab}$ mod 2. We conjecture that $t_{ac} + t_{bc} + t_{ad} + t_{bd} \equiv 0 \bmod 4$ for all $a,b,c,d$. In the course of our investigations we prove several results that could be of interest in other contexts. For example, we show that the number of perfect matchings in a $k$-regular bipartite graph on $2n$ vertices is divisible by $4$ when $n$ is odd and $k\equiv0\bmod 4$. We also show that $${\rm per}\, A(a \mid c)+{\rm per}\, A(b \mid c)+{\rm per}\, A(a \mid d)+{\rm per}\, A(b \mid d) \equiv 0 \bmod 4$$ for all $a,b,c,d$, when $A$ is an integer matrix of odd order with all row and columns sums equal to $k\equiv2\bmod4$

A Parametric Modeling Approach to Measuring the Gas Masses of Circumstellar Disks

The disks that surround young stars are mostly composed of molecular gas, which is harder to detect and interpret than the accompanying dust. Disk mass measurements have therefore relied on large and uncertain extrapolations from the dust to the gas. We have developed a grid of models to study the dependencies of isotopologue CO line strengths on disk structure and temperature parameters and find that a combination of 13CO and C18O observations provides a robust measure of the gas mass. We apply this technique to Submillimeter Array observations of nine circumstellar disks and published measurements of six well studied disks. We find evidence for selective photodissociation of C18O and determine masses to within a factor of about three. The inferred masses for the nine disks in our survey range from 0.7-6 M_Jup, and all are well below the extrapolation from the interstellar medium gas-to-dust ratio of 100. This is consistent with the low masses of planets found around such stars, and may be due to accretion or photoevaporation of a dust-poor upper atmosphere. However, the masses may be underestimated if there are more efficient CO depletion pathways than those known in molecular clouds and cold cores.Comment: Accepted for publication in the ApJ. 15 pages, 11 figures, full model grid (Table 3) available in the source file

Children's acquisition of science terms: does fast mapping work?

About the book: This proceedings contains 99 selected papers from the 8th Conference of the International Association for the Study of Child Language (IASCL) held in Donostia-San Sebastián in the Spanish Basque Country in July 1999. The proceedings includes the plenary addresses by Jean-Paul Bronckart, Brian MacWhinney, and Miquel Siguan. The other 96 papers are organized into sections on bilingualism, discourse, phonology, language disorders, lexicon, morphology, syntax, and signed languages. Several of these sections include symposia with introductions as well as individual papers

The triggering probability of radio-loud AGN: A comparison of high and low excitation radio galaxies in hosts of different colors

Low luminosity radio-loud active galactic nuclei (AGN) are generally found in massive red elliptical galaxies, where they are thought to be powered through gas accretion from their surrounding hot halos in a radiatively inefficient manner. These AGN are often referred to as "low-excitation" radio galaxies (LERGs). When radio-loud AGN are found in galaxies with a young stellar population and active star formation, they are usually high-power radiatively-efficient radio AGN ("high-excitation", HERG). Using a sample of low-redshift radio galaxies identified within the Sloan Digital Sky Survey (SDSS), we determine the fraction of galaxies that host a radio-loud AGN, $f_{RL}$, as a function of host galaxy stellar mass, $M_*$, star formation rate, color (defined by the 4000 \angstrom break strength), radio luminosity and excitation state (HERG/LERG). We find the following: 1. LERGs are predominantly found in red galaxies. 2. The radio-loud AGN fraction of LERGs hosted by galaxies of any color follows a $f^{LE}_{RL} \propto M^{2.5}_*$ power law. 3. The fraction of red galaxies hosting a LERG decreases strongly for increasing radio luminosity. For massive blue galaxies this is not the case. 4. The fraction of green galaxies hosting a LERG is lower than that of either red or blue galaxies, at all radio luminosities. 5. The radio-loud AGN fraction of HERGs hosted by galaxies of any color follows a $f^{HE}_{RL} \propto M^{1.5}_*$ power law. 6. HERGs have a strong preference to be hosted by green or blue galaxies. 7. The fraction of galaxies hosting a HERG shows only a weak dependence on radio luminosity cut. 8. For both HERGs and LERGs, the hosting probability of blue galaxies shows a strong dependence on star formation rate. This is not observed in galaxies of a different color.[abridged]Comment: 7 pages, 6 figure

Detoxification in rehabilitation in England: effective continuity of care or unhappy bedfellows?

There is evidence that residential detoxification alone does not provide satisfactory treatment outcomes and that outcomes are significantly enhanced when clients completing residential detoxification attend rehabilitation services (Gossop, Marsden, Stewart, & Rolfe, 1999; Ghodse, Reynolds, Baldacchino, et al., 2002). One way of increasing the likelihood of this continuity of treatment is by providing detoxification and rehabilitation within the same treatment facility to prevent drop-out, while the client awaits a rehabilitation bed or in the transition process. However, there is little research evidence available on the facilities that offer both medical detoxification and residential rehabilitation. The current study compares self-reported treatment provision in 87 residential rehabilitation services in England, 34 of whom (39.1%) reported that they offered detoxification services within their treatment programmes. Although there were no differences in self-reported treatment philosophies, residential rehabilitation services that offered detoxification were typically of shorter duration overall, had significantly more beds and reported offering more group work than residential rehabilitation services that did not offer detoxification. Outcomes were also different, with twice as many clients discharged on disciplinary grounds from residential rehabilitation services without detoxification facilities. The paper questions the UK classification of residential drug treatment services as either detoxification or rehabilitation and suggests the need for greater research focus on the aims, processes and outcomes of this group of treatment providers

The International Urban Energy Balance Comparison Project: Initial Results from Phase 2.

Many urban land surface schemes have been developed, incorporating different assumptions about the features of, and processes occurring at, the surface. Here, the first results from Phase 2 of an international comparison are presented. Evaluation is based on analysis of the last 12 months of a 15 month dataset. In general, the schemes have best overall capability to model net all-wave radiation. The models that perform well for one flux do not necessarily perform well for other fluxes. Generally there is better performance for net all wave radiation than sensible heat flux. The degree of complexity included in the models is outlined, and impacts on model performance are discussed in terms of the data made available to modellers at four successive stages

Theoretical and experimental research on parameter tracking systems Final report, 15 Jul. 1964 - Aug. 1965

Parameter tracking systems based on equation error approach for mathematical model of unknown plan