Maximal increasing sequences in fillings of almost-moon polyominoes

It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino that do not contain a northeast chain of size $k$ depends only on the set of columns of the polyomino, but not the shape of the polyomino. Rubey's proof is an adaption of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. In this paper we present a bijective proof for this result by considering fillings of almost-moon polyominoes, which are moon polyominoes after removing one of the rows. Explicitly, we construct a bijection which preserves the size of the largest northeast chains of the fillings when two adjacent rows of the polyomino are exchanged. This bijection also preserves the column sum of the fillings. We also present a bijection that preserves the size of the largest northeast chains, the row sum and the column sum if every row of the fillings has at most one 1.Comment: 18 page

An analysis of the general content, grade placement, and philosophy of state courses of study in arithmetic for grades one to six.

Thesis (Ed.M.)--Boston Universit

The Scottish school leavers cohort: linkage of education data to routinely collected records for mortality, hospital discharge and offspring birth characteristics

Purpose: The Scottish school leavers cohort provides population-wide prospective follow-up of local authority secondary school leavers in Scotland through linkage of comprehensive education data with hospital and mortality records. It considers educational attainment as a proxy for socioeconomic position in young adulthood and enables the study of associations and causal relationships between educational attainment and health outcomes in young adulthood. Participants: Education data for 284 621 individuals who left a local authority secondary school during 2006/2007–2010/2011 were linked with birth, death and hospital records, including general/acute and mental health inpatient and day case records. Individuals were followed up from date of school leaving until September 2012. Age range during follow-up was 15 years to 24 years. Findings: to date Education data included all formal school qualifications attained by date of school leaving; sociodemographic information; indicators of student needs, educational or non-educational support received and special school unit attendance; attendance, absence and exclusions over time and school leaver destination. Area-based measures of school and home deprivation were provided. Health data included dates of admission/discharge from hospital; principal/secondary diagnoses; maternal-related, birth-related and baby-related variables and, where relevant, date and cause of death. This paper presents crude rates for all-cause and cause-specific deaths and general/acute and psychiatric hospital admissions as well as birth outcomes for children of female cohort members. Future plans: This study is the first in Scotland to link education and health data for the population of local authority secondary school leavers and provides access to a large, representative cohort with the ability to study rare health outcomes. There is the potential to study health outcomes over the life course through linkage with future hospital and death records for cohort members. The cohort may also be expanded by adding data from future school leavers. There is scope for linkage to the Prescribing Information System and the Scottish Primary Care Information Resource

Quasifinite representations of classical Lie subalgebras of W_{1+infty}

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight representations of the central extension \hat{D}^{\pm} of the Lie subalgebra of this algebra fixed by - sigma_{\pm}, and find the unitary ones. We realize them in terms of highest weight representations of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the truncated polynomial algebra C[u] / (u^{m+1}) and its classical Lie subalgebras of B, C and D types. Character formulas for positive primitive representations of \hat{D}^{\pm} (including all the unitary ones) are obtained. We also realize a class of primitive representations of \hat{D}^{\pm} in terms of free fields and establish a number of duality results between these primitive representations and finite-dimensional irreducible representations of finite-dimensional Lie groups and supergroups. We show that the vacuum module V_c of \hat{D}^+ carries a vertex algebra structure and establish a relationship between V_c for half-integral central charge c and W-algebras.Comment: Latex, 77 page

A Reconsideration of the Effects of Unionism on Relative Wages and Employment in the United States, 1920-80

H. Gregg Lewis' estimates of the relative wage effect of unionism between 1920 and 1958 are routinely cited though they have rarely been subject to scrutiny. This paper extends Lewis' data to 1980 and, in particular, we construct a series on union membership that links up with the data available in the 1970's from the Current Population Surveys. We proceed to reexamine the effects of trade unions both on relative wages and on relative man hours worked.Our estimates of the relative wage effect are similar to Lewis' though these are not measured with precision and a wide range of estimates are consistent with the results. With respect to the effect of unionism on relative man hours worked, we are not at all satisfied that the analysis of these data clearly points to the existence of a negative effect.

How and why do South Asians attend GUM clinics? Evidence from contrasting GUM clinics across England

Background: Improving access to sexual healthcare is a priority in the UK, especially for ethnic minorities. Though South Asians in the UK report low levels of sexual ill health, few data exist regarding their use of genitourinary medicine (GUM) services. Objectives: To describe reasons for attendance at GUM clinics among individuals of South Asian origin relative to patients of other ethnicities. Methods: 4600 new attendees (5% South Asian; n=226) at seven sociodemographically and geographically contrasting GUM clinics across England completed a questionnaire between October 2004 and March 2005, which were linked to routine clinical data. Results: South Asians were more likely than other groups to be signposted to the GUM clinic by another health service-for example, in women 14% versus 8% respectively (p=0.005) reported doing so from a family planning clinic. These women also reported that they would be less likely to go to the clinic if their symptoms resolved spontaneously compared with other women (51% vs 31%, p=0.024). However, relative to other clinic attendees, no differences in the proportions of South Asians who had acute STI(s) diagnosed at clinic were noted. Furthermore, South Asian men were more likely to report as their reason for attendance that they wanted an HIV test (23.4% vs 14.8%, p=0.005). Conclusion: Despite having similar STI care needs to attendees from other ethnic groups, South Asians, especially women, may be reluctant to seek care from GUM clinics, especially if their symptoms resolve. Sexual health services need to develop locally-delivered and culturally-appropriate initiatives to improve care pathways