Taut distance-regular graphs and the subconstituent algebra

We consider a bipartite distance-regular graph $G$ with diameter $D$ at least 4 and valency $k$ at least 3. We obtain upper and lower bounds for the local eigenvalues of $G$ in terms of the intersection numbers of $G$ and the eigenvalues of $G$. Fix a vertex of $G$ and let $T$ denote the corresponding subconstituent algebra. We give a detailed description of those thin irreducible $T$-modules that have endpoint 2 and dimension $D-3$. In an earlier paper the first author defined what it means for $G$ to be taut. We obtain three characterizations of the taut condition, each of which involves the local eigenvalues or the thin irreducible $T$-modules mentioned above.Comment: 29 page

The Uses and Abuses of the Euro in the Canadian Currency Debate. Jean Monnet/Robert Schuman Paper Series, Vol. 3 No. 3, August 2003

(From the introduction). In the late 1990s, some prominent Canadian economists – notably Thomas Courchene, Herbert Grubel, Richard Harris, and Robert Mundell – began arguing that a North American common currency would solve the problems underlying the growing gap between U.S. and Canadian real GDP per capita.1 They succeeded in provoking a lively economic policy debate that occurred in parallel with the launch of the euro. The purpose of this paper is to examine the uses – and abuses – of European parallels by both sides in the economic policy debate that peaked in the 1999-2001 period. The body of the paper begins by providing an understanding of the European case. Hence, the second section outlines our interpretation of the major developments in the birth of the euro. The third section, the core of the paper, examines in detail the use of European parallels in the Canadian currency debate. We start by providing a brief overview of the protagonists in the debate. We then continue by arguing that the euro provided a “temporal spur” for the Canadian discussion but that it was only one among several important factors. We argue further that the proponents of a North American common currency relied very little on the European experience to support their case for the need for a common currency. Where they did use the European experience, however, was in their analysis of the institutional form that a common currency in North America might take. We argue that the opponents of a North American common currency were correct in viewing this as an abuse of the European parallel. In the concluding fourth section, we summarize our findings and argue that the most important parallel between the European and North American forces for a common currency is that both were driven primarily by politics

Household Size Economies: Malaysian Evidence

People live in households with different size and composition and they consume a variety of goods; categorised as private and public goods. With the existence of public goods in the household, doubling the household size need not increase the consumption expenditure twofold to maintain the same standard of living. Using households’ per capita expenditure from the Household Expenditure Survey 2004-2005, we estimate the household size economies indices for household consumption goods through the Seemingly Unrelated Regression. The results suggested that the lower income households enjoy savings from a wider range of public goods compared to the higher income households.Household size economies, Seemingly Unrelated Regression, household composition, public goods, Malaysia.

The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme

Let $Y$ denote a $D$-class symmetric association scheme with $D \geq 3$, and suppose $Y$ is almost-bipartite P- and Q-polynomial. Let $x$ denote a vertex of $Y$ and let $T=T(x)$ denote the corresponding Terwilliger algebra. We prove that any irreducible $T$-module $W$ is both thin and dual thin in the sense of Terwilliger. We produce two bases for $W$ and describe the action of $T$ on these bases. We prove that the isomorphism class of $W$ as a $T$-module is determined by two parameters, the dual endpoint and diameter of $W$. We find a recurrence which gives the multiplicities with which the irreducible $T$-modules occur in the standard module. We compute this multiplicity for those irreducible $T$-modules which have diameter at least $D-3$.Comment: 22 page

Efficacy of Reported Issue Times as a Means for Effort Estimation

Software effort is a measure of manpower dedicated to developing and maintaining and software. Effort estimation can help project managers monitor their software, teams, and timelines. Conversely, improper effort estimation can result in budget overruns, delays, lost contracts, and accumulated Technical Debt (TD). Issue Tracking Systems (ITS) have become mainstream project management tools, with over 65,000 companies using Jira alone. ITS are an untapped resource for issue resolution effort research. Related work investigates issue effort for specific issue types, usually Bugs or similar. They model their developer-documented issue resolution times using features from the issues themselves. This thesis explores a novel issue effort estimation and prediction approach using developer-documented ITS effort in tandem with implementation metrics (commit metrics, package metrics, refactoring metrics, and smell metrics). We find consistent correlations between ITS effort and implementation metrics, ranging from weak to moderate strength. We also construct and evaluate several exploratory models to predict future package effort using our novel effort estimation, with inconclusive results