Moments of Inertia and Graph Separators

Graphs that arise from the finite element or finite difference methods often include geometric information such as the coordinates of the nodes of the graph. The geometric separator algorithm of Miller, Teng, Thurston, and Vavasis uses some of the available geometric information to find small node separators of graphs. The algorithm utilizes a random sampling technique based on the uniform distribution to find a good separator. We show that sampling from an elliptic distribution based on the inertia matrix of the graph can significantly improve the quality of the separator. More generally, given a cost function f on the unit d-sphere Ud, we can define an elliptic distribution based on the second moments of f. The expectation of f with respect to the elliptic distribution is less than or equal to the expectation with respect to the uniform distribution, with equality only in degenerate cases. We also demonstrate experimentally that the benefit gained by the use of the additional geometric information is significant. Some previous algorithms have used the moments of inertia heuristically, and suffer from extremely poor worst case performance. This is the first result, to our knowledge, that incorporates the moments of inertia into a provably good strategy.     

Immigrants' Language Skills: The Australian Experience in a Longitudinal Survey

This article is concerned with the determinants of English language proficiency (speaking, reading and writing) among immigrants. It presents a model of immigrant destination language proficiency based on economic incentives, exposure to the destination language, and efficiency in second language acquisition. A unique data set, the Longitudinal Survey of Immigrants to Australia, is used to test the model. This survey had three waves, at about six months, eighteen months and three‐and‐a‐half years after immigration. The analyses are performed by wave, type of language skill and gender using probit analysis. Bivariate probit analysis is used across waves. The hypotheses are supported by the data. The bivariate probit analysis indicates a positive correlation in the unexplained component that declines with time between waves, suggesting a “regression to the mean” in the unobserved components of English language proficiency.     

Estate Inheritance: A Sociological Lacuna*

Estate inheritance, a frequently mentioned but rarely examined feature of stratification systems, has been a neglected area of research in sociology. In this paper, several possible causes of the sociological neglect are discussed. The treatment of inheritance patterns in functionalist and conflict theories of stratification is analyzed, and an overview of existing research on inheritance is presented. Finally, a conflict theory of stratification that incorporates the phenomenon of inheritance is proposed, and avenues for further research are suggested.     

Editorial

Publication of these conference papers on the theme of communitydevelopment in the ‘new’ Europe comes at a particularlysignificant moment as the people of different ‘old’European nation states     

THE McMASTER FAMILY ASSESSMENT DEVICE: RELIABILITY AND VALIDITY*

This paper reports a series of studies investigating the reliability and validity of the McMaster Family Assessment Device (FAD). The results indicated that the FAD has: (a) adequate test-retest reliability, (b) low correlations with social desirability, (c) moderate correlations with other self-report measures of family functioning, and (d) differentiates significantly between clinician-rated healthy and unhealthy families. Cut-off scores for identifying healthy and unhealthy families also were developed which have adequate sensitivity and specificity. Additionally, the relationships between the FAD, Family Unit Inventory, and FACES-II suggests that the cohension and adaptability scales from the FACES-II have a linear relationship with health/pathology.