Distribution of angles between unit vectors and the multiple comparison problem for unit vectors

We suppose that L x i = Fq(μi, KiK) for i=1,...,p, where the independent Fisher distributions on the unit sphere in Rq have modal vectors μi and known concentrations KiK, where K will be large—in fact, to obtain asymptotic distributions, we will let K tend to infinity. The term x'iXj=cos 0ij estimates cos 0ij= μiμy. The asymptotic joint distribution of the terms will be studied when all the vectors μi μ are distinct, and for the special case when all the vectors μi=μ, so that all the terms are zero. These very different results have a variety of applications as well as being interesting in themselves. One of these applications is the 'multiple comparisons problem' for unit vectors. However, it was found necessary to give here a different way of solving this problem.     

SHORT REVIEWS

Books reviewed in this article: Chris Beyrer, War in the Blood: Sex, Politics and AIDS in Southeast Asia Caroline H. Bledsoe et al. (eds.), Critical Perspectives on Schooling and Fertility in the Developing World Donald J. Hernandez and Evan Charney (eds)., From Generation to Generation: The Health and Well-Being of Children in Immigrant Families Nana Poku and David T. Graham (eds.), Redefining Security: Population Movements and National Security Jyoti Shankar Singh, Creating a New Consensus on Population Jael Silliman and Ynestra King (eds.), Dangerous Intersections: Feminist Perspectives on Population, Environment, and Development; A Project of the Committee on Women, Population, and the Environment Michael S. Teitelbaum and Jay Winter, A Question of Numbers: High Migration, Low Fertility, and the Politics of National Identity United Nations Department of Economic and Social Affairs, Population Division, World Population Monitoring 1997 Anthony Young, Land Resources: Now and for the Future     

Learning from genocide? A study in the failure of Holocaust education

The importance of learning lessons from the Holocaust and from the mass slaughter in Rwanda was recognised in the theme underpinning Britain's Holocaust Memorial Day in 2004. This article is principally concerned with the lessons learnt from the Holocaust by a culturally diverse group of students aged 14 to 16. They all attended schools in an outer London borough and were interviewed after taking part in a local event held to mark the 2004 commemoration. The article concludes with a discussion of the main findings of the investigation.     

Franklin D. Roosevelt's Shangri-La: foreshadowing the Independent Living Movement in Warm Springs, Georgia, 1926-1945

American President Franklin Delano Roosevelt is well known to have disguised and minimized his disability in his role as a political leader. Less well known is the remarkable nature of the colony he established for people with disabilities from polio in Warm Springs, Georgia in the 1920s, 1930s and 1940s. The colony at Warm Springs represents a unique historical community in which disability was not stigmatized; where people with disabilities controlled their own resources and their own lives; and where the medical model of disability was repudiated. As such, the Warm Springs community represents a remarkable period and place in disability history that warrants continued study. New evidence drawn from the archives of the Roosevelt Warm Springs Institute for Rehabilitation, the FDR Presidential Library in Hyde Park, New York and the personal scrapbooks of former residents of the Warm Springs colony provides further support for the theory that FDR's Warm Springs colony represented an early precursor to the philosophies and values promoted by the Independent Living Movement that emerged 50 years later. The Warm Springs colony offered an unprecedented approach to rehabilitation and independent living for people with disabilities from polio in the 1920s, 1930s and 1940s, and because of this provides an invaluable lesson from history that deserves ongoing attention.     

Local Understanding of Fish Consumption Advisory Risks in Michigan's Upper Peninsula: The Role of Structure,Culture, and Agency*

Abstract Fish consumption advisories fail to adequately help communities address the benefits and risks of eating potentially contaminated fish. We engaged community members and relevant institutions in identifying and implementing more effective risk communication in Michigan's rural Upper Peninsula. In 2004–2005, we collected data in four Michigan counties through focus groups, community dinners, public meetings and angler interviews. Residents express a strong affinity toward eating Great Lakes fish, though a minority of participants have read the official fish advisory. Participants lack an understanding of how bioaccumulation affects consumption risk depending on the type of contaminant. We attribute the situation to conditions of post‐normal risk that emerge through interaction of the structural dimensions of science and bureaucracy with a strong natural resource‐based culture that affects the agency of residents. The implications loom large as Michigan's Department of Community Health no longer distributes hard copies of the Michigan Fish Advisory.     

Change and Paradox in Family Therapy

This paper shows that when the interpersonal context in a family alters, solutions which have previously been successful may paradoxically increase the family's difficulties rather than resolve them. Therapy minors this process, in that when the family system is flexible, “commonsense” interventions may be effective, whereas with a rigid dysfunctional family system therapeutic interventions may be necessary which, among other things, paradoxically imply that no change is required. Some concepts derived from Watzlawick, Weakland and Fish are redefined and the mathematical group theory used by these authors is replaced by system theory in combination with the theory of logical types. A “behaviour disorder” family is used to illustrate the paradoxical mode of symptom development and also the use of a number of paradoxical therapeutic interventions. Possible reasons for the therapeutic power of these interventions are discussed; the concept of first and second order therapeutic paradoxes is introduced.     

Stochastic blockmodels: First steps

A stochastic model is proposed for social networks in which the actors in a network are partitioned into subgroups called blocks. The model provides a stochastic generalization of the blockmodel. Estimation techniques are developed for the special case of a single relation social network, with blocks specified a priori. An extension of the model allows for tendencies toward reciprocation of ties beyond those explained by the partition. The extended model provides a one degree-of-freedom test of the model. A numerical example from the social network literature is used to illustrate the methods.     

Record values and the geometric distribution

Suppose {X_n, n≥1} is a sequence of independent and identically distributed discrete random variables having the common distribution function F(x). The exact distribution of the n-th record value is given under the assumption that F(x) has the geometric distribution. Various properties of the record values and some new characterizations of the geometric distribution are presented.