Graph and semigroup homomorphisms on networks of relations

The algebraic definitions presented here are motivated by our search for an adequate formalization of the concepts of social roles as regularities in social network patterns. The theorems represent significant homomorphic reductions of social networks which are possible using these definitions to capture the role structure of a network. The concepts build directly on the pioneering work of S.F. Nadel (1957) and the pathbreaking approach to blockmodeling introduced by Lorrain and White (1971) and refined in subsequent years (White, Boorman and Breiger 1976;Boorman and White 1976; Arabie, Boorman and Levitt, 1978; Sailer, 1978).Blockmodeling is one of the predominant techniques for deriving structural models of social networks. When a network is represented by a directed multigraph, a blockmodel of the multigraph can be characterized as mapping points and edges onto their images in a reduced multigraph. The relations in a network or multigraph can also be composed to form a semigroup.In the first part of the paper we examine “graph” homomorphisms, or homomorphic mappings of the points or actors in a network. A family of basic concepts of role equivalence are introduced, and theorems presented to show the structure preserving properties of their various induced homomorphisms. This extends the “classic” approach to blockmodeling via the equivalence of positions.Lorrain and White (1971), Pattison (1980), Boyd, 1980, Boyd, 1982, and most recently Bonacich (1982) have explored the topic taken up in the second part of this paper, namely the homomorphic reduction of the semigroup of relations on a network, and the relation between semigroup and graph homomorphisms. Our approach allows us a significant beginning in reducing the complexity of a multigraph by collapsing relations which play a similar “role” in the network.     

Imagining Sevastopol: history and postwar community construction, 1942–1953

By exploring the reconstruction of the city of Sevastopol after the Second World War and the memorialisation that accompanied this process, this article seeks to examine the identities embedded into this process, particularly the relationship between local and Soviet identities.     

A Review of: “Crossing Sexual Boundaries: Transgender Journeys,Uncharted Paths. Edited by J. Ari Kane-DeMaios & Vern L. Bullough.”

THE SEXUAL VICTIMIZATION OF CHILDREN. Mary de Young. Jefferson, NC: McFarland &; Company, 1982; 179 pages; $18.95.

“FEMININITY,” “MASCULINITY,” AND “ANDROGYNY” A Modern Philosophical Discussion. Mary Vetterling‐Braggin (Ed.). Totowa, NJ: Littlefield, Adams, &; Co., 1982; 326 pages; $8.95.

IMPOTENCE: Physiological, Psychological, Surgical Diagnosis and Treatment. Gorm Wagner and Richard Green. New York: Plenum Press, 1981; 182 pages; $24.50.

Bullough, V. L. Age at Menarche: A Misunderstanding. Science 1981, 213, 365–366.     

Choice under complete uncertainty when outcome spaces are state dependent

One central objection to the maximin payoff criterion is that it focuses on the state that yields the lowest payoffs regardless of how low these are. We allow different states to have different sets of possible outcomes and show that the original axioms of Milnor (1954) continue to characterize the maximin payoff criterion, provided that the sets of payoffs achievable across states overlap. If instead payoffs in some states are always lower than in all others then ignoring the “bad” states is no longer inconsistent with these axioms. Similar dependence on overlap of outcome spaces across states holds for the minimax regret and maximin joy criteria.      

The effect of infrequent trading on detecting price jumps

The subject of the present study is to analyze how accurately an elaborated price jump detection methodology by Barndorff-Nielsen and Shephard (J. Financ. Econom. 2:1–37, 2004a; 4:1–30, 2006) applies to financial time series characterized by less frequent trading. In this context, it is of primary interest to understand the impact of infrequent trading on two test statistics, applicable to disentangle contributions from price jumps to realized variance. In a simulation study, evidence is found that infrequent trading induces a sizable distortion of the test statistics towards overrejection. A new empirical investigation using high frequency information of the most heavily traded electricity forward contract of the Nord Pool Energy Exchange corroborates the evidence of the simulation. In line with the theory, a “zero-return-adjusted estimation” is introduced to reduce the bias in the test statistics, both illustrated in the simulation study and empirical case.     

Estrangement Between Mothers and Adult Children: The Role of Norms and Values

Relationships between mothers and their children are expected to be lifelong and rewarding for both members of the dyad. Because of the salience of these ties, they are likely to be disrupted only under conditions of extreme relational tension and dissatisfaction. In this work, the authors drew on theoretical arguments regarding societal norm violations and value similarity to examine the processes that lead to estrangement between mothers and adult children. To address this issue, they used quantitative and qualitative data on 2,013 mother–adult child dyads nested within 561 later life families, including 64 in which mothers reported being estranged from at least 1 of their children. Value dissimilarity was found to be a strong predictor of estrangement, whereas violation of serious societal norms was not. Qualitative data revealed that value dissimilarity created severe relational tension between mothers and adult children leading to estrangement.