On tree representations of relations and graphs: symbolic ultrametrics and cograph edge decompositions

Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g. in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics define an edge-colored complete graph that allows to represent the topology of this graph as a vertex-colored tree. Here, we are interested in the structure and the complexity of certain combinatorial problems resulting from considerations based on symbolic ultrametrics, and on algorithms to solve them.This includes, the characterization of symbolic ultrametrics that additionally distinguishes between edges and non-edges of arbitrary edge-colored graphs G and thus, yielding a tree representation of G, by means of so-called cographs. Moreover, we address the problem of finding “closest” symbolic ultrametrics and show the NP-completeness of the three problems: symbolic ultrametric editing, completion and deletion. Finally, as not all graphs are cographs, and hence, do not have a tree representation, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of an arbitrary non-cograph G. This is equivalent to find an optimal cograph edge k-decomposition \(\{E_1,\dots ,E_k\}\) of E so that each subgraph \((V,E_i)\) of G is a cograph. We investigate this problem in full detail, resulting in several new open problems, and NP-hardness results.For all optimization problems proven to be NP-hard we will provide integer linear program formulations to solve them.     

Capturing hearts and minds: The influence of relational identification with the leader on followers' mobilization and cardiovascular reactivity

The influence of relational identification (RI) on leadership processes and the effects of social identity leadership on followers' responses to stress have received scant theoretical and research attention. The present research advances theoretical understanding by testing the assertion that high RI with the leader drives follower mobilization of effort and psychophysiological responses to stress. Two experimental scenario studies (Study 1 and Study 2) support the hypothesis that being led by an individual with whom followers perceive high RI increases follower intentional mobilization. Study 2 additionally showed that high (vs. low) RI increases follower resource appraisals and cognitive task performance. A laboratory experiment (Study 3) assessing cardiovascular (CV) reactivity showed that, compared to neutral (i.e., non-affiliated) leadership, being led by an individual with whom participants felt low RI elicited a maladaptive (i.e., threat) response to a pressurized task. In addition, relative to the low RI and neutral conditions, high RI with the leader did not engender greater challenge or threat reactivity. In conclusion, advancing social identity leadership and challenge and threat theory, findings suggest that leaders should be mindful of the deleterious effects (i.e., reduced mobilization and greater threat state) of low RI to optimize follower mobilization of effort and psychophysiological responses to stress.     

Group betweenness and co-betweenness: Inter-related notions of coalition centrality

Vertex betweenness centrality is a metric that seeks to quantify a sense of the importance of a vertex in a network in terms of its ‘control’ on the flow of information along geodesic paths throughout the network. Two natural ways to extend vertex betweenness centrality to sets of vertices are (i) in terms of geodesic paths that pass through at least one of the vertices in the set, and (ii) in terms of geodesic paths that pass through all vertices in the set. The former was introduced by Everett and Borgatti [Everett, M., Borgatti, S., 1999. The centrality of groups and classes. Journal of Mathematical Sociology 23 (3), 181–201], and called group betweenness centrality. The latter, which we call co-betweenness centrality here, has not been considered formally in the literature until now, to the best of our knowledge. In this paper, we show that these two notions of centrality are in fact intimately related and, furthermore, that this relationship may be exploited to obtain deeper insight into both. In particular, we provide an expansion for group betweenness in terms of increasingly higher orders of co-betweenness, in a manner analogous to the Taylor series expansion of a mathematical function in calculus. We then demonstrate the utility of this expansion by using it to construct analytic lower and upper bounds for group betweenness that involve only simple combinations of (i) the betweenness of individual vertices in the group, and (ii) the co-betweenness of pairs of these vertices. Accordingly, we argue that the latter quantity, i.e., pairwise co-betweenness, is itself a fundamental quantity of some independent interest, and we present a computationally efficient algorithm for its calculation, which extends the algorithm of Brandes [Brandes, U., 2001. A faster algorithm for betweenness centrality. Journal of Mathematical Sociology 25, 163] in a natural manner. Applications are provided throughout, using a handful of different communication networks, which serve to illustrate the way in which our mathematical contributions allow for insight to be gained into the interaction of network structure, coalitions, and information flow in social networks.     

The Gender Pay Gap in the US: Does Sector Make a Difference?

Analyses of data from the 2000 US Census show that the gender pay gap differs by sector of employment and according to the part of the earnings distribution that is considered. The gender pay differential in the private sector in the US does not display either the glass ceiling or sticky floor effects that have been reported for many other countries. The government sector is, however, characterized by a distinct sticky floor effect in the female–male pay differential. Regardless of the sector of employment, females have lower hourly rates of pay than men across the entire earnings distribution.

Social Problems Work: The Cases of Children and Youth

This article reviews the literature on social problems work concerned with children and young people. Social problems work involves assessing particular people, events and circumstances as instances of social problems. We focus on how social problems work is organized within discourses of childhood and youth, how it is a site for holding children and young people accountable, and how normalization is an aspect of social problems work. Our review brings together analytic themes in the literature on social problems and that on children and young people. We also point to topics that might be elaborated upon in future research on social problems work concerned with children and young people.     

Identity Formation in Children and Young People in Open Adoptions from Out-of-home Care in New South Wales,Australia

Semi-structured interviews were used to explore identity development for nine adoptees (aged 9–23 years) who were adopted by their foster carers in New South Wales, Australia. Adoptions were open, with court-ordered face-to-face contact with birth families. Findings suggest that participants had healthy adoptive identities, with coherent and meaningful narratives about their life histories. Adoption provided a sense of security and belonging. Openness provided information to build a self-narrative and encouraged discussion of adoption issues within adoptive families. Adoptive parents were critical in helping children understand their adoption and facilitating direct contact with birth families, thus laying foundations for positive identity development.     

On the characterization of weighted simple games

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.