On the kidney exchange problem: cardinality constrained cycle and chain problems on directed graphs: a survey of integer programming approaches

The Kidney Exchange Problem (KEP) is a combinatorial optimization problem and has attracted the attention from the community of integer programming/combinatorial optimisation in the past few years. Defined on a directed graph, the KEP has two variations: one concerns cycles only, and the other, cycles as well as chains on the same graph. We call the former a Cardinality Constrained Multi-cycle Problem (CCMcP) and the latter a Cardinality Constrained Cycles and Chains Problem (CCCCP). The cardinality for cycles is restricted in both CCMcP and CCCCP. As for chains, some studies in the literature considered cardinality restrictions, whereas others did not. The CCMcP can be viewed as an Asymmetric Travelling Salesman Problem that does allow subtours, however these subtours are constrained by cardinality, and that it is not necessary to visit all vertices. In existing literature of the KEP, the cardinality constraint for cycles is usually considered to be small (to the best of our knowledge, no more than six). In a CCCCP, each vertex on the directed graph can be included in at most one cycle or chain, but not both. The CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights, particularly due to their similarities to some travelling salesman- and vehicle routing-family of problems. In this paper, our main focus is to review the existing mathematical programming models and solution methods in the literature, analyse the performance of these models, and identify future research directions. Further, we propose a polynomial-sized and an exponential-sized mixed-integer linear programming model, discuss a number of stronger constraints for cardinality-infeasible-cycle elimination for the latter, and present some preliminary numerical results.     

Was <Emphasis Type="Italic">that</Emphasis> Racist? An Experimental Study of Microaggression Ambiguity and Emotional Reactions for Racial–Ethnic Minority and White Individuals

This study examined racial–ethnic minority and white identified participants’ perceptions of racial microaggressions in four video scenarios involving a white professor and a black student. Participants (N = 261) were randomly assigned to observe a one of the four video conditions. The video involved an interaction with no microaggression, a very ambiguous microaggression, an ambiguous microaggression, or an overt microaggression. Participants rated their observations of (a) negative emotions toward the committer (white professor) and receiver (black student) of the microaggression, (b) positive emotions toward the committer and receiver of the microaggression, (c) perceptions on the degree of biasedness of committer, and (d) degree of positive perceptions of the committer. Analysis compared ratings of two groups, including racial–ethnic minority and white observers. We found a significant difference between the overt condition and other three conditions on negative emotions, positive emotions, and attributions of the professor (i.e., cultural biasedness and positive perceptions). However, there were no differences between the no microaggression, very ambiguous, and ambiguous conditions. No significant differences between racial–ethnic minority and white participants’ ratings were detected. Implications for training, practice, and future research are offered in our discussion.     

Who is More Likely to “Not See Race”? Individual Differences in Racial Colorblindness

Many Americans endorse a colorblind racial ideology, meaning they strive to “not see race” and emphasize sameness and equal distribution of resources across racial lines. Currently, there is an absence of studies examining the personality and individual difference correlates of racial colorblindness. The current study investigated the association between three different aspects of racial colorblindness (unawareness of racial privilege, unawareness of institutional discrimination, and unawareness of blatant racism) and the Big 5, empathy, and aggression in white undergraduates. Our results revealed two divergent patterns. Unawareness of racial privilege was related to lower openness and perspective taking, but more empathic concern, whereas unawareness of blatant racism and unawareness of institutional discrimination were related to lower agreeableness, perspective taking, and empathic concern. These results are discussed in relation to the broader literature on prejudice and personality.     

Immigrant Latino Families Saving Against Great Odds: The Case of CSAs and the Prosperity Kids Program

Children’s savings account programs are interventions that seek to engage disadvantaged children and their families in early college saving, cultivate college-saver identities, and reduce disparities in educational and economic outcomes. Existing research has revealed positive effects of CSAs on children’s outcomes, but questions remain about how and for whom CSAs facilitate these outcomes. This study uses account data from 493 accountholders and findings from interviews with 50 participants to examine asset accumulation and savings experiences among mostly low income, Latino families in New Mexico’s Prosperity Kids CSA program. One-third of the families made a deposit into their child’s account designated as “savers” with a median total contribution of $123 and a median account balance, including initial seed deposit, of $345. Longer duration of program enrollment and fewer number of unexcused absences predicted savers status. Qualitative findings highlight emerging college-saver identities, viewed through the framework of identity-based motivation, understood to include salience, normalization of difficulty, and group congruence. Qualitative interview data further suggest that initial seed money, deposit incentives, and withdrawal restrictions were important influences on participants’ saving. These findings suggest CSA features that may encourage positive savings outcomes for economically disadvantaged households and, then, that may have implications for future CSA policy development.     

Congregational Composition and Explanations for Racial Inequality Among Black Religious Affiliates

Prior research suggests that congregational characteristics are associated with the racial attitudes of Black churchgoers. This study examines the relationship between congregational diversity and beliefs about the Black/White socioeconomic gap among Black religious adherents. Drawing upon pooled data from the General Social Survey and the National Congregations Study, we fit binary logistic regression models to estimate the association between congregational diversity and the explanations of Black/White economic inequality among Black religious adherents. Findings from our study reveal that congregational diversity is one factor that accounts for intragroup differences in racial attitudes among Black religious affiliates. Relative to Blacks that attend religious services in overwhelmingly Black congregations, Blacks that attend religious services in congregations that are overwhelmingly White are significantly less likely to attribute Black/White socioeconomic gaps to a lack of educational opportunities. Our study demonstrates that congregational diversity is a source of intragroup variation in racial attitudes among Black religious affiliates, which may attenuate the ability of such congregations to bridge racial divisions.     

African American Adolescents’ Psychological Well-Being: The Impact of Parents’ Religious Socialization on Adolescents’ Religiosity

The dearth of research literature on the religious beliefs and practices of African American adolescents has led to increased empirical inquiry, yet a lack of research considers African American adolescents’ religious beliefs and practices as an important developmental milestone. This study explored how African American parents’ religious socialization affected youth religious experiences and served as a culturally specific strength-based asset that promotes psychological well-being. Our sample included a socioeconomically diverse sample of 154 African American families. Accounting for demographics, adolescents’ relationship and communication with God were found to be associated with a healthier psychological well-being. Additionally, parents’ religious socialization impacted the relationship between youths religious beliefs and practice and psychological well-being. Overall, results suggest that parents’ and adolescents’ religious beliefs can promote psychological well-being.     

Mosque-Based Social Support and Collective and Personal Self-Esteem Among Young Muslim American Adults

This study investigated the association between congregational relationships and personal and collective self-esteem among young Muslim American adults. Mosque-based emotional support and negative interactions with congregants were assessed in relation to personal and collective self-esteem. Data analysis was based on a sample of 231 respondents residing in southeast Michigan. Results indicated that receiving emotional support from congregants was associated with higher levels of collective self-esteem but was unassociated with personal self-esteem. Negative interaction with congregants was associated with personal self-esteem. Together, these findings indicate that mosque-based emotional support and negative interactions function differently for personal and collective self-esteem, which provides evidence that although personal and collective self-esteem are interrelated constructs, they are also conceptually discrete aspects self-evaluations.     

Dual class shares,board of directors’ effectiveness and firm’s market value: an empirical study

This study aims to identify whether a relationship exists between the controlling shareholders’ voting power and outside directors’ effectiveness in maximizing firms’ financial performance. We analyze a panel data with 3057 observations for the 2000–2012 period using a random effects model, logit and probit regressions, and the two-stage model of Heckman in the Brazilian stock market. Our findings show that firms whose controlling shareholders use dual class shares to leverage their voting power have less independence from the board and worse financial performance and market value. Further, the percentage of outside directors tends to be ineffective in increasing the firm’s value, and in changing the firm’s chief executive officer (CEO) when (1) the controlling shareholder’s voting power is leveraged, or (2) when the CEO assumes a position on the board of directors simultaneously. We interpreted that these results are in line with the arguments in favor of the existence of a new agency cost, which is related to the undue obedience of board members to authority, such as the largest controlling shareholder or the CEO in Brazilian listed firms.     

The Weight Function Lemma for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble byt a vertex. Deciding if the pebbling number is at most k is \(\Pi _2^\mathsf{P}\)-complete. In this paper we develop a tool, called the Weight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply the Weight Function Lemma to several specific graphs, including the Petersen, Lemke, \(4\mathrm{th}\) weak Bruhat, and Lemke squared, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. In doing so we partly answer a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.