Limited packings of closed neighbourhoods in graphs

The k-limited packing number, $L_k(G)$, of a graph $G$, introduced by Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set $X$ of vertices of $G$ such that every vertex of $G$ has at most $k$ elements of $X$ in its closed neighbourhood. The main aim in this paper is to prove the best-possible result that if $G$ is a cubic graph, then $L_2(G) \geq |V (G)|/3$, improving the previous lower bound given by Gallant, \emph{et al.} In addition, we construct an infinite family of graphs to show that lower bounds given by Gagarin and Zverovich are asymptotically best-possible, up to a constant factor, when $k$ is fixed and $\Delta(G)$ tends to infinity. For $\Delta(G)$ tending to infinity and $k$ tending to infinity sufficiently quickly, we give an asymptotically best-possible lower bound for $L_k(G)$, improving previous bounds

The Gender Earnings Gap in Britain

The earnings gap between male and female employees is substantial and persistent. Using new data for Britain, this paper shows that an important contribution to this gap is made by the workplace in which the employee works. Evidence for workplace and occupational segregation as partial explanations of the earnings gap is presented. Having allowed also for individual worker characteristics there remains a substantial within-workplace and within-occupation gender earnings gap. The contribution of these factors, as well as the earnings gap itself, differ significantly across sectors of the labour market. The relative unimportance of occupational segregation and the large remaining gender earnings gap suggest that stronger enforcement of Equal Pay legislation is likely to be the most appropriate policy response.Gender earnings; wage-gap; fixed-effects; segregation

Men, Women and the Hiring Function

This paper examines the idea of ranking of groups and genders in terms of hiring probabilities. By incorporating a range of complementary data sources, measures of the three possible gross worker flows into employment, and the stocks of job seekers from which they come, are provided for both genders in the Australian labour market. We find a clear ranking of men over women in the hiring process. Indeed, in aggregate women appear to be effectively segregated from the male hiring market, whereas this is not true with males in the female hiring market. We also find that amongst males, employed job seekers are ranked above those unemployed and, in turn, above those not in the labour force. For women, the unemployed and employed are not found to be competing with each other, whilst those not in the labour force are ranked below the unemployed. We believe that this is the first study explicitly investigating these three major gross worker flows for women as well as men, enabling us to further explore the interdependent processes in the labour market by considering more fully the interactions across job seekers of different genders and from different labour market states.

Job Tenure in Britain: Employee Characteristics Versus Workplace Effects

We consider differences in current job tenure of individuals using linked employee and workplace data. This enables us to distinguish between variation in tenure associated with the characteristics of individual employees and those of the workplace in which they work. The various individual characteristics are, as a group, found to be essentially uncorrelated with the workplace effect, however, this is not true for women and non-white employees. We find that the lower tenure associated with membership of these demographic groups is predominantly captured by workplace effects suggesting some degree of labour market segmentation in Britain.Job tenure; individual; fixed-effects; voice; segmentation

Job Tenure in Australia and Britain: Individual Versus Workplace effects

We explore determinants of job reallocation and the implications for employment change and average job tenure in this paper. A model which associates technological advances with the process of economic growth is modified and analysed. Data on average job tenure within workplaces and gross job flows across workplaces in Australia are constructed by us from a single panel of workplace data and examined. Substantial simultaneous job creation and destruction are found in a year of strong job growth, suggesting that workplace heterogeneity is an important feature of the Australian labour market. The predictions generated from the theoretical model are examined with the data for job flows and average job tenure. Our results support the key features of the model.labour market flows; job reallocation; creative-destruction; average-tenure

mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location

This paper develops mfEGRA, a multifidelity active learning method using data-driven adaptively refined surrogates for failure boundary location in reliability analysis. This work addresses the issue of prohibitive cost of reliability analysis using Monte Carlo sampling for expensive-to-evaluate high-fidelity models by using cheaper-to-evaluate approximations of the high-fidelity model. The method builds on the Efficient Global Reliability Analysis (EGRA) method, which is a surrogate-based method that uses adaptive sampling for refining Gaussian process surrogates for failure boundary location using a single-fidelity model. Our method introduces a two-stage adaptive sampling criterion that uses a multifidelity Gaussian process surrogate to leverage multiple information sources with different fidelities. The method combines expected feasibility criterion from EGRA with one-step lookahead information gain to refine the surrogate around the failure boundary. The computational savings from mfEGRA depends on the discrepancy between the different models, and the relative cost of evaluating the different models as compared to the high-fidelity model. We show that accurate estimation of reliability using mfEGRA leads to computational savings of $\sim$46% for an analytic multimodal test problem and 24% for a three-dimensional acoustic horn problem, when compared to single-fidelity EGRA. We also show the effect of using a priori drawn Monte Carlo samples in the implementation for the acoustic horn problem, where mfEGRA leads to computational savings of 45% for the three-dimensional case and 48% for a rarer event four-dimensional case as compared to single-fidelity EGRA

THE INFLUENCE OF DEPRESSIVE SYMPTOMS ON FATHERS’ BEHAVIORS AND ATTITUDES

The present study examines the impact of young, poor, unwed fathers on their family by investigating the influence of depressive symptom frequency on fathers’ relationship with their children and partners. Couples from seven American cities with populations over 200,000 were recruited and interviewed about such areas of life as romantic and parental relationships, health, and employment at the hospital within 24 hours after the birth of their child. An Item Response Theory (IRT) within-group analysis of the 1,759 African-, Caucasian-, Hispanic-, Asian-, and Native American fathers in the study yielded a 3-class clustering of depressive symptoms. Class 1 fathers had the lowest frequency of depressive symptom expression; class 2 fathers had a low frequency; and class 3 fathers had low to medium rates of depressive symptoms. Multivariate statistics revealed that depressive class membership predicted domestic violence toward fathers’ partners but not affection toward their children. The importance of the parental behavior of teaching children about life, however, varied by class, with class 2 fathers most highly endorsing this behavior. Implications of young, unwed, poor fathers' behaviors and attitudes toward their children and romantic partners will be discussed in terms of men's contributions to family life.