Some results on the injective chromatic number of?graphs

A k-coloring of a graph G=(V,E) is a mapping c:V??{1,2,??,k}. The coloring c is injective if, for every vertex v??V, all the neighbors of v are assigned with distinct colors. The injective chromatic number ?? _i (G) of G is the smallest k such that G has an injective k-coloring. In this paper, we prove that every K ₄-minor free graph G with maximum degree ????1 has $\chi_{i}(G)\le \lceil \frac{3}{2}\Delta\rceil$ . Moreover, some related results and open problems are given.     

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.     

Tests for Stochastic Orders and Mean Order Statistics

The aim of this article is to emphasize the fact, not observed previously in the literature, that many discrepancy measures used in tests related to different stochastic orders can be expressed as expectations of order statistics. In this way, we provide a new meaning to the corresponding test statistics which allows us to understand better, and potentially improve, the testing procedures. As illustration, we consider tests to detect overdispersion with respect to a specific probability model. In this setting, a test for the Weibull distribution is discussed in detail.     

A method for estimating lorenz curves

This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.     

Fathers’ Use of Childbirth Leave in Spain. The Effects of the 13-Day Paternity Leave

This article investigates, for the case of Spain, to what extent the introduction in March 2007 of a non-transferable 13-day paternity leave has encouraged men to make greater use of childbirth leave. Data were drawn from the Spanish Economically Active Population Survey, covering the period 2005–2009. We use a natural experiment approach, comparing the behavior of wage earners fathers with children of less than 1 year of age before and after the reform and using mothers as control group. After estimating a difference-in-differences logistic regression model we obtain statistical evidence that there is a higher percentage of males on leave in the reference week in the post-reform period (after 2007). The article also analyzes some of the personal and socio-economic determinants of the fathers’ use of childbirth leave. Fathers are more likely to be on leave if they have stability in employment, if there are facilities for reconciling work and family life (working in the public sector) and if the partner is employed. The father’s age has an interesting U-shaped influence.     

Work and Sexual Trajectories Among African American Youth

The beneficial or deleterious effects of employment on youth and well-being have been highly contested. This study explores whether work influences youths' sexual risk correlates in a sample of African Americans (N = 562; 55% females; M = 14.5 years, SD = 0.6 years) followed longitudinally from adolescence to early adulthood. The study used growth curve modeling to test the association between number of hours worked and condom use, sex partners' age differences, and number of partners over time. Working a greater number of hours was associated with less condom use, with the effect varying by youths' grade point average. Working a greater number of hours was associated with older sex partners among female youth. No association was found between work and number of partners. The findings suggest that working during adolescence and early adulthood increased participants' sexual activity, thus lending some support for the work consequences perspective. The implications for future research and youth development programs are discussed.     

Measuring power and satisfaction in societies with opinion leaders: an axiomatization

Opinion leaders are actors who have some power over their followers as they are able to influence their followers’ choice of action in certain instances. In van den Brink et al. (Homo Oeconomicus 28:161–185, 2011) we proposed a two-action model for societies with opinion leaders. We introduced a power and a satisfaction score and studied some common properties. In this paper we strengthen two of these properties and present two further properties, which allows us to axiomatize both scores for the case that followers require unanimous action inclinations of their opinion leaders to follow them independently from their own action inclinations.     

Evaluation of a Seven State Criminal History Screening Pilot Program for Long-Term Care Workers

This article summarizes results from an evaluation of a federally sponsored criminal history screening (CHS) pilot program to improve screening for workers in long-term care settings. The evaluation addressed eight key issues specified through enabling legislation, including efficiency, costs, and outcomes of screening procedures. Of the 204,339 completed screenings, 3.7% were disqualified due to criminal history, and 18.8% were withdrawn prior to completion for reasons that may include relevant criminal history. Lessons learned from the pilot program experiences may inform a new national background check demonstration program.     

The history of gay bathhouses. 1984

Public policy regarding bathhouses has been criticized as being based on political expediency rather than on medical or social science. To affect that shortcoming, we include here a brief history of gay bathhouses. The history of the baths is rarely told, but whenever it is told it necessarily reflects the times in which it was written. For that reason, we include a history written in 1984, at the time that much of what was known about AIDS, routes of transmission and the role of the bathhouses was very much in flux. This history not only gives a context for the current discussion, but also allows the reader to see the history from that distant point in time. This paper was first published in December 1984 as an article in Coming Up!, a lesbian and gay community newspaper published monthly in San Francisco (California). It was later edited and reprinted in a book titled Policing Public Sex (1996). The version of the paper presented here is from the original 1984 article (pp. 15-19); several images appeared with the article that are not reproduced here. As with all the reprinted papers in this volume, no editorial changes were made to the paper and only minor typographical errors were corrected.     

A new estimate of Ukrainian population losses during the crises of the 1930s and 1940s

Ukraine experienced two very acute demographic crises during the Soviet era: the 1933 famine and the Second World War. While different estimates of total losses have been produced previously, we have tried here to distinguish the specific impact of the crises on mortality from their impact on fertility and migration. Taking into account all existing sources of registered data and estimates, a painstaking reconstruction of annual demographic changes has been produced and complete annual life tables have been computed for the years 1926-59. Life expectancy at birth fell to a level as low as 10 years for females and 7 for males in 1933 and plateaued around 25 for females and 15 for males in the period 1941-44.