On computing a minimum secure dominating set in block graphs

In a graph \(G=(V,E)\), a set \(D \subseteq V\) is said to be a dominating set of G if for every vertex \(u\in V{\setminus }D\), there exists a vertex \(v\in D\) such that \(uv\in E\). A secure dominating set of the graph G is a dominating set D of G such that for every \(u\in V{\setminus }D\), there exists a vertex \(v\in D\) such that \(uv\in E\) and \((D{\setminus }\{v\})\cup \{u\}\) is a dominating set of G. Given a graph G and a positive integer k, the secure domination problem is to decide whether G has a secure dominating set of cardinality at most k. The secure domination problem has been shown to be NP-complete for chordal graphs via split graphs and for bipartite graphs. In Liu et al. (in: Proceedings of 27th workshop on combinatorial mathematics and computation theory, 2010), it is asked to find a polynomial time algorithm for computing a minimum secure dominating set in a block graph. In this paper, we answer this by presenting a linear time algorithm to compute a minimum secure dominating set in block graphs. We then strengthen the known NP-completeness of the secure domination problem by showing that the secure domination problem is NP-complete for undirected path graphs and chordal bipartite graphs.     

Ausbildung zum Ausbildungssupervisor für Verhaltenstherapie

Psychotherapy requires a high qualification which is gained mainly in practical training. Own treatments of mentally ill patients during training requires close-meshed supervision. This also has to meet the highest standards, which require a systematic training as a training supervisor. This article discusses the various aspects that have to be taken into consideration in behavior therapy. Beyond adherence to therapy manuals, extremely complex interaction processes have to be taken into account that cannot be substantiated by the classical behavior therapy. To this extent, supervision appears as a bridge between science and the art of psychotherapy.     

If My Blood Pressure Is High,Do I Take It to Heart? Behavioral Effects of Biomarker Collection in the Health and Retirement Study

Starting in 2006, respondents in the biennial U.S. Health and Retirement Study were asked to submit biomarkers every other wave and were notified of several results. Rates of undiagnosed high blood pressure and diabetes according to these biomarkers were 1.5 % and 0.7 %, respectively. An intent-to-treat analysis suggests that collection and notification had small effects on the average respondent and may have reduced health care utilization. Among respondents who received notification of potentially dangerous biomarker levels, subsequent rates of new diagnosis and associated pharmaceutical usage increased by 20 to 40 percentage points, an order of magnitude above baseline. High blood glucose A1C was associated with a 2.2 % drop in weight and an increase in exercise among respondents without a previous diagnosis of diabetes. Notifications appear also to have altered health behaviors by spouses, suggesting household responses to health maintenance. Biomarker collection seems to have altered circumstances for an interesting minority of HRS respondents.     

Changes in Parenting and Youth Adjustment Across the Military Deployment Cycle

This study examined how changes in at‐home parents' mental health and parenting practices related to changes in their children's adjustment throughout the course of a service members' military deployment. Participants included at‐home parents from 114 National Guard families who were interviewed at four different occasions across the deployment cycle. The results revealed changes across the deployment cycle among the following three indicators: parental warmth, depressive symptoms, and children's externalizing behaviors. Changes in parental warmth were associated with changes in children's adjustment. Overall, these findings indicate that during parental separation, at‐home parents' responses to children have important implications for children's adjustment.     

ACADEMIC PROBATION,STUDENT PERFORMANCE,AND STRATEGIC COURSE‐TAKING

We use a regression discontinuity design to study how academic probation affects outcomes and course‐taking behaviors at a large public university in the United States. Consistent with past work, students placed on probation improve their grade point average (GPA) in the subsequent semester. We document that part of this GPA improvement is attributable to strategic course‐taking, and there is significant heterogeneity in these behaviors across race. Non‐minority students placed on probation attempt fewer credits, easier courses, and are more likely to withdraw from courses in the following term. In contrast, underrepresented minorities exhibit few of these behaviors, consistent with past work that suggests black and Hispanic students are less likely to possess helpful institutional knowledge and use available support systems such as academic counseling. (JEL I20, I23)     

The victim–offender overlap in late adulthood

This study contributes to the general knowledge of the victim–offender overlap by determining whether the phenomenon exists among older adults and whether known correlates of crime and victimization explain the relationship. Cross-sectional survey data from telephone interviews conducted with individuals 60 years and older (N = 2,000) residing in Arizona and Florida are used to estimate confirmatory factor models for both victimization and criminal offending. The results from a series of multivariate regression models show that victimization is associated with criminal offending. While factors such as low self-control, depression, and spending time in commercial drinking establishments partially attenuate the victimization–crime link, the statistically significant relationship persists in a multivariate context. Further testing indicates that the observed findings are robust across measurement and modeling strategies. Coupled with prior research, the results support the argument that the victim–offender overlap exists (and is difficult to explain) over the life course.     

THE USE OF AGGREGATE DATA TO ESTIMATE GOMPERTZ‐TYPE OLD‐AGE MORTALITY IN HETEROGENEOUS POPULATIONS

We consider two related aspects of the study of old‐age mortality. One is the estimation of a parameterized hazard function from grouped data, and the other is its possible deceleration at extreme old age owing to heterogeneity described by a mixture of distinct sub‐populations. The first is treated by half of a logistic transform, which is known to be free of discretization bias at older ages, and also preserves the increasing slope of the log hazard in the Gompertz case. It is assumed that data are available in the form published by official statistical agencies, that is, as aggregated frequencies in discrete time. Local polynomial modelling and weighted least squares are applied to cause‐of‐death mortality counts. The second, related, problem is to discover what conditions are necessary for population mortality to exhibit deceleration for a mixture of Gompertz sub‐populations. The general problem remains open but, in the case of three groups, we demonstrate that heterogeneity may be such that it is possible for a population to show decelerating mortality and then return to a Gompertz‐like increase at a later age. This implies that there are situations, depending on the extent of heterogeneity, in which there is at least one age interval in which the hazard function decreases before increasing again.     

VARIATIONAL BAYESIAN ANALYSIS FOR HIDDEN MARKOV MODELS

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with Gaussian observation densities illustrate this. If the variational algorithm is initialized with a large number of hidden states, redundant states are eliminated as the method converges to a solution, thereby leading to a selection of the number of hidden states. In addition, through the use of a variational approximation, the deviance information criterion for Bayesian model selection can be extended to the hidden Markov model framework. Calculation of the deviance information criterion provides a further tool for model selection, which can be used in conjunction with the variational approach.     

Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.     

A new estimation method for Weibull-type tails based on the mean excess function

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ$\gamma$. The class γ>0$\gamma >0$ corresponds to Pareto-type or heavy tailed distributions, while γ<0$\gamma <0$ indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0$\gamma =0$. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.