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.     

Calculating the density and distribution function for the singly and doubly noncentral F

Simple, closed form saddlepoint approximations for the distribution and density of the singly and doubly noncentral F distributions are presented. Their overwhelming accuracy is demonstrated numerically using a variety of parameter values. The approximations are shown to be uniform in the right tail and the associated limitating relative error is derived. Difficulties associated with some algorithms used for exact computation of the singly noncentral F are noted.     

The impact of education on third births. A multilevel discrete-time hazard analysis

We propose to use multilevel discrete-time hazard models to assess the impact of societal and individual level covariates on the timing and occurrence of third births. We focus mainly on the impact of educational attainment on third births across 15 European countries. From the analysis in this paper, the effect of education on the propensity to have a third child is found to be negative. This education effect is not significantly weakened by the Nordic countries, but living in Scandinavia does increase the hazard for a third birth.     

Keeping Surveys Valid,Reliable, and Useful: A Tutorial

This tutorial focuses on how to produce reliable and generalizable data from random‐digit‐dialing (RDD) landline and cell phone surveys. The article notes that RDD response rates have declined and explores the impact of this pronounced decline. The tutorial addresses order, response mode, and many other biases, sample size, cooperation and response rates, weighting, and hybrid designs‐all using examples from risk analysis to illustrate the key points. The article ends with a brief review of the advantages and disadvantages of major Internet and paper surveys tools, and how these can be molded and sometimes combined in repeated, longitudinal, and other designs to answer questions about risk preferences and perceptions.     

Development of a Quantitative Microbial Risk Assessment for Human Salmonellosis Through Household Consumption of Fresh Minced Pork Meat in Belgium

A quantitative microbial risk assessment (QMRA) according to the Codex Alimentarius Principles is conducted to evaluate the risk of human salmonellosis through household consumption of fresh minced pork meat in Belgium. The quantitative exposure assessment is carried out by building a modular risk model, called the METZOON-model, which covers the pork production from farm to fork. In the METZOON-model, the food production pathway is split up in six consecutive modules: (1) primary production, (2) transport and lairage, (3) slaughterhouse, (4) postprocessing, (5) distribution and storage, and (6) preparation and consumption. All the modules are developed to resemble as closely as possible the Belgian situation, making use of the available national data. Several statistical refinements and improved modeling techniques are proposed. The model produces highly realistic results. The baseline predicted number of annual salmonellosis cases is 20,513 ( SD 9061.45). The risk is estimated higher for the susceptible population (estimate  4.713 × 10⁻⁵; SD 1.466 × 10⁻⁵  ) compared to the normal population  (estimate 7.704 × 10⁻⁶; SD 5.414 × 10⁻⁶)  and is mainly due to undercooking and to a smaller extent to cross-contamination in the kitchen via cook's hands.     

Risk-Reducing Legal Documents: Controlling Personal Health and Financial Resources

Every adult can eliminate the risk of losing control of personal health decisions and financial resources by having a last will and testament, health proxy, power of attorney, and living trust. Yet evidence suggests that less than a majority of adult Americans have these documents. We surveyed 900 adult Americans (25 plus years old) to determine what factors predict the possession of these risk-reducing documents. In total, 46% had a living will and testament, 32% a durable power of attorney, 30% a health proxy, and 18% a living trust. Events that prompt people with wealth to secure these documents, such as increasing age, getting married, having children, and experiencing a life-threatening event were the strongest predictors of having a will. These were also among the strongest predictors of having a health proxy, along with a personal history of being proactive, and a family history that fostered trust of attorneys. Affluence, age, and education were the strongest predictors of having a living trust, and the strongest correlate of having a durable power of attorney was having faced a life-threatening event, positive experiences with attorneys, and higher educational achievement.