Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state ({\em killing}) is possible from any state rather than just one state. The purpose of this paper is to investigate to what extent properties of birth-death processes, in particular with regard to the existence of quasi-stationary distributions, remain valid in the generalized setting. It turns out that the elegant structure of the theory of quasi-stationarity for birth-death processes remains intact as long as killing is possible from only finitely many states, but breaks down otherwise

The development of a new measure of quality of life for children with congenital cardiac disease

The purpose of the study was to develop a questionnaire measuring health-related R1 quality of life for children and adolescents with congenital heart disease, the ConQol, that would have both clinical and research applications. We describe here the process of construction of a questionnaire, the piloting and the development of a weighted scoring system, and data on the psychometric performance of the measure in a sample of 640 children and young people recruited via 6 regional centres for paediatric cardiology from across the United Kingdom. The ConQol has two versions, one designed for children aged from 8 to 11 years, and the other for young people aged from 12 to 16 years. Initial findings suggest that it is a valid and reliable instrument, is acceptable to respondents, and is simple to administer in both a research and clinical context

Quasi-stationary distributions for a class of discrete-time Markov chains

This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step ({\it killing}) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general

Paramecium: An Extensible Object-Based Kernel

In this paper we describe the design of an extensible kernel, called Paramecium. This kernel uses an object-based software architecture which together with instance naming, late binding and explicit overrides enables easy reconfiguration. Determining which components reside in the kernel protection domain is up to the user. An certification authority or one of its delegates certifies which components are trustworthy and therefore permitted to run in the kernel protection domain. These delegates may include validation programs, correctness provers, and system administrators. The main advantage of certifications is that it can handle trust and sharing in a non-cooperative environment

Observing trajectories of KOSs Across Space and Time: The DANS KOS Observatory (KOSo)

Knowledge Organization Systems (KOSs) include a wide variety of schemas ranging from ontologies, to classifications, thesauri, taxonomies, semantic networks, etc. These schemas can be updated and revised (or conversely become obsolete or lost) and are therefore prone to change over time. A wish expressed frequently by the research front in the KO community was for an “observatory” of KOSs. In 2017, via the KNAW Visiting Professor programme, DANS [1] began to focus more on understanding how KOSs change over time, how they can be archived, how version identification and control can be addressed, and also, how KOSs can be aligned to the ‘FAIR’ Data Principles (Findable, Accessible, Interoperable, Reusable). This research ambition coupled with community interest lead to the creation of the KOSo (Knowledge Organization Systems Observatory). Concretely, the observatory involves the identification of KOSs within the social sciences and humanities or the life sciences. KOSs have been described and ordered in the observatory through a process of empirical association in order to resist the potential pitfall of already organizing these resources through the lens of other KOSs (e.g. already describing the KOS in terms of existing controlled vocabularies). KOSo employs both metadata terms and formal classifications, using the Information Coding Classification in a synthetic format together with the KO Literature Classification, thus rendering for each KOS a domain-centric term faceted with a KOS-form term. Additionally, we classify domains using the NARCIS Classification, which is a framework to represent the research foci of the Dutch national research infrastructure