A methodology is proposed for studying rare events in stochastic partial differential equations in systems that are so large that standard large deviation theory does not apply. The idea is to deduce the behavior of the original model by breaking the system into appropriately scaled subsystems that are sufficiently small for large deviation theory to apply but sufficiently large to be asymptoti...

Design and analysis of clinical trials for small rare disease populations Ralf‐Dieter Hilgers1*, Franz König2, Geert Molenberghs3 and Stephen Senn4 1Department of Medical Statistics, RWTH Universit Aachen, Pauwelstr 30, D‐ 52074 Aachen, Germany 2Center for Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Vienna, Austria 3I‐BioStat, Universiteit Hasselt, B‐3...

In the case of voluntary vaccination, people have to face the benefit of vaccinate against the adverse effects that may result from the act of vaccination. This dilemma is even more important when parents have to decide whether or not to vaccinate their children. The decision depends on the perceived risks from vaccination and infection, but also depends on the decision of all other people: if ...

Comparing and ordering of risks is a basic problem of actuarial theory and practice. Risks are generally modeled by random variables or distribution functions. There is a great variety of stochastic models in use which reflect the diversity of insurances like theft insurance, car insurance, liability insurance, etc. The diversity of insured populations is reproduced in the stochastic models by ...

Thirty years of control of the mosquito Culex pipiens using organophosphate insecticides (OP) has selected for OP-resistance alleles on a world-wide scale. As reviewed here, studies at the levels of gene and population allow identification of the main forces driving this process of adaptation. Three loci are involved in OP-resistance in C. pipiens. For two of these, adaptive mutations were foun...

Background: A randomized controlled trial is considered the gold standard in clinical research, also in rare diseases. However, in small populations, single large-scale well-powered trials are often not possible. For valid decision-making, both on efficacy and on safety, evidence generated from series of trials could be exploited. Methods: We conducted a review over a five-year period between J...

We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the popu...

objective pfeiffer syndrome is as rare as apert syndrome in the western population. this condition is very rare in the asian population. at the best of our knowledge this is the first genetically proven case report from iran. the authors report with a review of literature, the case of a infant with pfeiffer syndrome, manifested by lacunar skull, ventriculomegaly, bicoronal craniosynostosis,fron...