Equicontinuous Families of Markov Operators in View of Asymptotic Stability

Relation between equicontinuity, the so called e property and stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its support is nonempty satisfies the e property

Global integrability of cosmological scalar fields

We investigate the Liouvillian integrability of Hamiltonian systems describing a universe filled with a scalar field (possibly complex). The tool used is the differential Galois group approach, as introduced by Morales-Ruiz and Ramis. The main result is that the generic systems with minimal coupling are non-integrable, although there still exist some values of parameters for which integrability remains undecided; the conformally coupled systems are only integrable in four known cases. We also draw a connection with chaos present in such cosmological models, and the issues of integrability restricted to the real domain.Comment: This is a conflated version of arXiv:gr-qc/0612087 and arXiv:gr-qc/0703031 with a new theory sectio

Simultaneous mapping of multiple gene loci with pooled segregants

The analysis of polygenic, phenotypic characteristics such as quantitative traits or inheritable diseases remains an important challenge. It requires reliable scoring of many genetic markers covering the entire genome. The advent of high-throughput sequencing technologies provides a new way to evaluate large numbers of single nucleotide polymorphisms (SNPs) as genetic markers. Combining the technologies with pooling of segregants, as performed in bulked segregant analysis (BSA), should, in principle, allow the simultaneous mapping of multiple genetic loci present throughout the genome. The gene mapping process, applied here, consists of three steps: First, a controlled crossing of parents with and without a trait. Second, selection based on phenotypic screening of the offspring, followed by the mapping of short offspring sequences against the parental reference. The final step aims at detecting genetic markers such as SNPs, insertions and deletions with next generation sequencing (NGS). Markers in close proximity of genomic loci that are associated to the trait have a higher probability to be inherited together. Hence, these markers are very useful for discovering the loci and the genetic mechanism underlying the characteristic of interest. Within this context, NGS produces binomial counts along the genome, i.e., the number of sequenced reads that matches with the SNP of the parental reference strain, which is a proxy for the number of individuals in the offspring that share the SNP with the parent. Genomic loci associated with the trait can thus be discovered by analyzing trends in the counts along the genome. We exploit the link between smoothing splines and generalized mixed models for estimating the underlying structure present in the SNP scatterplots