Wick's theorem for q-deformed boson operators

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated ``Feynman diagrams'' the normally ordered form of a general expression in the creation and annihilation operators can be written as a sum over all q-weighted Feynman diagrams, representing Wick's theorem in the present context.Comment: 9 page

On Linear Differential Equations Involving a Para-Grassmann Variable

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to n-generalized Fibonacci numbers is established. Several other classes of differential equations (systems of first order, equations with variable coefficients, nonlinear equations) are also considered and the analogies or differences to the usual (''bosonic'') differential equations discussed

Identification of novel schizophrenia loci by homozygosity mapping using DNA microarray analysis.

The recent development of high-resolution DNA microarrays, in which hundreds of thousands of single nucleotide polymorphisms (SNPs) are genotyped, enables the rapid identification of susceptibility genes for complex diseases. Clusters of these SNPs may show runs of homozygosity (ROHs) that can be analyzed for association with disease. An analysis of patients whose parents were first cousins enables the search for autozygous segments in their offspring. Here, using the Affymetrix® Genome-Wide Human SNP Array 5.0 to determine ROHs, we genotyped 9 individuals with schizophrenia (SCZ) whose parents were first cousins. We identified overlapping ROHs on chromosomes 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 20, and 21 in at least 3 individuals. Only the locus on chromosome 5 has been reported previously. The ROHs on chromosome 5q23.3-q31.1 include the candidate genes histidine triad nucleotide binding protein 1 (HINT1) and acyl-CoA synthetase long-chain family member 6 (ACSL6). Other overlapping ROHs may contain novel rare recessive variants that affect SCZ specifically in our samples, given the highly heterozygous nature of SCZ. Analysis of patients whose parents are first cousins may provide new insights for the genetic analysis of psychiatric diseases

Gene editing in the context of an increasingly complex genome

Abstract The reporting of the first draft of the human genome in 2000 brought with it much hope for the future in what was felt as a paradigm shift toward improved health outcomes. Indeed, we have now mapped the majority of variation across human populations with landmark projects such as 1000 Genomes; in cancer, we have catalogued mutations across the primary carcinomas; whilst, for other diseases, we have identified the genetic variants with strongest association. Despite this, we are still awaiting the genetic revolution in healthcare to materialise and translate itself into the health benefits for which we had hoped. A major problem we face relates to our underestimation of the complexity of the genome, and that of biological mechanisms, generally. Fixation on DNA sequence alone and a ‘rigid’ mode of thinking about the genome has meant that the folding and structure of the DNA molecule —and how these relate to regulation— have been underappreciated. Projects like ENCODE have additionally taught us that regulation at the level of RNA is just as important as that at the spatiotemporal level of chromatin. In this review, we chart the course of the major advances in the biomedical sciences in the era pre- and post the release of the first draft sequence of the human genome, taking a focus on technology and how its development has influenced these. We additionally focus on gene editing via CRISPR/Cas9 as a key technique, in particular its use in the context of complex biological mechanisms. Our aim is to shift the mode of thinking about the genome to that which encompasses a greater appreciation of the folding of the DNA molecule, DNA- RNA/protein interactions, and how these regulate expression and elaborate disease mechanisms. Through the composition of our work, we recognise that technological improvement is conducive to a greater understanding of biological processes and life within the cell. We believe we now have the technology at our disposal that permits a better understanding of disease mechanisms, achievable through integrative data analyses. Finally, only with greater understanding of disease mechanisms can techniques such as gene editing be faithfully conducted