A regression based transmission/disequilibrium test for binary traits: the power of joint tests for linkage and association

BACKGROUND: In this analysis we applied a regression based transmission disequilibrium test to the binary trait presence or absence of Kofendred Personality Disorder in the Genetic Analysis Workshop 14 (GAW14) simulated dataset and determined the power and type I error rate of the method at varying map densities and sample sizes. To conduct this transmission disequilibrium test, the logit transformation was applied to a binary outcome and regressed on an indicator variable for the transmitted allele from informative matings. All 100 replicates from chromosomes 1, 3, 5, and 9 for the Aipotu and the combined Aipotu, Karangar, and Danacaa populations were used at densities of 3, 1, and 0.3 cM. Power and type I error were determined by the number of replicates significant at the 0.05 level. RESULTS: The maximum power to detect linkage and association with the Aipotu population was 93% for chromosome 3 using a 0.3-cM map. For chromosomes 1, 5, and 9 the power was less than 10% at the 3-cM scan and less than 22% for the 0.3-cM map. With the larger sample size, power increased to 38% for chromosome 1, 100% for chromosome 3, 31% for chromosome 5, and 23% for chromosome 9. Type I error was approximately 7%. CONCLUSION: The power of this method is highly dependent on the amount of information in a region. This study suggests that single-point methods are not particularly effective in narrowing a fine-mapping region, particularly when using single-nucleotide polymorphism data and when linkage disequilibrium in the region is variable

Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and Rota-Baxter Operators

We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a "generalized" Rota-Baxter identity of weight zero. Such operators are called generalized Rota-Baxter operators. We will show that generalized Rota-Baxter operators are characterized by a cocycle condition so that Poisson structures are so. By analogy with twisted Poisson structures, we propose a new operator "twisted Rota-Baxter operators" which is a natural generalization of generalized Rota-Baxter operators. It is known that classical Rota-Baxter operators are closely related with dendriform algebras. We will show that twisted Rota-Baxter operators induce NS-algebras which is a twisted version of dendriform algebra. The twisted Poisson condition is considered as a Maurer-Cartan equation up to homotopy. We will show the twisted Rota-Baxter condition also is so. And we will study a Poisson-geometric reason, how the twisted Rota-Baxter condition arises.Comment: 18 pages. Final versio

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page

A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology

We examine the string cosmology equations with a dilaton potential in the context of the Pre-Big Bang Scenario with the desired scale factor duality, and give a generic algorithm for obtaining solutions with appropriate evolutionary properties. This enables us to find pre-big bang type solutions with suitable dilaton behaviour that are regular at $t=0$, thereby solving the graceful exit problem. However to avoid fine tuning of initial data, an `exotic' equation of state is needed that relates the fluid properties to the dilaton field. We discuss why such an equation of state should be required for reliable dilaton behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review

String-inspired cosmology

I discuss cosmological models either derived from, or inspired by, string theory or M-theory. In particular I discuss solutions in the low-energy effective theory and the role of the dilaton, moduli and antisymmetric form fields in the dimensionally reduced effective action. The pre big bang model is an attempt to use cosmological solutions to make observational predictions. I then discuss the effective theory of gravity found in recent brane-world models where we live on a 3-brane embedded in a five-dimensional spacetime and how the study of cosmological perturbations may enable us to test these ideas.Comment: 15 pages, 5 figures, latex with iopart, invited talk at `The Early Universe and Cosmological Observations: a Critical Review', Cape Town, July 200

Rota-Baxter algebras and new combinatorial identities

The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are indicated.Comment: 8 pages, improved versio

Studying genetic determinants of natural variation in human gene expression using Bayesian ANOVA

Standard genetic mapping techniques scan chromosomal segments for location of genetic linkage and association signals. The majority of these methods consider only correlations at single markers and/or phenotypes with explicit detailing of the genetic structure. These methods tend to be limited by their inability to consider the effect of large numbers of model variables jointly. In contrast, we propose a Bayesian analysis of variance (ANOVA) method to categorize individuals based on similarity of multidimensional profiles and attempt to analyze all variables simultaneously. Using Problem 1 of the Genetic Analysis Workshop 15 data set, we demonstrate the method's utility for joint analysis of gene expression levels and single-nucleotide polymorphism genotypes. We show that the method extracts similar information to that of previous genetic mapping analyses, and suggest extensions of the method for mining unique information not previously found

Renormalization: a quasi-shuffle approach

In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with values in a Rota-Baxter algebra of amplitudes. We associate in this paper to any such algebra a universal semi-group (different in nature from the Connes-Marcolli "cosmical Galois group"). Its action on the physical amplitudes associated to Feynman graphs produces the expected operations: Bogoliubov's preparation map, extraction of divergences, renormalization. In this process a key role is played by commutative and noncommutative quasi-shuffle bialgebras whose universal properties are instrumental in encoding the renormalization process

Adiabatic perturbations in pre big bang models: matching conditions and scale invariance

At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase in full generality. We show that, generically, one obtains $n=0$ for the spectrum of scalar perturbations in the original pre big model (with vanishing potential). When an exponential potential for the dilaton is included, a scale invariant spectrum ($n=1$) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre big bang and ekpyrotic scenario. We also derive general results valid for power law scale factors matched to a radiation dominated era.Comment: 11 pages, 1 figure, revised version with small corrections to match version in print. Results and conclusions unchange

Using late-time optical and near-infrared spectra to constrain Type Ia supernova explosion properties

The late-time spectra of Type Ia supernovae (SNe Ia) are powerful probes of the underlying physics of their explosions. We investigate the late-time optical and near-infrared spectra of seven SNe Ia obtained at the VLT with XShooter at $>$200 d after explosion. At these epochs, the inner Fe-rich ejecta can be studied. We use a line-fitting analysis to determine the relative line fluxes, velocity shifts, and line widths of prominent features contributing to the spectra ([Fe II], [Ni II], and [Co III]). By focussing on [Fe II] and [Ni II] emission lines in the ~7000-7500 \AA\ region of the spectrum, we find that the ratio of stable [Ni II] to mainly radioactively-produced [Fe II] for most SNe Ia in the sample is consistent with Chandrasekhar-mass delayed-detonation explosion models, as well as sub-Chandrasekhar mass explosions that have metallicity values above solar. The mean measured Ni/Fe abundance of our sample is consistent with the solar value. The more highly ionised [Co III] emission lines are found to be more centrally located in the ejecta and have broader lines than the [Fe II] and [Ni II] features. Our analysis also strengthens previous results that SNe Ia with higher Si II velocities at maximum light preferentially display blueshifted [Fe II] 7155 \AA\ lines at late times. Our combined results lead us to speculate that the majority of normal SN Ia explosions produce ejecta distributions that deviate significantly from spherical symmetry.Comment: 17 pages, 12 figure, accepted for publication in MNRA