A Flexible Computational Framework Using R and Map-Reduce for Permutation Tests of Massive Genetic Analysis of Complex Traits.

In quantitative trait locus (QTL) mapping significance of putative QTL is often determined using permutation testing. The computational needs to calculate the significance level are immense, 10 up to 10 or even more permutations can be needed. We have previously introduced the PruneDIRECT algorithm for multiple QTL scan with epistatic interactions.

MAPfastR: quantitative trait loci mapping in outbred line crosses.

MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets.

Fast and accurate detection of multiple quantitative trait Loci.

We present a new computational scheme that enables efficient and reliable quantitative trait loci (QTL) scans for experimental populations. Using a standard brute-force exhaustive search effectively prohibits accurate QTL scans involving more than two loci to be performed in practice, at least if permutation testing is used to determine significance. Some more elaborate global optimization approaches, for example, DIRECT have been adopted earlier to QTL search problems.

An adaptive pseudospectral method for wave packet dynamics.

We solve the time-dependent Schrödinger equation for molecular dynamics using a pseudospectral method with global, exponentially decaying, Hagedorn basis functions. The approximation properties of the Hagedorn basis depend strongly on the scaling of the spatial coordinates. Using results from control theory we develop a time-dependent scaling which adaptively matches the basis to the wave packet.

Assessing a multiple QTL search using the variance component model.

Development of variance component algorithms in genetics has previously mainly focused on animal breeding models or problems in human genetics with a simple data structure. We study alternative methods for constrained likelihood maximization in quantitative trait loci (QTL) analysis for large complex pedigrees. We apply a forward selection scheme to include several QTL and interaction effects, as well as polygenic effects, with up to five variance components in the model.

Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits.

We present a two-phase strategy for optimizing a multidimensional, nonconvex function arising during genetic mapping of quantitative traits. Such traits are believed to be affected by multiple so called quantitative trait loci (QTL), and searching for d QTL results in a d-dimensional optimization problem with a large number of local optima. We combine the global algorithm DIRECT with a number of local optimization methods that accelerate the final convergence, and adapt the algorithms to problem-specific features.

Accurate time propagation for the Schrodinger equation with an explicitly time-dependent Hamiltonian.

Several different numerical propagation techniques for explicitly time-dependent Hamiltonians are discussed and compared, with the focus on models of pump-probe experiments. The quality of the rotating wave approximation is analyzed analytically, and we point out under which circumstances the modeling becomes inaccurate. For calculations with the fully time-dependent Hamiltonian, we show that for multistate systems, with either time or space dependence in the interstate coupling, the fourth order truncated Magnus expansion can be reformulated so that no commutators appear.

Increasing the efficiency of variance component quantitative trait loci analysis by using reduced-rank identity-by-descent matrices.

Recent technological development in genetics has made large-scale marker genotyping fast and practicable, facilitating studies for detection of QTL in large general pedigrees. We developed a method that speeds up restricted maximum-likelihood (REML) algorithms for QTL analysis by simplifying the inversion of the variance-covariance matrix of the trait vector. The method was tested in an experimental chicken pedigree including 767 phenotyped individuals and 14 genotyped markers on chicken chromosome 1.

Efficient algorithms for quantitative trait loci mapping problems.

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation.