Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior

Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics

Efficient Exact Maximum a Posteriori Computation for Bayesian SNP Genotyping in Polyploids

The problem of genotyping polyploids is extremely important for the creation of genetic maps and assembly of complex plant genomes. Despite its significance, polyploid genotyping still remains largely unsolved and suffers from a lack of statistical formality. In this paper a graphical Bayesian model for SNP genotyping data is introduced. This model can infer genotypes even when the ploidy of the population is unknown. We also introduce an algorithm for finding the exact maximum a posteriori genotype configuration with this model. This algorithm is implemented in a freely available web-based software package SuperMASSA. We demonstrate the utility, efficiency, and flexibility of the model and algorithm by applying them to two different platforms, each of which is applied to a polyploid data set: Illumina GoldenGate data from potato and Sequenom MassARRAY data from sugarcane. Our method achieves state-of-the-art performance on both data sets and can be trivially adapted to use models that utilize prior information about any platform or species

OpenMS: a flexible open-source software platform for mass spectrometry data analysis

High-resolution mass spectrometry (MS) has become an important tool in the life sciences, contributing to the diagnosis and understanding of human diseases, elucidating biomolecular structural information and characterizing cellular signaling networks. However, the rapid growth in the volume and complexity of MS data makes transparent, accurate and reproducible analysis difficult. We present OpenMS 2.0 (http://www.openms.de), a robust, open-source, cross-platform software specifically designed for the flexible and reproducible analysis of high-throughput MS data. The extensible OpenMS software implements common mass spectrometric data processing tasks through a well-defined application programming interface in C++ and Python and through standardized open data formats. OpenMS additionally provides a set of 185 tools and ready-made workflows for common mass spectrometric data processing tasks, which enable users to perform complex quantitative mass spectrometric analyses with ease