Noncommutative partially convex rational functions

Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially convex admit novel butterfly-type realizations that necessitate square roots. The notion of xy-convexity, a strengthening of partial convexity arising in connection with BMIs, is also considered. A characterization of xy-convex polynomials is given

Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.

This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be more accurate, efficient, reliable, and convenient

Genome modeling system: A knowledge management platform for genomics

In this work, we present the Genome Modeling System (GMS), an analysis information management system capable of executing automated genome analysis pipelines at a massive scale. The GMS framework provides detailed tracking of samples and data coupled with reliable and repeatable analysis pipelines. The GMS also serves as a platform for bioinformatics development, allowing a large team to collaborate on data analysis, or an individual researcher to leverage the work of others effectively within its data management system. Rather than separating ad-hoc analysis from rigorous, reproducible pipelines, the GMS promotes systematic integration between the two. As a demonstration of the GMS, we performed an integrated analysis of whole genome, exome and transcriptome sequencing data from a breast cancer cell line (HCC1395) and matched lymphoblastoid line (HCC1395BL). These data are available for users to test the software, complete tutorials and develop novel GMS pipeline configurations. The GMS is available at https://github.com/genome/gms

DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 reference manual

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 developers manual.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes

Genome remodelling in a basal-like breast cancer metastasis and xenograft

Massively parallel DNA sequencing technologies provide an unprecedented ability to screen entire genomes for genetic changes associated with tumour progression. Here we describe the genomic analyses of four DNA samples from an African-American patient with basal-like breast cancer: peripheral blood, the primary tumour, a brain metastasis and a xenograft derived from the primary tumour. The metastasis contained two de novo mutations and a large deletion not present in the primary tumour, and was significantly enriched for 20 shared mutations. The xenograft retained all primary tumour mutations and displayed a mutation enrichment pattern that resembled the metastasis. Two overlapping large deletions, encompassing CTNNA1, were present in all three tumour samples. The differential mutation frequencies and structural variation patterns in metastasis and xenograft compared with the primary tumour indicate that secondary tumours may arise from a minority of cells within the primary tumour

Multiplatform Analysis of 12 Cancer Types Reveals Molecular Classification within and across Tissues of Origin

Recent genomic analyses of pathologically-defined tumor types identify “within-a-tissue” disease subtypes. However, the extent to which genomic signatures are shared across tissues is still unclear. We performed an integrative analysis using five genome-wide platforms and one proteomic platform on 3,527 specimens from 12 cancer types, revealing a unified classification into 11 major subtypes. Five subtypes were nearly identical to their tissue-of-origin counterparts, but several distinct cancer types were found to converge into common subtypes. Lung squamous, head & neck, and a subset of bladder cancers coalesced into one subtype typified by TP53 alterations, TP63 amplifications, and high expression of immune and proliferation pathway genes. Of note, bladder cancers split into three pan-cancer subtypes. The multi-platform classification, while correlated with tissue-of-origin, provides independent information for predicting clinical outcomes. All datasets are available for data-mining from a unified resource to support further biological discoveries and insights into novel therapeutic strategies

Full-order eigenpair perturbations with mode tracking applications in aeroelasticity and optimization.

General methodology for calculating changes in eigenvalues and eigenvectors resulting from parameter perturbations in the eigenproblems is presented for self-adjoint and nonself-adjoint cases. Perturbing the eigenproblems and retaining all terms leads to coupled equations for the eigenpair perturbations which must be solved iteratively. The familiar singularity in the solution for the eigenvector change is removed using Nelson's method, which is successful despite the approximate nature of the singularity. The normalization task necessary for the eigenvector perturbation also retains all terms, leading to a quadratic equation for a weighting factor which, for the self-adjoint case, has a uniquely defined correct root. For the nonself-adjoint case, magnitude normalization is not sufficient to define unique perturbed left and right eigenvectors, and an additional phase correction is imposed. Enhancements to the basic algorithm that are discussed are the use of under-relaxation and the computation of perturbations in the presence of repeated eigenvalues. The resulting algorithms, the higher order eigenpair perturbation algorithm (HOEP) and its complex extension (C-HOEP), are robust in that they can converge to the exact eigenpairs for very large parameter perturbations. Mode tracking techniques are developed and applied to problems in structural optimization and aeroelastic analysis. The goal is to eliminate difficulties caused by mode-switching (i.e. frequency crossing). Out of several candidate methods, two methods for mode tracking are successful. The first method is the higher order eigenpair perturbation algorithm. By computing perturbations for each eigenpair individually, it maintains the correspondence between the baseline and perturbed eigenpairs. The second method is the cross-orthogonality check method which uses mass orthogonality (self-adjoint case) or mass biorthogonality (nonself-adjoint case) to reestablish correspondence after a standard reanalysis. Applications of mode tracking technology that are presented are frequency-constrained optimization, optimization with mode shape constraints, V-g aeroelastic analysis, and p-k aeroelastic analysis. Each application procedure is outlined and examples are given. Recommendations are made based on method efficiency and robustness in the example problems.Ph.D.Aerospace engineeringApplied SciencesComputer scienceMechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129185/2/9409681.pd