Parallel Factor Analysis Enables Quantification and Identification of Highly Convolved Data-Independent-Acquired Protein Spectra

The latest high-throughput mass spectrometry-based technologies can record virtually all molecules from complex biological samples, providing a holistic picture of proteomes in cells and tissues and enabling an evaluation of the overall status of a person\u27s health. However, current best practices are still only scratching the surface of the wealth of available information obtained from the massive proteome datasets, and efficient novel data-driven strategies are needed. Powered by advances in GPU hardware and open-source machine-learning frameworks, we developed a data-driven approach, CANDIA, which disassembles highly complex proteomics data into the elementary molecular signatures of the proteins in biological samples. Our work provides a performant and adaptable solution that complements existing mass spectrometry techniques. As the central mathematical methods are generic, other scientific fields that are dealing with highly convolved datasets will benefit from this work

Ninth NASTRAN (R) Users' Colloquium

The general application of finite element methodology and the specific application of NASTRAN to a wide variety of static and dynamic structural problems is addressed. Comparison with other approaches and new methods of analysis with nastran are included

Decomposing and packing polygons / Dania el-Khechen.

In this thesis, we study three different problems in the field of computational geometry: the partitioning of a simple polygon into two congruent components, the partitioning of squares and rectangles into equal area components while minimizing the perimeter of the cuts, and the packing of the maximum number of squares in an orthogonal polygon. To solve the first problem, we present three polynomial time algorithms which given a simple polygon P partitions it, if possible, into two congruent and possibly nonsimple components P 1 and P 2 : an O ( n 2 log n ) time algorithm for properly congruent components and an O ( n 3 ) time algorithm for mirror congruent components. In our analysis of the second problem, we experimentally find new bounds on the optimal partitions of squares and rectangles into equal area components. The visualization of the best determined solutions allows us to conjecture some characteristics of a class of optimal solutions. Finally, for the third problem, we present three linear time algorithms for packing the maximum number of unit squares in three subclasses of orthogonal polygons: the staircase polygons, the pyramids and Manhattan skyline polygons. We also study a special case of the problem where the given orthogonal polygon has vertices with integer coordinates and the squares to pack are (2 {604} 2) squares. We model the latter problem with a binary integer program and we develop a system that produces and visualizes optimal solutions. The observation of such solutions aided us in proving some characteristics of a class of optimal solutions

Computational methods and software systems for dynamics and control of large space structures

This final report on computational methods and software systems for dynamics and control of large space structures covers progress to date, projected developments in the final months of the grant, and conclusions. Pertinent reports and papers that have not appeared in scientific journals (or have not yet appeared in final form) are enclosed. The grant has supported research in two key areas of crucial importance to the computer-based simulation of large space structure. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area, as reported here, involves massively parallel computers

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced

Kinematic Signatures of Bulges Correlate with Bulge Morphologies and S\'ersic Index

We use the Marcario Low Resolution Spectrograph (LRS) at the Hobby-Eberly-Telescope (HET) to study the kinematics of pseudobulges and classical bulges in the nearby universe. We present major-axis rotational velocities, velocity dispersions, and h3 and h4 moments derived from high-resolution (sigma ~ 39 km/s) spectra for 45 S0 to Sc galaxies; for 27 of the galaxies we also present minor axis data. We combine our kinematics with bulge-to-disk decompositions. We demonstrate for the first time that purely kinematic diagnostics of the bulge dichotomy agree systematically with those based on S\'ersic index. Low S\'ersic index bulges have both increased rotational support (higher v/sigma values) and on average lower central velocity dispersions. Furthermore, we confirm that the same correlation also holds when visual morphologies are used to diagnose bulge type. The previously noted trend of photometrically flattened bulges to have shallower velocity dispersion profiles turns to be significant and systematic if the S\'ersic index is used to distinguish between pseudobulges and classical bulges. The correlation between h3 and v/sigma observed in elliptical galaxies is also observed in intermediate type galaxies, irrespective of bulge type. Finally, we present evidence for formerly undetected counter rotation in the two systems NGC 3945 and NGC 4736. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universit\"at M\"unchen, and Georg-August-Universit\"at G\"ottingen.Comment: 49 pages, 16 figures. Accepted for publication in Ap

In pursuit of linear complexity in discrete and computational geometry

Many computational problems arise naturally from geometric data. In this thesis, we consider three such problems: (i) distance optimization problems over point sets, (ii) computing contour trees over simplicial meshes, and (iii) bounding the expected complexity of weighted Voronoi diagrams. While these topics are broad, here the focus is on identifying structure which implies linear (or near linear) algorithmic and descriptive complexity. The first topic we consider is in geometric optimization. More specifically, we define a large class of distance problems, for which we provide linear time exact or approximate solutions. Roughly speaking, the class of problems facilitate either clustering together close points (i.e. netting) or throwing out outliers (i.e pruning), allowing for successively smaller summaries of the relevant information in the input. A surprising number of classical geometric optimization problems are unified under this framework, including finding the optimal k-center clustering, the kth ranked distance, the kth heaviest edge of the MST, the minimum radius ball enclosing k points, and many others. In several cases we get the first known linear time approximation algorithm for a given problem, where our approximation ratio matches that of previous work. The second topic we investigate is contour trees, a fundamental structure in computational topology. Contour trees give a compact summary of the evolution of level sets on a mesh, and are typically used on massive data sets. Previous algorithms for computing contour trees took Θ(n log n) time and were worst-case optimal. Here we provide an algorithm whose running time lies between Θ(nα(n)) and Θ(n log n), and varies depending on the shape of the tree, where α(n) is the inverse Ackermann function. In particular, this is the first algorithm with O(nα(n)) running time on instances with balanced contour trees. Our algorithmic results are complemented by lower bounds indicating that, up to a factor of α(n), on all instance types our algorithm performs optimally. For the final topic, we consider the descriptive complexity of weighted Voronoi diagrams. Such diagrams have quadratic (or higher) worst-case complexity, however, as was the case for contour trees, here we push beyond worst-case analysis. A new diagram, called the candidate diagram, is introduced, which allows us to bound the complexity of weighted Voronoi diagrams arising from a particular probabilistic input model. Specifically, we assume weights are randomly permuted among fixed Voronoi sites, an assumption which is weaker than the more typical sampled locations assumption. Under this assumption, the expected complexity is shown to be near linear