Statistical significance of variables driving systematic variation

There are a number of well-established methods such as principal components analysis (PCA) for automatically capturing systematic variation due to latent variables in large-scale genomic data. PCA and related methods may directly provide a quantitative characterization of a complex biological variable that is otherwise difficult to precisely define or model. An unsolved problem in this context is how to systematically identify the genomic variables that are drivers of systematic variation captured by PCA. Principal components (and other estimates of systematic variation) are directly constructed from the genomic variables themselves, making measures of statistical significance artificially inflated when using conventional methods due to over-fitting. We introduce a new approach called the jackstraw that allows one to accurately identify genomic variables that are statistically significantly associated with any subset or linear combination of principal components (PCs). The proposed method can greatly simplify complex significance testing problems encountered in genomics and can be utilized to identify the genomic variables significantly associated with latent variables. Using simulation, we demonstrate that our method attains accurate measures of statistical significance over a range of relevant scenarios. We consider yeast cell-cycle gene expression data, and show that the proposed method can be used to straightforwardly identify statistically significant genes that are cell-cycle regulated. We also analyze gene expression data from post-trauma patients, allowing the gene expression data to provide a molecularly-driven phenotype. We find a greater enrichment for inflammatory-related gene sets compared to using a clinically defined phenotype. The proposed method provides a useful bridge between large-scale quantifications of systematic variation and gene-level significance analyses.Comment: 35 pages, 1 table, 6 main figures, 7 supplementary figure

Higher-Dimensional Algebra VII: Groupoidification

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of "degroupoidification": a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present three applications of groupoidification. The first is to Feynman diagrams. The Hilbert space for the quantum harmonic oscillator arises naturally from degroupoidifying the groupoid of finite sets and bijections. This allows for a purely combinatorial interpretation of creation and annihilation operators, their commutation relations, field operators, their normal-ordered powers, and finally Feynman diagrams. The second application is to Hecke algebras. We explain how to groupoidify the Hecke algebra associated to a Dynkin diagram whenever the deformation parameter q is a prime power. We illustrate this with the simplest nontrivial example, coming from the A2 Dynkin diagram. In this example we show that the solution of the Yang-Baxter equation built into the A2 Hecke algebra arises naturally from the axioms of projective geometry applied to the projective plane over the finite field with q elements. The third application is to Hall algebras. We explain how the standard construction of the Hall algebra from the category of representations of a simply-laced quiver can be seen as an example of degroupoidification. This in turn provides a new way to categorify - or more precisely, groupoidify - the positive part of the quantum group associated to the quiver.Comment: 67 pages, 14 eps figures; uses undertilde.sty. This is an expanded version of arXiv:0812.486

Hypersonic vehicle simulation model: Winged-cone configuration

Aerodynamic, propulsion, and mass models for a generic, horizontal-takeoff, single-stage-to-orbit (SSTO) configuration are presented which are suitable for use in point mass as well as batch and real-time six degree-of-freedom simulations. The simulations can be used to investigate ascent performance issues and to allow research, refinement, and evaluation of integrated guidance/flight/propulsion/thermal control systems, design concepts, and methodologies for SSTO missions. Aerodynamic force and moment coefficients are given as functions of angle of attack, Mach number, and control surface deflections. The model data were estimated by using a subsonic/supersonic panel code and a hypersonic local surface inclination code. Thrust coefficient and engine specific impulse were estimated using a two-dimensional forebody, inlet, nozzle code and a one-dimensional combustor code and are given as functions of Mach number, dynamic pressure, and fuel equivalence ratio. Rigid-body mass moments of inertia and center of gravity location are functions of vehicle weight which is in turn a function of fuel flow

Boston Hospitality Review: Summer 2013

Hospitality Management: Perspectives from Industry Advisors by Rachel Roginsky and Matthew Arrants -- Te Four ‘Ps’ of Hospitality Recruiting by John D. Murtha -- Te Morris Nathanson Design Collection by Christopher Muller -- Still Searching for Excellence by Bradford Hudso

Integrated support structure

This Major Qualifying Project is part of the Advanced Space Design Program at WPI. The goal is to design a support structure for a NASA GetAway Special experimental canister. The payload integration, weight, volume, and structural integrity of the canister as specified by NASA guidelines were studied. The end result is a complete set of design drawings with interface drawings and data to specify the design and leave a base on which the next group can concentrate

Enhanced atomic layer etching of native aluminum oxide for ultraviolet optical applications

We report on the development and application of an atomic layer etching (ALE) procedure based on alternating exposures of trimethylaluminum and anhydrous hydrogen fluoride (HF) implemented to controllably etch aluminum oxide. Our ALE process utilizes the same chemistry previously demonstrated in the atomic layer deposition of aluminum fluoride thin films, and can therefore be exploited to remove the surface oxide from metallic aluminum and replace it with thin fluoride layers in order to improve the performance of ultraviolet aluminum mirrors. This ALE process is modified relative to existing methods through the use of a chamber conditioning film of lithium fluoride, which is shown to enhance the loss of fluorine surface species and results in conformal layer-by-layer etching of aluminum oxide films. Etch properties were explored over a temperature range of 225 to 300 {\deg}C with the Al2O3 etch rate increasing from 0.8 to 1.2 {\AA} per ALE cycle at a fixed HF exposure of 60 ms per cycle. The effective etch rate has a dependence on the total HF exposure, but the process is shown to be scalable to large area substrates with a post-etch uniformity of better than 2% demonstrated on 125 mm diameter wafers. The efficacy of the ALE process in reducing interfacial native aluminum oxide on evaporated aluminum mirrors is demonstrated with characterization by x-ray photoelectron spectroscopy and measurements of ultraviolet reflectance at wavelengths down to 120 nm