Optimal Data Collection For Informative Rankings Expose Well-Connected Graphs

Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method for collecting data for which the least squares estimator for the ranking problem has maximal Fisher information. Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer problem is to identify data which maximizes the informativeness of the ranking. Under certain assumptions, the data collection problem decouples, reducing to a problem of finding multigraphs with large algebraic connectivity. This reduction of the data collection problem to graph-theoretic questions is one of the primary contributions of this work. As an application, we study the Yahoo! Movie user rating dataset and demonstrate that the addition of a small number of well-chosen pairwise comparisons can significantly increase the Fisher informativeness of the ranking. As another application, we study the 2011-12 NCAA football schedule and propose schedules with the same number of games which are significantly more informative. Using spectral clustering methods to identify highly-connected communities within the division, we argue that the NCAA could improve its notoriously poor rankings by simply scheduling more out-of-conference games.Comment: 31 pages, 10 figures, 3 table

In situ observations of BrO over Antarctica: ER-2 aircraft results from 54 S to 72 S latitude

Bromine monoxide was observed in situ at approximately 18 km altitude during nine flights of the NASA ER-2 aircraft from Punta Arenas, Chile (54 altitude) to 72 S latitude over the Palmer Peninsula, Antarctica. The first flight for the BrO detection system was on 28 August. Here, the results from the flights over Antarctica and from the ferry flights from Punta Arenas to Moffett Field, CA (37 N latitude are reported. A key question concerning BrO, then, is how it is distributed with respect to the chemical containment vessel defined by elevated ClO mixing ratios. This question is answered with greatest statistical significance if the data are averaged into five regions: outside the vessel, aircraft heading south; inside the vessel on the same potential temperature surface; in the dive region; inside the vessel on a given potential temperature surface, aircraft heading north; and outside the vessel on the same surface. The result is that the BrO distribution inside the chemical containment vessel was different from that found outside. Inside, the BrO mixing ratio was (5.0 plus or minus 1.1) pptv between the 400 K and 460 K potential temperature surfaces, decreasing only slightly with potential temperature, and was less than 3.6 pptv below the 4 00 K surface. The abundance of BrO inside the chemical containment vessel showed no discernible temporal trend during the course of the nine flights. Outside the vessel, the BrO mixing ratio was (4.7 plus or minus 1.3) pptv near the 450 K surface, but decreased to (2.8 plus or minus 1.0) pptv near the 420 K surface

An Improved Version of the NASA-Lockheed Multielement Airfoil Analysis Computer Program

An improved version of the NASA-Lockheed computer program for the analysis of multielement airfoils is described. The predictions of the program are evaluated by comparison with recent experimental high lift data including lift, pitching moment, profile drag, and detailed distributions of surface pressures and boundary layer parameters. The results of the evaluation show that the contract objectives of improving program reliability and accuracy have been met

Upgraded viscous flow analysis of multi-element airfoils

A description of an improved version of the NASA/Lockheed multi-element airfoil analysis computer program is presented. The improvements include several major modifications of the aerodynamic model as well as substantial changes of the computer code. The modifications of the aerodynamic model comprise the representation of the boundary layer and wake displacement effects with an equivalent source distribution, the prediction of wake parameters with Green's lag-entrainment method, the calculation of turbulent boundary layer separation with the method of Nash and Hicks, the estimation of the onset of confluent boundary layer separation with a modified form of Goradia's method, and the prediction of profile drag with the formula of Squire and Young. The modifications of the computer program for which the structured approach to computer software development was employed are also described. Important aspects of the structured program development such as the functional decomposition of the aerodynamic theory and its numerical implementation, the analysis of the data flow within the code, and the application of a pseudo code are discussed

Uncertainty quantification applied to the analysis and design of a hypersonic inflatable aerodynamic decelerator for spacecraft reentry

The primary objective of this research is to investigate the uncertainty in the multidisciplinary analysis of a Hypersonic Inflatable Aerodynamic Decelerator configuration for Mars entry, subject to uncertainty sources in the high-fidelity computational models and the operating conditions. Efficient uncertainty quantification methods based on stochastic expansions are applied to the analysis of the hypersonic flowfield, fluid-structure interaction, and flexible thermal protection system response of a deformable inflatable decelerator. Uncertainty analysis is first applied to the hypersonic flowfield simulations to quantify the uncertainty in the surface convective and radiative heat flux, pressure, and shear stress of a fixed inflatable decelerator, subject to uncertainties in the binary collision integrals of the transport properties, chemical kinetics, non-Boltzmann radiation modeling, and the freestream conditions. The uncertainty analysis for fluid-structure interaction modeling is conducted to quantify the uncertainty in the deflection and resulting surface heat flux, shear stress, and pressure of a deformable inflatable decelerator, subject to uncertainties in material structural properties, inflation pressure, and important flowfield uncertain variables identified in the initial study. The deflection uncertainty is shown to be primarily driven by the structural modeling uncertain variables and found to be insignificant in contributing to the resulting surface condition uncertainties. Uncertainty analysis is finally applied to the flexible thermal protection system bondline temperature for a ballistic Mars entry trajectory, subject to uncertainties in the material thermal properties and important flowfield variables from the initial study. The uncertainty in the bondline temperature is compared to its allowable temperature limit and shown to be primarily driven by the material thermal properties of the outer fabric and insulator layers, and the freestream density --Abstract, page iv

Probabilistic Risk Analysis and Margin Process for a Flexible Thermal Protection System

Atmospheric entry vehicle thermal protection systems are margined due to the uncertainties that exist in entry aeroheating environments and the thermal response of the materials and structures. Entry vehicle thermal protections systems are traditionally over-margined for the heat loads that are experienced along the entry trajectory by designing to survive stacked worst-case scenarios. Additionally, the conventional heat shield design and margin process offers very little insight into the risk of over-temperature during flight and the corresponding reliability of the heat shield performance. A probabilistic margin process can be used to appropriately margin the thermal protection system based on rigorously calculated risk of failure. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory design, and risk trades while preventing excessive margin from being applied. This study presents the methods of the probabilistic margin process and how the uncertainty analysis is used to determine the reliability of the entry vehicle thermal protection system and associated risks of failure

Reliability-Based Design of Thermal Protection Systems with Support Vector Machines

The primary objective of this work was to develop a computationally efficient and accurate approach to reliability analysis of thermal protection systems using support vector machines. An adaptive sampling approach was introduced informs a iterative support vector machine approximation of the limit state function used for measuring reliability. The proposed sampling approach efficient adds samples along the limit state function until the reliability approximation is converged. This methodology is applied to two samples, mathematical functions to test and demonstrate the applicability. Then, the adaptive sampling-based support vector machine approach is applied to the reliability analysis of a thermal protection system. The results of all three problems highlight the potential capability of the new approach in terms of accuracy and computational saving in determining thermal protection system reliability

Calibration Probe Uncertainty and Validation for the Hypersonic Material Environmental Test System

This paper presents an uncertainty analysis of the stagnation-point calibration probe surface predictions for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System facility located at NASA Langley Research Center. A second-order stochastic expansion was constructed over 47 uncertain parameters to evaluate the sensitivities, identify the most significant uncertain variables, and quantify the uncertainty in the stagnation-point heat flux and pressure predictions of the calibration probe for a low- and high-enthalpy test condition. A sensitivity analysis showed that measurement bias uncertainty is the most significant contributor to the stagnation-point pressure and heat flux variance for the low-enthalpy condition. For the high-enthalpy condition, a paradigm shift in sensitivities revealed the computational fluid dynamics model input uncertainty as the main contributor. A comparison between the prediction and measurement of the stagnation-point conditions under uncertainty showed that there was evidence of statistical disagreement. A validation metric was proposed and applied to the prediction uncertainty to account for the statistical disagreement when compared to the possible stagnation-point heat flux and pressure measurements

Island size distributions in submonolayer growth: successful prediction by mean field theory with coverage dependent capture numbers

We show that mean-field rate equations for submonolayer growth can successfully predict island size distributions in the pre-coalescence regime if the full dependence of capture numbers on both the island size and the coverage is taken into account. This is demonstrated by extensive Kinetic Monte Carlo simulations for a growth kinetics with hit and stick aggregation. A detailed analysis of the capture numbers reveals a nonlinear dependence on the island size for small islands. This nonlinearity turns out to be crucial for the successful prediction of the island size distribution and renders an analytical treatment based on a continuum limit of the mean-field rate equations difficult.Comment: 4 pages, 4 figue

Parameter evaluation in Michaelis-menten kinetics.

Parameter estimation reliability in enzyme kinetics depends upon the substrate range concentrations under assay. An inappropriate concentration set may lead to spurious values of km and Vmax in the Michaelis-Menten approach. In this paper, the theoretical arguments for a practical criterium concerning the best work range of substrate concentration are discussed on a velocity ratio basis (V1/Vn) as response to the pertinent substrate concentration ratio (S1/Sn)