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FDR doesn't Tell the Whole Story: Joint Influence of Effect Size and Covariance Structure on the Distribution of the False Discovery Proportions

As part of a 2009 Annals of Statistics paper, Gavrilov, Benjamini, and Sarkar report results of simulations that estimated the false discovery rate (FDR) for equally correlated test statistics using a well-known multiple-test procedure. In our study we estimate the distribution of the false discovery proportion (FDP) for the same procedure under a variety of correlation structures among multiple dependent variables in a MANOVA context. Specifically, we study the mean (the FDR), skewness, kurtosis, and percentiles of the FDP distribution in the case of multiple comparisons that give rise to correlated non-central t-statistics when results at several time periods are being compared to baseline. Even if the FDR achieves its nominal value, other aspects of the distribution of the FDP depend on the interaction between signed effect sizes and correlations among variables, proportion of true nulls, and number of dependent variables. We show examples where the mean FDP (the FDR) is 10% as designed, yet there is a surprising probability of having 30% or more false discoveries. Thus, in a real experiment, the proportion of false discoveries could be quite different from the stipulated FDR.

Feiveson, Alan H.

The Fusion Driven Rocket: Nuclear Propulsion through Direct Conversion of Fusion Energy

The future of manned space exploration and development of space depends critically on the creation of a dramatically more efficient propulsion architecture for in-space transportation. A very persuasive reason for investigating the applicability of nuclear power in rockets is the vast energy density gain of nuclear fuel when compared to chemical combustion energy. The Fusion Driven rocket (FDR) represents a revolutionary approach to fusion propulsion where the power source releases its energy directly into the propellant, not requiring conversion to electricity. It employs a solid lithium propellant that requires no significant tankage mass. The propellant is rapidly heated and accelerated to high exhaust velocity (> 30 km/s), while having no substantial physical interaction with the spacecraft thereby avoiding damage to the rocket and limiting both the thermal heat load and radiator mass. The key to achieving this stems from research at MSNW and the UW on the magnetically driven implosion of metal foils onto a magnetized plasma target to obtain fusion conditions. A logical extension of this work leads to a method that utilizes these metal shells (or liners) to not only achieve fusion conditions, but to serve as the propellant as well. Several low-mass, magnetically driven metal liners are inductively driven to converge radially and axially and form a thick blanket surrounding the target plasmoid and compress the plasmoid to fusion conditions. Virtually all of the radiant, neutron and particle energy from the plasma is absorbed by the encapsulating, thick metal blanket thereby isolating the spacecraft from the fusion. This energy, in addition to the intense Ohmic heating at peak magnetic field compression, is adequate to vaporize and ionize the metal blanket. The expansion of this hot, ionized metal propellant through a magnetically insulated nozzle produces high thrust at the optimal Isp. The energy from the fusion process, along with the waste heat, is thus utilized at very high efficiency. The basic scheme for FDR is illustrated and described in the report (see Fig. 2) The two most critical issues in meeting challenges introduced employing magneto-inertial fusion as the power source is driver efficiency and “stand-off” – the ability to isolate and protect fusion and thruster from the resultant fusion energy. By employing metal shells for compression, it is possible to produce the desired convergent motion inductively by inserting the metal sheets along the inner surface of cylindrical or conically tapered coils. Both stand-off and energy efficiency issues are solved by this arrangement. 3 This two year effort focused on achieving three key criteria for the Fusion Driven Rocket to move forward for technological development: (1) the physics of the FDR must be fully understood and validated, (2) the design and technology development for the FDR required for its implementation in space must be fully characterized, and (3) an in-depth analysis of the rocket design and spacecraft integration as well as mission architectures enabled by the FDR need to be performed. A subscale, laboratory liner compression test facility was assembled at the University of Washington Plasma Dynamics Laboratory with sufficient liner kinetic energy (~ 0.5 MJ) to reach conditions required for fusion breakeven conditions. Detailed experimental studies of the dynamic behavior of the driven liners as well as liner convergence and magnetic compression were performed. The development of both the 1D liner dynamics code and the full 3D ANSYS® liner calculations was achieved. The characterization of both the FDR and spacecraft as well as a design architecture analysis was conducted that included an examination of a wide range of mission architectures and destinations for which this fusion propulsion system would be enabling or critical. In particular a rapid, single launch manned Mars mission was developed.

Energy

Reconstruction of the 1994 Pittsburgh Airplane Accident Using a Computer Simulation

On September 8, 1994, a Boeing 737-300 passenger airplane was on a downwind approach to the Pittsburgh International Airport at an altitude of 5000 feet above ground level (6000 feet MSL). While in a shallow left turn onto a downwind approach heading, the airplane crossed into the vortex trail of a Boeing 727 flying in the same approach pattern about 4 miles ahead. The B-737 airplane rolled and turned sharply to the left, exited the vortex wake and plunged into the ground. Weather was not a factor in the accident. The airplane was equipped with a 11+ channel digital Flight Data Recorder (FDR) and a multiple channel Cockpit Voice Recorder (CVR). Both recorders were recovered from the crash site and provided excellent data for the development of an accident scenario. Radar tracking of the two airplanes as well as the indicated air speed (IAS) perturbations clearly visible on the B-737 FDR recordings indicate that the upset was apparently initiated by the airplane's crossing into the wake of the B-727 flying ahead in the same traffic pattern. A 6 degree-of-freedom simulation program for the B-737 airplane using MATLAB and SIMULINK was constructed. The simulation was initialized at the stabilized flight conditions of the airplane about 13 seconds prior to its entry into the vortex trail of the B-727 airplane. By assuming a certain combination of control inputs, it was possible to produce a simulated motion that closely matched that recorded on the FDR.

Parks, Edwin K.

Predictions of three-body-decays of mesons from pole-dominated dispersion relations

The investigation shows that the method of finite dispersion relations (FDR) as developed by Aviv and Nussinov (1970) is consistent with a wide range of three-body meson decays. The specific results vary with each reaction. For each possibility a definite form for the t-channel Regge-pole terms is selected. The results of the investigation indicate the basic reliability of an approach based on the FDR method and the finite-energy sum rules.

Thews, R. L.

Characterizing the Joint Effect of Diverse Test-Statistic Correlation Structures and Effect Size on False Discovery Rates in a Multiple-Comparison Study of Many Outcome Measures

In their 2009 Annals of Statistics paper, Gavrilov, Benjamini, and Sarkar report the results of a simulation assessing the robustness of their adaptive step-down procedure (GBS) for controlling the false discovery rate (FDR) when normally distributed test statistics are serially correlated. In this study we extend the investigation to the case of multiple comparisons involving correlated non-central t-statistics, in particular when several treatments or time periods are being compared to a control in a repeated-measures design with many dependent outcome measures. In addition, we consider several dependence structures other than serial correlation and illustrate how the FDR depends on the interaction between effect size and the type of correlation structure as indexed by Foerstner s distance metric from an identity. The relationship between the correlation matrix R of the original dependent variables and R~, the correlation matrix of associated t-statistics is also studied. In general R~ depends not only on R, but also on sample size and the signed effect sizes for the multiple comparisons.

Feiveson, Alan H.

An Experimental and Numerical Study of Icing Effects on the Performance and Controllability of a Twin Engine Aircraft

In September 1997 the National Transportation Safety Board (NTSB) requested assistance from the NASA Lewis Research Center (LeRC) Icing Branch in the investigation of an aircraft accident that was suspected of being caused by ice contamination. In response to the request NASA agreed to perform an experimental and computational study. The main activities that NASA performed were LERC Icing Research Tunnel (IRT) testing to define ice shapes and 2-D Navier-Stokes analysis to determine the performance degradation that those ice shapes would have caused. An IRT test was conducted in January 1998. Most conditions for the test were based upon raw and derived data from the Flight Data Recorder (FDR) recovered from the accident and upon the current understanding of the Meteorological conditions near the accident. Using a two-dimensional Navier-Stokes code, the flow field and resultant lift and drag were calculated for the wing section with various ice shapes accreted in the IRT test. Before the final calculations could be performed extensive examinations of geometry smoothing and turbulence were conducted. The most significant finding of this effort is that several of the five-minute ice accretions generated in the IRT were found by the Navier-Stokes analysis to produce severe lift and drag degradation. The information generated by this study suggests a possible scenario for the kind of control upset recorded in the accident. Secondary findings were that the ice shapes accreted in the IRT were mostly limited to the protected pneumatic boot region of the wing and that during testing, activation of the pneumatic boots cleared most of the ice.

Reehorst, A.

Navier-Stokes Analysis of the Flowfield Characteristics of an Ice Contaminated Aircraft Wing

An analytical study was performed as part of the NASA Lewis support of a National Transportation Safety Board (NTSB) aircraft accident investigation. The study was focused on the performance degradation associated with ice contamination on the wing of a commercial turbo-prop-powered aircraft. Based upon the results of an earlier numerical study conducted by the authors, a prominent ridged-ice formation on the subject aircraft wing was selected for detailed flow analysis using 2-dimensional (2-D), as well as, 3-dimensional (3-D) Navier-Stokes computations. This configuration was selected because it caused the largest lift decrease and drag increase among all the ice shapes investigated in the earlier study. A grid sensitivity test was performed to find out the influence of grid spacing on the lift, drag, and associated angle-of-attack for the maximum lift (C(sub lmax)). This study showed that grid resolution is important and a sensitivity analysis is an essential element of the process in order to assure that the final solution is independent of the grid. The 2-D results suggested that a severe stability and control difficulty could have occurred at a slightly higher angle-of-attack (AOA) than the one recorded by the Flight Data Recorder (FDR). This stability and control problem was thought to have resulted from a decreased differential lift on the wings with respect to the normal loading for the configuration. The analysis also indicated that this stability and control problem could have occurred whether or not natural ice shedding took place. Numerical results using an assumed 3-D ice shape showed an increase of the angle at which this phenomena occurred of about 4 degrees. As it occurred with the 2-D case, the trailing edge separation was observed but started only when the AOA was very close to the angle at which the maximum lift occurred.

Chung, J.

Remote Strain Sensing of CFRP Using Microwave Frequency Domain Reflectometry

NASA's Advanced Composites Project is investigating technologies that increase automated remote inspection of aircraft composite structures. Therefore, microwave Frequency Domain Reflectometry (FDR) is being investigated as a method of enabling rapid remote measurement of strain occurring at the first ply of a composite fiber reinforced polymer (CFRP) structure using Radio Frequency (RF) Electro-Magnetic (EM) radiation. While microwave reflectometry has been used to detect disbonds in CFRP structures, its use in detecting strain has been limited. This work will present data demonstrating the measurement of the reactance changes due to loading conditions that are indicative of strain in a CFRP structure. In addition, the basic EM signature will be presented along with an analysis of temperature and humidity effects.

Wilson, William C.

Carbon Fiber TOW Angle Determination Using Microwave Reflectometry

NASA's Advanced Composites Project is investigating technologies that increase automated remote inspection of aircraft composite structures. Therefore, microwave Frequency Domain Reflectometry (FDR) is being investigated as a method of enabling rapid remote inspection of angular orientation of the tow using microwave radiation. This work will present preliminary data demonstrating that frequency shifts in the reflection spectrum of a carbon fiber tow sample are indicative of the angle of the tow with respect to an interrogating antenna's linear polarized output.

Wilson, William C.