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Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Sen, Syamal K.↗

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

Mathematical models of many physical/statistical problems are systems of linear equations~ Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Sen, Symal K.↗

The Atacama Cosmology Telescope: delensed power spectra and parameters

We present ΛCDM cosmological parameter constraints obtained from delensed microwave background power spectra. Lensing maps from a subset of DR4 data from the Atacama Cosmology Telescope (ACT) are used to undo the lensing effect in ACT spectra observed at 150 and 98 GHz. At 150 GHz, we remove the lensing distortion with an effective efficiency of 30% (T T), 30% (EE), 26% (T E) and 20% (BB); this results in detections of the delensing effect at 8.7σ (T T), 5.1σ (EE), 2.6σ (T E), and 2.4σ (BB) significance. The combination of 150 and 98 GHz T T, EE, and T E delensed spectra is well fit by a standard ΛCDM model. We also measure the shift in best-fit parameters when fitting delensed versus lensed spectra; while this shift does not inform our ability to measure cosmological parameters, it does provide a three-way consistency check among the lensing inferred from the best-fit parameters, the lensing in the CMB power spectrum, and the reconstructed lensing map. This shift is predicted to be zero when fitting with the correct model since both lensed and delensed spectra originate from the same region of sky. Fitting with a ΛCDM model and marginalizing over foregrounds, we find that the shift in cosmological parameters is consistent with zero. Our results show that gravitational lensing of the microwave background is internally consistent within the framework of the standard cosmological model.

Dongwon Han↗

Study of fault tolerant software technology for dynamic systems

The major aim of this study is to investigate the feasibility of using systems-based failure detection isolation and compensation (FDIC) techniques in building fault-tolerant software and extending them, whenever possible, to the domain of software fault tolerance. First, it is shown that systems-based FDIC methods can be extended to develop software error detection techniques by using system models for software modules. In particular, it is demonstrated that systems-based FDIC techniques can yield consistency checks that are easier to implement than acceptance tests based on software specifications. Next, it is shown that systems-based failure compensation techniques can be generalized to the domain of software fault tolerance in developing software error recovery procedures. Finally, the feasibility of using fault-tolerant software in flight software is investigated. In particular, possible system and version instabilities, and functional performance degradation that may occur in N-Version programming applications to flight software are illustrated. Finally, a comparative analysis of N-Version and recovery block techniques in the context of generic blocks in flight software is presented.

Caglayan, A. K.↗

Theory of wing-body drag at supersonic speeds

The relation of Whitcomb's "area rule" to the linear formulas for wave drag at lightly supersonic speeds is discussed. By adopting an approximate relation between the source strength and the geometry of a wing-body combination, the wave-drag theory is expressed in terms involving the areas intercepted by oblique planes or Mach planes. The resulting formulas are checked by comparison with the drag measurements obtained in wind-tunnel experiments and in experiments with falling models in free air. Finally, a theory for determining wing-body shapes of minimum drag at supersonic Mach numbers is discussed and some preliminary experiments are reported.

Jones, Robert T↗

Error-Based Design Space Windowing

Windowing of design space is considered in order to reduce the bias errors due to low-order polynomial response surfaces (RS). Standard design space windowing (DSW) uses a region of interest by setting a requirement on response level and checks it by a global RS predictions over the design space. This approach, however, is vulnerable since RS modeling errors may lead to the wrong region to zoom on. The approach is modified by introducing an eigenvalue error measure based on point-to-point mean squared error criterion. Two examples are presented to demonstrate the benefit of the error-based DSW.

Papila, Melih↗

Global Assessment of Volcanic Debris Hazards from Space

Hazard (slope stability) assessment for different sectors of volcano edifices was successfully obtained from volcanoes in North and South America. The assessment entailed Hyperion images to locate portions of the volcano that were hydrothermally altered to clay rich rocks with zones that were also rich in alunite and other minerals. The identified altered rock zones were field checked and sampled. The rock strength of these zones was calculated from the field and laboratory measurements. Volcano modeling utilizing the distinct element method and limit equilibrium technique, with the calculated strength data was used to assess stability and deformation of the edifice. Modeling results give indications of possible failure volumes, velocities and direction. The models show the crucial role hydrothermally weak rock plays in reducing the strength o the volcano edifice and the rapid identification of weak rock through remote sensing techniques. Volcanoes were assessed in the Cascade Range (USA), Mexico, and Chile (ongoing).

Watters, Robert J.↗

Reaching for the APEX at Ames

The multidimensional design of the APEX program is the result of an extensive research and development effort dating back nearly a decade. "In the late 1990s and early 2000, we were pretty successful at getting new research and technology projects here at the center," Johnson says, "and we had a lack of critical mass of project managers. We were taking people who were primarily researchers and putting them in the position of managing projects." Smith and Johnson held a series of workshops across the center during 2000 and 2001 to gather feedback about how to address this issue. When they briefed the center's senior management on their findings, one of the top recommendations was to establish a project manager development program at Ames. At that point, they cast a wide net for ideas and information. "We did centerwide needs assessment, we did focus groups, we did surveys," Smith says. "We came up with a proposal for what a program would look like, tying in what we knew about the Academy of Program1 Project Leadership (now the Academy for Program/Project and Engineering Leadership, or APPEL), what we've seen at other centers, what other centers have tried. We were always checking to make sure our program mapped to APPEL. We also looked at the PMI [Project Management Institute] model, INCOSE [International Council on Systems Engineering], CMMI [Capability Maturity Model Integration], you name it." "We had a lot of conversations with the Jet Propulsion Lab and Goddard," Johnson adds. "We saw those centers as models for what Ames was aspiring to be in terms of a center for managing space flight missions." Their research confirmed what they already knew-that strong practitioner involvement would be critical to their program design process. 'XPEX is for the practitioner by the practitioner," Smith says. "They have to be a part of designing it. Otherwise there's no way we could design a program that meets their needs." At the same time that they worked at the grassroots level, they also solicited feedback from the center's senior management. "We recognized that in order for anything to succeed here, we needed to have a champion at the center management level," Johnson said. "You have to have champions, and you have to listen to what the senior managers are saying. They have their own ideas." In the case of APEX, one of those ideas fundamentally reshaped the program. "When we originally started, it was a project management development program," Johnson says, "but in our meeting with our center director, he said, 'Project management is important, but we also need to strengthen our systems engineering.' So we basically added that component to the program based on what he wanted."

Kohut, Matthew↗

Research on Spectroscopy, Opacity, and Atmospheres

I propose to continue providing observers with basic data for interpreting spectra from stars, novas, supernovas, clusters, and galaxies. These data will include allowed and forbidden line lists, both laboratory and computed, for the first five to ten ions of all atoms and for all relevant diatomic molecules. I will eventually expand to all ions of the first thirty elements to treat far UV and X-ray spectra, and for envelope opacities. I also include triatomic molecules provided by other researchers. I have also made CDs with Partridge and Schwenke's water data for work on UV stars. The line data also serve as input to my model atmosphere and synthesis programs that generate energy distributions, photometry, limb darkening, and spectra that can be used for planning observations and for fitting observed spectra. The spectrum synthesis programs produce detailed plots with the lines identified. Grids of stellar spectra can be used for radial velocity-, rotation-, or abundance templates and for population synthesis. I am fitting spectra of bright stars to test the data and to produce atlases to guide observers. For each star the whole spectrum is computed from the UV to the far IR. The line data, opacities, models, spectra, and programs are freely distributed on CDs and on my Web site and represent a unique resource for many NASA programs. I am now in full production of new line lists for atoms. I am computing all ions of all elements from H to Zn and the first 5 ions of all the heavier elements, about 800 ions. For each ion I treat as many as 61 even and 61 odd configurations, computing all energy levels and eigenvectors. The Hamiltonian is determined from a scaled-Hartree-Fock starting guess by least squares fitting the observed energy levels. The average energy of each configuration is used in computing scaled-Thomas-Fermi-Dirac wavefunctions for each configuration which in turn are used to compute allowed and forbidden transition integrals. These are multiplied into the LS allowed and forbidden transition arrays. The transition arrays are transformed to the observed coupling to yield the allowed and forbidden line lists. Results are put on the web as they are finished. Provided I get funding,there will be more than 500 million lines. I will then compare ion by ion, to all the laboratory and computed data in the literature and make up a working line list for spectrum synthesis and opacity calculations with the best available data. As the laboratory spectrum analyses are improved, I will redo the calculations with the new energy levels. My original plan when I started the new calculations was to run through all the atoms using my old Cray programs from the 1980's that were limited to 1100 x 1100 arrays in the Hamiltonian for each J. Then I would go back and rerun the more complicated cases with 3000 x 3000 arrays so that I could include many more configurations and more configuration interactions. At present I am limited to 61 even and 61 odd configurations and I try to include everything up through n = 9. The current program runs on Alpha workstations. I decided to test the big program on Fe I and Fe II to see whether there was any great difference in the low configurations compared to those from the Cray program. Besides increasing the number of E1 lines by a factor of 6 to 7.7 million, there was an unexpected result: the electric quadrupole transitions were 10 times stronger than before because the transition integrals are weighted by r(exp 2) ---they become very large for high n, and because there are numerous configuration interactions that mix the low and high configurations. As a check I was able to reproduce Carstang's (1962) lower results by running his three configurations with my program. Since my model atom is still only a subset of a real Fe II ion, the true quadrupole A values are probably larger than mine. The magnetic dipole lines are affected by the mixing but the overall scale does not change. Because of this scovery I decided that there was no point in computing the small array cases. I have been running with as many configurations as I can and with thousands of parameters in the Hamiltonian. The computer runs take much longer to set up and produce than I had expected. I have concentrated on redoing the low iron group spectra, especially to get data for supernova modelers. I have done only Ca I -- Zn I, Ca II -- Zn II, CU I -- Cu XXIX, Zn I - Zn XXX, for practice at high stages of ionization, C I, C II, S I, and CL I and Ag I for people who were working on the laboratory spectra. Check my web site kurucz.harvard.edu for current additions. My latest calculations have been for carbon I and sulphur I, and silicon I is under way using the same elaborate approach as for C I, which took many months to do. These line lists greatly increase the number of lines in the ultraviolet, in the visible, and especially in the infrared. They will increase the opacity in A, F, and G stars. They will account for many unidentified lines in the sun.

Kurucz, Robert L.↗

Ground effect for V/STOL aircraft configurations and its simulation in the wind tunnel. Part 2: Experimental studies

Wind tunnel tests on a finite, knee-blowing-flapped wing and on a direct jet lift configuration were performed in a 30 x 42 inch wind tunnel. The objectives of these tests were, in experimental order:(1) to obtain definitive fixed-versus-moving ground comparisons on a powered, high-lift finite wing and on a lifting jet configuration as a function of model height and lift, (2) to understand the flow mechanism which lead to observed differences between moving and fixed-ground results, (3) to discover whether the above effects of a moving ground plane can be simulated by tangential-blowing boundary layer control at the wind tunnel floor, and (4) to check the form and the numerical constants for the wall jet blowing equation derived theoretically in Part I of this report. This relates wall jet blowing quantities to model lift coefficient.

Hackett, J. E.↗

Development of an expert planning system for OSSA

This paper presents concepts related to preliminary work for the development of an expert planning system for NASA's Office for Space Science and Applications (OSSA). The expert system will function as a planner's decision aid in preparing mission plans encompassing sets of proposed OSSA space science initiatives. These plans in turn will be checked against budgetary and technical constraints and tested for constraint violations. Appropriate advice will be generated by the system for making modifications to the plans to bring them in line with the constraints. The OSSA Planning Expert System (OPES) has been designed to function as an integral part of the OSSA mission planning process. It will be able to suggest a best plan, be able to accept and check a user-suggested strawman plan, and should provide a quick response to user request and actions. OPES will be written in the C programming language and have a transparent user interface running under Windows 386 on a Compaq 386/20 machine. The system's sorted knowledge and inference procedures will model the expertise of human planners familiar with the OSSA planning domain. Given mission priorities and budget guidelines, the system first sets the launch dates for each mission. It will check to make sure that planetary launch windows and precursor mission relationships are not violated. Additional levels of constraints will then be considered, checking such things as the availability of a suitable launch vehicle, total mission launch mass required vs. the identified launch mass capability, and the total power required by the payload at its destination vs. the actual power available. System output will be in the form of Gantt charts, spreadsheet hardcopy, and other presentation quality materials detailing the resulting OSSA mission plan.

Groundwater, B.↗

Modeling Off-Nominal Behavior in SysML

Specification and development of fault management functionality in systems is performed in an ad hoc way - more of an art than a science. Improvements to system reliability, availability, safety and resilience will be limited without infusion of additional formality into the practice of fault management. Key to the formalization of fault management is a precise representation of off-nominal behavior. Using the upcoming Soil Moisture Active-Passive (SMAP) mission for source material, we have modeled the off-nominal behavior of the SMAP system during its initial spin-up activity, using the System Modeling Language (SysML). In the course of developing these models, we have developed generic patterns for capturing off-nominal behavior in SysML. We show how these patterns provide useful ways of reasoning about the system (e.g., checking for completeness and effectiveness) and allow the automatic generation of typical artifacts (e.g., success trees and FMECAs) used in system analyses.

fault protection↗

Probing the PeV region in the astrophysical neutrino spectrum using 𝜈 𝜇 from the Southern sky

IceCube has observed a diffuse astrophysical neutrino flux over the energy region from a few TeV to a few PeV. At PeV energies, the spectral shape is not yet well measured due to the low statistics of the data. This analysis probes the gap between 1 and 10 PeV by using high-energy downgoing muon neutrinos. Here, to reject the large atmospheric muon background, two complementary techniques are combined. The first technique selects events with high stochasticity to reject atmospheric muon bundles whose stochastic energy losses are smoothed due to high muon multiplicity. The second technique vetoes atmospheric muons with the IceTop surface array. Using 9 yrs of data, we found two neutrino candidate events in the signal region, consistent with expectation from background, each with relatively high signal probabilities. A joint maximum likelihood estimation is performed using this sample and an independent 9.5-yr sample of tracks to measure the neutrino spectrum. A likelihood ratio test is done to compare the single power-law (SPL) vs SPL+cutoff hypothesis; the SPL+cutoff model is not significantly better than the SPL. High-energy astrophysical objects from four source catalogs are also checked around the direction of the two events. No significant coincidence was found.

Abbasi, R. [Loyola University Chicago] (ORCID:0000↗

Absolute flux measurements in the rocket ultraviolet

A two-channel spectrometer was calibrated in the wavelength region 1200-3400 A and flown on an Aerobee rocket to observe the stars alpha Lyr, eta UMa, and zeta Oph. Standard tungsten lamps provided the absolute calibration down to 2250 A, and a photodiode calibrated by the National Bureau of Standards was the reference at shorter wavelengths. The molecular branching-ratio technique of relative calibration using the gases CO, NO, and N2 was a check on the absolute calibration. The flux from eta UMa agrees with the prediction of a hydrogen line blanketed model atmosphere within 10% between 1700 and 3400 A and within 4% over most of this wavelength region.

Bohlin, R. C.↗

Elemental technetium as a cosmic-ray clock

Several radioactive isotopes have been proposed as clocks for the study of the mean cosmic ray confinement time, T sub e. Measurements of Be-10 and Al-26 give a value for T sub e of about 10 Myr when one uses a leaky box cosmic ray propagation model. It is important to obtain additional measurements of T sub e from other radioactive isotopes in order to check whether the confinement is the same throughout the periodic table. The possible use of Tc (Z = 43) as a cosmic clock is investigated. Since all isotopes of Tc are radioactive, one might be able to group these isotopes and use the elemental abundance as a whole. The results of the calculations are somewhat inconclusive for two reasons. First, the beta + decay half lives of two of the Tc isotopes relevant to our calculation are not known. Second, the dependence of the Tc abundance on the mean confinement time is rather weak when one considers the number of events expected in 4 trays of plastic track detectors. However, a future, finite measurement of the Beta + half lives and the possible use of the entire collecting area of the HNC to detect Tc nuclei could make the use of Tc as a cosmic ray clock more attractive.

Drach, J.↗

Modified Newtonian dynamics and the Coma cluster

The consistency of Milgrom's theory of modified Newtonian dynamics is checked against optical and X-ray data for the Coma cluster of galaxies. It is found that viable models for the cluster containing no dark matter can be constructed. They require an extensive gaseous atmosphere through which galaxies move on near-radial orbits. The gas temperature is predicted to have a shallow minimum near the cluster center; this structure may conflict with the best X-ray spectra of the cluster.

The, Lih Sin↗

[New Determination of the Abundances of Oxygen, Nitrogen and Sulfur as a Function of Galactocentric Distance

The goals of this program were to obtain data which could provide the basis for a new determination of the abundances of Oxygen, Nitrogen, and Sulfur as a function of galactocentric distance. This program was preceded by a detailed VLA high resolution radio study of the ultracompact (UC) HII region G29.96 to demonstrate that reliable electron temperatures could be obtained with nonLTE modeling of the line intensities for a few radio recombination lines distributed over a reasonable range of principle quantum numbers. These results were published. Having demonstrated the technique, a survey of 28 UC HII regions located in the galactocentric distance range of 0- 17 kpc was undertaken. The lines of H42(alpha), H66(alpha), H76(alpha), and H93(alpha) were observed with spatial resolutions of 3.7 to 6.7 arc secs. The nonLTE models constrained by the new data produced a well-defined temperature gradient. This study provided an entirely independent check on direct measurements of abundances via the measurement of spectral lines from atomic coolants.

Churchwell, E. B.↗

Initial PIP-II Beam Current Monitor Fault Case Analyses & Beam Position Monitor Linearity Studies in CST Studio Suite

The use of non-invasive sensors & systems to measure particle beam characteristics is a crucial part of modern accelerator control systems due to their ability to return real time beam data while minimizing negative effects on beam quality. To ensure that one can be reasonably confident these sensors will behave as desired upon be-ing implemented within the beamline, simulations pre-dicting the performance of these sensors under beamline conditions can be used as a valuable tool for checking sensor functionality without a physical test bench. This paper details the design, testing, and results of two sensor models developed using CST Studio Suite soft-ware designed to mimic two sensors to be implemented within the PIP-III beamline: an elliptical, large-aperture beam position monitor (BPM) for which vertical & hori-zontal position signal linearity was analyzed, and an AC current transformer (ACCT) beam current monitor (BCM) used to search for potential fault cases within the BCM and beam pipe flange gaps. Special focus is given to the discovery of linearity variations within the BPM and the use of frequency domain techniques in the BCM fault case analyses.

Rouzky, A. R.↗