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At least 181 records · Page 10

Deriving Laws from Ordering Relations

It took much effort in the early days of non-Euclidean geometry to break away from the mindset that all spaces are flat and that two distinct parallel lines do not cross. Up to that point, all that was known was Euclidean geometry, and it was difficult to imagine anything else. We have suffered a similar handicap brought on by the enormous relevance of Boolean algebra to the problems of our age-logic and set theory. Previously, I demonstrated that the algebra of questions is not Boolean, but rather is described by the free distributive algebra. To get to this stage took much effort, as many obstacles-most self-placed-had to be overcome. As Boolean algebras were all I had ever known, it was almost impossible for me to imagine working with an algebra where elements do not have complements. With this realization, it became very clear that the sum and product rules of probability theory at the most basic level had absolutely nothing to do with the Boolean algebra of logical statements. Instead, a measure of degree of inclusion can be invented for many different partially ordered sets, and the sum and product rules fall out of the associativity and distributivity of the algebra. To reinforce this very important idea, this paper will go over how these constructions are made, while focusing on the underlying assumptions. I will derive the sum and product rules for a distributive lattice in general and demonstrate how this leads to probability theory on the Boolean lattice and is related to the calculus of quantum mechanical amplitudes on the partially ordered set of experimental setups. I will also discuss the rules that can be derived from modular lattices and their relevance to the cross-ratio of projective geometry.

Knuth, Kevin H.↗

Coupled Groups of g-Modes in a Sun with Mixed Core

Groups of linear g-modes can sum to create long-lived nonlinear oscillations in small "hot volumes" very deep in the Sun that help drive the modes. In these volumes (dimensions -10 Mm), the time average rate of He-3 burning doubles as temperature fluctuations exceed 10% and rises by an order of magnitude for fluctuations of 25%. To be consistent with locally large motions, we impose a mixed shell on an otherwise standard solar model before computing g-mode solutions. Mixing in the assumed shell r = (0.10+/-0.03) R(sub sun) is rapid (<<10(exp 6) yr) with slower mixing somewhat beyond. If l is the principal spherical harmonic index, a set of g-modes for any single l less than or equal to 15 with five consecutive radial harmonics can be excited with nearly linear thermal amplitudes, A(sub T) less than or equal to 0.053, throughout the star and a fractional temperature fluctuation in its hot volume of (Delta)T/T less than or equal to 0.18. These thresholds for excitation will become smaller when sets for several values of l are computed simultaneously. There is some evidence for the rotation of g-mode sets in the long solar activity record and g-mode upward wave flux has been suggested to explain the 1.3 yr reversing flows tentatively detected below the Sun's convective envelope (CE). The large local amplitudes needed for excitation implies that g-modes may transport a non-negligible fraction of the solar luminosity, yet their near linear amplitudes outside the hot volume suggests amplitudes over most of the solar surface that would be barely detectable for l > 3. A formalism is presented for summing the g-modes and estimating growth rates under the approximation that modes are strictly linear except in a hot volume which holds only a few percent of mode kinetic energy. Finally over the range 2 less than or equal to l less than or equal to 30, we summed all zonal harmonics, m, for a given l and computed the relative angular orientations that would release the most nuclear energy. This should be close to the physically preferred angular state of such a family and a few examples were displayed.

Wolff, Charles L.↗

Antenna feed system for receiving circular polarization and transmitting linear polarization

An object is to provide for receiving a circularly polarized signal from an antenna feed (10) connected to orthogonally spaced antenna elements (11, 12, 13, 14) and for transmitting a linearly polarized signal through the same feed without switches, and without suffering a 3 dB polarization mismatch loss, using an arrangement of hybrid junctions. The arrangement is comprised of two dividing hybrid junctions (15, 16), each connected to a different pair of antenna elements and a summing hybrid junction (17). In one embodiment, a receiver (18) is connected to the summing hybrid junction directly. A diplexer (19a or 19b) is used to connect a transmitter (20a or 20b) to only one pair of antenna elements. In an alternative embodiment, designated left and right circularly polarized (LCP and RCP) transmitters (21, 22) are connected to the summing hybrid junction by separate diplexers (23, 24), and separate LCP and RCP sensitive receivers (25, 26) are connected to the diplexers in order to transmit linearly polarized signals using all four antenna elements while receiving circularly polarized signals as before. An orthomode junction (30) and horn antenna (32) may replace the two dividing hybrid junctions (15, 16) and antenna feed (10).

Seidel, Boris L.↗

Auditory alert systems with enhanced detectability

Methods and systems for distinguishing an auditory alert signal from a background of one or more non-alert signals. In a first embodiment, a prefix signal, associated with an existing alert signal, is provided that has a signal component in each of three or more selected frequency ranges, with each signal component in each of three or more selected level at least 3-10 dB above an estimated background (non-alert) level in that frequency range. The alert signal may be chirped within one or more frequency bands. In another embodiment, an alert signal moves, continuously or discontinuously, from one location to another over a short time interval, introducing a perceived spatial modulation or jitter. In another embodiment, a weighted sum of background signals adjacent to each ear is formed, and the weighted sum is delivered to each ear as a uniform background; a distinguishable alert signal is presented on top of this weighted sum signal at one ear, or distinguishable first and second alert signals are presented at two ears of a subject.

Begault, Durand R.↗

Using Fractional Clock-Period Delays in Telemetry Arraying

A set of special digital all-pass finite-impulse- response (FIR) filters produces phase shifts equivalent to delays that equal fractions of the sampling or clock period of a telemetry-data-processing system. These filters have been used to enhance the arraying of telemetry signals that have been received at multiple ground stations from spacecraft (see figure). Somewhat more specifically, these filters have been used to align, in the time domain, the telemetry-data sequences received by the various antennas, in order to maximize the signal-to-noise ratio of the composite telemetric signal obtained by summing the signals received by the antennas. The term arraying in this context denotes a method of enhanced reception of telemetry signals in which several antennas are used to track a single spacecraft. Each antenna receives a signal that comprises a sum of telemetry data plus noise, and these sum data are sent to an arraying combiner for processing. Correlation is the means used to align the set of data from one antenna with that from another antenna. After the data from all the antennas have been aligned in the time domain, they are all added together, sample by sample.

Fort, David↗

The Valence of Iron in CM Chondrite Serpentine as Measured by Synchrotron Xanes

Fe-bearing phyllosilicates are the dominant product of aqueous alteration in carbonaceous chondrites, and serpentine is the most abundant phyllosilicate in CM2 chondrites that are the most abundant carbonaceous chondrite. Browning et al. predicted that Fe(3+)/(sum of Fe) ratios of serpentine in CM chondrites should change with progressive alteration. They proposed that progressive CM alteration is best monitored by evaluating the progress of Si and Fe3+ substitutions that necessarily attend the transition from end-member cronstedtite to serpentine. Their proposed Mineralogic Alteration Index, 2-(Fe(3+)/(2-Si)), was intended to highlight and utilize the relevant ex-change information in the stoichiometric phyllosilicate formulas based upon the coupled substitution of 2(Fe(3+), Al) = Si + (Mg, Fe(2+)...) in serpentine. The value of this ratio increases as alteration proceeds. We always wanted to directly test Browning s pre-diction through actual measurements of the Fe3+ con-tent of serpentine at the micron scale appropriate to EPMA analyses (Zega et al. have measured it at much finer scale), and this test can now be made using Synchrotron Radiation X-ray Absorption Near-Edge Structure (SR-XANES). Thus, we have recently begun investigation with CMs that span a large portion of the range of observed aqueous alteration, and we first analyzed Murray, Nogoya, and ALH84029 by SR-XANES. However, we did not find clear correlation between Fe3+/(sum of Fe) ratios of serpentine and their alteration degrees. We thus analyzed serpentine in three more CMs and here report their Fe3+/(sum of Fe) ratios in comparison with our previous results.

Mikouchi, T.↗

CRUQS: A Miniature Fine Sun Sensor for Nanosatellites

A new miniature fine Sun sensor has been developed that uses a quadrant photodiode and housing to determine the Sun vector. Its size, mass, and power make it especially suited to small satellite applications, especially nanosatellites. Its accuracy is on the order of one arcminute, and it will enable new science in the area of nanosatellites. The motivation for this innovation was the need for high-performance Sun sensors in the nanosatellite category. The design idea comes out of the LISS (Lockheed Intermediate Sun Sensor) used by the sounding rocket program on their solar pointing ACS (Attitude Control System). This system uses photodiodes and a wall between them. The shadow cast by the Sun is used to determine the Sun angle. The new sensor takes this concept and miniaturizes it. A cruciform shaped housing and a surface-mount quadrant photodiode package allow for a two-axis fine Sun sensor to be packaged into a space approx.1.25xl x0.25 in. (approx.3.2x2.5x0.6 cm). The circuitry to read the photodiodes is a simple trans-impedance operational amplifier. This is much less complex than current small Sun sensors for nanosatellites that rely on photo-arrays and processing of images to determine the Sun center. The simplicity of the circuit allows for a low power draw as well. The sensor consists of housing with a cruciform machined in it. The cruciform walls are 0.5-mm thick and the center of the cruciform is situated over the center of the quadrant photodiode sensor. This allows for shadows to be cast on each of the four photodiodes based on the angle of the Sun. A simple operational amplifier circuit is used to read the output of the photodiodes as a voltage. The voltage output of each photodiode is summed based on rows and columns, and then the values of both rows or both columns are differenced and divided by the sum of the voltages for all four photodiodes. The value of both difference over sums for the rows and columns is compared to a table or a polynomial fit (depending on processor power and accuracy requirements) to determine the angle of the Sun in the sensor frame.

Heatwole, Scott↗

Colonoscopy Screening in the US Astronaut Corps

BACKGROUND: Historically, colonoscopy screenings for astronauts have been conducted to ensure that astronauts are in good health for space missions. Recently this historical data has been identified as being useful for developing an occupational surveillance requirement. It can be used to assess overall colon health and to have a point of reference for future tests in current and former astronauts, as well as to follow-up and track rates of colorectal cancer and polyps. These rates can be compared to military and other terrestrial populations. In 2003, the active astronaut colonoscopy requirements changed to require less frequent colonoscopies. Since polyp removal during a colonoscopy is an intervention that prevents the polyp from potentially developing into cancer, the procedure decreases the individual's risk for colon cancer. The objective of this study is to evaluate the possible effect of increased follow-up times between colonoscopies on the number and severity of polyps identified during the procedures among both current and former NASA astronauts. Initial results and forward work regarding astronaut colonoscopy screenings will be presented. METHODS: A retrospective study of all colonoscopy procedures performed on NASA astronauts between 1962 and 2015 (both during active career and retirement) was conducted by review of the JSC Clinic Electronic Medical Record and Lifetime Surveillance of Astronaut Health (LSAH) database for colonoscopy screening procedures and pathology reports. The timeframe of interest was from the time of selection into the Astronaut Corps through May 2015 or death. For each colonoscopy report, the following data were captured: date of procedure, age at time of procedure, reason for procedure, quality of bowel prep, completion of procedure and/or reason for termination of procedure, findings of procedure, subsequent treatment (if any), recommended follow-up interval, actual follow up interval, family history of polyps or colon cancer, and other significant items or discrepancies. The population consisted of 338 astronauts: 52 females, 286 males. Of these, 56 were deceased, and 11 astronauts had no record of any colonoscopies. Because of a screening requirement change in 2003, analyses were conducted to determine if there were differences between the two time periods. One-sided Wilcoxon rank sum tests were used to identify statistically significant differences between the two time periods. RESULTS: There was a combined total of 1,964 colonoscopy screenings identified. The average follow-up intervals between colonoscopies were indeed longer after the screening requirement change than before the change. The mean follow-up interval pre -2003 was 3.59 years, while post-2003 it increased to 4.35 years. The statistical significance of this difference was confirmed using a one sided Wilcoxon rank sum test which yielded p<.001. Colonoscopies performed after the requirement change tended to have a higher incidence and greater severity of polyps. From pre-2003 to post-2003 the percentage of colonoscopy procedures yielding no polyps decreased from 83.77% to 74.70%. Not only did post-2003 procedures yield more polyp findings, but the polyps recorded were more often of severe pathology. Before 2003 3.62% of colonoscopy findings were polyps of the hyperplastic type (the least severe polyp type) and only 3.35% were of greater severity. Post-2003, 4.21% of findings were hyperplastic polyps while 11.44% were of greater severity. Upon the investigation of other possible contributing factors to these results, we also found that mean age post-2003 was 54.55 years which was significantly higher than during the pre-2003 timeframe (47.32 years). This was observed with a one-sided Wilcoxon rank sum test, resulting in a p<0.001. The increased average age of astronauts could also be a contributing factor to the greater number of polyps found since the risk of developing polyps increases with age. Further work is needed to better understand the increased incidence and greater severity of polyps found in astronaut colonoscopy outcomes.

Masterova, K.↗

Intercomparison of MODIS AQUA and VIIRS I-Band Fires and Emissions in an Agricultural Landscape - Implications for Air Pollution Research

Quantifying emissions from crop residue burning is crucial as it is a significant source of air pollution. In this study, we first compared the fire products from two different sensors, the Visible Infrared Imaging Radiometer Suite (VIIRS) 375 m active fire product (VNP14IMG) and Moderate Resolution Imaging Spectroradiometer (MODIS) 1 km fire product (MCD14ML) in an agricultural landscape, Punjab, India. We then performed an intercomparison of three different approaches for estimating total particulate matter (TPM) emissions which includes the fire radiative power (FRP) based approach using VIIRS and MODIS data, the Global Fire Emissions Database (GFED) burnt area emissions and a bottom-up emissions approach involving agricultural census data. Results revealed that VIIRS detected fires were higher by a factor of 4.8 compared to MODIS Aqua and Terra sensors. Further, VIIRS detected fires were higher by a factor of 6.5 than Aqua. The mean monthly MODIS Aqua FRP was found to be higher than the VIIRS FRP; however, the sum of FRP from VIIRS was higher than MODIS data due to the large number of fires detected by the VIIRS. Besides, the VIIRS sum of FRP was 2.5 times more than the MODIS sum of FRP. MODIS and VIIRS monthly FRP data were found to be strongly correlated (r2 = 0.98). The bottom-up approach suggested TPM emissions in the range of 88.19-91.19 Gg compared to 42.0-61.71 Gg, 42.59-58.75 Gg and 93.98-111.72 Gg using the GFED, MODIS FRP, and VIIRS FRP based approaches, respectively. Of the different approaches, VIIRS FRP TPM emissions were highest. Since VIIRS data are only available since 2012 compared to MODIS Aqua data which have been available since May 2002, a prediction model combining MODIS and VIIRS FRP was derived to obtain potential TPM emissions from 2003-2016. The results suggested a range of 2.56-63.66 (Gg) TPM emissions per month, with the highest crop residue emissions during November of each year. Our results on TPM emissions for seasonality matched the ground-based data from the literature. As a mitigation option, stringent policy measures are recommended to curtail agricultural residue burning in the study area.

Global Fire Emissions Database (GFED)↗

Target Optimal Aperture Selection

This document describes the computation of optimal pixels for planetary transit targets. The method we describe is based on that used in the End-to-End Model (ETEM), which simulates Kepler science output. An optimal aperture for a target is defined as the set of pixels which maximizes the signal-to-noise ratio (SNR) for that target. The optimal aperture for a target is determined by using catalog data to generate, for that target, a synthetic image with all background stars and signals and a second synthetic image with the target star's flux only. These images are incorporated into a noise model, from which the SNR of each pixel is computed. The pixels around a target are summed in an order that maximizes the SNR with each term. As dimmer and dimmer pixels contribute to this sum, the SNR reaches a maximum and further terms decrease the SNR. The set of pixels whose SNR sums to this maximum value defines the optimal aperture.

Bryson, Stephen↗

Multi-variate Factorisation of Numerical Simulations

Factorisation is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously-proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the Stein and Alpert (1993) factorisation, and the Lunt et al (2012) factorisation. We show that, when more than two variables are being considered, none of these three methods possess all three properties of "uniqueness", "symmetry", and "completeness". Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations – the "linear-sum" factorisation, the "shared-interaction" factorisation, and the "scaled-total" factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical. We present the results of the factorisations in the context of studies that used the previously-proposed factorisations. This reveals that only the linear-sum/shared-interaction factorisation possesses a fourth property – "boundedness", and as such we recommend the use of this factorisation in applications for which these properties are desirable.

Numerican simulations↗

Multi-Variate Factorisation of Numerical Simulations

Factorisation (also known as “factor separation”) is widely used in the analysis of numerical simulations. It allows changes in properties of a system to be attributed to changes in multiple variables associated with that system. There are many possible factorisation methods; here we discuss three previously proposed factorisations that have been applied in the field of climate modelling: the linear factorisation, the Stein and Alpert (1993) factorisation, and the Lunt et al. (2012) factorisation. We show that, when more than two variables are being considered, none of these three methods possess all four properties of “uniqueness”, “symmetry”, “completeness”, and “purity”. Here, we extend each of these factorisations so that they do possess these properties for any number of variables, resulting in three factorisations – the “linear-sum” factorisation, the “shared-interaction” factorisation, and the “scaled-residual” factorisation. We show that the linear-sum factorisation and the shared-interaction factorisation reduce to be identical in the case of four or fewer variables, and we conjecture that this holds for any number of variables. We present the results of the factorisations in the context of three past studies that used the previously proposed factorisations.

Numerical simulations↗

A simple differential game.

Necessary and sufficient conditions for optimal strategies for differential /two person zero-sum/ game with sum determined by ordinary differential equations

Leitmann, G.↗

Synchronizing redundant power oscillators

Outputs of oscillators are synchronized by summing the power transformer phase voltages, the summed voltages are applied to the frequency determining inductors of the individual voltage-controlled power oscillators. The beat frequency is eliminated when synchronization is achieved.

Jenson, K. J.↗

Digital decorrelator saves time and expense in acoustic testing of structures

Instantaneous signals from coherent random sound field are summed and time delayed to avoid introducing vectorial addition errors. Resultant statistically independent signals are applied to spectrometer. Displayed sound pressure level is proportional to square root of sum of squares of sound pressure levels taken over frequency range of interest.

Nakich, R. B.↗

Liapunov functions for non-linear difference equation stability analysis.

Liapunov functions to determine the stability of non-linear autonomous difference equations can be developed through the use of auxiliary exact difference equations. For this purpose definitions are introduced for the gradient of an implicit function of a discrete variable, a principal sum, a definite sum and an exact difference equation, and a theorem for exactness of a difference form is proved. Examples illustrate the procedure.

Park, K. E.↗

Input noise approximation in tracker modeling

The validity of approximating random Gaussian distributed inputs used in human response modeling by sums of discrete sine waves is studied. An ideal rectangular power density spectrum is simulated using both filtered Gaussian white noise and sums-of-discrete sine waves with three different input cutoff frequencies in the same compensatory tracking task. Resulting normalized tracking error and quality operator observations are used to investigate apparent discrepancies in human operator characteristics. Results show that discrete and continuous input tracking data compare favorable when the power in the crossover region is taken into account.

Torrey, P. F.↗

Methods of computing vocabulary size for the two-parameter rank distribution

A summation method is described for computing the vocabulary size for given parameter values in the 1- and 2-parameter rank distributions. Two methods of determining the asymptotes for the family of 2-parameter rank-distribution curves are also described. Tables are computed and graphs are drawn relating paris of parameter values to the vocabulary size. The partial product formula for the Riemann zeta function is investigated as an approximation to the partial sum formula for the Riemann zeta function. An error bound is established that indicates that the partial product should not be used to approximate the partial sum in calculating the vocabulary size for the 2-parameter rank distribution.

Edmundson, H. P.↗