Sample quadratic variation of sample continuous second order martingales Technical report no. 12
Sample quadratic variation of sample continuous second order martingales
STATISTICAL PROBABILITY↗
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Kepler's Multiple Planet Systems
Among the 1800 Kepler targets that have candidate planets, 20% have two or more candidate planets. While most of these objects have not yet been confirmed as true planets, several considerations strongly suggest hat the vast majority of these multi-candidate systems are true planetary systems. Virtually all candidate systems are stable, as tested by numerical integrations (assuming a nominal mass-radius relationship). Statistical studies performed on these candidates reveal a great deal about the architecture of planetary systems, including the typical spacing of orbits and flatness of planetary systems. The distribution of observed period ratios shows that the vast majority ofcandidate pairs are neither in nor near low-order mean motion resonances. Nonetheless, there are small but statistically significant excesses of candidate pairs both in resonance and spaced slightly too far apart to be in resonance, particularly near the 2:1 resonance. The characteristics of the confirmed Kepler multi-planet systems will also be discussed.
Lissauer, Jack↗
Kepler's Multiple Planet Systems
Among the 1800 Kepler targets that have candidate planets, 20% have two or more candidate planets. While most of these objects have not yet been confirmed as true planets, several considerations strongly suggest that the vast majority of these multi-candidate systems are true planetary systems. Virtually all candidate systems are stable, as tested by numerical integrations (assuming a nominal mass-radius relationship). Statistical studies performed on these candidates reveal a great deal about the architecture of planetary systems, including the typical spacing of orbits and flatness of planetary systems. The distribution of observed period ratios shows that the vast majority of candidate pairs are neither in nor near low-order mean motion resonances. Nonetheless, there are small but statistically significant excesses of candidate pairs both in resonance and spaced slightly too far apart to be in resonance, particularly near the 2:1 resonance. The characteristics of the confirmed Kepler multi-planet systems will also be discussed.
Lissauer, Jack J.↗
Cancer Risk in Astronauts: A Constellation of Uncommon Consequences
Excess cancers resulting from external radiation exposures have been noted since the early 1950s, when a rise in leukemia rates was first reported in young atomic bomb survivors [1]. Further studies in atomic bomb survivors, cancer patients treated with radiotherapy, and nuclear power plant workers have confirmed that radiation exposure increases the risk of not only leukemia, but also a wide array of solid cancers [2,3]. NASA has long been aware of this risk and limits astronauts' risk of exposure-induced death (REID) from cancer by specifying permissible mission durations (PMD) for astronauts on an individual basis. While cancer is present among astronauts, current data does not suggest any excess of known radiation-induced cancers relative to a comparable population of U.S. adults; however, very uncommon cancers have been diagnosed in astronauts including nasopharyngeal cancer, lymphoma of the brain, and acral myxoinflammatory fibroblastic sarcoma. In order to study cancer risk in astronauts, a number of obstacles must be overcome. Firstly, several factors make the astronaut cohort considerably different from the cohorts that have previously been studied for effects resulting from radiation exposure. The high rate of accidents and the much healthier lifestyle of astronauts compared to the U.S. population make finding a suitable comparison population a problematic task. Space radiation differs substantially from terrestrial radiation exposures studied in the past; therefore, analyses of galactic cosmic radiation (GCR) in animal models must be conducted and correctly applied to the human experience. Secondly, a large enough population of exposed astronauts must exist in order to obtain the data necessary to see any potential statistically significant differences between the astronauts and the control population. Thirdly, confounders and effect modifiers, such as smoking, diet, and other space stressors, must be correctly identified and controlled for in those analyses. In order to begin work assessing the astronaut population, the earliest groups of astronauts (selection groups 1-7) provide a unique model. These astronauts were relatively homogenous, white males whose lifestyle characteristics were similar to an average U.S. citizen of the same birth cohort. This work reviews radiation exposure levels, age, and causes of mortality among these early NASA astronauts and discusses the benefits and limitations of assessing such a cohort for radiation-induced cancer risk.
Milder, Caitlin M.↗
An analysis of short pulse and dual frequency radar techniques for measuring ocean wave spectra from satellites
Scanning beam microwave radars were used to measure ocean wave directional spectra from satellites. In principle, surface wave spectral resolution in wave number can be obtained using either short pulse (SP) or dual frequency (DF) techniques; in either case, directional resolution obtains naturally as a consequence of a Bragg-like wave front matching. A four frequency moment characterization of backscatter from the near vertical using physical optics in the high frequency limit was applied to an analysis of the SP and DF measurement techniques. The intrinsic electromagnetic modulation spectrum was to the first order in wave steepness proportional to the large wave directional slope spectrum. Harmonic distortion was small and was a minimum near 10 deg incidence. NonGaussian wave statistics can have an effect comparable to that in the second order of scattering from a normally distributed sea surface. The SP technique is superior to the DF technique in terms of measurement signal to noise ratio and contrast ratio.
Jackson, F. C.↗
Cumulative time statistics of surface-point rainfall rates
Statistics on rainfall rates near and above the earth's surface are needed in order to estimate the percentage of time of absorption, or scattering of radio waves that affect radio system design and electrospace management. The most useful averaging time for computing such rates is on the order of 1 min or less. This paper extrapolates excessive short-duration precipitation data to provide such statistics from data routinely reported by the National Weather Service. For the 8766 h in an average year, and for a median or random location in any part of the world, the model described here estimates the fraction of time during which t-minute average rainfall rates exceed any given value.
Rice, P. L.↗
Iterated Sigma-Point Kalman Filtering for Trajectory Reconstruction
Two second-order Kalman filtering methods are added to the New Statistical Trajec-tory Estimation Program (NewSTEP). The two filters are of the class of Sigma-Point Kalman Filters, namely the Unscented Kalman Filter and the Divided Difference Filter. Both filters are implemented with an iterative measurement update step. Results from simulation test case and a flight data test case are provided to show the filter performance. The results indicate that the new second-order filters pro-duce trajectory estimates with reduced uncertainties when compared to the existing first-order filtering method.
Sophia Vedvik↗
Uncertainty Analysis of Instrument Calibration and Application
Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.
Tripp, John S.↗
A simulation study exploring the effects of sensor spatial resolution on estimates of cloud cover from satellites.
Investigation of the effects of sensor spatial resolution on estimating the amount of clouds covering the earth by simulating various cloud distributions and sizes, and measuring the known cloud amount with resolution of different sizes using a cloud-no cloud threshold technique often applied in automatic data processing. Cloud amount statistics have been tabulated for a three-orders-of-magnitude range in the ratio (R) of areal cloud size to areal resolution size for seven cloud amounts between 6 and 90%. Three different cloud patterns were used. These were 1) a regularly spaced pattern of homogeneous dots arranged in rows and columns (to simulate cloud streets), 2) a randomly spaced pattern of the same dots (to simulate randomly oriented cumulus clouds), and 3) a heterogeneous cloud size distribution irregularly spaced (to simulate a view of different cloud types and sizes). Two cloud amount estimation techniques were tested. Cloud amounts of 100% (method 1) and 50% (method 2) were assigned to partially filled resolution elements. Using criteria applicable to some studies carried out in the past, it is shown that cloud amount estimations can be in error by as much as 86 and 38%, respectively, for the two methods. Nomograms have been developed which subtantially improve the estimate of the true cloud cover for R less than 100, provided that R can be determined.
Shenk, W. E.↗
Study of the Brazil and Falkland currents using their images of Nimbus 5 and oceanographic data in 1972 - 1973
The Western Edge of the Sub-tropical Convergence of the South-western Atlantic Ocean, called the Front, which is a thermal discontinuity between the Brazil and Falkland Currents, was studied utilizing the Temperature Humidity Infrared Radiometer (THIR) of Nimbus V in the 10.5 to 12.5 micrometers channel and historical oceanographic data. Some important results obtained are: the oceanographic Front could be detected from Nimbus THIR data; oceanographic charts showed that the transition zone where the Brazil and the Falkland Currents meet was the Front detected from satellite data; ocean current speeds calculated with THIR data were of the same order of magnitude as those calculated oceanographically; fisheries statistics for Pargo Roseo showed that the maximum catches were in September of 1973, in the period when the Front was observed most distinctly and clearly. The results showed the great potentiality of satellite data to study surface thermal structures, surface currents and oceanic fisheries.
Tseng, Y. C.↗
Long-term radiation effects on GaAs solar cell characteristics
This report investigates preliminary design considerations which should be considered for a space experiment involving Gallium Arsenide (GaAs) solar cells. The electron radiation effects on GaAs solar cells were conducted in a laboratory environment, and a statistical analysis of the data is presented. In order to augment the limited laboratory data, a theoretical investigation of the effect of radiation on GaAs solar cells is also developed. The results of this study are empirical prediction equations which can be used to estimate the actual damage of electrical characteristics in a space environment. The experimental and theoretical studies also indicate how GaAs solar cell parameters should be designed in order to withstand the effects of electron radiation damage.
Heinbockel, J. H.↗
Dipole and quadrupole anisotropy of the 2.7 K radiation
Results of measurements of the dipole and quadrupole anisotropy of the microwave background radiation are reported. Balloon-borne measurements of the temperature difference between two horn antennas pointed 90 deg apart and 45 deg from the zenith were carried out at frequencies of 24.8, 31.4 and 46.0 GHz to determine three dipole and four quadrupole parameters. When combined with data from two previous balloon flights, a dipole anisotropy of 3.78 + or - 0.30 mK in the direction 11.6 + or - 0.2 h RA, -12 + or - 5 deg dec is obtained. The measurements reveal a spectral index of 0.04 + or - 0.28 between 19.0 and 46.0 GHz, indicating that the dipole effect arises from an intrinsic anisotropy in the temperature of the background and/or a first-order Doppler shift due to solar motions. A statistically significant quadrupole effect is also detected which is attributed to the intrinsic anisotropy of the 2.7 K background.
Boughn, S. P.↗
OSO 8 observational limits to the acoustic coronal heating mechanism
An improved analysis of time-resolved line profiles of the C IV resonance line at 1548 A has been used to test the acoustic wave hypothesis of solar coronal heating. It is shown that the observed motions and brightness fluctuations are consistent with the existence of acoustic waves. Specific account is taken of the effect of photon statistics on the observed velocities, and a test is devised to determine whether the motions represent propagating or evanescent waves. It is found that on the average about as much energy is carried upward as downward such that the net acoustic flux density is statistically consistent with zero. The statistical uncertainty in this null result is three orders of magnitue lower than the flux level needed to heat the corona.
Bruner, E. C., Jr.↗
Mapping sand and gravel pits in the Patuxent River watershed
LANDSAT data from July 1973 and June 1978 for the Patuxent River Watershed of Maryland were processed in an effort to devise an economical method of monitoring the reclamation of sand and gravel pits. ASTEP-II and IDIMS software were utilized to derive signatures for sand and gravel pits and other land use/land cover types. Both unsupervised and supervised classifications of the two data sets were produced. Resultant statistics and color output products were compared in order to determine the extent of reclamation and expansion of sand and gravel pits over the five-year time span and to check the locations of more recent sand and gravel pits. Preliminary results indicate that, for a selected northern sub-acre, signatures derived for sand and gravel pits were nearly 90 percent accurate.
Schmidt, T. J.↗
Characterization and measurement of phase-locked loop performance
A set of performance measures and tests are presented which can be implemented at the 'black box' level for the characterization of such statistical aspects of phase-locked loop behavior as the acquisition and tracking threshold, phase error jitter, Doppler accuracy, etc. Also presented is an automatic measurement system, designated the Statistical Loop Analyzer, which has been developed in order to undertake these phase-locked device performance measurements.
Lindsey, W. C.↗
Control of optical systems
Some of the current and planned activities at the Air Force Systems Command in structures and controls for optical-type systems are summarized. Many of the activities are contracted to industry; one task is an in-house program which includes a hardware test program. The objective of the in-house program, referred to as the Aluminum Beam Expander Structure (ABES), is to address issues involved in on-orbit system identification. The structure, which appears similar to the LDR backup structure, is about 35 feet tall. The activity to date has been limited to acquisition of about 250 hours of test data. About 30 hours of data per excitation force is gathered in order to obtain sufficient data for a good statistical estimate of the structural parameters. The development of an Integrated Structural Modeling (ISM) computer program is being done by Boeing Aerospace Company. The objective of the contracted effort is to develop a combined optics, structures, thermal, controls, and multibody dynamics simulation code.
Founds, D.↗
Intraseasonal oscillations in the global atmosphere. II - Southern Hemisphere
A systematic examination of oscillatory modes in the global atmosphere is completed by studying 12 years of 500 mb geopotential heights in the Southern Hemisphere. The data were band-pass filtered to focus on intraseasonal (IS) phenomena, and spatial empirical orthogonal functions (EOFs) were obtained. The leading principal components were subjected to singular spectrum analysis in order to identify nonlinear IS oscillations with high statistical confidence. In the Southern Hemisphere, the dominant mode has a period of 23 days, with spatial patterns carried by the second and third winter EOF of the IS band. It has a zonal wavenumber-four structure. The 40-day mode is second, and is dominated by wavenumbers three and four, while a 16-day mode is too weak to separate its spatial behavior from the previous two. The IS dynamics in the Southern Hemisphere is more complex and dominated by shorter wavenumbers than the Northern Hemisphere. No statistically significant correlations between the Southern Hemisphere and the tropics or the Northern Hemisphere are apparent in the IS band.
Ghil, Michael↗
The ACTS propagation program
The success or failure of the ACTS experiment will depend on how accurately the rain-fade statistics and fade dynamics can be predicted in order to derive an appropriate algorithm that will combat weather vagaries, specifically for links with small terminals, such as very small aperture terminals (VSAT's) where the power margin is a premium. The planning process and hardware development program that will comply with the recommendations of the ACTS propagation study groups are described.
Chakraborty, D.↗