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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Frame synchronization for a channel with different data rates

In some communication links, different data rates are used at different times on the same channel and each is assigned a separate frame synchronization (sync) marker. The frame search is completed within a finite number of frame intervals once both phase-lock and bit-sync are achieved because the incoming data rate can change. The probability of failure to frame-lock, and an upper bound of probability of false frame-lock in a frame search mode are derived for a communication link with a 10 to the -5th bit error probability. The probability of failure to detect data-rate change and the probability of false detection of data-rate change in a frame-lock mode are discussed. In a frame-lock mode, the probability of failure to detect data-rate change and probability detection of data-rate change an equal to 4.96 x 10 to the -12th. A frame-lock device can be used for the Space Station Freedom Ku-band return link.

Kwon, Hyuck M.↗
NASA NTRS1992

Inverse sequential detection of parameter changes in developing time series

Progressive values of two probabilities are obtained for parameter estimates derived from an existing set of values and from the same set enlarged by one or more new values, respectively. One probability is that of erroneously preferring the second of these estimates for the existing data ('type 1 error'), while the second probability is that of erroneously accepting their estimates for the enlarged test ('type 2 error'). A more stable combined 'no change' probability which always falls between 0.5 and 0 is derived from the (logarithmic) width of the uncertainty region of an equivalent 'inverted' sequential probability ratio test (SPRT, Wald 1945) in which the error probabilities are calculated rather than prescribed. A parameter change is indicated when the compound probability undergoes a progressive decrease. The test is explicitly formulated and exemplified for Gaussian samples.

Radok, Uwe↗
NASA NTRS1999

Kennedy Space Center Coronary Heart Disease Risk Screening Program

The number one cause of death in the U.S. is coronary heart disease (CHD). It is probably a major cause of death and disability in the lives of employees at Kennedy Space Center (KSC) as well. The KSC Biomedical Office used a multifactorial mathematical formula from the Framingham Heart Study to calculate CHD risk probabilities for individuals in a segment of the KSC population that required medical evaluation for job certification. Those assessed to be high-risk probabilities will be targeted for intervention. Every year, several thousand KSC employees require medical evaluations for job related certifications. Most medical information for these evaluations is gathered on-site at one of the KSC or Cape Canaveral Air Station (CCAS) medical clinics. The formula used in the Framingham Heart Study allows calculation of a person's probability of acquiring CHD within 10 years. The formula contains the following variables: Age, Diabetes, Smoking, Left Ventricular Hypertrophy, Blood Pressure (Systolic or Diastolic), Cholesterol, and HDL cholesterol. The formula is also gender specific. It was used to calculate the 10-year probabilities of CHD in KSC employees who required medical evaluations for job certifications during a one-year time frame. This KSC population was profiled and CHD risk reduction interventions could be targeted to those at high risk. Population risk could also be periodically reevaluated to determine the effectiveness of intervention. A 10-year CHD risk probability can be calculated for an individual quite easily while gathering routine medical information. An employee population's CHD risk probability can be profiled graphically revealing high risk segments of the population which can be targeted for risk reduction intervention. The small audience of NASA/contractor physicians, nurses and exercise/fitness professionals at the breakout session received the lecture very well. Approximately one third indicated by a show of hands that they would be interested in implementing a similar program at their NASA Center. Questions were asked pertaining to standardization for age, the validity of using the idealized male values also for the female population, and indications of the screening test's sensitivity and specificity.

Tipton, David A.↗
NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗
NASA NTRS2001

Spacecraft attitude control systems with dynamic methods and structures for processing star tracker signals

Methods are provided for dynamically processing successively-generated star tracker data frames and associated valid flags to generate processed star tracker signals that have reduced noise and a probability greater than a selected probability P.sub.slctd of being valid. These methods maintain accurate spacecraft attitude control in the presence of spurious inputs (e.g., impinging protons) that corrupt collected charges in spacecraft star trackers. The methods of the invention enhance the probability of generating valid star tracker signals because they respond to a current frame probability P.sub.frm by dynamically selecting the largest valid frame combination whose combination probability P.sub.cmb satisfies a selected probability P.sub.slctd. Noise is thus reduced while the probability of finding a valid frame combination is enhanced. Spacecraft structures are also provided for practicing the methods of the invention.

Liu, Yong↗
NASA NTRS2008

Completion of the Edward Air Force Base Statistical Guidance Wind Tool

The goal of this task was to develop a GUI using EAFB wind tower data similar to the KSC SLF peak wind tool that is already in operations at SMG. In 2004, MSFC personnel began work to replicate the KSC SLF tool using several wind towers at EAFB. They completed the analysis and QC of the data, but due to higher priority work did not start development of the GUI. MSFC personnel calculated wind climatologies and probabilities of 10-minute peak wind occurrence based on the 2-minute average wind speed for several EAFB wind towers. Once the data were QC'ed and analyzed the climatologies were calculated following the methodology outlined in Lambert (2003). The climatologies were calculated for each tower and month, and then were stratified by hour, direction (10" sectors), and direction (45" sectors)/hour. For all climatologies, MSFC calculated the mean, standard deviation and observation counts of the Zminute average and 10-minute peak wind speeds. MSFC personnel also calculated empirical and modeled probabilities of meeting or exceeding specific 10- minute peak wind speeds using PDFs. The empirical PDFs were asymmetrical and bounded on the left by the 2- minute average wind speed. They calculated the parametric PDFs by fitting the GEV distribution to the empirical distributions. Parametric PDFs were calculated in order to smooth and interpolate over variations in the observed values due to possible under-sampling of certain peak winds and to estimate probabilities associated with average winds outside the observed range. MSFC calculated the individual probabilities of meeting or exceeding specific 10- minute peak wind speeds by integrating the area under each curve. The probabilities assist SMG forecasters in assessing the shuttle FR for various Zminute average wind speeds. The A M ' obtained the processed EAFB data from Dr. Lee Bums of MSFC and reformatted them for input to Excel PivotTables, which allow users to display different values with point-click-drag techniques. The GUI was created from the PivotTables using VBA code. It is run through a macro within Excel and allows forecasters to quickly display and interpret peak wind climatology and probabilities in a fast-paced operational environment. The GUI was designed to look and operate exactly the same as the KSC SLF tool since SMG forecasters were already familiar with that product. SMG feedback was continually incorporated into the GUI ensuring the end product met their needs. The final version of the GUI along with all climatologies, PDFs, and probabilities has been delivered to SMG and will be put into operational use.

Dreher, Joseph G.↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS2003

Automated Monitoring with a BCP Fault-Decision Test

The Bayesian conditional probability (BCP) technique is a statistical fault-decision technique that is suitable as the mathematical basis of the fault-manager module in the automated-monitoring system and method described in the immediately preceding article. Within the automated-monitoring system, the fault-manager module operates in conjunction with the fault-detector module, which can be based on any one of several fault-detection techniques; examples include a threshold-limit-comparison technique or the BSP or SPRT technique mentioned in the preceding article. The present BCP technique is used to evaluate a series of one or more fault-detection events for the purpose of filtering out occasional false alarms produced by many types of statistical fault-detection procedures. The BCP technique increases the probability that an automated monitoring system produces a correct decision regarding the presence or absence of a fault. Because occasional false alarms are an inevitable consequence of the SPRT, BSP, or any other statistically based fault-detection test, there is a need for a logical procedure to distinguish between true and false alarms. Heretofore, it has been common practice to make a fault decision on an ad hoc basis for example by following a multiple-observation voting strategy in which a signal is declared to be indicative of a fault if m of the last n observations produced a fault-detection alarm. The BCP technique was developed to obtain results more reliable than those afforded by a voting strategy. The BCP technique involves a test in which one applies Bayesian inference techniques to a series of one or more single-observation alarms produced by a fault-detection test. One considers the last n decisions generated by a fault-detection test in order to evaluate the conditional probability that a failure is indicated (see figure). Each new decision reached by a fault-detection test is treated as a new piece of evidence about the state of the monitored asset, and the conditional probability of failure for the system is updated on the basis of this new evidence. The conditional probability of failure is compared with a predefined limit. For a probability below the limit, the asset is declared to be healthy. For a probability above the limit, the asset is declared to be faulty.

Bickford, Randall L.↗
NASA NTRS2005

Forecasting Lightning at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The Applied Meteorology Unit (AMU) developed a set of statistical forecast equations that provide a probability of lightning occurrence on Kennedy Space Center (KSC) I Cape Canaveral Air Force Station (CCAFS) for the day during the warm season (May September). The 45th Weather Squadron (45 WS) forecasters at CCAFS in Florida include a probability of lightning occurrence in their daily 24-hour and weekly planning forecasts, which are briefed at 1100 UTC (0700 EDT). This information is used for general scheduling of operations at CCAFS and KSC. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts for the KSC/CCAFS area during Shuttle flight operations. Much of the current lightning probability forecast at both groups is based on a subjective analysis of model and observational data. The objective tool currently available is the Neumann-Pfeffer Thunderstorm Index (NPTI, Neumann 1971), developed specifically for the KSCICCAFS area over 30 years ago. However, recent studies have shown that 1-day persistence provides a better forecast than the NPTI, indicating that the NPTI needed to be upgraded or replaced. Because they require a tool that provides a reliable estimate of the daily thunderstorm probability forecast, the 45 WS forecasters requested that the AMU develop a new lightning probability forecast tool using recent data and more sophisticated techniques now possible through more computing power than that available over 30 years ago. The equation development incorporated results from two research projects that investigated causes of lightning occurrence near KSCICCAFS and over the Florida peninsula. One proved that logistic regression outperformed the linear regression method used in NPTI, even when the same predictors were used. The other study found relationships between large scale flow regimes and spatial lightning distributions over Florida. Lightning, probabilities based on these flow regimes were used as candidate predictors in the equation development. Fifteen years (1 989-2003) of warm season data were used to develop the forecast equations. The data sources included a local network of cloud-to-ground lightning sensors called the Cloud-to-Ground Lightning Surveillance System (CGLSS), 1200 UTC Florida synoptic soundings, and the 1000 UTC CCAFS sounding. Data from CGLSS were used to determine lightning occurrence for each day. The 1200 UTC soundings were used to calculate the synoptic-scale flow regimes and the 1000 UTC soundings were used to calculate local stability parameters, which were used as candidate predictors of lightning occurrence. Five logistic regression forecast equations were created through careful selection and elimination of the candidate predictors. The resulting equations contain five to six predictors each. Results from four performance tests indicated that the equations showed an increase in skill over several standard forecasting methods, good reliability, an ability to distinguish between non-lightning and lightning days, and good accuracy measures and skill scores. Given the overall good performance the 45 WS requested that the equations be transitioned to operations and added to the current set of tools used to determine the daily lightning probability of occurrence.

Lambert, Winfred↗
DOE OSTI2014

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-fly during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. The filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Hydrogen atom excitation in intense attosecond laser field: Gauge dependence of dipole approximation

It is assumed that, the atomic excitations probability can be calculated using first order perturbation theory and dipole approximations. The validity of the dipole approximations had been examined by comparing the results with the results obtained by exact calculations within the first order perturbation theory[2]. Figure 1 shows the time dependence of the transition probability in the dipole approximation. From these plots it is obvious that, the probabilities obtained in the length gauge are higher than that in the velocity gauge, in the interaction period (−τ/2<t<τ/2). After passing this time interval, transition probabilities for these two gauges became equal to each other precisely. Moreover those results are equal to the corresponding exact (without the dipole approximation) calculations results. (Figure 2) Though the time evolution of the same transition probabilities are different for these cases, the final results are the same for all three cases, excluding the 6s-6p{sub 0} transition. For the later case, only the length gauge give a false results, but the velocity gauge give the same result as the exact one, for the final value of the transition probability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Six-dimensional quantum dynamics study for the dissociative adsorption of DCl on Au(111) surface

We carried out six-dimensional quantum dynamics calculations for the dissociative adsorption of deuterium chloride (DCl) on Au(111) surface using the initial state-selected time-dependent wave packet approach. The four-dimensional dissociation probabilities are also obtained with the center of mass of DCl fixed at various sites. These calculations were all performed based on an accurate potential energy surface recently constructed by neural network fitting to density function theory energy points. The origin of the extremely small dissociation probability for DCl/HCl (v = 0, j = 0) fixed at the top site compared to other fixed sites is elucidated in this study. The influence of vibrational excitation and rotational orientation of DCl on the reactivity was investigated by calculating six-dimensional dissociation probabilities. The vibrational excitation of DCl enhances the reactivity substantially and the helicopter orientation yields higher dissociation probability than the cartwheel orientation. The site-averaged dissociation probability over 25 fixed sites obtained from four-dimensional quantum dynamics calculations can accurately reproduce the six-dimensional dissociation probability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Critique of information geometry

As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Modeling convective core overshoot and diffusion in Procyon constrained by asteroseismic data

We compare evolved stellar models, which match Procyon's mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 36% and 43%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within 1σ of the observed mass 1.497 ± 0.037 M {sub ☉}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier Sensing

Here, we propose using Carrier Sensing (CS) for distributed interference management in millimeter-wave (mmWave) cellular networks where spectrum is shared by multiple operators that do not coordinate among themselves. In addition, even the base station sites can be shared by the operators. We describe important challenges in using traditional CS in this setting and propose enhanced CS protocols to address these challenges. Using stochastic geometry, we develop a general framework for downlink coverage probability analysis of our shared mmWave network in the presence of CS and derive the downlink coverage probability expressions for several CS protocols. Our work is the first to investigate and analyze (using stochastic geometry) CS for mmWave networks with spectrum and BS sites shared among non-coordinating operators. We evaluate the downlink coverage probability of our shared mmWave network using simulations as well as numerical examples based on our analysis. Our evaluations show that our proposed approach leads to an improvement in coverage probability, compared to the coverage probability with no CS, for higher values of signal-to-interference and noise ratio (SINR). Interestingly, our evaluations also reveal that for lower values of SINR, not using any CS is the best strategy in terms of the downlink coverage probability.

42 ENGINEERING↗
DOE OSTI2015

SU-E-J-183: Quantification of Motion During Hypo-Fractionated Prostate Cancer Radiation Therapy

Purpose: To quantify patient motion during hypo-fractionated prostate cancer treatment as tracked by Calypso™ 4D localization system. Methods: 50 prostate cancer patients with implanted Calypso beacons underwent hypofractionated IMRT treatment. Typical fraction size was 5 with doses of 5–8 Gy/fraction. 213 traces from the 50 patients were analyzed to quantify the probability of motion vs time starting from beam-on. Couch corrections applied by therapists were undone to obtain the natural course of patient motion. The Calypso data was used to identify vector displacements greater than 2 mm from the starting position. The direction of this vector was classified into one of the 26 directions (combinations of L/R, A/P, S/I). The probability of motion >2mm was estimated by computing the fraction of traces that exceed the 2mm threshold at each time point. The violating motion points were also binned by direction in order to identify specific directions that were more prone to movement. Results: The overall probability of motion greater than 2 mm at 5 and 10 minutes from beam-on were 27 % and 50% respectively. The primary directions in which motion occurred were Posterior-Inferior (PI) and Inferior (I) with a probability of 8.5% and 4% at 5 minutes and 10% for both at 10 minutes. Motion was classified into the following bins: 0–2, 2–3, 3–4, 4–5, 5–6, 6–7, 7–8 and greater than 8 mm. It is observed that motion < 2mm decreases from the first 5 minutes to the next while the higher magnitude components increase with time. Conclusion: The probability of prostate motion increases with time. The trend seen in the PI and I directions can be attributed to physiological factors like bladder filling. This probability can be factored in for scheduling intrafraction imaging and used to compare dosimetric impact of VMAT vs. IMRT plans. This work is supported in part by Varian Medical Systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

A DARK ENERGY CAMERA SEARCH FOR AN OPTICAL COUNTERPART TO THE FIRST ADVANCED LIGO GRAVITATIONAL WAVE EVENT GW150914

We report the results of a deep search for an optical counterpart to the gravitational wave (GW) event GW150914, the first trigger from the Advanced LIGO GW detectors. We used the Dark Energy Camera (DECam) to image a 102 deg{sup 2} area, corresponding to 38% of the initial trigger high-probability sky region and to 11% of the revised high-probability region. We observed in the i and z bands at 4–5, 7, and 24 days after the trigger. The median 5 σ point-source limiting magnitudes of our search images are i = 22.5 and z = 21.8 mag. We processed the images through a difference-imaging pipeline using templates from pre-existing Dark Energy Survey data and publicly available DECam data. Due to missing template observations and other losses, our effective search area subtends 40 deg{sup 2}, corresponding to a 12% total probability in the initial map and 3% in the final map. In this area, we search for objects that decline significantly between days 4–5 and day 7, and are undetectable by day 24, finding none to typical magnitude limits of i = 21.5, 21.1, 20.1 for object colors ( i − z ) = 1, 0, −1, respectively. Our search demonstrates the feasibility of a dedicated search program with DECam and bodes well for future research in this emerging field.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1996

Predictions of malaria vector distribution in Belize based on multispectral satellite data

Use of multispectral satellite data to predict arthropod-borne disease trouble spots is dependent on clear understandings of environmental factors that determine the presence of disease vectors. A blind test of remote sensing-based predictions for the spatial distribution of a malaria vector, Anopheles pseudopunctipennis, was conducted as a follow-up to two years of studies on vector-environmental relationships in Belize. Four of eight sites that were predicted to be high probability locations for presence of An. pseudopunctipennis were positive and all low probability sites (0 of 12) were negative. The absence of An. pseudopunctipennis at four high probability locations probably reflects the low densities that seem to characterize field populations of this species, i.e., the population densities were below the threshold of our sampling effort. Another important malaria vector, An. darlingi, was also present at all high probability sites and absent at all low probability sites. Anopheles darlingi, like An. pseudopunctipennis, is a riverine species. Prior to these collections at ecologically defined locations, this species was last detected in Belize in 1946.

Non-NASA Center↗