SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Discrete parameter covariance stationary stochastic process in rotation sampling, deriving minimum variance unbiased linear population mean estimator by constrained optimization procedure
As computers are added to the cockpit, the pilot's job is changing from of manually flying the aircraft, to one of supervising computers which are doing navigation, guidance and energy management calculations as well as automatically flying the aircraft. In this supervisorial role the pilot must divide his attention between monitoring the aircraft's performance and giving commands to the computer. Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies.
Optimal adaptive filter for sampled stochastic processes with unknown parameter
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
This paper presents a machine-learning approach to predict flight delays. Whereas neural networks are extensively studied for predictive capabilities, they involve non-intuitive design and extensive analysis, particularly in training and optimization processes. Instead, the proposed framework employs Gaussian Processes as a supervised learning technique for flight delay prediction. This data-driven approach trains the model using prior information, specifically the mean and covariance tied to existing data. The proposed Gaussian Process Regression (GPR) model employs the day of flight as a pivotal feature for delay forecasting. We analyze flights from various routes and gauge the accuracy of the presented learning technique by comparing the predicted delays with the actual ones. Given the inherent challenges in precisely forecasting delays, we predict the delays with a 95 % confidence interval. Also, an error propagation analysis in the prediction horizon is carried out to determine the optimal time frame for prediction. The proposed method for flight delay prediction is important as airlines can strategize flight operations and issue timely advisories.
Epsilon-delta entropy for probabilistic metric spaces applied to stochastic processes in data transmission
Alias free sampling concept extended to random sampling sequences of stochastic processes
Book on stationary and related stochastic processes covering sample function properties and applications, Hilbert space geometry, etc
Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].
Understanding the processes that influence the structure of biotic communities is one of the major ecological topics, and both stochastic and deterministic processes are expected to be at work simultaneously in most communities. Here, we investigated the vertical distribution patterns of bacterial communities in a 10-m-long soil core taken within permafrost of the Qinghai-Tibet Plateau. To get a better understanding of the forces that govern these patterns, we examined the diversity and structure of bacterial communities, and the change in community composition along the vertical distance (spatial turnover) from both taxonomic and phylogenetic perspectives. Measures of taxonomic and phylogenetic beta diversity revealed that bacterial community composition changed continuously along the soil core, and showed a vertical distance-decay relationship. Multiple stepwise regression analysis suggested that bacterial alpha diversity and phylogenetic structure were strongly correlated with soil conductivity and pH but weakly correlated with depth. There was evidence that deterministic and stochastic processes collectively drived bacterial vertically-structured pattern. Bacterial communities in five soil horizons (two originated from the active layer and three from permafrost) of the permafrost core were phylogenetically random, indicator of stochastic processes. However, we found a stronger effect of deterministic processes related to soil pH, conductivity, and organic carbon content that were structuring the bacterial communities. We therefore conclude that the vertical distribution of bacterial communities was governed primarily by deterministic ecological selection, although stochastic processes were also at work. Furthermore, the strong impact of environmental conditions (for example, soil physicochemical parameters and seasonal freeze-thaw cycles) on these communities underlines the sensitivity of permafrost microorganisms to climate change and potentially subsequent permafrost thaw.
This analysis utilizes computer simulation and statistical estimation. Realizations of stationary gaussian stochastic processes with selected autocorrelation functions are computer simulated. Analysis of the simulated data revealed that the mean and the variance of a process were functionally dependent upon the autocorrelation parameter and crossing level. Using predicted values for the mean and standard deviation, by the method of moments, the distribution parameters was estimated. Thus, given the autocorrelation parameter, crossing level, mean, and standard deviation of a process, the probability of exceeding the crossing level for a particular length of time was calculated.
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
It is shown that the algorithms for determining the generating function and prediction error matrix of multivariate stationary stochastic processes developed by Wiener and Masani (1957), and later by Masani (1960) will work in some more general setting.
Prompt γ-ray and early X-ray afterglow emissions in gamma-ray bursts (GRBs) are characterized by a bursty behavior and are often interspersed with long quiescent times. There is compelling evidence that X-ray flares are linked to prompt γ-rays. However, the physical mechanism that leads to the complex temporal distribution of γ-ray pulses and X-ray flares is not understood. Here we show that the waiting time distribution (WTD) of pulses and flares exhibits a power-law tail extending over four decades with an index of about two and can be the manifestation of a common time-dependent Poisson process. This result is robust and is obtained on different catalogs. Surprisingly, GRBs with many (⩾8) γ-ray pulses are very unlikely to be accompanied by X-ray flares after the end of the prompt emission (3.1σ Gaussian confidence). These results are consistent with a simple interpretation: a hyperaccreting disk breaks up into one or a few groups of fragments, each of which is independently accreted with the same probability per unit time. Prompt γ-rays and late X-ray flares are nothing but different fragments being accreted at the beginning and at the end, respectively, following the very same stochastic process and likely the same mechanism.
The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.
The algorithms developed by Wiener and Masani (1957 and 1958) and Masani (1960) for the characterization of a class of multivariate stationary stochastic processes are investigated analytically. The algorithms permit the determination of (1) the generating function, (2) the prediction-error matrix, and (3) an autoregressive representation of the linear least-squares predictor. A number of theorems and lemmas are proved, and it is shown that the range of validity of the algorithms can be extended significantly beyond that given by Wiener and Masani.
An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.
A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.