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Results for “Probabilities Mathematics”

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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Interrelated structure of high altitude atmospheric profiles

A preliminary development of a mathematical model to compute probabilities of thermodynamic profiles is presented. The model assumes an exponential expression for pressure and utilizes the hydrostatic law and equation of state in the determination of density and temperature. It is shown that each thermodynamic variable can be factored into the produce of steady state and perturbation functions. The steady state functions have profiles similar to those of the 1962 standard atmosphere while the perturbation functions oscillate about 1. Limitations of the model and recommendations for future work are presented.

Engler, N. A.↗
NASA NTRS1982

Analysis of space telescope data collection system

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

Ingels, F. M.↗
NASA NTRS1984

An urnful of blinding functions

There is a fundamental connection between the mathematical theory of discrete probability distributions and the parametric curves and surfaces of computer-aided geometric design. It is no accident that the blending functions of Bezier curves and surfaces have an obvious probabilistic interpretation, nor is it a coincidence that the normalized uniform B-spline basis functions also model a simple stochastic process. The link between probability and geometry, and how to exploit simple probabilistic arguments to derive many of the classical geometric properties of the parametric curves and surfaces currently in vogue in computer-aided geometric design is discussed. This probabilistic approach is also used to introduce many new types of curves and surfaces, and it is demonstrated how probability theory can be used to simplify, unify, and generalize many well-known results.

Goldman, R. N.↗
NASA NTRSDate not supplied

The Reliability Function

Mathematically, reliability is the probability of success. First, we will present the calculus needed to comprehend basic probability theory. Second, we will introduce The Reliability Function and its basic properties. Last, we will demonstrate The Reliability Function in a notional fatigue life example.

Reliability↗
DOE OSTI2021

Grid Cyber-Security Strategy in an Attacker-Defender Model

The progression of cyber-attacks on the cyber-physical system is analyzed by the Probabilistic, Learning Attacker, and Dynamic Defender (PLADD) model. Although our research does apply to all cyber-physical systems, we focus on power grid infrastructure. The PLADD model evaluates the effectiveness of moving target defense (MTD) techniques. We consider the power grid attack scenarios in the AND configurations and OR configurations. In addition, we consider, for the first time ever, power grid attack scenarios involving both AND configurations and OR configurations simultaneously. Cyber-security managers can use the strategy introduced in this manuscript to optimize their defense strategies. Specifically, our research provides insight into when to reset access controls (such as passwords, internet protocol addresses, and session keys), to minimize the probability of a successful attack. Our mathematical proof for the OR configuration of multiple PLADD games shows that it is best if all access controls are reset simultaneously. For the AND configuration, our mathematical proof shows that it is best (in terms of minimizing the attacker's average probability of success) that the resets are equally spaced apart. We introduce a novel concept called hierarchical parallel PLADD system to cover additional attack scenarios that require combinations of AND and OR configurations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Optimality of Empirical Z-R Relations

This paper attempts to justify mathematically the two empirical approaches to the problem of deriving Z-R relations from (Z,R) measurements, namely the power-law regression and the probability matching method (PMM). The basic mathematical assumptions that apply in each case are explicitly identified.

rainfall estimation radar reflectivity Z-R relatio↗
DOE OSTI2018

Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

This paper is a further development of the results of [20] where, based on the negative binomial model for the duration of wet periods measured in days [16], an asymptotic approximation was proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the form of a scale mixture of the Fr´echet distribution with the gamma mixing distribution and coincides with the distribution of a positive power of a random variable having the Snedecor–Fisher distribution. Here we extend this result to the mth extremes, m ∈ ℕ, and sample quantiles. The proof of this result is based on the representation of the negative binomial distribution as a mixed geometric (and hence, mixed Poisson) distribution [17] and limit theorems for extreme order statistics in samples with random sizes having mixed Poisson distributions [10]. Some analytic properties of the obtained limit distribution are described. In particular, it is demonstrated that under certain conditions the limit distribution of the maximum precipitation is mixed exponential and hence, is infinitely divisible. It is shown that under the same conditions this limit distribution can be represented as a scale mixture of stable or Weibull or Pareto or folded normal laws. The corresponding product representations for the limit random variable can be used for its computer simulation. The results of fitting this distribution to real data are presented illustrating high adequacy of the proposed model. It is also shown that the limit distribution of sample quantiles is the well-known Student distribution. Several methods are proposed for the estimation of the parameters of the asymptotic distributions. The obtained mixture representations for the limit laws and the corresponding asymptotic approximations provide better insight into the nature of mixed probability (“Bayesian”) models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Survival probabilities in the Sisyphus random walk model with absorbing traps

We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position x{sub 0}. In particular, we present a remarkably compact derivation of the time-dependent survival probability function S(t;x{sub 0}) which characterizes the random walkers in the presence of an absorbing trap at the origin. The survival probabilities are expressed in a compact mathematical form in terms of the x{sub 0}-generalized Fibonacci-like numbers G{sub t}{sup (x{sub 0})}. Interestingly, it is proved that, as opposed to the standard random walk model in which the survival probabilities depend linearly on the initial distance x{sub 0} of the walkers from the trap and decay asymptotically as an inverse power of the time, in the Sisyphus random walk model the asymptotic survival probabilities decay exponentially in time and are characterized by a non-trivial (non-linear) dependence on the initial gap x{sub 0} from the absorbing trap. We use the analytically derived results in order to analyze the underlying dynamics of the ‘survival-game’, a highly risky investment strategy in which non-absorbed agents receive a reward P(t) which gradually increases in time.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

Model-based prognostics for batteries which estimates useful life and uses a probability density function

This invention develops a mathematical model to describe battery behavior during individual discharge cycles as well as over its cycle life. The basis for the form of the model has been linked to the internal processes of the battery and validated using experimental data. Effects of temperature and load current have also been incorporated into the model. Subsequently, the model has been used in a Particle Filtering framework to make predictions of remaining useful life for individual discharge cycles as well as for cycle life. The prediction performance was found to be satisfactory as measured by performance metrics customized for prognostics for a sample case. The work presented here provides initial steps towards a comprehensive health management solution for energy storage devices.

Saha, Bhaskar↗
DOE OSTI2019

Review, Evaluation, and Directions for Gene-Targeted Assembly for Ecological Analyses of Metagenomes

Shotgun metagenomics has greatly advanced our understanding of microbial communities over the last decade. Metagenomic analyses often include assembly and genome binning, computationally daunting tasks especially for big data from complex environments such as soil and sediments. In many studies, however, only a subset of genes and pathways involved in specific functions are of interest; thus, it is not necessary to attempt global assembly. In addition, methods that target genes can be computationally more efficient and produce more accurate assembly by leveraging rich databases, especially for those genes that are of broad interest such as those involved in biogeochemical cycles, biodegradation, and antibiotic resistance or used as phylogenetic markers. Here, we review six gene-targeted assemblers with unique algorithms for extracting and/or assembling targeted genes: Xander, MegaGTA, SAT-Assembler, HMM-GRASPx, GenSeed-HMM, and MEGAN. We tested these tools using two datasets with known genomes, a synthetic community of artificial reads derived from the genomes of 17 bacteria, shotgun sequence data from a mock community with 48 bacteria and 16 archaea genomes, and a large soil shotgun metagenomic dataset. We compared assemblies of a universal single copy gene (rplB) and two N cycle genes (nifH and nirK). We measured their computational efficiency, sensitivity, specificity, and chimera rate and found Xander and MegaGTA, which both use a probabilistic graph structure to model the genes, have the best overall performance with all three datasets, although MEGAN, a reference matching assembler, had better sensitivity with synthetic and mock community members chosen from its reference collection. Also, Xander and MegaGTA are the only tools that include post-assembly scripts tuned for common molecular ecology and diversity analyses. Additionally, we provide a mathematical model for estimating the probability of assembling targeted genes in a metagenome for estimating required sequencing depth.

59 BASIC BIOLOGICAL SCIENCES↗