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At least 217 records · Page 12

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NASA NTRS1979

Fisher classifier and its probability of error estimation

Computationally efficient expressions are derived for estimating the probability of error using the leave-one-out method. The optimal threshold for the classification of patterns projected onto Fisher's direction is derived. A simple generalization of the Fisher classifier to multiple classes is presented. Computational expressions are developed for estimating the probability of error of the multiclass Fisher classifier.

Chittineni, C. B.↗

NASA NTRS1979

Most probable states in magnetohydrodynamics

A method is developed for selecting 'most probable' MHD states compatible with certain global constraints (e.g., the energy, the toroidal magnetic flux, the total toroidal electric current, or the magnetic helicity). These states occur as the solutions of nonlinear partial differential equations which are far simpler than the original MHD equations. The stabilized Z pinch is discussed by way of illustration of the theory of probable states.

Montgomery, D.↗

NASA NTRS1979

Rapid, single-step most-probable-number method for enumerating fecal coliforms in effluents from sewage treatment plants

A single-step most-probable-number method for determining the number of fecal coliform bacteria present in sewage treatment plant effluents is discussed. A single growth medium based on that of Reasoner et al. (1976) and consisting of 5.0 gr. proteose peptone, 3.0 gr. yeast extract, 10.0 gr. lactose, 7.5 gr. NaCl, 0.2 gr. sodium lauryl sulfate, and 0.1 gr. sodium desoxycholate per liter is used. The pH is adjusted to 6.5, and samples are incubated at 44.5 deg C. Bacterial growth is detected either by measuring the increase with time in the electrical impedance ratio between the innoculated sample vial and an uninnoculated reference vial or by visual examination for turbidity. Results obtained by the single-step method for chlorinated and unchlorinated effluent samples are in excellent agreement with those obtained by the standard method. It is suggested that in automated treatment plants impedance ratio data could be automatically matched by computer programs with the appropriate dilution factors and most probable number tables already in the computer memory, with the corresponding result displayed as fecal coliforms per 100 ml of effluent.

Munoz, E. F.↗

NASA NTRS1979

Atomic electron excitation probabilities during orbital electron capture by the nucleus

Approximate probabilities of electron excitation (shakeup/shakeoff) from various atomic states during nuclear ns electron capture have been calculated in the sudden approximation, using Hartree-Fock wave functions. Total excitation probabilities are much lower than during inner-shell ionization by photons or electrons, and ns states are more likely to be excited than np states. This latter result is borne out by K-alpha X-ray satellite spectra.

Crasemann, B.↗

NASA NTRS1979

The probability distribution of the predicted CFM-induced ozone depletion

It is argued from the central limit theorem that the uncertainty in model predicted changes of the ozone column density is best represented by a normal probability density distribution. This conclusion is validated by comparison with a probability distribution generated by a Monte Carlo technique. In the case of the CFM-induced ozone depletion, and based on the estimated uncertainties in the reaction rate coefficients alone the relative mean standard deviation of this normal distribution is estimated to be 0.29.

Ehhalt, D. H.↗

NASA NTRS1981

Computer simulation of random variables and vectors with arbitrary probability distribution laws

Assume that there is given an arbitrary n-dimensional probability distribution F. A recursive construction is found for a sequence of functions x sub 1 = f sub 1 (U sub 1, ..., U sub n), ..., x sub n = f sub n (U sub 1, ..., U sub n) such that if U sub 1, ..., U sub n are independent random variables having uniform distribution over the open interval (0,1), then the joint distribution of the variables x sub 1, ..., x sub n coincides with the distribution F. Since uniform independent random variables can be well simulated by means of a computer, this result allows one to simulate arbitrary n-random variables if their joint probability distribution is known.

Bogdan, V. M.↗

NASA NTRS1981

Poster error probability in the Mu-11 Sequential Ranging System

An expression is derived for the posterior error probability in the Mu-2 Sequential Ranging System. An algorithm is developed which closely bounds the exact answer and can be implemented in the machine software. A computer simulation is provided to illustrate the improved level of confidence in a ranging acquisition using this figure of merit as compared to that using only the prior probabilities. In a simulation of 20,000 acquisitions with an experimentally determined threshold setting, the algorithm detected 90% of the actual errors and made false indication of errors on 0.2% of the acquisitions.

Coyle, C. W.↗

NASA NTRS1980

Theoretical foundations for quantitative paleogenetics. III - The molecular divergence of nucleic acids and proteins for the case of genetic events of unequal probability

Theoretical equations are derived for molecular divergence with respect to gene and protein structure in the presence of genetic events with unequal probabilities: amino acid and base compositions, the frequencies of nucleotide replacements, the usage of degenerate codons, the distribution of fixed base replacements within codons and the distribution of fixed base replacements among codons. Results are presented in the form of tables relating the probabilities of given numbers of codon base changes with respect to the original codon for the alpha hemoglobin, beta hemoglobin, myoglobin, cytochrome c and parvalbumin group gene families. Application of the calculations to the rabbit alpha and beta hemoglobin mRNAs and proteins indicates that the genes are separated by about 425 fixed based replacements distributed over 114 codon sites, which is a factor of two greater than previous estimates. The theoretical results also suggest that many more base replacements are required to effect a given gene or protein structural change than previously believed.

Holmquist, R.↗

NASA NTRS1982

Probability of laminar flow loss because of ice crystal encounters

A method for combining the cloud detector observation results from the Global Atmospheric Sampling Program (GASP) with Knollenberg probe observations of cloud particle concentration from other programs to derive estimates of the ambient concentration of particles larger than a given size was developed. The method was applied to estimate the probability of encountering particle concentrations which would degrade the performance of laminar flow control (LFC) aircraft. It is concluded that LF loss should occur only about one percent of the time in clear air and that flight within clouds should always result in a significant loss of LF, with 90 percent LF loss occurring about one percent of the time. Preliminary estimates of cloud encounter probability are presented for four airline routes, and conclusions are presented as to the best altitudes for cloud avoidance in extratropical and tropical latitudes.

Davis, R. E.↗

NASA NTRS1982

Error probabilities in optical PPM receivers with Gaussian mixture densities

A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.

Gagliardi, R. M.↗

NASA NTRS1982

The probability distributions of S/+/ gyrospeeds in the Io torus

The first detailed thermal speed probability distribution for a Jovian plasma ion is presented. The distribution of heavy ion thermal speeds appears to be highly significant for an evaluation of the processes by which the particle and energy budgets of the Io plasma torus are maintained. Attention is given to the measurement, reduction, and analysis procedures which yield the reported probability distribution. A kinetic energy inventory of the Jovian plasma heavy ion component can be obtained from high-resolution, high-precision spectrophotometry of emission lines. The current S(+) study finds that detection of the line wings results in a mean energy (approximately 60 eV) which is higher by a factor of approximately 10 than is implied by the line core. This illustrates that a dispersive measurement may provide only a lower limit to the kinetic energy content.

Brown, R. A.↗

NASA NTRS1981

Theoretical quasar emission line ratios. IV - General asymptotic escape probabilities and the effects of linear Stark broadening

Established techniques permitting the evaluation of exact asymptotic forms of photon escape probabilities for a wide range of absorption coefficient profile types are used for QSO radiative transfer effect studies, and it is shown that the exact formulae are easily evaluated. It is found that some of the commonly used expressions overestimate the true value by a factor of about two, and a computationally expedient approximate expression is derived for the asymptotic form of the photon escape probability when linear Stark broadening contributes to the line absorption coefficient profile in hydrogenic lines. Attention is given to Lyman-alpha, for the case in which partial redistribution, over the linear Stark component of the line absorption coefficient profile, dominates single-flight photon escape.

Puetter, R. C.↗

NASA NTRS1983

Approximation to the Probability Density at the Output of a Photmultiplier Tube

The probability density of the integrated output of a photomultiplier tube (PMT) is approximated by the Gaussian, Rayleigh, and Gamma probability densities. The accuracy of the approximations depends on the signal energy alpha: the Gamma distribution is accurate for all alpha, the Raleigh distribution is accurate for small alpha (approximate or less than 1 photon) and the Gaussian distribution is accurate for large alpha (approximate or greater than 10 photons).

Stokey, R. J.↗

NASA NTRS1983

On the probability of undetected error for the maximum distance separable codes

The performance of maximum-distance-separable codes with symbols from GF(1) when they are used for pure error detection or for simultaneous error correction and detection is investigated. These codes are good for symbol error detection. Their probability of undetected error is upper bounded by q to the -r and decreases monotonically as the symbol error probability epsilon decreases from (q-1)/q to 0, where r is the number of parity-check symbols of a code.

Kasami, T.↗

NASA NTRS1984

Undetected error probability and throughput analysis of a concatenated coding scheme

The performance of a proposed concatenated coding scheme for error control on a NASA telecommand system is analyzed. In this scheme, the inner code is a distance-4 Hamming code used for both error correction and error detection. The outer code is a shortened distance-4 Hamming code used only for error detection. Interleaving is assumed between the inner and outer codes. A retransmission is requested if either the inner or outer code detects the presence of errors. Both the undetected error probability and the throughput of the system are analyzed. Results indicate that high throughputs and extremely low undetected error probabilities are achievable using this scheme.

Costello, D. J.↗

NASA NTRS1984

Photon escape probabilities in a semi-infinite plane-parallel medium

It is shown in this work how to obtain the probabilities of photons escaping from a cold electron plasma environment after having undergone an arbitrary number of scatterings. This is done by retaining the exact differential cross section for Thomson scattering as opposed to using its polarization and angle averaged form. The results are given in the form of recursion relations. The geometry used is the semi-infinite plane-parallel geometry witlh a photon source located on a plane at an arbitrary optical depth below the surface. Analytical expressions are given for the probabilities which are accurate over a wide range of initial optical depth. These results can be used to model compact X-ray galactic sources which are surrounded by an electron-rich plasma.

Williams, A. C.↗

NASA NTRS1984

Measurements of transition probabilities for spin-changing lines of atomic ions used in diagnostics of astrophysical plasmas

The intensities of ultraviolet, spin-changing, 'intersystem' lines of low-Z atomic ions are frequently used in determinations of electron densities and temperatures in astrophysical plasmas as well as in measurements of element abundances in the interstellar gas. The transition probabilities (A-values) of these lines, which are about five orders of magnitude weaker than allowed lines, have not been measured heretofore and various calculations produce A-values for these lines that differ by as much as 50 percent A radio-frequency ion trap has been used for the first measurements of transition probabilities for intersystem lines seen in astronomical spectra. The measurement procedure is discussed and results for Si III, O III, N II, and C III are reviewed and compared to calculated values. Discrepancies exist; these indicate that some of the calculated A-values may be less reliable than has been beleived and that revisions to the electron densities determined for some astrophysical plasmas may be required.

Smith, P. L.↗

NASA NTRS1984

On the probability of undetected error for the maximum distance separable codes

Kasami, T.↗