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DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Carbon Dioxide Pressure and Catalyst Quantity Dependencies in Artificial Photosynthesis of Hydrocarbon Chains on Nanostructured Co/CoO Surfaces

In this study, we investigated the influence of pressure and the quantity of Co/CoO catalyst on an artificial photosynthesis process that converts CO 2 and H 2 O into hydrocarbons (C n H 2n+2 , where n ≤ 18). The adsorption of CO 2 and H 2 O on Co/CoO surfaces proved to be pivotal in this photo-catalytic reaction. Photoexcited carbon dioxide and water molecules ((CO 2 )* and (H 2 O)*) generated by illuminating the catalyst surface led to the formation of alkene hydrocarbon molecules with carbon numbers following an approximate Poisson distribution. The optimal pressure was found to be 0.40 MPa. Pressure less than 0.40 MPa resulted in low CO 2 adsorption, impeding excitation for photosynthesis. At greater pressure, oil/wax accumulation on Co/CoO surfaces hindered CO 2 adsorption, limiting further photosynthesis reactions. The average number of carbon atoms in the hydrocarbons and hydrocarbon yield were correlated. The amount of Co/CoO was also found to affect the hydrocarbon yield. Our study contributes to the understanding of Co/CoO-catalyzed photosynthesis and suggests that an open-flow system could potentially enhance the productivity of long-chain hydrocarbons.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

A Search for Neutrino Point-source Populations in 7 yr of IceCube Data with Neutrino-count Statistics

The presence of a population of point sources in a data set modifies the underlying neutrino-count statistics from the Poisson distribution. This deviation can be exactly quantified using the non-Poissonian template fitting technique, and in this work we present the first application of this approach to the IceCube high-energy neutrino data set. Using this method, we search in 7 yr of IceCube data for point-source populations correlated with the disk of the Milky Way, the Fermi bubbles, the Schlegel, Finkbeiner, and Davis dust map, or with the isotropic extragalactic sky. No evidence for such a population is found in the data using this technique, and in the absence of a signal, we establish constraints on population models with source-count distribution functions that can be described by a power law with a single break. Here, the derived limits can be interpreted in the context of many possible source classes. In order to enhance the flexibility of the results, we publish the full posterior from our analysis, which can be used to establish limits on specific population models that would contribute to the observed IceCube neutrino flux.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1969

Design and sparing techniques to meet specified performance life

Specified performance life technique starts with the general description of what is wanted, defines in block diagram the operational needs, and then defines the functional systems required. The technique is similar to a truncated reliability model, but the calculation is simplified by use of a Poisson distribution approach to failure probability.

Holstead, A. J., Jr.↗

NASA NTRS1971

The application of signal detection theory to optics

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Helstrom, C. W.↗

NASA NTRS1972

Statistical accuracy of cosmic radiation neutron component recorders

A method is examined for calculating the error of experimental data from a standard neutron monitor with the multiplicity of neutron generation. It is shown that use of the Poisson distribution to estimate the real statistical error is inadequate. The method proposed is for analysis of low-amplitude periodicities in the cosmic-ray variations.

Dorman, L. I.↗

NASA NTRS1973

Optical Signal Processing: Poisson Image Restoration and Shearing Interferometry

Optical signal processing can be performed in either digital or analog systems. Digital computers and coherent optical systems are discussed as they are used in optical signal processing. Topics include: image restoration; phase-object visualization; image contrast reversal; optical computation; image multiplexing; and fabrication of spatial filters. Digital optical data processing deals with restoration of images degraded by signal-dependent noise. When the input data of an image restoration system are the numbers of photoelectrons received from various areas of a photosensitive surface, the data are Poisson distributed with mean values proportional to the illuminance of the incoherently radiating object and background light. Optical signal processing using coherent optical systems is also discussed. Following a brief review of the pertinent details of Ronchi's diffraction grating interferometer, moire effect, carrier-frequency photography, and achromatic holography, two new shearing interferometers based on them are presented. Both interferometers can produce variable shear.

Hong, Yie-Ming↗

NASA NTRS1974

An application of queueing theory to the design of channel requirements for special purpose communications satellites

Special purpose satellites are very cost sensitive to the number of broadcast channels, usually will have Poisson arrivals, fairly low utilization (less than 35%), and a very high availability requirement. To solve the problem of determining the effects of limiting C the number of channels, the Poisson arrival, infinite server queueing model will be modified to describe the many server case. The model is predicated on the reproductive property of the Poisson distribution.

Hein, G. F.↗

NASA NTRS1974

Mathematical estimation of the level of microbial contamination on spacecraft surfaces by volumetric air sampling

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

Oxborrow, G. S.↗

NASA NTRS1977

Sampling errors in the measurement of rain and hail parameters

Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.

Gertzman, H. S.↗

NASA NTRS1980

Evaluation of pulsed RFI effects on digital satellite repeaters

This paper presents an analytical approach for assessing the effect of pulsed RFI on the error probability of a coherent phase-shift keyed signal through a nonlinear satellite repeater. The RFI is assumed to affect the uplink channel and to consist of CW pulses with random power levels and arriving randomly in time with a Poisson distribution. A model to approximate the effect of intermodulation products is introduced and the error probability conditioned on the output of the satellite repeater is computed. The classical moment technique is then used as an efficient method of averaging the conditional error probability over the numerous random parameters associated with the uplink signal.

Huang, T. C.↗

NASA NTRS1986

At least some errors are randomly generated (Freud was wrong)

An experiment was carried out to expose something about human error generating mechanisms. In the context of the experiment, an error was made when a subject pressed the wrong key on a computer keyboard or pressed no key at all in the time allotted. These might be considered, respectively, errors of substitution and errors of omission. Each of seven subjects saw a sequence of three digital numbers, made an easily learned binary judgement about each, and was to press the appropriate one of two keys. Each session consisted of 1,000 presentations of randomly permuted, fixed numbers broken into 10 blocks of 100. One of two keys should have been pressed within one second of the onset of each stimulus. These data were subjected to statistical analyses in order to probe the nature of the error generating mechanisms. Goodness of fit tests for a Poisson distribution for the number of errors per 50 trial interval and for an exponential distribution of the length of the intervals between errors were carried out. There is evidence for an endogenous mechanism that may best be described as a random error generator. Furthermore, an item analysis of the number of errors produced per stimulus suggests the existence of a second mechanism operating on task driven factors producing exogenous errors. Some errors, at least, are the result of constant probability generating mechanisms with error rate idiosyncratically determined for each subject.

Sellen, A. J.↗

NASA NTRS1987

A systematic search for long-term variability in a large sample of X-ray sources

A method which uses the correct measurement error distribution (Poisson) and which naturally takes into account detections as well as upper limits has been developed to search for flux variability in X-ray sources. The method is applied to 256 sources observed at least twice with the Einstein Observatory Imaging Proportional Counter. These sources have, in the very large majority of cases, an X-ray flux in the range 1 x 10 to the -13th to 6 x 10 to the -12th erg/sq cm/s (0.2-3.5 keV). Thirty-one sources show flux variations with amplitude ranging from about 20 percent to a factor of 6. Flux variations of small amplitude seem to be fairly common, but can be detected only in bright sources or in sources observed with very long exposures. Variations of a factor of 2 or more are seen in about 15 percent of the sources for which variations of such an amplitude are detectable.

Maccacaro, Tommaso↗

NASA NTRS1988

Characteristics and kinetics of laser-pumped Ti:sapphire oscillators

The experimental performance of a gain-switched Ti:sapphire laser oscillator pumped by a frequency-doubled Q-switched Nd:YAG laser system is presented for a variety of operating conditions. A theoretical model developed for this oscillator predicts well its performance. The observed curved input-output energy plots for the oscillator result from the kinetics of gain switching and fluorescence decay during the gain buildup period. Fluorescence decay also produces observed oscillator thresholds higher than those normally predicted by the standard gain-equals-loss condition. Gain-switched parasitic modes, with a higher threshold but shorter round-trip time than the resonator mode, cause the resonator mode to oscillate only over a finite range of pump energies. Spectroscopic investigations show that the Ti:sapphire cross-section spectrum is well fit by a Poisson distribution, giving a peak cross section of 3 x 10 to the -19th sq cm for the pi polarization.

Eggleston, John M.↗

NASA NTRS1988

A composite L-band HH radar backscattering model for coniferous forest stands

The radar backscattering model developed by Richards et al. (1987), has been improved and further tested in this research. The trunk term may now be calculated from the exact solution to the electromagnetic wave equations instead of the corner reflector equation. Rough surface models have been introduced into the radar model, so that the forward reflectance and the backscattering from the ground surface are now calculated from the same model and, thus, are consistent. The number of trees in an individual pixel is assumed to be Poisson distributed, with tree height in a stand log-normally distributed. The simulated results show that the match of backscattering coefficients for eight forest stands between SIR-B image data and the simulated results are satisfying, and that the trunk term now seems to be convincingly established as the dominant term in the L-band HH radar return from coniferous forest stands.

Sun, Guoquing↗

NASA NTRS1991

On the optimality of code options for a universal noiseless coder

A universal noiseless coding structure was developed that provides efficient performance over an extremely broad range of source entropy. This is accomplished by adaptively selecting the best of several easily implemented variable length coding algorithms. Custom VLSI coder and decoder modules capable of processing over 20 million samples per second are currently under development. The first of the code options used in this module development is shown to be equivalent to a class of Huffman code under the Humblet condition, other options are shown to be equivalent to the Huffman codes of a modified Laplacian symbol set, at specified symbol entropy values. Simulation results are obtained on actual aerial imagery, and they confirm the optimality of the scheme. On sources having Gaussian or Poisson distributions, coder performance is also projected through analysis and simulation.

Yeh, Pen-Shu↗

NASA NTRS1990

Functional relation among subpixel canopy cover, ground shadow, and illuminated ground at large sampling scales

The functional relation among subpixel canopy cover, illuminated soil, and shadowed soil, which progressively develops with increasing pixel size, is investigated for Poisson distributed plants using a geometric canopy simulation model. An analytical relation among cover components is shown to be applicable when the scale of the pixel is much larger than the scale of the plant and ground shadow. The analysis is facilitated through the use of a nondimensional solar-geometric similarity parameter, eta, equal to the ratio of the area of one plant canopy to its associated ground shadow area, as viewed from nadir. A sampling scale ratio, defined as the ratio of the area of the pixel to the mean area of a single plant shadow, is tested as a quantitative criterion to evaluate when the functional relation among subpixel components occurs. The results of a remote sensing experiment over a natural conifer landscape provide preliminary confirmation of the theoretical analysis.

Jasinski, Michael F.↗

NASA NTRS1991

Determination of confidence limits for experiments with low numbers of counts

Two different methods, classical and Bayesian, for determining confidence intervals involving Poisson-distributed data are compared. Particular consideration is given to cases where the number of counts observed is small and is comparable to the mean number of background counts. Reasons for preferring the Bayesian over the classical method are given. Tables of confidence limits calculated by the Bayesian method are provided for quick reference.

Kraft, Ralph P.↗