Approximate calculation of cumulative probability from a moment-generating function
Numerical method for calculating cumulative distribution of positive random variable
Helstrom, C. W.↗
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Photoionization branching ratios and vibrational intensity distribution for N2, CO; and CO2 between 53 and 75 nm
The probability of radiation producing ions in specific electronic and vibrational levels was documented. For example, when a narrow band-pass of solar ionizing photons is incident on an atmospheric species it is now possible to describe, accurately, how the radiant energy is shared among the various electronic states of the ions produced. The molecules studied were N2, CO, and CO2. These molecules were photoionized by radiation between 53 and 75 nm. The effects of autoionization are discussed and continuum vibrational intensities are tabulated and compared with theoretical Franck-Condon factors where available. The branching ratios and partial cross sections for ionization into various electronic states are tabulated.
Samson, J. A. R.↗
A Novel Analytical Population Tumor Control Probability Model Includes Cell Density and Volume Variations: Application to Canine Brain Tumor
Tumor control probability (TCP) models based on Poisson statistics characterize the distribution of surviving clonogens. Thus enabling the calculation of TCP for individuals. To mathematically describe clinically observed survival data of patient cohorts it is necessary to extend the Poisson TCP model. This is typically done by either incorporating variations of model parameters or by using an empirical logistic model. The purpose of this work is the development of an analytical population TCP model by mechanistic extension of the Possion model.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
Studies of the chemistry of vibrationally and electronically excited species in planetary upper atmospheres
The vibrational distribution of O2(+) in the atmospheres of Venus and Mars was investigated to compare with analogous values in the Earth's atmosphere. The dipole moment of the Z(2) Pi sub u - X(2) Pi sub g transition of O2(+) is calculated as a function of internuclear distance. The band absorption oscillator strengths and band transition probabilities of the second negative system are derived. The vibrational distribution of O2(+) in the ionosphere of Venus is calculated for a model based on data from the Pioneer Venus neutral mass spectrometer.
Fox, J. L.↗
Gravitational collapse of small-scale structure as the origin of the Lyman-alpha forest
If gravitational clustering is a hierarchical process, the present large-scale structure of the galaxy distribution implies that structures on smaller scales must have formed at high redshift. We simulate the formation of small-scale structure (average cell mass: (delta) bar m(sub b) = 10(sup 4.2) solar mass) and the evolution of photoionized gas, in the specific case of the CDM + Lambda model. The photoionized gas has a natural minimal scale of collapse, the Jeans scale (m(sub b,J) is approximately equal to 10(exp 9) solar mass). We find that low column density (N(sub HI) is less than or equal to 10(exp 14)/sq cm) lines originate in regions resembling Zel'dovich pancakes, where gas with overdensities in the range 3-30 is enclosed by two shocks but is typically reexpanding at approximately the Hubble velocity. However, higher column density lines stem from more overdense regions where the shocked gas is cooling. We show that this model can probably account for the observed number of lines, their distribution in column density and b-parameters, as well as the cloud physical sizes as observed in gravitationally lensed quasars. We find a redshift evolution that is too steep; however, this may be due to insufficient dynamical range in the simulation or because the specific model is incorrect. The model predicts that high signal-to-noise observations should find systematic deviations from Voigt profiles, mainly in the form of broad wings in the line profiles, and that a fluctuating Gunn-Peterson effect will be detected, which can be modeled as a superposition of weak lines with a wide range of b-parameters.
Cen, Renyue↗
Statistical Characterization of 18650-Format Lithium-Ion Cell Thermal Runaway Energy Distributions
Effective thermal management systems, designed to handle the impacts of thermal runaway (TR) and to prevent cell-to-cell propagation, are key to safe operation of lithium-ion (Li-ion) battery assemblies. Critical factors for optimizing these systems include the total energy released during a single cell TR event and the fraction of the total energy that is released through the cell casing vs. through the ejecta material. A unique calorimeter was utilized to examine the TR behavior of a statistically significant number of 18650-format Li-ion cells with varying manufacturers, chemistries, and capacities. The calorimeter was designed to contain the TR energy in a format conducive to discerning the fractions of energy released through the cell casing vs. through the ejecta material. Other benefits of this calorimeter included the ability to rapidly test of large quantities of cells and the intentional minimization of secondary combustion effects. High energy (270 Wh/kg) and moderate energy (200 Wh/kg) 18650 cells were tested. Some of the cells had an imbedded short circuit (ISC) device installed to aid in the examination of TR mechanisms under more realistic conditions. Other variations included cells with bottom vent (BV) features and cells with thin casings (0.22 1/4m). After combining the data gathered with the calorimeter, a statistical approach was used to examine the probability of certain TR behavior, and the associated energy distributions, as a function of capacity, venting features, cell casing thickness and temperature.
Thermal Runaway Energy Distribution↗
Effect of Latitude Bias in Entry Angle on Ground Casualty Risk from Naturally Decaying Space Objects
An improvement to the long-term estimation of ground casualties from naturally decaying space objects is the refinement to the distribution of entry angle at the entry interface as a function of latitude. Previous analyses were based on an assumed "small angle," typically -0.1°, and entry interface at the equator. This study expands on work by Bacon and Matney that indicated there is significant latitude bias in the location of reentries, compared to prior assumptions of equal temporal probability. A new model has been developed, which describes the distribution of entry angle as a function of orbital inclination and argument of latitude. This model has been used to generate inputs for ODPO’s certified reentry survivability software, Object Reentry Survival Analysis Tool (ORSAT). These new results are compared with the prior standard model to assess the magnitude of the effects on reentry casualty risk.
Ostrom, Chris L.↗
Modulation of the Jovian emission below 8 MHz
RAE-1 data on Jovian decametric emission between 1 and 8 MHz are analyzed to investigate modulation of the emission with respect to the rotation phase of the planet and Io phase as well as a possible variation with flux density of the rotation-phase and Io-phase control below 8 MHz. Attention is given to the observing interval, identification of Jovian emission, orbital-phase constraint, and calculated emission occurrence probabilities. Five frequencies are selected for the analysis (6550, 4700, 3930, 2200, and 1310 kHz), and System III coordinates are used to illustrate the rotation-phase behavior. The spectral distribution of peak flux density is examined along with the overall occurrence probability, the individual modulations, theoretical implications of invariance of active Io phases, and possible modulation by Europa. The results show that Io exerts a suprisingly high degree of control at the low frequencies, that rotation-phase control is only marginal, and that the manner in which Io control is found to vary with flux density is consistent with previous findings at higher frequencies.
Desch, M. D.↗
Coupling of volatile transport and internal heat flow on Triton
Recently Brown et al. (1991) showed that Triton's internal heat source could amount to 5-20% of the absorbed insolation on Triton, thus significantly affecting volatile transport and atmospheric pressure. Subsequently, Kirk and Brown (1991a) used simple analytical models of the effect of internal heat on the distribution of volatiles on Triton's surface, confirming the speculation of Brown et al. that Triton's internal heat flow could strongly couple to the surface volatile distribution. To further explore this idea, we present numerical models of the permanent distribution of nitrogen ice on Triton that include the effects of sunlight, the two-dimensional distribution of internal heat flow, the coupling of internal heat flow to the surface distribution of nitrogen ice, and the finite viscosity of nitrogen ice. From these models we conclude that: (1) The strong vertical thermal gradient induced in Triton's polar caps by internal heat-flow facilitates viscous spreading to lower latitudes, thus opposing the poleward transport of volatiles by sunlight, and, for plausible viscosities and nitrogen inventories, producing permanent caps of considerable latitudinal extent; (2) It is probable that there is a strong coupling between the surface distribution of nitrogen ice on Triton and internal heat flow; (3) Asymmetries in the spatial distribution of Triton's heat flow, possibly driven by large-scale, volcanic activity or convection in Triton's interior, can result in permanent polar caps of unequal latitudinal extent, including the case of only one permanent polar cap; (4) Melting at the base of a permanent polar cap on Triton caused by internal heat flow can significantly enhance viscous spreading, and, as an alternative to the solid-state greenhouse mechanism proposed by Brown et al. (1990), could provide the necessary energy, fluids, and/or gases to drive Triton's geyser-like plumes; (5) The atmospheric collapse predicted to occur on Triton in the next 20 years (Spencer, 1990) may be plausibly avoided because of the large latitudinal extent expected for permanent polar caps on Triton.
Brown, Robert H.↗
Early-time measure in eternal inflation
In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is ~ 10 130 years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kähler and complex structure moduli.
79 ASTRONOMY AND ASTROPHYSICS↗
Acquisition and Early Losses of Rare Gases from the Deep Earth
Direct observations show that the deep Earth contains rare gases of solar composition distinct from those in the atmosphere. We examine the implications of mantle rare gas characteristics on acquisition of rare gases from the solar nebula and subsequent losses due to a large impact. Deep mantle rare gas concentrations and isotopic compositions can be obtained from a model of transport and distribution of mantle rare gases. This model assumes the lower mantle closed early, while the upper mantle is open to subduction from the atmosphere and mass transfer from the lower mantle. Constraints are derived that can be incorporated into models for terrestrial volatile acquisition: (1) Calculated lower-mantle Xe-isotopic ratios indicate that the fraction of radiogenic Xe produced by I-129 and Pu-244 during the first about 10(exp 8) yr was lost, a conclusion also drawn for atmospheric Xe. Thus, either the Earth was made from materials that had lost >99% of rare gases about (0.7-2) x 10(exp 8) yr after the solar system formed, or gases were then lost from the fully formed Earth. (2) Concentrations of 3He and 20Ne in the lower mantle were established after these losses. (3) Neon-isotopic data indicates that mantle Ne has solar composition. The model allows for solar Ar/Ne and Xe/Ne in the lower mantle if a dominant fraction of upper mantle Ar and Xe are subduction-derived. If Earth formed in the presence of the solar nebula, it could have been melted by accretional energy and the blanketing effect of a massive, nebula-derived atmosphere. Gases from this atmosphere would have been sequestered within the molten Earth by dissolution at the surface and downward mixing. It was found that too much Ne would be dissolved in the Earth unless the atmosphere began to escape when the Earth was only partially assembled. Here we consider conditions required to initially dissolve sufficient rare gases to account for the present lower mantle concentrations after subsequent losses at 10(exp 8) yr. It is assumed that equilibration of the atmosphere with a thoroughly molten mantle was rapid, so that initial abundances of gases retained in any mantle layer reflected surface conditions when the layer solidified. For subsequent gas loss of 99.5% and typical solubility coefficients, a total pressure of 100 atm was required for an atmosphere of solar composition. Calculations of the pressure at the base of a primordial atmosphere indicate that this value might be exceeded by an order of magnitude or more for an atmosphere supported by accretional energy. Surface temperatures of about 4000 K would have been produced, probably high enough to melt the deep mantle. Initial distributions of retained rare gases would then be determined by the history of surface pressure and temperature during mantle cooling and solidification, i.e., the coupled cooling of Earth and atmosphere. The Earth's thermal state was determined by its surface temperature and the efficiency of convection in the molten mantle, estimated to be sufficient to maintain an adiabatic gradient. Because the melting curve is steeper than the adiabat, solidification of the mantle proceeded outward from the interior. Incorporation of atmospheric gases in the mantle therefore occurred over a range in surface temperature of a few thousand degrees Kelvin. The thermal state of the atmosphere was controlled by total luminosity of the Earth (energy) released by accreting planetesimals and the cooling Earth), nebular temperature and pressure, and atmospheric opacity. The energy released by accretion declined with time as did nebular pressure. Analytical solutions for an idealized (constant opacity radiative atmosphere show that declining energy sources under constant nebular conditions result in slowly diminishing surface temperature but dramatically increasing surface pressure. For such an atmosphere with declining nebular pressure but constant total luminosity, surface pressure decreases gradually with decreasing temperaure. A decline in accretion luminosity might be compensated by energy released as the mantle cools for about 10(exp 5) year, after which luminosity must decline. The total complement of dissolved rare gases will depend on the particular evolutionary path determined by the declining accretional luminosity, the Earth thermal history, removal of the nebula, and opacity variations of the atmosphere. Models for these coupled evolutionary histories for Earth's acquisition of nebular-derived noble gases are in progress. The later losses required at about 10(exp 8) yr (depleting the interior concentrations of the sequestered solar gases by a factor of > 100) were presumably related to the major impact in which the Moon formed.
Porcelli, D.↗
On the distribution of computation for sequential decoding using the stack algorithm
A method is developed for estimating the computational distribution for the stack algorithm for sequential decoding, that is, the probability that the computation required to decode the first branch of the tree is greater than or equal to N, for small N. The analysis relies heavily on the theory of multitype branching processes. A step in the analysis is the determination of the distribution of the minimum of the cumulative metrics along the transmitted path in the code tree. This is used to obtain the distribution of the number of computations made by the decoder in order to decode the first branch in the tree, and this random variable serves as an approximation of the average number of computations per decoded branch. At information rates below the cutoff rate, the calculated computational performance is virtually identical to that obtained by time-consuming simulations.
Johannesson, R.↗
Antitropical distribution and evolution in the Indo-West Pacific Ocean
Antitropical distributions of continental shelf, Indo-West Pacific species are probably not due to transgression of the tropics during the glacial periods, isothermic submergence, island integration, rising Neogene temperatures, or the Mesozoic dispersal of fragments from a Pacific continental mass. Characteristics of common antitropical patterns, plus information from systematic works on a variety on a variety of animal and plant groups, indicate that the long discarded "relict theory" of Theel (1885) appears to best fit the evidence, for it provides a mechanism whereby antitropical distribution may be brought about. The relict theory is compatible with the concept that the East Indies part of the Indo-West Pacific has been functioning as a center of evolutionary origin. It suggests that antitropical and associated disjunct patterns are produced as an older species, that has spread out to occupy a broad range, loses ground and gradually becomes supplanted by a younger species that had subsequently evolved in the East Indies. As this process goes on, the older species becomes restricted to a few isolated localities on the fringe of its original range. These isolates are often found to the north and south of the equatorial region but may include relict populations at the western edge of the Indian Ocean.
NASA Discipline Exobiology↗
Exploration of a Potential Desirability of Outcome Ranking Endpoint for Complicated Intra-Abdominal Infections Using 9 Registrational Trials for Antibacterial Drugs
Abstract Background Desirability of outcome ranking (DOOR) is a novel approach to clinical trial design that incorporates safety and efficacy assessments into an ordinal ranking system to evaluate overall outcomes of clinical trial participants. Here, we derived and applied a disease-specific DOOR endpoint to registrational trials for complicated intra-abdominal infection (cIAI). Methods Initially, we applied an a priori DOOR prototype to electronic patient-level data from 9 phase 3 noninferiority trials for cIAI submitted to the US Food and Drug Administration between 2005 and 2019. We derived a cIAI-specific DOOR endpoint based on clinically meaningful events that trial participants experienced. Next, we applied the cIAI-specific DOOR endpoint to the same datasets and, for each trial, estimated the probability that a participant assigned to the study treatment would have a more desirable DOOR or component outcome than if assigned to the comparator. Results Three key findings informed the cIAI-specific DOOR endpoint: (1) a significant proportion of participants underwent additional surgical procedures related to their baseline infection; (2) infectious complications of cIAI were diverse; and (3) participants with worse outcomes experienced more infectious complications, more serious adverse events, and underwent more procedures. DOOR distributions between treatment arms were similar in all trials. DOOR probability estimates ranged from 47.4% to 50.3% and were not significantly different. Component analyses depicted risk-benefit assessments of study treatment versus comparator. Conclusions We designed and evaluated a potential DOOR endpoint for cIAI trials to further characterize overall clinical experiences of participants. Similar data-driven approaches can be utilized to create other infectious disease–specific DOOR endpoints.
Immunology↗
On the decoder error probability of block codes
By using coding and combinational techniques, an explicit formula is derived which enumerates the complete weight distribution of decodable words of block codes using partially known weight distributions. Also an approximation formula for nonbinary block codes is obtained. These results in turn give exact and approximate expressions for the decoder error probability PE(u) of block codes.
Cheung, Kar-Ming↗
Ultraviolet spectrophotometry of three LINERs
Three galaxies known to be LINERs were observed spectroscopically in the ultraviolet in an attempt to detect the presumed nonthermal continuum source thought to be the source of photoionization in the nuclei. NGC 4501 was found to be too faint for study with the IUE spectrographs, while NGC 5005 had an extended ultraviolet light profile. Comparison with the optical light profile of NGC 5005 indicates that the ultraviolet source is distributed spatially in the same manner as the optical starlight, probably indicating that the ultraviolet excess is due to a component of hot stars in the nucleus. These stars contribute detectable absorption features longward of 2500 A; together with optical data, the IUE spectra suggest a burst of star formation about 1 billion yr ago, with a lower rate continuing to produce a few OB stars. In NGC 4579, a point source contributing most of the ultraviolet excess is found that is much different than the optical light distribution. Furthermore, the ultraviolet to X-ray spectral index in NGC 4579 is 1.4, compatible with the UV to X-ray indices found for samples of Seyfert galaxies. This provides compelling evidence for the detection of the photoionizing continuum in NGC 4579 and draws the research fields of normal galaxies and active galactic nuclei closer together. The emission-line spectrum of NGC 4579 is compared with calculations from a photoionization code, CLOUDY, and several shock models. The photoionization code is found to give superior results, adding to the increasing weight of evidence that the LINER phenomenon is essentially a scaled-down version of the Seyfert phenomenon.
Goodrich, R. W.↗
Probability-matched reflectivity-rainfall relations for a hurricane from aircraft observations
The relation between the distribution of equivalent reflectivity, Z(sub e), measured by an airborne C-band radar and that for rain rate, R, measured concurrently by a disdrometer on the same aircraft in the eyewall and outer bands of Hurricane Anita (1977) was investigated using the probability-matching method (PMM). It was found that the pdf of R is much narrower in the outer rainbands of Hurricane Anita than in the eyewall, and that the mean rain rates are also much smaller. It is shown that the use of PMM provides more realistic relations than the conventional power-law Z-R regression relations based upon scatter-plots of disdrometer measurements, showing higher eyewall reflectivities for the same rain rates at rates in excess of 6.3 mm/h.
Marks, Frank D., Jr.↗
Characterizing Peatland Microtopography Using Gradient and Microform-Based Approaches
Abstract Peatlands represent an important component of the global carbon cycle, storing 180–621 Gt of carbon (C). Small-scale spatial variations in elevation, frequently referred to as microtopography, influence ecological processes associated with the peatland C cycle, including Sphagnum photosynthesis and methane flux. Microtopography can be characterized with measures of topographic variability and by using conceptual classes (microforms) linked to function: most commonly hummocks and hollows. However, the criteria used to define these conceptual classes are often poorly described, if at all, and vary between studies. Such inconsistencies compel development of explicit quantitative methods to classify microforms. Furthermore, gradient-based characterizations that describe spatial variability without the use of microforms are lacking in the literature. Therefore, the objectives of this study were to (1) calculate peatland microtopographical elevation gradients and measures of spatial variability, (2) develop three microform classification methods intended for specific purposes, and (3) evaluate and contrast classification methods. Our results suggest that at spatial scales much larger than microforms, elevation distributions are unimodal and are well approximated with parametric probability density functions. Results from classifications were variable between methods and years and exhibited significant differences in mean hollow areal coverages of a raised ombrotrophic bog. Our results suggest that the conceptualization and classification of microforms can significantly influence microtopographic structural metrics. The three explicit methods for microform classification described here may be used and built upon for future applications.
54 ENVIRONMENTAL SCIENCES↗