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At least 109 records · Page 6

The Non-Gaussian Nature of Prostate Motion Based on Real-Time Intrafraction Tracking

Purpose: The objective of this work is to test the validity of the Gaussian approximation for prostate motion through characterization of its spatial distribution. Methods and Materials: Real-time intrafraction prostate motion was observed using Calypso 4-dimensional (4D) nonradioactive electromagnetic tracking system. We report the results from a total of 1024 fractions from 31 prostate cancer patients. First, the correlation of prostate motion in right/left (RL), anteroposterior (AP), and superoinferior (SI) direction were determined using Pearson's correlation of coefficient. Then the spatial distribution of prostate motion was analyzed for individual fraction, individual patient including all fractions, and all patients including all fractions. The displacement in RL, AP, SI, oblique, or total direction is fitted into a Gaussian distribution, and a Lilliefors test was used to evaluate the validity of the hypothesis that the displacement is normally distributed. Results: There is high correlation in AP/SI direction (61% of fractions with medium or strong correlation). This is consistent with the longitudinal oblique motion of the prostate, and likely the effect from respiration on an organ confined within the genitourinary diaphragm with the rectum sitting posteriorly and bladder sitting superiorly. In all directions, the non-Gaussian distribution is more common for individual fraction, individual patient including all fractions, and all patients including all fractions. The spatial distribution of prostate motion shows an elongated shape in oblique direction, indicating a higher range of motion in the AP and SI directions. Conclusions: Our results showed that the prostate motion is highly correlated in AP and SI direction, indicating an oblique motion preference. In addition, the spatial distribution of prostate motion is elongated in an oblique direction, indicating that the organ motion dosimetric modeling using Gaussian kernel may need to be modified to account for the particular organ motion character of prostate.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Effect of rapid thermal annealing temperature on the dispersion of Si nanocrystals in SiO{sub 2} matrix

Effect of rapid thermal annealing temperature on the dispersion of silicon nanocrystals (Si-NC’s) embedded in SiO{sub 2} matrix grown by atom beam sputtering (ABS) method is reported. The dispersion of Si NCs in SiO{sub 2} is an important issue to fabricate high efficiency devices based on Si-NC’s. The transmission electron microscopy studies reveal that the precipitation of excess silicon is almost uniform and the particles grow in almost uniform size upto 850 °C. The size distribution of the particles broadens and becomes bimodal as the temperature is increased to 950 °C. This suggests that by controlling the annealing temperature, the dispersion of Si-NC’s can be controlled. The results are supported by selected area diffraction (SAED) studies and micro photoluminescence (PL) spectroscopy. The discussion of effect of particle size distribution on PL spectrum is presented based on tight binding approximation (TBA) method using Gaussian and log-normal distribution of particles. The study suggests that the dispersion and consequently emission energy varies as a function of particle size distribution and that can be controlled by annealing parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simultaneous observations of giant pulses from the crab pulsar, with the Murchison Widefield Array and Parkes radio telescope: Implications for the giant pulse emission mechanism

We report on observations of giant pulses from the Crab pulsar performed simultaneously with the Parkes radio telescope and the incoherent combination of the Murchison Widefield Array (MWA) antenna tiles. The observations were performed over a duration of approximately one hour at a center frequency of 1382 MHz with 340 MHz bandwidth at Parkes, and at a center frequency of 193 MHz with 15 MHz bandwidth at the MWA. Our analysis has led to the detection of 55 giant pulses at the MWA and 2075 at Parkes above a threshold of 3.5σ and 6.5σ, respectively. We detected 51% of the MWA giant pulses at the Parkes radio telescope, with spectral indices in the range of −3.6>α>−4.9 (S{sub ν}∝ν{sup α}). We present a Monte Carlo analysis supporting the conjecture that the giant pulse emission in the Crab is intrinsically broadband, the less than 100% correlation being due to the relative sensitivities of the two instruments and the width of the spectral index distribution. Our observations are consistent with the hypothesis that the spectral index of giant pulses is drawn from normal distribution of standard deviation 0.6, but with a mean that displays an evolution with frequency from −3.00 at 1382 MHz, to −2.85 at 192 MHz.

79 ASTRONOMY AND ASTROPHYSICS↗

ASSESSMENT OF NORMALITY FOR CRITICALITY SAFETY BIAS AND BIAS UNCERTAINTY CALCULATION

The single-sided lower tolerance factors frequently used for non-trending assessment of the validation bias and bias uncertainty are sensitive to departures from normality. When used properly, the tolerance limits ensure that an appropriate fraction of the true population of applicable critical experiments lies above the calculated lower tolerance limit with the required statistical confidence level. One condition necessary to ensure that the appropriate proportion of the true population of keff values in the validation suite lies above the lower tolerance limit is that the assumption that the normality of the underlying population of critical experiments is valid or conservative.This paper discusses various methods used to assess whether the assumption that the validation suite may be treated as a random sample drawn from a normal distribution is acceptable. Techniques for assessing the validity of this underlying assumption include common omnibus hypothesis tests for normality, assessment of sample skewness and kurtosis of the validation suite, and graphical techniques. These techniques are used to assess the nature and potential conservatism/nonconservatism imparted by various departures from normality where possible. A review of hypothesis testing is also presented to frame the discussion of omnibus normality tests. Additionally, two cases are analysed with these techniques to provide an example of how they should be implemented.

Clarity, Justin↗

Inference for Nonparanormal Partial Correlation via Regularized Rank-Based Nodewise Regression

Abstract Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. In this paper, we propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model where the observed data are normally distributed after certain monotone transformations. The NPN partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy-to-implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

97 MATHEMATICS AND COMPUTING↗

Numerical simulations of turbulent molecular clouds regulated by radiation feedback forces. I. Star formation rate and efficiency

Radiation feedback from stellar clusters is expected to play a key role in setting the rate and efficiency of star formation in giant molecular clouds. To investigate how radiation forces influence realistic turbulent systems, we have conducted a series of numerical simulations employing the Hyperion radiation hydrodynamics solver, considering the regime that is optically thick to ultraviolet and optically thin to infrared radiation. Our model clouds cover initial surface densities between Σ{sub cl,0}∼10--300 M{sub ⊙} pc{sup −2}, with varying initial turbulence. We follow them through turbulent, self-gravitating collapse, star cluster formation, and cloud dispersal by stellar radiation. All our models display a log-normal distribution of gas surface density Σ; for an initial virial parameter α{sub vir,0}=2, the log-normal standard deviation is σ{sub lnΣ}=1--1.5 and the star formation rate coefficient ε{sub ff, ρ-bar }=0.3--0.5, both of which are sensitive to turbulence but not radiation feedback. The net star formation efficiency (SFE) ε{sub final} increases with Σ{sub cl,0} and decreases with α{sub vir,0}. We interpret these results via a simple conceptual framework, whereby steady star formation increases the radiation force, such that local gas patches at successively higher Σ become unbound. Based on this formalism (with fixed σ{sub lnΣ}), we provide an analytic upper bound on ε{sub final}, which is in good agreement with our numerical results. The final SFE depends on the distribution of Eddington ratios in the cloud and is strongly increased by the turbulent compression of gas.

79 ASTRONOMY AND ASTROPHYSICS↗

Angular Momentum Transfer and Fractional Moment of Inertia in Pulsar Glitches

We use the Jodrell Bank Observatory glitch database containing 472 glitches from 165 pulsars to investigate the angular momentum transfer during rotational glitches in pulsars. Our emphasis is on pulsars with at least five glitches, of which there are 26 that exhibit 261 glitches in total. This paper identifies four pulsars in which the angular momentum transfer, after many glitches, is almost linear with time. The Lilliefore test on the cumulative distribution of glitch spin-up sizes in these glitching pulsars shows that glitch sizes in 12 pulsars are normally distributed, suggesting that their glitches originate from the same momentum reservoir. In addition, the distribution of the fractional moment of inertia (i.e., the ratio of the moment of inertia of neutron star components that are involved in the glitch process) have a single mode, unlike the distribution of fractional glitch size (Δ ν / ν ), which is usually bimodal. The mean fractional moment of inertia in the glitching pulsars we sampled has a very weak correlation with the pulsar spin properties, thereby supporting a neutron star interior mechanism for the glitch phenomenon.

79 ASTRONOMY AND ASTROPHYSICS↗

The ELM Survey. VII. Orbital properties of low-mass white dwarf binaries

We present the discovery of 15 extremely low-mass (5<logg<7) white dwarf (WD) candidates, 9 of which are in ultra-compact double-degenerate binaries. Our targeted extremely low-mass Survey sample now includes 76 binaries. The sample has a lognormal distribution of orbital periods with a median period of 5.4 hr. The velocity amplitudes imply that the binary companions have a normal distribution of mass with 0.76 M{sub ⊙} mean and 0.25 M{sub ⊙} dispersion. Thus extremely low-mass WDs are found in binaries with a typical mass ratio of 1:4. Statistically speaking, 95% of the WD binaries have a total mass below the Chandrasekhar mass, and thus are not type Ia supernova progenitors. Yet half of the observed binaries will merge in less than 6 Gyr due to gravitational wave radiation; probable outcomes include single massive WDs and stable mass transfer AM CVn binaries.

79 ASTRONOMY AND ASTROPHYSICS↗

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗

Modeling Seasonal Sudden Stratospheric Warming Climatology Based on Polar Vortex Statistics

This report explores the climatological frequency distribution of sudden stratospheric warmings (SSWs). General circulation models (GCMs) tend to produce SSW maxima later in winter than observations, which has been considered as a model deficiency. Yet, the observed record is short, calling into question the representativeness of the observational record. To study the seasonality of SSWs and the factors behind it, the authors use observations, a long control simulation with a stratosphere resolving GCM, and also a simple statistical model that is based on the climatological seasonal cycle of the polar vortex winds. From the combined analysis, the authors conclude that the late-winter SSW maximum seen in most climate models is realistic and that observations would also have a late-winter SSW maximum if more data were available. The authors identify the seasonally varying strengths of the polar vortex and stratospheric wave driving as the two main factors behind the seasonal SSW distribution. The statistical model also indicates that there exists a continuum of weak polar vortex states and that SSWs simply form the tail of normally distributed stratospheric winds.

54 ENVIRONMENTAL SCIENCES↗

The probabilistic distribution of metal whisker lengths

Significant reliability concerns in multiple industries are related to metal whiskers, which are random high aspect ratio filaments growing on metal surfaces and causing shorts in electronic packages. We derive a closed form expression for the probabilistic distribution of metal whisker lengths. Our consideration is based on the electrostatic theory of metal whiskers, according to which whisker growth is interrupted when its tip enters a random local “dead region” of a weak electric field. Here, we use the approximation neglecting the possibility of thermally activated escapes from the “dead regions,” which is later justified. We predict a one-parameter distribution with a peak at a length that depends on the metal surface charge density and surface tension. In the intermediate range, it fits well the log-normal distribution used in the experimental studies, although it decays more rapidly in the range of very long whiskers. In addition, our theory quantitatively explains how the typical whisker concentration is much lower than that of surface grains. Finally, it predicts the stop-and-go phenomenon for some of the whiskers growth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-E-T-121: Analyzing the Broadening Effect On the Bragg Peak Due to Heterogeneous Geometries and Implementing User-Routines in the Monte-Carlo Code FLUKA in Order to Reduce Computation Time

Purpose: Aim of this study was to analyze the modulating, broadening effect on the Bragg Peak due to heterogeneous geometries like multi-wire chambers in the beam path of a particle therapy beam line. The effect was described by a mathematical model which was implemented in the Monte-Carlo code FLUKA via user-routines, in order to reduce the computation time for the simulations. Methods: The depth dose curve of 80 MeV/u C12-ions in a water phantom was calculated using the Monte-Carlo code FLUKA (reference curve). The modulating effect on this dose distribution behind eleven mesh-like foils (periodicity ∼80 microns) occurring in a typical set of multi-wire and dose chambers was mathematically described by optimizing a normal distribution so that the reverence curve convoluted with this distribution equals the modulated dose curve. This distribution describes a displacement in water and was transferred in a probability distribution of the thickness of the eleven foils using the water equivalent thickness of the foil’s material. From this distribution the distribution of the thickness of one foil was determined inversely. In FLUKA the heterogeneous foils were replaced by homogeneous foils and a user-routine was programmed that varies the thickness of the homogeneous foils for each simulated particle using this distribution. Results: Using the mathematical model and user-routine in FLUKA the broadening effect could be reproduced exactly when replacing the heterogeneous foils by homogeneous ones. The computation time was reduced by 90 percent. Conclusion: In this study the broadening effect on the Bragg Peak due to heterogeneous structures was analyzed, described by a mathematical model and implemented in FLUKA via user-routines. Applying these routines the computing time was reduced by 90 percent. The developed tool can be used for any heterogeneous structure in the dimensions of microns to millimeters, in principle even for organic materials like lung tissue.

60 APPLIED LIFE SCIENCES↗

Impedance Response Influenced by Variability in the Random Distribution of Physical Properties of Coated Materials in Two-Dimensional Space

Heterogeneous physical characteristics of a system featuring a single-layer film on a metallic surface have been explored via its impedance response. The Nyquist plot showed a distorted semicircle, indicative of the system's unique distribution characteristics. Utilizing a copula-based probability method, a two-dimensional deterministic impedance model was successfully integrated, accounting for spatial physical properties such as permittivity and electrical conductivity. This strategy enabled in-depth exploration and mechanistic quantification of a broad spectrum of properties. A quantitative understanding of impedance signal alterations, characterized by normally or log-normally correlated variables, was achieved through the variation in aspect ratio and characteristic frequency of the impedance spectra. Log-normally distributed electrical properties provided a superior representation of the distorted impedance spectra. As coefficient of variation (CV) values fluctuated, the aspect ratio and characteristic frequency showed heightened sensitivity to log-normal permittivity compared to log-normal electrical conductivity. Notably, a marked positive linear correlation between electrical properties resulted in an impedance response that approximated perfect semicircular spectra. The variability in the electrical properties' distribution was demonstrated by considering the correlation coefficient between electrical conductivity and the z-direction position. Furthermore, the highest aspect ratio of the impedance spectra was observed when the electrical conductivity was randomly distributed across the z-direction space.

36 MATERIALS SCIENCE↗

Evaluating the impact of anatomical and physiological variability on human equivalent doses using PBPK models

Abstract Addressing human anatomical and physiological variability is a crucial component of human health risk assessment of chemicals. Experts have recommended probabilistic chemical risk assessment paradigms in which distributional adjustment factors are used to account for various sources of uncertainty and variability, including variability in the pharmacokinetic behavior of a given substance in different humans. In practice, convenient assumptions about the distribution forms of adjustment factors and human equivalent doses (HEDs) are often used. Parameters such as tissue volumes and blood flows are likewise often assumed to be lognormally or normally distributed without evaluating empirical data for consistency with these forms. In this work, we performed dosimetric extrapolations using physiologically based pharmacokinetic (PBPK) models for dichloromethane (DCM) and chloroform that incorporate uncertainty and variability to determine if the HEDs associated with such extrapolations are approximately lognormal and how they depend on the underlying distribution shapes chosen to represent model parameters. We accounted for uncertainty and variability in PBPK model parameters by randomly drawing their values from a variety of distribution types. We then performed reverse dosimetry to calculate HEDs based on animal points of departure for each set of sampled parameters. Corresponding samples of HEDs were tested to determine the impact of input parameter distributions on their central tendencies, extreme percentiles, and degree of conformance to lognormality. This work demonstrates that the measurable attributes of human variability should be considered more carefully and that generalized assumptions about parameter distribution shapes may lead to inaccurate estimates of extreme percentiles of HEDs.

Toxicology↗

Evaluating the Magnitude and Duration of Cold Load Pick-up on Residential Distribution Feeders Using Multi-State Load Models

The increased level of demand that is associated with the restoration of service after an outage, Cold Load Pick-Up (CLPU), can be significantly higher than pre-outage levels, even exceeding the normal distribution feeder peak demand. These high levels of demand can delay restoration efforts and in extreme cases damage equipment. The negative impacts of CLPU can be mitigated with strategies that restore the feeder in sections, minimizing the load current. The challenge for utilities is to manage the current level on critical equipment while minimizing the time to restore service to all customers. Accurately modeling CLPU events is the first step in developing improved restoration strategies that minimize restoration times. This paper presents a new method for evaluating the magnitude of the CLPU peak, and its duration, using multi-state load models. The use of multi-state load models allows for a more accurate representation of the end-use loads that are present on residential distribution feeders.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Corrosion of rebar in concrete. Part II: Literature survey and statistical analysis of existing data on chloride threshold

The literature is reviewed with respect to defining, measuring, and interpreting the chloride threshold (CT). CT was defined with a strong fundamental basis in the Point Defect Model. which also dictates the nature of the statistical analysis of surveyed CT values. A database of CT for various primary and secondary independent variables has been established. Statistical analyses reveal that CT is lognormally distributed, in accordance with the PDM, with most probable values being 0.85, 0.69, and 1.19 for %total Cl/cem, %free Cl/cem, and [Cl - ]/[OH - ], respectively. The breakdown and corrosion potentials follow normal distributions with means of 0.056 and -0.322 V SCE , respectively.

36 MATERIALS SCIENCE↗

THE EFFECTS OF RADIATIVE TRANSFER ON THE PROBABILITY DISTRIBUTION FUNCTIONS OF MOLECULAR MAGNETOHYDRODYNAMIC TURBULENCE

We study the effects of radiative transfer on the probability distribution functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied {sup 13}CO 2-1 transition. We find that the integrated intensity maps generally follow a log-normal distribution, with the cases that have {tau} Almost-Equal-To 1 best matching the PDF of the column density. We fit a two-dimensional variance-sonic Mach number relationship to our logarithmic PDFs of the form {sigma}{sub ln}{sup 2}{sub ({Sigma}/{Sigma}0}) = A x ln(1+b{sup 2}M{sub s}{sup 2}) and find that, for parameter b = 1/3, parameter A depends on the radiative transfer environment. We also explore the variance, skewness, and kurtosis of the linear PDFs finding that higher moments reflect both higher sonic Mach number and lower optical depth. Finally, we apply the Tsallis incremental PDF function and find that the fit parameters depend on both Mach numbers, but also are sensitive to the radiative transfer parameter space, with the {tau} Almost-Equal-To 1 case best fitting the incremental PDF of the true column density. We conclude that, for PDFs of low optical depth cases, part of the gas is always subthermally excited so that the spread of the line intensities exceeds the spread of the underlying column densities and hence the PDFs do not reflect the true column density. Similarly, PDFs of optically thick cases are dominated by the velocity dispersion and therefore do not represent the true column density PDF. Thus, in the case of molecules like carbon monoxide, the dynamic range of intensities, structures observed, and, consequently, the observable PDFs are less determined by turbulence and more often determined by radiative transfer effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Phosphorus Removal from Si-Fe Alloy Using SiO{sub 2}-Al{sub 2}O{sub 3}-CaO Slag

Phosphorus removal from silicon using a combination of solvent and slag refining, with lower carbon footprint and lower energy requirement than the current industrial process, is investigated by evaluating the distribution of phosphorus between Si-Fe alloy and SiO{sub 2}-Al{sub 2}O{sub 3}-CaO slag. An alloy with the composition of silicon-20 wt pct iron was treated with a slag of CaO-Al{sub 2}O{sub 3}-SiO{sub 2} at 1600 °C. The effects of slag basicity and oxygen potential on the distribution of phosphorus were studied via changing the slag composition. The critical oxygen potential, at which the maximum removal of phosphorus is obtained, was calculated as 6.3 × 10{sup −18} atm. Normalized distribution and phosphate capacity values were calculated for each slag composition with the purpose of isolating the effect of basicity. In a separate experiment, calcium was also added to the alloy with the purpose of improving the removal efficiency of phosphorus. Results show that the addition of calcium can almost double the partition ratio of phosphorus. The removal rate of phosphorus was quantified via kinetics calculations, and the total mass-transfer rate of phosphorus was estimated to be 8.58 × 10{sup −7} cm/s.

36 MATERIALS SCIENCE↗