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An extension of the standard concept of the statistical ensembles is suggested. Namely, the statistical ensembles with extensive quantities fluctuating according to an externally given distribution are introduced. Applications in the statistical models of multiple hadron production in high energy physics are discussed.
We benchmark performance of long-short term memory (LSTM) network machine learning model and autoregressive integrated moving average (ARIMA) statistical model in temporal forecasting of distributed temperature sensing (DTS). Data in this study consists of fluid temperature transient measured with two co-located Rayleigh scattering fiber optic sensors (FOS) in a forced convection mixing zone of a thermal tee. We treat each gauge of a FOS as an independent temperature sensor. We first study prediction of DTS time series using Vanilla LSTM and ARIMA models trained on prior history of the same FOS that is used for testing. The results yield maximum absolute percentage error (MaxAPE) and root mean squared percentage error (RMSPE) of 1.58% and 0.06% for ARIMA, and 3.14% and 0.44% for LSTM, respectively. Next, we investigate zero-shot forecasting (ZSF) with LSTM and ARIMA trained on history of the co-located FOS only, which is advantageous when limited training data is available. The ZSF MaxAPE and RMSPE values for ARIMA are comparable to those of the Vanilla use case, while the error values for LSTM increase. We show that in ZSF, performance of LSTM network can be improved by training on most correlated gauges between the two FOS, which are identified by calculating the Pearson correlation coefficient. The improved ZSF MaxAPE and RMSPE for LSTM are 4.4% and 0.33%, respectively. Performance of ZSF LSTM can be further enhanced through transfer learning (TL), where LSTM is re-trained on a subset of the FOS that is the target of forecasting. We show that LSTM pre-trained on correlated dataset and re-trained on 30% of testing target dataset achieves MaxAPE and RMSPE values of 2.32% and 0.28%, respectively.
Purpose: To develop a generalized statistical model that incorporates the treatment uncertainty from the rotational error of single iso-center technique, and calculate the additional PTV (planning target volume) margin required to compensate for this error. Methods: The random vectors for setup and additional rotation errors in the three-dimensional (3D) patient coordinate system were assumed to follow the 3D independent normal distribution with zero mean, and standard deviations σx, σy, σz, for setup error and a uniform σR for rotational error. Both random vectors were summed, normalized and transformed to the spherical coordinates to derive the chi distribution with 3 degrees of freedom for the radical distance ρ. PTV margin was determined using the critical value of this distribution for 0.05 significant level so that 95% of the time the treatment target would be covered by ρ. The additional PTV margin required to compensate for the rotational error was calculated as a function of σx, σy, σz and σR. Results: The effect of the rotational error is more pronounced for treatments that requires high accuracy/precision like stereotactic radiosurgery (SRS) or stereotactic body radiotherapy (SBRT). With a uniform 2mm PTV margin (or σx =σy=σz=0.7mm), a σR=0.32mm will decrease the PTV coverage from 95% to 90% of the time, or an additional 0.2mm PTV margin is needed to prevent this loss of coverage. If we choose 0.2 mm as the threshold, any σR>0.3mm will lead to an additional PTV margin that cannot be ignored, and the maximal σR that can be ignored is 0.0064 rad (or 0.37°) for iso-to-target distance=5cm, or 0.0032 rad (or 0.18°) for iso-to-target distance=10cm. Conclusions: The rotational error cannot be ignored for high-accuracy/-precision treatments like SRS/SBRT, particularly when the distance between the iso-center and target is large.
A statistical model is formulated to compute exotic rotational correlations that arise as inertial frames and causal structure emerge on large scales from entangled Planck scale quantum systems. Noncommutative quantum dynamics are represented by random transverse displacements that respect causal symmetry. Entanglement is represented by covariance of these displacements in Planck scale intervals defined by future null cones of events on an observer's world line. Light that propagates in a nonradial direction inherits a projected component of the exotic rotational correlation that accumulates as a random walk in phase. A calculation of the projection and accumulation leads to exact predictions for statistical properties of exotic Planck scale correlations in an interferometer of any configuration. The cross-covariance for two nearly co-located interferometers is shown to depart only slightly from the autocovariance. Specific examples are computed for configurations that approximate realistic experiments, and show that the model can be rigorously tested.
Chris Marshall: Memorial Introduction Donald Edmonds Herbert Jr., or Don to his colleagues and friends, exemplified the “big tent” vision of medical physics, specializing in Applied Statistics and Dynamical Systems theory. He saw, more clearly than most, that “Making models is the difference between doing science and just fooling around [ref Woodworth, 2004]”. Don developed an interest in chemistry at school by “reading a book” - a recurring theme in his story. He was awarded a Westinghouse Science scholarship and attended the Carnegie Institute of Technology (later Carnegie Mellon University) where his interest turned to physics and led to a BS in Physics after transfer to Northwestern University. After (voluntary) service in the Navy he earned his MS in Physics from the University of Oklahoma, which led him to Johns Hopkins University in Baltimore to pursue a PhD. The early death of his wife led him to take a salaried position in the Physics Department of Colorado College in Colorado Springs so as to better care for their young daughter. There, a chance invitation from Dr. Juan del Regato to teach physics to residents at the Penrose Cancer Hospital introduced him to Medical Physics, and he decided to enter the field. He received his PhD from the University of London (UK) under Prof. Joseph Rotblat, where I first met him, and where he taught himself statistics. He returned to Penrose as a clinical medical physicist, also largely self-taught. In 1975 he formalized an evolving interest in statistical analysis as Professor of Radiology and Head of the Division of Physics and Statistics at the College of Medicine of the University of South Alabama in Mobile, AL where he remained for the rest of his career. He also served as the first Director of their Bio-Statistics and Epidemiology Core Unit working in part on a sickle-cell disease. After retirement he remained active as Professor Emeritus. Don served for several years as a consultant to the Nuclear Regulatory Commission and may be remembered for his critique of the National Academy of Sciences BEIR III report (stating that their methodology “imposes a Delphic quality to the .. risk estimates”.) This led to his appointment as a member of the BEIR V committee. Don presented refresher courses at the AAPM, ASTRO and RSNA meetings and was active in the AAPM as a member or chair of several committees. He was the principal author of AAPM Report 43, which is essentially a critique of established clinical studies prior to 1992. He was co-editor of the Proceedings of many symposia on Time, Dose and Fractionation held in Madison, Wisconsin. He received the AAPM lifetime Achievement award in 2004. Don’s second wife of 46 years, Ann, predeceased him and he is survived by daughters Hillary and Emily, son John and two grandsons. Don was a true gentleman with a unique and erudite writing style illuminated by pithy quotations. If he had a fault it was, perhaps, that he did not realize how much smarter he was than the rest of us. This presentation draws heavily on a biography and video interview in the History and Heritage section of the AAPM website. The quote is his own. Andrzej Niemierko: Statistical modeling plays an essential role in modern medicine for quantitative evaluation of the effect of treatment. This session will feature an overview of statistical modeling techniques used for analyzing the many types of research data and an exploration of recent advances in new statistical modeling methodologies. Learning Objectives: To learn basics of statistical modeling methodology. To discuss statistical models that are frequently used in radiation oncology To discuss advanced modern statistical modeling methods and applications.
Chris Marshall: Memorial Introduction Donald Edmonds Herbert Jr., or Don to his colleagues and friends, exemplified the “big tent” vision of medical physics, specializing in Applied Statistics and Dynamical Systems theory. He saw, more clearly than most, that “Making models is the difference between doing science and just fooling around [ref Woodworth, 2004]”. Don developed an interest in chemistry at school by “reading a book” - a recurring theme in his story. He was awarded a Westinghouse Science scholarship and attended the Carnegie Institute of Technology (later Carnegie Mellon University) where his interest turned to physics and led to a BS in Physics after transfer to Northwestern University. After (voluntary) service in the Navy he earned his MS in Physics from the University of Oklahoma, which led him to Johns Hopkins University in Baltimore to pursue a PhD. The early death of his wife led him to take a salaried position in the Physics Department of Colorado College in Colorado Springs so as to better care for their young daughter. There, a chance invitation from Dr. Juan del Regato to teach physics to residents at the Penrose Cancer Hospital introduced him to Medical Physics, and he decided to enter the field. He received his PhD from the University of London (UK) under Prof. Joseph Rotblat, where I first met him, and where he taught himself statistics. He returned to Penrose as a clinical medical physicist, also largely self-taught. In 1975 he formalized an evolving interest in statistical analysis as Professor of Radiology and Head of the Division of Physics and Statistics at the College of Medicine of the University of South Alabama in Mobile, AL where he remained for the rest of his career. He also served as the first Director of their Bio-Statistics and Epidemiology Core Unit working in part on a sickle-cell disease. After retirement he remained active as Professor Emeritus. Don served for several years as a consultant to the Nuclear Regulatory Commission and may be remembered for his critique of the National Academy of Sciences BEIR III report (stating that their methodology “imposes a Delphic quality to the .. risk estimates”.) This led to his appointment as a member of the BEIR V committee. Don presented refresher courses at the AAPM, ASTRO and RSNA meetings and was active in the AAPM as a member or chair of several committees. He was the principal author of AAPM Report 43, which is essentially a critique of established clinical studies prior to 1992. He was co-editor of the Proceedings of many symposia on Time, Dose and Fractionation held in Madison, Wisconsin. He received the AAPM lifetime Achievement award in 2004. Don’s second wife of 46 years, Ann, predeceased him and he is survived by daughters Hillary and Emily, son John and two grandsons. Don was a true gentleman with a unique and erudite writing style illuminated by pithy quotations. If he had a fault it was, perhaps, that he did not realize how much smarter he was than the rest of us. This presentation draws heavily on a biography and video interview in the History and Heritage section of the AAPM website. The quote is his own. Andrzej Niemierko: Statistical modeling plays an essential role in modern medicine for quantitative evaluation of the effect of treatment. This session will feature an overview of statistical modeling techniques used for analyzing the many types of research data and an exploration of recent advances in new statistical modeling methodologies. Learning Objectives: To learn basics of statistical modeling methodology. To discuss statistical models that are frequently used in radiation oncology To discuss advanced modern statistical modeling methods and applications.
In this paper, we consider radiation source localization in an urban environment as an inverse problem and use Bayesian parameter estimation techniques to infer the source location and intensity. Since parameter estimation generally requires a large number of model evaluations, we employ a simplified photon transport model, as in a 2017 paper by Stefanescu, et al., to reduce computational requirements. However, the model in the 2017 paper does not account for the physical reality that background radiation varies with position within an urban locale. We incorporate statistical mixed-effects modeling into the simplified transport equation from the Stefanescu, et al. paper to reflect individual variation among the background radiation measurements at multiple detector locations. With our new model, we use a Bayesian DRAM-within-Gibbs technique, which incorporates the Delayed Rejection Adaptive Metropolis (DRAM) algorithm, to estimate the mixed-effects parameters. We note that without adequate prior information, we were unable to simultaneously estimate the set of parameters corresponding to the source intensity, source location, and individual background radiation counts. By calibrating the background in the absence of a source, we obtained narrow prior distributions, which permitted us to jointly infer the source intensity and location and the background radiation distribution.
Purpose: Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks. Methods: The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDI{sub vol} =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d′. Results: (1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels. Conclusions: Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.
Purpose: To apply a statistical modeling approach, threshold modeling (TM), for quality control of intensity-modulated radiation therapy (IMRT) treatment plans. Methods: A quantitative measure, which was the weighted sum of violations of dose/dose-volume constraints, was first developed to represent the quality of each IMRT plan. Threshold modeling approach, which is is an extension of extreme value theory in statistics and is an effect way to model extreme values, was then applied to analyze the quality of the plans summarized by our quantitative measures. Our approach modeled the plans generated by planners as a series of independent and identically distributed random variables and described the behaviors of them if the plan quality was controlled below certain threshold. We tested our approach with five locally advanced head and neck cancer patients retrospectively. Two statistics were incorporated for numerical analysis: probability of quality improvement (PQI) of the plans and expected amount of improvement on the quantitative measure (EQI). Results: After clinical planners generated 15 plans for each patient, we applied our approach to obtain the PQI and EQI as if planners would generate additional 15 plans. For two of the patients, the PQI was significantly higher than the other three (0.17 and 0.18 comparing to 0.08, 0.01 and 0.01). The actual percentage of the additional 15 plans that outperformed the best of initial 15 plans was 20% and 27% comparing to 11%, 0% and 0%. EQI for the two potential patients were 34.5 and 32.9 and the rest of three patients were 9.9, 1.4 and 6.6. The actual improvements obtained were 28.3 and 20.5 comparing to 6.2, 0 and 0. Conclusion: TM is capable of reliably identifying the potential quality improvement of IMRT plans. It provides clinicians an effective tool to assess the trade-off between extra planning effort and achievable plan quality. This work was supported in part by NIH/NCI grant CA130814.
Purpose: To derive and validate a statistical model of motion and deformation for the clinical target volume (CTV) of early-stage rectal cancer patients. Methods and Materials: For 16 patients, 4 to 5 magnetic resonance images (MRI) were acquired before each fraction was administered. The CTV was delineated on each MRI. Using a leave-one-out methodology, we constructed a population-based principal component analysis (PCA) model of the CTV motion and deformation of 15 patients, and we tested the model on the left-out patient. The modeling error was calculated as the amount of the CTV motion-deformation of the left-out-patient that could not be explained by the PCA model. Next, the PCA model was used to construct a PCA target volume (PCA-TV) by accumulating motion-deformations simulated by the model. A PCA planning target volume (PTV) was generated by expanding the PCA-TV by uniform margins. The PCA-PTV was compared with uniform and nonuniform CTV-to-PTV margins. To allow comparison, geometric margins were determined to ensure adequate coverage, and the volume difference between the PTV and the daily CTV (CTV-to-PTV volume) was calculated. Results: The modeling error ranged from 0.9 ± 0.5 to 2.9 ± 2.1 mm, corresponding to a reduction of the CTV motion-deformation between 6% and 60% (average, 23% ± 11%). The reduction correlated with the magnitude of the CTV motion-deformation (P<.001, R=0.66). The PCA-TV and the CTV required 2-mm and 7-mm uniform margins, respectively. The nonuniform CTV-to-PTV margins were 4 mm in the left, right, inferior, superior, and posterior directions and 8 mm in the anterior direction. Compared to uniform and nonuniform CTV-to-PTV margins, the PCA-based PTV significantly decreased (P<.001) the average CTV-to-PTV volume by 128 ± 20 mL (49% ± 4%) and by 35 ± 6 mL (20% ± 3.5%), respectively. Conclusions: The CTV motion-deformation of a new patient can be explained by a population-based PCA model. A PCA model-generated PTV significantly improved sparing of organs at risk compared to uniform and nonuniform CTV-to-PTV margins.
Purpose: To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system. Methods: Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods. Results: (1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a “redder” NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose){sup −β} with the component β ≈ 0.25, which violated the classical σ ∝ (dose){sup −0.5} power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2. Conclusions: The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.
In the present work, we attempt to describe the nuclear EMC effect by using the proton structure functions obtained from the non-extensive statistical quark model. We record that such model has three fundamental variables, the temperature T, the radius, and the Tsallis parameter q. By combining different small changes, a good agreement with the experimental data may be obtained. Another interesting point of the model is to allow phenomenological interpretation, for instance, with q constant and changing the radius and the temperature or changing the radius and q and keeping the temperature.
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The mode of asymmetric induction in an enantioselective intramolecular allylic substitution reaction catalyzed by a combination of palladium and a chiral phosphoric acid was investigated by a combined experimental and statistical modeling approach. Experiments to probe nonlinear effects, the reactivity of deuterium-labeled substrates, and control experiments revealed that nucleophilic attack to the π-allylpalladium intermediate is the enantio-determining step, in which the chiral phosphate anion is involved in stereoinduction. Here, using multivariable linear regression analysis, we determined that multiple noncovalent interactions with the chiral environment of the phosphate anion are integral to enantiocontrol in the transition state. The synthetic protocol to form chiral pyrrolidines was further applied to the asymmetric construction of C-O bonds at fully substituted carbon centers in the synthesis of chiral 2,2-disubstituted benzomorpholines.
The purpose of this document is to describe the statistical modeling effort for gas concentrations in WIPP storage containers. The concentration (in ppm) of CO 2 in the headspace volume of standard waste box (SWB) 68685 is shown. A Bayesian approach and an adaptive Metropolis-Hastings algorithm were used.
This paper summarizes the modeling, statistics, simulation, and computing needs of direct dark matter detection experiments in the next decade.
We summarize the contributions of the Texas A\&M University Group to the project (DE-FG02-09ER25949/DE-SC0002505: Topology for Statistical Modeling of Petascale Data - an ASCR-funded collaboration between Sandia National Labs, Texas A\&M U, and U Utah) during 6/9/2011 -- 2/27/2013.
Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport.