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DOE OSTI2024

Model orthogonalization and Bayesian forecast mixing via principal component analysis

One can improve predictability in the unknown domain by combining forecasts of imperfect complex computational models using a Bayesian statistical machine learning framework. In many cases, however, the models used in the mixing process are similar. In addition to contaminating the model space, the existence of such similar, or even redundant, models during the multimodeling process can result in misinterpretation of results and deterioration of predictive performance. In this paper we describe a method based on the principal component analysis that eliminates model redundancy. We show that by adding model orthogonalization to the proposed Bayesian model combination framework, one can arrive at better prediction accuracy and reach excellent uncertainty quantification performance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

The fusion-fission process in the reaction {sup 34}S+{sup 186}W near the interaction barrier

The reaction {sup 34}S+{sup 186}W at E{sub lab}=160 MeV was investigated with the aim of diving into the features of the fusion-fission process. Gamma rays in coincidence with binary reaction fragments were measured using the high efficiency gamma-ray spectrometer ORGAM at the TANDEM Accelerator facility of I.P.N., Orsay, and the time-of-flight spectrometer for fission fragments (FF) registration CORSET of the Flerov Laboratory of Nuclear Reactions (FLNR), Dubna. The coupling of the ORGAM and CORSET setups offers the unique opportunity of extracting details for characterizing the fusion-fission process and gives information regarding production of neutron-rich heavy nuclei. The FF–γ coincidence method is of better use then the γ – γ coincidence method when dealing with low statistic measurements and also offers the opportunity to precisely correct the Dopler shift for in-flight emitted gamma rays. Evidence of symmetric and asymmetric fission modes were observed in the mass and TKE distributions, occurring due to shell effects in the fragments. Coincident measurements allow for discrimination between the gamma rays by accepting a specific range within the mass distribution of the reaction products. Details regarding the experimental setup, methods of processing the acquisitioned data and preliminary results are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Component separation of a isotropic Gravitational Wave Background

A Gravitational Wave Background (GWB) is expected in the universe from the superposition of a large number of unresolved astrophysical sources and phenomena in the early universe. Each component of the background (e.g., from primordial metric perturbations, binary neutron stars, milli-second pulsars etc.) has its own spectral shape. Many ongoing experiments aim to probe GWB at a variety of frequency bands. In the last two decades, using data from ground-based laser interferometric gravitational wave (GW) observatories, upper limits on GWB were placed in the frequency range of 0∼ 50−100 Hz, considering one spectral shape at a time. However, one strong component can significantly enhance the estimated strength of another component. Hence, estimation of the amplitudes of the components with different spectral shapes should be done jointly. Here we propose a method for 'component separation' of a statistically isotropic background, that can, for the first time, jointly estimate the amplitudes of many components and place upper limits. The method is rather straightforward and needs negligible amount of computation. It utilises the linear relationship between the measurements and the amplitudes of the actual components, alleviating the need for a sampling based method, e.g., Markov Chain Monte Carlo (MCMC) or matched filtering, which are computationally intensive and cumbersome in a multi-dimensional parameter space. Using this formalism we could also study how many independent components can be separated using a given dataset from a network of current and upcoming ground based interferometric detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Final Technical Report Recovery Act: Online Nonintrusive Condition Monitoring and Fault Detection for Wind Turbines

The penetration of wind power has increased greatly over the last decade in the United States and across the world. The U.S. wind power industry installed 1,118 MW of new capacity in the first quarter of 2011 alone and entered the second quarter with another 5,600 MW under construction. By 2030, wind energy is expected to provide 20% of the U.S. electricity needs. As the number of wind turbines continues to grow, the need for effective condition monitoring and fault detection (CMFD) systems becomes increasingly important [3]. Online CMFD is an effective means of not only improving the reliability, capacity factor, and lifetime, but it also reduces the downtime, energy loss, and operation and maintenance (O&M) of wind turbines. The goal of this project is to develop novel online nonintrusive CMFD technologies for wind turbines. The proposed technologies use only the current measurements that have been used by the control and protection system of a wind turbine generator (WTG); no additional sensors or data acquisition devices are needed. Current signals are reliable and easily accessible from the ground without intruding on the wind turbine generators (WTGs) that are situated on high towers and installed in remote areas. Therefore, current-based CMFD techniques have great economic benefits and the potential to be adopted by the wind energy industry. Specifically, the following objectives and results have been achieved in this project: (1) Analyzed the effects of faults in a WTG on the generator currents of the WTG operating at variable rotating speed conditions from the perspective of amplitude and frequency modulations of the current measurements; (2) Developed effective amplitude and frequency demodulation methods for appropriate signal conditioning of the current measurements to improve the accuracy and reliability of wind turbine CMFD; (3) Developed a 1P-invariant power spectrum density (PSD) method for effective signature extraction of wind turbine faults with characteristic frequencies in the current or current demodulated signals, where 1P stands for the shaft rotating frequency of a WTG; (4) Developed a wavelet filter for effective signature extraction of wind turbine faults without characteristic frequencies in the current or current demodulated signals; (5) Developed an effective adaptive noise cancellation method as an alternative to the wavelet filter method for signature extraction of wind turbine faults without characteristic frequencies in the current or current demodulated signals; (6) Developed a statistical analysis-based impulse detection method for effective fault signature extraction and evaluation of WTGs based on the 1P-invariant PSD of the current or current demodulated signals; (7) Validated the proposed current-based wind turbine CMFD technologies through extensive computer simulations and experiments for small direct-drive WTGs without gearboxes; and (8) Showed, through extensive experiments for small direct-drive WTGs, that the performance of the proposed current-based wind turbine CMFD technologies is comparable to traditional vibration-based methods. The proposed technologies have been successfully applied for detection of major failures in blades, shafts, bearings, and generators of small direct-drive WTGs. The proposed technologies can be easily integrated into existing wind turbine control, protection, and monitoring systems and can be implemented remotely from the wind turbines being monitored. The proposed technologies provide an alternative to vibration-sensor-based CMFD. This will reduce the cost and hardware complexity of wind turbine CMFD systems. The proposed technologies can also be combined with vibration-sensor-based methods to improve the accuracy and reliability of wind turbine CMFD systems. When there are problems with sensors, the proposed technologies will ensure proper CMFD for the wind turbines, including their sensing systems. In conclusion, the proposed technologies offer an effective means to achieve condition-based smart maintenance for wind turbines and have a great potential to be adopted by the wind energy industry due to their almost no-cost, nonintrusive features. Although only validated for small direct-drive wind turbines without gearboxes, the proposed technologies are also applicable for CMFD of large-size wind turbines with and without gearboxes. However, additional investigations are recommended in order to apply the proposed technologies to those large-size wind turbines.

17 WIND ENERGY↗
DOE OSTI2011

Accelerated Partial Breast Irradiation for Pure Ductal Carcinoma in Situ

Purpose: To report outcomes for ductal carcinoma in situ (DCIS) treated with breast-conserving therapy using accelerated partial breast irradiation (APBI). Methods and Materials: From March 2001 to February 2009, 53 patients with Stage 0 breast cancer were treated with breast conserving surgery and adjuvant APBI. Median age was 62 years. All patients underwent excision with margins negative by {>=}1 mm before adjuvant radiotherapy (RT). A total of 39 MammoSite brachytherapy (MS) patients and 14 three-dimensional conformal external beam RT (3DCRT) patients were treated to the lumpectomy bed alone with 34 Gy and 38.5 Gy, respectively. Of the DCIS cases, 94% were mammographically detected. All patients with calcifications had either specimen radiography or postsurgical mammography confirmation of clearance. Median tumor size was 6 mm, and median margin distance was 5 mm. There were no statistically significant differences according to APBI method for race/ethnicity, tumor detection method, tumor grade, estrogen receptor (ER) status, or use of tamoxifen (p = NS). Recurrence and survival were calculated using the Kaplan-Meier method. Cosmesis was scored by the Harvard criteria. Results: With a median follow-up of 3.6 years (range, 0.4-6.3 years), the overall and cause-specific survival rates were 98% and 100%, respectively. Three-year actuarial ipsilateral breast tumor recurrence was 2%. One failure was observed at the resection bed 11 months post-RT. No other elsewhere breast failures, regional recurrences, or distant metastases were noted. Cosmesis was excellent or good in 92.4% of cases, with no statistically significant differences according to the APBI method (92.3% with MammoSite and 92.8% with 3DCRT; p = 0.649). Conclusions: APBI as part of breast-conserving therapy for pure DCIS was associated with excellent local control and survival rates, with the vast majority of patients having good to excellent cosmesis. This finding supports the recent analysis by the American Society of Breast Surgeons on a subset of DCIS patients treated efficaciously with APBI.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Statistical Modeling of the Eye for Multimodal Treatment Planning for External Beam Radiation Therapy of Intraocular Tumors

Purpose: Ocular anatomy and radiation-associated toxicities provide unique challenges for external beam radiation therapy. For treatment planning, precise modeling of organs at risk and tumor volume are crucial. Development of a precise eye model and automatic adaptation of this model to patients' anatomy remain problematic because of organ shape variability. This work introduces the application of a 3-dimensional (3D) statistical shape model as a novel method for precise eye modeling for external beam radiation therapy of intraocular tumors. Methods and Materials: Manual and automatic segmentations were compared for 17 patients, based on head computed tomography (CT) volume scans. A 3D statistical shape model of the cornea, lens, and sclera as well as of the optic disc position was developed. Furthermore, an active shape model was built to enable automatic fitting of the eye model to CT slice stacks. Cross-validation was performed based on leave-one-out tests for all training shapes by measuring dice coefficients and mean segmentation errors between automatic segmentation and manual segmentation by an expert. Results: Cross-validation revealed a dice similarity of 95% {+-} 2% for the sclera and cornea and 91% {+-} 2% for the lens. Overall, mean segmentation error was found to be 0.3 {+-} 0.1 mm. Average segmentation time was 14 {+-} 2 s on a standard personal computer. Conclusions: Our results show that the solution presented outperforms state-of-the-art methods in terms of accuracy, reliability, and robustness. Moreover, the eye model shape as well as its variability is learned from a training set rather than by making shape assumptions (eg, as with the spherical or elliptical model). Therefore, the model appears to be capable of modeling nonspherically and nonelliptically shaped eyes.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

FilDReaMS: II. Application to the analysis of the relative orientations between filaments and the magnetic field in four Herschel fields

Context. Both simulations and observations of the interstellar medium show that the study of the relative orientations between filamentary structures and the magnetic field can bring new insight into the role played by magnetic fields in the formation and evolution of filaments and in the process of star formation. Aims. We provide a first application of FilDReaMS, the new method presented in the companion paper to detect and analyze filaments in a given image. The method relies on a template that has the shape of a rectangular bar with variable width. Our goal is to investigate the relative orientations between the detected filaments and the magnetic field. Methods. We apply FilDReaMS to a small sample of four Herschel fields (G210, G300, G82, G202) characterized by different Galactic environments and different evolutionary stages. First, we look for the most prevalent bar widths, and we examine the networks formed by filaments of different bar widths as well as their hierarchical organization. Second, we compare the filament orientations to the magnetic field orientation inferred from Planck polarization data and, for the first time, we study the statistics of the relative orientation angle as functions of both spatial scale and H2 column density. Results. We find preferential relative orientations in the four Herschel fields: small filaments with low column densities tend to be slightly more parallel than perpendicular to the magnetic field; in contrast, large filaments, which all have higher column densities, are oriented nearly perpendicular (or, in the case of G202, more nearly parallel) to the magnetic field. In the two nearby fields (G210 and G300), we observe a transition from mostly parallel to mostly perpendicular relative orientations at an H 2 column density ≃ 1.1 × 10 21 cm -2 and 1.4 × 10 21 cm -2 , respectively, consistent with the results of previous studies. Conclusions. Our results confirm the existence of a coupling between magnetic fields at cloud scales and filaments at smaller scale. They also illustrate the potential of combining Herschel and Planck observations, and they call for further statistical analyses with our dedicated method.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

THE {gamma}SF METHOD

The {gamma}-ray strength function ({gamma}SF) interconnects radiative neutron capture and photoneutron emission as a common ingredient in the statistical model. Outlined here is an indirect method of determining radiative neutron-capture cross sections for unstable nuclei based on the {gamma}-ray strength function. Application examples of the {gamma}SF method are demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Optimal experimental design: Formulations and computations

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Validating the simulation of large-scale parallel applications using statistical characteristics

Simulation is a widely adopted method to analyze and predict the performance of large-scale parallel applications. Validating the hardware model is highly important for complex simulations with a large number of parameters. Common practice involves calculating the percent error between the projected and the real execution time of a benchmark program. However, in a high-dimensional parameter space, this coarse-grained approach often suffers from parameter insensitivity, which may not be known a priori. Moreover, the traditional approach cannot be applied to the validation of software models, such as application skeletons used in online simulations. In this work, we present a methodology and a toolset for validating both hardware and software models by quantitatively comparing fine-grained statistical characteristics obtained from execution traces. Although statistical information has been used in tasks like performance optimization, this is the first attempt to apply it to simulation validation. Lastly, our experimental results show that the proposed evaluation approach offers significant improvement in fidelity when compared to evaluation using total execution time, and the proposed metrics serve as reliable criteria that progress toward automating the simulation tuning process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Multi-fidelity machine learning models for accurate bandgap predictions of solids

Here, we present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. Additionally, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. In using a set of 600 elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of fidelities, we demonstrate the excellent learning performance of the method against actual high fidelity quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Determination of the critical manifold tangent space and curvature with Monte Carlo renormalization group

We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. Furthermore, we study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Self-assessed performance improves statistical fusion of image labels

Purpose: Expert manual labeling is the gold standard for image segmentation, but this process is difficult, time-consuming, and prone to inter-individual differences. While fully automated methods have successfully targeted many anatomies, automated methods have not yet been developed for numerous essential structures (e.g., the internal structure of the spinal cord as seen on magnetic resonance imaging). Collaborative labeling is a new paradigm that offers a robust alternative that may realize both the throughput of automation and the guidance of experts. Yet, distributing manual labeling expertise across individuals and sites introduces potential human factors concerns (e.g., training, software usability) and statistical considerations (e.g., fusion of information, assessment of confidence, bias) that must be further explored. During the labeling process, it is simple to ask raters to self-assess the confidence of their labels, but this is rarely done and has not been previously quantitatively studied. Herein, the authors explore the utility of self-assessment in relation to automated assessment of rater performance in the context of statistical fusion. Methods: The authors conducted a study of 66 volumes manually labeled by 75 minimally trained human raters recruited from the university undergraduate population. Raters were given 15 min of training during which they were shown examples of correct segmentation, and the online segmentation tool was demonstrated. The volumes were labeled 2D slice-wise, and the slices were unordered. A self-assessed quality metric was produced by raters for each slice by marking a confidence bar superimposed on the slice. Volumes produced by both voting and statistical fusion algorithms were compared against a set of expert segmentations of the same volumes. Results: Labels for 8825 distinct slices were obtained. Simple majority voting resulted in statistically poorer performance than voting weighted by self-assessed performance. Statistical fusion resulted in statistically indistinguishable performance from self-assessed weighted voting. The authors developed a new theoretical basis for using self-assessed performance in the framework of statistical fusion and demonstrated that the combined sources of information (both statistical assessment and self-assessment) yielded statistically significant improvement over the methods considered separately. Conclusions: The authors present the first systematic characterization of self-assessed performance in manual labeling. The authors demonstrate that self-assessment and statistical fusion yield similar, but complementary, benefits for label fusion. Finally, the authors present a new theoretical basis for combining self-assessments with statistical label fusion.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

BAM: bias assignment method to generate mock catalogues

Combining the statistics of dark matter tracers from a high-resolution cosmological N-body simulation and the dark matter density field calculated from down-sampled initial conditions using efficient structure formation solvers, we extract the halo-bias relation on a mesh of a 3$h^{-1}$ Mpc cell side resolution as a function of properties of the dark matter density field (e.g. local density, cosmic web type), automatically including stochastic, deterministic, local and non-local components. We use this information to sample the halo density field, accounting for ignored dependencies through an iterative process. By construction, our approach reaches ~1% accuracy in the majority of the k-range up to the Nyquist frequency without systematic deviations for power spectra (about $k ~ 1h$ Mpc -1 ) using either particle mesh or Lagrangian perturbation theory based solvers. When using phase-space mapping to compensate the low resolution of the approximate gravity solvers, our method reproduces the bispectra of the reference within 10% precision studying configurations tracing the quasi-non-linear regime. BAM has the potential to become a standard technique to produce mock halo and galaxy catalogues for future galaxy surveys and cosmological studies being highly accurate, efficient and parameter free.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Coordinated JWST Imaging of Three Distance Indicators in a Supernova Host Galaxy and an Estimate of the Tip of the Red Giant Branch Color Dependence

Boasting a 6.5 m mirror in space, JWST can increase by several times the number of supernovae (SNe) to which a redshift-independent distance has been measured with a precision distance indicator (e.g., tip of the red giant branch (TRGB) or Cepheids); the limited number of such SN calibrators currently dominates the uncertainty budget in distance ladder Hubble constant (H 0 ) experiments. JWST/NIRCAM imaging of the Virgo Cluster galaxy NGC 4536 is used here to preview JWST program GO-1995, which aims to measure H 0 using three stellar distance indicators (Cepheids, TRGB, and J-branch asymptotic giant branch/carbon stars). Each population of distance indicator was here successfully detected—with sufficiently large number statistics, well-measured fluxes, and characteristic distributions consistent with ingoing expectations—so as to confirm that we can acquire distances from each method precise to about 0.05 mag (statistical uncertainty only). We leverage overlapping Hubble Space Telescope imaging to identify TRGB stars, crossmatch them with the JWST photometry, and present a preliminary constraint on the slope of the TRGB's F115W versus (F115W – F444W) relation equal to -0.99 ± 0.16 mag mag -1 . This slope is consistent with prior slope measurements in the similar Two Micron All-Sky Survey J band, as well as with predictions from the BaSTI isochrone suite. We use the new TRGB slope estimate to flatten the 2D TRGB feature and measure a (blinded) TRGB distance relative to a set of fiducial TRGB colors, intended to represent the absolute fiducial calibrations expected from geometric anchors such as NGC 4258 and the Magellanic Clouds. In doing so, we empirically demonstrate that the TRGB can be used as a standardizable candle at the IR wavelengths accessible with JWST.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Using Generalized Equivalent Uniform Dose Atlases to Combine and Analyze Prospective Dosimetric and Radiation Pneumonitis Data From 2 Non-Small Cell Lung Cancer Dose Escalation Protocols

Purpose: To demonstrate the use of generalized equivalent uniform dose (gEUD) atlas for data pooling in radiation pneumonitis (RP) modeling, to determine the dependence of RP on gEUD, to study the consistency between data sets, and to verify the increased statistical power of the combination. Methods and Materials: Patients enrolled in prospective phase I/II dose escalation studies of radiation therapy of non-small cell lung cancer at Memorial Sloan-Kettering Cancer Center (MSKCC) (78 pts) and the Netherlands Cancer Institute (NKI) (86 pts) were included; 10 (13%) and 14 (17%) experienced RP requiring steroids (RPS) within 6 months after treatment. gEUD was calculated from dose-volume histograms. Atlases for each data set were created using 1-Gy steps from exact gEUDs and RPS data. The Lyman-Kutcher-Burman model was fit to the atlas and exact gEUD data. Heterogeneity and inconsistency statistics for the fitted parameters were computed. gEUD maps of the probability of RPS rate {>=}20% were plotted. Results: The 2 data sets were homogeneous and consistent. The best fit values of the volume effect parameter a were small, with upper 95% confidence limit around 1.0 in the joint data. The likelihood profiles around the best fit a values were flat in all cases, making determination of the best fit a weak. All confidence intervals (CIs) were narrower in the joint than in the individual data sets. The minimum P value for correlations of gEUD with RPS in the joint data was .002, compared with P=.01 and .05 for MSKCC and NKI data sets, respectively. gEUD maps showed that at small a, RPS risk increases with gEUD. Conclusions: The atlas can be used to combine gEUD and RPS information from different institutions and model gEUD dependence of RPS. RPS has a large volume effect with the mean dose model barely included in the 95% CI. Data pooling increased statistical power.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

A method for evaluating the expectation value of a power spectrum using the probability density function of phases

Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known properties of the power spectrum when the time series contains a periodic signal. The approach is also validated in general with numerical simulations. The method puts into evidence the importance that is played by the probability density function of the phases associated to each time stamp for a given frequency, and how this distribution can be perturbed by the uncertainties of the parameters in the pulsar ephemeris. We applied this method to solve the power spectrum in the case the first derivative of the pulsar frequency is unknown and not negligible. We also undertook the study of the most general case of a blind search, in which both the frequency and its first derivative are uncertain. We found the analytical solutions of the above cases invoking the sum of Fresnel's integrals squared.

79 ASTRONOMY AND ASTROPHYSICS↗