Symmetry preserving truncations of the gap and Bethe-Salpeter equations
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Binosi, Daniele↗
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TU-F-CAMPUS-I-05: Parameterization of the Noise Power Spectrum in X-Ray Computed Tomography
Purpose: The purpose of this work was to develop a method so that the noise power spectrum (NPS) can be approximated for arbitrary levels of mAs, from a single determination in CT. Methods: The NPS is factorized into 2 components, 1) a parameterized function representing the 1D normalized spatial frequency distribution and 2) a function to scale the magnitude of 1) for arbitrary values of mAs. The 1D NPS, normalized by image variance (NNPS), was determined for 2 FBP reconstruction kernels (smoothing and edge enhancing) for 400 mAs. The NNPS were fit to the parameterized function and a scaling function was established to approximate the image variance at arbitrary values of mAs. Using the root mean square error normalized by the maximum value (NRMSE), the NPS approximated with the factorization method was compared to the NPS determined at 5 different mAs levels. Results: The factorization resulted in a set of 7 coefficients that can be used to approximate the 1D NPS, for arbitrary levels of mAs, for the convolution kernels studied in this work. The approximated NPS (factorization) agreed well with the determined NPS for all mAs levels. The greatest NRMSE was 0.02 and was observed for the edge enhancing kernel. Conclusion: The proposed factorization method has been demonstrated as applicable for FBP reconstruction. It can be used to approximate the 1D NPS for arbitrary levels of mAs, from a single NPS determination. Furthermore, approximations of the 1D NPS can conveniently be distributed since the factorization method only used 7 coefficients in the approximation.
60 APPLIED LIFE SCIENCES↗
Determining the effects of microsphere and surrounding material composition on {sup 90}Y dose kernels using egsnrc and mcnp5
Purpose: Recent advances in the imaging of {sup 90}Y using positron emission tomography (PET) and improved uncertainty in the branching ratio for the internal pair production component of {sup 90}Y decay allow for a more accurate determination of the activity distribution of {sup 90}Y microspheres within a patient. This improved activity distribution can be convolved with the dose kernel of {sup 90}Y to calculate the dose distribution within a patient. This work investigates the effects of microsphere and surrounding material composition on {sup 90}Y dose kernels using egsnrc and mcnp5 and compares the results of these two transport codes. Methods: Monte Carlo simulations were performed with egsnrc and mcnp5 to calculate the dose rate at multiple radial distances around various {sup 90}Y sources. Point source simulations were completed with mcnp5 to determine the optimal electron transport settings for this work. After determining the optimal settings, point source simulations were completed using egsnrc (user code edknrc) and mcnp5 in water and liver [as defined by the International Commission on Radiation Units and Measurements (ICRU) Report 44]. The results were compared to ICRU Report 72 reference data. Point source simulations were also completed in water with a density of 1.06 g{center_dot}cm{sup -3} to evaluate the effect of the density of the surrounding material. Glass and resin microsphere simulations were performed with average and maximum diameter and density values (based on values given in the literature) in water and in liver. The results were compared to point source simulation results using the same transport code and in the same surrounding material. All simulations had statistical uncertainties less than 1%. Results: The optimal transport settings in mcnp5 for this work included using the energy-and step-specific algorithm (DBCN 17J 2) and ESTEP set to 10. These settings were used for all subsequent simulations with mcnp5. The point source simulations in water for both egsnrc and mcnp5 were found to agree within 2% of the ICRU 72 reference data over the investigated range. Point source simulations in liver had large differences relative to ICRU 72, approaching -60% near the maximum range of {sup 90}Y. These differences are mostly attributed to the difference in density between water (1.0 g{center_dot}cm{sup -3}) and liver (1.06 g{center_dot}cm{sup -3}). Glass and resin microsphere simulations showed a slight decrease in the dose rate near the maximum range of {sup 90}Y relative to the point source simulations. The largest relative differences were approximately -4.2% and -2.8% for the glass and resin microspheres, respectively. Agreement between the egsnrc and mcnp5 simulations results was generally good. Conclusions: The presence of the microsphere material causes slight differences in the {sup 90}Y dose kernel compared to those calculated with point sources. Large differences were seen between simulations in water and those in liver. For the most accurate calculation of the dose distribution, the density of the patient's liver should be accounted for in the calculation of the dose kernel. Lastly, due to the need to determine the optimal transport settings with mcnp5, electron transport with this code should be used with caution.
61 RADIATION PROTECTION AND DOSIMETRY↗
Estimation of Smoothing Error in SBUV Profile and Total Ozone Retrieval
Data from the Nimbus-4, Nimbus-7 Solar Backscatter Ultra Violet (SBUV) and seven of the NOAA series of SBUV/2 instruments spanning 41 years are being reprocessed using V8.6 algorithm. The data are scheduled to be released by the end of August 2011. An important focus of the new algorithm is to estimate various sources of errors in the SBUV profiles and total ozone retrievals. We discuss here the smoothing errors that describe the components of the profile variability that the SBUV observing system can not measure. The SBUV(/2) instruments have a vertical resolution of 5 km in the middle stratosphere, decreasing to 8 to 10 km below the ozone peak and above 0.5 hPa. To estimate the smoothing effect of the SBUV algorithm, the actual statistics of the fine vertical structure of ozone profiles must be known. The covariance matrix of the ensemble of measured ozone profiles with the high vertical resolution would be a formal representation of the actual ozone variability. We merged the MLS (version 3) and sonde ozone profiles to calculate the covariance matrix, which in general case, for single profile retrieval, might be a function of the latitude and month. Using the averaging kernels of the SBUV(/2) measurements and calculated total covariance matrix one can estimate the smoothing errors for the SBUV ozone profiles. A method to estimate the smoothing effect of the SBUV algorithm is described and the covariance matrixes and averaging kernels are provided along with the SBUV(/2) ozone profiles. The magnitude of the smoothing error varies with altitude, latitude, season and solar zenith angle. The analysis of the smoothing errors, based on the SBUV(/2) monthly zonal mean time series, shows that the largest smoothing errors were detected in the troposphere and might be as large as 15-20% and rapidly decrease with the altitude. In the stratosphere above 40 hPa the smoothing errors are less than 5% and between 10 and 1 hPa the smoothing errors are on the order of 1%. We validate our estimated smoothing errors by comparing the SBUV ozone profiles with other ozone profiling sensors.
Kramarova, N. A.↗
Effective Cloud Detection and Segmentation Using a Gradient-Based Algorithm for Satellite Imagery: Application to Improve PERSIANN-CCS
The effective identification of clouds and monitoring of their evolution are important toward more accurate quantitative precipitation estimation and forecast. In this study, a new gradient-based cloud-image segmentation algorithm is developed using image processing techniques. This method integrates morphological image gradient magnitudes to separate cloud systems and patches boundaries. A varying scale kernel is implemented to reduce the sensitivity of image segmentation to noise and to capture objects with various finenesses of the edges in remote sensing images. The proposed method is flexible and extendable from single to multispectral imagery. Case studies were carried out to validate the algorithm by applying the proposed segmentation algorithm to synthetic radiances for channels of the Geostationary Operational Environmental Satellite ( GOES-16) simulated by a high-resolution weather prediction model. The proposed method compares favorably with the existing cloud-patch-based segmentation technique implemented in the Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Cloud Classification System (PERSIANN-CCS) rainfall retrieval algorithm. Evaluation of event-based images indicates that the proposed algorithm has potentials comparing to the conventional segmentation technique used in PERSIANN-CCS to improve rain detection and estimation skills with an accuracy rate of up to 98% in identifying cloud regions.
54 ENVIRONMENTAL SCIENCES↗
Development of a Radial Deconsolidation Method
A series of experiments have been initiated to determine the retention or mobility of fission products* in AGR fuel compacts [Petti, et al. 2010]. This information is needed to refine fission product transport models. The AGR-3/4 irradiation test involved half-inch-long compacts that each contained twenty designed-to-fail (DTF) particles, with 20-μm thick carbon-coated kernels whose coatings were deliberately fabricated such that they would crack under irradiation, providing a known source of post-irradiation isotopes. The DTF particles in these compacts were axially distributed along the compact centerline so that the diffusion of fission products released from the DTF kernels would be radially symmetric [Hunn, et al. 2012; Hunn et al. 2011; Kercher, et al. 2011; Hunn, et al. 2007]. Compacts containing DTF particles were irradiated at Idaho National Laboratory (INL) at the Advanced Test Reactor (ATR) [Collin, 2015]. Analysis of the diffusion of these various post-irradiation isotopes through the compact requires a method to radially deconsolidate the compacts so that nested-annular volumes may be analyzed for post-irradiation isotope inventory in the compact matrix, TRISO outer pyrolytic carbon (OPyC), and DTF kernels. An effective radial deconsolidation method and apparatus appropriate to this application has been developed and parametrically characterized.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Phase quantification in low carbon Nb-Mo bearing steel by electron backscatter diffraction technique coupled with kernel average misorientation
Highlights: • The microstructures in a low carbon Nb-Mo bearing steel have been investigated. • EBSD combined with a (KAM) map has been used for quantification. • The effects of step size and kernel size on quantification are systemically discussed. • The result indicates that the kernel size should be close to the sub-structure of the granular bainite. - Abstract: An efficient and accurate method is developed for microstructural quantification of complex phases in a low carbon Nb-Mo bearing steel, of which optical micrographs show that it consists of granular bainite and a small amount of ferrite. Our previous work, proposing a method to measure the misorientation angles via electron backscatter diffraction (EBSD) to differentiate granular bainite and ferrite, has been reported. That method is accurate for phase quantification but laborious for the characterization process. To resolve this difficulty, in this study, EBSD combined with a kernel average misorientation (KAM) map is used for phase characterization. Comparisons are made among KAM maps with different kernel sizes (300 to 600 nm) and various step sizes (100 to 600 nm). It is found that a kernel size close to the sub-structure size of granular bainite (500 nm) is optimal for phase identification, while varied step sizes produce relatively invariant results. Therefore, KAM maps can be used for fast and reliable phase quantification, provided that an appropriate kernel size and a large step size are used.
36 MATERIALS SCIENCE↗
Explore Information Content Efficiently from Current and Future Hyperspectral Satellite Missions using a Spectral Fingerprinting Method
Hyperspectral remote sensors from current and future missions provide measurements of the Top of Atmosphere (TOA) radiance or reflectance spectra with high information content. For example, the Atmospheric Infrared Sounder (AIRS), together with the Cross-track Infrared Sounder (CrIS), and the Infrared Atmospheric Sounding Interferometer (IASI) have provided more than 20 years radiance measurements with thousands of spectral channels. These measurements will be continued for the next two decades with the same or more advanced hyperspectral sensors. The upcoming missions such as NASA’s CLARREO Pathfinder (CPF) and ESA’s TRUTHS will provide unprecedented accurate TOA hyperspectral radiance measurements in solar spectral region. Traditional ways to derive Climate Data Records (CDRs) from these measurements are performing spatial and temporal averages of the retrieved Level-2 products. However, it is a time-consuming process to generate decades of Level-2 data from Level-1 data. Furthermore, the differences in Level-2 algorithms used for different satellite sensors will introduce errors in derived CDRs. In this presentation, we will describe a spectral fingerprinting method to generate high-quality CDRs directly from spatiotemporally averaged Level-1 data. By using consistent radiative kernels which contain the spectral information of various atmospheric and surface CDRs, we can reduce the errors due to algorithm inconsistency. Additionally, the spectral fingerprinting method reduces the time needed to generate CDRs by more than three orders of magnitude. This makes it easy to reprocess CDRs once the Level-1 data from different satellites have been improved via either re-calibrations or inter-satellite calibrations. We will present results of applying spectral fingerprinting method to 20-years of AIRS and CrIS data. The resulting CDRs include: 1) vertical profiles of atmospheric temperature and water vapor, 2) cloud properties such as optical depth, effective size, and height, 3) vertical profiles or column amounts for atmospheric trace gases such as O3 and CO, and 4) surface emissivity spectra and skin temperatures. These CDRs will be publicly available at NASA GES DISC in late 2024. The same fingerprinting method is planned to be applied to future CPF and TRUTHS data for solar spectral region.
hyperspectral remote sensing↗
Anytime interval-valued outputs for kernel machines: fast support vector machine classification via distance geometry
We introduce a computational geometry method for which classification cost becomes roughly proportional to the difficulty of each example.
interval value outputs kernal vector distance geom↗
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Calculation of electron and isotopes dose point kernels with fluka Monte Carlo code for dosimetry in nuclear medicine therapy
Purpose: The calculation of patient-specific dose distribution can be achieved by Monte Carlo simulations or by analytical methods. In this study, fluka Monte Carlo code has been considered for use in nuclear medicine dosimetry. Up to now, fluka has mainly been dedicated to other fields, namely high energy physics, radiation protection, and hadrontherapy. When first employing a Monte Carlo code for nuclear medicine dosimetry, its results concerning electron transport at energies typical of nuclear medicine applications need to be verified. This is commonly achieved by means of calculation of a representative parameter and comparison with reference data. Dose point kernel (DPK), quantifying the energy deposition all around a point isotropic source, is often the one. Methods: fluka DPKs have been calculated in both water and compact bone for monoenergetic electrons (10{sup -3} MeV) and for beta emitting isotopes commonly used for therapy ({sup 89}Sr, {sup 90}Y, {sup 131}I, {sup 153}Sm, {sup 177}Lu, {sup 186}Re, and {sup 188}Re). Point isotropic sources have been simulated at the center of a water (bone) sphere, and deposed energy has been tallied in concentric shells. fluka outcomes have been compared to penelope v.2008 results, calculated in this study as well. Moreover, in case of monoenergetic electrons in water, comparison with the data from the literature (etran, geant4, mcnpx) has been done. Maximum percentage differences within 0.8{center_dot}R{sub CSDA} and 0.9{center_dot}R{sub CSDA} for monoenergetic electrons (R{sub CSDA} being the continuous slowing down approximation range) and within 0.8{center_dot}X{sub 90} and 0.9{center_dot}X{sub 90} for isotopes (X{sub 90} being the radius of the sphere in which 90% of the emitted energy is absorbed) have been computed, together with the average percentage difference within 0.9{center_dot}R{sub CSDA} and 0.9{center_dot}X{sub 90} for electrons and isotopes, respectively. Results: Concerning monoenergetic electrons, within 0.8{center_dot}R{sub CSDA} (where 90%-97% of the particle energy is deposed), fluka and penelope agree mostly within 7%, except for 10 and 20 keV electrons (12% in water, 8.3% in bone). The discrepancies between fluka and the other codes are of the same order of magnitude than those observed when comparing the other codes among them, which can be referred to the different simulation algorithms. When considering the beta spectra, discrepancies notably reduce: within 0.9{center_dot}X{sub 90}, fluka and penelope differ for less than 1% in water and less than 2% in bone with any of the isotopes here considered. Complete data of fluka DPKs are given as Supplementary Material as a tool to perform dosimetry by analytical point kernel convolution. Conclusions: fluka provides reliable results when transporting electrons in the low energy range, proving to be an adequate tool for nuclear medicine dosimetry.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization
Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.
79 ASTRONOMY AND ASTROPHYSICS↗
Operator-level quantum acceleration of non-logconcave sampling
Sampling from probability distributions of the form 𝝈 ∝ e −𝜷V , where V is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when V is nonconvex, the resulting distribution becomes non-logconcave, and classical methods such as Langevin dynamics often exhibit poor performance. We introduce a quantum algorithm that provably accelerates a broad class of continuous-time sampling dynamics. For Langevin dynamics, our method encodes the target Gibbs measure into the amplitudes of aquantum state, identified as the kernel of a block matrix derived from a factorization of the Witten Laplacian operator. This connection enables Gibbs sampling via singular value thresholding and yields up to a quartic quantum speedup over best-knownclassical Langevin-based methods in the non-logconcave setting. Building on this framework, we further develop the first quantum algorithm that accelerates replica exchange Langevin diffusion, a widely used method for sampling from complex, rugged energy landscapes.
97 MATHEMATICS AND COMPUTING↗
New Machine Learning Techniques for Simulation-Based Inference: InferoStatic Nets, Kernel Score Estimation, and Kernel Likelihood Ratio Estimation
We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential $\varphi$. In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Performance Analysis of Traditional and Data-Parallel Primitive Implementations of Visualization and Analysis Kernels
Measurements of absolute runtime are useful as a summary of performance when studying parallel visualization and analysis methods on computational platforms of increasing concurrency and complexity. We can obtain even more insights by measuring and examining more detailed measures from hardware performance counters, such as the number of instructions executed by an algorithm implemented in a particular way, the amount of data moved to/from memory, memory hierarchy utilization levels via cache hit/miss ratios, and so forth. This work focuses on performance analysis on modern multi-core platforms of three different visualization and analysis kernels that are implemented in different ways: one is "traditional", using combinations of C++ and VTK, and the other uses a data-parallel approach using VTK-m. Our performance study consists of measurement and reporting of several different hardware performance counters on two different multi-core CPU platforms. The results reveal interesting performance differences between these two different approaches for implementing these kernels, results that would not be apparent using runtime as the only metric.
97 MATHEMATICS AND COMPUTING↗
New machine learning techniques for simulation-based inference: InferoStatic nets, kernel score estimation, and kernel likelihood ratio estimation
We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not computed directly. The ISN uses a backend neural network that models a scalar function called the inferostatic potential \varphi φ . In addition, we introduce new strategies, respectively called Kernel Score Estimation (KSE) and Kernel Likelihood Ratio Estimation (KLRE), to learn the score and the likelihood ratio functions from simulated data. We illustrate the new techniques with some toy examples and compare to existing approaches in the literature. We mention en passant some new loss functions that optimally incorporate latent information from simulations into the training procedure.
Kong, Kyoungchul↗
Test particle propagation in magnetostatic turbulence. 2: The local approximation method
An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.
Klimas, A. J.↗
MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems
Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.
97 MATHEMATICS AND COMPUTING↗