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This software implements the fast, self-consistent probability density estimation described by O'Brien et al. (2014, doi: ). It uses a non-uniform fast Fourier transform technique to reduce the computational cost of an objective and self-consistent kernel density estimation method.
The main components of scatter correction procedures are scatter estimation and a scatter compensation algorithm. This paper completes a previous paper where a general framework for scatter compensation was presented under the prerequisite that a scatter estimation method is already available. In the current paper, the authors give a systematic review of the variety of scatter estimation approaches. Scatter estimation methods are based on measurements, mathematical-physical models, or combinations of both. For completeness they present an overview of measurement-based methods, but the main topic is the theoretically more demanding models, as analytical, Monte-Carlo, and hybrid models. Further classifications are 3D image-based and 2D projection-based approaches. The authors present a system-theoretic framework, which allows to proceed top-down from a general 3D formulation, by successive approximations, to efficient 2D approaches. A widely useful method is the beam-scatter-kernel superposition approach. Together with the review of standard methods, the authors discuss their limitations and how to take into account the issues of object dependency, spatial variance, deformation of scatter kernels, external and internal absorbers. Open questions for further investigations are indicated. Finally, the authors refer on some special issues and applications, such as bow-tie filter, offset detector, truncated data, and dual-source CT.
We present the Kinetic-j code, a computational kernel for evaluating the linearized Vlasov equation withapplication to calculating the kinetic plasma response (current) to an applied time harmonic wave electricfield. This code addresses the need for a configuration space evaluation of the plasma current to enablekinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourierspectral methods. We benchmark the kernel via comparison with the standard k-space forms of the hotplasma conductivity tensor.
We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.
The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.
The present work concerns the transferability of coarse-grained (CG) modeling in reproducing the dynamic properties of the reference atomistic systems across a range of parameters. In particular, we focus on implicit-solvent CG modeling of polymer solutions. The CG model is based on the generalized Langevin equation, where the memory kernel plays the critical role in determining the dynamics in all time scales. Thus, we propose methods for transfer learning of memory kernels. The key ingredient of our methods is Gaussian process regression. By integration with the model order reduction via proper orthogonal decomposition and the active learning technique, the transfer learning can be practically efficient and requires minimum training data. Through two example polymer solution systems, we demonstrate the accuracy and efficiency of the proposed transfer learning methods in the construction of transferable memory kernels. The transferability allows for out-of-sample predictions, even in the extrapolated domain of parameters. Built on the transferable memory kernels, the CG models can reproduce the dynamic properties of polymers in all time scales at different thermodynamic conditions (such as temperature and solvent viscosity) and for different systems with varying concentrations and lengths of polymers.
A Monte Carlo method to estimate the sensitivity of reaction rates like dose and flux spectra to geometric perturbations using kernel density estimators is demonstrated for shielding problems. The method is used to estimate the sensitivity of the spectrum emitted from a Cf-252 source at the center of an iron sphere as well as the sensitivity of the dose due to Cf-252 neutrons shielded using various materials. Results are compared against reference solutions obtained using Monte Carlo direct perturbations with central differences, with agreement within 5% and 3σ for the majority of results. The results indicate that a bandwidth that is 10-20% of the shielding thickness produces accurate results with statistically insignificant bias for the chosen test problems. (authors)
Computing the singular values and vectors of a matrix is a crucial kernel in numerous scientific and industrial applications. As such, numerous methods have been proposed to handle this problem in a computationally efficient way. This paper considers a family of methods for incrementally computing the dominant SVD of a large matrix A. Specifically, we describe a unification of a number of previously disparate methods for approximating the dominant SVD via a single pass through A. We tie the behavior of these methods to that of a class of optimization-based iterative eigensolvers on A'*A. An iterative procedure is proposed which allows the computation of an accurate dominant SVD via multiple passes through A. We present an analysis of the convergence of this iteration, and provide empirical demonstration of the proposed method on both synthetic and benchmark data.
Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.
The OECD Nuclear Energy Agency (NEA) Working Party on International Nuclear Data Evaluation Cooperation (WPEC) was established in 1989 to facilitate collaboration in nuclear data activities. Over its thirty year history, different Subgroups have been created to address topics in nearly every aspect of nuclear data, including: experimental measurements, evaluation, validation, model development, quality assurance of databases and the development of software tools. WPEC has recently completed activities on fission yield evaluation, the general nuclear database structure (GNDS) to replace the ENDF-6 format, methods to provide feedback to evaluation, studies of specific capture cross sections, new methods in thermal scattering kernel evaluation and the Collaborative International Evaluated Library Organisation (CIELO) Pilot Project. Ongoing activities in GNDS application programming interface (API) development, methods for covariance evaluation and quality assurance in nuclear data validation using the International Criticality Safety Benchmark Evaluation Project (ICSBEP) database are complemented by the work of two Expert Groups that oversee the High-Priority Request List (HPRL) for Nuclear Data and the continuous development of the GNDS. New activities on the use of integral experiments for nuclear data validation and adjustment, as well as the use of the Shielding Integral Benchmark Archive and Database (SINBAD) for validation have begun and will be coordinated alongside future Subgroups. After three decades we will review the status of WPEC, how it integrates other collections and activities organised by the NEA and how it dovetails with the initiatives of the IAEA and other bodies to effectively coordinate international activities in nuclear data.
Highlights: • PET, HPDE or PP types of plastics are considered. • An automated classification of plastic bottles based on the feature extraction and classification methods is performed. • The decision mechanism consists of PCA, Kernel PCA, FLDA, SVD and Laplacian Eigenmaps methods. • SVM is selected to achieve the classification task and majority voting technique is used. - Abstract: Since recycling of materials is widely assumed to be environmentally and economically beneficial, reliable sorting and processing of waste packaging materials such as plastics is very important for recycling with high efficiency. An automated system that can quickly categorize these materials is certainly needed for obtaining maximum classification while maintaining high throughput. In this paper, first of all, the photographs of the plastic bottles have been taken and several preprocessing steps were carried out. The first preprocessing step is to extract the plastic area of a bottle from the background. Then, the morphological image operations are implemented. These operations are edge detection, noise removal, hole removing, image enhancement, and image segmentation. These morphological operations can be generally defined in terms of the combinations of erosion and dilation. The effect of bottle color as well as label are eliminated using these operations. Secondly, the pixel-wise intensity values of the plastic bottle images have been used together with the most popular subspace and statistical feature extraction methods to construct the feature vectors in this study. Only three types of plastics are considered due to higher existence ratio of them than the other plastic types in the world. The decision mechanism consists of five different feature extraction methods including as Principal Component Analysis (PCA), Kernel PCA (KPCA), Fisher’s Linear Discriminant Analysis (FLDA), Singular Value Decomposition (SVD) and Laplacian Eigenmaps (LEMAP) and uses a simple experimental setup with a camera and homogenous backlighting. Due to the giving global solution for a classification problem, Support Vector Machine (SVM) is selected to achieve the classification task and majority voting technique is used as the decision mechanism. This technique equally weights each classification result and assigns the given plastic object to the class that the most classification results agree on. The proposed classification scheme provides high accuracy rate, and also it is able to run in real-time applications. It can automatically classify the plastic bottle types with approximately 90% recognition accuracy. Besides this, the proposed methodology yields approximately 96% classification rate for the separation of PET or non-PET plastic types. It also gives 92% accuracy for the categorization of non-PET plastic types into HPDE or PP.
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and the marginal distribution, and discretize Fourier space. We show that this technique solves most technical difficulties encountered with kernel deconvolution-based methods and reconstructs overall better and smoother Wigner functions. We also give estimators of the reconstruction errors for both methods and show improvement in noise handling properties and resilience to statistical errors.
In order to avoid contamination of unobservable and uncertain effective radiative forcing (ERF) on the diagnosis of radiative feedbacks based on short-term climate variability, we verify the Kernel-Gregory feedback calculation method using atmospheric model experiments with prescribed ERF. We show that both clear-sky radiative fluxes and all-sky radiative feedbacks have a closure between model simulations and kernel derivations. A near-zero global mean net cloud feedback is found in the simulation with prescribed ERF, which results in a more negative global net climate feedback, -2 W m -2 K -1 . Consistent with AMIP6 ensemble mean results, the lapse rate feedback is the largest contributor among all feedbacks to temperature amplification over the three poles (Arctic, Antarctic and Tibetan Plateau), followed by surface albedo feedback and Planck feedback deviation from its global mean. Except for the higher surface albedo feedback in the Antarctic, other feedbacks are almost same between the Arctic and Antarctic.
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using adaptive kernels. The first two methods are new, and allow detection and characterization of structures of arbitrary shape and at a wide range of spatial scales. These methods should elucidate not only clusters, but also the more distributed, wide-ranging filaments and sheets, and further allow the possibility of detecting and characterizing an even broader class of shapes. The methods are demonstrated and compared in application to three data sets: a carefully selected volume-limited sample from the Sloan Digital Sky Survey redshift data, a similarly selected sample from the Millennium Simulation, and a set of points independently drawn from a uniform probability distribution-a so-called Poisson distribution. We demonstrate a few of the many ways in which these methods elucidate large-scale structure in the distribution of galaxies in the nearby universe.
Herein, we describe a method for decorrelating image differences produced by the Alard and Lupton (1998) method of PSF matching. Inspired by the recent work of Zackay et al. (2016) and the prior work of Kaiser [2004], this proposed method uses a single post-subtraction convolution of an image difference to remove the neighboring pixel covariances in the image difference that result from the convolution of the template image by the PSF matching kernel. We describe the method in detail, analyze its effects on image differences (both real and simulated) as well as on detections and photometry of detected sources in decorrelated image differences. We also compare the decorrelated image differences with those resulting from a basic implementation of Zackay et al. (2016). We describe the implementation of the new correction in the LSST image differencing pipeline, and discuss potential issues and areas of future research.
The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI'/MOM) scheme, as well as the conversion factor from the RI'/MOM-renormalized quasi-TMDPDF to the \( \overline{\mathrm{MS}} \) scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.
For computational efficiency, both Monte Carlo and deterministic neutron transport codes often rely on pre-tabulated cross section sets and simple interpolation schemes to represent the Doppler broadening of the cross sections at a needed temperature. Accurate accounting of Doppler effects is of paramount importance for reactor analysis since it impacts the power distribution and the reactor response during transients. Temperature interpolation methods for Doppler broadening have traditionally been physically motivated engineering curve-fits, selected upon best-performance criteria on important nuclides. Kernel reconstruction methods have recently been introduced to perform fast and efficient Doppler broadening interpolation as the result of an optimization problem,, . Out of all the possible kernels analyzed, the temperature-optimized free Doppler kernel reconstruction method was shown to significantly outperform traditional Doppler broadening interpolation methods. Detailed derivations will be part of an upcoming journal paper. In this article, key formulae and results for performing free Doppler kernel reconstruction are summarized, and a study of the optimal temperature grid (T{sub j}) selection is presented. (authors)
Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.