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Here, in this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds for the preconditioned system. Several numerical examples are provided to demonstrate the efficiency of this preconditioner, especially for stochastic problems with large variance.
Convolutional neural networks (CNN) provide state-of-the-art performance in many computer vision tasks, including those related to remote-sensing image analysis. Successfully training a CNN to generalize well to unseen data, however, requires training on samples that represent the full distribution of variation of both the target classes and their surrounding contexts. With remote sensing data, acquiring a sufficiently representative training set is a challenge due to both the inherent multi-modal variability of satellite or aerial imagery and the general high cost of labeling data. To address this challenge, we have developed ISOSCELES, an Iterative Self-Organizing SCEne LEvel Sampling method for hierarchical sampling of large image sets. Using affinity propagation, ISOSCELES automates the selection of highly representative training images. Compared to random sampling or using available reference data, the distribution of the training is principally data driven, reducing the chance of oversampling uninformative areas or undersampling informative ones. In comparison to manual sample selection by an analyst, ISOSCELES exploits descriptive features, spectral and/or textural, and eliminates human bias in sample selection. Using a hierarchical sampling approach, ISOSCELES can obtain a training set that reflects both between-scene variability, such as in viewing angle and time of day, and within-scene variability at the level of individual training samples. We verify the method by demonstrating its superiority to stratified random sampling in the challenging task of adapting a pre-trained model to a new image and spatial domain for country-scale building extraction. Using a pair of hand-labeled training sets comprising 1,987 sample image chips, a total of 496,000,000 individually labeled pixels, we show, across three distinct model architectures, an increase in accuracy, as measured by F1-score, of 2.2–4.2%.
In this work, we extend the damped Zaremba-Kohn model (dZK) for long-range dispersion interaction between a molecule and a planar surface to molecules adsorbed on a curved cylindrical surface, and employ this extended model as an additive correction to the semilocal density functionals PBE (Perdew-Burke-Ernzerhof) and SCAN (strongly constrained and appropriately normed). The resulting PBE+vdW (van der Waals)-dZK and SCAN+vdW-dZK are applied to two systems, NH3 and NO2 molecules adsorbed on a single-wall carbon nanotube (CNT), for calculations of binding energies and equilibrium distances. For comparison, the results from vdW nonlocal functionals, such as SCAN+rVV10 and PBE+rVV10, are also presented. The binding energies from PBE+rVV10 (Vydrov and Van Voorhis), SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK are about 70–115 meV for the system of CNT + NH 3 and 300–500 meV for the system of CNT + NO 2 . The results from PBE+vdW-dZK and SCAN+vdW-dZK are closer to each other than those from PBE+rVV10 and SCAN+rVV10 are. The relatively closer results from PBE+vdW-dZK and SCAN+vdW-dZK indicate the consistency of our developed vdW–dZK model for cylindrical surfaces. All methods, including PBE, SCAN, PBE+rVV10, SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK, give approximately the same binding energy differences between two adsorption configurations (types I and II) for the two systems. This implies that the two adsorption sites have approximately the same adsorption stability. The exponent of the vdW interaction power law from our vdW-dZK model for the two systems is about 0 at short distance, largely due to the damping factor, and tends slowly to –4 to –4.5 at distances D about 20–50 Å. At even larger distances, the vdW power-law exponent approaches –5. This feature is very similar to the one calculated with random-phase approximation and renormalization group approaches, supporting the applicability of our methods. Our developed vdW-dZK method provides a highly efficient and reliable method for large systems with cylindrical surfaces, such as vdW interactions with nanotubes.
We present an approach that uses a deep learning model, in particular, a MultiLayer Perceptron, for estimating the missing values of a variable in multivariate time series data. We focus on filling a long continuous gap (e.g., multiple months of missing daily observations) rather than on individual randomly missing observations. Our proposed gap filling algorithm uses an automated method for determining the optimal MLP model architecture, thus allowing for optimal prediction performance for the given time series. We tested our approach by filling gaps of various lengths (three months to three years) in three environmental datasets with different time series characteristics, namely daily groundwater levels, daily soil moisture, and hourly Net Ecosystem Exchange. We compared the accuracy of the gap-filled values obtained with our approach to the widely used R-based time series gap filling methods ImputeTS and mtsdi. The results indicate that using an MLP for filling a large gap leads to better results, especially when the data behave nonlinearly. Thus, our approach enables the use of datasets that have a large gap in one variable, which is common in many long-term environmental monitoring observations.
Abstract Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality and cannot be applied to systems that are not entangled. Here, we introduce a robust method that achieves self-testing of individual systems by taking advantage of contextuality. The scheme is based on the simplest contextuality witness for the simplest contextual quantum system—the Klyachko-Can-Binicioğlu-Shumovsky inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements as a function of the value of the witness under a pragmatic assumption on the measurements. We apply the method in an experiment on a single trapped 40 Ca + using randomly chosen measurements and perfect detection efficiency. Using the observed statistics, we obtain an experimental demonstration of self-testing of a single quantum system.
In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.
Objectives. The purpose of this study was to investigate the influence of Tai Chi on cardiorespiratory fitness (CRF) in elderly people using meta-analysis. Methods. This study used seven electronic databases and data retrieved from randomized controlled trials (RCTs) investigating the role of Tai Chi on CRF in the elderly. All these 24 RCTs were screened and selected from 7 literature databases. The Stata 11.2 software (StataCorp, USA) was used for the meta-analysis, subgroup analysis, and bias test, while the Cochrane Collaboration’s tool was used for the assessment of the risk of bias (RoB). 4 researchers independently participated in sample selection, data extraction, and RoB assessment. Results. Following the inclusion criteria, 24 eligible studies were included in our analysis. The meta-analysis indicated that Tai Chi practice significantly increased the maximum rate of oxygen consumption (VO2 max) (weighted mean difference (WMD) = 3.76, 95% CI: 1.25 to 6.26, P < 0.1 ), leading to an overall reduction in the heart rate (HR) (WMD = −1.84, 95% CI: −2.04 to −1.63, P ≤ 0.001 ) and an increase in the O2 pulse (WMD = 0.94, 95% CI: 0.60 to 1.28, P ≤ 0.001 ) in individuals who practiced Tai Chi regularly compared with those who did not. The subgroup analysis suggested that overall in those who practiced Tai Chi, males (WMD = 1.48, 95% CI: 0.85 to 2.12, P ≤ 0.001 ) had higher O2 pulse than females (WMD = 0.73, 95% CI: 0.33 to 1.12, P ≤ 0.001 ). The subgroup analysis also showed an increase in the vital capacity (VC) (WMD = 316.05, 95% CI: 239.74 to 392.35, P ≤ 0.001 ) in individuals practicing Tai Chi. When the samples were further stratified by Tai Chi practicing time, the subgroup analysis suggested that individuals practicing Tai Chi over a period of 24 weeks showed no significant difference in VC (WMD = 82.95, 95% CI: -98.34 to 264.23, P = 0.370 ), while those practicing Tai Chi over a period of 48 weeks showed a significant increase (WMD = 416.62, 95% CI: 280.68 to 552.56, P ≤ 0.001 ). Furthermore, the subgroup analysis demonstrated that the increase in VC is significantly correlated with the Tai Chi practicing time (WMD = 344.97, 95% CI: 227.88 to 442.06, P ≤ 0.001 ). Conclusion. Regular Tai Chi practice could improve the CRF in the elderly, as indicated by significant improvement in indicators including VO2max, O2pulse, VC, and HR. However, gender and practice time might influence the overall beneficial outcomes.
Fast construction of hierarchical N-dimensional experimental design. The software allows construction of sampling strategies that are self-avoiding, tunable in resolution in N dimensions. This code is a drop-in replacement for seeding optimization runs often performed using uniform random sampling. The hierarchical approach allows for a rapid, top down method for construction the most effective design that drives towards a global optimum.
This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.
Energy Delivery Systems (EDS) must be verified to be free from intrusive and malicious software. One way of verifying this software is to perform device scans to detect malicious code. Because it is possible to have “fileless” malware that exists only in device (volatile) memory, offline scanning and even many forms of online scanning is insufficient for detection. This project (“Verify”) addresses this need by performing direct sampling of memory during device operation to detect unexpected or modified software while not interfering with device operation. The Verify project provides a proof-of-concept of detection by random sampling combined with remote software- and timing-based attestation methods for robust detection of in-memory threats. An external review of Verify was performed by our partner, General Electric (GE), and a summary of their findings is provided.
Characterizing the mechanical behavior of rocks plays a crucial role to optimize the fracturing process in unconventional reservoirs. However, due to the intrinsic anisotropy and heterogeneity in unconventional resources, fracture process prediction remains the most significant challenge for sustainable and economic hydrocarbon production. During the deformation tracking under compression, deploying conventional methods (strain gauge, extensometer, etc.) is insufficient to measure the deformation since the physical attachment of the device is restricted to the size of the sample, monitoring limited point-wise deformation, producing difficulties in data retrieval, and a tendency to lose track in failure points, etc. Where conventional methods are limited, the application of digital image correlation (DIC) provides detailed and additional information of strain evolution and fracture patterns under loading. DIC is an image-based optical method that records an object with a camera and monitors the random contrast speckle pattern painted on the facing surface of the specimen. To overcome the existing limitations, this paper presents numerical modeling of Brazilian disc tests under quasi-static conditions to understand the full-field deformation behaviors and finally, it is validated by DIC. As the direct tensile test has limitations in sample preparation and test execution, the Brazilian testing principle is commonly used to evaluate indirectly the tensile strength of rocks. The two-dimensional numerical model was built to predict the stress distribution and full-field deformation on Brazilian disc under compression based on the assumptions of a homogenous, isotropic and linear elastic material. The uniaxial compression test was conducted using the DIC technique to determine the elastic properties of Spider Berea sandstone, which were used as inputs for the simulation model. The model was verified by the analytical solution and compared with the digital image correlation. The numerical simulation results showed that the solutions matched reasonably with the analytical solutions where the maximum deviation of stress distribution was obtained as 14.59%. The strain evolution (normal and shear strains) and displacements along the central horizontal and vertical planes were investigated in three distinguishable percentages of peak loads (20%, 40%, and 90%) to understand the deformation behaviors in rock. The simulation results demonstrated that the strain evolution contours consistently matched with DIC generated contours with a reasonable agreement. The changes in displacement along the central horizontal and vertical planes showed that numerical simulation and DIC generated experimental results were repeatable and matched closely. In terms of validation, Brazilian testing to measure the indirect tensile strength of rocks is still an issue of debate. The numerical model of fracture propagation supported by digital image correlation from this study can be used to explain the fracturing process in the homogeneous material and can be extended to non-homogeneous cases by incorporating heterogeneity, which is essential for rock mechanics field applications.
Random variations of terrestrial rotation rate effects on pulsar observations, discussing methods to minimize effects
The results are described of geological and morphological interpretation of large-scale photographs of the surface of lunar maria. A morphological classification is proposed for small craters. It is shown that the classification of a crater in a given morphological category, reflecting the degree of its morphological maturity, is determined by the age of the given crater. A check on the nature of distribution of small craters, as done on the basis of the nearest neighbor method, show that the distribution is governed by a near-random law. It is found that variations of the probability density function for the craters conform to a normal distribution law. An empirical relation is found for the coefficient of variation as a function of crater diameter and the dimensions of the area on which the counts are made. The rockfalls near craters of various morphological classes are described.
The effect of gravity gradient torque disturbances (which is an order of magnitude greater than the other torque disturbances and is sinusoidal with a frequency of two cycles per orbit) on pointing accuracy can be predicted very precisely. However, since the sensor noise such as star tracker and gyro inherent noise, is random, their effect can only be predicted statistically. The most common method used is computer simulation with appropriate sensor model and adjusting spacecraft control laws for minimum pointing error, as presented by Harris (1972). The general investigation outlined theoretically relates spacecraft controls to pointing accuracy in terms of the sensor noise power spectrum. The results are presented in graphical form.
The propagation of transient scalar waves in a three-dimensional random medium is considered. The analysis is based on the smoothing method. An integro-differential equation for the coherent (or average) wave is derived and solved for the case of a statistically homogeneous and isotropic medium and a delta-function source. This yields the coherent Green's function of the medium. It is found that the waveform of the coherent wave depends generally on the distance from the source measured in terms of a certain dimensionless parameter. Based on the magnitude of this parameter, three propagation zones, called the near zone, the far zone, and the intermediate zone, are defined.
A series of experimental, theoretical, and review papers dealing with various aspects of applied mechanics, including structural analysis, mathematical methods, and fluid dynamics. Some of the topics covered are: the direct formulation of two-dimensional mechanics problems, the mechanical aspects of athletics, Laplace's tidal equations, cochlear mechanics, dynamic constitutive equations, optical techniques for the determination of displacement and strain fields, chemical and biochemical problems involving nonlinear diffusion processes, thermal stresses, the rotating rod viscometer, finite-element methods in plasticity, ships of minimum resistance, and wide-band random vibration of structures. Individual items are announced in this issue.
New trace element analyses of 25 basalt samples from a vertical traverse in an 11 m thick flow of Icelandic tholeiite show compositional differences which exceed analytical uncertainties and are random with respect to height. These variations suggest a short-range segregation model in which the amounts of phenocrysts, groundmass materials, and residual liquid vary randomly in different samples of the flow; a least-squares method is applied to determine if these variations reflect different proportions of crystallizing phases and residual liquid. Monte Carlo computations indicate that short-range segregation results in inhomogeneity of a magnitude of interflow compositional differences; this causes incoherence in elements with different geochemical behaviors while preserving coherence in elements of similar behavior.
Random events were simulated by computer and subjected to various statistical methods to extract important parameters. Various forms of curve fitting were explored, such as least squares, least distance from a line, maximum likelihood. Problems considered were dead time, exponential decay, and spectrum extraction from cosmic ray data using binned data and data from individual events. Computer programs, mostly of an iterative nature, were developed to do these simulations and extractions and are partially listed as appendices. The mathematical basis for the compuer programs is given.