Best Predictive GLMM using LASSO with Application on High-Speed Network
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97 MATHEMATICS AND COMPUTING↗
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Results for “Generalized Linear Model”
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Cosmological perturbations in massive bigravity
We present a comprehensive analysis of classical scalar, vector and tensor cosmological perturbations in ghost-free massive bigravity. In particular, we find the full evolution equations and analytical solutions in a wide range of regimes. We show that there are viable cosmological backgrounds but, as has been found in the literature, these models generally have exponential instabilities in linear perturbation theory. However, it is possible to find stable scalar cosmological perturbations for a very particular choice of parameters. For this stable subclass of models we find that vector and tensor perturbations have growing solutions. We argue that special initial conditions are needed for tensor modes in order to have a viable model.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Single-phase power distribution system power flow and fault analysis
Alternative methods for power flow and fault analysis of single-phase distribution systems are presented. The algorithms for both power flow and fault analysis utilize a generalized approach to network modeling. The generalized admittance matrix, formed using elements of linear graph theory, is an accurate network model for all possible single-phase network configurations. Unlike the standard nodal admittance matrix formulation algorithms, the generalized approach uses generalized component models for the transmission line and transformer. The standard assumption of a common node voltage reference point is not required to construct the generalized admittance matrix. Therefore, truly accurate simulation results can be obtained for networks that cannot be modeled using traditional techniques.
Halpin, S. M.↗
Brittle failure of rock: A review and general linear criterion
A failure criterion typically is phenomenological since few models exist to theoretically derive the mathematical function. Indeed, a successful failure criterion is a generalization of experimental data obtained from strength tests on specimens subjected to known stress states. For isotropic rock that exhibits a pressure dependence on strength, a popular failure criterion is a linear equation in major and minor principal stresses, independent of the intermediate principal stress. A general linear failure criterion called Paul-Mohr-Coulomb (PMC) contains all three principal stresses with three material constants: friction angles for axisymmetric compression $\phi$ c and extension $\phi$ e and isotropic tensile strength V 0 . PMC provides a framework to describe a nonlinear failure surface by a set of planes “hugging” the curved surface. Brittle failure of rock is reviewed and multiaxial test methods are summarized. Equations are presented to implement PMC for fitting strength data and determining the three material parameters. A piecewise linear approximation to a nonlinear failure surface is illustrated by fitting two planes with six material parameters to form either a 6- to 12-sided pyramid or a 6- to 12- to 6-sided pyramid. Finally, the particular nature of the failure surface is dictated by the experimental data.
58 GEOSCIENCES↗
Temporal deposition of copper and zinc in the sediments of metal removal constructed wetlands
The objective of this study was to explore the effects of time, seasons, and total carbon (TC) on Copper (Cu) and Zinc (Zn) deposition in the surface sediments. This study was performed at the H-02 constructed wetland on the Savannah River Site (Aiken, SC, USA). Covering both warm (April-September) and cool (October-March) seasons, several sediment cores were collected twice a year from the H-02 constructed wetland cells from 2007 to 2013. Total concentrations of Cu and Zn were measured in the sediments. Concentrations of Cu and Zn (mean ± standard deviation) in the surface sediments over 7 years of operation increased from 6.0 ± 2.8 and 14.6 ± 4.5 mg kg -1 to 139.6 ± 87.7 and 279.3 ± 202.9 mg kg -1 dry weight, respectively. The linear regression model explained the behavior and the variability of Cu deposition in the sediments. On the other hand, using the generalized least squares extension with the linear regression model allowed for unequal variance and thus produced a model that explained the variance properly, and as a result, was more successful in explaining the pattern of Zn deposition. Total carbon significantly affected both Cu ( p = 0.047) and Zn ( p < 0.001). Time effect on Cu deposition was statistically significant ( p = 0.013), whereas Zn was significantly affected by the season ( p = 0.009).
54 ENVIRONMENTAL SCIENCES↗
Parallel, iterative solution of sparse linear systems - Models and architectures
Solving large, sparse, linear systems of equations is a fundamental problem in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.
Reed, D. A.↗
Adaptive reduction of constitutive model-form error using a posteriori error estimation techniques
In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se , but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. As a result, the algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion.
42 ENGINEERING↗
Linear Solver for Electromagnetic Simulation of General Distribution Feeders
High-fidelity electromagnetic transient (EMT) modeling is required for accurate simulation and analysis of power system dynamics in modern distribution feeders. However, the high-fidelity of EMT models often leads to significant computational challenges, particularly in terms of computational resources and simulation time. This paper investigates the development and application of a detailed EMT model for general distribution feeders, with a focus on improving computational efficiency. A direct linear solver is proposed for a bordered block diagonal (BBD) matrix structure commonly encountered in a EMT model of distribution feeders. The solver integrates the Schur complement method with the block tridiagonal matrix algorithm to enhance the computational performance. The proposed solver is validated using the primary feeder of the IEEE 342-node test system, demonstrating its accuracy and efficiency in EMT simulations. Furthermore, the solver’s performance is benchmarked against MATLAB’s built-in linear solvers, showing significant improvements in computation time while maintaining high fidelity and accuracy in simulation results.
Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗
Eight decades of research on the long-term health effects of radiation in atomic bomb survivors and their offspring
Abstract This year marks the 80th anniversary of the atomic bombings of Hiroshima and Nagasaki. Over the past eight decades, large-scale cohort studies of atomic bomb survivors and their offspring conducted by the Radiation Effects Research Foundation and its predecessor, the Atomic Bomb Casualty Commission, have provided critical insights into the long-term health effects of radiation exposure. Key findings include early identification of radiation-associated leukemia, as well as excess risks of all solid cancers combined, and most individual cancer sites. Observed radiation dose–response relationships have generally followed a linear-quadratic model for leukemia and a linear model for all solid cancers. Recent findings indicating possible upward curvature in the dose–response for all solid cancers may reflect underlying heterogeneity in factors related to individual cancer sites and should be explored further. Generally, younger age at exposure, lower attained age, and female sex appear to show greater radiation sensitivity for all solid cancers combined but results differ by individual cancer site. Recent studies have also identified potential radiation-related excesses for non-cancer diseases such as cataracts, various circulatory diseases, and others. Studies of heritable effects on the offspring of exposed atomic bomb survivors, in contrast, have shown no elevated risk to date in offspring from parental radiation exposure, either at the molecular or disease level. With the cooperation of the atomic bomb survivors and their families, Radiation Effects Research Foundation’s research will continue to play a crucial role in informing the health of survivors, their families, and global radiation protection in the decades to come.
Oncology↗
A model of asynchronous iterative algorithms for solving large, sparse, linear systems
Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.
Reed, D. A.↗
Evaluating Carbon Extremes in a Coupled Climate-Carbon Cycle Simulation
Gross primary production (GPP) measures the photosynthetic update of carbon by terrestrial ecosystems. Accurately quantifying and simulating GPP and its extremes remains a challenge in global carbon cycle sciences. Here, we evaluate GPP extremes in a coupled biogeochemistry (BGC) simulation by the Department of Energy's Energy Exascale Earth System Model (E3SMv1.1) using the Generalized Extreme Value (GEV) distribution statistical model. The simulation is evaluated against the Global Bio-Atmosphere Flux (GBAF) data. Temporal trends and ENSO dependence are also investigated by using GEV models where time and the Niño3.4 index are introduced as linear covariates. The E3SMv1.1 model simulation generally predicts stronger negative and positive GPP extremes as compared to GBAF data. It also tends to simulate stronger temporal trends of GPP extremes than GBAF data. While negative GPP extreme trends are not significant in either E3SM or GBAF, positive GPP trends are statistically significant over several regions only for the E3SMv1.1 model simulation. ENSO dependence is generally stronger in the E3SMv1.1 model simulation, but ENSO dependence is found not to be significant for the time period analyzed (1980-2006) to match GBAF data. For the longer simulation period of 1900-2006, ENSO dependence is found to be statistically significant over Amazon, the maritime continent and Northern Australia for both negative and positive extremes.
Xu, Min↗
A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty
When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.
Luke J Miller↗
Theoretical priors on modified growth parametrisations
Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will enable us to test the relationships between matter over-densities, the curvature perturbation and the Newtonian potential. Any large-distance modification of gravity or exotic nature of dark energy modifies these relationships as compared to those predicted in the standard smooth dark energy model based on General Relativity. In linear theory of structure growth such modifications are often parameterised by virtue of two functions of space and time that enter the relation of the curvature perturbation to, first, the matter over- density, and second, the Newtonian potential. We investigate the predictions for these functions in Brans-Dicke theory, clustering dark energy models and interacting dark energy models. We find that each theory has a distinct path in the parameter space of modified growth. Understanding these theoretical priors on the parameterisations of modified growth is essential to reveal the nature of cosmic acceleration with the help of upcoming observations of structure formation.
79 ASTRONOMY AND ASTROPHYSICS↗
Calibrating constitutive models with full‐field data via physics informed neural networks
Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.
Hamel, Craig M.↗
Causal network inference using biochemical kinetics
Motivation: Networks are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of biochemical systems are generally non-linear, suggesting that suitable non-linear formulations may offer gains with respect to causal network inference and aid in associated prediction problems. Results: We present a general framework for network inference and dynamical prediction using time course data that is rooted in nonlinear biochemical kinetics. This is achieved by considering a dynamical system based on a chemical reaction graph with associated kinetic parameters. Both the graph and kinetic parameters are treated as unknown; inference is carried out within a Bayesian framework. This allows prediction of dynamical behavior even when the underlying reaction graph itself is unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that non-linear formulations can yield gains in causal network inference and permit dynamical prediction and uncertainty quantification in the challenging setting where the reaction graph is unknown. Availability and implementation: MATLAB R2014a software is available to download from warwick.ac.uk/chrisoates.
60 APPLIED LIFE SCIENCES↗
The impacts of oceanic deep temperature perturbations in the North Atlantic on decadal climate variability and predictability
Decadal climate predictability in the North Atlantic is largely related to ocean low frequency variability, whose sensitivity to initial conditions is not very well understood. Recently, three-dimensional oceanic temperature anomalies optimally perturbing the North Atlantic Mean Temperature (NAMT) have been computed via an optimization procedure using a linear adjoint to a realistic ocean general circulation model. The spatial pattern of the identified perturbations, localized in the North Atlantic, has the largest magnitude between 1000 and 4000 m depth. In the present study, the impacts of these perturbations on NAMT, on the Atlantic meridional overturning circulation (AMOC), and on climate in general are investigated in a global coupled model that uses the same ocean model as was used to compute the three-dimensional optimal perturbations. In the coupled model, these perturbations induce AMOC and NAMT anomalies peaking after 5 and 10 years, respectively, generally consistent with the ocean-only linear predictions. To further understand their impact, their magnitude was varied in a broad range. For initial perturbations with a magnitude comparable to the internal variability of the coupled model, the model response exhibits a strong signature in sea surface temperature and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that only the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.
54 ENVIRONMENTAL SCIENCES↗
Molecular Simulation of the Diffusion of Uranyl Carbonate Species in Aqueous Solution
Molecular dynamics simulations of aqueous uranyl carbonate species were carried out with two different potential models to gain molecular-level insight into the hydration properties of these species and evaluate the ability of the two models to reproduce published ab initio and experimental data. The simulation results were used to estimate the self-diffusion coefficients of uranyl carbonate species that often dominate uranyl speciation in groundwater systems. The first potential model was based on a series of shell models developed by Parker and co-workers (including (DE LEEUW and PARKER, 1998; KERISIT and PARKER, 2004; PAVESE et al., 1996). The second potential model was a rigid-ion model based on the flexible SPC water model (TELEMAN et al., 1987), the uranyl model of Guilbaud and Wipff (GUILBAUD and WIPFF, 1996), and the parameters for the carbonate ion given by Greathouse and co-workers (GREATHOUSE and CYGAN, 2005; GREATHOUSE et al., 2002). Analysis of structural (mean interatomic distances and coordination numbers) and dynamical (water residence times in hydration shell and self-diffusion coefficients) properties showed that, overall, the first potential model performed best when compared to published data, although the only major discrepancy with the second model was a misrepresentation of the configuration adopted by the alkaline-earth uranyl carbonate ions. The diffusion coefficients obtained for the alkaline-earth cations and the uranyl ion were compared with three variants of the Stokes-Einstein (SE) equation and it was found that none of the three SE models were able to reproduce both the absolute values and the overall trend determined from the molecular dynamics simulations. However, as would be expected based on the SE equation, a plot of the diffusion coefficients of the uranyl carbonate complexes as a function of the inverse of the equivalent spherical radius showed a general linear dependence with the two models yielding almost identical gradients. The nature of the alkaline-earth cation in the uranyl carbonate complexes was found to have only a small effect on the ion’s diffusion coefficient.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance
In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. Additionally, all these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.
33 ADVANCED PROPULSION SYSTEMS↗