Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Optimal algorithms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Parameter Transfer for Quantum Approximate Optimization of Weighted MaxCut

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. Here we show that for a given QAOA depth, a single “typical” vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Testing Linear Temporal Logic Formulae on Finite Execution Traces

We present an algorithm for efficiently testing Linear Temporal Logic (LTL) formulae on finite execution traces. The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive. In most past applications of LTL. theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications. Such tests correspond to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property. We then suggest an optimized algorithm based on transforming LTL formulae. The work is done using the Maude rewriting system. which turns out to provide a perfect notation and an efficient rewriting engine for performing these experiments.

Havelund, Klaus↗
NASA NTRS2001

Monitoring Programs Using Rewriting

We present a rewriting algorithm for efficiently testing future time Linear Temporal Logic (LTL) formulae on finite execution traces, The standard models of LTL are infinite traces, reflecting the behavior of reactive and concurrent systems which conceptually may be continuously alive in most past applications of LTL, theorem provers and model checkers have been used to formally prove that down-scaled models satisfy such LTL specifications. Our goal is instead to use LTL for up-scaled testing of real software applications, corresponding to analyzing the conformance of finite traces against LTL formulae. We first describe what it means for a finite trace to satisfy an LTL property end then suggest an optimized algorithm based on transforming LTL formulae. We use the Maude rewriting logic, which turns out to be a good notation and being supported by an efficient rewriting engine for performing these experiments. The work constitutes part of the Java PathExplorer (JPAX) project, the purpose of which is to develop a flexible tool for monitoring Java program executions.

Havelund, Klaus↗
NASA NTRS2015

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗
DOE OSTI2022

A differentiable approach to the maximum independent set problem using dataless neural networks

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. Here, in this paper, we propose a different approach in that no data is required for training the neural networks that produce the solution. In this sense, what we present is not a machine learning solution, but rather one that is dependent on neural networks and where backpropagation is applied to a loss function defined by the structure of the neural network architecture as opposed to a training dataset. In particular, we reduce the popular combinatorial optimization problem of finding a maximum independent set to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. Additionally, we propose a universal graph reduction procedure to handle large-scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental results on both real and synthetic graphs demonstrate that our proposed method performs on par or outperforms state-of-the-art learning-based methods in terms of the size of the found set without requiring any training data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

CONMIN: A FORTRAN program for constrained function minimization: User's manual

CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.

Vanderplaats, G. N.↗
NASA NTRS1988

Modal identification using single-mode projection filters and comparison with ERA and MLE results

The Single-Mode Projection Filter (SPF) is a newly developed algorithm for eigensystem parameter identification from both analytical results and test data. The SPF is formulated with a single mode only and practical for parallel processing implementation. Explicit formulations of SPF are derived for the multi-input multi-output (MIMO) system by using the orthogonal matrices of the controllability and observability matrices in the general sense. The modal parameters of SPF are initially obtained from an analytical model in modal space. The experimental data are then processed through SPF to update its modal parameters and to minimize a cost function defined by the norm of an error matrix. The updated modal parameters represent the characteristics of the test data. A two-dimensional global minimum optimization algorithm is developed and applied for the filter update by using the interval analysis method. The SPF is developed based on a single-mode subsystem and identifies only one modal frequency and one modal damping within a specified region. For an n-modes structure, n SPF can be implemented for parallel processing to reduce the computational burden. The SPF is applied to analyze the simulated data for the MAST beam structure. The estimated modal parameters are comparable to those from the Eigensystem Realization Algorithm (ERA) and repeated modal frequencies are identified. The modal analysis of the Spacecraft Control Laboratory Experiment (SCOLE) data is also performed by using the ERA and the Maximum Likelihood Estimate (MLE). The result shows that the first five modal frequencies are very close from ERA and MLE. However, there are slight disparities in the damping rates and the computational burdens are quite different among these two algorithms.

Huang, Jen-Kuang↗
DOE OSTI2023

Modeling noise in global Mølmer-Sørensen interactions applied to quantum approximate optimization

Many-qubit Mølmer-Sørensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parametrizes these errors from simple experimental measurements, without free parameters. Herein, we validate the model in comparison with experiments that implement sequences of MS interactions on two 171 Yb + ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $χ^{2}_{red}$≈2. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are 91% and 83% of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations, the model achieves approximation ratios that are 99% of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Uncovering Hazards Using a Multi-Objective Optimization to Explore the Faulty State-Space

Considering resilience when designing complex engineered systems is crucial to ensure the system is safe under unexpected hazardous scenarios. Traditional risk-based approaches, such as Failure Modes and Effects Analysis (FMEA) are useful for designing the system to mitigate hazardous scenarios that can be identified by the designer, but often require experience or prior knowledge of system failures to generate. More recently, researchers have developed simulation tools that enable the designer to model large sets of hazardous scenarios (driven by both internal faults and external factors) through simulation. While these tools enable a wider scope of fault modes to be evaluated (e.g., by injecting combined set of fault modes or injecting modes at different times), the resulting assessments (like FMEA) still require knowledge of the specific modes to be evaluated. However, failure to analyze a wide variety of fault scenarios can lead to an incomplete picture of the system resilience, especially to "surprise events'' which may be difficult for the designer to identify and predict beforehand. To overcome this challenge, previous work developed a fault sampling approach for resilience simulations which would procedurally-generate a wide variety of potential faults by systematically perturbing the health states of the system. While the resulting fault modes generated covered a much larger space hazards than would be otherwise considered (and identified many unique failure trajectories which would not have otherwise been identified), it also significantly increased the computational cost of the analysis and resulted in the simulation and analysis of a large set of essentially duplicate scenarios. Additionally, as the number of dimensions in the faulty state-space increases, the full elaboration of possible modes becomes computationally infeasible, justifying the use of a more targeted search. To resolve this limitation, this work proposes the use of a multiobjective optimization algorithm to search the health state space for potential fault modes that are both (1) hazardous and (2) unique. To solve this type of problem, this work proposes the use of a cooperative co-evolutionary algorithm. To demonstrate this approach, it will be applied to a model of an autonomous rover which uses line markings to navigate, focusing on potential hazards in the drive system which could cause the rover to crash. To determine the merit of the approach, it will further be compared with the previously-presented range elaboration approach and a random mode generation approach on the basis of computational efficiency and found modes.

Resilience↗
DOE OSTI2025

Particle Swarm Optimization of Dynamic Load Model Parameters in Large Systems

This paper considers two dynamic load models that are widely used in industry to account for induction motor behavior: CMLD and CLOD. These models must be parametrized for the specific utility system in a general way so that they can be used in planning studies and provide a conservative but realistic representation of load behavior. This study considers a measurement-based approach to tuning both models. The load modeling study compares the response of the tuned models to generic candidate models using historical events. This study considers one area-based subsystem to simplify the modeling approach and reduce the number of models required for simulations. Additionally, because dynamic load models often produce similar results for different sets of parameters, a sensitivity study was conducted to assess the parameter impacts on the voltage response. The sensitivity study covers the parameters that are tuned using event measurements. The process to estimate the parameters uses the particle-swarm optimization algorithm. Overall, the performance of the tuned model more accurately captures recovery voltage, delayed recovery, and settling voltage than its predecessor models while not being overly tuned so that it remains general for peak summer conditions.

dynamic load modeling↗
DOE OSTI2018

Auxetic metamaterials from disordered networks

Recent theoretical work suggests that systematic pruning of disordered networks consisting of nodes connected by springs can lead to materials that exhibit a host of unusual mechanical properties. In particular, global properties such as Poisson's ratio or local responses related to deformation can be precisely altered. Tunable mechanical responses would be useful in areas ranging from impact mitigation to robotics and, more generally, for creation of metamaterials with engineered properties. However, experimental attempts to create auxetic materials based on pruningbased theoretical ideas have not been successful. In this study, we introduce a more realistic model of the networks, which incorporates angle-bending forces and the appropriate experimental boundary conditions. A sequential pruning strategy of select bonds in this model is then devised and implemented that enables engineering of specific mechanical behaviors upon deformation, both in the linear and in the nonlinear regimes. In particular, it is shown that Poisson's ratio can be tuned to arbitrary values. The model and concepts discussed here are validated by preparing physical realizations of the networks designed in this manner, which are produced by laser cutting 2D sheets and are found to behave as predicted. Furthermore, by relying on optimization algorithms, we exploit the networks' susceptibility to tuning to design networks that possess a distribution of stiffer and more compliant bonds and whose auxetic behavior is even greater than that of homogeneous networks. Finally, taken together, the findings reported here serve to establish that pruned networks represent a promising platform for the creation of unique mechanical metamaterials.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution

The effcient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for common discretizations makes them a good candidate for an efficient parallel solver. Yet, modern architectures for high-performance computing systems continue to challenge the parallel scalability of multilevel solvers. While algebraic multigrid methods are robust for solving a variety of problems, the increasing importance of data locality and cost of data movement in modern architectures motivates the need to carefully exploit structure in the problem. Robust logically structured variational multigrid methods, such as Black Box Multigrid (BoxMG), maintain structure throughout the multigrid hierarchy. This avoids indirection and increased coarse- grid communication costs typical in parallel algebraic multigrid. Nevertheless, the parallel scalability of structured multigrid is challenged by coarse-grid problems where the overhead in communication dominates computation. In this paper, an algorithm is introduced for redistributing coarse-grid problems through incremental agglomeration. Guided by a predictive performance model, this algorithm provides robust redistribution decisions for structured multilevel solvers. A two-dimensional diffusion problem is used to demonstrate the significant gain in performance of this algorithm over the previous approach that used agglomeration to one processor. In addition, the parallel scalability of this approach

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

LigninGraphs: lignin structure determination with multiscale graph modeling

Lignin is an aromatic biopolymer found in ubiquitous sources of woody biomass. Designing and optimizing lignin valorization processes requires a fundamental understanding of lignin structures. Experimental characterization techniques, such as 2D-heteronuclear single quantum coherence (HSQC) nuclear magnetic resonance (NMR) spectra, could elucidate the global properties of the polymer molecules. Computer models could extend the resolution of experiments by representing structures at the molecular and atomistic scales. We introduce a graph-based multiscale modeling framework for lignin structure generation and visualization. The framework employs accelerated rejection-free polymerization and hierarchical Metropolis Monte Carlo optimization algorithms. We obtain structure libraries for various lignin feedstocks based on literature and new experimental NMR data for poplar wood, pinewood, and herbaceous lignin. The framework could guide researchers towards feasible lignin structures, efficient space exploration, and future kinetics modeling. Its software implementation in Python, LigninGraphs, is open-source and available on GitHub.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Subsonic flight test evaluation of a performance seeking control algorithm on an F-15 airplane

The subsonic flight test evaluation phase of the NASA F-15 (powered by F 100 engines) performance seeking control program was completed for single-engine operation at part- and military-power settings. The subsonic performance seeking control algorithm optimizes the quasi-steady-state performance of the propulsion system for three modes of operation. The minimum fuel flow mode minimizes fuel consumption. The minimum thrust mode maximizes thrust at military power. Decreases in thrust-specific fuel consumption of 1 to 2 percent were measured in the minimum fuel flow mode; these fuel savings are significant, especially for supersonic cruise aircraft. Decreases of up to approximately 100 degree R in fan turbine inlet temperature were measured in the minimum temperature mode. Temperature reductions of this magnitude would more than double turbine life if inlet temperature was the only life factor. Measured thrust increases of up to approximately 15 percent in the maximum thrust mode cause substantial increases in aircraft acceleration. The system dynamics of the closed-loop algorithm operation were good. The subsonic flight phase has validated the performance seeking control technology, which can significantly benefit the next generation of fighter and transport aircraft.

Gilyard, Glenn B.↗
DOE OSTI2020

Efficient numerical methods to solve sparse linear equations with application to PageRank

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. Here, we propose three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Exploring Effective Best Management Practices in the Miyun Reservoir Watershed, China

Miyun reservoir watershed is a major source of drinking water for China’s capital, Beijing, which has a population of 21.75 million. Recently, the capacity of the Miyun reservoir to supply clean drinking water is threatened by increasing eutrophication (or algae bloom), mainly due to the discharge of wastewater and excessive fertilization application in the upstream watershed. Therefore, there is an urgent need to design effective best management practices (BMPs) to reduce upstream nutrient load and improve water quality in the Miyun reservoir. In this study, we built a watershed model (i.e. the Soil and Water Assessment Tool) in the Miyun Reservoir Watershed (MRW), and calibrated and validated it using long term sediment, nitrogen (N) and phosphorus (P) data. Further, we developed a Markov Chain based multi-objective optimization program to explore optimal BMPs with tradeoffs between economic costs and water quality responses. With the watershed model and the multi-objective optimization algorithms, we explored potential effectiveness of BMPs under two scenarios that are currently being considered: scenario 1 assumes funding of BMP implementation is from national grants and targets high water quality standard, while scenario 2 assumes funding is from farmers and targets water quality that barely meet the drinking water standard. We found substantial discrepancy between these two scenarios with respect to type and spatial configuration of BMPs and associated economic costs, highlighting the need of reconciling concerns from different stakeholders in order to arrive at a BMP plan that all parties will agree upon. In addition, we found that cross-subwatershed coordination and targeting flood season instead of year-round water quality standards could pronouncedly reduce economic cost of BMP implementation while not substantially degrade water quality. The watershed scale optimization method developed here hold the promise serve as an effective tool to explore tradeoffs between economic costs, water quality improvements, and decisions makers and stakeholders’ concerns in BMPs design, thereby informing sustainable watershed scale water resources management.

Qiu, Jiali↗
DOE OSTI2022

Model predictive control of heating, ventilation, and air conditioning (HVAC) systems: A state-of-the-art review

Due to the fast advancement of communication and information technology, intelligent buildings have garnered great interest. These buildings can forecast weather, ambient temperature, and sun irradiation and can modify heating, ventilation, and air conditioning (HVAC) operations appropriately, based on current and previous data. This change is intended to reduce HVAC system energy usage while maintaining an appropriate degree of thermal comfort and indoor air quality. Since its inception, model predictive control (MPC) has been one of the prospective solutions for HVAC management systems to reduce both costs and energy usage. Additionally, MPC is becoming increasingly practical as the processing capacity of building automation systems increases and a large quantity of monitored building data becomes available. MPC also provides the potential to improve the energy efficiency of HVAC systems via its capacity to consider limitations, to predict disruptions, and to factor in multiple competing goals such as interior thermal comfort and building energy consumption. Although substantial research has been conducted on MPC in building HVAC systems, there is a shortage of critical reviews and a lack of a comprehensive framework that formulates and defines the applications. Here, this article provides a comprehensive state-of-the-art overview of MPC in HVAC systems. Detailed discussions of modeling approaches and optimization algorithms are included. Numerous design aspects such as prediction horizon, occupancy behavior, building type, and cost function, that impact MPC performance are discussed in detail. The technical characteristics, advantages, and disadvantages of various types of modeling software are discussed. The primary objective of this work is to highlight critical design characteristics for the MPC control scheme and to give improved suggestions for future research. Moreover, numerous prospective scenarios have been suggested that might provide future research direction.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2012

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William↗