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At least 199 records · Page 11

Spatial operator algebra framework for multibody system dynamics

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Rodriguez, G.

Spatial Operator Algebra for multibody system dynamics

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

Rodriguez, G.

A Mathematical Analysis of an Example Delay Tolerant Network using the Theory of Sheaves

NASA’s High-Data Rate Architecture (HiDRA) project is working towards a general yet practical toolkit and knowledge base to help usher in the era of new technologies for space systems communications, such as optical links. The High-Rate Delay Tolerant Networking (HDTN) implementation falls under the umbrellas of both the toolkit and the knowledge base, as its advancements illuminate more general areas of Delay Tolerant Networking (DTN) that need growth. The goal of this paper is to explore the usage of particular mathematical machineries, namely temporal flow networks and sheaves, to identify fundamental, underlying structures in DTN for space systems. Satellites, space assets, ground stations, etc. give rise to a disconnected network, and it is the goal of DTN to glue disparate links together into a cohesive system, that is, a network. Depending on a given link, the latencies might be beyond that which the Transmission Control Protocol (TCP) can handle, and contact times might have one-way light times in excess of minute (sometimes significantly longer). Some links might be periodic (say, due to orbital mechanics) or they might not be. This diversity has made it difficult to probe the underlying structure. An immediate consequence is that DTNs in practice today are controlled by globally distributed contact plans (schedules), which are the input to the contact graph routing (CGR) algorithm. While this is effective for smaller networks, it will be very difficult to scale for future networks. Deeper and more rigorous theory is needed to bring DTN to the next evolutionary step. To this end, this paper introduces and suggests a mathematical framework for DTN, and applies it to a space network that is simulated using an orbital analysis toolkit. The tag-line for the structure known as sheaves is that they are the mathematically precise way of gluing local data together into unique, global data. If we consider routing, we see that networking is a “sheafy” science. We then discuss a simplified sheaf model, known as the cellular sheaf. The sheaf-theoretic analysis is presented and discussed, as it is hoped that this and related papers will help form the primordial ooze of DTN theory. Finally there is a section of future work suggesting follow-on research.

Delay Tolerant Networking

5S ribosomal ribonucleic acid sequences in Bacteroides and Fusobacterium: evolutionary relationships within these genera and among eubacteria in general

The 5S ribosomal ribonucleic acid (rRNA) sequences were determined for Bacteroides fragilis, Bacteroides thetaiotaomicron, Bacteroides capillosus, Bacteroides veroralis, Porphyromonas gingivalis, Anaerorhabdus furcosus, Fusobacterium nucleatum, Fusobacterium mortiferum, and Fusobacterium varium. A dendrogram constructed by a clustering algorithm from these sequences, which were aligned with all other hitherto known eubacterial 5S rRNA sequences, showed differences as well as similarities with respect to results derived from 16S rRNA analyses. In the 5S rRNA dendrogram, Bacteroides clustered together with Cytophaga and Fusobacterium, as in 16S rRNA analyses. Intraphylum relationships deduced from 5S rRNAs suggested that Bacteroides is specifically related to Cytophaga rather than to Fusobacterium, as was suggested by 16S rRNA analyses. Previous taxonomic considerations concerning the genus Bacteroides, based on biochemical and physiological data, were confirmed by the 5S rRNA sequence analysis.

NASA Discipline Exobiology

Recent Progress in OVERFLOW Convergence Improvements

Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.

Joseph M Derlaga

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail.

mission design

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail. GenETOC was developed in C# using the .NET framework with Windows Presentation Foundation (WPF) serving as the framework from which to create the graphical user interface (GUI). GenETOC user inputs can be categorized into three major data components: definition of the problem (areas of interest, satellite decision parameters, and sensor configurations), definition of performance objectives, and specification of the genetic algorithm (GA) parameters. In the problem definition component, the user is prompted to define the areas of interest against which the performance metrics will be computed, define the sensor parameters and attach them to specific spacecraft, select which satellite orbital parameters will be added to the decision space of the GA, and specify the range of desired values for each optimization parameter. For performance objectives, the user is presented with a list of available coverage and revisit performance based calculation options from which two metrics are chosen to serve as the objective functions that the GA will use to evaluate solutions during the optimization process. Finally, the definition of the GA parameters provides user control over the number of generations (number of optimization iterations), the population size (number of candidate constellations created in each generation), and the adaptive mutation and crossover threshold values (control parameters for how frequently each process occurs during the optimization). GenETOC has been extensively tested to verify the individual components of the optimization process. The GA has been tested against a suite of GA test problems to confirm convergence to the known two and three-dimensional Pareto fronts. The coverage and revisit performance metrics obtained in GenETOC are compared with STK desktop scenarios, confirming the constellations are being appropriately modeled within GenETOC simulations. A walkthrough of a simple, example problem is provided to illustrate the workings of GenETOC and to demonstrate the output available to the mission designer.

mission design

An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics

This report is a repository of the results obtained from a large scale empirical comparison of seven iterative and evolution-based optimization heuristics. Twenty-seven static optimization problems, spanning six sets of problem classes which are commonly explored in genetic algorithm literature, are examined. The problem sets include job-shop scheduling, traveling salesman, knapsack, binpacking, neural network weight optimization, and standard numerical optimization. The search spaces in these problems range from 2368 to 22040. The results indicate that using genetic algorithms for the optimization of static functions does not yield a benefit, in terms of the final answer obtained, over simpler optimization heuristics. Descriptions of the algorithms tested and the encodings of the problems are described in detail for reproducibility.

Baluja, Shumeet

A Novel, Real-Valued Genetic Algorithm for Optimizing Radar Absorbing Materials

A novel, real-valued Genetic Algorithm (GA) was designed and implemented to minimize the reflectivity and/or transmissivity of an arbitrary number of homogeneous, lossy dielectric or magnetic layers of arbitrary thickness positioned at either the center of an infinitely long rectangular waveguide, or adjacent to the perfectly conducting backplate of a semi-infinite, shorted-out rectangular waveguide. Evolutionary processes extract the optimal physioelectric constants falling within specified constraints which minimize reflection and/or transmission over the frequency band of interest. This GA extracted the unphysical dielectric and magnetic constants of three layers of fictitious material placed adjacent to the conducting backplate of a shorted-out waveguide such that the reflectivity of the configuration was 55 dB or less over the entire X-band. Examples of the optimization of realistic multi-layer absorbers are also presented. Although typical Genetic Algorithms require populations of many thousands in order to function properly and obtain correct results, verified correct results were obtained for all test cases using this GA with a population of only four.

Hall, John Michael

Application of Domain Knowledge to Software Quality Assurance

This work focused on capturing, using, and evolving a qualitative decision support structure across the life cycle of a project. The particular application of this study was towards business process reengineering and the representation of the business process in a set of Business Rules (BR). In this work, we defined a decision model which captured the qualitative decision deliberation process. It represented arguments both for and against proposed alternatives to a problem. It was felt that the subjective nature of many critical business policy decisions required a qualitative modeling approach similar to that of Lee and Mylopoulos. While previous work was limited almost exclusively to the decision capture phase, which occurs early in the project life cycle, we investigated the use of such a model during the later stages as well. One of our significant developments was the use of the decision model during the operational phase of a project. By operational phase, we mean the phase in which the system or set of policies which were earlier decided are deployed and put into practice. By making the decision model available to operational decision makers, they would have access to the arguments pro and con for a variety of actions and can thus make a more informed decision which balances the often conflicting criteria by which the value of action is measured. We also developed the concept of a 'monitored decision' in which metrics of performance were identified during the decision making process and used to evaluate the quality of that decision. It is important to monitor those decision which seem at highest risk of not meeting their stated objectives. Operational decisions are also potentially high risk decisions. Finally, we investigated the use of performance metrics for monitored decisions and audit logs of operational decisions in order to feed an evolutionary phase of the the life cycle. During evolution, decisions are revisisted, assumptions verified or refuted, and possible reassessments resulting in new policy are made. In this regard we implemented a machine learning algorithm which automatically defined business rules based on expert assessment of the quality of operational decisions as recorded during deployment.

Wild, Christian W.

Quantum Search in Hilbert Space

A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.

Zak, Michail

AlloSHP: deconvoluting single homeologous polymorphism for phylogenetic analysis of allopolyploids

Background The genomic and evolutionary study of allopolyploid organisms involves multiple copies of homeologous chromosomes, making their assembly, annotation, and phylogenetic analysis challenging. Bioinformatics tools and protocols have been developed to study polyploid genomes, but sometimes require the assembly of their genomes, or at least the genes, limiting their use. Results We have developed AlloSHP, a command-line tool for detecting and extracting single homeologous polymorphisms (SHPs) from the subgenomes of allopolyploid species. This tool integrates three main algorithms, WGA, VCF2ALIGNMENT and VCF2SYNTENY, and allows the detection of SHPs for the study of diploid-polyploid complexes with available diploid progenitor genomes, without assembling and annotating the genomes of the allopolyploids under study. AlloSHP has been validated on three diploid-polyploid plant complexes, Brachypodium, Brassica, and Triticum-Aegilops, and a set of synthetic hybrid yeasts and their progenitors of the genus Saccharomyces. The results and congruent phylogenies obtained from the four datasets demonstrate the potential of AlloSHP for the evolutionary analysis of allopolyploids with a wide range of ploidy and genome sizes. Conclusions AlloSHP combines the strategies of simultaneous mapping against multiple reference genomes and syntenic alignment of these genomes to call SHPs, using as input data a single VCF file and the reference genomes of the known or closest extant diploid progenitor species. This novel approach provides a valuable tool for the evolutionary study of allopolyploid species, both at the interspecific and intraspecific levels, allowing the simultaneous analysis of a large number of accessions and avoiding the complex process of assembling polyploid genomes.

Allopolyploids

Open system magnetic evolution of the taos plateau volcanic field, Northern New Mexico. I - The petrology and geochemistry of the servilleta basalt

MULTIFIT, an embodiment of the conceptual structure needed in modeling multisource and multiprocess magmatic systems, is described. This program, which uses familiar materials balance methodology and the equilibrium form of the Rayleigh equations, links evolutionary arrays, which is turn collectively relate the starting and final compositions of a given magmatic system. Moreover, MULTIFIT incorporates variations within major element data arrays; the linkage between them can be tested using an extension of the least squares algorithm, which selects the best branch point according to the minimum-sum-of-squared-residuals criterion. Advantages and disadvantages of the materials balance approach used in this program are discussed, an example is provided, and equations utilized by MULTIFIT are summarized. While MULTIFIT may not be the best approach for poorly constrained models involving partial melting for complex mixing, it may ultimately prove useful for ascertaining trace element partition coefficients in magnetic systems.

Dungan, M. A.

Cluster Analysis of IRIS Spectroscopic Line Profiles and SDO/AIA EUV Emission in Observations and RMHD Simulations of the Solar Atmosphere

Spatially-resolved observations from the IRIS and SDO/AIA satellites, especially when coupled with realistic 3D RMHD simulations, are a powerful tool for analysis of processes in the solar chromosphere, transition region, and corona. However, the complexity of the data makes understanding the observations and modeling results difficult. In this work, we apply unsupervised clustering algorithms for analysis of observational and synthetic chromospheric Mg II h&k 2796Å&2803Å and transition region C II 1334Å&1335Å line profiles observed by IRIS, and extreme ultraviolet (EUV) emission observed by SDO/AIA, for various types of problems. The synthetic line profiles are computed for simulations of the quiescent solar atmosphere (using the StellarBox and RH1.5 codes). The K-Means clustering algorithm is applied, and the selection of an optimal number of clusters is supported by the average silhouette width technique. We discuss applications of the line profile clustering method to 1) visualization of computational and observational spectroscopic imaging data; 2) understanding of evolutionary trends and behavior patterns of quiet Sun emission and during solar flares; and 3) recognition of heating events and shock waves.

Sadykov, Viacheslav

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING