Unnormalized associated Legendre functions: A compendium of graphs, expansions, properties, and integrals
Compendium of graphs, expansions, propertites, and integrals for unnormalized associated Legendre functions
Heffron, W. G.↗
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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.
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Formation Flying Control of Multiple Spacecraft: Graph Theoretic Properties and Switching Schemes
We present several results on the leader-following (LF) paradigm in the formation flying of multiple spacecraft in free space.
Formation↗
Topology for efficient information dissemination in ad-hoc networking
In this paper, we explore the information dissemination problem in ad-hoc wirless networks. First, we analyze the probability of successful broadcast, assuming: the nodes are uniformly distributed, the available area has a lower bould relative to the total number of nodes, and there is zero knowledge of the overall topology of the network. By showing that the probability of such events is small, we are motivated to extract good graph topologies to minimize the overall transmissions. Three algorithms are used to generate topologies of the network with guaranteed connectivity. These are the minimum radius graph, the relative neighborhood graph and the minimum spanning tree. Our simulation shows that the relative neighborhood graph has certain good graph properties, which makes it suitable for efficient information dissemination.
network topology↗
Topologies on directed graphs
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Lieberman, R. N.↗
Collision integrals and high temperature transport properties for N-N, O-O, and N-O
Accurate collision integrals for the interactions of N(4S0) + N(4S0), O(3P) + O(3P), and N(4S0) + O(3P) are reported. These are computed from a semiclassical formulation of the scattering using the best available representations of all of the potential energy curves needed to describe the collisions. Spectroscopic curves and other accurate measured data are used where available; the results of accurate ab initio electronic structure calculations are used to determine the remaining potential curves. The high-lying states are found to give the largest contributions to the collision cross sections. The nine collision integrals needed to determine transport properties to second order are tabulated for translational temperatures in the range 250-100,000 K. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor for a gas composed of nitrogen and oxygen atoms in thermal equilibrium have been calculated. It is found that the second-order contribution to the transport properties is small. Graphs of these transport properties for various mixture ratios are presented for temperatures in the range 5000-15,000 K.
Levin, E.↗
Collision integrals and high temperature transport properties for N-N, O-O, and N-O
Accurate collision integrals are reported for the interactions of N(4 S 0) + N(4 S 0), O(3 P), and N(4 S 0) + O(3 P). These are computed from a semiclassical formulation of the scattering using the best available representations of all of the potential energy curves needed to describe the collisions. Experimental RKR curves and other accurate measured data are used where available; the results of accurate ab initio electronic structure calculations are used to determine the remaining potential curves. The high-lying states are found to give the largest contributions to the collision cross sections. The nine collision integrals, needed to determine transport properties to second order, are tabulated for translational temperatures in the range 250 K to 100,000 K. These results are intended to reduce the uncertainty in future predictions of the transport properties of nonequilibrium air, particularly at high temperatures. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor for a gas composed of nitrogen and oxygen atoms in thermal equilibrium are calculated. It was found that the second order contribution to the transport properties is small. Graphs of these transport properties for various mixture ratios are presented for temperatures in the range 5000 to 15000 K.
Levin, E.↗
A note on a corrector formula for the numerical solution of ordinary differential equations
A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.
Chien, Y.-C.↗
QuantifyML: How good is my machine learning model?
This paper presents an approach, QuantifyML, which employs model counting to assess the learnability and robustness of machine learning models. Typically the efficacy of machine learning models is determined by computing their accuracy statistically on test data sets. However, this may be misleading, if the test data is not representative of the problem that is being studied. Further, two different models may have the same accuracy on a given data set, measured statistically, but may be very different in their behavior on unseen data. Also, models with high accuracy could have poor adversarial robustness. In QuantifyML, our goal is to precisely quantify the extent to which machine learning models have learned and generalized from the given data. In QuantifyML, a trained model is translated into a C program, which is fed to the CBMC model checking tool to produce a formula in Conjunctive Normal Form (CNF), which in turn is analyzed with state-of-the-art model counters to efficiently obtain precise counts w.r.t different outputs. QuantifyML enables i) evaluating the learnability of models by comparing the counts for the outputs to ground truth, expressed as logical predicates (if available), ii) comparing the performance of different models that may be built with different machine learning algorithms (e.g., decision-trees vs. neural networks), and iii) quantifying the robustness of trained models around given inputs. Our evaluation demonstrates these applications of QuantifyML on decision trees and neural networks trained to learn relational properties of graphs, for which we know the ground truth, and to perform image classification, for which we do not have the ground truth, but we can quantify local robustness.
Deep Neural Networks↗
A Graph Based Backtracking Algorithm for Solving General CSPs
Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.
Pang, Wanlin↗
Model checking
Automatic formal verification methods for finite-state systems, also known as model-checking, successfully reduce labor costs since they are mostly automatic. Model checkers explicitly or implicitly enumerate the reachable state space of a system, whose behavior is described implicitly, perhaps by a program or a collection of finite automata. Simple properties, such as mutual exclusion or absence of deadlock, can be checked by inspecting individual states. More complex properties, such as lack of starvation, require search for cycles in the state graph with particular properties. Specifications to be checked may consist of built-in properties, such as deadlock or 'unspecified receptions' of messages, another program or implicit description, to be compared with a simulation, bisimulation, or language inclusion relation, or an assertion in one of several temporal logics. Finite-state verification tools are beginning to have a significant impact in commercial designs. There are many success stories of verification tools finding bugs in protocols or hardware controllers. In some cases, these tools have been incorporated into design methodology. Research in finite-state verification has been advancing rapidly, and is showing no signs of slowing down. Recent results include probabilistic algorithms for verification, exploitation of symmetry and independent events, and the use symbolic representations for Boolean functions and systems of linear inequalities. One of the most exciting areas for further research is the combination of model-checking with theorem-proving methods.
Dill, David L.↗
Generation of precedence relations for mechanical assemblies
Planning of assembly sequences is essential to the manufacturing system design process. Several methodologies have been proposed to represent all the feasible assembly sequences. In this thesis, three algorithms are presented to generate three sets of precedence relations based on all the infeasible assembly tasks, all the infeasible assembly states, and all the feasible assembly sequences, respectively. The equivalence of the resulting sets of precedence relations to the AND/OR graph is established. A new property, the real time property, of a representation of assembly sequences is defined and discussed. A representation of assembly sequences is said to have the real time property, if it is possible to generate the next assembly task by testing locally in the representation, and it will guarantee that the generated assembly task will not lead the assembly sequence to a dead end situation, in which no feasible assembly task can be performed any more. It is shown that the correctness and completeness of one representation can not guarantee the real time property of the representation. It is proven that the directed graph representation and the set of precedence relations based on all the infeasible assembly states have the real time property, while the AND/OR graph representation and the set of precedence relations based on all the infeasible assembly tasks do not have the real time property. Finally in the thesis, the PLEIDEAS system, a PLanning Environment for Integrated DEsign of Assembly Systems, is described and illustrated by an example.
Zhang, Hui↗
Prediction of fiber composite mechanical behavior made simple
The elastic properties and failure stresses of angleplied fiber composite laminates were determined using a pocket calculator. The procedure uses simple equations and appropriate graphs of elastic properties versus angle plies, and can handle all types of fiber composites including hybrids. The versatility and generality of the method is illustrated in several step-by-step numerical examples.
Chamis, C. C.↗
Task scheduling in dataflow computer architectures
Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.
Katsinis, Constantine↗
The fully indecomposable matrix and its associated bipartite graph - An investigation of combinatorial and structural properties
Combinatorial properties of classes of nonnegative matrices
Roberts, E. J.↗
On Directed Graphs and Related Topological Spaces Technical Report No. 2
Connective properties between theory of directed graphs and point-set topology
VECTOR SPACE↗
Structural evaluation of candidate space shuttle thermal protection systems
The characteristics and development of a lightweight reusable thermal protection system for the space shuttle are discussed. The test articles consisted of metallic substrates with upper surfaces covered with all-silica, reusable, surface insulation material. The material is processed in the form of tiles. The external surfaces of the tiles are provided with a coating system which consists of a borosilicate coating with a silicon carbide emittance agent and impregnation with a hydrophobic agent. The finished tiles are attached to the metal substrate by adhesive bonding. Charts and graphs of the properties of the material are provided.
Burns, A. B.↗
Path planning for assembly of strut-based structures
A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.
Muenger, Rolf↗
The CORSAIR Turbomachinery Code: Status and Plans
This viewgraph presentation gives an overview of the CORSAIR turbomachinery code's status and plans. Details are provided on the CORSAIR algorithms, full- and partial-admission turbine simulations, the Simplex turbine, instantaneous Mach number, unsteady pressure admission graphs, variable fluid property RLV-133 simulations, instantaneous entropy function, pumps and inducers, and future plans.
Dorney, Daniel J.↗