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Structure and strategy in encoding simplified graphs

Tversky and Schiano (1989) found a systematic bias toward the 45-deg line in memory for the slopes of identical lines when embedded in graphs, but not in maps, suggesting the use of a cognitive reference frame specifically for encoding meaningful graphs. The present experiments explore this issue further using the linear configurations alone as stimuli. Experiments 1 and 2 demonstrate that perception and immediate memory for the slope of a test line within orthogonal 'axes' are predictable from purely structural considerations. In Experiments 3 and 4, subjects were instructed to use a diagonal-reference strategy in viewing the stimuli, which were described as 'graphs' only in Experiment 3. Results for both studies showed the diagonal bias previously found only for graphs. This pattern provides converging evidence for the diagonal as a cognitive reference frame in encoding linear graphs, and demonstrates that even in highly simplified displays, strategic factors can produce encoding biases not predictable solely from stimulus structure alone.

Schiano, Diane J.↗

A Graph Based Interface for Representing Volume Visualization Results

This paper discusses a graph based user interface for representing the results of the volume visualization process. As images are rendered, they are connected to other images in a graph based on their rendering parameters. The user can take advantage of the information in this graph to understand how certain rendering parameter changes affect a dataset, making the visualization process more efficient. Because the graph contains more information than is contained in an unstructured history of images, the image graph is also helpful for collaborative visualization and animation.

Patten, James M.↗

Decomposition Algorithm for Global Reachability on a Time-Varying Graph

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

Kuwata, Yoshiaki↗

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗

Directed Acyclic Graphs: A Tool for Understanding the NASA Human Spaceflight System Risks - Human System Risk Board

For over a decade, the National Aeronautics and Space Administration (NASA) has tracked and configuration-managed approximately 30 risks to astronaut health and performance that occur before, during and after spaceflight. The Human System Risk Board (HSRB), a Health and Medical Technical Authority (HMTA) Board at NASA Johnson Space Center, is the entity responsible for identifying, assessing, analyzing, and monitoring the official understanding of the risk or risk posture for each of the Human System Risks and determining – based on evaluation of the available evidence – when that risk posture changes. The ultimate purpose of tracking and researching these risks is to find ways to reduce the risk that astronaut crews face during spaceflight. Historically, research, development and operations relevant to one risk have been conducted in isolation from other risks; these individual risk ‘silos’ enabled initial characterization of each specific risk. In spaceflight however, the impact of exposure to risk for astronaut crews is cumulative, and not independent of exposures or other risks, as all the adverse effects of the spaceflight environment begin at launch, continue throughout the duration of the mission and in some cases across the lifetime of the crews. In January of 2020, the HSRB at NASA embarked on a pilot project designed to assess the potential value of causal diagramming as a tool to facilitate understanding of these cumulative and interdependent effects as applied within Human System Risk management. This process uses directed acyclic graphs as a means of formalizing a shared mental model of the causal flow of risk among Risk Board stakeholders. Initially this model was to improve communication among those stakeholders, but the potential value exceeds communication alone. The causal diagrams are formulated as directed acyclic graphs (DAGs) to function as a type of knowledge graph for reference for the board and its stakeholders. This document is a sister document to NASA/TM 20220006812 Directed Acyclic Graph Guidance Documentation (1). In that document, the basic guidance for creating and standardizing directed acyclic graphs as tools for cross-risk analysis is provided. This document contains the initial configuration managed DAGs that were created as a result of applying those principles. These initial versions were accepted by the HSRB in January of 2022. Each of the Human System Risks are represented by a DAG that has been reviewed by the larger Human Health and Performance community at NASA including life scientists, physical scientists, physicians, nurses, pharmacists, exercise specialists and more. These results show the starting point for Human System Risk DAGs as shared mental models and communication aids across the boundaries of the various expertise needed to understand and mitigate the human risks in spaceflight. Because they are a starting point, each of these DAGs can be expected to change over time as new or refined evidence becomes available. The process for updating these DAGs can be found in the JSC-66705 Human System Risk Management Plan (2) that is publicly available on the NASA Technical Reports Server.

Erik L. Antonsen↗

An algorithm for automatic reduction of complex signal flow graphs

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

Young, K. R.↗

A formal definition of data flow graph models

In this paper, a new model for parallel computations and parallel computer systems that is based on data flow principles is presented. Uninterpreted data flow graphs can be used to model computer systems including data driven and parallel processors. A data flow graph is defined to be a bipartite graph with actors and links as the two vertex classes. Actors can be considered similar to transitions in Petri nets, and links similar to places. The nondeterministic nature of uninterpreted data flow graphs necessitates the derivation of liveness conditions.

Kavi, Krishna M.↗

A user-friendly, menu-driven, language-free laser characteristics curves graphing program for desk-top IBM PC compatible computers

A facility was established that uses collected data and feeds it into mathematical models that generate improved data arrays by correcting for various losses, base line drift, and conversion to unity scaling. These developed data arrays have headers and other identifying information affixed and are subsequently stored in a Laser Materials and Characteristics data base which is accessible to various users. The two part data base: absorption - emission spectra and tabulated data, is developed around twelve laser models. The tabulated section of the data base is divided into several parts: crystalline, optical, mechanical, and thermal properties; aborption and emission spectra information; chemical name and formulas; and miscellaneous. A menu-driven, language-free graphing program will reduce and/or remove the requirement that users become competent FORTRAN programmers and the concomitant requirement that they also spend several days to a few weeks becoming conversant with the GEOGRAF library and sequence of calls and the continual refreshers of both. The work included becoming thoroughly conversant with or at least very familiar with GEOGRAF by GEOCOMP Corp. The development of the graphing program involved trial runs of the various callable library routines on dummy data in order to become familiar with actual implementation and sequencing. This was followed by trial runs with actual data base files and some additional data from current research that was not in the data base but currently needed graphs. After successful runs, with dummy and real data, using actual FORTRAN instructions steps were undertaken to develop the menu-driven language-free implementation of a program which would require the user only know how to use microcomputers. The user would simply be responding to items displayed on the video screen. To assist the user in arriving at the optimum values needed for a specific graph, a paper, and pencil check list was made available to use on the trial runs.

Klutz, Glenn↗

Decision net, directed graph, and neural net processing of imaging spectrometer data

A decision-net solution involving a novel hierarchical classifier and a set of multiple directed graphs, as well as a neural-net solution, are respectively presented for large-class problem and mixture problem treatments of imaging spectrometer data. The clustering method for hierarchical classifier design, when used with multiple directed graphs, yields an efficient decision net. New directed-graph rules for reducing local maxima as well as the number of perturbations required, and the new starting-node rules for extending the reachability and reducing the search time of the graphs, are noted to yield superior results, as indicated by an illustrative 500-class imaging spectrometer problem.

Casasent, David↗

A user-friendly menu-driven language-free laser characteristics curves graphing program

In the selection of laser materials to be used as active sensors, it is essential to know how various factors of the specific material composition interact. Questions such as how does the rod size and frequency or absorption relate and how might this be affected by temperature variations must be answered before the materials are selected. A menu-driven language-free program was developed that would graph the interrelationship of many physical parameters of laser materials. This program reduced or removed the requirement that all users be competent in FORTRAN. A menu-driven language-free program was then developed that requires the use of a microcomputer to graph a two-dimensional display of data. The ability to graph more than one graph-line on the same chart was accomplished. The program is now generic in that it will take any data file whether in the data base or not. The program generates the format for the data read statement if it is not contained in the file header and the user does not know how to write them.

Klutz, Glenn↗

A VLSI decomposition of the deBruijn graph

The nth order deBruijn graph Bn is the state diagram for an n-stage binary shift register. It is a directed graph with 2 to the n vertices, each labeled with an n-bit binary string, and 2 to the n+1 edges, each labeled with an (n+1)-bit binary string. It is shown that Bn can be built by appropriately connecting together with extra edges many isomorphic copies of a fixed graph, which is called a building block for Bn. The efficiency of such a building block is refined as the fraction of the edges of Bn which are present in the copies of the building block. It is then shown that for any alpha less than 1, there exists a graph which is a building block for Bn of efficiency greater than alpha for all sufficiently large n. The results are illustrated by showing how a special hierarchical family of building blocks has been used to construct a very large Viterbi decoder which will be used on the Galileo mission.

Collins, Oliver↗

A componential model of human interaction with graphs: 1. Linear regression modeling

Task analyses served as the basis for developing the Mixed Arithmetic-Perceptual (MA-P) model, which proposes (1) that people interacting with common graphs to answer common questions apply a set of component processes-searching for indicators, encoding the value of indicators, performing arithmetic operations on the values, making spatial comparisons among indicators, and repsonding; and (2) that the type of graph and user's task determine the combination and order of the components applied (i.e., the processing steps). Two experiments investigated the prediction that response time will be linearly related to the number of processing steps according to the MA-P model. Subjects used line graphs, scatter plots, and stacked bar graphs to answer comparison questions and questions requiring arithmetic calculations. A one-parameter version of the model (with equal weights for all components) and a two-parameter version (with different weights for arithmetic and nonarithmetic processes) accounted for 76%-85% of individual subjects' variance in response time and 61%-68% of the variance taken across all subjects. The discussion addresses possible modifications in the MA-P model, alternative models, and design implications from the MA-P model.

Gillan, Douglas J.↗

Scale-free Graphs for General Aviation Flight Schedules

In the late 1990s a number of researchers noticed that networks in biology, sociology, and telecommunications exhibited similar characteristics unlike standard random networks. In particular, they found that the cummulative degree distributions of these graphs followed a power law rather than a binomial distribution and that their clustering coefficients tended to a nonzero constant as the number of nodes, n, became large rather than O(1/n). Moreover, these networks shared an important property with traditional random graphs as n becomes large the average shortest path length scales with log n. This latter property has been coined the small-world property. When taken together these three properties small-world, power law, and constant clustering coefficient describe what are now most commonly referred to as scale-free networks. Since 1997 at least six books and over 400 articles have been written about scale-free networks. In this manuscript an overview of the salient characteristics of scale-free networks. Computational experience will be provided for two mechanisms that grow (dynamic) scale-free graphs. Additional computational experience will be given for constructing (static) scale-free graphs via a tabu search optimization approach. Finally, a discussion of potential applications to general aviation networks is given.

Alexandov, Natalia M.↗

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↗

International Space Station Centrifuge Rotor Models A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

The assembly and operation of the International Space Station (ISS) require extensive testing and engineering analysis to verify that the Space Station system of systems would work together without any adverse interactions. Since the dynamic behavior of an entire Space Station cannot be tested on earth, math models of the Space Station structures and mechanical systems have to be built and integrated in computer simulations and analysis tools to analyze and predict what will happen in space. The ISS Centrifuge Rotor (CR) is one of many mechanical systems that need to be modeled and analyzed to verify the ISS integrated system performance on-orbit. This study investigates using Bond Graph modeling techniques as quick and simplified ways to generate models of the ISS Centrifuge Rotor. This paper outlines the steps used to generate simple and more complex models of the CR using Bond Graph Computer Aided Modeling Program with Graphical Input (CAMP-G). Comparisons of the Bond Graph CR models with those derived from Euler-Lagrange equations in MATLAB and those developed using multibody dynamic simulation at the National Aeronautics and Space Administration (NASA) Johnson Space Center (JSC) are presented to demonstrate the usefulness of the Bond Graph modeling approach for aeronautics and space applications.

Nguyen, Louis H.↗

Graph-Based Path-Planning for Titan Balloons

A document describes a graph-based path-planning algorithm for balloons with vertical control authority and little or no horizontal control authority. The balloons are designed to explore celestial bodies with atmospheres, such as Titan, a moon of Saturn. The algorithm discussed enables the balloon to achieve horizontal motion using the local horizontal winds. The approach is novel because it enables the balloons to use arbitrary wind field models. This is in contrast to prior approaches that used highly simplified wind field models, such as linear, or binary, winds. This new approach works by discretizing the space in which the balloon operates, and representing the possible states of the balloon as a graph whose arcs represent the time taken to move from one node to another. The approach works with arbitrary wind fields, by looking up the wind strength and direction at every node in the graph from an arbitrary wind model. Having generated the graph, search techniques such as Dijkstra s algorithm are then used to find the set of vertical actuation commands that takes the balloon from the start to the goal in minimum time. In addition, the set of reachable locations on the moon or planet can be determined.

Blackmore, Lars James↗

Contact Graph Routing

Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic. The information carried by CGR contact plan messages is useful not only for dynamic route computation, but also for the implementation of rate control, congestion forecasting, transmission episode initiation and termination, timeout interval computation, and retransmission timer suspension and resumption.

Burleigh, Scott C.↗

Building Scalable Knowledge Graphs for Earth Science

Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.

Ramachandran, Rahul↗