Random Graphs and Probability Models
Preliminary results concerning random graphs, digraphs, time dependent processes, and probability models
Bhargava, T. N.↗
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Results for “random graphs”
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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On certain information-theoretic concepts in the theory of graphs
Information-theoretic concepts in theory of random graphs - entropy functions for probability distributions and Markov chains
ENTROPY↗
Quantum Adiabatic Optimization and Combinatorial Landscapes
In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.
Smelyanskiy, V. N.↗
Experience with parametric binary dissection
Parametric Binary Dissection (PBD) is a new algorithm that can be used for partitioning graphs embedded in 2- or 3-dimensional space. It partitions explicitly on the basis of nodes + (lambda)x(edges cut), where lambda is the ratio of time to communicate over an edge to the time to compute at a node. The new algorithm is faster than the original binary dissection algorithm and attempts to obtain better partitions than the older algorithm, which only takes nodes into account. The performance of parametric dissection with plain binary dissection on 3 large unstructured 3-d meshes obtained from computational fluid dynamics and on 2 random graphs were compared. It was showm that the new algorithm can usually yield partitions that are substantially superior, but that its performance is heavily dependent on the input data.
Bokhari, Shahid H.↗
Evaluation of Opportunistic Contact Graph Routing in Random Mobility Environments
Routing in networks where nodes move randomly is particularly challenging due their potentially unpredictable, and rapidly changing topology. Several routing algorithms have been presented in the literature to address the needs of such networks, most of them implementing variants of controlled network flooding in the hope of successful data delivery. In this note, we compare the results of previous routing algorithms with Opportunistic Contact Graph Routing (OCGR), an enhanced version of Contact Graph Routing (CGR) that is suitable for networks where contacts cannot always be scheduled ahead of time. To perform the benchmark, we simulate a network of nodes moving in a certain space according to the Random Waypoint Mobility Model, and then take measurements of bundle delivery probabilty and overhead ratio as metrics of performance and cost respectively. Through this exercise, we demonstrate that the performance of OCGR is highly dependent on the type of network under consideration (e.g. very sparse vs. densely connected) and the assumed mobility model.
Burleigh, Scott↗
Evaluation of Opportunistic Contact Graph Routing in Random Mobility Environments
UNKNOWN
Burleigh, Scott↗
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.↗
JavaGenes and Condor: Cycle-Scavenging Genetic Algorithms
A genetic algorithm code, JavaGenes, was written in Java and used to evolve pharmaceutical drug molecules and digital circuits. JavaGenes was run under the Condor cycle-scavenging batch system managing 100-170 desktop SGI workstations. Genetic algorithms mimic biological evolution by evolving solutions to problems using crossover and mutation. While most genetic algorithms evolve strings or trees, JavaGenes evolves graphs representing (currently) molecules and circuits. Java was chosen as the implementation language because the genetic algorithm requires random splitting and recombining of graphs, a complex data structure manipulation with ample opportunities for memory leaks, loose pointers, out-of-bound indices, and other hard to find bugs. Java garbage-collection memory management, lack of pointer arithmetic, and array-bounds index checking prevents these bugs from occurring, substantially reducing development time. While a run-time performance penalty must be paid, the only unacceptable performance we encountered was using standard Java serialization to checkpoint and restart the code. This was fixed by a two-day implementation of custom checkpointing. JavaGenes is minimally integrated with Condor; in other words, JavaGenes must do its own checkpointing and I/O redirection. A prototype Java-aware version of Condor was developed using standard Java serialization for checkpointing. For the prototype to be useful, standard Java serialization must be significantly optimized. JavaGenes is approximately 8700 lines of code and a few thousand JavaGenes jobs have been run. Most jobs ran for a few days. Results include proof that genetic algorithms can evolve directed and undirected graphs, development of a novel crossover operator for graphs, a paper in the journal Nanotechnology, and another paper in preparation.
Globus, Al↗
Improvement of Automated POST Case Success Rate Using Support Vector Machines
During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.
Zwack, Matthew R.↗
Recurrence Rate and Magma Effusion Rate for the Latest Volcanism on Arsia Mons, Mars
Magmatism and volcanism have evolved the Martian lithosphere, surface, and climate throughout the history of Mars. Constraining the rates of magma generation and timing of volcanism on the surface clarifies the ways in which magma and volcanic activity have shaped these Martian systems. The ages of lava flows on other planets are often estimated using impact crater counts, assuming that the number and size-distribution of impact craters per unit area reflect the time the lava flow has been on the surface and exposed to potential impacts. Here we show that impact crater age model uncertainty is reduced by adding stratigraphic information observed at locations where neighboring lavas abut each other, and demonstrate the significance of this reduction in age uncertainty for understanding the history of a volcanic field comprising 29 vents in the 110-kilometer-diameter caldera of Arsia Mons, Mars. Each vent within this caldera produced lava flows several to tens of kilometers in length; these vents are likely among the youngest on Mars, since no impact craters in their lava flows are larger than 1 kilometer in diameter. First, we modeled the age of each vent with impact crater counts performed on their corresponding lava flows and found very large age uncertainties for the ages of individual vents, often spanning the estimated age for the entire volcanic field. The age model derived from impact crater counts alone is broad and unimodal, with estimated peak activity in the field around 130Ma (megaannum, 1 million years). Next we applied our volcano event age model (VEAM), which uses a directed graph of stratigraphic relationships and random sampling of the impact crater age determinations to create alternative age models. Monte Carlo simulation was used to create 10,000 possible vent age sets. The recurrence rate of volcanism is calculated for each possible age set, and these rates are combined to calculate the median recurrence rate of all simulations. Applying this approach to the 29 volcanic vents, volcanism likely began around 200-300Ma then first peaked around 150Ma, with an average production rate of 0.4 vents per Myr (million years). The recurrence rate estimated including stratigraphic data is distinctly bimodal, with a second, lower peak in activity around 100Ma. Volcanism then waned until the final vents were produced 10-90Ma. Based on this model, volume flux is also bimodal, reached a peak rate of 1-8 cubic kilometers per million years by 150Ma and remained above half this rate until about 90Ma, after which the volume flux diminished greatly. The onset of effusive volcanism from 200-150Ma might be due to a transition of volcanic style away from explosive volcanism that emplaced tephra on the western flank of Arsia Mons, while the waning of volcanism after the 150Ma peak might represent a larger-scale diminishing of volcanic activity at Arsia Mons related to the emplacement of flank apron lavas.
Richardson, Jacob A.↗
Network Theory: A Primer and Questions for Air Transportation Systems Applications
A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.
Holmes, Bruce J.↗
Structural dynamics analysis using an unsymmetric block Lanczos algorithm
A method for reducing the order of a dynamical model of a large structure with arbitrary damping is developed analytically and demonstrated. A Lanczos algorithm is described which can reduce square unsymmetric system matrices to block-tridiagonal form, and a procedure for defining the reduced-order model from the right and left Lanczos vectors is outlined. Results for sample problems involving the 8-DOF FEM model of a beam-rotor assembly subjected to random and stepped external forces are presented in extensive graphs and briefly characterized.
Craig, Roy R., Jr.↗
Inference in Directed Acyclic Graphs with Applications to Hidden Markov Model Structures
Graphical techniques for modeling the dependencies of random variables have been explored in a.
Markov Model↗
Graph Representation Learning for Dengue Forecasting
In 2017, the largest recorded dengue outbreak in Sri Lanka’s history occurred. Since then, dengue has continued to threaten national health across Sri Lanka. The development of an effective Early Warning System (EWS) for dengue outbreaks is essential for Sri Lanka’s Ministry of Health to take preventative measures. We propose the use of Graph Neural Networks as EWS. Using earth observational data from NASAs global satellites and dengue incidence data from Sri Lanka s Ministry of Health, we developed a series of traditional and graph representation EWS to forecast Dengue cases across Sri Lanka’s 25 districts between 2013 and 2022. We demonstrate empirically that Graph Neural Networks which incorporate spatiotemporal relations significantly outperform traditional EWS such as Autoregressive Integrated Moving Average (ARIMA), Random Forest, and Long Short-Term Memory (LSTM). Our source code is available on GitHub and will be provided in the final submission.
Graph Neural Networks↗
Flowgraph techniques for closed systems.
Flowgraph techniques for closed systems, discussing properties, approximation method, topology equation, frequency response, constraints, oscillatory and stochastic processes, etc
HARMONIC OSCILLATOR↗
A computer-controlled, on-board data acquisition system for wind-tunnel testing
A computer-controlled data acquisition system has been developed for the 40x80-foot wind tunnel at Ames Research Center. The system, consisting of several small onboard units installed in the model and a data-managing, data-displaying ground station, is capable of sampling up to 256 channels of raw data at a total sample rate of 128,000 samples/sec. Complete signal conditioning is contained within the on-board units. The sampling sequence and channel gain selection is completely random and under total control of the ground station. Outputs include a bar-graph display, digital-to-analog converters, and digital interface to the tunnel's central computer, an SEL 840MP. The system can be run stand-alone or under the control of the SEL 840MP.
Finger, H. J.↗
Identifying Molecules as Biosignatures with Assembly Theory and Mass Spectrometry
The search for evidence of life elsewhere in the universe is hard because it is not obvious what signatures are unique to life. Here we postulate that complex molecules found in high abundance are universal biosignatures as they cannot form by chance. To explore this, we developed the first intrinsic measure of molecular complexity that can be experimentally determined, and this is based upon a new approach called assembly theory which gives the molecular assembly number (MA) of a given molecule. MA allows us to compare the intrinsic complexity of molecules using the minimum number of steps required to construct the molecular graph starting from basic objects, and a probabilistic model shows how the probability of any given molecule forming randomly drops dramatically as its MA increases. To map chemical space, we calculated the MA of ca. 2.5 million compounds, and collected data which showed the complexity of a molecule can be experimentally determined by using three independent techniques including infra-red spectroscopy, nuclear magnetic resonance, and by fragmentation in a mass spectrometer, and this data has an excellent corelation with the values predicted from our assembly theory. We then set out to see if this approach could allow us to identify molecular biosignatures with a set of diverse samples from around the world, outer space, and the laboratory including prebiotic soups. The results show that there is a non-living to living threshold in MA complexity and the higher the MA for a given molecule, the more likely that it had to be produced by a biological process. This work demonstrates it is possible to use this approach to build a life detection instrument that could be deployed on missions to extra-terrestrial locations to detect biosignatures, map the extent of life on Earth, and be used as a molecular complexity scale to quantify the constraints needed to direct prebiotically plausible processes in the laboratory. Such an approach is vital if we are going to find new life elsewhere in the universe or create de-novo life in the lab.
Stuart M Marshall↗
Evaluation of a procedure for the analysis of nonstationary vibroacoustic data
Numerical techniques for the spectral analysis of vibration data from space-vehicle launches are described and demonstrated. A nonstationary product model described by Bendat and Piersol (1986) and its locally stationary version (Silverman, 1957) are applied to Space Shuttle flight data, and the results are presented in extensive graphs. It is shown that the nonstationary model can analyze data from longer sampling periods and thus significantly reduce random error; this in turn leads to vibration spectra lower than those obtained with short-duration models.
Himelblau, Harry↗