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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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At least 487 records · Page 27

A weak zero-one law for sequences of random distance graphs

We study zero-one laws for properties of random distance graphs. Properties written in a first-order language are considered. For p(N) such that pN{sup {alpha}}{yields}{infinity} as N{yields}{infinity}, and (1-p)N{sup {alpha}} {yields} {infinity} as N {yields} {infinity} for any {alpha}>0, we succeed in refuting the law. In this connection, we consider a weak zero-one j-law. For this law, we obtain results for random distance graphs which are similar to the assertions concerning the classical zero-one law for random graphs. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗

Subdominant pseudoultrametric on graphs

Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.

97 MATHEMATICS AND COMPUTING↗

A mass graph-based approach for the identification of modified proteoforms using top-down tandem mass spectra

Motivation: Although proteomics has rapidly developed in the past decade, researchers are still in the early stage of exploring the world of complex proteoforms, which are protein products with various primary structure alterations resulting from gene mutations, alternative splicing, post-translational modifications, and other biological processes. Proteoform identification is essential to mapping proteoforms to their biological functions as well as discovering novel proteoforms and new protein functions. Top-down mass spectrometry is the method of choice for identifying complex proteoforms because it provides a “bird’s eye view” of intact proteoforms. The combinatorial explosion of various alterations on a protein may result in billions of possible proteoforms, making proteoform identification a challenging computational problem. Results: We propose a new data structure, called the mass graph, for efficient representation of proteoforms and design mass graph alignment algorithms. We developed TopMG, a mass graph-based software tool for proteoform identification by top-down mass spectrometry. Experiments on top-down mass spectrometry data sets showed that TopMG outperformed existing methods in identifying complex proteoforms.

Dynamic Programming↗

An finite element analysis surrogate model with boundary oriented graph embedding approach for rapid design

Abstract In this work, we present a boundary oriented graph embedding (BOGE) approach for the graph neural network to assist in rapid design and digital prototyping. The cantilever beam problem has been solved as an example to validate its potential of providing physical field results and optimized designs using only 10 ms. Providing shortcuts for both boundary elements and local neighbor elements, the BOGE approach can embed unstructured mesh elements into the graph and performs an efficient regression on large-scale triangular-mesh-based finite element analysis (FEA) results, which cannot be realized by other machine-learning-based surrogate methods. It has the potential to serve as a surrogate model for other boundary value problems. Focusing on the cantilever beam problem, the BOGE approach with 3-layer DeepGCN model achieves the regression with mean square error (MSE) of 0.011 706 (2.41% mean absolute percentage error) for stress field prediction and 0.002 735 MSE (with 1.58% elements having error larger than 0.01) for topological optimization. The overall concept of the BOGE approach paves the way for a general and efficient deep-learning-based FEA simulator that will benefit both industry and Computer Aided Design (CAD) design-related areas.

42 ENGINEERING↗

Graphical rule of transforming continuous-variable graph states by local homodyne detection

Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules--local complement operation and vertex deletion (single quadrature-amplitude x measurement)--the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum snake walk on graphs

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Searches on star graphs and equivalent oracle problems

We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we wish to find. We examine the case in which the unmarked vertices can be of different types, so the background against which the search is done is not uniform. We find that the search can still be successful, but the probability of success is lower than in the uniform background case, and that probability decreases with the number of types of unmarked vertices. We also show how the graph searches can be rephrased as equivalent oracle problems.

97 MATHEMATICS AND COMPUTING↗

Optimal preparation of graph states

We show how to prepare any graph state of up to 12 qubits with (a) the minimum number of controlled-Z gates and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any graph state belongs to an equivalence class under local Clifford operations. We extend up to 12 qubits the classification of graph states according to their entanglement properties, and identify each class using only a reduced set of invariants. For any state, we provide a circuit with both properties (a) and (b), if it does exist, or, if it does not, one circuit with property (a) and one with property (b), including the explicit one-qubit gates needed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum-information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum graph models for transport in filamentary switching

The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices the behavior of which is closely tied to the properties of the filament. Until recently, experimental investigation of the low-temperature regime and quantum transport effects has been limited. However, with growing interest in understanding the true impacts of the filament on device conductance, comprehending quantum effects has become crucial for quantum neuromorphic hardware. Here, we discuss quantum transport resulting from filamentary switching in a narrow region where the continuous approximation of the contact is not valid, and only a few atoms are involved. In this scenario, the filament can be represented by a graph depicting the adjacency of atoms and the overlap between atomic orbitals. Using the theory of quantum graphs with locally diffusive node scattering, we calculate the scattering amplitude of charge carriers on this graph and explore the interplay between filamentary formation and quantum transport effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions

Here, we present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We also derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. We obtain accurate estimates of first passage times with an order of magnitude reduction of CPU time and mesh size using the proposed method.

54 ENVIRONMENTAL SCIENCES↗

Deformation pathway and defect generation in crystals: a combined group theory and graph theory description

The generation and motion of crystalline defects during plastic deformation are critical processes that determine the mechanical properties of a crystal. The types of defect generated are not only related to the symmetry of a crystal but also associated with the symmetry-breaking process during deformation. Proposed here is a new mathematical framework to capture the intrinsic coupling between crystal symmetry and deformation-induced symmetry breaking. Using a combination of group theory and graph theory, a general approach is demonstrated for the systematic determination of the types of crystalline defect induced by plastic deformation, through the construction of a crystal deformation group and a deformation pathway graph. The types of defect generated in the deformation of a face-centered cubic crystal are analyzed through the deformation pathway graph and compared with experimental observations.

36 MATERIALS SCIENCE↗

Graph-Based Prediction of Spatio-Temporal Vaccine Hesitancy From Insurance Claims Data

Growing vaccine hesitancy is contributing to the decline in immunization rates for highly contagious, vaccine-preventable childhood diseases. Therefore, there has been a significant interest in understanding how hesitancy is spreading at higher spatio-temporal resolutions, enabling more targeted interventions. Motivated by this, we study the problem of prediction of vaccine hesitancy at the ZIP Code level, referred to as the VaxHesitancy problem. A significant challenge for this problem is the lack of high-resolution data that indicates hesitancy. Here, we develop a hybrid VaxHesSTL framework that combines a Graph Neural Network (GNN) and a Recurrent Neural Network (RNN) to address the VaxHesitancy problem. The GNN uses a ZIP Code-level network to capture spatial signals from neighboring areas, while the RNN models the temporal dynamics present in the data. We train and evaluate VaxHesSTL using a large dataset, namely the All-Payer Claims Databases (APCD), for Virginia, consisting of insurance claims from over five million individuals for six years. We find that an aggregated contact network or graph, developed from a detailed activity-based population network, plays an important role in the performance of VaxHesSTL, compared to graph models based solely on spatial proximity. Experiments demonstrate that VaxHesSTL outperforms a range of state-of-the-art baselines, which rely solely on historical time series data without accounting for spatial relationships. Since hesitancy data at higher spatial resolution is often unavailable or hard to get, we incorporate an active learning approach with our VaxHesSTL framework to optimize the training set without compromising the prediction performance. We find that hesitancy data for only 18% of ZIP Codes selected by active learning allows us to forecast hesitancy for all the ZIP Codes in the Virginia.

60 APPLIED LIFE SCIENCES↗

Graph Analytics on Jellyfish topology

Because large unstructured datasets is important for many science domains, distributed graph analytics is critical to many scientists. Unfortunately, obtaining scaling and performance for irregular communication is challenging because contemporary network interconnects are primarily designed to maximize bandwidths of fixed-neighborhoods large-message exchanges (e.g., stencils). Although there is no consensus on the “best” network topologies for irregular communication, unstructured graph-based interconnects can be more suitable. We analyze three popular graph workloads – clustering, pattern enumeration, and traversal — on comparable networks (in terms of resources and costs) constructed from Jellyfish Random Regular, Dragonfly and Fat tree topologies, varying the routing algorithms. Using packet-level simulations, we demonstrate up to 60% improvement in communication time with Jellyfish due to diversity of the short paths between arbitrary endpoints, which can reduce overall network stalls and congestion.

Graph Analytics, network topology, interconnect, H↗

1-D Convolutional Graph Convolutional Networks for Fault Detection in Distributed Energy Systems

This paper presents a 1-D convolutional and graph convolutional networks for fault detection in microgrids. The combination of 1-D convolutional neural networks (1D-CNN) and graph convolutional networks (GCN) helps extract both spatial-temporal correlations from the voltage measurements in microgrids. The fault detection scheme includes fault event detection, fault type and phase classification, and fault location. There are five neural network model training to handle these tasks. Transfer learning and fine-tuning are applied to reduce training efforts. The combined 1-D convolutional and graph convolutional networks (1D-CGCN) is compared with the traditional ANN structure on the Potsdam 13-bus microgrid dataset. The accuracy of 99.5%, 98.4%, 99.2%, and 95.5% are achieved in fault event detection, fault type classification, fault phase identification, and fault location respectively. The detailed confusion matrices of fault type and fault phase classification are provided for validation.

deep neural network↗

A Transductive Graph Neural Network learning for Grid Resilience Analysis

Power grids are critical infrastructures that require robust resilience analysis to ensure reliable and uninterrupted electricity supply. Traditional simulation-based methods for grid resilience analysis suffer from computational complexity and limited ability to capture the full spectrum of potential disruptions. This paper presents a novel approach to enhance grid resilience by leveraging transductive graph neural network (GNN) learning to identify critical nodes and links. By leveraging the graph structure and system features, GNNs effectively learn resilience metrics and accurately identify critical nodes based on actual grid operational behavior. The efficacy of the proposed approach is demonstrated through case studies on node criticality scoring and critical node/line identification in cascading outage scenarios. The results highlight the advantages of learning-based methods over traditional simulation-based approaches and their potential to revolutionize grid resilience analysis. The contributions of this paper include a graph-based scalable approach for fast cascading analysis, an inductive formulation for training GNN models, and a transfer learning-based approach to scale the model to largescale power systems.

grid resilience, graph neural networks, transducti↗

Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting path is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.

97 MATHEMATICS AND COMPUTING↗

Algorithms for Balanced Graph Colorings with Applications in Parallel Computing

Graph coloring is used to identify subsets of independent tasks in parallel scientific computing applications. Traditional coloring heuristics aim to reduce the number of colors used as that number also corresponds to the number of parallel steps in the application. However, if the color classes produced have a skew in their sizes, utilization of hardware resources becomes inefficient, especially for the smaller color classes. Equitable coloring is a theoretical formulation of coloring that guarantees a perfect balance among color classes, and its practical relaxation is referred to as balanced coloring. In this paper, we revisit the problem of balanced coloring in the context of parallel computing. The goal is to achieve a balanced coloring of an input graph without increasing the number of colors that an algorithm oblivious to balance would have used. We propose and study multiple heuristics that aim to achieve such a balanced coloring for two variants of coloring problem, distance-1 coloring and partial distance-2 coloring (defined on a bipartite graph). We present parallelization approaches for multi-core and manycore architectures, and cross-evaluate their effectiveness with respect to the quality of balance achieved and performance. Furthermore, we study the impact of the proposed balanced coloring heuristics on a concrete application - viz. parallel community detection, which is an example of an irregular application. In addition, we propose several extensions to our balancing schemes and evaluate their balancing efficacy and performance characteristics. The thorough treatment of balanced coloring presented in this paper from algorithms to application is expected to serve as a valuable resource to parallel application developers who seek to improve parallel performance of their applications using coloring.

graph coloring, multithreaded algorithms↗