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At least 181 records · Page 10

Graph-Based Dynamic Assignment Of Multiple Processors

Algorithm-to-architecture mapping model (ATAMM) is strategy minimizing time needed to periodically execute graphically described, data-driven application algorithm on multiple data processors. Implemented as operating system managing flow of data and dynamically assigns nodes of graph to processors. Predicts throughput versus number of processors available to execute given application algorithm. Includes rules ensuring application algorithm represented by graph executed periodically without deadlock and in shortest possible repetition time. ATAMM proves useful in maximizing effectiveness of parallel computing systems.

Hayes, Paul J.↗

Benchmarking the PCMCI Causal Discovery Algorithm for Spatiotemporal Systems

Causal discovery algorithms construct hypothesized causal graphs that depict causal dependencies among variables in observational data. While powerful, the accuracy of these algorithms is highly sensitive to the underlying dynamics of the system in ways that have not been fully characterized in the literature. In this report, we benchmark the PCMCI causal discovery algorithm in its application to gridded spatiotemporal systems. Effectively computing grid-level causal graphs on large grids will enable analysis of the causal impacts of transient and mobile spatial phenomena in large systems, such as the Earth’s climate. We evaluate the performance of PCMCI with a set of structural causal models, using simulated spatial vector autoregressive processes in one- and two-dimensions. We develop computational and analytical tools for characterizing these processes and their associated causal graphs. Our findings suggest that direct application of PCMCI is not suitable for the analysis of dynamical spatiotemporal gridded systems, such as climatological data, without significant preprocessing and downscaling of the data. PCMCI requires unrealistic sample sizes to achieve acceptable performance on even modestly sized problems and suffers from a notable curse of dimensionality. This work suggests that, even under generous structural assumptions, significant additional algorithmic improvements are needed before causal discovery algorithms can be reliably applied to grid-level outputs of earth system models.

54 ENVIRONMENTAL SCIENCES↗

Power and Efficiency Optimized in Traveling-Wave Tubes Over a Broad Frequency Bandwidth

A traveling-wave tube (TWT) is an electron beam device that is used to amplify electromagnetic communication waves at radio and microwave frequencies. TWT's are critical components in deep space probes, communication satellites, and high-power radar systems. Power conversion efficiency is of paramount importance for TWT's employed in deep space probes and communication satellites. A previous effort was very successful in increasing efficiency and power at a single frequency (ref. 1). Such an algorithm is sufficient for narrow bandwidth designs, but for optimal designs in applications that require high radiofrequency power over a wide bandwidth, such as high-density communications or high-resolution radar, the variation of the circuit response with respect to frequency must be considered. This work at the NASA Glenn Research Center is the first to develop techniques for optimizing TWT efficiency and output power over a broad frequency bandwidth (ref. 2). The techniques are based on simulated annealing, which has the advantage over conventional optimization techniques in that it enables the best possible solution to be obtained (ref. 3). Two new broadband simulated annealing algorithms were developed that optimize (1) minimum saturated power efficiency over a frequency bandwidth and (2) simultaneous bandwidth and minimum power efficiency over the frequency band with constant input power. The algorithms were incorporated into the NASA coupled-cavity TWT computer model (ref. 4) and used to design optimal phase velocity tapers using the 59- to 64-GHz Hughes 961HA coupled-cavity TWT as a baseline model. In comparison to the baseline design, the computational results of the first broad-band design algorithm show an improvement of 73.9 percent in minimum saturated efficiency (see the top graph). The second broadband design algorithm (see the bottom graph) improves minimum radiofrequency efficiency with constant input power drive by a factor of 2.7 at the high band edge (64 GHz) and increases simultaneous bandwidth by 500 MHz.

Wilson, Jeffrey D.↗

A Scale‐Adaptive Urban Hydrologic Framework: Incorporating Network‐Level Storm Drainage Pipes Representation

Abstract Below‐ground urban stormwater networks (BUSNs) significantly influence urban flood dynamics, yet their representation at the watershed or larger scales remains challenging. We introduce a scalable urban hydrologic framework that centers on a novel network‐level BUSN representation, balancing the needs for physical basis, parameter parsimony, and computational efficiency. Our framework conceptualizes an urban watershed into four interacting zones: hillslopes (natural), storm‐sewersheds (urban), a sub‐network channel (tributaries), and a main channel. We develop an innovative Graph Theory‐based algorithm to derive network‐level BUSN parameters from publicly available datasets, enabling efficient, scalable parameterization. We demonstrate this framework's applicability at nine representative watersheds in the Houston metropolitan region, USA, with urban imperviousness ranging from 0% to 64% and drainage areas ranging from 24 to 302 . Our model achieves satisfying computational efficiency, completing hourly time step simulations for 18 years in less than 5 sec per watershed on a standard PC. Validation against observed daily streamflow confirms that the model can capture small‐to‐large flood peaks and seasonal and annual water balance over these watersheds. Comparisons with the National Water Model show better performance in predicting flood peaks and overall water balance, underscoring the promises of our new framework for urban hydrologic modeling at large scales. Furthermore, analysis reveals nonlinear relationships between BUSNs' designed capacities and flood reduction effects. Our approach bridges the gap between detailed hydraulic and large‐scale hydrologic models, providing a valuable tool for urban flood prediction and management across broader spatial and temporal scales.

54 ENVIRONMENTAL SCIENCES↗

Representation and display of vector field topology in fluid flow data sets

The visualization of physical processes in general and of vector fields in particular is discussed. An approach to visualizing flow topology that is based on the physics and mathematics underlying the physical phenomenon is presented. It involves determining critical points in the flow where the velocity vector vanishes. The critical points, connected by principal lines or planes, determine the topology of the flow. The complexity of the data is reduced without sacrificing the quantitative nature of the data set. By reducing the original vector field to a set of critical points and their connections, a representation of the topology of a two-dimensional vector field that is much smaller than the original data set but retains with full precision the information pertinent to the flow topology is obtained. This representation can be displayed as a set of points and tangent curves or as a graph. Analysis (including algorithms), display, interaction, and implementation aspects are discussed.

Helman, James↗

Obtaining schedules for digital systems

A systematic technique is presented to derive correct schedules for a synchronous digital system, given a signal flow graph for an algorithm. It is also shown how to use this technique to derive designs that are optimal in having the lowest latency, the highest throughput, or the smallest number of registers. The same technique can also be used to verify digital systems that have already been designed.

Jagadish, H. V.↗

Operations for Learning with Graphical Models

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian net- works, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. These operations adapt existing techniques from statistics and automatic differentiation to graphs. Two standard algorithm schemes for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Some algorithms are developed in this graphical framework including a generalized version of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing some popular algorithms that fall within the framework presented. The main original contributions here are the decomposition techniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.

Buntine, Wray L.↗

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↗

Rare Higgs Processes at CMS and Precision Timing Detector Studies for HL-LHC CMS Upgrade

This thesis describes the search for two rare Higgs processes. The first analysis describes the CMS Run 2 search for $H$ $\rightarrow$ $\mu$$\mu$ decays, with 137.3 fb$^{-1}$ of data at $\sqrt{s}$ = 13 TeV. The analysis targeted four different Higgs production modes: the gluon fusion (ggH), the vector boson fusion (VBF), the Higgs-strahlung process (VH), and the production in association with a pair of top quarks (ttH). Each category used a dedicated machine learning based classifier to separate the signal from the background processes. A combined fit from all these categories saw a slight excess in the data corresponding to 3.0 standard deviations at $M$$_{H}$ = 125.38 GeV, and gave the first evidence for the Higgs boson decay to second-generation fermions. The best-fit signal strength and the corresponding 68% CL interval was found to be +0.17?????? = 1.19 $_{-0.39}^{+0.41}$ (stat)$_{-0.16}^{+0.17}$(syst) at $M$$_{H}$ = 125.38 GeV. The second analysis describes the CMS Run 2 search for 𝐻𝐻 → 𝑏𝑏𝑏𝑏 with highly boosted Higgs bosons. This analysis used a dedicated jet identification algorithm based on graph neural networks (ParticleNet) to identify boosted H→ bb jets. This search targeted the gluon fusion and the vector boson fusion HH production modes, and put constraints on the allowed values of the various Higgs couplings as: 𝜅𝜆 ∈ [−9.9, 16.9] when 𝜅𝑉 = 1, 𝜅2𝑉 = 1; 𝜅𝑉 ∈ [−1.17, −0.79] ∪ [0.81, 1.18] when 𝜅𝜆 = 1, 𝜅2𝑉 = 1; 𝜅2𝑉 ∈ [0.62, 1.41] when 𝜅𝜆 = 1, 𝜅𝑉 = 1. A scenario with 𝜅2𝑉 = 0 was excluded with a significance of 6.3 standard deviations for the first time, when other H couplings are fixed to their SM values. The combined observed (expected) 95% upper limit on the HH production cross section was found to be 9.9 (5.1) × SM. Finally, this thesis also discusses the planned MIP Timing Detector (MTD) upgrade for CMS at the HL-LHC. The MTD will be a time-of-flight (TOF) detector, designed to provide a precision timing information for charged particles using SiPMs + LYSO scintillating crystals, with a time resolution of ∼30 ps. This thesis describes several R&D tests that have been performed for characterizing the sensor properties (time resolution, light yield, etc.) and optimizing the sensor design geometry. This thesis also contains a description of mock test setups for cooling the sensors, since it is known to be an effective way of mitigating the increased dark current rates in the sensors due to radiation damage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Strategies for concurrent processing of complex algorithms in data driven architectures

The performance modeling and enhancement for periodic execution of large-grain, decision-free algorithms in data flow architectures is examined. Applications include real-time implementation of control and signal processing algorithms where performance is required to be highly predictable. The mapping of algorithms onto the specified class of data flow architectures is realized by a marked graph model called ATAMM (Algorithm To Architecture Mapping Model). Performance measures and bounds are established. Algorithm transformation techniques are identified for performance enhancement and reduction of resource (computing element) requirements. A systematic design procedure is described for generating operating conditions for predictable performance both with and without resource constraints. An ATAMM simulator is used to test and validate the performance prediction by the design procedure. Experiments on a three resource testbed provide verification of the ATAMM model and the design procedure.

Stoughton, John W.↗

Graph-Based Representations and Applications to Process Simulation

Rapid and robust convergence of a process flowsheet is critical to enable large-scale simulations that address core scientific questions related to process design, optimization, and sustainability. However, due to the highly coupled and nonlinear nature of chemical processes, efficiently solving a flowsheet remains a challenge. In this work, we show that graph representations of the underlying physical phenomena in unit operations may help identify potential avenues to systematically reformulate the network of equations and enable more robust topology-based convergence of flowsheets. To this end, we developed graph abstractions of the governing equations of vapor-liquid and liquid-liquid equilibrium separation equipment. These graph abstractions consist of a mesh of interconnected variable nodes and equation nodes that are systematically generated through PhenomeNode, a new open-source library in Python developed in this study. We show that partitioning the graph into separate mass, energy, and equilibrium subgraphs can help decouple nonlinearities and guide decomposition algorithms. By employing the graph abstraction on an industrial separation process for separating glacial acetic acid from water, we implemented a new block decomposition scheme in BioSTEAM and demonstrated that this can accelerate convergence over a traditional sequential modular approach.

Distillation↗

A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs).

Forestano, Roy T. (ORCID:0000000203552076)↗

Explaining Missing Data in Graphs: A Constraint-based Approach

Abstract: This paper introduces a constraint-based approach to clarify missing values in graphs. Our method capitalizes on a set S of graph data constraints. An explanation is a sequence of operational enforcement of S towards the recovery of interested yet missing data (e.g., attribute values, edges). We show that constraint-based approach helps us to understand not only why a value is missing, but also how to recover the missing value. We study S-explanation problem, which is to compute the optimal explanations with guarantees on the informativeness and conciseness. We show the problem is in ?P^2 for established graph data constraints such as graph keys and graph association rules. We develop an efficient bidirectional algorithm to compute optimal explanations, without enforcing S on the entire graph. We also show our algorithm can be easily extended to support graph refinement within limited time, and to explain missing answers. Using real-world graphs, we experimentally verify the effectiveness and efficiency of our algorithms.

Data Analytics↗

Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.

asynchronous↗

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↗

Code for Value Decomposition Graph Network and environment for AMR on linear advection

This is the code for the paper [Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement](https://arxiv.org/abs/2211.00801), published at AAMAS 2023. It contains the implementation of a new algorithm, called Value Decomposition Graph Network (VDGN), for applying multi-agent reinforcement learning to the problem of adaptive mesh refinement (AMR). It also contains the implementation of a multi-agent environment for AMR on a linear advection problem. VDGN is the first learning algorithm to display anticipatory refinement behavior in AMR, and it outperforms local error threshold-based heuristic strategies.

Yang, Jiachen↗

Matching Complexes of Trees and Applications of the Matching Tree Algorithm

A matching complex of a simple graph G is a simplicial complex with faces given by the matchings of G. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that matching complexes of forests are contractible or homotopy equivalent to a wedge of spheres. We study two specific families of trees. For caterpillar graphs, we give explicit formulas for the number of spheres in each dimension and for perfect binary trees we find a strict connectivity bound. We also use a tool from discrete Morse theory called the Matching Tree Algorithm to study the connectivity of honeycomb graphs, partially answering a question raised by Jonsson.

97 MATHEMATICS AND COMPUTING↗