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Symbolic method for solving linear equations of flow graphs by multivariate polynomial extension of two-step integer-preserving elimination algorithm
One of the current debates raging in the world of gamma-ray burst physics is whether the sources of these enigmatic bursts arise from a single or from multiple distributions. Several authors contend that the histograms of GRB observables imply the latter. The two most-likely candidate components are galactic and cosmological. For example, some researchers claim that a dip in the V/V max distribution is a result of such a two-component source distribution. Others have used a parameter called the 'burst variability' calculated by dividing the maximum count rate on the 64-msec timescale by that from the 1024-msec timescale to show that a correlation of this parameter with bursts brightness implies a two-component model. This method has met vigorous criticism. We have developed two parameters that measure the variability or structure in the time profiles of BATSE gamma-ray bursts. Both parameters ('structure' and 'spike height') are based on the statistics of 'runs up' and 'runs down.' In short, the structure parameter is the observed number of runs (at several lengths) minus the number expected in a chance distribution. The 'spike height' is the sum of all run heights minus the expected sum. These two are straight-forward to calculate, robust, and measure the variability over the complete profile--not just at the peak. We have applied this algorithm to the profiles of 156 GRB's. In this paper we present graphs of the two parameters as functions of the following: (1) burst duration, (2) burst hardness ratio, (3) V/V max, (4) source galactic longitude, and (5) source galactic latitude. We seek correlations as well as groupings in the data that might indicate a multi-component source distribution.
Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.
A quantitative analysis based on both preemptive and nonpreemptive critical-path scheduling algorithms is presently conducted for the optimal degree of parallelism required in evaluating a given AND tree. The optimal degree of parallelism is found to depend on problem complexity, precedence-graph shape, and task-time distribution along each path. In addition to demonstrating the optimality of the preemptive critical-path scheduling algorithm for evaluating an arbitrary AND tree on a fixed number of processors, the possibility of efficiently ascertaining tight bounds on the number of processors for optimal processor-time efficiency is illustrated.
Satellites are leaving the realms of niche use, extending our day-to-day networked infrastructure to space – thereby forcing a generalization of network architectures. The Delay Tolerant Networking (DTN) protocol is being developed to give rise to this new Solar System Internet. Predominantly, DTNs in space use globally-distributed contact tables to compute routes. In this paper, we propose and analyze a novel optimized approach for route computations that improves upon traditional approaches. As the general DTN will always include some scheduled links, our new algorithm enables greater scalability and practicality of DTN routing. These contact tables include windows when two nodes can communicate and were classically organized into a contact graph, where the vertices represent contact opportunities. Because the complexity of a contact graph grows with the number of contacts, pathfinding on it does not scale. A new structure using multigraphs with the same data is proposed. We show that a multigraph-based approach, which we call contact multigraph routing, exhibits performance superior to routing based on contact graphs, allowing greater scaling to schedule-based routing. In this paper, the multigraph-based algorithm is detailed and a proof is included showing it outperforms the previous algorithm given the same input. Pseudocode is included, as are simulation results. We conclude with suggested future work.
This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.
Graph theoretical cluster technique for producing index terms thesaurus for information retrieval system, discussing algorithms
Two criteria are introduced for the evaluation and selection of assembly plans. The first criterion is to maximize the number of different sequences encompassed by the assembly plan. The second criterion is to maximize the amount of parallelism (i.e., simultaneity) that is possible in the execution of the assembly tasks. While the metrics corresponding to the criteria used in previous work can be expressed as a sum of terms, each being a function of a task or a state, the metrics corresponding to the criteria introduced are more complex functions of the whole assembly plan. An algorithm that performs a heuristic search for the best assembly plan over the AND/OR graph representation of assembly plans introduced in previous work is presented. Admissible heuristics for each of the two criteria are presented.
The authors introduce two criteria for the evaluation and selection of assembly plans. The first criterion is to maximize the number of different sequences in which the assembly tasks can be executed. The second criterion is to minimize the total assembly time through simultaneous execution of assembly tasks. An algorithm that performs a heuristic search for the best assembly plan over the AND/OR graph representation of assembly plans is discussed. Admissible heuristics for each of the two criteria introduced are presented. Some implementation issues that affect the computational efficiency are addressed.
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.
Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and address challenges of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used in the Global Natural Products Social Molecular Networking platform, are a prominent strategy for exploring and visualizing molecular relationships and improving annotation. MNs are mathematical graphs showing the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated with a single molecular identity. Here, this paper introduces “molecular hypernetworks” (MHNs) as more complex MN models able to natively represent multiway relationships among observations. Compared to MNs, MHNs can more parsimoniously represent the inherent complexity present among groups of observations, initially supporting improved exploratory data analysis and visualization. MHNs also promise to increase confidence in annotation propagation, for both human and analytical processing. We first illustrate MHNs with simple examples, and build them from liquid chromatography- and ion mobility spectrometry-separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.
Knowledge distillation is a form of model compression that allows artificial neural networks of different sizes to learn from one another. Its main application is the compactification of large deep neural networks to free up computational resources, in particular on edge devices. In this article, we consider proton-proton collisions at the High-Luminosity Large Hadron Collider (HL-LHC) and demonstrate a successful knowledge transfer from an event-level graph neural network (GNN) to a particle-level small deep neural network (DNN). Our algorithm, DistillNet, is a DNN that is trained to learn about the provenance of particles, as provided by the soft labels that are the GNN outputs, to predict whether or not a particle originates from the primary interaction vertex. The results indicate that for this problem, which is one of the main challenges at the HL-LHC, there is minimal loss during the transfer of knowledge to the small student network, while improving significantly the computational resource needs compared to the teacher. This is demonstrated for the distilled student network on a CPU, as well as for a quantized and pruned student network deployed on a field programmable gate array. Our study proves that knowledge transfer between networks of different complexity can be used for fast artificial intelligence (AI) in high-energy physics that improves the expressiveness of observables over non-AI-based reconstruction algorithms. Such an approach can become essential at the HL-LHC experiments, e.g. to comply with the resource budget of their trigger stages.
A Python project for calculating (binomial) efficiencies and their uncertainties. The mathematical theory and derivation of the formulas can be found in FERMILAB-TM-2286-CD. If you use this software for published work, please cite this note. The default algorithm for finding the shortest interval is based on Hyndman, R. J. (1996). Computing and graphing highest density regions, The American Statistician, 50(2), 120-126.
Details the use of a custom embedding model on knowledge graphs to aid in downstream natural language processing (NLP) models for Derivative Classification Assist. Motivations, algorithms, and results were discussed.
We nonconstructively prove the existence of decision algorithms with low-degree polynomial running times for a number of well-studied graph layout, placement, and routing problems. Some were not previously known to be in p at all; others were only known to be in p by way of brute force or dynamic programming formulations with unboundedly high-degree polynomial running times. Our methods include the application of the recent Robertson-Seymour theorems on the well-partial-ordering of graphs under both the minor and immersion orders. We also briefly address the complexity of search versions of these problems.
The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.
This paper introduces an advanced input data processing layer for EMT simulations of large-scale bulk power systems. The paper proposes two versions of the RE-INTEGRATE EMT simulation tool, RE-INTEGRATE Gen-0 and RE-INTEGRATE Gen-1, which are developed to enhance simulation generalizability, scalability, and accuracy. The framework leverages a generic class design for components to incorporate linear equations, which are generated by discretizing the Differential-Algebraic Equations (DAEs) that represent the dynamics of the components. In addition, the framework employs a parsing algorithm that parses a power system’s raw and dyr files to generate a connectivity graph which is then traversed to form the overall system’s dynamics. The proposed input data processing layer is used to simulate the IEEE 39-bus test system. The obtained results demonstrate the framework’s capability to achieve simulation scalability and accuracy. Further, the results indicate that EMT simulations performed using the proposed automations can effectively handle complex grid configurations.
Resource allocation in High Performance Computing (HPC) environments presents a complex and multifaceted challenge for job scheduling algorithms. Beyond the efficient allocation of system resources, schedulers must account for and optimize multiple performance metrics, including job wait time and system throughput. Traditional heuristic-based scheduling algorithms increasingly struggle and lack the efficiency needed to meet the demands and address the complexity and scale of modern HPC systems. Consequently, recent research efforts have focused on leveraging advancements in Artificial Intelligence (AI) and Deep Learning (DL), particularly Reinforcement Learning (RL), to develop more adaptable and intelligent scheduling strategies. Previous RL-based scheduling approaches have explored a range of algorithms, from Deep Q-Networks (DQN) to Proximal Policy Optimization (PPO), and more recently, hybrid methods that integrate Graph Neural Networks (GNNs) with RL techniques. However, a common limitation across these methods is their reliance on relatively small datasets, with few methods being evaluated using large-scale, multi-million-job trace datasets representative of real-world HPC workloads. Moreover, existing RL schedulers face scalability issues due to centralized policy updates, which hinder training efficiency and performance when applied to large datasets. This study introduces a novel RL-based scheduler utilizing Decentralized Distributed Proximal Policy Optimization (DD-PPO) algorithm, which supports large-scale distributed training across multiple workers without requiring parameter synchronization at every step. By eliminating reliance on centralized updates to a shared policy, the DD-PPO scheduler enhances scalability, training efficiency, and sample utilization. Experimental validation using a large real-world dataset containing over 11.5 million job traces collected from petascale HPC systems over six years assesses the influence of dataset scale on training effectiveness and compares DD-PPO performance to traditional and advanced scheduling approaches. The experimental results demonstrate improved scheduling performance in comparison to both heuristic-based schedulers and existing RL-based scheduling algorithms.