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At least 253 records · Page 14

Quantum algorithms for Gibbs sampling and hitting-time estimation

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2 ), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

97 MATHEMATICS AND COMPUTING↗

The WTP Immobilized LAW Formulation Algorithm: Recent Efforts Toward Software Development - 17342

The immobilized low-activity waste (ILAW) product from WTP must meet certain requirements and processing constraints. The strategy for controlling ILAW product composition uses the ILAW formulation algorithm. This algorithm is approved by the DOE Office of River Protection (ORP) for use in calculating melter feed recipes that will produce acceptable ILAW product during Low-Activity Waste (LAW) Facility commissioning. The calculations performed by the algorithm have been demonstrated using a sophisticated spreadsheet, but this spreadsheet is not expected to support continuous operation. Efforts are underway to develop software that will support glass formulation during operation. Recent work toward software development includes an examination of assumptions made in the algorithm about expected LAW Facility operation, and spreadsheet calculations to formulate glass for potential LAW compositions under the direct feed LAW (DFLAW) strategy that ORP has adopted. The documentation of the ILAW algorithm is the planned basis for software development. However, some assumptions made in the current algorithm's mass balance logic do not match the matured design and expected operation of the LAW Facility. A self-assessment effort evaluated the validity of these assumptions by reviewing design documents, in order to identify opportunities to align the algorithm's mass balance logic with the matured design and ensure that the developed software supports continuous LAW Facility operation. Several improvement opportunities were identified and are discussed. The results of ILAW algorithm calculations to formulate glass for eighteen challenging LAW compositions indicate that the current WTP baseline LAW glass models are sufficiently robust to accommodate DFLAW. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Algorithmic Improvements for Portable Event-Based Monte Carlo Transport Using the Nvidia Thrust Library

High performance computing environments are progressively moving towards many-core computing architectures. The Los Alamos National Laboratory Trinity machine, available in late 2016, will use both Intel Xeon Haswell processors and Intel Xeon Phi Knights Landing many integrated core (MIC) coprocessors. The Lawrence Livermore National Laboratory Sierra machine, available in 2018, will use an IBM PowerPC architecture along with Nvidia graphics processing units (GPUs). Applications that must work in this supercomputing environment must continue to adapt in order to take advantage of the diverse hardware architectures that are coming. A significant consideration is not only the performance of the application on a given platform but also the portability of the application to other platforms. The algorithmic improvements presented in this paper build upon recently-reported work on event-based Monte Carlo transport in the ALPSMC code that models particle transport in one-dimensional binary stochastic media. That paper discussed the lack of available vectorization in the traditional history-based algorithm used for Monte Carlo transport and presented a data parallel event-based algorithm implemented using the Nvidia Thrust library for portability. The performance of the data parallel event-based algorithm implemented using Thrust was compared to a native CUDA implementation. The conclusions from that work were that the Thrust library abstraction technique caused too significant a loss in performance but that the event-based method was a viable option that should be further investigated. In this paper, we describe algorithmic improvements to the data parallel event-based algorithm previously presented. We made further algorithmic optimizations to the event-based CUDA implementation, most notably: data structure changes, a new conditional particle removal scheme in the event-based process, and the use of multiple GPUs. In addition to improvements to the algorithm, we re-implemented the Thrust version from the now further optimized CUDA version, giving a greater chance for success at a performant abstraction. Finally, we revisited our previous assumptions about the inability of the history-based method to achieve performance on vector style architectures such as the MICs and GPUs, with surprising and promising results. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗

Pencil Beam Algorithms Are Unsuitable for Proton Dose Calculations in Lung

Purpose: To compare analytic and Monte Carlo–based algorithms for proton dose calculations in the lung, benchmarked against anthropomorphic lung phantom measurements. Methods and Materials: A heterogeneous anthropomorphic moving lung phantom has been irradiated at numerous proton therapy centers. At 5 centers the treatment plan could be calculated with both an analytic and Monte Carlo algorithm. The doses calculated in the treatment plans were compared with the doses delivered to the phantoms, which were measured using thermoluminescent dosimeters and film. Point doses were compared, as were planar doses using a gamma analysis. Results: The analytic algorithms overestimated the dose to the center of the target by an average of 7.2%, whereas the Monte Carlo algorithms were within 1.6% of the physical measurements on average. In some regions of the target volume, the analytic algorithm calculations differed from the measurement by up to 31% in the internal gross target volume (iGTV) (46% in the planning target volume), over-predicting the dose. All comparisons showed a region of at least 15% dose discrepancy within the iGTV between the analytic calculation and the measured dose. The Monte Carlo algorithm recalculations showed dramatically improved agreement with the measured doses, showing mean agreement within 4% for all cases and a maximum difference of 12% within the iGTV. Conclusions: Analytic algorithms often do a poor job predicting proton dose in lung tumors, over-predicting the dose to the target by up to 46%, and should not be used unless extensive validation counters the consistent results of the present study. Monte Carlo algorithms showed dramatically improved agreement with physical measurements and should be implemented to better reflect actual delivered dose distributions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A communication-avoiding 3D algorithm for sparse LU factorization on heterogeneous systems

We propose a new algorithm to improve the strong scalability of right-looking sparse LU factorization on distributed memory systems. Our 3D algorithm for sparse LU uses a three-dimensional MPI process grid, exploits elimination tree parallelism, and trades off increased memory for reduced per-process communication. We also analyze the asymptotic improvements for planar graphs (e.g., those arising from 2D grid or mesh discretizations) and certain non-planar graphs (specifically for 3D grids and meshes). For a planar graph with $n$ vertices, our algorithm reduces communication volume asymptotically in $n$ by a factor of $\mathscr{O}$ $\Big(\sqrt{log \ n}\Big)$ and latency by a factor of $\mathscr{O}$ $(log \ n)$. For nonplanar cases, our algorithm can reduce the per-process communication volume by 3× and latency by $\mathscr{O}$ $\Big(n^\frac13\Big)$ times. In all cases, the memory needed to achieve these gains is a constant factor. We implemented our algorithm by extending the 2D data structure used in SuperLU_DIST. Our new 3D code achieves empirical speedups up to 27× for planar graphs and up to 3.3× for non-planar graphs over the baseline 2D SuperLU_DIST when run on 24,000 cores of a Cray XC30. We extend the 3D algorithm for heterogeneous architectures by adding the Highly Asynchronous Lazy Offload (Halo) algorithm for co-processor offload. On 4096 nodes of a Cray XK7 with 32,768 CPU cores and 4096 Nvidia K20x GPUs, the 3D algorithm achieves empirical speedups up to 24× for planar graphs and 3.5× for non-planar graphs over the baseline 2D SuperLU_DIST with co-processor acceleration.

97 MATHEMATICS AND COMPUTING↗

On Parallel Push-Relabel based Algorithms for Bipartite Maximum Matching

We study multithreaded push-relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial (graph) problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing maximum transversal of a matrix. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a testset comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for the parallel push-relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push-relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.

Push-relabel, matching, bipartite↗

Intercomparison of Thermal Regime Algorithms in 1-D Lake Models

Lakes are an important component of the global weather and climate system, but the modeling of their thermal regimes has shown large uncertainties due to the highly diverse lake properties and model configurations. Here we evaluate the algorithms of four key lake thermal processes including turbulent heat fluxes, wind-driven mixing, light extinction, and snow density, using a highly diverse lake dataset provided by the Inter-sectoral Impact Model Intercomparison Project (ISIMIP) 2a lake sector. Algorithm codes are configured and run separately within the same parent model to rule out any interference from factors apart from the algorithms examined. Evaluations are based on both simulation accuracy and recalibration complexity for application to global lakes. For turbulent heat fluxes, the non-Monin-Obukhov similarity (MOS) based, more simplified algorithms perform better in predicting lake epilimnion temperatures and achieve high convergence in the values of the calibrated parameters. For wind-driven mixing, a two-algorithm strategy considering lake shape and season is suggested with the regular mixing algorithm used for spring and earlier summer and the mixing-enhanced algorithm for summer steady stratification and fall overturn periods. There are no evident differences in the simulated thermocline depths using different light extinction algorithms or the observation. Finally, for lake ice phenology, a constant snow density at around 110 kg m-3 is found to be sufficient for most northern lakes while the Arctic lakes require a higher value. Our study provides highly practical guides for improving 1-D lake models and feasible parameterization strategies to better simulate global lake thermal regimes.

58 GEOSCIENCES↗

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. Here we subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: $Θ‖\mathscr{H}‖|t|+ln(1/ϵ)+ln(1/δ)$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inexact Newton-CG algorithms with complexity guarantees

Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).

Mathematics↗

A Work-Efficient Parallel Sparse Matrix-Sparse Vector Multiplication Algorithm

We design and develop a work-efficient multithreaded algorithm for sparse matrix-sparse vector multiplication (SpMSpV) where the matrix, the input vector, and the output vector are all sparse. SpMSpV is an important primitive in the emerging GraphBLAS standard and is the workhorse of many graph algorithms including breadth-first search, bipartite graph matching, and maximal independent set. As thread counts increase, existing multithreaded SpMSpV algorithms can spend more time accessing the sparse matrix data structure than doing arithmetic. Our shared-memory parallel SpMSpV algorithm is work efficient in the sense that its total work is proportional to the number of arithmetic operations required. The key insight is to avoid each thread individually scan the list of matrix columns. Our algorithm is simple to implement and operates on existing column-based sparse matrix formats. It performs well on diverse matrices and vectors with heterogeneous sparsity patterns. A high-performance implementation of the algorithm attains up to 15x speedup on a 24-core Intel Ivy Bridge processor and up to 49x speedup on a 64-core Intel KNL manycore processor. In contrast to implementations of existing algorithms, the performance of our algorithm is sustained on a variety of different input types include matrices representing scale-free and high-diameter graphs.

97 MATHEMATICS AND COMPUTING↗

Adaptation of the CVT algorithm for catheter optimization in high dose rate brachytherapy

Purpose: An innovative, simple, and fast method to optimize the number and position of catheters is presented for prostate and breast high dose rate (HDR) brachytherapy, both for arbitrary templates or template-free implants (such as robotic templates).Methods: Eight clinical cases were chosen randomly from a bank of patients, previously treated in our clinic to test our method. The 2D Centroidal Voronoi Tessellations (CVT) algorithm was adapted to distribute catheters uniformly in space, within the maximum external contour of the planning target volume. The catheters optimization procedure includes the inverse planning simulated annealing algorithm (IPSA). Complete treatment plans can then be generated from the algorithm for different number of catheters. The best plan is chosen from different dosimetry criteria and will automatically provide the number of catheters and their positions. After the CVT algorithm parameters were optimized for speed and dosimetric results, it was validated against prostate clinical cases, using clinically relevant dose parameters. The robustness to implantation error was also evaluated. Finally, the efficiency of the method was tested in breast interstitial HDR brachytherapy cases.Results: The effect of the number and locations of the catheters on prostate cancer patients was studied. Treatment plans with a better or equivalent dose distributions could be obtained with fewer catheters. A better or equal prostate V100 was obtained down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of prostate V100 and D90. Implantation errors up to 3 mm were acceptable since no statistical difference was found when compared to 0 mm error (p > 0.05). No significant difference in dosimetric indices was observed for the different combination of parameters within the CVT algorithm. A linear relation was found between the number of random points and the optimization time of the CVT algorithm. Because the computation time decrease with the number of points and that no effects were observed on the dosimetric indices when varying the number of sampling points and the number of iterations, they were respectively fixed to 2500 and to 100. The computation time to obtain ten complete treatments plans ranging from 9 to 18 catheters, with the corresponding dosimetric indices, was 90 s. However, 93% of the computation time is used by a research version of IPSA. For the breast, on average, the Radiation Therapy Oncology Group recommendations would be satisfied down to 12 catheters. Plans with nine or less catheters would not be clinically acceptable in terms of V100, dose homogeneity index, and D90.Conclusions: The authors have devised a simple, fast and efficient method to optimize the number and position of catheters in interstitial HDR brachytherapy. The method was shown to be robust for both prostate and breast HDR brachytherapy. More importantly, the computation time of the algorithm is acceptable for clinical use. Ultimately, this catheter optimization algorithm could be coupled with a 3D ultrasound system to allow real-time guidance and planning in HDR brachytherapy.

61 RADIATION PROTECTION AND DOSIMETRY↗

Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for \({\boldsymbol{\mathcal{H}_2}}\) Model Reduction

This paper presents an extension of the Adaptive-Antoulas-Anderson (AAA) algorithm for rational modelling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing stability constraints on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published RKFIT algorithm. Vector Fitting and RKFIT both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must re-start Vector Fitting or RKFIT with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by AAA is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. In conclusion, the examples presented demonstrate that smiAAA can efficiently produce approximations of similar or better accuracy than Vector Fitting and RKFIT while requiring less input from the user.

97 MATHEMATICS AND COMPUTING↗

Fast tensor disentangling algorithm

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.

Slagle, Kevin↗

High performance graphics processor based computed tomography reconstruction algorithms for nuclear and other large scale applications.

The goal of this work is to develop a fast computed tomography (CT) reconstruction algorithm based on graphics processing units (GPU) that achieves significant improvement over traditional central processing unit (CPU) based implementations. The main challenge in developing a CT algorithm that is capable of handling very large datasets is parallelizing the algorithm in such a way that data transfer does not hinder performance of the reconstruction algorithm. General Purpose Graphics Processing (GPGPU) is a new technology that the Science and Technology (S&T) community is starting to adopt in many fields where CPU-based computing is the norm. GPGPU programming requires a new approach to algorithm development that utilizes massively multi-threaded environments. Multi-threaded algorithms in general are difficult to optimize since performance bottlenecks occur that are non-existent in single-threaded algorithms such as memory latencies. If an efficient GPU-based CT reconstruction algorithm can be developed; computational times could be improved by a factor of 20. Additionally, cost benefits will be realized as commodity graphics hardware could potentially replace expensive supercomputers and high-end workstations. This project will take advantage of the CUDA programming environment and attempt to parallelize the task in such a way that multiple slices of the reconstruction volume are computed simultaneously. This work will also take advantage of the GPU memory by utilizing asynchronous memory transfers, GPU texture memory, and (when possible) pinned host memory so that the memory transfer bottleneck inherent to GPGPU is amortized. Additionally, this work will take advantage of GPU-specific hardware (i.e. fast texture memory, pixel-pipelines, hardware interpolators, and varying memory hierarchy) that will allow for additional performance improvements.

97 MATHEMATICS AND COMPUTING↗

Neuromorphic Graph Algorithms

Graph algorithms enable myriad large-scale applications including cybersecurity, social network analysis, resource allocation, and routing. The scalability of current graph algorithm implementations on conventional computing architectures are hampered by the demise of Moore’s law. We present a theoretical framework for designing and assessing the performance of graph algorithms executing in networks of spiking artificial neurons. Although spiking neural networks (SNNs) are capable of general-purpose computation, few algorithmic results with rigorous asymptotic performance analysis are known. SNNs are exceptionally well-motivated practically, as neuromorphic computing systems with 100 million spiking neurons are available, and systems with a billion neurons are anticipated in the next few years. Beyond massive parallelism and scalability, neuromorphic computing systems offer energy consumption orders of magnitude lower than conventional high-performance computing systems. We employ our framework to design and analyze new spiking algorithms for shortest path and dynamic programming problems. Our neuromorphic algorithms are message-passing algorithms relying critically on data movement for computation. For fair and rigorous comparison with conventional algorithms and architectures, which is challenging but paramount, we develop new models of data-movement in conventional computing architectures. This allows us to prove polynomial-factor advantages, even when we assume a SNN consisting of a simple grid-like network of neurons. To the best of our knowledge, this is one of the first examples of a rigorous asymptotic computational advantage for neuromorphic computing.

97 MATHEMATICS AND COMPUTING↗

Retrieval of temperature and humidity profiles from ground-based high-resolution infrared observations using an adaptive fast iterative algorithm

Various retrieval algorithms have been developed for retrieving temperature and water vapor profiles from Atmospheric Emitted Radiance Interferometer (AERI) observations. The physical retrieval algorithm, named AERI Optimal Estimation (AERIoe), outperforms other retrieval algorithms in many aspects except the retrieval time, which is significantly increased due to the complex radiative transfer process. The calculation of the Jacobian matrix is the most computationally intensive step of the physical retrieval algorithm. Interestingly, an analysis of the change in AERI observations' information content with respect to Jacobians revealed that the AERIoe algorithm's performance presents negligible dependence on these metrics. Thus, the Jacobian matrix could remain unchanged when the variation in the atmospheric state is small in the retrieval process to reduce the most time-consuming computation. On the basis of the above findings, a fast physical–iterative retrieval algorithm was proposed by adaptively recalculating Jacobians in keeping with the changes in the atmospheric state. Experiments with synthetic observations demonstrate that the proposed method experiences an average reduction in retrieval time by an impressive 59 % compared to the original AERIoe algorithm while achieving maximum root-mean-square errors of less than 0.95 K and 0.22 log(ppmv) for heights below 3 km for the temperature and water vapor profile, respectively. Further analyses revealed that the fast-retrieval algorithm reached an acceptable convergence rate of 98.7 %, marginally lower than AERIoe's 99.9 % convergence rate for the 826 cases used in this study.

54 ENVIRONMENTAL SCIENCES↗

DyG-DPCD: A Distributed Parallel Community Detection Algorithm for Large-Scale Dynamic Graphs

Dynamic (Temporal) graphs capture the valuable evolution of real-world systems, from the continuously evolving patterns of social interactions and genetic pathways to the dynamic fluctuations of economic forces. Detecting communities for such evolving networks poses unique challenges. Detecting and analyzing the evolution of communities within dynamic graphs unlocks valuable insights into the underlying structural and temporal patterns of real-world systems. However, the sheer volume of modern graph data and the inherent complexity of the temporal dimension pose significant challenges to scalable community detection algorithms. Addressing this gap, our work explores the limited landscape of scalable distributed-memory parallel methods specifically designed for dynamic network community detection. We propose a novel parallel algorithm, DyG-DPCD (Dynamic Graph Distributed Parallel Community Detection), to detect communities in dynamic networks using the Message Passing Interface (MPI) framework. We present a vertex-centric approach, allowing us to detect communities through local optimization. Furthermore, we enhance our baseline algorithm by incorporating three heuristics, which improve the algorithm’s performance significantly while maintaining the quality of the solutions. We demonstrate the efficiency of our algorithm by experimenting on several real-world large-scale networks with hundreds of millions of edges spanning diverse domains. Notably, DyG-DPCD achieves speedups between 25× and 30× for large networks that we experimented on using NERSC compute nodes. In conclusion, our algorithm outperforms the STINGER parallel re-agglomeration algorithm by 30×.

97 MATHEMATICS AND COMPUTING↗