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At least 739 records · Page 41

Real-time Ridesharing for Transportation Hubs with Demand and Supply Uncertainty

Transportation hubs in major cities generate a significant amount of trips by taxis and for-hail vehicles (FHV), with many of the trips sharing similar destinations. This suggests promising opportunities to leverage the collective travel needs with dedicated ridesharing solutions to reduce the externalities of excessive traffic at transportation hubs. In this study, we develop a novel dynamic ridesharing approach to serve trips from the transportation hub by considering (1) demand (new passengers) and supply (newly available vehicles) in the near future and (2) the uncertainty of future predictions. Our approach consists of two stages. In the first stage, we develop a data structure called hub mobility tree to generate potential combinations of shareable trips as candidate schedules efficiently. Then the generated schedules are used in the second stage to formulate the stochastic hub-based ridesharing problem (SHRP), which is a stochastic integer programming problem with the objective to maximize the total expected ridesharing profit over time. Due to the prohibitive number of shareable trips, we then approximately solve SHRP by the sample average approximate method (SAA), and a dual Lagrangian technique is implemented to further improve the scalability of the solution approach. We demonstrate the performances of the proposed method by simulating the ridesharing service at JFK airport using NYC taxi and FHV data. The results indicate that the proposed method outperforms the myopic ridesharing (maximize profit for a single time step) and the rolling horizon method with point estimation of future demand and supply.

dynamic ridesharing↗

Integration of Pumped Heat Energy Storage with Fossil-Fired Power Plant (Final Report)

The project team of Southwest Research Institute ® (SwRI ® ), Malta Inc. (Malta), and Luminant Generation Company LLC (Luminant) completed a feasibility study for the integration of a 100-MW, 10-hour (1000-MWh) Malta Pumped Heat Energy Storage (MPHES) system with multiple full-sized fossil-fired electricity generation units (EGU) in Luminant portfolio. MPHES is a long-duration, molten-salt-energy storage technology that uses turbomachinery and heat exchangers to transfer energy to a thermal storage media when charging, and removes the heat in a similar fashion when discharging. With high round trip efficiency (60-65%) and long lifespan (30+ years), MPHES provides economic benefits to the fossil-asset owners that can be scaled to integrate with assets across their portfolio. This technology uses hardware components, workforce personnel, and skillsets similar to those used by fossil EGUs, allowing for synergy when co-locating the two technologies. Luminant has approximately 39,000 megawatts of generation across 12 states, operating in six of the seven competitive markets in the U.S. and powered by a diverse portfolio of natural gas, nuclear, coal, and solar facilities. The DeCordova plant in Granbury, Texas, a simple cycle natural gas peaker power plant, was used as the fossil-fired asset in this project. The local market in Granbury, Texas has many influences, including several nearby power plants, a Luminant-owned nuclear plant (Comanche Peak), and substantial wind energy, which causes both negative pricing at night and high market volatility. Reducing false starts of the DeCordova plant and better responding to market volatility would be an economic advantage. Luminant is currently integrating battery storage plant on site to begin addressing these challenges. Integrating long-duration storage, like MPHES, would expand this capability beyond one hour of storage and have the potential to greatly reduce the total number of gas turbine starts. The MPHES charging requirement could help offset the overnight operating costs of Comanche Peak, which cannot load follow, and the nearby Luminant-owned Wise County combined cycle plant that cycles too often. Following the assessment of Luminant’s ERCOT-based portfolio for integration compatibility with Malta’s PHES system and the project tasks of conceptual study, technoeconomic analysis, technology gap assessment, and commercialization plan, the project team effort has resulted in several key outcomes: (1) Identification of market trends in a high-wind penetration market outside a major metropolitan area; (2) Creation of a dispatching model for the MPHES system and the pairing of Li-ion battery with a gas turbine in a real time market; (3) Revenue and cost estimations for operating MPHES alongside a gas peaker plant with real dispatching considerations and comparison with variations in the Malta implementation, including doubling the storage capacity and using two discharge drivetrains; (4) Potential carbon emission reductions possible by replacing gas turbine operation with Malta PHES operation; and (5) Summary of literature-based future market predictions for Texas.

20 FOSSIL-FUELED POWER PLANTS↗

Summary of Consolidated Interim Storage Advantages and Disadvantages from an Integrated Systems Perspective from Prior Reports and Studies

The question of whether centralized storage of civilian spent nuclear fuel (SNF) should be part of the federal waste management system as an intermediate step before permanent disposal has been debated for more than four decades. Centralized storage facilities were included as a potential component of the U.S. spent fuel management system in the Nuclear Waste Policy Act of 1982 (NWPA), but these facilities were not identified as being essential. When the NWPA was passed, it was expected that a permanent repository would be available around the turn of the century to meet the commitments that were made to start accepting waste by that time. For a number of reasons, a permanent repository was not available at that stage. This report summarizes the advantages and disadvantages of including an ISF as part of an integrated waste management system that have been identified in numerous analyses of the impacts of a consolidated interim storage facility (ISF), previously discussed as monitored retrievable storage, the form of ISF authorized in the NWPA) by the U.S. Department of Energy (DOE) and independent groups. Storing SNF before disposal is a functional requirement for an integrated waste management system. As described below, the studies reviewed in this report have identified a range of benefits that could be obtained by adding a consolidated ISF to the waste management system, including (1) earlier acceptance of fuel by the federal government, (2) reduction in the number of unintended long-term storage sites, (3) added system flexibility and opportunity for better integration, and (4) near-term development and demonstration of institutional and technical infrastructures for large-scale management of SNF. At the same time, these studies have identified potential drawbacks to deployment of an ISF, including (1) potential adverse impacts on development of a repository, (2) additional transportation of SNF, and (3) a large upfront economic investment to establish the consolidated storage capability. In general, the studies that have considered the positive and negative impacts of consolidated storage most comprehensively have concluded that in light of these considerations, the benefits of including an ISF as part of an integrated waste management system can outweigh any real or perceived disadvantages.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Understanding collective human movement dynamics during large-scale events using big geosocial data analytics

Conventional approaches for modeling human mobility pattern often focus on human activity and movement dynamics in their regular daily lives and cannot capture changes in human movement dynamics in response to large-scale events. With the rapid advancement of information and communication technologies, many researchers have adopted alternative data sources (e.g., cell phone records, GPS trajectory data) from private data vendors to study human movement dynamics in response to large-scale natural or societal events. Big geosocial data such as georeferenced tweets are publicly available and dynamically evolving as real-world events are happening, making it more likely to capture the real-time sentiments and responses of populations. However, precisely-geolocated geosocial data is scarce and biased toward urban population centers. In this research, we developed a big geosocial data analytical framework for extracting human movement dynamics in response to large-scale events from publicly available georeferenced tweets. The framework includes a two-stage data collection module that collects data in a more targeted fashion in order to mitigate the data scarcity issue of georeferenced tweets; in addition, a variable bandwidth kernel density estimation(VB-KDE) approach was adopted to fuse georeference information at different spatial scales, further augmenting the signals of human movement dynamics contained in georeferenced tweets. To correct for the sampling bias of georeferenced tweets, we adjusted the number of tweets for different spatial units (e.g., county, state) by population. To demonstrate the performance of the proposed analytic framework, we chose an astronomical event that occurred nationwide across the United States, i.e., the 2017 Great American Eclipse, as an example event and studied the human movement dynamics in response to this event. Finally, this analytic framework can easily be applied to other types of large-scale events such as hurricanes or earthquakes.

54 ENVIRONMENTAL SCIENCES↗

Insights from FEED studies for retrofitting existing fossil power plants with carbon capture technology

Recent United States Department of Energy (DOE) sponsored front-end engineering design (FEED) studies for retrofitting existing fossil-fueled power plants with state-of-the-art carbon capture technology contain previously overlooked real-world design considerations for near-term deployment of carbon capture. Insights from examining seven recently published FEED study reports are summarized in this paper. This includes a discussion of the design, performance, and cost implications associated with (1) location-specific considerations such as water availability, land availability, and accessibility; (2) host-plant-specific factors such as flue gas specifications, allowable degree of integration between the capture system and host plant, and operational mode; and (3) miscellaneous factors such as market conditions, permitting requirements, and business case incentives. In conclusion, this manuscript highlights (1) water availability as a key design and cost driver, with host plant steam extraction increasing capture system cooling water availability, (2) modularization and constructability impacts on the number of capture trains, (3) the impacts of host plant operational mode and capacity factor on the business case for installing capture, and (4) the merit of continued research, development, and demonstration efforts addressing steam extraction, host plant tie-in at the stack, solvent reclamation and air emissions control.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Bi-Level Linear Programming Model for Automatic Load Shedding: A Distributed Wide-Area Measurement System-based Solution

Load shedding is currently implemented as a two-step based approach. In the first step, manual load shedding is taken place, were system operators, using estimates, inform distribution utilities of predicted stressful conditions. Information provided include the potential use of energy reserves, as well as load shedding amount. In a second step, automatic load shedding is done. The latter is realized using protection relays. While considering frequency variation, pre-defined values of load to be shed and correspondent number of stages for such to be realized are transformed into relay settings. Under-frequency protection relays use only local measurements towards decision making, thus operate in a decentralized architecture. Decision making is done in milliseconds plus breaker time. While this approach has provided much system reliability, considering the new smart grid paradigm, where system dynamics are much faster due to increasing renewable resources penetration, in some operating conditions it will generate sub-optimal solutions, such as islanding. Phasor measurement units provide a source of information which can be useful for this problem. Centralized architecture-based solutions for automatic load shedding, as present in the state-of-the-art, require though total processing times which are not acceptable for real-life implementation. In this work, considering the above, a bi-level linear programming model is presented. The model is implemented considering a distributed architecture while leveraging phasor measurement units data. The upper-level model estimates the current system state. Results of this model are embedded in a lower-level model, which decision variables are the location and load value to be shed. Easy-to-implement model, built-on the classic weighted least squares solution, highlight potential aspects towards real-life applications.

Bretas, Arturo Suman↗

Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors

The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

FOS: Physical sciences↗

Integrating chromatin conformation information in a self-supervised learning model improves metagenome binning

Metagenome binning is a key step, downstream of metagenome assembly, to group scaffolds by their genome of origin. Although accurate binning has been achieved on datasets containing multiple samples from the same community, the completeness of binning is often low in datasets with a small number of samples due to a lack of robust species co-abundance information. In this study, we exploited the chromatin conformation information obtained from Hi-C sequencing and developed a new reference-independent algorithm, Metagenome Binning with Abundance and Tetra-nucleotide frequencies—Long Range (metaBAT-LR), to improve the binning completeness of these datasets. This self-supervised algorithm builds a model from a set of high-quality genome bins to predict scaffold pairs that are likely to be derived from the same genome. Then, it applies these predictions to merge incomplete genome bins, as well as recruit unbinned scaffolds. We validated metaBAT-LR’s ability to bin-merge and recruit scaffolds on both synthetic and real-world metagenome datasets of varying complexity. Benchmarking against similar software tools suggests that metaBAT-LR uncovers unique bins that were missed by all other methods.

59 BASIC BIOLOGICAL SCIENCES↗

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as O(Ne4) where Ne is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to O(Ne 3 ) in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the O(Ne 3 ) complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. In this work, we demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

97 MATHEMATICS AND COMPUTING↗

Real-Time Operator Evolution in Two and Three Dimensions via Sparse Pauli Dynamics

We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in one-dimensional (1D) spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model that is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources. Published by the American Physical Society 2025

Begušić, Tomislav (ORCID:0000000279424134)↗

Mitigating Shear-dependent Object Detection Biases with Metacalibration

M ETACALIBRATION is a new technique for measuring weak gravitational lensing shear that is unbiased for isolated galaxy images. Here we test M ETACALIBRATION with overlapping, or "blended" galaxy images. Using standard M ETACALIBRATION , we find a few percent shear measurement bias for galaxy densities relevant for current surveys, and that this bias increases with increasing galaxy number density. We show that this bias is not due to blending itself, but rather to shear-dependent object detection. If object detection is shear-independent, no deblending of images is needed, in principle. We demonstrate that detection biases are accurately removed when including object detection in the M ETACALIBRATION process, a technique we call M ETADETECTION . This process involves applying an artificial shear to images of small regions of sky and performing detection on the sheared images, as well as measurements that are used to calculate a shear response. We demonstrate that the method can accurately recover weak shear signals even in highly blended scenes. In the M ETACALIBRATION process, the space between objects is sheared coherently, which does not perfectly match the real universe in which some, but not all, galaxy images are sheared coherently. We find that even for the worst case scenario, in which the space between objects is completely unsheared, the resulting shear bias is at most a few tenths of a percent for future surveys. We discuss additional technical challenges that must be met in order to implement M ETADETECTION for real surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks

To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗

Inferring transmission heterogeneity using virus genealogies: estimation and targeted prevention

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin’s index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

59 BASIC BIOLOGICAL SCIENCES↗

CMSSW Scaling Limits on Many-Core Machines

Today the LHC offline computing relies heavily on CPU resources, despite the interest in compute accelerators, such as GPUs, for the longer term future. The number of cores per CPU socket has continued to increase steadily, reaching the levels of 64 cores (128 threads) with recent AMD EPYC processors, and 128 cores on Ampere Altra Max ARM processors. Over the course of the past decade, the CMS data processing framework, CMSSW, has been transformed from a single-threaded framework into a highly concurrent one. The first multithreaded version was brought into production by the start of the LHC Run 2 in 2015. Since then, the framework's threading efficiency has gradually been improved by adding more levels of concurrency and reducing the amount of serial code paths. The latest addition was support for concurrent Runs. In this work we review the concurrency model of the CMSSW, and measure its scalability with real CMS applications, such as simulation and reconstruction, on mode rn many-core machines. We show metrics such as event processing throughput and application memory usage with and without the contribution of I/O, as I/O has been the major scaling limitation for the CMS applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Studying visual search without an eye tracker: an assessment of artificial foveation

Abstract Eye tracking is a useful tool for studying human cognition, both in the laboratory and in real-world applications. However, there are cases in which eye tracking is not possible, such as in high-security environments where recording devices cannot be introduced. After facing this challenge in our own work, we sought to test the effectiveness of using artificial foveation as an alternative to eye tracking for studying visual search performance. Two groups of participants completed the same list comparison task, which was a computer-based task designed to mimic an inventory verification process that is commonly performed by international nuclear safeguards inspectors. We manipulated the way in which the items on the inventory list were ordered and color coded. For the eye tracking group, an eye tracker was used to assess the order in which participants viewed the items and the number of fixations per trial in each list condition. For the artificial foveation group, the items were covered with a blurry mask except when participants moused over them. We tracked the order in which participants viewed the items by moving their mouse and the number of items viewed per trial in each list condition. We observed the same overall pattern of performance for the various list display conditions, regardless of the method. However, participants were much slower to complete the task when using artificial foveation and had more variability in their accuracy. Our results indicate that the artificial foveation method can reveal the same pattern of differences across conditions as eye tracking, but it can also impact participants’ task performance.

47 OTHER INSTRUMENTATION↗

FINETUNA: fine-tuning accelerated molecular simulations

Abstract Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomistic systems. However, simulation techniques based on first principles, such as density functional theory (DFT), are limited in their practical use due to their high computational expense. Machine learning approaches have the potential to approximate DFT in a computationally efficient manner, which could dramatically increase the impact of computational simulations on real-world problems. However, they are limited by their accuracy and the cost of generating labeled data. Here, we present an online active learning framework for accelerating the simulation of atomic systems efficiently and accurately by incorporating prior physical information learned by large-scale pre-trained graph neural network models from the Open Catalyst Project. Accelerating these simulations enables useful data to be generated more cheaply, allowing better models to be trained and more atomistic systems to be screened. We also present a method of comparing local optimization techniques on the basis of both their speed and accuracy. Experiments on 30 benchmark adsorbate-catalyst systems show that our method of transfer learning to incorporate prior information from pre-trained models accelerates simulations by reducing the number of DFT calculations by 91%, while meeting an accuracy threshold of 0.02 eV 93% of the time. Finally, we demonstrate a technique for leveraging the interactive functionality built in to Vienna ab initio Simulation Package (VASP) to efficiently compute single point calculations within our online active learning framework without the significant startup costs. This allows VASP to work in tandem with our framework while requiring 75% fewer self-consistent cycles than conventional single point calculations. The online active learning implementation, and examples using the VASP interactive code, are available in the open source FINETUNA package on Github.

97 MATHEMATICS AND COMPUTING↗

Closing the Accuracy Gap in Tandem Photovoltaic Testing: An Accessible and Efficient Spectral Tuning Method Using LED-Based Simulators for Research Laboratories and Industry

Accurate performance calibration of multijunction (MJ) solar cells is critical for advancing this technology toward large-scale terrestrial application, yet existing testing methods developed by photovoltaics calibration laboratories remain prohibitively complex and resource intensive for most research laboratories. Current approaches rely on expensive multisource simulators and/or intricate spectral tuning algorithms, limiting accessibility and hindering standardized comparisons of emerging MJ technologies such as perovskite-based tandems. This paper introduces a streamlined spectral irradiance adjustment method for light-emitting diode (LED)-based solar simulators, which are increasingly adopted in the photovoltaics community due to their versatility and cost-effectiveness. The method we present bins LED channels into groups based on the number of junctions of the MJ photovoltaic device under test (DUT) and their corresponding band gaps and incorporates an automated tuning algorithm that eliminates the need to adjust each channel’s irradiance individually. This tuning algorithm requires the relative spectral responsivities of both the DUT and a broadband reference cell, as well as a calibrated spectroradiometer. Measurement validation across various MJ devices, including III-V and perovskite/silicon tandems, demonstrates excellent agreement within 1% with well-established xenon-tungsten multisource simulators and associated tuning algorithms. By enabling precise spectral tuning with readily available equipment and a simple tuning algorithm, our approach bridges the measurement accuracy gap between research laboratories and accredited testing facilities, fostering more reliable device comparisons and accelerating the translation of MJ technologies into real-world energy systems.

14 SOLAR ENERGY↗

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. In conclusion, parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.

97 MATHEMATICS AND COMPUTING↗