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At least 721 records · Page 40

Development of Whole System Digital Twins for Advanced Reactors: Leveraging Graph Neural Networks and SAM Simulations

Here, in this work, we introduce a novel method to develop whole system digital twins (DTs) for advanced nuclear reactors. This method treats a complex reactor system as a heterogeneous graph: with the system components as different types of graph nodes and their physical interconnections as edges. Based on the heterogeneous graph, a graph neural network combining graph convolution and temporal node attention is developed as the DT, facilitating a comprehensive understanding of the system's dynamic behavior. By utilizing the System Analysis Module (SAM) code for simulating various operational transients, we develop a graph-based database that trains the DT. This DT is characterized by two primary functions: It can infer the entire system's status using sparse node information, and it can predict the progress of transients based on current and historical system information. Our approach is validated through case studies on the Experimental Breeder Reactor II (EBR-II) system and a generic Fluoride-salt-cooled High-temperature Reactor (gFHR), demonstrating the DT's accuracy in forecasting operational transients. The DT's rapid computation capabilities enhance its potential for supporting advanced reactor operations, offering benefits in intelligent simulation, autonomous control, and anomaly detection, paving the way for improved safety analysis and intelligent component health management for advanced reactor systems and reducing their operations and maintenance cost.

EBR-II↗

Extending XACC for Quantum Optimal Control

Quantum computing vendors are beginning to open up application programming interfaces for direct pulse-level quantum control. With this, programmers can begin to describe quantum kernels of execution via sequences of arbitrary pulse shapes. This opens new avenues of research and development with regards to smart quantum compilation routines that enable direct translation of higher-level digital assembly representations to these native pulse instructions. In this work, we present an extension to the XACC system-level quantum-classical software framework that directly enables this compilation lowering phase via user-specified quantum optimal control techniques. This extension enables the translation of digital quantum circuit representations to equivalent pulse sequences that are optimal with respect to the backend system dynamics. Our work is modular and extensible, enabling third party optimal control techniques and strategies in both C++ and Python. We demonstrate this extension with familiar gradient-based methods like gradient ascent pulse engineering (GRAPE), gradient optimization of analytic controls (GOAT), and Krotov's method. Our work serves as a foundational component of future quantum-classical compiler designs that lower high-level programmatic representations to low-level machine instructions.

Nguyen, Thien↗

Robustness and Validation of Model and Digital Twins Deployment

For digital twins (DTs) to become a central fixture in mission critical systems, a better understanding is required of potential modes of failure, quantification of uncertainty, and the ability to explain a model’s behavior. These aspects are particularly important as the performance of a digital twin will evolve during model development and deployment for real-world operations.

97 MATHEMATICS AND COMPUTING↗

Telestream Chronicle File

This is a chronicle file from the Telestream video digitization software that the NSRC Digital Collections Group has installed on the Red. We have not gotten this software to totally function and want to be able to do a workalong with a Telestream representative. One of their technician’s said this file might be helpful to replicate the problem we see in our digitization lab. (The main pointer to the red network that is in this file are file paths. They have been scrubbed so that “valid path to mxf” replaces the real file path.)

97 MATHEMATICS AND COMPUTING↗

A Comparison of Three Types of Computer-Based Procedures: An Experiment Using the Rancor Microworld Simulator

The nuclear power industry has historically used paper-based procedures, but a shift towards computer-based procedures (CBPs) has the potential to reduce human errors, alleviate mental workload, and improve work performance. Twenty-seven participants were randomly assigned to one of three CBP types using the Rancor Microworld Simulator, and each performed two different types of operational scenarios (startup and loss of feedwater). The three CBP types varied in levels of digitalization. It was hypothesized that there would be less favorable impressions of the most basic procedures, and that these would demonstrate lower usability than types with greater digitalization. Overall, our predictions were partially supported with some interesting caveats, specifically with some performance benefits for CBPs that provided indicators but not embedded controls. We discuss our findings in terms of optimal levels of digitalization/automation within nuclear operations and suggest pathways for future directions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Development of HPC based phase field simulations tool for modification of alloy morphology to enhance material properties during additive manufacturing (AM) process

Currently, additive manufacturing (AM) technology is extensively used to manufacture aerospace components because of the unique advantages of the technique in producing custom designs, complex geometries in a near-net fashion that significantly reduces the manufacturing cost, and improved energy efficiency. However, the thermodynamic properties of existing aerospace alloys and the thermal conditions that prevail in most of the powder-bed based additive manufacturing processes lead to undesirable columnar / columnar-dendritic microstructures that promote solidification cracking during the process, and the development of anisotropy in the mechanical properties of the as-built components. Time consuming, energy-intensive post AM treatments are required to recover the mechanical properties of the wrought components for which the existing alloy compositions were designed for. However, novel alloy compositions, that exploit the AM thermal conditions to produce fine, equiaxed grain structures in the as-built condition, with mechanical properties equal to or exceeding those of the wrought work-horse alloy, Ti-6Al-4V has recently been demonstrated in Ti-Cu alloys. Significant energy savings up to 66% can be obtained for a typical aerospace component through digitally designing the AM process, process parameters, and alloy composition. The current project focused on developing a fundamental understanding of the evolution of the columnar to equiaxed transition (CET) occurring during solidification under AM thermal conditions in Ti-Cu and Ti-Cu-X alloys using high-fidelity phase field (PF) simulations using the leadership class computing facilities that exist in the national laboratories. The simulations were able to capture the effect of alloy and process conditions on CET, and clearly showed the beneficial effect of a ternary solute addition to Ti-Cu binary alloys on CET. The simulations indicated that bulk nucleation in the liquid ahead of the solidifying epitaxial front was promoted by a large, transient, thermal undercooling promoted by the mismatch between the growth rate of the dendrite tips in the epitaxial front and the imposed solidification rate. AM experiments performed at Raytheon Technologies Research Center using the same thermal conditions used in the PF simulations indicated the formation of equiaxed grains, although the grain size was bigger than the ones reported in the literature. On the other hand, the equiaxed grain size predicted by PF simulations were smaller than the grain size of Ti-Cu alloys reported in the literature. The industry will follow up the existing work in a future program that would involve further optimization of the process for the Ti-Cu-X alloys to demonstrate the application of the process and the alloy to a specific aerospace component.

36 MATERIALS SCIENCE↗

Revisiting Dropout: Escaping Pressure for Training Neural Networks with Multiple Costs

A common approach to jointly learn multiple tasks with a shared structure is to optimize the model with a combined landscape of multiple sub-costs. However, gradients derived from each sub-cost often conflicts in cost plateaus, resulting in a subpar optimum. In this work, we shed light on such gradient conflict challenges and suggest a solution named Cost-Out, which randomly drops the sub-costs for each iteration. We provide the theoretical and empirical evidence of the existence of escaping pressure induced by the Cost-Out mechanism. While simple, the empirical results indicate that the proposed method can enhance the performance of multi-task learning problems, including two-digit image classification sampled from MNIST dataset and machine translation tasks for English from and to French, Spanish, and German WMT14 datasets.

97 MATHEMATICS AND COMPUTING↗

The NREL Cyber Range

With the National Renewable Energy Laboratory's (NREL's) cyber range, researchers can replicate cybersecurity scenarios as they would occur on real, complex energy systems. With supercomputing and advanced emulation capabilities, the cyber range allows users to build digital twins of real systems and connect the emulated environment to actual physical devices throughout NREL's laboratories. The space offers unlimited potential to test the frontier of energy systems security.

cyber range↗

Shedding light on U.S. small and midsize data centers: Exploring insights from the CBECS survey

As demand for digital services accelerates, the energy and environmental footprint of data centers faces increasing scrutiny. While hyperscale cloud facilities have driven efficiency gains, small and midsize U.S. data centers remain a critical yet underexamined segment with significant untapped potential for energy savings. This study leverages data from the Commercial Buildings Energy Consumption Survey (CBECS) to analyze trends in server stocks, computing customers, cooling system adoption and efficiency, and geospatial distribution from 2012 to 2018. Findings reveal a sharp decline in small and midsize data centers, from 1.764 million to 1.398 million, with server counts dropping from 5.177 million to 4.262 million—aligning with the broader shift toward cloud computing. More than 40 % of servers in small data centers and 55 % in midsize data centers are housed in office buildings, and over half of all servers are concentrated in climate zones 5A (cold), 3A (mixed-humid), and 4A (mixed-humid), with the highest densities in metropolitan hubs. While direct expansion units remain the dominant cooling system, a clear transition toward more energy-efficient solutions, particularly air economizers, is evident. By integrating server and cooling system distributions, we estimate Power Usage Effectiveness (PUE) and Water Usage Effectiveness (WUE) for U.S. data centers by size and year. Results show that midsize data centers are more energy-efficient but more water-intensive due to the widespread use of water-cooled chillers. These findings highlight the trade-offs in cooling system selection and provide a critical foundation for policies aimed at enhancing efficiency in an evolving data center landscape.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

National-Tribal Critical Infrastructure Protection: Collaboration for Extraordinary National Security Benefit

This paper examines national and tribal collaborative opportunities to get ahead of the critical infrastructure insecurity problem. Recommendations are viewed through the lens of the Sandia Labs Tribal Cyber-Energy initiative and national security projects. Recommendations include 1) Collaboratively address national priority and shared challenges to gain faster and better solutions to national priority problems on a smaller yet comprehensive American Indian and Alaskan Native sovereign single-point of authority scale 2) Utilize newer standards-based technologies to provide scalable, capable, and manageable solutions for greatly expanded and connected national critical infrastructures 3) Employ Cyber-Physical-Resilient design preliminary analysis to define concept- to-disposition design requirements for preemptive critical infrastructure risk mitigation and baked-in security; 4) Develop data-centric protection to provide increased information asset protection as data shifts from data-owner operated on-premises infrastructure to virtual service provider data-steward owned and operated off-premises infrastructure; and 5) Balance shared solutions with the National Institute of Science and Technology (NIST) Cybersecurity and Risk Management frameworks, and the System Security Engineering Guidelines. As yet unallocated federal funding would support research, development, the timely application of National-Tribal critical infrastructure protection, and critical infrastructure Cyber disruption response and recovery with extraordinary mutual benefits for the foreseeable future. The Critical Infrastructure Insecurity Problem: Rapid modernization and expansive connectivity are due to advances in Information and Communications Technologies that have sweeping cyber impact across all critical infrastructure sectors. Supervisory Control and Data Acquisition and Industrial Control Systems are particularly impacted as systems long separated from the Internet are now being connected and computerized. Virtualization and mobility create a Data Everywhere-User Anywhere paradigm that has evaporated the enterprise network perimeter. There are multi-front technological challenges at play, where long depended on technologies simply don't scale to current needs resulting in a digital dichotomy of competing old and new standards. New standards-based technologies scale but are not as well-known or as widely deployed, which leaves decision makers, stakeholders, and the workforce in a quandary, caught mid-stream between the technological past and the virtual future. Rapid and expansive cyber threat accompanies disruptive change in connectivity and computational dependencies. A lack of action will exacerbate the problem if new technologies roll out without baked-in security design. The Risk: If National-Tribal CIP collaboration to design in security is not done, then an ongoing state of insufficient bolt-on security and elevated threat exposure will remain for years to come.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Demonstrating the data center as a flexible grid asset using a C-HIL setup

Increasing data center demand is outpacing grid infrastructure development. Artificial intelligence workloads and hyperscale cloud growth are creating unprecedented demand for power, while traditional grid expansion faces multiyear development timelines. Verrus is developing an innovative datacenter solution for this challenge, data centers that act as active grid-supportive assets rather than passive loads. Our approach integrates a novel grid-aware power flow management system with battery energy storage systems(BESS) into a microgrid-controlled, medium-voltage power distribution architecture that delivers critical capabilities, such as: * Fast response to grid disturbances such over/ under voltage or over/ under frequency * Demand flexibility that can service requests from the utility within 10 s * Uninterrupted transition to islanded operation during grid outages * Continuous uptime assurance for compute loads while maintaining all customer service level agreements. Through Verrus' strategic partnership with the National Renewable Energy Laboratory (NREL), these capabilities were validated using NREL's Advanced Research on Integrated Energy Systems (ARIES) virtual emulation environment to model a 70-MW grid-interactive data center. This paper outlines the design, methodology, and results of this emulated deployment, demonstrating that data centers can provide both critical load resilience and ancillary grid support without compromising uptime requirements. Specifically, we present a digital real time simulation of a 70 MW data center integrated with a physical microgrid controller, and demonstrate the data center response in the event of a grid voltage and frequency event, utility demand response request and utility outage.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A review of privacy in energy applications

As the distribution system continues to experience an increase in distributed energy resource (DER) and electric vehicle (EV) penetration, so does the need for new solutions that can help grid operators manage and leverage their capabilities. This will undoubtedly lead to new operational schemes and business opportunities that will transform the traditional consumer into a prosumer who will be more actively engaged in grid operations. Although the field is still under active development, many of the potential use cases presented in literature or industry are built upon edge computing, two-way communications, and other innovative computational constructs to attain their goals. However, at their core, many use cases assume a great level of data access to aid with the decision-making process, an assumption that may need to be revised to ensure fair and equitable operational processes are maintained. This may be particularly true as edge resources are predicted to participate in retail-side, many-to-many, or peer-to-peer markets and thus may lead to financial impacts if data access considerations are ignored. The need to revise data access mechanisms can be further justified by the introduction of new participants into the operational process, who do not have the same level of trust, nor the incentives to focus on energy delivery as their primary objective. At the same time, more consumers are becoming aware of their own data, and the potential impacts of its abuse. To help solution developers better understand these risks, this report has been developed to offer an initial introduction to the topic of privacy. This is achieved by 1) Highlighting the need for privacy-aware solutions; 2) Encouraging system designers to be inquisitive about the status quo; 3) Documenting the existing threat space; 4) Presenting and evaluating tools that may be helpful towards enabling better privacy postures; and 5) Making recommendations to encourage the adoption of better practices. From a technical perspective, the report focuses on evaluating two potential techniques by applying them to the Transactive Energy Space. Based on the obtained results, it can be established that differential privacy (DP) methods may have limited applicability when highly correlated, time-series data records need to be protected. However, DP may be a powerful tool when it is used to aggregate and analyze mid-size and large-size data sets in a more traditional statistical environment. The second tool under evaluation is threshold cryptography, which can guarantee complete secrecy (and thus privacy) but requires the establishment of key management procedures and dedicated communication channels for key coordination. Therefore, due to its increased computational overhead, the use of threshold cryptography must be weighted using a cost/benefit analysis on a per-application basis.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The Digital Assurance for High Consequence Systems (DAHCS) Mission Campaign Whitepaper

The DAHCS (pronounced “Dax”) MC is a 7-year, $\$$45 million research portfolio within Sandia’s Laboratory Directed Research and Development program. The DAHCS MC arose in response to a great need: to ensure that the use of digital technologies does not weaken our nation’s high consequence systems. Digital technologies offer many benefits in speed, cost, and flexibility, and we seek to reap those benefits without introducing new system failures. However, digital technologies cannot be evaluated the same way as analog technologies. Initiatives across the nation highlight the capability gap that prevents efficient, effective digital assurance. The Challenge Today’s digital assurance tools, techniques, and methods are inadequate to confidently characterize, assess, and manage digital risk; they are ad hoc, slow, costly, and rarely scalable to increasingly complex digital technologies. The rapidly evolving cyber threat landscape exacerbates this problem because digital assurance now must secure against digital risks now and in the future, including those introduced by rapidly evolving technologies, adversaries, and systems.

97 MATHEMATICS AND COMPUTING↗

Identification of Galaxy Shreds in Large Photometric Catalogs Using Convolutional Neural Networks

Contamination from galaxy fragments, identified as sources, is a major issue in large photometric galaxy catalogs. In this paper, we prove that this problem can be easily addressed with computer vision techniques. We use image cutouts to train a convolutional neural network (CNN) to identify cataloged sources that are in reality just star-formation regions and/or shreds of larger galaxies. The CNN reaches an accuracy ~98% on our testing data sets. We apply this CNN to galaxy catalogs from three among the largest surveys available today: the Sloan Digital Sky Survey, the DESI Legacy Imaging Surveys, and the Panoramic Survey Telescope and Rapid Response System Survey. We find that, even when strict selection criteria are used, all catalogs still show a ~5% level of contamination from galaxy shreds. Our CNN gives a simple yet effective solution to clean galaxy catalogs from these contaminants.

79 ASTRONOMY AND ASTROPHYSICS↗

Convergent Manufacturing of Large-Scale Components for Nuclear Applications, via Additive Manufacturing and Powder Metallurgy Hot Isostatic Pressing

Powder metallurgy (PM)–hot isostatic pressing (PM-HIP) has long been recognized as a powerful route for producing fully dense, near net shape metallic components. By consolidating powders under high temperature and pressure, HIP provides isotropic properties, uniform microstructures, and scalability to complex geometries that are vital for sectors such as aerospace, energy, and nuclear power. Yet despite these advantages, the technology has remained constrained by costly trial and error canister fabrication, limitations of conventional forging, and incomplete knowledge about how the canister design influences final part properties. Additive manufacturing (AM), by contrast, thrives on design freedom and geometric flexibility but struggles with speed, scalability, and cost when applied to very large structures. The research presented in this report investigated how a convergent manufacturing approach, combining AM with PM-HIP, can merge the strengths of both technologies, leveraging AM’s flexibility for canister design and HIP’s consolidation capability to deliver reliable, large, and complex parts. The work progressed through three case studies that built on one another in scale and complexity. Small cylindrical canisters fabricated by conventional methods, laser powder bed fusion, and directed energy deposition were filled with stainless steel powders and subjected to HIP. The resulting parts demonstrated near-full density and mechanical properties on par with wrought stainless steel, showing for the first time that AM canisters can be a direct substitute for conventional ones without sacrificing quality. The next step involved a medium-scale, noncentrosymmetric T-valve, which is an enclosed, multibranch geometry that tested the limits of AM + PM-HIP integration. The T-valve achieved predictable shrinkage and uniform densification, confirming feasibility for enclosed designs. However, this study also revealed oxide inclusions and interfacial challenges at the AM + HIP boundary, underscoring the critical importance of controlling interface chemistry and employing robust, in situ strategies, such as melt pool monitoring and thermal monitoring, coupled with nondestructive evaluation techniques such as x-ray computed tomography. Finally, the effort culminated in fabricating a large-scale impeller weighing nearly 2000 lb and spanning 5 ft in diameter. Produced via multirobot wire arc AM and hot isostatic pressed to near-full density, the impeller validated industrial-scale feasibility. Predictive models closely matched experimental shrinkage, tensile properties were spatially uniform across the component, and the AM + PM-HIP interface proved mechanically sound despite the presence of oxide-decorated prior particle boundaries. This large-scale demonstration is a major milestone, showing that hybrid AM + PM‑HIP can reliably deliver components at reactor-relevant scales. Collectively, these studies charted a logical pathway: small-scale work built scientific confidence, medium-scale work highlighted opportunities and challenges, and large-scale work proved industrial impact. The overarching conclusion of this report is that AM + PM-HIP should not be seen as a replacement for forging but as a complementary pathway that provides the US with flexibility, resilience, and new options for manufacturing nuclear-grade components. Looking ahead, several directions emerge as critical to sustaining progress. Predictive modeling must become faster, more accessible, and more accurate, with digital twins and machine learning reducing reliance on trial and error. Powders and alloys must be optimized for HIP, with improved cleanliness, reduced oxides, and tailored chemistries that enhance creep, fatigue, and irradiation resistance. Interfaces between AM and HIP regions must be better engineered through coatings, machining strategies, and surface treatments to mitigate oxide formation and ensure reliable bonding to explore opportunities for HIP of targeted compositional parts, as well as multimaterial HIP cladding applications. Monitoring and nondestructive evaluation need to expand, incorporating multimodal sensors, x-ray computed tomography, and real-time data integration through platforms such as Pelican. At the same time, the pathway to industrial adoption requires techno-economic analysis, machinability studies, and qualification frameworks aligned with industry and regulatory standards. Finally, workforce and academic engagement must be strengthened. Programs that train technicians and engineers for US Navy and US Department of Energy manufacturing challenges should be paired with academic partnerships to support fundamental research, with open sharing of non-export-controlled data to accelerate innovation and build the next generation of experts. In conclusion, this report demonstrates that hybrid AM + PM-HIP is scientifically viable and strategically important. By combining the design agility of AM with the consolidation strength of HIP and embedding modeling, monitoring, and workforce development, this approach provided a transformative new capability for US manufacturing. The path forward is clear: hybrid AM + PM-HIP is not just a promising research direction but is also potentially an industrially relevant pathway that can reshape how nuclear-grade components are designed, qualified, and deployed.

36 MATERIALS SCIENCE↗

Imaging pyrometry for most color cameras using a triple pass filter

A simple combination of the Planck blackbody emission law, optical filters, and digital image processing is demonstrated to enable most commercial color cameras (still and video) to be used as an imaging pyrometer for flames and explosions. The hardware and data processing described take advantage of the color filter array (CFA) that is deposited on the surface of the light sensor array present in most digital color cameras. In this work, a triple-pass optical filter incorporated into the camera lens allows light in three 10-nm wide bandpass regions to reach the CFA/light sensor array. These bandpass regions are centered over the maxima in the blue, green, and red transmission regions of the CFA, minimizing the spectral overlap of these regions normally present. A computer algorithm is used to retrieve the blue, green, and red image matrices from camera memory and correct for remaining spectral overlap. A second algorithm calibrates the corrected intensities to a gray body emitter of known temperature, producing a color intensity correction factor for the camera/filter system. The Wien approximation to the Planck blackbody emission law is used to construct temperature images from the three color (blue, green, red) matrices. A short pass filter set eliminates light of wavelengths longer than 750 nm, providing reasonable accuracy (±10%) for temperatures between 1200 and 6000 K. The effectiveness of this system is demonstrated by measuring the temperature of several systems for which the temperature is known.

47 OTHER INSTRUMENTATION↗

Prioritizing ICS Beachhead Systems for Cyber Vulnerability Testing

Cyber Testing for Resilient Industrial Control Systems™ (CyTRICS™) is the Department of Energy’s (DOE’s) program for cybersecurity vulnerability testing, digital subcomponent enumeration, and forensic assessment. CyTRICS leverages best-in-class test facilities and analytic capabilities at six DOE National Laboratories and strategic partnerships with key stakeholders including technology developers, manufacturers, asset owners and operators, and interagency partners. During the program’s development, CyTRICS established a unique methodology for prioritizing digital components within operational technology (OT) and industrial control systems (ICS) in the Energy Sector Industrial Base (ESIB) for cyber vulnerability testing. The CyTRICS Prioritization Process leverages multiple characteristics of systems, components, and their contextual deployment to calculate a quantification of individual digital components for CyTRICS testing. The initial version of the CyTRICS Prioritization Process was premised largely upon the impact which could result to an industrial control system if the digital component under testing was compromised, either through malicious means, faulty engineering, or other modes. The worldwide compromise of the SolarWinds Orion platform, first reported in December 2020, through malicious interference with the digital patching cycle was a watershed event in cyber supply chain security. The SolarWinds compromised demonstrated the strategic importance of certain types of ubiquitous software, and the ability to generate widespread cybersecurity effects. To address this challenge and as a part of the Department of Energy’s response to the SolarWinds compromise, DOE’s Office of Cybersecurity, Energy Security, and Emergency Response (CESER) directed the National Laboratories to evolve the CyTRICS Prioritization Process methodology to encompass additional factors related to the strategic importance of digital components. CESER directed CyTRICS researchers to identify, characterize, and append strategic factors to the CyTRICS Prioritization Process to provide additional weight to these characteristics. National Laboratory expert researchers identified functionality, distribution, and platform characteristics for digital components in ICS and OT that they assessed would be likely targeted in strategic initial-access cyber attack. CyTRICS has termed these factors “ICS Beachhead Systems,” leveraging a definition first advanced by Schneider Electric, which is intended as a blanket term to encompass digital components, products, and systems in OT. This paper describes the ICS Beachhead Systems identified and the rationale for inclusion. As a next step in the research and refinement process, the National Laboratories will validate this initial set of characteristics against digital components evaluated by the CyTRICS program and current implementation of the CyTRICS Prioritization Process. After validation, CyTRICS researchers will then develop a scoring methodology to generate a quantitative score to assess the degree to which a digital component is characterized as an ICS Beachhead System. Finally, the National Laboratories will append this scoring to the existing CyTRICS Prioritization Process algorithm.

97 MATHEMATICS AND COMPUTING↗