Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “metadata evaluation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Envelope-driven comfort risk in residential demand response

Residential demand response (DR) is a valuable resource for grid reliability, but remains challenging because the highly heterogeneous residential building stock leads to widely varying and hard-to-predict load and comfort responses during DR events. Although prior research has estimated the technical potential of DR-capable technologies for achieving energy demand savings, little is known about how they affect thermal comfort. In particular, it remains unclear how indoor thermal conditions due to DR depend on the thermal envelope characteristics of the housing stock. To address this gap, this study provides a systematic, location-specific assessment of indoor thermal performance during DR-events across the US housing stock using both typical DR weather data and detailed building metadata. We evaluate how envelope characteristics influence indoor temperatures during realistic simulated summer and winter DR events across 37 US locations, applying both temperature threshold and rate of temperature change criteria to estimate region-level probabilities of discomfort. Additionally, we show the impact of distinct weather patterns that intensify or abate thermal stress on comfort outcomes. Results show a near-universal overheating risk in summer DR events, where comfort outcomes are strongly influenced by rapid risk of comfort violations. In contrast, overall winter DR discomfort risk is lower, risk escalation is more gradual and shows greater sensitivity to event duration. These findings offer a data-driven quantification of comfort risk across diverse climates and building envelopes, demonstrating the need for region-specific DR scheduling and discomfort mitigation strategies tailored to local weather patterns and the performance of existing residential buildings.

Demand response↗
DOE OSTI2024

Quantifying Error in Photovoltaic Installation Metadata: Preprint

In this research, we quantify the level of metadata error for a fleet of 2860 photovoltaic (PV) systems, using metadata values provided by fleet owners. Using satellite imagery and time series analysis techniques available in open-source Python packages Panel-Segmentation and PVAnalytics, respectively, we evaluate the accuracy of PV system metadata such as location, azimuth, tilt, and mounting configuration (fixed tilt vs. tracking). We find that approximately 75% of provided latitude-longitude coordinates are within 190 meters of the actual solar installation. We were unable to link 7.8% of latitude-longitude coordinates to any solar installation via satellite imagery analysis. We evaluate the level of error in owner-provided mounting configuration (fixed tilt vs. single-axis tracking), finding only 8 systems with an incorrect mounting configuration. When evaluating azimuth and tilt parameters, we find that approximately 64% of the data is correct, with data for 860 systems (approximately 30%) not provided by system owners. To illustrate the importance of having correct solar metadata, we evaluate how incorrect metadata affects solar performance estimates by modeling system AC energy output at ground-truth vs. incorrect latitude-longitude coordinates, mounting configurations, and azimuth-tilt configurations. Energy output estimates can vary significantly if incorrect metadata parameters are used, with incorrect mounting configuration leading to the largest discrepancy with over 20% variation in expected energy output.

azimuth↗
DOE OSTI2026

SetGo: Metadata Readiness for Scientific AI Datasets

Scientific datasets intended for AI use require both computational readiness for model training and metadata readiness for discovery, sharing, and reuse. The Readiness Engine for Data Integration (REDI) addresses computational readiness, but no corresponding tool evaluates whether a dataset’s metadata are sufficiently complete, governed, and standards-compliant for publication and agent-based consumption. Existing FAIR assessors operate only on published repository records, and no single system covers FAIR compliance, licensing, provenance, governance, reproducibility, and catalog readiness together. We present SetGo, an open-source Python toolkit that assesses and repairs metadata readiness across these six dimensions before a dataset is published or archived. Applied to four scientific corpora, SetGo surfaces deficiencies that general-purpose tools do not detect: ERA5 climate metadata scores 4% on ACDD 1.3 compliance; materials datasets fail OPTIMADE species-definition requirements; and PDB-derived proteomics data carries licensing terms incompatible with standard SPDX identifiers. Guided enrichment raises overall FAIR scores from 52–57% to 81–91%, and a single setgo publish command pushes to Hugging Face Hub, CKAN, or OpenMetadata with ML Commons Croissant 1.0 metadata sidecars. To support interactive and automated workflows, SetGo integrates with coding agents powered by large language models (LLMs) through a /setgo skill that enables natural-language execution of the full assess–enrich–publish loop, with user involvement limited to supplying missing metadata values.

Wilkinson, Sean [ORNL] (ORCID:0000000214437479)↗
DOE OSTI2024

Prompt Phrase Ordering Using Large Language Models in HPC: Evaluating Prompt Sensitivity

Large language models (LLMs) have demonstrated effective performance in domain-specific tasks, often requiring a well-designed prompt to guide their responses. However, optimizing the right prompt is challenging due to prompt sensitivity—the phenomenon where small changes in the prompt can lead to significant variations in performance. In this study, we evaluate prompt performance by examining all permutations of independent phrases to investigate prompt sensitivity and robustness. We used two datasets: the GSM8k dataset, which assesses mathematical reasoning, and a custom template prompt for summarizing database metadata. Our goal was to evaluate the performance across all permutations of a sequence of prompt phrases. The study was conducted using the llama3-instruct- 7B model hosted on Ollama, with computations parallelized in a high-performance computing environment. By comparing the average index of phrases in the best and worst-performing prompts, we found that the order of independent phrases within a prompt significantly impacts LLM performance. Additionally, we used Hamming distance to assess changes between phrase orderings, concluding that prompt modifications can dramatically affect scores, often by almost random chance. These findings support existing research on prompt sensitivity. We discuss the challenges of prompt optimization, noting that altering phrases in a successful prompt does not always result in another successful prompt.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

AI-Ready Data Pilot Project Report

The proliferation of artificial intelligence in scientific research has created an urgent need to define "AI-ready data" for researchers and, more importantly, provide resources to help them produce AI-ready data. At Pacific Northwest National Laboratory, we conducted a pilot study with three data scientists evaluating three CSV datasets from different scientific domains, followed by semi-structured interviews capturing assessment practices. Our findings reveal that AI-readiness evaluation is intuition-based, with practitioners asking "How fast can I go from raw data to my machine learning pipeline?" Data scientists consistently prioritized workflow efficiency, human interpretability, and quality stewardship signals. From these insights, we developed a practical evaluation framework comprising data requirements, metadata standards, and validation tests that provides actionable criteria for producing and curating AI-ready datasets, addressing the gap between theoretical understanding and practical implementation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Analytical methods for online data quality assessment

This chapter provides a comprehensive overview of the main steps for algorithmic sensor signal quality assessment, which can enhance the decision-making process for water resource recovery facility (WRRF) operation and optimization. It introduces the concept of redundancy as the basis for data quality assessment. It also explains the typical data processing pipeline, which consists of preliminary analysis, data pre-processing, and specific algorithmic approaches. Each of these processes is presented and discussed in three separate sections. Importantly, this chapter introduces the main approaches for data quality assessment, provides guidelines for selecting the most suitable one and the key performance indicators to evaluate them and explains how to collect metadata through such an algorithmic approach.

Aguado, Daniel↗
DOE OSTI2024

Automating the Analysis of Large Language Models Responses through Zero-Shot Question Answering

Recent advancements in Large Language Models (LLMs) have shown significant potential in various applications, yet their evaluation, particularly in zero-shot question answering scenarios, remains a challenging task. In this study, our objective was to explore precision metrics for Large Language Models (LLM) and design and implement a software pipeline to automatically evaluate LLMs' outputs under zero-shot question answering. Zero-shot question answering involves a model providing answers to questions about topics it hasn't seen during training. It leverages the principles of zero-shot learning by relying on semantic understanding and generalization from related knowledge. The data used was metadata from medical databases on congenital heart disease. We explored eleven LLM metrics and selected three for our evaluation: BLEU, BERTScore, and MoverScore. BLEU calculates a score based on the overlap of n-grams (contiguous sequences of n items, typically words) between the machine-generated translation and the reference translations. Higher BLEU scores indicate better correspondence between the machine-generated and human-generated translations. BERTScore is a metric used to evaluate the quality of machine-generated text by measuring the similarity of token embeddings produced by BERT (Bidirectional Encoder Representations from Transformers) between the generated text and reference text. MoverScore is a metric that quantifies the dissimilarity between the distributions of word embeddings from machine-generated text and reference text, emphasizing semantic similarity over exact token overlap. We also introduced HBKI, a composite metric summarizing these approaches. We tested five models —GPT-3, Llama-2, Gemini 1.5 Pro, Solar 10.7B, and Mixtral-8x7b. Our software pipeline, designed and implemented using Object-Oriented Programming principles, allows users to customize the selection and extraction of features for topics of interest in their own research. Our results show that MoverScore delivered the most precise evaluation of the LLM's outputs, while Mixtral-8x7b achieved the best overall performance in extracting metadata from the databases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A cost and community perspective on the barriers to microbiome data reuse

Microbiome research is becoming a mature field with a wealth of data amassed from diverse ecosystems, yet the ability to fully leverage multi-omics data for reuse remains challenging. To provide a view into researchers’ behavior and attitudes towards data reuse, we surveyed over 700 microbiome researchers to evaluate data sharing and reuse challenges. We found that many researchers are impeded by difficulties with metadata records, challenges with processing and bioinformatics, and problems with data repository submissions. We also explored the cost constraints of data reuse at each step of the data reuse process to better understand “pain points” and to provide a more quantitative perspective from sixteen active researchers. The bioinformatics and data processing step was estimated to be the most time consuming, which aligns with some of the most frequently reported challenges from the community survey. From these two approaches, we present evidence-based recommendations for how to address data sharing and reuse challenges with concrete actions for future work.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Development of a Discrepancy Checker for the Digital Twin in a Supervisory Control System for a Thermal Energy Delivery System

Defined as a virtual representation of a physical object, process, or service, and used to support real-world decision-making, a digital twin (DT) can be utilized to combine classical and novel frameworks in sensors, state predictions, and multi-input/multi-output systems, and to enable optimal autonomous operations. However, a DT’s usefulness largely depends on its ability to adequately mirror the state of its physical counterpart, and this adequacy should be reflected by the level of uncertainty in the underlying simulation models when estimating and predicting quantities of interest (QOIs). Moreover, simulation models in a DT may involve multiple fidelities of representations—ranging from physics-based models to data-driven ones—but classical uncertainty quantification (UQ) methods struggle to handle numerous uncertainty sources, nor are they designed for real-time applications. This work presents a UQ-based discrepancy checking and diagnosis tool for a DT-based supervisory control system applied to a thermal energy delivery system (TEDS) at Idaho National Laboratory. The discrepancy checker was developed using metadata from an automated DT development process, and these metadata included different combinations of physical model forms and model parameters, training data and hyperparameters for surrogate models, and design parameters for supervisory control systems. Next, correlations between the uncertainty results and the metadata were established and then applied to the DT operations. The discrepancy checker evaluates the discrepancies between model predictions from virtual and sensor measurements and backtraces them to the corresponding major sources of uncertainty. The discrepancy checker showed reasonable performance in detecting discrepancies and diagnosing sources of uncertainty in testing scenarios.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Soil biogeochemical properties and metrics of tree-mycorrhizal dominance for a 25-Ha forest in South Central Indiana, USA.

This data package contains a dataset used in the papers “Seeing the forest for all the trees: Mycorrhizal-associated nutrient economies are modulated by stem density and the synchrony between overstory and understory communities” and “Mycorrhizal associations of tree species influence soil nitrogen dynamics via effects on soil acid–base chemistry”. Four csv files are included along with a dataset. The dataset features chemical soil properties for a single sampling campaign within the 25 Ha Lilly-Dickey Woods Smithsonian Forest Global Earth Observatory (ForestGEO) plot in South Central Indiana, USA (ldw_dat_raw.csv). Also included are separate files focused on pH (pH_data.csv), carbon and nitrogen (CN_data.csv), and nitrification rates (Nitrification_data.csv). These variables are commonly associated with the tree-mycorrhizal dominance of forest stands. In these data subsets, each soil variable was matched to a 10 meter radius neighborhood wherein metrics of tree-mycorrhizal dominance (basal area, stem count, importance value, etc.) were calculated. Models between these soil variables and dominance metrics were used to investigate how different assessments of mycorrhizal associated nutrient economies (MANE) capture these relationships. This research was performed as a part of the Smithsonian ForestGEO project. This data package can be used to explore spatial variability in soil chemistry within a mature hardwood forest, or it can be combined with the included tree data, other fine-scale spatial information, or other tree inventory data for the site to evaluate how soil chemistry varies with tree community composition or edaphic or topographic properties.

Craig, Matthew [ORNL] (ORCID:0000000288907920)↗
DOE OSTI2024

Human Host Cellular Response to HCoV-229E Infection Proteomics (ACS-JM-DP2)

The purpose of this experiment was to evaluate the human host cellular response to wild-type Human coronavirus strain 229E (HCoV-229E) infection. Sample data was obtained for mock and infected immortalized human lung epithelial cells (A549) (MOI 5) nuclear extracts, immortalized human lung fibroblasts cells (MRC5) (MOI5) nuclear extracts, and primary human airway epithelial (HAE) (MOI 3) cells from lung tissue and processed for proteome analysis. Processed datasets are openly accessible from the download button and contain secondary processed proteomic results files and supporting metadata materials. Experimental proteomics samples were prepared using Limited Proteolysis (LiP) methods for Label-free quantification (LFQ) and global proteomic evaluation. Sample data was acquired using a Q-Exactive HF-X mass spectrometer and was processed and compiled using MaxQuant software (v.1.6.17.0). Processed proteomic data downloads include a sample naming key, processed MaxQuant results/parameters, and protein annotated relative abundance files. See corresponding primary data accessions below and Viral Experiment LiP Analysis source code supporting data transparency and reuse. Experimental transcriptomics samples were collected in parallel and processed for RNA sequencing (RNA-Seq) as summarized under ACS-DP1 (https://data.pnnl.gov/group/nodes/dataset/34069).

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

DEDUPKV: A Space-Efficient and High-Performance Key-Value Store via Fine-Grained Deduplication

Log-Structured Merge Tree (LSM-tree) based key-value stores excel in write-intensive environments but suffer from data duplication, consuming up to 49% of storage space in LSM-tree-based key-value store deployments. Traditional solutions like compression and coarse-grained file system-level deduplication introduce overhead or have limited effectiveness. In this study, we propose DedupKV, a fine-grained deduplication framework tailored for LSM-tree, maximizing data reduction efficiency while minimizing write stalls and read overheads. DedupKV features three key innovations: (1) FLUSH-integrated inline deduplication, which removes duplicates during memory-to-storage writes; (2) WAL file-based offline deduplication, repurposing write-ahead logs to avoid double writes; and (3) elastic execution, dynamically balancing inline and offline deduplication based on memory pressure and workload intensity. Additionally, dynamic granularity management reduces deduplication metadata overhead. We implemented these four ideas in RocksDB for the first time and conducted experiments in a Linux environment. Our evaluation shows that WAL file-based offline deduplication and DedupKV outperform BlobDB by 33% and 23%, respectively, in write-heavy workloads, while reducing write amplification by 1.2 ×, 2 ×, and 1.6 × for real KV datasets.

Jamil, Safdar [Sogang University]↗
DOE OSTI2025

Compilation of Experimental Yield Data for Spontaneous Fission of 252 Cf

We present a comprehensive compilation and curation of experimental fission yield (FY) data for the spontaneous fission of 252 Cf, extracted from the EXFOR database. The compilation follows a structured methodology developed for prior compilations of neutron-induced fission yields, and incorporates both independent (IFY) and cumulative (CFY) yields. A total of 62 datasets were reviewed, with entries spanning from 1955 to 2021. A significant portion of the literature reports pre-neutron emission yields, which were excluded from the present compilation due to limitations in format compatibility. Each accepted dataset was processed into a standardized JSON format, including metadata, uncertainties, and bibliographic references. Where available, decay radiation information was used to update the FY data using the latest ENSDF evaluations; 237 data points were corrected accordingly. These corrections are fully traceable and preserve original values. The result is a curated dataset suitable for use in nuclear data evaluations. This work is part of an ongoing effort to modernize the handling of FY data and provide evaluators with high-quality, machine-readable experimental inputs

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

AIACHNE's contribution for Nuclear Energy Agency Working Party on International Nuclear Data Evaluation Co-operation Subgroup 50

The AIACHNE (AI/ML Informed cAlifornium CHi Nuclear data Experiment) project aims at designing an experiment for the 252 Cf Prompt Fission Neutron Spectrum (PFNS) that explores systematic biases in an experimental database retrieved from the EXFOR databases. To that end, machine learning (ML) methods were applied to pint-point measurement features likely related to bia. From that information, we selected a feature that should be explored by the AIACHNE experiment. Measurement features are metadata encapsulating all pertinent information about the physical measurement and analysis techniques. Examples are, for instance, what neutron and fission detectors were used for the physical metadata, and what background reduction techniques were employed for analysis techniques. Such metadata were retrieved both from EXFOR entries as well as the literature of data sets described in detail in Ref. [2]. The prerequisite for applying machine learning techniques is casting the metadata into a format that can be parsed by the algorithm. This step might seem trivial but requires to find a unique language where metadata that carry the same physics meaning across several experiments must have the same identifier. One example is, for instance, the neutron detector. As seen in Figure 1, the machine learning code identified the use of 6 Li detectors as being related to bias in some datasets of the AIACHNE 252 Cf PFNS experimental database. In fact, here are several experiments that used neutron detectors containing 6Li in the database, for instance for the example below. EXFOR format has a unique keywords describing detectors such as “SCIN” or “GLASD”. One may think that these keywords are already sufficient descriptors for ML to uniquely find an issue. However, “SCIN” (used for [3, 4]) and “GLASD” (used for [5]) fail to inform the algorithm what is the active material in the detector. And, the key common issue leading to bias in 252 Cf related to neutron detectors is not whether it is a glass detector or a scintillator. No, the issue is that 6 Li was within both detector types and that even small mistakes in the detector response functions around approximately 200 keV are amplified by the 6 Li(n,α) resonance there leading to bias in data as highlighted in Fig. 1 and Ref. [1]. Hence, the features describing the neutron detector must call out the active material in the detector, rather than the existing EXFOR detector keyword, that the ML algorithm can find physically meaningful features related to bias. The AIACHNE team used a precursor of the WPEC (Working Party on International Nuclear Data Evaluation Co-operation) SG(Subgroup)-50 format to store the metadata for the ML analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Livewire: A Model Platform for Data Quality Assessment and AI Readiness Across DOE Missions

High-quality, well-governed data is essential for accelerating discovery and achieving operational excellence across DOE and national laboratory missions. The Livewire Data Platform is a DOE-supported platform that offers automated assessments of data quality, standardization, provenance, and Artificial Intelligence (AI) readiness. It allows researchers and data practitioners to systematically and easily evaluate datasets against established governance criteria and prepare them for advanced analytics. Livewire addresses critical challenges in DOE's data ecosystem with integrated capabilities for metadata validation, provenance tracking, and schema alignment. This platform's automated workflows assist users in identifying data quality gaps, enhancing interoperability between datasets collected from various stakeholders, and ensuring compliance with DOE data standards, all while reducing manual curation efforts. Additionally, we will discuss its AI readiness framework, which is being developed to prepare datasets for training models, developing advanced analytic tools, and machine learning applications. Using some of the more than one hundred tabular datasets on Livewire, processed with this open-source methodology, we will demonstrate how Livewire can serve as a model for scalable, standards-driven data management. This approach provides a pathway to leverage existing and future datasets within the DOE, boosting innovation and efficiency across national laboratories.

33 - ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

PPI DataHub Project Data Package: S. elongatus PCC 7942 Limited Proteolysis and Thermal Proteome Profiling Structural Proteomics (JM-PB-DP3)

The purpose of this experiment was to investigate structural alterations in proteins involved in central carbon metabolism and photosynthetic electron transfer pathways in Synechococcus elongatus PCC 7942. Sample data was obtained from S. elongatus cell lysates using three complementary mass spectrometry (MS) techniques using limited proteolysis (LiP-MS), thermal proteome profiling (TPP-MS), and redox enrichment (Redox-MS) in evaluating alterations solvent accessibility and structural stability caused by light perturbation at the molecular level. Experimentally processed sample data for LiP and TPP proteomic datasets were derived from the same cell culture stock, prepared simultaneously in parallel, and acquired by mass spectrometry. Processed datasets are openly accessible from the download button and contain secondary processed proteomic results files, computed outputs, and supporting metadata materials. Experimental samples processed for LiP-MS label-free quantification (LFQ) or TPP-MS tandem mass tag (TMT) 10-plex were acquired using a Q-Exactive HF-X mass spectrometer and processed/compiled using either MSGF+ (v2024.03.26) or ​​​​PlexedPiper for proteome evaluation. Additional software supporting downstream proteomic analysis include FragPipe (v.4.0), MSFragger (v.22.1), and an adapted Microbial Isolate LiP Analysis Workflow (located at Zenodo). Processed proteomic data downloads include a sample naming key, normalized quantification results files, and processed protein annotated abundance files.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Evaluation of Best Practices in Mitigating Startup Costs on Leadership-Class Supercomputers

Supercomputers at Department of Energy (DOE) National Laboratories face a widening range of workloads, from traditional modeling and simulation to Artificial Intelligence model training or complex multi-stage workflows, and beyond. At DOE Leadership Computing Facilities like the Oak Ridge Leadership Computing Facility (OLCF), these workloads demand concurrent access to large portions of the supercomputer’s resources. Launching a job across massive supercomputers is challenging from the start; the file system struggles with a large backlog of metadata requests as tens of thousands of processes read thousands of the same files, and the compute job cannot start until this is completed. There are multiple existing approaches to calm this metadata storm, ranging from vendor-developed tools like sbcast to National Laboratory-developed tools like Spindle and Copper. In this paper, we benchmark and discuss three common approaches to improving compute job launch latencies on Frontier: Slurm’s sbcast tool, Spindle, and Copper. We evaluate these tools by measuring the launch latencies of four workloads: OSU Microbenchmark’s osu_init, Pynamic, Python import mpi4py, and Python import torch. We provide discussion of the results, highlighting data that meet expectations and that do not meet expectations.

Hagerty, Nick [ORNL] (ORCID:0000000330014414)↗
DOE OSTI2025

Benchmark Tracking System for Performance Monitoring

Benchmarking is essential for high-performance software development, particularly for monitoring performance across code iterations. This project focused on enhancing the benchmarking process for Lamellar, an asynchronous runtime for High-Performance Computing (HPC) systems developed at Pacific Northwest National Laboratory. Prior to this work, benchmark results were difficult to track and compare across code versions, presenting significant challenges in identifying performance regressions and long-term trends. The primary objective was to establish a systematic, reproducible approach for measuring performance and detecting regressions following code commits. Our methodology involved three key components: standardizing benchmark outputs, implementing data versioning, and developing analysis tools. We standardized the benchmark output format to JSON Line records containing specific fields (execution time, hardware specifications, and environmental variables). To address data management challenges, we evaluated several options and eventually chose a git repository dedicated to benchmark data. We developed a suite of Python tools that processed benchmark results, enriched them with metadata, and facilitated search in the repository. The resulting system enables more efficient filtering and comparison of performance metrics across commit histories, hardware configurations, and benchmark variants through a unified query interface. Our implementation reduces computational overhead by first checking for existing results through configuration matching before initiating new benchmark runs, thereby conserving resources. The system has been validated by Lamellar developers. It organizes results by benchmark type and build configurations for efficient retrieval. Future developments include a planned Large Language Model interface for predicting benchmark performance, incorporating the criterion package for statistical analysis, which will enable automated detection of statistically significant performance changes, and integration with continuous integration pipelines. Despite these enhancements being reserved for future work, this project has successfully provided the Lamellar development team with a framework for maintaining consistent performance standards and identifying optimization opportunities across workloads and hardware environments.

97 MATHEMATICS AND COMPUTING↗