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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.

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At least 199 records · Page 11
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DOE OSTI2022

A Probabilistic Autoencoder for Type Ia Supernova Spectral Time Series

We construct a physically parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of Type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an autoencoder that is interpreted probabilistically after training using a normalizing flow. We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multistage training setup alongside our physically parameterized network, we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including the automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an rms of 0.091 ± 0.010 mag, which corresponds to 0.074 ± 0.010 mag if peculiar velocity contributions are removed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Geospatial coherence of surface-atmosphere fluxes in the upper Great Lakes region

Surface-atmosphere fluxes are known to vary at multiple time scales, but uncertainty is high as to how fluxes change spatially within regions. With an increase in the number of eddy covariance towers, we are now able to examine the geospatial coherence of ecosystem fluxes, using time-series correlation. Eighteen sites from Michigan and Wisconsin were used in this study, ranging from 100 m to 600 km apart. Surface-atmosphere fluxes from a six-month period were used to quantify spatial coherence on a pair-wise basis. Using geospatial statistics, carbon and sensible heat (H) fluxes were found to be 95% correlated directly outside of their flux footprint and 56% correlated up to a distance of ~35 km. Latent (LE) and momentum (τ) fluxes were less correlated, 83% directly outside of their flux footprint and 40% at a distance of ~130 km albeit, at a much larger spatial distance than for the carbon and sensible heat fluxes. All fluxes showed strong spectral resonance at diel and seasonal timescales, with 1-, 2- and 3-month periods being common modes of variability among H, LE, and τ fluxes. Results based on Empirical Orthogonal Function show distinct transitions of net ecosystem exchange from fall to winter before photosynthesis or respiration while H and τ do not exhibit coherent trends. Here, this work demonstrates the potential of quantifying geospatial coherence of surface-atmosphere fluxes in the Midwestern United States, with the ability to predict fluxes beyond the spatial limit of a single flux tower footprint. Ultimately, expanding the flux measurements to larger scales would allow better spatial scaling of terrestrial surface-atmosphere fluxes between tower footprint and modeling or remote sensing scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Conserving Land–Atmosphere Synthesis Suite (CLASS)

Accurate estimates of terrestrial water and energy cycle components are needed to better understand climate processes and improve models’ ability to simulate future change. Various observational estimates are available for the individual budget terms; however, these typically show inconsistencies when combined in a budget. In this work, a Conserving Land–Atmosphere Synthesis Suite (CLASS) of estimates of simultaneously balanced surface water and energy budget components is developed. Individual CLASS variable datasets, where possible, 1) combine a range of existing variable product estimates, and hence overcome the limitations of estimates from a single source; 2) are observationally constrained with in situ measurements; 3) have uncertainty estimates that are consistent with their agreement with in situ observations; and 4) are consistent with each other by being able to solve the water and energy budgets simultaneously. First, available datasets of a budget variable are merged by implementing a weighting method that accounts both for the ability of datasets to match in situ measurements and the error covariance between datasets. Then, the budget terms are adjusted by applying an objective variational data assimilation technique (DAT) that enforces the simultaneous closure of the surface water and energy budgets linked through the equivalence of evapotranspiration and latent heat. Comparing component estimates before and after applying the DAT against in situ measurements of energy fluxes and streamflow showed that modified estimates agree better with in situ observations across various metrics, but also revealed some inconsistencies between water budget terms in June over the higher latitudes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

HARMONY: Large-Scale Architecture Search for Efficient Hybrid Language Models

As large language models scale to trillions of parameters, their computational and memory requirements present critical challenges for efficient training and deployment. While Mixture of Experts (MoE) architectures enable efficient scaling through sparse parameter activation, and state-space models like Mamba offer linear-time complexity, principled methods for combining these paradigms remain undeveloped. We introduce HARMONY (Hybrid Architecture Research for Mamba, Optimized with Neural efficiencY), a multi-objective evolutionary neural architecture search framework for discovering efficient hybrid language models that integrate Transformer attention mechanisms, Mixture-of-Experts routing, and Mamba state-space components. Through large-scale distributed search using 16,384 MI250X GPUs on the Frontier supercomputer, HARMONY explores a comprehensive design space encompassing six attention variants (MHA, MQA, GQA, MLA, SWA, and Mamba-2), variable MoE configurations with both routed and shared experts, and extensive Mamba hyperparameters. Our framework discovers heterogeneous architectures that balance training performance with computational efficiency through multi-objective optimization incorporating latency penalties and fitness-based selection. Analysis of discovered architectures reveals that optimal hybrid designs favor heterogeneous component mixing rather than homogeneous patterns, with Mamba-2 and Multi-Head Latent Attention (MLA) emerging as preferred mechanisms. Discovered architectures demonstrate superior training efficiency: our best configuration achieves a final perplexity of 1.0874 with 2.38B parameters while processing 4,320 tokens/second, outperforming significantly larger manually designed models. Full-scale evaluation shows HARMONY's top architectures achieve better loss trajectories than equivalently-sized models using state-of-the-art configurations including Mixtral, Jamba, and Samba. Additionally, we demonstrate 91% weak scaling efficiency when training discovered 36B-parameter models across 1,024 GPUs. HARMONY is released as an open framework with comprehensive tools for building and training hybrid models using expert-data-pipeline parallelism, democratizing access to automated architecture design for next-generation language models.

Herron, Emily [ORNL] (ORCID:0000000273008172)↗
DOE OSTI2022

Hurricane‐Like Vortices in Conditionally Unstable Moist Convection

Abstract This study investigates the emergence of hurricane‐like vortices in idealized simulations of rotating moist convection. A Boussinesq atmosphere with simplified thermodynamics for phase transitions is forced by prescribing the temperature and humidity at the upper and lower boundaries. The governing equations are solved numerically using a variable‐density incompressible Navier‐Stokes solver with adaptive mesh refinement to explore the behavior of moist convection under a broad range of conditions. In the absence of rotation, convection aggregates into active patches separated by large unsaturated regions. Rotation modulates this statistical equilibrium state so that the self‐aggregated convection organizes hurricane‐like vortices. The warm and saturated air converges to the center of the vortices, and the latent heat released through the upwelling, forms the warm core structure. These hurricane‐like vortices share characteristics similar to tropical cyclones in the earth's atmosphere. The hurricane‐like vortices occur under conditionally unstable conditions where the potential energy given at the boundaries is large enough, corresponding to a moderate rate of rotation. This regime shares many similar characteristics to the tropical atmosphere indicating that the formation of intense meso‐scale vortices is a general characteristic of rotating moist convection. The model used here does not include any interactions with radiation, wind‐evaporation feedback, or cloud microphysics, indicating that, while these processes may be relevant for tropical cyclogenesis in the Earth atmosphere, they are not its primary cause. Instead, our results confirm that the formation and maintenance of hurricane‐like vortices involve a combination of atmospheric dynamics under the presence of rotation and of phase transitions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Explainable machine learning to quantify the value of proximal remote sensing in latent energy flux estimation

Proximal remote sensing has the potential to provide critical information on vegetation biophysical factors that can predict land-atmosphere exchange of water and energy. Latent energy (LE) flux is traditionally estimated using process-based models which rely on vegetation parameters that change during the growing season. Data-driven models have the potential to address these issues by offering flexible predictor selection and more efficient utilization of the information in predictor sets. These models require careful choice of predictors to avoid redundancy and allow robust cross-validation. In this study we present a systematic and comprehensive evaluation of machine learning (ML) models to assess the capability of meteorological and proximal sensing data for predicting LE at a half-hourly temporal resolution across multiple growing seasons for an agricultural system. The results presented here demonstrate that a model using four environmental predictors in combination with two proximal sensing variables can capture 88 % of the variability in LE. ML models using only three predictors (one meteorological and two proximal remote sensing) captured 81 % of LE variability, offering the best trade-off between performance and complexity. An ML model utilizing only two predictors, one proximal remote sensing variable and downwelling radiation, captured 77 % of LE variability. These results demonstrate the power of proximal remote sensing and meteorological observations to estimate land-atmosphere water vapor exchange, providing a solution where more direct methods such as eddy covariance are not available and for evaluations of agronomic management and genotypic variations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Effects of Surface Turbulence Flux Parameterizations on the MJO: The Role of Ocean Surface Waves

This study investigates the sensitivity of the Madden–Julian oscillation (MJO) to changes to the bulk flux parameterization and the role of ocean surface waves in air–sea coupling using a fully coupled ocean–atmosphere–wave model. The atmospheric and ocean model components of the Energy Exascale Earth System Model (E3SM) are coupled to a spectral wave model, WAVEWATCH III (WW3). Two experiments with wind speed–dependent bulk algorithms (NCAR and COARE3.0a) and one experiment with wave-state-dependent flux (COR3.0a-WAV) were conducted. We modify COARE3.0a to include surface roughness calculated within WW3 and also account for the buffering effect of waves on the relative difference between air-side and ocean-side momentum flux. Differences in surface fluxes, primarily caused by discrepancies in drag coefficients, result in significant differences in MJO’s properties. While COARE3.0a has better convection–circulation coupling than NCAR, it exhibits anomalous MJO convection east of the date line. The wave-state-dependent flux (COR3.0-WAV) improves the MJO representation over the default COARE3.0 algorithm. Strong easterlies over the Pacific Ocean in COARE3.0a enhance the latent heat flux (LHFLX). This is responsible for the anomalous MJO propagation after the date line. In COR3.0a-WAV, waves reduce the anomalous easterlies, leading to a decrease in LHFLX and MJO dissipation after the date line. These findings highlight the role of surface fluxes in MJO simulation fidelity. Most importantly, we show that the proper treatment of wave-induced effects in bulk flux parameterization improves the simulation of coupled climate variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Deconstructing criterion a of the alternative model for personality disorders.

Here, the construct composition of the Level of Personality Functioning Scale (LPFS; Criterion A) of the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition alternative model for personality disorders (American Psychiatric Association, 2013) was examined in a clinical vignette rating study. Multiple indices of level of personality functioning, psychiatric and psychosocial impairment, Criterion B maladaptive personality traits, and conceptually divergent variables (intellectual level, socioeconomic status, and likability) were used to deconstruct the LPFS. Most variables were highly intercorrelated, but partial correlational analyses showed the LPFS possesses meaningful personality construct variance not fully explained by severity of pathological traits, psychiatric and psychosocial impairment, or the conceptually divergent variables. This exploratory study offers initial evidence that the LPFS contains substantive LPF variance beyond PD severity. Results are framed and discussed in terms of the known conceptual and empirical overlap between Criterion A and Criterion B as well as the differing ways a dimension of personality disorder (PD) severity may be interpreted. Finally, we propose the LPFS is more than statistical artifact created by empirical covariation but less than a true latent dimension of PD severity. The LPFS may be understood as a methodologically pragmatic but theoretically substantive dimension of PD severity.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Effect of data assimilation in the Polar WRF with 3DVAR on the prediction of radiation, heat flux, cloud, and near surface atmospheric variables over Svalbard

Although the Polar Weather Research and Forecasting (PWRF) model has been developed for polar environments, simulations of atmospheric states in the polar region still have large uncertainties. Therefore, the effects of data assimilation (DA) to improve forecasts in the polar region were investigated for September 2017 using PWRF and the three-dimensional variational (3DVAR) DA method. The experiments without DA and those with DA assimilating only conventional observations and both conventional observations and satellite radiance data were performed. The forecasts from all experiments both without and with DA underestimated (overestimated) the downward longwave (shortwave) radiation flux due to the underestimation of the amount of Arctic clouds. When satellite radiance data (i.e., the Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS)) were assimilated in addition to conventional observations in the PWRF, the distribution and amount of water vapor became closer to observations, which improves cloud liquid water forecasts. Therefore, when both conventional observations and radiance data were assimilated, the 25–30 h forecast errors of the downward longwave and shortwave radiation fluxes and sensible and latent heat fluxes decreased by 12.7%, 8.1%, 3.2%, and 7.8% with the WSM5 scheme and by 17.1%, 4.7%, 2.5%, and 3.1% with the 2-moment Morrison scheme, respectively, compared to those in the experiments without DA. The forecast errors of the 10 m wind and 2 m temperature with DA were smaller than those without DA at most observation stations. Therefore, the uncertainties of the Arctic forecasts in the PWRF decreased when using DA. To further improve Arctic forecasts, the assimilation of various additional satellite data is necessary.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Inverse Modeling of Hydrologic Parameters in CLM4 via Generalized Polynomial Chaos in the Bayesian Framework

In this work, generalized polynomial chaos (gPC) expansion for land surface model parameter estimation is evaluated. We perform inverse modeling and compute the posterior distribution of the critical hydrological parameters that are subject to great uncertainty in the Community Land Model (CLM) for a given value of the output LH. The unknown parameters include those that have been identified as the most influential factors on the simulations of surface and subsurface runoff, latent and sensible heat fluxes, and soil moisture in CLM4.0. We set up the inversion problem in the Bayesian framework in two steps: (i) building a surrogate model expressing the input–output mapping, and (ii) performing inverse modeling and computing the posterior distributions of the input parameters using observation data for a given value of the output LH. The development of the surrogate model is carried out with a Bayesian procedure based on the variable selection methods that use gPC expansions. Our approach accounts for bases selection uncertainty and quantifies the importance of the gPC terms, and, hence, all of the input parameters, via the associated posterior probabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Boundary layer moisture variability at the Atmospheric Radiation Measurement (ARM) Eastern North Atlantic observatory during marine conditions

Abstract. Boundary layer moisture variability at the Eastern North Atlantic (ENA) site during marine conditions is examined at monthly and daily timescales using 5 years of ground-based observations and output from the European Center for Medium range Weather Forecast (ECMWF) reanalysis model. The annual cycle of the mixed-layer total water budgets is presented to estimate the relative contribution of large-scale advection, local moisture tendency, entrainment, and precipitation to balance the moistening due to surface latent heat flux on monthly timescales. When marine conditions prevail, advection of colder and dry air from the north acts as an important moisture sink (∼ 50 % of the overall budget) during fall and winter driving the seasonality of the budget. Entrainment and precipitation contribute to the drying of the boundary layer (∼ 25 % and ∼ 15 % respectively), and the local change in moisture contributes to a small residual part. On a daily temporal scale, moist and dry mesoscale columns of vapor (∼ 10 km) are analyzed during 10 selected days of precipitating stratocumulus clouds. Adjacent moist and dry columns present distinct mesoscale features that are strongly correlated with clouds and precipitation. Dry columns adjacent to moist columns have more frequent and stronger downdrafts immediately below the cloud base. Moist columns have more frequent updrafts, stronger cloud-top cooling, and higher liquid water path and precipitation compared to the dry columns. This study highlights the complex interaction between large-scale and local processes controlling the boundary layer moisture and the importance of spatial distribution of vapor to support convection and precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Ocean Surface Flux Algorithm Effects on Tropical Indo-Pacific Intraseasonal Precipitation

Surface latent heat fluxes help maintain tropical intraseasonal precipitation. We develop a latent heat flux diagnostic that depicts how latent heat fluxes vary with the near-surface specific humidity vertical gradient (Δq) and surface wind speed (|V|). Compared to fluxes estimated from |V| and Δq measured at tropical moorings and the Coupled Ocean Atmosphere Response Experiment 3.0 (COARE3.0) algorithm, tropical latent heat fluxes in the National Center for Atmospheric Research CEMS2 and Department of Energy E3SMv1 models are significantly overestimated at |V| and Δq extrema. Madden–Julian oscillation (MJO) sensitivity to surface flux algorithm is tested with offline and inline flux corrections. The offline correction adjusts model output fluxes toward mooring-estimated fluxes; the inline correction replaces the original bulk flux algorithm with the COARE3.0 algorithm in atmosphere-only simulations of each model. Both corrections indicate reduced latent heat flux feedback to intraseasonal precipitation, in better agreement with observations, suggesting that model-simulated fluxes are overly supportive for maintaining MJO convection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

ESMs Latent Space Exploration for Uncertainty Quantification and Spatiotemporal Downscaling

This final report for DOE Award DE-SC0023044 presents advances in two key areas of climate modeling: (1) representative climate model selection and (2) Earth System Model (ESM) downscaling using hybrid AI methods. The first section introduces a reordered, three-stage workflow to select representative GCM runs that more effectively balance historical skill with ensemble spread, validated across Texas, Bihar, and New York. The second section introduces two novel super-resolution frameworks, ViSIR and ViFOR, that integrate Vision Transformers with sinusoidal and Fourier-based implicit neural representations. These models achieve state-of-the-art reconstruction accuracy for ESM variables including surface temperature and heat fluxes. The report includes detailed methodology, benchmarks, and results, demonstrating significant gains in uncertainty quantification, spatial fidelity, and scalability for climate-impact studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Carbon Dioxide Flux Measurement System (CO2FLX) Instrument Handbook

The Southern Great Plains (SGP) carbon dioxide flux (CO2 flux) measurement systems provide half-hour average fluxes of CO2, H2O (latent heat), and sensible heat. The fluxes are obtained by the eddy covariance technique, which computes the flux as the mean product of the vertical wind component with CO2 and H2O densities, or estimated virtual temperature. A three-dimensional sonic anemometer is used to obtain the orthogonal wind components and the virtual (sonic) temperature. An infrared gas analyzer is used to obtain the CO2 and H2O densities. A separate sub-system also collects half-hour average measures of meteorological and soil variables from separate 4-m towers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

An Overview of Mesoscale Convective Systems: Global Climatology, Satellite Observations, and Modeling Strategies

Deep convection is responsible for redistributing water as well as energy and providing vital water resources for many regions of the world. Cumulonimbus clouds aggregation into a single storm system develop mesoscale convective systems (MCS). MCSs have precipitation covering a horizontal region on the scale of 100?km or more. After more than the last seven decades, MCS has been gradually received wide attention in the scientific community as an important component of the Earth's hydrologic cycle and energy balance. MCSs differ from ordinary deep convection because of the mesoscale circulations consisting of a layer of air overturning on a scale much larger than those created by individual convective updrafts or downdrafts. Moreover, a key feature that separates MCS from ordinary deep convection is the significant portion of stratiform precipitation that results in the production and detrainment of a large number of ice particles from their organized convective cores and continues the mesoscale ascent that supports ice growth and aggregation as the crystals fall. This significant stratiform precipitation gives rise to top-heavy latent heating profiles that have substantial impacts on the upper-level global circulations, especially for those MCS that have a larger portion of stratiform rainfall. Top-heavy latent heating profiles are more frequent over the ocean than over the land. These unique features of MCS suggest that they are important for the hydrologic cycle, general circulation, and radiative balance of the climate system. In this chapter, we focus on the recent advances in the climatological perspective of MCS as well as the research tools used to better understand MCS after the advent of the satellite era. We will discuss both tropical and midlatitude MCS, the influence of modes of tropical climate variability on MCS, and the new insight from satellite observations on MCS interaction with the land surface.

Chakraborty, Sudip↗
DOE OSTI2023

Ocean Mesoscale and Frontal-Scale Ocean–Atmosphere Interactions and Influence on Large-Scale Climate: A Review

Two decades of high-resolution satellite observations and climate modeling studies have indicated strong ocean–atmosphere coupled feedback mediated by ocean mesoscale processes, including semipermanent and meandrous SST fronts, mesoscale eddies, and filaments. The air–sea exchanges in latent heat, sensible heat, momentum, and carbon dioxide associated with this so-called mesoscale air–sea interaction are robust near the major western boundary currents, Southern Ocean fronts, and equatorial and coastal upwelling zones, but they are also ubiquitous over the global oceans wherever ocean mesoscale processes are active. Current theories, informed by rapidly advancing observational and modeling capabilities, have established the importance of mesoscale and frontal-scale air–sea interaction processes for understanding large-scale ocean circulation, biogeochemistry, and weather and climate variability. However, numerous challenges remain to accurately diagnose, observe, and simulate mesoscale air–sea interaction to quantify its impacts on large-scale processes. This article provides a comprehensive review of key aspects pertinent to mesoscale air–sea interaction, synthesizes current understanding with remaining gaps and uncertainties, and provides recommendations on theoretical, observational, and modeling strategies for future air–sea interaction research.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Modeling Land-Atmosphere Coupling at Cloud-Resolving Scale Within the Multiple Atmosphere Multiple Land (MAML) Framework in SP-E3SM

Representing subgrid variabilities of land surface processes and their upscaled effects is crucial for global climate modeling. Here, we implement a Multiple Atmosphere Multiple Land (MAML) framework in the superparamaterized version of E3SM (SP32 E3SM) to explicitly simulate the subgrid variabilities of land states and fluxes at cloud-resolving scale and their interactions with atmosphere. Comparing to the standard SP-E3SM in which all the atmospheric columns of the cloud resolving model embedded within the global atmospheric model grid interact with the same land surface (i.e., Multiple Atmosphere Single Land (MASL)), the impact of MAML on the strength of land-atmosphere coupling is limited, partly because the current implementation mainly facilitates one-way coupling between the cloud-resolving model and the land surface model. Despite such limitation, MAML increases the surface latent heat flux at the expense of sensible heat flux, and increases precipitation in India, Amazon, and Central Africa, reducing the model dry bias compared to the standard SP-E3SM. By employing a normalized gross moist stability (NGMS) diagnostic framework, we find that the increase in precipitation minus evaporation (PE) is primarily driven by the change in large-scale moisture convergence, particularly by the increase of water vapor in the lower atmosphere, while the local effect of total surface energy flux plays a minor role in the P-E change. More specifically, MAML changes the surface energy partitioning (evaporative fraction), increases the atmosphere water vapor, and further increases P-E by decreasing the NGMS. Finally, future development in the MAML framework is discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

An attention-based neural ordinary differential equation framework for modeling inelastic processes

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.

97 MATHEMATICS AND COMPUTING↗