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At least 91 records · Page 5

Hyper Suprime-Cam Year 3 results: Cosmology from galaxy clustering and weak lensing with HSC and SDSS using the emulator based halo model

We present cosmology results from a blinded joint analysis of cosmic shear, galaxy-galaxy weak lensing, and projected galaxy clustering, measured from the Hyper Suprime-Cam three-year (HSC-Y3) shape catalog and the Sloan Digital Sky Survey (SDSS) DR11 spectroscopic galaxy catalog—a cosmology analysis. We define luminosity-cut, and therefore nearly volume-limited, samples of SDSS galaxies to serve as the tracers of w p and as the lens samples for Δ⁢Σ in three spectroscopic redshift bins spanning the range 0.15± and Δ⁢Σ measurements, we use a single sample of about seven million source galaxies over 416 deg 2 , selected from HSC-Y3 based on having photometric redshifts (photo-z) greater than 0.75. The deep, high-quality HSC-Y3 data enable significant detections of the Δ⁢Σ signals, with integrated signal-to-noise ratio S/N~24 in the range 3≤R/[ℎ –1 Mpc]≤30 over the three lens samples. ξ ± has S/N ~19 in the range 8' ≤$\theta$ ≤5⁢0' and 30' ≤$\theta$ ≤15⁢0' for ξ + and ξ – , respectively. For cosmological parameter inference, we use the dark emulator package, combined with a halo occupation distribution prescription for the relation between galaxies and halos, to model w p and Δ⁢Σ down to quasinonlinear scales, and we estimate cosmological parameters after marginalizing over nuisance parameters. In our baseline analysis we employ an uninformative flat prior of the residual photo-z error, given by Π⁡(Δz ph )=$U$⁡(–1,1), to model a residual bias in the mean redshift of HSC source galaxies. Comparing the relative lensing amplitudes for Δ⁢Σ in the three redshift bins and for ξ ± with the single HSC source galaxy sample allows us to calibrate the photo-z parameter Δ⁢z ph to the precision of σ⁡(Δ⁢z ph )≃0.09. With these methods, we obtain a robust constraint on the cosmological parameters for the flat Λ⁢CDM model: S 8 =σ 8 ⁢(Ω m /0.3) 0.5 =$0.763^{+0.040}_{–0.036}$, or the best-constrained parameter given by $S^{'}_{8}$ = σ 8 ⁢(Ω m /0.3) 0.22 =0.721±0.028, determined with about 4% fractional precision. Based on multidimensional tension metrics, HSC-Y3 data exhibits about 2.5σ tension with the cosmological constraint inferred by Planck for the Λ⁢CDM model, and hints at a nonzero residual photo-z bias implying that the true mean redshift of the HSC galaxies at z ≳0.75 is higher than that implied by the original photo-z estimates.

79 ASTRONOMY AND ASTROPHYSICS↗

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

97 MATHEMATICS AND COMPUTING↗

CAMERA: A method for cost-aware, adaptive, multifidelity, efficient reliability analysis

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distributions, and Monte Carlo sampling methods are intractable when expensive high-fidelity simulations have to be queried. Here, we propose a method to use models of multiple fidelities that trade accuracy for computational efficiency. Specifically, we propose the use of multifidelity Gaussian process models to efficiently fuse models at multiple fidelity, thereby offering a cheap surrogate model that emulates the original model at all fidelities. Furthermore, we propose a novel sequential acquisition function based experiment design framework that can automatically select samples from appropriate fidelity models to make predictions about quantities of interest at the highest fidelity. We use our proposed approach in an importance sampling setting and demonstrate our method on the failure level set and probability estimation on synthetic test functions and two real-world applications, namely, the reliability analysis of a gas turbine engine blade using a finite element method and a transonic aerodynamic wing test case using Reynolds-averaged Navier-Stokes equations. We show that our method predicts the failure boundary and probability more accurately and at a fraction of the computational cost compared with using just a single expensive high-fidelity model. Finally, we show that our sequential approach is guaranteed to asymptotically converge to the true failure boundary with high probability.

97 MATHEMATICS AND COMPUTING↗

Modeling with uncertainty quantification reveals the essentials of a non-canonical algal carbon-concentrating mechanism

The thermoacidophilic red alga Cyanidioschyzon merolae survives its challenging environment likely in part by operating a carbon-concentrating mechanism (CCM). Here, we demonstrated that C. merolae 's cellular affinity for CO 2 is stronger than the affinity of its rubisco for CO 2 . This finding provided additional evidence that C. merolae operates a CCM while lacking the structures and functions characteristic of CCMs in other organisms. To test how such a CCM could function, we created a mathematical compartmental model of a simple CCM, distinct from those we have seen previously described in detail. The results of our modeling supported the feasibility of this proposed minimal and non-canonical CCM in C. merolae . To facilitate the robust modeling of this process, we measured and incorporated physiological and enzymatic parameters into the model. Additionally, we trained a surrogate machine-learning model to emulate the mechanistic model and characterized the effects of model parameters on key outputs. This parameter exploration enabled us to identify model features that influenced whether the model met the experimentally derived criteria for functional carbon concentration and efficient energy usage. Such parameters included cytosolic pH, bicarbonate pumping cost and kinetics, cell radius, carboxylation velocity, number of thylakoid membranes, and CO 2 membrane permeability. Our exploration thus suggested that a non-canonical CCM could exist in C. merolae and illuminated the essential features generally necessary for CCMs to function.

Steensma, Anne K. [Michigan State Univ., East Lans↗

Comparing emulation methods for a high‐resolution storm surge model

Abstract Realistic simulations of complex systems are fundamental for climate and environmental studies. Large computer systems are often not sufficient to run sophisticated computational models for large numbers of different input settings. Statistical surrogate models, or emulators, are key tools enabling fast exploration of the simulator input space. Gaussian processes have become standard for computer simulator emulation. However, they require careful implementation to scale appropriately, motivating alternative methods more recently introduced. We present a comparison study of surrogates of the Sea, Lake, and Overland Surges from Hurricanes (SLOSH) simulator—the simulator of choice for government agencies—using four emulation approaches: BASS; BART; SEPIA; and RobustGaSP. SEPIA and RobustGaSP use Gaussian processes, BASS implements adaptive splines, and BART is based on ensembles of regression trees. We describe the four models and compare them in terms of computation time and predictive metrics. These surrogates use proven and distinct methodologies, are available through accessible software, and quantify prediction uncertainty. Our data cover millions of response values. We find that SEPIA and RobustGaSP provide exceptional predictive power, but cannot scale to emulate experiments as large as the one considered in this paper as effectively as BASS and BART.

Hutchings, Grant↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO2, temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

James A Franke↗

Appendices to the model description document for a computer program for the emulation/simulation of a space station environmental control and life support system

A Model Description Document for the Emulation Simulation Computer Model was already published. The model consisted of a detailed model (emulation) of a SAWD CO2 removal subsystem which operated with much less detailed (simulation) models of a cabin, crew, and condensing and sensible heat exchangers. The purpose was to explore the utility of such an emulation simulation combination in the design, development, and test of a piece of ARS hardware, SAWD. Extensions to this original effort are presented. The first extension is an update of the model to reflect changes in the SAWD control logic which resulted from test. Also, slight changes were also made to the SAWD model to permit restarting and to improve the iteration technique. The second extension is the development of simulation models for more pieces of air and water processing equipment. Models are presented for: EDC, Molecular Sieve, Bosch, Sabatier, a new condensing heat exchanger, SPE, SFWES, Catalytic Oxidizer, and multifiltration. The third extension is to create two system simulations using these models. The first system presented consists of one air and one water processing system. The second consists of a potential air revitalization system.

Yanosy, James L.↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO 2 , temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

54 ENVIRONMENTAL SCIENCES↗

Loosely Conditioned Emulation of Global Climate Models With Generative Adversarial Networks

Climate models encapsulate our best understanding of the Earth system, allowing research to be conducted on its future under alternative assumptions of how human-driven climate forces are going to evolve. An important application of climate models is to provide metrics of mean and extreme climate changes, particularly under these alternative future scenarios, as these quantities drive the impacts of climate on society and natural systems. Because of the need to explore a wide range of alternative scenarios and other sources of uncertainties in a computationally efficient manner, climate models can only take us so far, as they require significant computational resources, especially when attempting to characterize extreme events, which are rare and thus demand long and numerous simulations in order to accurately represent their changing statistics. Here we use deep learning in a proof of concept that lays the foundation for emulating global climate model output for different scenarios. We train two "loosely conditioned" Generative Adversarial Networks (GANs) that emulate daily precipitation output from a fully coupled Earth system model: one GAN modeling Fall-Winter behavior and the other Spring-Summer. Our GANs are trained to produce spatiotemporal samples: 32 days of precipitation over a 64x128 regular grid discretizing the globe. We evaluate the generator with a set of related performance metrics based upon KL divergence, and find the generated samples to be nearly as well matched to the test data as the validation data is to test. We also find the generated samples to accurately estimate the mean number of dry days and mean longest dry spell in the 32 day samples. Our trained GANs can rapidly generate numerous realizations at a vastly reduced computational expense, compared to large ensembles of climate models, which greatly aids in estimating the statistics of extreme events.

climate emulation, extreme climate, impacts, machi↗

Bayesian Adaptive Polynomial Chaos Expansions

Polynomial chaos expansions (PCEs) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare—especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that the Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis and ordinal regression tasks.

97 MATHEMATICS AND COMPUTING↗

Impala

SAND2025-07450O Impala is a software tool that performs Bayesian model calibration for emulator-based models. The program uses R code to perform the calculations. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Tucker, James [Sandia National Lab. (SNL-CA), Live↗

Process membership in asynchronous environments

The development of reliable distributed software is simplified by the ability to assume a fail-stop failure model. The emulation of such a model in an asynchronous distributed environment is discussed. The solution proposed, called Strong-GMP, can be supported through a highly efficient protocol, and was implemented as part of a distributed systems software project at Cornell University. The precise definition of the problem, the protocol, correctness proofs, and an analysis of costs are addressed.

Ricciardi, Aleta M.↗

Hardware-Based Emulator with Deep Learning Model for Building Energy Control and Prediction Based on Occupancy Sensors’ Data

Heating, ventilation, and air conditioning (HVAC) is the largest source of residential energy consumption. Occupancy sensors’ data can be used for HVAC control since it indicates the number of people in the building. HVAC and sensors form a typical cyber-physical system (CPS). In this paper, we aim to build a hardware-based emulation platform to study the occupancy data’s features, which can be further extracted by using machine learning models. In particular, we propose two hardware-based emulators to investigate the use of wired/wireless communication interfaces for occupancy sensor-based building CPS control, and the use of deep learning to predict the building energy consumption with the sensor data. We hypothesize is that the building energy consumption may be predicted by using the occupancy data collected by the sensors, and question what type of prediction model should be used to accurately predict the energy load. Another hypothesis is that an in-lab hardware/software platform could be built to emulate the occupancy sensing process. The machine learning algorithms can then be used to analyze the energy load based on the sensing data. To test the emulator, the occupancy data from the sensors is used to predict energy consumption. The synchronization scheme between sensors and the HVAC server will be discussed. We have built two hardware/software emulation platforms to investigate the sensor/HVAC integration strategies, and used an enhanced deep learning model—which has sequence-to-sequence long short-term memory (Seq2Seq LSTM)—with an attention model to predict the building energy consumption with the preservation of the intrinsic patterns. Because the long-range temporal dependencies are captured, the Seq2Seq models may provide a higher accuracy by using LSTM architectures with encoder and decoder. Meanwhile, LSTMs can capture the temporal and spatial patterns of time series data. The attention model can highlight the most relevant input information in the energy prediction by allocating the attention weights. The communication overhead between the sensors and the HVAC control server can also be alleviated via the attention mechanism, which can automatically ignore the irrelevant information and amplify the relevant information during CNN training. Our experiments and performance analysis show that, compared with the traditional LSTM neural network, the performance of the proposed method has a 30% higher prediction accuracy.

Ye, Zhijing↗

Spatio–Temporal Machine Learning for Regional to Continental Scale Terrestrial Hydrology

Integrated hydrologic models can simulate coupled surface and subsurface processes but are computationally expensive to run at high resolutions over large domains. Here we develop a novel deep learning model to emulate subsurface flows simulated by the integrated ParFlow–CLM model across the contiguous US. We compare convolutional neural networks like ResNet and UNet run autoregressively against our novel architecture called the Forced SpatioTemporal RNN (FSTR). The FSTR model incorporates separate encoding of initial conditions, static parameters, and meteorological forcings, which are fused in a recurrent loop to produce spatiotemporal predictions of groundwater. We evaluate the model architectures on their ability to reproduce 4D pressure heads, water table depths, and surface soil moisture over the contiguous US at 1 km resolution and daily time steps over the course of a full water year. The FSTR model shows superior performance to the baseline models, producing stable simulations that capture both seasonal and event–scale dynamics across a wide array of hydroclimatic regimes. The emulators provide over 1,000× speedup compared to the original physical model, which will enable new capabilities like uncertainty quantification and data assimilation for integrated hydrologic modeling that were not previously possible. Our results demonstrate the promise of using specialized deep learning architectures like FSTR for emulating complex process–based models without sacrificing fidelity.

54 ENVIRONMENTAL SCIENCES↗

The DESI PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) Mock Challenge

The PRObabilistic Value-added Bright Galaxy Survey (PROVABGS) catalog will provide measurements of galaxy properties, such as stellar mass ($M*$), star formation rate (SFR), stellar metallicity (Z), and stellar age ($t_{age}$), for >10 million galaxies of the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey. Full posterior distributions of the galaxy properties will be inferred using state-of-the-art Bayesian spectral energy distribution (SED) modeling of DESI spectroscopy and Legacy Surveys photometry. In this work, we present the SED model, the neural emulator for the model, and the Bayesian inference framework of PROVABGS. Furthermore, we apply the PROVABGS SED modeling on realistic synthetic DESI spectra and photometry, constructed using the L-Galaxies semi-analytic model. We compare the inferred galaxy properties to the true values of the simulation using a hierarchical Bayesian framework to quantify accuracy and precision. Overall, we accurately infer the true $M*$, SFR, Z, and $t_{age}$ of the simulated galaxies. However, the priors on galaxy properties induced by the SED model have a significant impact on the posteriors, which we characterize in detail. This work also demonstrates that a joint analysis of spectra and photometry significantly improves the constraints on galaxy properties over photometry alone and is necessary to mitigate the impact of the priors. With the methodology presented and validated in this work, PROVABGS will maximize information extracted from DESI observations and extend current galaxy studies to new regimes and unlock cutting-edge probabilistic analyses. https://github.com/changhoonhahn/provabgs/

79 ASTRONOMY AND ASTROPHYSICS↗

Machine-learning-based estimates of global natural vegetated wetland methane emissions (2000–2025)

Wetlands are the largest natural source of atmospheric methane (CH 4 ), yet comprehensive global budgets are typically delayed by years, preventing a timely understanding of CH 4 sources, sinks, and trends. To reduce this delay, we present a model emulator-driven framework and accompanying workflow that enable timely, continuous emission updates using a machine-learning emulator to reconstruct spatially explicit monthly emission fields at 1° × 1° resolution. We apply this framework to a global dataset of natural vegetated wetland CH 4 emissions to extend the most recent Global Methane Budget (GMB; Saunois et al., 2025) record that covers the 2000–2020 emissions through 2025. In the test data (∼ 30 % of the total dataset), the emulator achieved a global R 2 of 0.65 ± 0.003 (mean ± 95 % CI, hereafter) and an RMSE of 5.49 ± 0.12×10 -3 Tg CH 4 yr −1 . The emulator is trained on 35 GMB model estimates, including 22 process-based models and 13 atmospheric inversions, paired with 10 ensemble realizations of 11 gridded climate predictor variables from atmospheric reanalyses. Our results show that the global mean predicted wetland CH 4 emissions for 2021–2025 (157.8 ± 2.4 Tg CH 4 yr −1 ) are not significantly higher (∼ 0.05 Tg CH 4 yr −1 ) than the 2000–2020 baseline. However, this stability masks a significant hemispheric redistribution of emissions. We detect an increase in Northern Hemisphere (NH) emissions in 2021–2025, with mid- and high-latitudes increasing by 0.76 ± 0.07 and 0.35 ± 0.03 Tg CH 4 yr −1 , respectively, while the tropics and Southern Hemisphere (SH) extratropics show offsetting negative trends (−0.95 ± 0.19 and -0.11 ± 0.02 Tg CH 4 yr −1 , respectively). The predicted emissions are able to capture the low emissions in 2023 in South America linked to El Niño-related drought, as reported by recent studies (Ciais et al., 2026; Quinn et al., 2025). Furthermore, we identify a distinct seasonal amplification of global emission trends that peaks in late boreal summer. This new modeled dataset and operational framework bridge the gap between the latest updated budgets and low-latency monitoring, providing a scalable capacity to frequently update global emission estimates and critical early warnings of regional wetland feedback loops. The data are publicly available at https://doi.org/10.5281/zenodo.18870108 (Li et al., 2026).

Li, Mengze [National University of Singapore (Sing↗

A machine learning approach targeting parameter estimation for plant functional type coexistence modeling using ELM-FATES (v2.0)

Tropical forest dynamics play a crucial role in the global carbon, water, and energy cycles. However, realistically simulating the dynamics of competition and coexistence between different plant functional types (PFTs) in tropical forests remains a significant challenge. This study aims to improve the modeling of PFT coexistence in the Functionally Assembled Terrestrial Ecosystem Simulator (FATES), a vegetation demography model implemented in the Energy Exascale Earth System Model (E3SM) land model (ELM), ELM-FATES. Specifically, we explore (1) whether plant trait relationships established from field measurements can constrain ELM-FATES simulations and (2) whether machine learning (ML)-based surrogate models can emulate the complex ELM-FATES model and optimize parameter selections to improve PFT coexistence modeling. We conducted three ensembles of ELM-FATES experiments at a tropical forest site near Manaus, Brazil. By comparing the ensemble experiments without (Exp-CTR) and with (Exp-OBS) consideration of observed trait relationships, we found that accounting for these relationships slightly improves the simulations of water, energy, and carbon variables when compared to observations but degrades the simulation of PFT coexistence. Using ML-based surrogate models trained on Exp-CTR, we optimized the trait parameters in ELM-FATES and conducted another ensemble of experiments (Exp-ML) with these optimized parameters. The proportion of PFT coexistence experiments significantly increased from 21 % in Exp-CTR to 73 % in Exp-ML. After filtering the experiments that allow for PFT coexistence to agree with observations (within 15 % tolerance), 33 % of the Exp-ML experiments were retained, which is a significant improvement compared to the 1.4 % in Exp-CTR. Exp-ML also accurately reproduces the annual means and seasonal variations in water, energy, and carbon fluxes and the field inventory of aboveground biomass. This study represents a reproducible method that utilizes machine learning to identify parameter values that improve model fidelity against observations and PFT coexistence in vegetation demography models for diverse ecosystems. Our study also suggests the need for new mechanisms to enhance the robust simulation of coexisting plants in ELM-FATES and has significant implications for modeling the response and feedbacks of ecosystem dynamics to climate change.

54 ENVIRONMENTAL SCIENCES↗

A Structured Microprogram Set for the SUMC Computer to Emulate the IBM System/360, Model 50

Similarities between regular and structured microprogramming were examined. An explanation of machine branching architecture (particularly in the SUMC computer), required for ease of structured microprogram implementation is presented. Implementation of a structured microprogram set in the SUMC to emulate the IBM System/360 is described and a comparison is made between the structured set with a nonstructured set previously written for the SUMC.

Gimenez, Cesar R.↗