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At least 523 records · Page 29

Interval Predictor Models for Robust System Identification

This paper proposes a framework for the identification and uncertainty quantification of plant models according to multivariable data. The only restriction imposed upon such models is for their outputs to depend continuously on their parameters. An Interval Predictor Model (IPM) prescribes the parameters of a computational model as a path-connected set thereby making each predicted output an interval-valued function of its inputs. The formulation proposed seeks the parameter set for which the predicted outputs tightly enclose the data. This set, which is modeled as a semi-algebraic set of low-degree polynomials, enables the characterization of possibly strong parameter dependencies commonly found in practice. This uncertainty characterization makes the resulting plant model amenable to robust control approaches using polynomial optimization. Furthermore, we use non-convex scenario theory to assess the reliability of the resulting IPM. This assessment yields a distribution-free upper bound on the probability that future data will fall outside the predicted intervals.

interval↗

How Low Can You Go? Using Synthetic 3D Imagery to Drastically Reduce Real-World Training Data for Object Detection

Deep convolutional neural networks (DCNNs) currently provide state-of-the-art performance on image classification and object detection tasks, and there are many global security mission areas where such models could be extremely useful. Crucially, the success of these models is driven in large part by the widespread availability of high-quality open source data sets such as Image Net, Common Objects in Context (COCO), and KITTI, which contain millions of images with thousands of unique labels. However, global security relevant objects-of-interest can be difficult to obtain: relevant events are low frequency and high consequence; the content of relevant images is sensitive; and adversaries and proliferators seek to obscure their activities. For these cases where exemplar data is hard to come-by, even fine-tuning an existing model with available data can be effectively impossible. Recent work demonstrated that models can be trained using a combination of real-world and synthetic images generated from 3D representations; that such models can exceed the performance of models trained using real-world data alone; and that the generated images need not be perfectly realistic (Tremblay, et al., 2018). However, this approach still required hundreds to thousands of real-world images for training and fine tuning, which for sparse, global security-relevant datasets can be an unrealistic hurdle. In this research, we validate the performance and behavior of DCNN models as we drive the number of real-world images used for training object detection tasks down to a minimal set. We perform multiple experiments to identify the best approach to train DCNNs from an extremely small set of real-world images. In doing so, we: Develop state-of-the-art, parameterized 3D models based on real-world images and sample from their parameters to increase the variance in synthetic image training data; Use machine learning explainability techniques to highlight and correct through targeted training the biases that result from training using completely synthetic images; and Validate our results by comparing the performance of the models trained on synthetic data to one another, and to a control model created by fine-tuning an existing ImageNet-trained model with a limited number (hundreds) of real-world images.

97 MATHEMATICS AND COMPUTING↗

Mach Stability Improvements Using an Existing Second Throat Capability at the National Transonic Facility

Recent data quality improvements at the National Transonic Facility have an intended goal of reducing the Mach number variation in a data point to within plus or minus 0.0005, with the ultimate goal of reducing the data repeatability of the drag coefficient for full-span subsonic transport models at transonic speeds to within half a drag count. This paper will discuss the Mach stability improvements achieved through the use of an existing second throat capability at the NTF to create a minimum area at the end of the test section. These improvements were demonstrated using both the NASA Common Research Model and the NTF Pathfinder-I model in recent experiments. Sonic conditions at the throat were verified using sidewall static pressure data. The Mach variation levels from both experiments in the baseline tunnel configuration and the choked tunnel configuration will be presented and the correlation between Mach number and drag will also be examined. Finally, a brief discussion is given on the consequences of using the second throat in its location at the end of the test section.

Chan, David T.↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Computer-aided light sheet flow visualization

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Stacy, Kathryn↗

Computer-Aided Light Sheet Flow Visualization

A computer-aided flow visualization process has been developed to analyze video images acquired from rotating and translating light sheet visualization systems. The computer process integrates a mathematical model for image reconstruction, advanced computer graphics concepts, and digital image processing to provide a quantitative and visual analysis capability. The image reconstruction model, based on photogrammetry, uses knowledge of the camera and light sheet locations and orientations to project two-dimensional light sheet video images into three-dimensional space. A sophisticated computer visualization package, commonly used to analyze computational fluid dynamics (CFD) data sets, was chosen to interactively display the reconstructed light sheet images, along with the numerical surface geometry for the model or aircraft under study. A description is provided of the photogrammetric reconstruction technique, and the image processing and computer graphics techniques and equipment. Results of the computer aided process applied to both a wind tunnel translating light sheet experiment and an in-flight rotating light sheet experiment are presented. The capability to compare reconstructed experimental light sheet images and CFD solutions in the same graphics environment is also demonstrated.

Stacy, Kathryn↗

Mach Stability Improvements Using an Existing Second Throat Capability at the National Transonic Facility

Recent data quality improvements at the National Transonic Facility (NTF) have an intended goal of reducing the Mach number variation in a data point to within unit vector A plus or minus 0.0005, with the ultimate goal of reducing the data repeatability of the drag coefficient for full-span subsonic transport models at transonic speeds to within half of a drag count. This paper will discuss the Mach stability improvements achieved through the use of an existing second throat capability at the NTF to create a minimum area at the end of the test section. These improvements were demonstrated using both the NASA Common Research Model and the NTF Pathfinder-I model in recent experiments. Sonic conditions at the throat were verified using sidewall static pressure data. The Mach variation levels from both experiments in the baseline tunnel configuration and the choked tunnel configuration will be presented. Finally, a brief discussion is given on the consequences of using the second throat in its location at the end of the test section.

Chan, David T.↗

Assessment of Modeling and Nuclear Data Needs for Active Neutron Interrogation

This document is the primary deliverable for a scoping study proposed to DOE National Laboratory Announcement Number LAB 19-2114 in the NNSA research area. The study supports user applications employing active neutron interrogation by providing a science plan to improve the modeling capability and the nuclear data that radiation transport codes use. Users rely on the accuracy of the elastic scattering and non-elastic cross-sections spanning thermal energies to 14 MeV (and higher in some cases) for modeling the neutron transport through complex geometries of materials potentially composed of many elements. While the elastic scattering cross-section data are accepted for all commonly occurring elements, the non-elastic cross-section data and the associated emission data include reaction channels that require attention. The study focused on the non-elastic reactions that emit secondary, also known as prompt, gammas with the premise that many users would benefit from improved modeling of these reactions. Many users develop material assay technologies based upon gamma signatures from radiative capture, inelastic scattering, and reactions on low-Z isotopes emitting multiple particles, so the nuclear data gaps, modeling deficiencies, and recommendations for addressing the shortfalls were assessed for these reactions. Fission gammas were excluded from this study because there are other efforts underway to address known shortfalls. Follow-on efforts that successfully execute the recommendations will tangibly improve to the ability to model gamma signatures and backgrounds for user applications, such as controlled substance detection, oil-well logging, and space exploration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Laser Beam Welding for in-Space Joining Demonstrated Under Vacuum on the Ground and By Parabolic Flight Experiments

High energy density electron beam welding enabled the first and, to date, only American weld performed in space during the M551 experiment on Skylab in 1973. Though welding is critical to 90% of durable goods manufacturing in America, there is not yet regular and reliable application of welding processes to the In-space Servicing, Assembly, and Manufacturing (ISAM) sector. Fundamental studies are needed to develop basic capabilities and to enhance fundamental process knowledge, which will support follow-on efforts to mature in-space welding for use in commercial, defense, and other aerospace applications. The current work seeks to build on past flights and improve understanding and quantification of materials joining in space conditions using laser beam welding (LBW). LBW offers several advantages over the electron beam welding of Skylab, amongst others: reduced electromagnetic interference, less exposure of operators to ionizing radiation, and flexible delivery through optical fibers supporting unique workpieces and joints. Since there is no orbital laboratory to mature laser beam welding for space, the current effort addresses maturation of laser beam welding through parabolic flights augmented with data collection to enable numerical modeling efforts that capture the physical effects of the space environment. This team has retrofitted an LBW experimental apparatus that can simulate the vacuum and, during a parabolic flight, the reduced gravity & microgravity conditions of in-space welding. A team of Capstone students modified the setup, originally developed by NASA Langley Research Center for electron beam free-form fabrication, to replace its electron gun with a 1 kW, 1070 nm Yb fiber laser. The apparatus was further instrumented with temperature sensing and high-speed welding cameras to monitor and record changes in the thermal state of the workpiece, the melt pool, the laser penetration level, and the development and orientation of spatter & plumes. The system will operate autonomously, demonstrating its utility to uncrewed missions. During upcoming parabolic flight campaigns expected summer 2024, this LBW equipment will weld common aerospace alloys of aluminum, stainless steel, and titanium under conditions representative of the space environment. This data will guide future computational modeling efforts of laser welding in space and help to qualify in-space welding as a viable ISAM technique.

laser beam welding↗

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗

Model Data Archive for Manuscript Titled "Evaluation of a Coupled Surface–Subsurface Hydrologic Model Using Dense Water‑Level Sensors in a Mixed Urban–Rural Watershed"

This archive provides scripts, input files, and datasets used for the implementation and evaluation of a fully coupled surface–subsurface hydrologic model in the Neches River Basin, southeast Texas. The study uses the Advanced Terrestrial Simulator (ATS) to simulate coupled surface–subsurface hydrologic processes over a mixed urban–rural watershed and evaluates model performance using a dense network of 136 in situ water-level sensors, nine U.S. Geological Survey (USGS) stream gauges, and SSEBop-derived evapotranspiration estimates during the period October 2014–June 2024. The workflow is implemented primarily in Python 3 using the Watershed Workflow package. The Jupyter notebooks can be executed using open-source software such as Anaconda JupyterLab or Visual Studio Code. Other data files include TXT, CSV, XML, SHP, TIF, NetCDF, HDF5, and ExodusII files, which can be processed using the provided Python scripts. ATS input files are provided in XML format and can be edited using any commonly used text editor. This archive contains: *Scripts and input files used to generate the ATS model setup, including watershed discretization, mesh generation, parameter mapping, and model configuration. *Jupyter notebooks used for preprocessing observational data, evaluating streamflow, water levels, and evapotranspiration, computing performance metrics, and generating the figures presented in the manuscript. *ATS simulation outputs and processed observational datasets, including OneRain and DD6 water-level sensors, USGS streamflow observations, GIS data, and supporting spatial datasets used throughout the study.

Dense water-level sensor network↗

Identifying schools at high-risk for elevated lead in drinking water using only publicly available data

Estimating the risk of lead contamination of schools' drinking water at the State level is a complex, important, and unexplored challenge. Variable water quality among water systems and changes in water chemistry during distribution affect lead dissolution rates from pipes and fittings. In addition, the locations of lead-bearing plumbing materials are uncertain. We tested the capability of six machine learning models to predict the likelihood of lead contamination of drinking water at the schools' taps using only publicly available datasets. The predictive features used in the models correspond to those with a proven correlation to the dominant, but commonly unavailable, factors that govern lead leaching: the presence of lead-bearing plumbing materials and water quality conducive to lead corrosion. By combining water chemistry data from public reports, socioeconomic information from the US census, and spatial features using Geographic Information Systems, we trained and tested models to estimate the likelihood of lead contaminated tap water in over 8,000 schools across California and Massachusetts. Our best-performing model was a Random Forest, with a 10-fold cross validation score of 0.88 for Massachusetts and 0.78 for California using the average Area Under the Receiver Operating Characteristic Curve (ROC AUC) metric. The model was then used to assign a lead leaching risk category to half of the schools across California (the other half was used for training). There was good agreement between the modeled risk categories and the actual lead leaching outcomes for every school; however, the model overestimated the lead leaching risk in up to 17% of the schools. This model is the first of its kind to offer a tool to predict the risk of lead leaching in schools at the State level. Further use of this model can help deploy limited resources more effectively to prevent childhood lead exposure from school drinking water.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

High Precision Thermal, Structural and Optical Analysis of an External Occulter Using a Common Model and the General Purpose Multi-Physics Analysis Tool Cielo

The efficient simulation of multidisciplinary thermo-opto-mechanical effects in precision deployable systems has for years been limited by numerical toolsets that do not necessarily share the same finite element basis, level of mesh discretization, data formats, or compute platforms. Cielo, a general purpose integrated modeling tool funded by the Jet Propulsion Laboratory and the Exoplanet Exploration Program, addresses shortcomings in the current state of the art via features that enable the use of a single, common model for thermal, structural and optical aberration analysis, producing results of greater accuracy, without the need for results interpolation or mapping. This paper will highlight some of these advances, and will demonstrate them within the context of detailed external occulter analyses, focusing on in-plane deformations of the petal edges for both steady-state and transient conditions, with subsequent optical performance metrics including intensity distributions at the pupil and image plane.

integrated modeling↗

Weather Prediction Improvement Using Advanced Satellite Technology

We discuss in this paper some of the problems that exist today in the fall utilization of satellite data to improve weather forecasts and we propose specific recommendations to solve them. This discussion can be viewed as an aspect of the general debate on how best to organize the transition from research to operational satellites and how to evaluate the impact of a research instrument on numerical weather predictions. A method for providing this transition is offered by the National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP). This mission will bridge the time between the present NOAA and Department of Defense (DOD) polar orbiting missions and the initiation of the converged NPOESS series and will evaluate some of the Earth Observing System (EOS) instruments as appropriate for operational missions. Thus, this mission can be viewed as an effort to meet the operational requirements of NOAA and DOD and the research requirements of NASA. More generally, however, it can be said that the process of going from the conception of new, more advanced instruments to their operational implementation and full utilization by the weather forecast communities is not optimal. Instruments developed for research purposes may have insufficient funding to explore their potential operational capabilities. Furthermore, instrument development programs designed for operational satellites typically have insufficient funding for assimilation algorithms needed to transform the satellite observations into data that can be used by sophisticated global weather forecast models. As a result, years often go by before satellite data are efficiently used for operational forecasts. NASA and NOAA each have unique expertise in the design of satellite instruments, their use for basic and applied research and their utilization in weather and climate research. At a time of limited resources, the two agencies must combine their efforts to work toward common goals of full utilization of satellite data. This is a challenge that requires the assimilation of myriad new data into increasingly sophisticated numerical forecast models that run on increasingly sophisticated computer systems. In section II, we briefly outline the impact of satellite data on the quality of the National Centers for Environmental Prediction (NCEP) forecasts. In section III, we describe the present status of the utilization of satellite data in NCEP models and the challenges that lie ahead. In section IV, we propose solutions whose goals are summarized in section V.

Einaudi, Franco↗

Selecting Meteorological Input for the Global Modeling Initiative Assessments

The Global Modeling Initiative (GMI) science team has developed a three dimensional chemistry and transport model (CTM) to evaluate the impact of the exhaust of supersonic aircraft on the stratosphere. An important goal of the GMI is to test modules for numerical transport, photochemical integration, and model dynamics within a common framework. This work is focussed on the dependence of the overall assessment on the wind and temperature fields used by the CTM. Three meteorological data sets for the stratosphere were available to GMI: the National Center for Atmospheric Research Community Climate Model (CCM2), the Goddard Earth Observing System Data Assimilation System (GEOS-DAS), and the Goddard Institute for Space Studies general circulation model (GISS-2'). Objective criteria were established by the GMI team to evaluate which of these three data sets provided the best representation of trace gases in the stratosphere today. Tracer experiments were devised to test various aspects of model transport. Stratospheric measurements of long-lived trace gases were selected as a test of the CTM transport. This presentation describes the criteria used in grading the meteorological fields and the resulting choice of wind fields to be used in the GMI assessment. This type of objective model evaluation will lead to a higher level of confidence in these assessments. We suggest that the diagnostic tests shown here be used to augment traditional general circulation model evaluation methods.

Strahan, Susan↗

Cognitive Modeling of Video Game Player User Experience

This paper argues for the use of cognitive modeling to gain a detailed and dynamic look into user experience during game play. Applying cognitive models to game play data can help researchers understand a player's attentional focus, memory status, learning state, and decision strategies (among other things) as these cognitive processes occurred throughout game play. This is a stark contrast to the common approach of trying to assess the long-term impact of games on cognitive functioning after game play has ended. We describe what cognitive models are, what they can be used for and how game researchers could benefit by adopting these methods. We also provide details of a single model - based on decision field theory - that has been successfUlly applied to data sets from memory, perception, and decision making experiments, and has recently found application in real world scenarios. We examine possibilities for applying this model to game-play data.

Bohil, Corey J.↗

Representations and strategies for transferable machine learning improve model performance in chemical discovery

Strategies for machine-learning (ML)-accelerated discovery that are general across material composition spaces are essential, but demonstrations of ML have been primarily limited to narrow composition variations. By addressing the scarcity of data in promising regions of chemical space for challenging targets such as open-shell transition-metal complexes, general representations and transferable ML models that leverage known relationships in existing data will accelerate discovery. Over a large set (~1000) of isovalent transition-metal complexes, we quantify evident relationships for different properties (i.e., spin-splitting and ligand dissociation) between rows of the Periodic Table (i.e., 3d/4d metals and 2p/3p ligands). We demonstrate an extension to the graph-based revised autocorrelation (RAC) representation (i.e., eRAC) that incorporates the group number alongside the nuclear charge heuristic that otherwise overestimates dissimilarity of isovalent complexes. To address the common challenge of discovery in a new space where data are limited, we introduce a transfer learning approach in which we seed models trained on a large amount of data from one row of the Periodic Table with a small number of data points from the additional row. We demonstrate the synergistic value of the eRACs alongside this transfer learning strategy to consistently improve model performance. Analysis of these models highlights how the approach succeeds by reordering the distances between complexes to be more consistent with the Periodic Table, a property we expect to be broadly useful for other material domains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Some remarks about simulation of cosmic ray phenomena with use of nuclear interaction models based on the current SPS proton-antiproton data

The x-y controversy is studied by introducing models with as many features (except for x and y distributions) in common, as possible, to avoid an extrapolation problem, only primary energies of 500 TeV are considered. To prove the point, Monte Carlo simulations are performed of EAS generated by 500 TeV vertical primary protons. Four different nuclear interaction models were used. Two of them are described elsewhere. Two are: (1) Model M-Y00 - with inclusive x and y distributions behaving in a scaling way; and (2) Model M-F00 - at and below ISR energies (1 TeV in Lab) exactly equivalent to the above, then gradually changing to provide the distributions in rapidity at 155 TeV as given by SPS proton-antiproton. This was achieved by gradual decrease in the scale unit in x distributions of produced secondaries, as interaction energy increases. Other modifications to the M-Y00 model were made.

Wrotniak, J. A.↗