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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 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Decentralized Collaborative Learning with Probabilistic Data Protection

We discuss future directions of Blockchain as a collaborative value co-creation platform, in which network participants can gain extra insights that cannot be accessed when disconnected from the others. As such, we propose a decentralized machine learning framework that is carefully designed to respect the values of democracy, diversity, and privacy. Specifically, we propose a federated multi-task learning framework that integrates a privacy-preserving dynamic consensus algorithm. We show that a specific network topology called the expander graph dramatically improves the scalability of global consensus building. We conclude the paper by making some remarks on open problems.

Ide, Tsuyoshi↗
DOE OSTI2026

When does global attention help: a unified empirical study on atomistic graph learning

Graph neural networks (GNNs) are widely used as surrogates for costly experiments and first-principles simulations to study the behavior of compounds at atomistic scale, and their architectural complexity is constantly increasing to enable the modeling of complex physics. While most recent GNNs combine more traditional message passing neural networks (MPNNs) layers to model short-range interactions with more advanced graph transformers (GTs) with global attention mechanisms to model long-range interactions, it is still unclear when global attention mechanisms provide real benefits over well-tuned MPNN layers due to inconsistent implementations, features, or hyperparameter tuning. We introduce the first unified, reproducible benchmarking framework–built on HydraGNN–that enables seamless switching among four controlled model classes: MPNN, MPNN with chemistry/topology encoders, GPS-style hybrids of MPNN with global attention, and fully fused localglobal models with encoders. Using seven diverse open-source datasets for benchmarking across regression and classification tasks, we systematically isolate the contributions of message passing, global attention, and encoder-based feature augmentation. Our study shows that encoder-augmented MPNNs form a robust baseline, while fused localglobal models yield the clearest benefits for properties governed by long-range interaction effects. We further quantify the accuracycompute trade-offs of attention, reporting its overhead in memory. Together, these results establish the first controlled evaluation of global attention in atomistic graph learning and provide a reproducible testbed for future model development.

Equivariant graph neural networks↗
DOE OSTI2022

Federated Learning and Differential Privacy: What might AI-Enhanced co-design of microelectronics learn?

Data is a valuable commodity, and it is often dispersed over multiple entities. Sharing data or models created from the data is not simple due to concerns regarding security, privacy, ownership, and model inversion. This limitation in sharing can hinder model training and development. Federated learning can enable data or model sharing across multiple entities that control local data without having to share or exchange the data themselves. Differential privacy is a conceptual framework that brings strong mathematical guarantee for privacy protection and helps provide a quantifiable privacy guarantee to any data or models shared. The concepts of federated learning and differential privacy are introduced along with possible connections. Lastly, some open discussion topics on how federated learning and differential privacy can tied to AI-Enhanced co-design of microelectronics are highlighted.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS2017

Use of Schema on Read in Earth Science Data Archives

Traditionally, NASA Earth Science data archives have file-based storage using proprietary data file formats, such as HDF and HDF-EOS, which are optimized to support fast and efficient storage of spaceborne and model data as they are generated. The use of file-based storage essentially imposes an indexing strategy based on data dimensions. In most cases, NASA Earth Science data uses time as the primary index, leading to poor performance in accessing data in spatial dimensions. For example, producing a time series for a single spatial grid cell involves accessing a large number of data files. With exponential growth in data volume due to the ever-increasing spatial and temporal resolution of the data, using file-based archives poses significant performance and cost barriers to data discovery and access. Storing and disseminating data in proprietary data formats imposes an additional access barrier for users outside the mainstream research community. At the NASA Goddard Earth Sciences Data Information Services Center (GES DISC), we have evaluated applying the schema-on-read principle to data access and distribution. We used Apache Parquet to store geospatial data, and have exposed data through Amazon Web Services (AWS) Athena, AWS Simple Storage Service (S3), and Apache Spark. Using the schema-on-read approach allows customization of indexing spatially or temporally to suit the data access pattern. The storage of data in open formats such as Apache Parquet has widespread support in popular programming languages. A wide range of solutions for handling big data lowers the access barrier for all users. This presentation will discuss formats used for data storage, frameworks with This presentation will discuss formats used for data storage, frameworks with support for schema-on-read used for data access, and common use cases covering data usage patterns seen in a geospatial data archive.

cloud applications↗
NASA NTRSDate not supplied

Simultaneous Aerosol and Ocean Polarimeter Products Using Coupled Atmosphere-Ocean Vector Radiative Transfer and Neural Networks: The PACE-MAPP Algorithm

We describe the PACE-MAPP algorithm that simultaneously retrieves aerosol and ocean optical parameters using multiangle and multi-channel polarimeter measurements from the SPEXone, Hyper-Angular Rainbow Polarimeter 2 (HARP2), and Ocean Color Instrument (OCI) instruments onboard the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) observing system PACE-MAPP is adapted from the Research Scanning Polarimeter (RSP) Microphysical Aerosol Properties from Polarimetry (RSP-MAPP) algorithm. A key feature of the MAPP family of algorithms is the use of a coupled vector radiative transfer model such that the atmosphere and ocean are always considered together as one system. Consequently, conservation of energy ensures that negative water-leaving radiances do not occur. PACE-MAPP uses optimal estimation to simultaneously characterize the optical and microphysical properties of aerosol and ocean constituents, find the optimal solution, and reliably account for the uncertainties of each parameter. This coupled approach, together with multiangle, multi-channel polarimeter measurements, will enable retrievals of aerosol and water properties across the Earth’s oceans. The PACE-MAPP algorithm provides aerosol and ocean products for both the open ocean and coastal areas and is designed to be accurate, modular, and efficient by using fast neural networks that replace the time-consuming vector radiative transfer calculations. We provide an overview of the PACE-MAPP framework and also describe its modular components including its aerosol and hydrosol models, ocean bio-optical models, and thin cirrus model.

Snorre Stamnes↗
DOE OSTI2020

BioSTEAMDevelopmentGroup/thermosteam

BioSTEAM is a fast and flexible package for the design, simulation, and techno-economic analysis of biorefineries under uncertainty. BioSTEAM’s framework is built to streamline and automate early-stage technology evaluations and to enable rigorous sensitivity and uncertainty analyses. Complete biorefinery configurations are available at the Bioindustrial-Park GitHub repository, BioSTEAM’s premier repository for biorefinery models and results. The long-term growth and maintenance of BioSTEAM is supported through both community-led development and the research institutions invested in BioSTEAM. Through the open-source and community-lead platform, BioSTEAM aims to foster communication and transparency within the biorefinery research community for an integrated effort to expedite the evaluation of candidate biofuels and bioproducts. Additionally, an agile life cycle assessment (LCA) platform has been designed to interface with BioSTEAM, BioSTEAM-LCA. This open-source, installable package allows users to perform streamlined LCAs of biorefineries. The focus of BioSTEAM-LCA is to streamline and automate early-stage environmental impact analyses of processes and technologies, and to enable rigorous sensitivity and uncertainty analyses linking process design, performance, economics, and environmental impacts. ThermoSTEAM is a standalone thermodynamic engine capable of estimating mixture properties, solving thermodynamic phase equilibria, and modeling stoichiometric reactions. ThermoSTEAM builds upon chemicals, the chemical properties component of the Chemical Engineering Design Library, with a robust and flexible framework that facilitates the creation of property packages. The Biorefinery Simulation and Techno-Economic Analysis Modules (BioSTEAM) is dependent on ThermoSTEAM for the simulation of unit operations.

Cortes-Peña, Yoel↗
DOE OSTI2022

Polariton Formation from Soret Band Excitons in Metal–Organic Frameworks and Plasmonic Lattices

This Letter describes strong coupling between a plasmonic nanoparticle (NP) lattice cavity and Soret excitons in a metal–organic framework (MOF) film. In optical transmission measurements, we observed a lower polariton mode that can be spectrally tuned by infiltrating MOF pores with solvents of different refractive index. Using transient absorption spectroscopy, both the lower and upper polariton modes can be resolved, with an estimated Rabi splitting of ~300 meV, nearly twice that of other plasmonic cavity–organic emitter systems. The polariton modes decay more rapidly than that of the uncoupled exciton. Furthermore, this hybrid system highlights the advantages of open plasmonic cavities for tunable coupling and the use of transient absorption spectroscopy to identify polariton modes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

The Climatic Impact‐Driver Framework for Assessment of Risk‐Relevant Climate Information

Abstract The climate science and applications communities need a broad and demand‐driven concept to assess physical climate conditions that are relevant for impacts on human and natural systems. Here, we augment the description of the “climatic impact‐driver” (CID) approach adopted in the Working Group I (WGI) contribution to the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report. CIDs are broadly defined as “physical climate system conditions (e.g., means, events, and extremes) that affect an element of society or ecosystems. Depending on system tolerance, CIDs and their changes can be detrimental, beneficial, neutral, or a mixture of each across interacting system elements and regions.” We give background information on the IPCC Report process that led to the development of the 7 CID types (heat and cold, wet and dry, wind, snow and ice, coastal, open ocean, and other) and 33 distinct CID categories, each of which may be evaluated using a variety of CID indices. This inventory of CIDs was co‐developed with WGII to provide a useful collaboration point between physical climate scientists and impacts/risk experts to assess the specific climatic phenomena driving sectoral responses and identify relevant CID indices within each sector. The CID Framework ensures that a comprehensive set of climatic conditions informs adaptation planning and risk management and may also help prioritize improvements in modeling sectoral dynamics that depend on climatic conditions. CIDs contribute to climate services by increasing coherence and neutrality when identifying and communicating relevant findings from physical climate research to risk assessment and planning activities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Quantum speed limit for the out-of-time-ordered correlator from an open-system perspective

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time-ordered correlator (OTOC). Employing the OTOC–Renyi-2 entropy theorem, we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the nonintegrable transverse field Ising model. Furthermore, our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter systems, and engineered quantum platforms.

Fermions↗
DOE OSTI2024

A reactive electrochemomechanical theory for growth and remodeling of polyelectrolyte hydrogels and application to dynamic polymerization of $\text{DNA}$ hydrogels

Here this study develops a framework for growth and remodeling of active polyelectrolyte hydrogels that accounts for effects of compositional changes on the mechanical response. By developing a reactive electrochemomechanical theory, thermodynamical constraints upon reactive and remodeling processes are elucidated within a general framework that allows any number of chemical reactions to evolve the response of the gel and transfer mass and charge between constituents. Fully coupled, nonlinear constitutive relations are adopted for molar fluxes, allowing exploration of effects including cross-diffusion, electrophoresis, and electro-osmosis. A robust finite element implementation is developed in the open source FEBio software (febio.org) by exploiting an equivalence between electrochemomechanics and mixture theory. The implementation is verified against analytical solutions for free swelling, and a proper reduction to a prior chemomechanical theory is demonstrated for neutral gels swollen only by a solvent with no solutes. The theory and implementation are then applied to model the tunable large swelling achieved through dynamic polymerization of DNA crosslinkers seen in our recently developed experimental hydrogel system (Cangialosi et al., 2017). A novel constitutive model for reaction-driven evolution of the locking stretch λ L in a non-Gaussian mechanical free energy was developed, where the increasing concentration of DNA crosslinkers makes further swelling energetically favorable. With a single free parameter, excellent agreement was found between measured and predicted equilibrium swelling ratios. This study demonstrated the ability to extend the electrochemomechanical framework to include chemical reactions and composition-aware constitutive models, and showed that development of reactive models allows simulation of complex dynamic polymerization phenomena not treated before. The theoretical frame here can be further expanded in scope to incorporate additional non-ideal and nonlinear phenomena.

42 ENGINEERING↗
DOE OSTI2022

MOOSE Reactor Module Meshing Enhancements to Support Reactor Physics Analysis

The U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program develops an integrated suite of advanced reactor physics tools built upon the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Each code generally requires an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The meshing process is often burdensome for the complex geometries present in reactors due to lack of easy-to-use, open-source meshing tools. To address the bottleneck associated with meshing complex geometries found in nuclear reactors, NEAMS initiated the development of the MOOSE Reactor Module starting in FY21. The Reactor Module builds off the existing MOOSE Mesh System to include targeted meshing capabilities such as the ability to generate hexagonal pin cells, assemblies with ducts, rotating control drums, cores, peripheral zones around a core, as well as the automatic labeling (“reporting IDs”) of pin, assembly, and planar zones to simplify post-processing of results. As a Physics Module in MOOSE, the Reactor Module is open-source, available with any MOOSE installation, directly compatible with MOOSE-based tools, and can be invoked from MOOSEbased applications to generate meshes. Functionality from the Reactor Module has been applied to several advanced reactor concepts to demonstrate user workflow improvements and accuracy. The primary objective of the Reactor Module is to improve useability of MOOSEbased tools by streamlining mesh generation and output inspection processes. During FY22, the functionality of the Reactor Module (and accompanying Mesh System) has been expanded based on user needs. First, the Reactor Geometry Mesh Builder capability developed primarily in FY21 has been refactored and merged to the public MOOSE repository. This capability wraps underlying Reactor Module mesh generators into a “Pin – Assembly – Core” workflow appropriate for conventional Cartesian and hexagonal geometries, and notably assigns material IDs during mesh generation stage and generates only the minimal number of blocks needed in order to reduce computational burden. Biasing and boundary layer options have been added to the base mesh generators as required by thermal hydraulics solvers. The reporting ID functionality has been expanded to differentiate ring-wise and azimuthal sectors within a pin for use with depletion algorithms, and VectorPostProcessor and Reporter objects are now available to integrate solution variables across zones based on ID combinations. Functionality to trim hexagonal meshes along the center or periphery has been developed so users may leverage symmetry and reflective boundary conditions to reduce the mesh size. A flexible and powerful tool to fill the space between two sidesets has been introduced to the framework and can be used for transition layers such as stitching two assemblies together with different numbers of pins, or for complex geometries which do not follow conventional Cartesian/hexagonal patterns. Finally, additional verification problems were performed with NEAMS physics tools in complement with existing NEAMS work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Effects of MOF linker rotation and functionalization on methane uptake and diffusion

The flexible degrees of freedom in metal–organic frameworks (MOFs) can have significant effects on guest molecule behavior. However, in the majority of studies applying molecular simulations to MOFs, the framework is assumed to be rigid in order to minimize computational cost. Here, in this work, we assess the significance of this assumption on a representative example of methane uptake and diffusion in UiO-66. We introduce an open-source code to modify MOFs through functionalization and linker rotation and we perform Grand Canonical Monte Carlo and molecular dynamics simulations of methane in each of the functionalized and linker-rotated derivatives of UiO-66. We find that linker rotation moderately influences methane uptake and significantly influences methane diffusion. Our assessment provides ranges of property values that serve as measures of uncertainty of these two properties associated with linker rotation. We further determine that void volume fraction and minimum pore size are the features that govern methane uptake and diffusion, respectively. These findings illustrate the impact of linker rotation on MOFs and provide design principles to guide future investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Enabling robust offline active learning for machine learning potentials using simple physics-based priors

Abstract Machine learning surrogate models for quantum mechanical simulations have enabled the field to efficiently and accurately study material and molecular systems. Developed models typically rely on a substantial amount of data to make reliable predictions of the potential energy landscape or careful active learning (AL) and uncertainty estimates. When starting with small datasets, convergence of AL approaches is a major outstanding challenge which has limited most demonstrations to online AL. In this work we demonstrate a Δ-machine learning (ML) approach that enables stable convergence in offline AL strategies by avoiding unphysical configurations with initial datasets as little as a single data point. We demonstrate our framework’s capabilities on a structural relaxation, transition state calculation, and molecular dynamics simulation, with the number of first principle calculations being cut down anywhere from 70%–90%. The approach is incorporated and developed alongside AMP torch , an open-source ML potential package, along with interactive Google Colab notebook examples.

Shuaibi, Muhammed↗
NASA NTRS2018

The NASA Eulerian Snow on Sea Ice Model (NESOSIM) v1.0: initial model development and analysis

The NASA Eulerian Snow On Sea Ice Model (NESOSIM) is a new, open-source snow budget model that is currentlyconfigured to produce daily estimates of the depth and density of snow on sea ice across the Arctic Ocean throughthe accumulation season. NESOSIM has been developed in a three-dimensional Eulerian framework and includes two(vertical) snow layers and several simple parameterizations (accumulation, wind packing, advection_divergence, blowingsnow lost to leads) to represent key sources and sinks of snow on sea ice. The model is forced with daily inputs of snowfall and near-surface winds (from reanalyses), sea ice concentration (from satellite passive microwave data) and sea ice drift (from satellite feature tracking) during the accumulation season (August through April). In this study, we present the NESOSIM formulation, calibration efforts, sensitivity studies and validation efforts across an Arctic Ocean domain (100 km horizontal resolution). The simulated snow depth and density are calibrated with in situ data collected on drifting ice stations during the 1980s. NESOSIM shows strong agreement with the in situ seasonal cycles of snow depth and density, and shows good (moderate) agreement with the regional snow depth (density) distributions. NESOSIM is run for a contemporary period (2000 to 2015), with the results showing strong sensitivity to the reanalysis derived snowfall forcing data, with the Modern-Era Retrospective analysis for Research and Applications (MERRA) and the Japanese Meteorological Agency 55-year reanalysis (JRA-55) forced snow depths generally higher than ERA-Interim,and the Arctic System Reanalysis (ASR) generally lower. We also generate and force NESOSIM with a consensus "median" daily snowfall dataset from these reanalyses.The results are compared against snow depth estimates derived from NASA's Operation IceBridge (OIB) snow radar data from 2009 to 2015, showing moderate_strong correlations and root mean squared errors of 10 cm depending on the OIB snow depth product analyzed, similar to the comparisons between OIB snow depths and the commonly used modified Warren snow depth climatology. Potential improvements to this initial NESOSIM formulation are discussed in the hopes of improving the accuracy and reliability of these simulated snow depths and densities.

Petty, Alek A.↗
NASA NTRSDate not supplied

Application of OpenFOAM to Plume Impingement in Space Environments

After 30 years of continuous human presence in low-earth orbit, NASA is returning to the moon and eventually will go to Mars. Travelling beyond low earth orbit requires NASA to learn how humans can live in Deep Space environments – beyond the protection of Earth’s magnetosphere and at distances from Earth that prevent a quick return in case of trouble. To this end, NASA is constructing the Lunar Gateway, an ISS-like space station to be put in orbit around the moon to act as a home base for Lunar exploration for NASA astronauts. The Gateway Lunar outpost will be built incrementally, via modules which will arrive at separate times and dock to the existing structure. The incremental addition of Gateway modules, and the docking of visiting vehicles, is achieved via a sequence of firings from the approaching body’s onboard reaction control system (RCS) thrusters to achieve the required approach trajectory. The typical hypergolic chemical RCS thrusters work by firing hot gases to produce adverse thrust and the needed change in velocity to safely finish the docking process. The exhaust gas from the RCS thrusters form plumes that expand into the vacuum of space and can impinge onto the outer surfaces of the Lunar Gateway, causing unwanted forces and moments, heat loads, sediment deposition, and in extreme cases, even surface erosion - all mechanisms that can damage the Lunar Gateway and must be minimized. Both permanent and visiting modules will have this RCS thruster exhaust impingement problem. This research aims to establish existing OpenFOAM solvers as a methodology for improving simulation techniques of rocket exhaust plume impingement in space environments. The flow structure of a plume in a space environment is complex; a plume that originates from a hypergolic chemical RCS thruster and expands into a vacuum will experience several regimes of rarefication. This range includes the continuum flow in the rocket nozzle through the fully rarefied free molecular flow further from the nozzle. The flow physics is different at these two extremes, and as such, the simulation approach for plumes is generally divided into a traditional computational fluid dynamics (CFD) simulation in and near the nozzle which is coupled to a subsequent direct simulation Monte Carlo (DSMC) simulation. At this time, the scope of this research is developing, verifying, and validating a method using existing solvers in the OpenFOAM framework for performing coupled CFD/DSMC calculations to determine the extent of plume impingement loading on generic space structures. This presentation will detail code-to-code comparisons between the hyStrath dsmcFoam+ solver, developed using OpenFOAM and available as open-source, and NASA’s in-house DSMC Analysis Code (DAC). Comparisons to several open-source publication findings using DAC [3,4] are presented, and advantages of using an OpenFOAM based solver are also discussed. The presentation concludes with a discussion of future work, and a plan for coupling the dsmcFoam+ solver with CFD simulations of chemical rocket engines for unified coupled plume simulation.

DSMC↗
NASA NTRSDate not supplied

A Partitioned -Task Parallel Implementation of the NASA Multiscale Analysis Tool for High Performance Computing

The NASA Multiscale Analysis Tool (NASMAT) is a “plug and play” software package that allows users to conduct massively multiscale modeling of hierarchical and nonlinear materials. This work extends the scalability and improves the High Performance Computing friendliness of NASMAT by adopting a Partitioned Task-Parallel approach. Interoperability of NASMAT with external software is enhanced through preCICE, a open source library for multiphysics coupling in a partitioned manner. Enhancement through preCICE allows for easy integration of NASMAT to other macro solvers and dissociates the parallelization strategy adopted within NASMAT from the macro solver. The task-parallel framework based on Master-Worker approach is implemented as the parallelization scheme. The scheme accounts for hierarchy of multiple scales (task-dependence) and heterogeneous nature (dynamic load balancing) of computations. The applicability and scalability of the framework will be evaluated by analyzing large scale engineering problems through massively multiscale methods.

NASMAT↗
DOE OSTI2021

Opening the reheating box in multifield inflation

The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as ~ 50%, while our semi-analytic estimates can reduce this error to ~ 10%. Finally, we conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the N = 6 solution

We compute the set of all extreme rays of the 6-party subadditivity cone that are compatible with strong subadditivity. In total, we identify 208 new (genuine 6-party) orbits, 52 of which violate at least one known holographic entropy inequality. For the remaining 156 orbits, which do not violate any such inequalities, we construct holographic graph models for 150 of them. For the final 6 orbits, it remains an open question whether they are holographic. Consistent with the strong form of the conjecture in [1], 148 of these graph models are trees. However, 2 of the graphs contain a “bulk cycle”, leaving open the question of whether equivalent models with tree topology exist, or if these extreme rays are counterexamples to the conjecture. The paper includes a detailed description of the algorithm used for the computation, which is presented in a general framework and can be applied to any situation involving a polyhedral cone defined by a set of linear inequalities and a partial order among them to find extreme rays corresponding to down-sets in this poset.

AdS-CFT correspondence↗