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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A k-mer based approach for classifying viruses without taxonomy identifies viral associations in human autism and plant microbiomes

Viruses are an underrepresented taxa in the study and identification of microbiome constituents; however, they play an essential role in health, microbiome regulation, and transfer of genetic material. Only a few thousand viruses have been isolated, sequenced, and assigned a taxonomy, which limits the ability to identify and quantify viruses in the microbiome. Additionally, the vast diversity of viruses represents a challenge for classification, not only in constructing a viral taxonomy, but also in identifying similarities between a virus’ genotype and its phenotype. However, the diversity of viral sequences can be leveraged to classify their sequences in metagenomic and metatranscriptomic samples, even if they do not have a taxonomy. To identify and quantify viruses in transcriptomic and genomic samples, we developed a dynamic programming algorithm for creating a classification tree out of 715,672 metagenome viruses. To create the classification tree, we clustered proportional similarity scores generated from the k-mer profiles of each of the metagenome viruses to create a database of metagenomic viruses. The resulting Kraken2 database of the metagenomic viruses can be found here: https://www.osti.gov/biblio/1615774 and is compatible with Kraken2. We then integrated the viral classification database with databases created with genomes from NCBI for use with ParaKraken (a parallelized version of Kraken provided in Supplemental Zip 1), a metagenomic/transcriptomic classifier. To illustrate the breadth of our utility for classifying metagenome viruses, we analyzed data from a plant metagenome study identifying genotypic and compartment specific differences between two Populus genotypes in three different compartments. We also identified a significant increase in abundance of eight viral sequences in post mortem brains in a human metatranscriptome study comparing Autism Spectrum Disorder patients and controls. We also show the potential accuracy for classifying viruses by utilizing both the JGI and NCBI viral databases to identify the uniqueness of viral sequences. Finally, we validate the accuracy of viral classification with NCBI databases containing viruses with taxonomy to identify pathogenic viruses in known COVID-19 and cassava brown streak virus infection samples. Our method represents the compulsory first step in better understanding the role of viruses in the microbiome by allowing for a more complete identification of sequences without taxonomy. Better classification of viruses will improve identifying associations between viruses and their hosts as well as viruses and other microbiome members. Despite the lack of taxonomy, this database of metagenomic viruses can be used with any tool that utilizes a taxonomy, such as Kraken, for accurate classification of viruses.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Model-independent form-factor constraints for electromagnetic spin-1 currents

Using local gauge invariance in the form of the Ward-Takahashi identity and the fact that properly constructed current operators must be free of kinematic singularities, it is shown that the magnetic moment μ and the quadrupole moment Q of an elementary spin-1 particle with mass m and charge e are related by 2mμ + m 2 Q = e, thus constraining the normalizations of the Sachs form factors. This relation holds true as a matter of course at the tree level in the standard model, but we prove that it remains true in general for dressed spin-1 states derived from elementary fields. Furthermore, general expressions for spin-1 propagators and currents with arbitrary hadronic dressing are given, which show that the result is independent of any dressing effect or model approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1986

Shuttle radar images for geologic mapping in tropical rainforest

Images of forested low-relief terrain in the Amazon basin of Brazil, obtained with airborne imaging radar in the Radambrasil project, are compared with SIR-A and Landsat MSS band-7 images to evaluate their usefulness in constructing geologic maps. Sample images are shown, and it is found that Radam images are more useful in distinguishing drainage patterns and mapping the region distribution of stream channels due to their relatively low depression angles (less than 25 deg as opposed to 43-37 deg for SIR-A), but that SIR-A images give superior discrimination of alluvial forest, where trees stand in water, due to the higher reflectivity of branches and water at the SIR-A wavelength (23.5 cm as opposed to 3 cm for Radam). Alluvial forest is also identified by Landsat band 7.

Ford, J. P.↗
NASA NTRS2020

Enabling Assurance in the MBSE Environment

A number of specific benefits that fit within the hallmarks of effective development are realized with implementation of model-based approaches to systems and assurance. Model Based Systems Engineering (MBSE) enabled by standardized modeling languages (e.g., SysML®) is at the core. These benefits in the context of spaceflight system challenges can include [1]: • Improved management of complex development • Reduced risk in the development process • Improved cost management • Improved design decisions With appropriate modeling techniques the assurance community also can improve early oversight and insight into project development. NASA has shown the basic constructs of SysML in an MBSE environment offer several key advantages, within a Model Based Mission Assurance (MBMA) initiative [2, 3]. These include the following: • Model viewpoints that promote rapid and systematic assessment of requirements coverage, hazard tagging and risk management • Embedded safety assessments for launch vehicles • Deployment of model assisted development of reliability products - Failure Modes and Effects Analyses (FMEAs) and Fault Trees • Test Planning • Validation and Verification of complex functions • Support of Assurance Case development for complex systems In addition, while there are benefits to be harvested, there is a realization that these do not come without effort and cost. Enabling model-based approaches requires structure, not only in an organizational context, but in a modeling context as well. There can be a steep learning curve and costs associated to train skilled modelers. But, on the other hand, not all of the assurance community need to be modelers. Models themselves must conform to ontologies that enable assurance. This places constraints upon the models and modelers. Optimums have yet to be developed where resources and constraints on modeling must be traded off in the organization and modeling efforts for projects. A number of barriers need to be overcome, as well, which pose challenges to the developers of the software that supports MBSE/MBMA. Information and data must be made to flow seamlessly through the life cycle. Because there is a wide variety of tools used in the community, to avoid the problems of the past of silos, delays, and diverging interests, information should flow among these tools to support the “single source of truth” paradigm of MBSE. This will greatly facilitate MBMA and advancement of assurance functions.

Evans, John W.↗
DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗
DOE OSTI2023

Finding Of Adverse Effect and Proposed Mitigation for the Removal of Joshua Trees at Building 23-210, Mercury, Area 23, Nevada National Security Site, Nye County, Nevada

The U.S. Department of Energy (DOE), National Nuclear Security Administration Nevada Field Office (NNSA/NFO) recently removed two fallen Joshua trees that were part of an Accessory Resource (AR) to the former Department of Defense (DOD) Motor Pool Maintenance Compound in Mercury (Nevada State Historic Preservation Office [SHPO] Resource No. C307) on the Nevada National Security Site (NNSS) in Nye County, Nevada (Figure 1). The Joshua trees were part of AR3, a landscaped feature at the entrance to the compound. There are two remaining Joshua trees at risk of falling which may require removal in the future. The NNSA/NFO is proactively consulting with the SHPO regarding the potential removal of the remaining two trees. The purpose of the undertaking is to ensure that dead or dying Joshua trees do not cause damage to the remaining landscape elements, nor injury to NNSS employees. The NNSA/NFO will implement this undertaking in accordance with the Programmatic Agreement between the National Nuclear Security Administration Nevada Field Office and the Nevada State Historic Preservation Officer Regarding Modernization and Operational Maintenance of the Nevada National Security Site, at Mercury in Nye County, Nevada, hereafter referred to as the Mercury PA. Building 23-210 was the DOD’s motor vehicle maintenance compound constructed in 1951. The compound included its own repair shop and fuel station. The town of Mercury and the immediate surrounding area have been formally determined eligible for listing in the National Register of Historic Places (National Register, NRHP) as the Mercury Historic District (MHD, SHPO Resource No. D230) under Criteria A and C for their importance in supporting nuclear testing and scientific research from 1951 through 1992. The former DOD Motor Pool Compound was identified as a contributing element to the MHD in a 2018 architectural survey of the district (Reno et al. 2018) and recorded on a Nevada Architectural Resource Assessment (ARA) form (Reno et al. 2017). The foundation for Building 23-210 was also identified in Appendix C of the Mercury PA as a Category III contributing element with three contributing ARs. Category III properties are those that may include elements for which there are several representatives in the MHD, such as foundations, and those elements which possess characteristics that are not unique to the MHD and are commonly found in other non-NNSS facilities. The former DOD compound, which is identified by the foundation for the Building 23-210 and its ARs, is a historic property for the purposes of compliance with Section 106 of the National Historic Preservation Act (NHPA) and subject to the stipulations of the Mercury PA.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

BOREAS TE-4 Gas Exchange Data from Boreal Tree Species

The BOREAS TE-4 team collected steady-state gas exchange and reflectance data from several species in the BOREAS SSA during 1994 and in the NSA during 1996. Measurements of light, CO2, temperature, and humidity response curves were made by the BOREAS TE-4 team during the summers of 1994 and 1996 using intact attached leaves of boreal forest species located in the BOREAS SSA and NSA. These measurements were conducted to calibrate models used to predict photosynthesis, stomatal conductance, and leaf respiration. The 1994 and 1996 data can be used to construct plots of response functions or for parameterizing models. Parameter values are suitable for application in SiB2 (Sellers et al., 1996) or the leaf model of Collatz et al. (1991), and programs can be obtained from the investigators. The data are stored in tabular ASCII files. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

Hall, Forrest G.↗
DOE OSTI2020

Assessing Shifts in Regional Hydroclimatic Conditions of U.S. River Basins in Response to Climate Change over the 21st Century

Characterization of shifts in regional hydroclimatic conditions helps reduce negative consequences on agriculture, environment, economy, society, and ecosystem. This study assesses shifts in regional hydroclimatic conditions across the conterminous United States in response to climate change over the 21 st Century. The hydrological responses of five downscaled climate models from the Multivariate Adaptive Constructed Analogs (MACA) dataset ranging from the driest to wettest and least warm to hottest were simulated using the Variable Infiltration Capacity (VIC) model. Shifts in regional hydroclimatic conditions at 8-digit hydrologic unit scale (HUC8) were evaluated by the magnitude and direction of movements in the Budyko space. HUC8 river basins were then clustered into seven unique hydroclimatic behavior groups using the K-means method. A tree classification method was proposed to illustrate the relationships between hydroclimatic behavior groups and regional characteristics. The results indicate that hydroclimatic responses may vary from a river basin to another, but basins in the same neighborhood follow a similar movement in the Budyko space. The systematic hydroclimatic behavior of river basins is highly associated with their regional landform, climate, and ecosystem characteristics. Most HUC8s with Mountain, Plateau and Basin landform types will likely experience less arid conditions. However, most HUC8s with Plain landform type behave differently according to the regional ecosystem and climate. This study provides a potential roadmap of shifts in regional hydroclimatic conditions of U.S. river basins, which can be used to improve regional preparedness and ability of various sectors to mitigate or adapt to the impacts of future hydroclimate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of 2 H, 3 H, and 3 He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers are calculated with the chiral two-nucleon (and three-nucleon) interactions including Δ intermediate states that have recently been constructed in configuration space. The A=3 wave functions are obtained from hyperspherical-harmonics solutions of the Schrödinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with Δ intermediate states are only retained at the OPE level and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact currents are determined by reproducing the magnetic moments of these few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2–3fm –1 . However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. In conclusion, a complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1985

Tree-oriented interactive processing with an application to theorem-proving, appendix E

The concept of unstructured structure editing and ted, an editor for unstructured trees, is described. Ted is used to manipulate hierarchies of information in an unrestricted manner. The tool was implemented and applied to the problem of organizing formal proofs. As a proof management tool, it maintains the validity of a proof and its constituent lemmas independently from the methods used to validate the proof. It includes an adaptable interface which may be used to invoke theorem provers and other aids to proof construction. Using ted, a user may construct, maintain, and verify formal proofs using a variety of theorem provers, proof checkers, and formatters.

Hammerslag, David↗
DOE OSTI2020

Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies at d =5

We carry out a systematic investigation for the minimal Dirac neutrino mass models emerging from generic one-loop and two-loop topologies that arise from d = 5 effective operator with a singlet scalar, σ. To ensure that the tree-level Dirac mass, as well as Majorana mass terms at all orders, are absent for the neutrinos, we work in the framework where the Standard Model is supplemented by the well-motivated U(1)B-L gauge symmetry. At the one-loop level, we analyze six possible topologies, out of which two of them have the potential to generate desired Dirac neutrino mass. Adopting a systematic approach to select minimal models, we construct seventeen viable one-loop Dirac neutrino mass models. By embracing a similar methodical approach at the two-loop, we work out twenty-three minimal candidates. Among the forty selected economical models, the majority of the models proposed in this work are new. In our search, we also include the scenarios where the particles in the loop carry charges under the color group. Furthermore, we discuss the possible dark matter candidates within a given model, if any, without extending the minimal particle content.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Unifying relations for scattering amplitudes

We derive new amplitudes relations revealing a hidden unity among a wideranging variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biadjoint scalar theory. Transmutation also relates amplitudes in string theory and its variants. As a corollary, celebrated aspects of gluon and graviton scattering like color-kinematics duality, the KLT relations, and the CHY construction are inherited traits of the transmuted amplitudes. With this being said, transmutation recasts the Adler zero as a trivial consequence of the Weinberg soft theorem and implies new subleading soft theorems for certain scalar theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Prognostic analysis of high-flow nasal cannula therapy and non-invasive ventilation in mild to moderate hypoxemia patients and construction of a machine learning model for 48-h intubation prediction—a retrospective analysis of the MIMIC database

Background This study aims to investigate the clinical outcome between high-flow nasal cannula (HFNC) and non-invasive ventilation (NIV) therapy in mild to moderate hypoxemic patients on the first ICU day and to develop a predictive model of 48-h intubation. Methods The study included adult patients from the MIMIC III and IV databases who first initiated HFNC or NIV therapy due to mild to moderate hypoxemia (100 < PaO2/FiO2 ≤ 300). The 48-h and 30-day intubation rates were compared using cross-sectional and survival analysis. Nine machine learning and six ensemble algorithms were deployed to construct the 48-h intubation predictive models, of which the optimal model was determined by its prediction accuracy. The top 10 risk and protective factors were identified using the Shapley interpretation algorithm. Result A total of 123,042 patients were screened, of which, 673 were from the MIMIC IV database for ventilation therapy comparison (HFNC n = 363, NIV n = 310) and 48-h intubation predictive model construction (training dataset n = 471, internal validation set n = 202) and 408 were from the MIMIC III database for external validation. The NIV group had a lower intubation rate (23.1% vs. 16.1%, p = 0.001), ICU 28-day mortality (18.5% vs. 11.6%, p = 0.014), and in-hospital mortality (19.6% vs. 11.9%, p = 0.007) compared to the HFNC group. Survival analysis showed that the total and 48-h intubation rates were not significantly different. The ensemble AdaBoost decision tree model (internal and external validation set AUROC 0.878, 0.726) had the best predictive accuracy performance. The model Shapley algorithm showed Sequential Organ Failure Assessment (SOFA), acute physiology scores (APSIII), the minimum and maximum lactate value as risk factors for early failure and age, the maximum PaCO 2 and PH value, Glasgow Coma Scale (GCS), the minimum PaO 2 /FiO 2 ratio, and PaO 2 value as protective factors. Conclusion NIV was associated with lower intubation rate and ICU 28-day and in-hospital mortality. Further survival analysis reinforced that the effect of NIV on the intubation rate might partly be attributed to the other impact factors. The ensemble AdaBoost decision tree model may assist clinicians in making clinical decisions, and early organ function support to improve patients’ SOFA, APSIII, GCS, PaCO 2 , PaO 2 , PH, PaO 2 /FiO 2 ratio, and lactate values can reduce the early failure rate and improve patient prognosis.

Fu, Wei↗
NASA NTRS1973

Identification of phenological stages and vegetative types for land use classification

The author has identified the following significant results. A large grassland was located on the Kenai Peninsula which may be a potential grazing land. Two 1:250 K vegetation maps were constructed from ERTS-1 scenes 1049-20505 and 1066-20453 using 70 mm MSS chips and black and white prints for an area of 3.5 million acres. Another area (464,000 acres) was mapped using digital data. The latter map is the most accurate and detailed vegetation map of that area produced to date. Areal extents of identified vegetation types were derived for the area mapped from digital data. Early spring (prior to leafing out of deciduous trees) is suspected as being the best time for mapping Alaskan vegetation from MSS data due to the best time for mapping Alaskan vegetation from MSS data due to the radiometrically distinctness of the vegetation communities at that time. Vegetative overlays produced at 1:250 K compare favorably with vegetative maps compiled by Lloyd A. Spetzman and assembled by the joint Federal-State Land Use Planning Commission for Alaska.

Branton, C. I.↗
DOE OSTI2022

The bottom-up EFT: complete UV resonances of the SMEFT operators

The standard model effective field theory (SMEFT) provides systematic parameterization of all possible new physics above the electroweak scale. According to the amplitude-operator correspondence, an effective operator can be decomposed into a linear combination of several j-basis operators, which correspond to local amplitudes carrying certain spin and gauge quantum numbers in a particular scattering channel. Based on the Poincare and gauge symmetries of scattering amplitude, we construct the j-basis using the Casimir method for both the Lorentz and gauge sectors. The quantum numbers of the j-basis operators fix the quantum numbers of any intermediate state in the corresponding amplitudes, such as a UV resonance. This can be re-interpreted as the j-basis/UV correspondence, thus obtaining the j-bases in all partitions of fields for an operator amounts to finding all of its UV origins at tree level, constituting the central part of the bottom-up EFT framework. Applying the j-basis analysis to SMEFT, we obtain a complete list of possible tree-level UV origins of the effective operators at the dimension 5, 6, 7, and all the bosonic operators at dimension 8.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1973

Identification of phenological stages and vegetative types for land use classification

The author has identified the following significant results. A large grassland was located on the Kenai Peninsula which may be a potential grazing land. Two 1:250,000 vegetation maps were constructed from ERTS-1 scenes 1049-20505 and 1066-20453 using 70 mm MSS chips and black and white prints for an area of 3.5 million acres. Another area (464,000 acres) was mapped using digital data. The latter map is the most accurate and detailed vegetation map of that area produced to date. Areal extents of identified vegetation types were derived for the area mapped from digital data. Early spring (prior to leafing out of the deciduous trees) is suspected as being the best time for mapping Alaskan vegetation from MSS data due to the radiometrically distinctness of the vegetation communities at that time.

Branton, C. I.↗
NASA NTRS2012

How Did I Get Here?

What country was responsible for much of the early work in laser altimetry, who was the first scientist to look at a vegetation profile generated by a laser, who first related laser ranges to forest structure? The purpose of this paper is to look back 3+ decades ago when forestry lidar was in its formative years and to give credit to those who first thought to employ a laser to measure the Earth's surface. As with much scientific research, advances were often made independently and concurrently in a number of countries. Functioning lasers were first demonstrated in 1960 in the USA and in 1961 in the USSR, but research into the use of lasers as forest measurement tools did not begin for another IS years. Initially, with respect to Earth resources, lasers were employed to measure sea ice surface roughness, to make near-shore bathymetric measurements, to penetrate forests to make detailed topographic measurements, and to fluoresce oceanic phytoplankton for surface current studies. Some of these early studies noted that forest profiles were evident but in fact added noise to topographic retrievals. Trees became the signal rather than noise in 1976 when researchers in the Canadian Forest Service went to an IUFRO conference in Oslo and reported on efforts to better estimate timber volume in tropical forests. They employed large-scale airphotos (1:500 up to 1:4000) to measure the top of the tropical canopy, an avionic radar to measure the location of the ground beneath the canopy, and a barometric sensor to record aircraft/radar height above a datum (e.g., sea level). Their radar did not work well in dense vegetation and mentioned in passing that a laser altimeter had worked well in Canadian forests. But in a report 2 years later they reported that, on a study area in Costa Rica, the radar ground line was much improved and no mention is made of a lidar altimeter. In the USSR in 1977, Russian researchers felled a birch and a spruce, aimed a helium-neon, 0.63 micron laser with a spot size of approx 25mm, at the horizontal trees, produced a profilograph, compared it to tape measurements, and concluded that, with increased power, such a laser could be mounted on an aircraft to remotely measure forest canopies. In 1979, they mounted their He-Ne laser on an AN-2 biplane and acquired their fIrSt airborne profiles. Scientists with TRANARG, a mapping/surveying company in Caracas, Venezuela, reported on 1976 flights employing a helium-neon lidar to collect over 11,000 km of lidar profiles spaced 1.5 km apart in order to construct a topographic map to help site a new reservoir. They noted 35-40 m median canopy heights with emergents up to 55 m in their profiles. These studies and others that utilize these height and canopy density metrics for forest mensuration are reviewed in this glance backwards at the history of forestry lidar.

Nelson, Ross↗
DOE OSTI2022

On effective field theories with celestial duals

We show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. These constraints are the same as those derived in [9] from the Jacobi identity of the algebra of soft modes. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed w 1+∞ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes involving gluons, gravitons and scalars in these theories. We find that all four-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints, which implies that all purely holomorphic or purely anti-holomorphic higher-point amplitudes vanish.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗