Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “causal models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Diagnosis and Reconfiguration using Bayesian Networks: An Electrical Power System Case Study

Automated diagnosis and reconfiguration are important computational techniques that aim to minimize human intervention in autonomous systems. In this paper, we develop novel techniques and models in the context of diagnosis and reconfiguration reasoning using causal Bayesian networks (BNs). We take as starting point a successful diagnostic approach, using a static BN developed for a real-world electrical power system. We discuss in this paper the extension of this diagnostic approach along two dimensions, namely: (i) from a static BN to a dynamic BN; and (ii) from a diagnostic task to a reconfiguration task. More specifically, we discuss the auto-generation of a dynamic Bayesian network from a static Bayesian network. In addition, we discuss subtle, but important, differences between Bayesian networks when used for diagnosis versus reconfiguration. We discuss a novel reconfiguration agent, which models a system causally, including effects of actions through time, using a dynamic Bayesian network. Though the techniques we discuss are general, we demonstrate them in the context of electrical power systems (EPSs) for aircraft and spacecraft. EPSs are vital subsystems on-board aircraft and spacecraft, and many incidents and accidents of these vehicles have been attributed to EPS failures. We discuss a case study that provides initial but promising results for our approach in the setting of electrical power systems.

Knox, W. Bradley↗
DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2000

Significant Findings: Tracking the SeaWiFS Record with a Coupled Physical/Biogeochemical/Radiative Model of the Global Oceans

The Sea-Viewing Wide Field-of-view Sensor (SeaWiFS) has observed 2.5 years of routine global chlorophyll observations from space. The mission was launched into a record El Nino event, which eventually gave way to one of the most intensive and longest-lasting La Nina events ever recorded. The SeaWiFS chlorophyll record captured the response of ocean phytoplankton to these significant events in the tropical Indo-Pacific basins, but also indicated significant interannual variability unrelated to the El Nino/La Nina events. This included large variability in the North Atlantic and Pacific basins, in the North Central and equatorial Atlantic, and milder patterns in the North Central Pacific. This SeaWiFS record was tracked with a coupled physical/biogeochemical/radiative model of the global oceans using near-real-time forcing data such as wind stresses, sea surface temperatures, and sea ice. This provided an opportunity to offer physically and biogeochemically meaningful explanations of the variability observed in the SeaWiFS data set, since the causal mechanisms and interrelationships of the model are completely understood. The coupled model was able to represent the seasonal distributions of chlorophyll during the SeaWiFS era, and was capable of differentiating among the widely different processes and dynamics occurring in the global oceans. The model was also reasonably successful in representing the interannual signal, especially when it was large, such as, the El Nino and La Nina events in the tropical Pacific and Indian Oceans. The model provided different phytoplankton group responses for the different events in these regions: diatoms were predominant in the tropical Pacific during the La Nina but other groups were predominant during El Nino. The opposite condition occurred in the tropical Indian Ocean. Both situations were due to the different responses of the basins to El Nino. The interannual variability in the North Atlantic, which was exhibited in SeaWiFS data as a decline in the spring/summer bloom in 1999 relative to 1998, resulted in the model from a more slowly shoaling mixed layer, allowing herbivore populations to keep pace with increasing phytoplankton populations. However, several aspects of the interannual cycle were not well-represented by the model. Explanations ranged from inherent model deficiencies, to monthly averaging of forcing fields, to biases in SeaWiFS atmospheric correction procedures.

Watson, Gregg W.↗
NASA NTRS1971

Crime prediction modeling

A study of techniques for the prediction of crime in the City of Los Angeles was conducted. Alternative approaches to crime prediction (causal, quasicausal, associative, extrapolative, and pattern-recognition models) are discussed, as is the environment within which predictions were desired for the immediate application. The decision was made to use time series (extrapolative) models to produce the desired predictions. The characteristics of the data and the procedure used to choose equations for the extrapolations are discussed. The usefulness of different functional forms (constant, quadratic, and exponential forms) and of different parameter estimation techniques (multiple regression and multiple exponential smoothing) are compared, and the quality of the resultant predictions is assessed.

Source record↗
DOE OSTI2026

Overview of the Nephele Perturbed Parameter Ensemble for Aerosol‐Cloud Interactions in E3SMv3

Aerosol-cloud interactions (aci) are the leading source of uncertainty in inferring climate sensitivity from the historical record. Earth system models (ESMs) struggle to represent aci because the processes responsible for these phenomena occur at much finer time and space scales than can be resolved by any ESM. Observational constraints provide key benchmarks to test ESMs, but cannot be used alone to fully understand aci processes except in very specific cases where causality is controlled; some degree of modeling is required to infer aci and estimate radiative forcing. Here, we generate and characterize a perturbed parameter ensemble (PPE) in version 3 of the Energy Exascale ESM (E3SMv3). We perturb 25 parameters that govern aci processes over 250 members and integrate the model over present-day and preindustrial aerosol emissions. We find that the process representation in E3SMv3 is flexible and can generate global-mean effective radiative forcings due to aci (ERFaci) ranging from −3.0 to +0.9 W m −2 . The positive ERFaci values simulated by a portion of the PPE are implausible and result from parameter combinations that produce unrealistic top-of-atmosphere energy fluxes. While global-mean cloud droplet number concentration always increases in response to anthropogenic aerosol, cloud liquid water path can both increase and decrease, suggesting that precipitation suppression is not the only aerosol-cloud adjustment represented by E3SMv3. Analysis of which processes control liquid cloud adjustment in the PPE points toward stratiform precipitation processes and aerosol activation, which is consistent with many previous ESMs, as well as the new two-moment convective cloud microphysics in E3SMv3.

Nugent, Jacqueline M. [Univ. of Wyoming, Laramie, ↗
NASA NTRS1987

The emissions of broadband electrostatic noise in the near vicinity of the Shuttle Orbiter

Measurements of the Space Shuttle environment from the STS-3 and Spacelab 2 missions indicate the presence of oblique ion streams and broadband electrostatic noise. A two-dimensional theoretical model is applied to study a possible causal relationship between the ion streams and the broadband noise, especially in terms of the ion acoustic wave and ion-ion wave modes. This model predicts the generation of waves with frequencies ranging from the ion cyclotron frequency up to values greater than the ion plasma frequency, with the maximum growth rate occurring in the 10-kHz range. These results are consistent with the observational data from the STS-3 mission. The model also shows that these two wave modes can coexist only when the wave vectors of the two wave modes are nearly perpendicular. The parametric dependence of the wave instabilities on the plasma parameters and the inclination of the wave propagation vector is also studied.

Hwang, K. S.↗
NASA NTRSDate not supplied

The Sufficient Component Cause Model Explaining Low-Dose Radiobiology through an Epidemiologic Lens

One of the major challenges in understanding space radiation-induced carcinogenesis is the uncertainty from translating radiobiological research in cellular and animal models to humans, especially at doses below 100 mSv. Biological studies have shown a host of potential outcomes at low doses in animal and cellular models. The existence of non-targeted effects as bystander and abscopal effects is well-documented from clinical research and basic science1,2,3. While some studies have shown increased effects at low doses, others have shown evidence of hormetic bystander effects, where radiation exposure may be beneficial4,5,6. Despite these varied and diverse findings, epidemiologic studies largely support the linear-no threshold (LNT) assumption used by radiation protection guidance7,8. Translational animal-to-human models have predominantly considered ratio values such as the relative biological effectiveness (RBE) and dose and dose-rate effectiveness factor (DDREF) that rely on the assumption of LNT rather than implementing specific dose-response shapes in the low-dose region, and translational cell-to-human models are uncommon. The sufficient component cause model presents an opportunity to examine biological findings at low doses from an epidemiological lens9. In this model, exposures “sufficient” to cause an outcome of interest are presented in pie charts, such that when all slices of a pie chart are fulfilled, the outcome will occur. Multiple pie charts may exist for a single outcome, illustrating individual differences9. In 1988,Greenland and Poole adapted the sufficient component cause model to incorporate interaction with other exposures (such as genetics or lifestyle factors)10. They show that a range of biological processes are possible in a population, but that an epidemiologic study will only reveal the mean outcome from the population at large10,11. Using this construct, the multiple outcomes presented in radiobiological models to date can be explained in the context of epidemiologic studies. This presentation aims to demonstrate a causal framework that can integrate radiobiological and epidemiological models to date. It is intended as a conversation starter to spur future research.

C M Milder↗
NASA NTRSDate not supplied

The Potential Outcome Model: Explaining Low-Dose Radiobiology through an Epidemiologic Lens

One of the major challenges in understanding space radiation-induced carcinogenesis is the uncertainty from translating radiobiological research in cellular and animal models to humans, especially at doses below 100 mSv. Biological studies have shown a host of potential outcomes at lowdoses in animal and cellular models. The existence of non-targeted effects as bystander and abscopal effects is well-documented from clinical research and basic science1,2,3. While some studies have shown increased effects at low doses, others have shown evidence of hormetic bystander effects, where radiation exposure may be beneficial4,5,6. Despite these varied and diverse findings, epidemiologic studies largely support the linear-no threshold (LNT) assumption used by radiation protection guidance7,8. Translational animal-to-human models have predominantly considered ratio values such as the relative biological effectiveness (RBE) and dose and dose-rate effectiveness factor (DDREF) that rely on the assumption of LNT rather than implementing specific dose-response shapes in the low-dose region, and translational cell-to-human models are uncommon. The sufficient component cause model presents an opportunity to examine biological findings at low doses from an epidemiological lens9. In this model, exposures “sufficient” to cause an outcome of interest are presented in pie charts, such that when all slices of a pie chart are fulfilled, the outcome will occur. Multiple pie charts may exist for a single outcome, illustrating individual differences9. In 1988,Greenland and Poole adapted the sufficient component cause model to incorporate interaction with other exposures (such as genetics or lifestyle factors)10. They show that a range of biological processes are possible in a population, but that an epidemiologic study will only reveal the mean outcome from the population at large10,11. Using this construct, the multiple outcomes presented in radiobiological models to date can be explained in the context of epidemiologic studies. This presentation aims to demonstrate a causal framework that can integrate radiobiological and epidemiological models to date. It is intended as a conversation starter to spur future research.

C M Milder↗
NASA NTRS1989

Causality of plasma permittivity with loss and restoring terms

The causality of the complex permittivity for a plasma model in which both loss and restoring terms are included is shown. Discussions as to what occurs in this causality property when the loss and restoring terms vanish are presented. Results are shown to agree with earlier work.

Cockrell, C. R.↗
NASA NTRS2022

A Coupled Evaluation of Operational MODIS and Model Aerosol Products for Maritime Environments Using Sun Photometry: Evaluation of the Fine and Coarse Mode

Although satellite retrievals and data assimilation have progressed to where there is a good skill for monitoring maritime Aerosol Optical Depth (AOD), there remains uncertainty in achieving further degrees of freedom, such as distinguishing fine and coarse mode dominated species in maritime environments (e.g., coarse mode sea salt and dust versus fine mode terrestrial anthropogenic emissions, biomass burning, and maritime secondary production). For the years 2016 through 2019, we performed an analysis of 550 nm total AOD550, fine mode AOD (FAOD550; also known as FM AOD in the literature), coarse mode AOD (CAOD550), and fine mode fraction (η550) between Moderate Resolution Spectral Imaging Radiometer (MODIS) V6.1 MOD/MYD04 dark target aerosol retrievals and the International Cooperative for Aerosol Prediction (ICAP) core four multi-model consensus (C4C) of analyses/short term forecasts that assimilate total MODIS AOD550. Differences were adjudicated by the global shipboard Maritime Aerosol Network (MAN) and selected island AERONET sun photometer observations with the application of the spectral deconvolution algorithm (SDA). Through a series of conditional and regional analyses, we found divergence included regions of terrestrial influence and latitudinal dependencies in the remote oceans. Notably, MODIS and the C4C and its members, while having good correlations overall, have a persistent +0.04 to +0.02 biases relative to MAN and AERONET for typical AOD550 values (84th% < 0.28), with the C4C underestimating significant events thereafter. Second, high biases in AOD550 are largely associated with the attribution of the fine mode in satellites and models alike. Thus, both MODIS and C4C members are systematically overestimating AOD550 and FAOD550 but perform better in characterizing the CAOD550. Third, for MODIS, findings are consistent with previous reports of a high bias in the retrieved Ångström Exponent, and we diagnosed both the optical model and cloud masking as likely causal factors for the AOD550 and FAOD550 high bias, whereas for the C4C, it is likely from secondary overproduction and perhaps numerical diffusion. Fourth, while there is no wind-speed-dependent bias for surface winds <12 m s−1, the C4C and MODIS AOD550s also overestimate CAOD550 and FAOD550, respectively, for wind speeds above 12 m/s. Finally, sampling bias inherent in MAN, as well as other circumstantial evidence, suggests biases in MODIS are likely MODIS and the C4C products have their own strengths and challenges for a given climate application and discuss needed research. even larger than what was diagnosed here. We conclude with a discussion on how

Aerosols↗
NASA NTRS2010

The Invigoration of Deep Convective Clouds Over the Atlantic: Aerosol Effect, Meteorology or Retrieval Artifact?

Associations between cloud properties and aerosol loading are frequently observed in products derived from satellite measurements. These observed trends between clouds and aerosol optical depth suggest aerosol modification of cloud dynamics, yet there are uncertainties involved in satellite retrievals that have the potential to lead to incorrect conclusions. Two of the most challenging problems are addressed here: the potential for retrieved aerosol optical depth to be cloud-contaminated, and as a result, artificially correlated with cloud parameters; and the potential for correlations between aerosol and cloud parameters to be erroneously considered to be causal. Here these issues are tackled directly by studying the effects of the aerosol on convective clouds in the tropical Atlantic Ocean using satellite remote sensing, a chemical transport model, and a reanalysis of meteorological fields. Results show that there is a robust positive correlation between cloud fraction or cloud top height and the aerosol optical depth, regardless of whether a stringent filtering of aerosol measurements in the vicinity of clouds is applied, or not. These same positive correlations emerge when replacing the observed aerosol field with that derived from a chemical transport model. Model-reanalysis data is used to address the causality question by providing meteorological context for the satellite observations. A correlation exercise between the full suite of meteorological fields derived from model reanalysis and satellite-derived cloud fields shows that observed cloud top height and cloud fraction correlate best with model pressure updraft velocity and relative humidity. Observed aerosol optical depth does correlate with meteorological parameters but usually different parameters from those that correlate with observed cloud fields. The result is a near-orthogonal influence of aerosol and meteorological fields on cloud top height and cloud fraction. The results strengthen the case that the aerosol does play a role in invigorating convective clouds.

Koren, Ilan↗
DOE OSTI2025

Mapping causal patterns in crystalline solids

The evolution of the atomic structures of the combinatorial library of Sm-substituted thin film BiFeO 3 along the phase transition boundary from the ferroelectric rhombohedral phase to the non-ferroelectric orthorhombic phase is explored using scanning transmission electron microscopy. Localized properties, including polarization, lattice parameter, and chemical composition, are parameterized from atomic-scale imaging, and their causal relationships are reconstructed using a linear non-Gaussian acyclic model. This approach is further extended to explore the spatial variability of the causal coupling using the sliding window transform method, which revealed that new causal relationships emerged at both the expected locations, such as domain walls and interfaces, and at additional regions forming clusters in the vicinity of the walls or spatially distributed features. While the exact physical origins of these relationships are unclear, they likely represent nanophase-separated regions in the morphotropic phase boundaries. Overall, we posit that an in-depth understanding of complex disordered materials away from thermodynamic equilibrium necessitates understanding not only the generative processes that can lead to observed microscopic states but also the causal links between multiple interacting subsystems.

Causal inference↗
DOE OSTI2025

Novel scalings of neutron star properties from analyzing dimensionless Tolman–Oppenheimer–Volkoff equations

The Tolman–Oppenheimer–Volkoff (TOV) equations govern the radial evolution of pressure and energy density in static neutron stars (NSs) in hydrodynamical equilibrium. Using the reduced pressure and energy density with respect to the NS central energy density, the original TOV equations can be recast into dimensionless forms. While the traditionally used integral approach for solving the original TOV equations require an input nuclear Equation of State (EOS), the dimensionless TOV equations can be anatomized by using the reduced pressure and energy density as polynomials of the reduced radial coordinate without using any input nuclear EOS. It has been shown in several of our recent works that interesting and novel perspectives about NS core EOS can be extracted directly from NS observables by using the latter approach. Our approach is based on intrinsic and perturbative analyses of the dimensionless (IPAD) TOV equations (IPAD-TOV). In this review article, we first discuss the length and energy density scales of NSs as well as the dimensionless TOV equations for scaled variables and their perturbative solutions near NS cores. We then review several new insights into NS physics gained from solving perturbatively the scaled TOV equations. Whenever appropriate, comparisons with the traditional approach from solving the original TOV equations will be made. In particular, we first show that the nonlinearity of the TOV equations basically excludes a linear EOS for dense matter in NS cores. We then show that perturbative analyses of the scaled TOV equations enable us to reveal novel scalings of the NS mass, radius and the compactness with certain combinations of the NS central pressure and energy density. Thus, observational data on either mass, radius or compactness can be used to constrain directly the core EOS of NS matter independent of the still very uncertain nuclear EOS models. As examples, the EOS of the densest visible matter in our Universe before the most massive neutron stars collapse into black holes (BHs) as well as the central EOS of a canonical or a 2.1 solar mass NS are extracted without using any nuclear EOS model. In addition, we show that causality in NSs sets an upper bound of about 0.374 for the ratio of pressure over energy density and correspondingly a lower limit for trace anomaly in supra-dense matter. We also demonstrate that the strong-field gravity plays a fundamental role in extruding a peak in the density/radius profile of the speed of sound squared (SSS) in massive NS cores independent of the nuclear EOS. Finally, some future perspectives of NS research using the new approach reviewed here by solving perturbatively the dimensionless TOV equations are outlined.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

FY24 Progress Report: Disposition of Cracks & Features Observed in the Inner Can Closure Weld Region (ICCWR) of the 3013 Package

The long-term integrity of the 3013 containers is of interest for the safe storage of Pu materials. Although the 3013 standard embodies multiple barrier concept, the integrity of the inner container is considered to be crucial since it protects the Safety Class outer container from its contents. The container is designed to withstand high pressures that could result from the complete radiolysis of the maximum water content permissible by the 3013 standard. Shelf-life studies and destructive examination have not found high gas pressures but have found that corrosive gases are generated. Pitting and stress corrosion cracking (SCC) are considered to be critical corrosion modes for the performance of the inner container and have been observed during destructive examinations. Considerable research has been conducted on the possibility of aqueous electrolytes condensing on the inner container that can promote SCC. These studies indicate the uncertainties surrounding the formation of corrosive environments and the corrosion behavior of container materials. In this initial report, a Bayesian network (BN) model is described that can consider the uncertainties and the causal connections between various factors influencing the corrosion modes of the inner container. The BN model is preliminary and provides an initial framework to identify the necessary information. The report also provides initial experimental results on the electrochemical behavior of stainless steels in anticipated condensed environments from gas phase migration of acidic gases. The experimental results are consistent with the corrosion model. Recommendation for further work on the BN model include assembling an expert group to provide input to the BN structure and quantification of the conditional probability matrix, experimental studies to characterize the microstructure of the container, electrochemical studies to identify critical potentials for localized corrosion and SCC, and crack growth rate studies

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1985

Aiding the operator during novel fault diagnosis

An aid is proposed for the operator who must deal with a novel failure. A novel failure is one that is not covered by the operator's training or procedures or by an expert system (if present). The aid contains a disaggregated model of the system for reasoning causally about the system. It is to work in parallel with the human and interact at various levels of control. It is designed specifically to mitigate some human suboptimalities and biases during decision making.

Yoon, W. C.↗
DOE OSTI2025

Constraining aerosol–cloud adjustments by uniting surface observations with a perturbed parameter ensemble

Abstract. Aerosol–cloud interactions (ACIs) are the largest source of uncertainty in inferring the magnitude of future warming consistent with the observational record. The effective radiative forcing due to ACI (ERFaci) is dominated by liquid clouds and is composed of two terms: the change in cloud albedo due to redistributing liquid over a larger number of cloud droplets (Nd) and the change in cloud macrophysical properties due to changes in cloud microphysics. These terms are, respectively, referred to as the radiative forcing due to ACI (RFaci) and aerosol–cloud adjustments. While the magnitude of RFaci is uncertain, its sign is confidently negative and results in a cooling in the historical record. In contrast, the adjustment of cloud liquid water path (LWP) to enhanced Nd and associated radiative forcing is uncertain in sign. Increased LWP in response to increased Nd is consistent with precipitation suppression, while decreased LWP in response to increased Nd is consistent with enhanced evaporation from cloud top. Observational constraints of these processes are poor in part because of causal ambiguity in the relationship between Nd and LWP. To better understand this relationship, precipitation (P), Nd, and LWP surface observations from the Eastern North Atlantic (ENA) atmospheric observatory are combined with the output from a perturbed parameter ensemble (PPE) hosted in the Community Atmosphere Model version 6 (CAM6). This allows for causal interpretation of observed covariability. Observations of precipitation and cloud from ENA constrain the range of possible LWP aerosol–cloud adjustments relative to the prior from the PPE by 15 %, resulting in a global value that is confidently positive (a historical cooling) ranging from 2.1 to 6.9 g m−2. It is found that observed covariability between Nd and LWP is dominated by coalescence scavenging and that this observed covariability is not strongly related to aerosol–cloud adjustments.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1996

Behavioral Implications of Piezoelectric Stack Actuators for Control of Micromanipulation

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for microrobotic applications requiring accurate position and/or force control. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of non-intuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. The authors incorporate a generalized Maxwell resistive capacitor as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.

Goldfarb, Michael↗
NASA NTRS1992

An architecture for the development of real-time fault diagnosis systems using model-based reasoning

Presented here is an architecture for implementing real-time telemetry based diagnostic systems using model-based reasoning. First, we describe Paragon, a knowledge acquisition tool for offline entry and validation of physical system models. Paragon provides domain experts with a structured editing capability to capture the physical component's structure, behavior, and causal relationships. We next describe the architecture of the run time diagnostic system. The diagnostic system, written entirely in Ada, uses the behavioral model developed offline by Paragon to simulate expected component states as reflected in the telemetry stream. The diagnostic algorithm traces causal relationships contained within the model to isolate system faults. Since the diagnostic process relies exclusively on the behavioral model and is implemented without the use of heuristic rules, it can be used to isolate unpredicted faults in a wide variety of systems. Finally, we discuss the implementation of a prototype system constructed using this technique for diagnosing faults in a science instrument. The prototype demonstrates the use of model-based reasoning to develop maintainable systems with greater diagnostic capabilities at a lower cost.

Hall, Gardiner A.↗