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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with Hamiltonians H 0 and H 1 = H 0 + V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of H 1 at inverse temperature β ≥ 0 starting from a purification of the thermal state of H 0 . The complexity of the quantum algorithm, given by the number of uses of certain unitaries, is $\mathcal{O}$ (e β(ΔA - w l )/2 ), where ΔA is the free-energy difference between H 1 and H 0 , and w l is a work cutoff that depends on the properties of the work distribution and the approximation error ϵ > 0. If the non-equilibrium process is trivial, this complexity is exponential i β∥V∥, where ∥V∥ is the spectral norm of V. This represents a significant improvement of prior quantum algorithms that have complexity exponential in β∥H 1 ∥ in the regime where ∥V∥$\ll$ ∥H 1 ∥. The dependence of the complexity in ϵ varies according to the structure of the quantum systems. It can be exponential in 1/ϵ in general, but we show it to be sublinear in 1/ϵ if H 0 and H 1 commute, or polynomial in 1/ϵ if H 0 and H 1 are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value of w l and improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.

Rao, Nageswara↗
DOE OSTI2025

Evaluating spectral cloud effective radius retrievals from the Enhanced MODIS Airborne Simulator (eMAS) during ORACLES

Satellite remote sensing retrievals of cloud effective radius (CER) are widely used for studies of aerosol–cloud interactions. Such retrievals, however, rely on forward radiative transfer (RT) calculations using simplified assumptions that can lead to retrieval errors when the real atmosphere deviates from the forward model. Here, coincident airborne remote sensing and in situ observations obtained during NASA's ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) field campaign are used to evaluate retrievals of CER for marine boundary layer stratocumulus clouds and to explore impacts of forward RT model assumptions and other confounding factors. Specifically, spectral CER retrievals from the Enhanced MODIS Airborne Simulator (eMAS) and the Research Scanning Polarimeter (RSP) are compared with polarimetric retrievals from RSP and with CER derived from droplet size distributions (DSDs) observed by the Phase Doppler Interferometer (PDI) and a combination of the Cloud and Aerosol Spectrometer (CAS) and the Two-Dimensional Stereo Probe (2D-S). The sensitivities of the eMAS and RSP spectral retrievals to assumptions about the DSD effective variance (CEV) and liquid water complex index of refraction are explored. CER and CEV inferred from eMAS spectral reflectance observations of the backscatter glory provide additional context for the spectral CER retrievals. The spectral and polarimetric CER retrieval agreement is case dependent, and updating the retrieval RT assumptions, including using RSP polarimetric CEV retrievals as a constraint, yields mixed results that are tied to differing sensitivities to vertical heterogeneity. Moreover, the in situ cloud probes, often used as the benchmark for remote sensing CER retrieval assessments, themselves do not agree, with PDI DSDs yielding CER values 1.3–1.6 µm larger than CAS and with CEV roughly 50 %–60 % smaller than CAS. Implications for the interpretation of spectral and polarimetric CER retrievals and their agreement are discussed.

Meyer, Kerry [NASA Goddard Space Flight Center (GS↗
DOE OSTI2023

Accurate Prediction of Algal Biomass Lipid, Protein, and Carbohydrate Composition with Machine Learning Regression Modelling of Near-IR Spectra

During large scale algal biomass cultivation, it is difficult to reliably control relative composition to target levels. Rapid determination of chemical composition is feasible by using near infrared (NIR) spectral data. We sought to build and improve on reliable high-throughput screening prediction method based on partial least squares regression (PLSR) by the application of artificial neural networks (ANN) and associated optimization strategies. The algal biomass sample set was designed and created in an iterative process of culturing in physiologically diverse conditions at the GAI field site, followed by compositional analyses at NREL. The workflow allowed us to identify gaps in compositional space for informing the subsequent cultivation and sampling efforts and generated a high quality set of 210 unique samples with chemical analysis results, spectral scanning data, and cultivation metadata. We observed a significant improvement in the performance of carbohydrate content predictions using an optimized ANN model compared to PLSR, with > 16% reduction in mean absolute percent error (MAPE) when tested on the same set of reserved data. The optimized ANN models for FAME and protein prediction performed exceptionally well with 5.99% and 5.09% MAPE, respectively. Application of these methods to detection and quantification of minor biomass constituents that are relevant to certain product streams has shown positive preliminary results, opening the possibility for extensions to the outputs of this powerful data type. All models are accompanied by prediction uncertainties and unsupervised spectral outlier detection to alert an operator to unreliable spectral data. These tools can be deployed for rapid determination of algal culture status, and cultivation and biomass quality improvement.

algal biofuels↗
DOE OSTI2023

SALT2 versus SALT3: updated model surfaces and their impacts on type Ia supernova cosmology

ABSTRACT For the past decade, SALT2 has been the most common model used to fit Type Ia supernova (SN Ia) light curves for dark energy analyses. Recently, the SALT3 model was released, which upgraded a number of model features but has not yet been used for measurements of dark energy. Here, we evaluate the impact of switching from SALT2 to SALT3 for a SN cosmology analysis. We train SALT2 and SALT3 on an identical training sample of 1083 well-calibrated Type Ia supernovae, ensuring that any differences found come from the underlying model framework. We publicly release the results of this training (the SALT ‘surfaces’). We then run a cosmology analysis on the public Dark Energy Survey 3-Yr Supernova data sample (DES-SN3YR), and on realistic simulations of those data. We provide the first estimate of the SN + CMB systematic uncertainty arising from the choice of SALT model framework (i.e. SALT2 versus SALT3), Δw = + 0.001 ± 0.005 – a negligible effect at the current level of dark energy analyses. We also find that the updated surfaces are less sensitive to photometric calibration uncertainties than previous SALT2 surfaces, with the average spectral energy density dispersion reduced by a factor of two over optical wavelengths. This offers an opportunity to reduce the contribution of calibration errors to SN cosmology uncertainty budgets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Development of a Convolutional Neural Network Classifier for Data Starved Spectra - 20199

The Institute for Clean Energy Technology (ICET) at Mississippi State University is exploring the utility of machine learning in augmenting its mobile radiation surveying platforms, which are currently being developed as means to survey depleted uranium contaminated areas in support of remediation and decommissioning efforts. Mobile survey platforms provide a means to efficiently scan large areas of interest while reducing human exposure to radiation and other hazards. The survey platforms can also be used for scanning for any gamma emitting isotope in addition to depleted uranium. The spectral data that the platforms collect may be data starved with relatively low counts and poorly defined spectral features depending on the speed of the platforms and scintillation detector selection. Such data-starved spectra are difficult to use for isotope identification, requiring advanced knowledge of the possible radionuclides that could be present and environmental factors that could attenuate signals or introduce background noise. These factors in combination with the volume of survey data increases the time it takes to perform analysis of survey data when the source type is unknown. There are a number of algorithms in the field of machine learning that can be used to classify data that would be challenging and time-consuming for a human to identify. Supervised machine learning algorithms train models based on extensive amounts of human-labeled training data. Once sufficiently trained, these models can be used to quickly make high-fidelity predictions on new data. Convolutional neural networks are machine learning algorithms that excel in learning representations of 'shapes'. They do this by taking numerical input data and convolving them with spatial feature detectors referred to as filters. These filters are incrementally adjusted to reduce the prediction error on the data during the backpropagation step of training. Discussed in this paper is the development of a convolutional neural network classifier (CNNC) that can utilize spectral survey data for source discrimination and isotope identification. Bench-top laboratory experiments data using LaBr{sub 3}(Ce) scintillation detectors were used to train and evaluate the performance of the developed CNNC. The CNNC is capable of discriminating a variety of gamma emitting source types, differentiating different forms of uranium (depleted vs. natural), and estimating the amount of uranium for a known geometry. The discussed CNNC may be useful in scenarios where survey systems are deployed in situations where hazardous radioactive material maybe present, but the type is unknown. When used in remediation applications the CNNC can be used to screen-out false positives, helping reduce remediation costs. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2023

Multiwavelength Observations of a New Redback Millisecond Pulsar 4FGL J1910.7-5320

We present the study of multiwavelength observations of an unidentified Fermi Large Area Telescope (LAT) source, 4FGL J1910.7-5320, a new candidate redback millisecond pulsar binary. In the 4FGL 95% error region of 4FGL J1910.7-5320, we find a possible binary with a 8.36 hr orbital period from the Catalina Real-Time Transient Survey, confirmed by optical spectroscopy using the SOAR telescope. This optical source was recently independently discovered as a redback pulsar by the TRAPUM project, confirming our prediction. We fit the optical spectral energy distributions of 4FGL J1910.7-5320 with a blackbody model, inferring a maximum distance of 4.1 kpc by assuming that the companion fills its Roche lobe with a radius of R = 0.7 R ⊙ . Using a 12.6 ks Chandra X-ray observation, we identified an X-ray counterpart for 4FGL J1910.7-5320, with a spectrum that can be described by an absorbed power law with a photon index of 1.0 ± 0.4. The spectrally hard X-ray emission shows tentative evidence for orbital variability. Using more than 12 yr of Fermi-LAT data, we refined the position of the γ-ray source, and the optical candidate still lies within the 68% positional error circle. In addition to 4FGL J1910.7-5320, we find a variable optical source with a periodic signal of 4.28 hr inside the 4FGL catalog 95% error region of another unidentified Fermi source, 4FGL J2029.5-4237. However, the γ-ray source does not have a significant X-ray counterpart in an 11.7 ks Chandra observation, with a 3σ flux upper limit of 2.4 × 10 -14 erg cm -2 s -1 (0.3–7 keV). Moreover, the optical source is outside our updated Fermi-LAT 95% error circle. These observational facts all suggest that this new redback millisecond pulsar powers the gamma-ray source 4FGL J1910.7-5320 while 4FGL J2029.5-4237 is unlikely the γ-ray counterpart to the 4.28 hr variable.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The Simons Observatory: Design, Integration, and Testing of the Small Aperture Telescopes

The Simons Observatory (SO) is a cosmic microwave background survey experiment that includes small-aperture telescopes (SATs) observing from an altitude of 5200 m in the Atacama Desert in Chile. The SO SATs will cover six spectral bands between 27 and 280 GHz to search for primordial B-modes to a sensitivity of σ(r) = 0.002, with quantified systematic errors well below this value. Each SAT is a self-contained cryogenic telescope with a 35° field of view, 42 cm diameter optical aperture, 40 K half-wave plate, 1 K refractive optics, and <0.1 K focal plane that holds >12,000 transition edge sensor detectors. We describe the nominal design of the SATs and present details about the integration and testing for one operating at 93 and 145 GHz.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2021

Verification of a quasi-linear model for gyrokinetic turbulent transport

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper (Staebler et al 2020 Plasma Phys. Control. Fusion 63 015013), a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium E × B velocity shear (Staebler et al 2013 Phys. Rev. Lett. 110 055003) and the zonal flow mixing model for electron-scale turbulence (Staebler et al 2016 Phys. Plasmas 23 062518) are both revised to be compatible with this new model. Furthermore, the models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations (Staebler et al 2005 Phys. Plasmas 12 102508) are also changed to improve the linear eigenmodes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Effects of cosine tapering window on quantum phase estimation

Here, we provide a modification to the quantum phase estimation algorithm (QPEA) [Abrams and Lloyd, Phys. Rev. Lett. 83, 5162 (1999); Cleve et al., Proc. R. Soc. A 454, 339 (1998); Nielsen and Chuang, Quantum computation and quantum information, 2002.] inspired by classical windowing methods for spectral density estimation. From this modification we obtain an upper bound in the cost that implies a cubic improvement with respect to the algorithm's error rate. Numerical evaluation of the costs also demonstrates an improvement. Moreover, with similar techniques, we detail an iterative projective measurement method for ground state preparation that gives an exponential improvement over previous bounds using QPEA. Numerical tests that confirm the expected scaling behavior are also obtained. For these numerical tests we have used a lattice Thirring model as testing ground. Using well-known perturbation theory results, we also show how to more appropriately estimate the cost scaling with respect to state error instead of evolution operator error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Beam combining of high-power terahertz lasers with semiconductor metasurface gratings

Spectral beam combining (SBC) of an array of single-mode lasers has the potential for realizing a chip-scale electrically tunable multispectral laser source without any moving parts and with emission at closely spaced discrete frequencies. Here, we demonstrate SBC of an array of single-mode THz quantum-cascade lasers (QCLs) with small frequency spacing. Semiconductor-based metasurface THz blazed gratings are developed for integration with QCLs in a compact cryocooler setup. Single-lobed beams of four QCLs emitting around 3.2 THz and spectrally separated by ~14 GHz are combined to achieve collinear propagation of spatially overlapped and collimated beams in the far field with ≲ 0.1° of pointing error. Peak optical power in the range 50–100 mW is detected from each of the QCLs after combining. The dense frequency spacing in our method provides a pathway to incorporate tens of QCLs on a chip to realize a high-power discretely tunable THz laser source for applications in THz spectroscopy.

Jia, Fei [Lehigh Univ., Bethlehem, PA (United Stat↗
DOE OSTI2021

The Initial–Final Mass Relation for Hydrogen-deficient White Dwarfs

The initial–final mass relation represents the total mass lost by a star during the entirety of its evolution from the zero age main sequence to the white-dwarf cooling track. The semiempirical initial–final mass relation (IFMR) is largely based on observations of DA white dwarfs, the most common spectral type of white dwarf and the simplest atmosphere to model. We present a first derivation of the semiempirical IFMR for hydrogen-deficient (non-DA) white dwarfs in open star clusters. We identify a possible discrepancy between the DA and non-DA IFMRs, with non-DA white dwarfs ≈0.07 M {sub ⊙} less massive at a given initial mass. Such a discrepancy is unexpected based on theoretical models of non-DA formation and observations of field white dwarf mass distributions. If real, the discrepancy is likely due to enhanced mass loss during the final thermal pulse and renewed post-AGB evolution of the star. However, we are dubious that the mass discrepancy is physical and instead is due to the small sample size, to systematic issues in model atmospheres of non-DAs, and to the uncertain evolutionary history of Procyon B (spectral type DQZ). A significantly larger sample size is needed to test these assertions. In addition, we also present Monte Carlo models of the correlated errors for DA and non-DA white dwarfs in the initial–final mass plane. We find the uncertainties in initial–final mass determinations for individual white dwarfs can be significantly asymmetric, but the recovered functional form of the IFMR is grossly unaffected by the correlated errors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A flexible polymer-based luminescent ink for combined thermographic phosphors and digital image correlation (TP+DIC)

Recent work on the development of integrated thermographic phosphors and digital image correlation (TP+DIC) for combined thermal–mechanical measurements has revealed the need for a flexible, stretchable phosphor coating for metal surfaces. Herein, we coat stainless steel substrates with a polymer-based phosphor ink in a DIC speckle pattern and demonstrate that the ink remains well bonded under substrate deformation. In contrast, a binderless phosphor DIC coating produced via aerosol deposition (AD) partially debonded from the substrate. DIC calculations reveal that the strain on the ink coating matches the strain on the substrate within 4% error at the highest substrate loads (0.05 mm/mm applied substrate strain), while the strain on the AD coating remains near 0 mm/mm as the substrate deforms. Spectrally resolved emission from the phosphor is measured through the transparent binder throughout testing, and the ratio method is used to infer temperature with an uncertainty of 1.7 °C. In conclusion, this phosphor ink coating will allow for accurate, non-contact strain and temperature measurements of a deforming surface.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Multigroup Thermal Radiation Transport with Tensor Trains

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally infeasible on conventional hardware. We show that solutions to certain multigroup problems possess an intrinsic low-rank structure, which the TT representation leverages effectively. This enables us to solve problems where the discretized solution size exceeds a trillion parameters on a single node. The solver is evaluated on a range of test problems with varying levels of complexity, consistently achieving compression factors greater than 100× and speedups exceeding 2×. We also investigate alternative TT topologies by analyzing the low-rank structure of the merged spatio-spectral core to assess the potential for greater compression. This analysis suggests that compression gains could increase by factors as large as 7. Our results indicate that the low-rank structure of the merged spatio-spectral core captures the spatio-spectral complexity of the solution, largely driven by the opacity structure of the medium. Beyond identifying opportunities for improved compression, this analysis highlights the types of errors that may arise in angle-integrated quantities when exploiting this low-rank structure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Automatic Échelle Spectrograph Wavelength Calibration

Time-domain astronomy and the increasing number of exoplanet candidates call for reliable, robust, and automatic wavelength calibration. We present an algorithm for wavelength-calibrating échelle spectrographs that uses order-by-order extracted spectra and a list of laboratory wavelengths. Our approach is fully automatic and does not need the pixel locations of certain spectral features with which to anchor the wavelength solution, nor the true order number of each diffraction order. We use spectral features that are duplicated in adjacent orders to establish the scale-invariant component of the wavelength solution. We then match the central wavelengths of spectral features to laboratory wavelengths to establish the scale and higher-order components of the wavelength solution. We demonstrate our method on the four spectrographs of Las Cumbres Observatory’s Network of Robotic Échelle Spectrographs (NRES), on the High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph, and on synthetic data. We obtain a velocity-equivalent precision of ∼10 m s{sup −1} on NRES. We achieve ∼1 m s{sup −1} on HARPS, which agrees with the precision reported by the HARPS team. On synthetic data, we achieve the velocity precision set by Gaussian centroiding errors. Our algorithm likely holds for a wide range of spectrographs beyond the five presented here. We provide an open-source Python package, xwavecal, which outputs wavelength-calibrated spectra as well as the wavelengths of spectral features.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

On the mechanisms of ion adsorption to aqueous interfaces: air-water vs. oil-water

The adsorption of ions to water-hydrophobe interfaces influences a wide range of phenomena, including chemical reaction rates, ion transport across biological membranes, and electrochemical and many catalytic processes; hence, developing a detailed understanding of the behavior of ions at water-hydrophobe interfaces is of central interest. Here, we characterize the adsorption of the chaotropic thiocyanate anion (SCN − ) to two prototypical liquid hydrophobic surfaces, water-toluene and water-decane, by surface-sensitive nonlinear spectroscopy and compare the results against our previous studies of SCN − adsorption to the air-water interface. For these systems, we observe no spectral shift in the charge transfer to solvent spectrum of SCN − , and the Gibb’s free energies of adsorption for these three different interfaces all agree within error. We employed molecular dynamics simulations to develop a molecular-level understanding of the adsorption mechanism and found that the adsorption for SCN − to both water-toluene and water-decane interfaces is driven by an increase in entropy, with very little enthalpic contribution. This is a qualitatively different mechanism than reported for SCN − adsorption to the air-water and graphene-water interfaces, wherein a favorable enthalpy change was the main driving force, against an unfavorable entropy change.

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

A Radiative Transfer Model for Patchy Landscapes Based on Stochastic Radiative Transfer Theory

The availability of global high-resolution land cover maps provides promising a priori knowledge for characterizing subpixel heterogeneity and improving predictions of directional reflectance of coarse-resolution pixels. Due to mutual shadowing and sheltering effects between the adjacent forest and cropland patches, the spectral nonlinear mixing of patchy ecotones is significant, especially when the sun illuminates the ecotone from the forest side with high solar zenith angle. The spectral linear mixture (SLM) approach leads to overestimation of the bidirectional reflectance factor (BRF) in the red band in the principal plane (PP), with a maximum absolute error (MAE) of 0.0063 and a maximum relative error (MRE) of 52.5%, and to underestimation in the near-infrared band in PP with an MAE of 0.0940 and an MRE of 14.5%. In a scenario with randomly distributed boundary orientations, the overestimation of SLM increases with the degree of fragmentation and the view zenith angle. We propose a Radiative Transfer model for patchy ECotones (RTEC). which improves R² from 0.61 to 0.94 in the red band of Landsat-8 directional reflectance at the validation site. The RTEC model provides an efficient and analytical approach for directional reflectance predictions over heterogeneous patchy landscapes at coarse resolution and will be used for biophysical parameter retrievals [e.g., the leaf area index (LAI)] in future applications.

Zeng, Yelu↗