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Anomalies of global symmetries on the lattice

't Hooft anomalies of global symmetries play a fundamental role in quantum many-body systems and quantum field theory (QFT). In this paper, we make a systematic analysis of lattice anomalies - the analog of 't Hooft anomalies in lattice systems - for which we give a precise definition. Crucially, a lattice anomaly is not a feature of a specific Hamiltonian, but rather is a topological invariant of the symmetry action. The controlled setting of lattice systems allows for a systematic and rigorous treatment of lattice anomalies, shorn of the technical challenges of QFT. We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways, but also have crucial differences. In particular, lattice anomalies and QFT anomalies are not, contrary to a common expectation, in one-to-one correspondence, and there can be non-trivial anomalies on the lattice that are infrared (IR) trivial: they admit symmetric trivial gapped ground states, and map to trivial QFT anomalies at low energies. Nevertheless, we show that lattice anomalies (including IR-trivial ones) have a number of interesting consequences in their own right, including connections to commuting projector models, phases of many-body localized (MBL) systems, and quantum cellular automata (QCA). We make substantial progress on the classification of lattice anomalies and develop several theoretical tools to characterize their consequences on symmetric Hamiltonians. Our work places symmetries of quantum many-body lattice systems into a unified theoretical framework and may also suggest new perspectives on symmetries in QFT.

Disordered Systems and Neural Networks (cond-mat.d↗

$\mathcal{N}$ = (1, 0) anomaly multiplet relations in six dimensions

We consider conformal and ’t Hooft anomalies in six-dimensional $\mathcal{N}$ = (1, 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2) R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c-anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c-anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a-anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

On exotic consistent anomalies in (1+1)$d$: A ghost story

We revisit ’t Hooft anomalies in (1+1) d d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1) d d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) \times × SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1) d d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic bc b c ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Anomalies in Condensed Matter

Quantum materials provide a fertile ground in which to test and realize unusual phenomena such as quantum anomalies predicted by quantum field theory. There are three important symmetries that are broken when classical field theory is moved into the quantum regime, the scale anomaly, the axial (chiral) anomaly, and the parity anomaly. Several potential device applications may be realized by the discovery of quantum anomalies in condensed matter, enabled by the new physics they embody, including ultra‐sensitive dark matter detectors, far infrared optical modulators, micro‐bolometric detectors, low‐dissipation ballistic transporters, terahertz‐based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions, and qubits topologically protected against decoherence. In this perspective article, the definition of these quantum anomalies is laid out, how little is known in the context of condensed matter, and how quantum anomalies are predicted to manifest as anomalous electronic, thermal, and magnetic behavior in experiments on topological quantum materials, including Weyl and Dirac semimetals. Furthermore, the importance that mechanical strain and defects will play in modifying signatures of quantum anomalies is discussed.

36 MATERIALS SCIENCE↗

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

We study ’t Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the “anomaly cocycle” using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group H^3(G,U(1)) × H^2(G,U(1)) H 3 ( G , U ( 1 ) ) × H 2 ( G , U ( 1 ) ) . The first factor captures the anomaly in the internal symmetry group G, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving G and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.

Physics↗

SPIDARman: System-Level Physics-Informed Detection of Anomalies in Reactor Collected Data Considering Human Errors

In nuclear power plants (NPPs), anomalies arising from sensors or human errors (HEs) can undermine the performance and reliability of plant operations. Anomaly detection models can be employed to detect sensor errors and HEs. Additionally, physics-informed machine learning models can utilize the known physics of the system, as described by mathematical equations, to ensure that sensor values are consistent with physical laws. Hence, we propose SPIDARman: System-level Physics-Informed Detection of Anomalies in Reactor Collected Data Considering Human Errors, a holistic physics-informed anomaly detection approach based on generative adversarial networks (GANs) to detect anomalies in both automatically collected sensor data and manually collected surveillance data. Here we test our approach on data collected from a flow loop testbed, showcasing its potential to detect anomalies. Results demonstrate that the proposed model performs better than the baseline GAN-based models in detecting sensor and surveillance anomalies, suggesting the potential of physics-informed anomaly detection GAN models in NPPs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Reinforcement Learning for Anomaly Detection in Nuclear Power Plant Operation and Maintenance

In nuclear power plants (NPPs), timely identification of sensor and human errors is critical to ensure safe and efficient plant operations. Anomaly detection models can be employed for this task. However, traditional anomaly detection approaches may have high dependency on labeled datasets and struggle with adaptability in complex, dynamic environments. Reinforcement learning (RL) has demonstrated significant potential in fault diagnosis and anomaly detection; however, its application to anomaly detection in NPPs remains a relatively underexplored research direction. Hence, to address this gap, in this study, we present a novel physics-informed reinforcement learning model, PIRL-AD: Physics-Informed Reinforcement Learning for Anomaly Detection, that integrates domain knowledge from calorimetric equations into the RL framework for enhanced sensor and human error anomaly detection. We evaluate the performance of PIRL-AD against a non-physics informed RL benchmark and a support vector machine (SVM) on data collected from a forced flow loop testbed. Experimental results suggest that PIRL-AD outperforms other baselines on a range of anomalous datasets that include both sensor and human-induced anomalies across key performance metrics, statistically outperforming the RL and SVM benchmarks with respect to geometric mean (respectively, 92.96% vs. 91.06% vs. 83.01%) and F1-score (respectively, 89.23% vs. 86.98% vs. 77.01%). Furthermore, the findings suggest the potential of physics-integrated reinforcement learning models for enhanced anomaly detection performance in NPPs.

Reinforcement learning↗

Anomaly detection in Hyper Suprime-Cam galaxy images with generative adversarial networks

ABSTRACT The problem of anomaly detection in astronomical surveys is becoming increasingly important as data sets grow in size. We present the results of an unsupervised anomaly detection method using a Wasserstein generative adversarial network (WGAN) on nearly one million optical galaxy images in the Hyper Suprime-Cam (HSC) survey. The WGAN learns to generate realistic HSC-like galaxies that follow the distribution of the data set; anomalous images are defined based on a poor reconstruction by the generator and outlying features learned by the discriminator. We find that the discriminator is more attuned to potentially interesting anomalies compared to the generator, and compared to a simpler autoencoder-based anomaly detection approach, so we use the discriminator-selected images to construct a high-anomaly sample of ∼13 000 objects. We propose a new approach to further characterize these anomalous images: we use a convolutional autoencoder to reduce the dimensionality of the residual differences between the real and WGAN-reconstructed images and perform UMAP clustering on these. We report detected anomalies of interest including galaxy mergers, tidal features, and extreme star-forming galaxies. A follow-up spectroscopic analysis of one of these anomalies is detailed in the Appendix; we find that it is an unusual system most likely to be a metal-poor dwarf galaxy with an extremely blue, higher-metallicity H ii region. We have released a catalogue with the WGAN anomaly scores; the code and catalogue are available at https://github.com/kstoreyf/anomalies-GAN-HSC; and our interactive visualization tool for exploring the clustered data is at https://weirdgalaxi.es.

79 ASTRONOMY AND ASTROPHYSICS↗

Atmospheric Variability Drives Anomalies in the Bering Sea Air–Sea Heat Exchange

Abstract High latitudes, including the Bering Sea, are experiencing unprecedented rates of change. Long-term Bering Sea warming trends have been identified, and marine heatwaves (MHWs), event-scale elevated sea surface temperature (SST) extremes, have also increased in frequency and longevity in recent years. Recent work has shown that variability in air–sea coupling plays a dominant role in driving Bering Sea upper-ocean thermal variability and that surface forcing has driven an increase in the occurrence of positive ocean temperature anomalies since 2010. In this work, we characterize the drivers of the anomalous surface air–sea heat fluxes in the Bering Sea over the period 2010–22 using ERA5 fields. We show that the surface turbulent heat flux dominates the net surface heat flux variability from September to April and is primarily a result of near-surface air temperature and specific humidity anomalies. The airmass anomalies that account for the majority of the turbulent heat flux variability are a function of wind direction, with southerly (northerly) wind advecting anomalously warm (cool), moist (dry) air over the Bering Sea, resulting in positive (negative) surface turbulent flux anomalies. During the remaining months of the year, anomalies in the surface radiative fluxes account for the majority of the net surface heat flux variability and are a result of anomalous cloud coverage, anomalous lower-tropospheric virtual temperature, and sea ice coverage variability. Our results indicate that atmospheric variability drives much of the Bering Sea upper-ocean temperature variability through the mediation of the surface heat fluxes during the analysis period. Significance Statement A long-term ocean warming trend and a recent increase in marine heatwaves in the Bering Sea have been identified. Previous work showed that anomalies in the exchange of heat between the ocean and the atmosphere were the primary driver of Bering Sea temperature variability, but the processes responsible for the heat exchange anomalies were unknown. In this work, we show that the atmosphere is the primary driver of anomalies in the Bering Sea air–sea heat exchange and therefore plays an important role in altering the thermal state of the Bering Sea. Our results highlight the importance of understanding more about how the ocean and the atmosphere interact at high latitudes and how this relationship will be affected by future climate change.

Hayden, Emily E. [a College of Earth, Ocean, and A↗

Elastic depths for detecting shape anomalies in functional data

This this paper, we propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that have considerably different geometric forms or features from the rest of the data. Identifying them is generally more difficult than identifying magnitude anomalies because shape anomalies are often not distinguishable from the bulk of the data with visualization methods. The proposed elastic depths use the recently developed elastic distances to directly measure the centrality of functions in the amplitude and phase spaces. Measuring shape outlyingness in these spaces provides a rigorous quantification of shape which, in turn, gives the elastic depths a strong theoretical and practical advantage over other methods in detecting shape anomalies. A simple boxplot and thresholding method are introduced to identify shape anomalies using the elastic depths. We assess the elastic depth's detection skill on simulated shape outlier scenarios and compare them against popular shape anomaly detectors. Finally, bond yields, image outlines, and hurricane trajectories are used to demonstrate our method's applicability to functional data observed on three different manifolds.

97 MATHEMATICS AND COMPUTING↗

Coincident learning for unsupervised anomaly detection of scientific instruments

Abstract Anomaly detection is an important task for complex scientific experiments and other complex systems (e.g. industrial facilities, manufacturing), where failures in a sub-system can lead to lost data, poor performance, or even damage to components. While scientific facilities generate a wealth of data, labeled anomalies may be rare (or even nonexistent), and expensive to acquire. Unsupervised approaches are therefore common and typically search for anomalies either by distance or density of examples in the input feature space (or some associated low-dimensional representation). This paper presents a novel approach called coincident learning for anomaly detection (CoAD), which is specifically designed for multi-modal tasks and identifies anomalies based on coincident behavior across two different slices of the feature space. We define an unsupervised metric, F ^ β , out of analogy to the supervised classification F β statistic. CoAD uses F ^ β to train an anomaly detection algorithm on unlabeled data , based on the expectation that anomalous behavior in one feature slice is coincident with anomalous behavior in the other. The method is illustrated using a synthetic outlier data set and a MNIST-based image data set, and is compared to prior state-of-the-art on two real-world tasks: a metal milling data set and our motivating task of identifying RF station anomalies in a particle accelerator.

43 PARTICLE ACCELERATORS↗

Annual Solar Irradiance Anomaly Features Over the USA During 1998-2017 Using NSRDB V3: Preprint

Annual solar irradiance anomalies (or departures from the long-term mean annual value) have a direct effect on various phases of solar energy projects, from prefeasibility to deploy-ment. Anomalies can happen because of normal climate varia-bility or exceptional weather patterns. This study investigates such anomalies for both global horizontal irradiance (GHI) and direct normal irradiance (DNI) using Version 3 of the National Solar Radiation Database (NSRDB V3) and surface irradiance measurements at eight U.S. locations. At each site, the annual anomaly is analyzed here by evaluating the irradi-ance deviation from the long-term average for each specific year during 1998–2017. A positive anomaly indicates that the solar resource was higher than the long-term average during that specific year, and vice versa in the case of a negative anomaly. The results show that, in most cases, the anomaly is within ±5% for GHI and ±10% for DNI, using either ground-based irradiance measurements or modeled data from the NSRDB.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Robust Spectral Anomaly Detection in EELS Spectral Images via 3D Convolutional Variational Autoencoders

Abstract A 3D Convolutional Variational Autoencoder (3D‐CVAE) is introduced for automated anomaly detection in electron energy‐loss spectroscopy spectrum imaging (EELS‐SI) data. This approach leverages the full 3D structure of EELS‐SI data to detect subtle spectral anomalies while preserving both spatial and spectral correlations across the datacube. By employing cross‐entropy loss and training on bulk spectra, the model learns to reconstruct bulk features characteristic of the defect‐free material. In exploring methods for anomaly detection, both the 3D‐CVAE approach and principal component analysis (PCA) are evaluated, testing their performance using FeL‐edge ΔEpeak shifts designed to simulate material defects. These results show that 3D‐CVAE achieves superior anomaly detection and maintains consistent performance across various shift magnitudes. The method demonstrates clear bimodal separation between bulk and anomalous spectra, enabling reliable classification. Further analysis verifies that lower‐dimensional representations are robust to anomalies in the data. While performance advantages over PCA diminish with decreasing anomaly concentration, our method maintains high reconstruction quality even in challenging, noise‐dominated spectral regions. This approach provides a robust framework for unsupervised automated detection of spectral anomalies in EELS‐SI data, particularly valuable for analyzing complex material systems.

Chemistry↗

Anomalies of 4d SpinG theories

Abstract We consider ’t Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits Spin G (4) generalized spin structure, withGeither gauged or a global symmetry. We discuss methods to directly computew 2 ∪w 3 ’t Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g.M 4 = ℂℙ 2 . Such anomalies have been discussed for SU(2) gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of$$ \mathcal{N} $$ N = 2 SYM theory. We directly compute these anomalies for a variety of theories, including generalGgauge theories with adjoint fermions, SU(2) gauge theory with fermions in general representations, and Spin(N) gauge theories with fundamental matter. We discuss aspects of matching these and other ’t Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for generalG gauge theory withN f adjoint Weyl fermions. For example, in the case ofN f = 2 we discuss anomaly matching in the IR phase consisting of$$ {h}_{G_{\textrm{gauge}}}^{\vee } $$ h G gauge ∨ copies of a ℂℙ 1 non-linear sigma model, including for thew 2 w 3 anomalies when formulated with$$ {\textrm{Spin}}_{\textrm{SU}{(2)}_{\textrm{global}}}(4) $$ Spin SU 2 global 4 structure.

Physics↗

Near-global summer circulation response to the spring surface temperature anomaly in Tibetan Plateau –– the GEWEX/LS4P first phase experiment

Subseasonal to seasonal (S2S) prediction of droughts and floods is one of the major challenges of weather and climate prediction. Recent studies suggest that the springtime land surface temperature/subsurface temperature (LST/SUBT) over the Tibetan Plateau (TP) can be a new source of S2S predictability. The project “Impact of Initialized Land Surface Temperature and Snowpack on Subseasonal to Seasonal Prediction (LS4P)” was initiated to study the impact of springtime LST/SUBT anomalies over high mountain areas on summertime precipitation predictions. The present work explores the simulated global scale response of the atmospheric circulation to the springtime TP land surface cooling by 16 current state-of-the-art Earth System Models (ESMs) participating in the LS4P Phase I (LS4P-I) experiment. The LS4P-I results show, for the first time, that springtime TP surface anomalies can modulate a persistent quasi-barotropic Tibetan Plateau-Rocky Mountain Circumglobal (TRC) wave train from the TP via the northeast Asia and Bering Strait to the western part of the North America, along with the springtime westerly jet from TP across the whole North Pacific basin. The TRC wave train modulated by the TP thermal anomaly play a critical role on the early summer surface air temperature and precipitation anomalies in the regions along the wave train, especially over the northwest North America and the southern Great Plains. The participant models that fail in capturing the TRC wave train greatly under-predict climate anomalies in reference to observations and the successful models. These results suggest that the TP LST/SUBT anomaly via the TRC wave train is the first order source of the S2S variability in the regions mentioned. Furthermore, the TP surface temperature anomaly can influence the Southern Hemispheric circulation by generating cross-equator wave trains. However, the simulated propagation pathways from the TP into the Southern Hemisphere show large inter-model differences. More dynamical understanding of the TRC wave train as well as its cross-equator propagation into the Southern Hemisphere will be explored in the newly launched LS4P phase II experiment.

54 ENVIRONMENTAL SCIENCES↗

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗

Extreme Precipitation Over the Southern Slope of the Tibetan Plateau and the Associated Atmospheric Circulation Anomalies

The southern slope of the Tibetan Plateau (SSTP) is one of the rainiest regions in the world where geological hazards caused by extreme precipitation often occur. This study investigates the characteristics and mechanisms of extreme precipitation over SSTP from June to September during 2001–2020 using Global Precipitation Measurement satellite observation. The extreme precipitation days are defined as the days with top 5% of regional-mean daily precipitation over SSTP in this period, which has an average precipitation of 27.2 mm/d. Averaging over the extreme precipitation days, precipitation peaks at an altitude of about 300 m, coinciding with the climatological maximum precipitation, but with a much larger value of 37.2 mm/d than the climatology of 11.9 mm/d. Composite analysis of circulations on extreme days reveals significant circulation anomalies in both the lower and upper troposphere. Specifically, the lower-tropospheric circulations are characterized by significant westerly anomalies over northern India, and the upper-tropospheric circulations are characterized by northerly anomalies over the central Tibetan Plateau, which are statistically independent. The lower-tropospheric westerly anomalies blowing toward SSTP are blocked by the topography, favoring extreme precipitation over SSTP. The upper-tropospheric northerly anomalies, on the other hand, correspond to anomalous northeasterlies north of SSTP in the middle troposphere and southeasterlies to the south in the lower troposphere, and the convergence of these circulation anomalies favors extreme precipitation over SSTP. Lastly, the lower-tropospheric westerly and upper-tropospheric northerly anomalies, respectively, correspond to less precipitation over the South Asian monsoon region and the Tibetan Plateau.

Extreme precipitation, Tibetan Plateau↗

Effect of Rocky Mountains and Tibetan Plateau 1998 Spring Land Temperature on N. American and East Asian Summer Precipitation Anomalies

This work follows up on the GEWEX/LS4P Phase I (LS4P-I) experiments, a community effort highlighting the spring land surface temperature anomalies in the Tibetan Plateau (TP) as a useful source for subseasonal to seasonal (S2S) prediction of summer precipitation in global hot spot regions, particularly in East Asia and North America. This paper extends the investigation to both the US Rocky Mountain (RM) region and the TP, considering the 1998 summer drought/flood event in North America/East Asia, respectively, as a case study. A previously developed initialization method for land surface temperature/subsurface temperature (LST/SUBT) is used in the NCEP Global Forecast System, coupled with a land model, SSiB2 (GFS/SSiB2), to produce observed RM cold May temperature anomaly. Forward simulation yields June precipitation anomalies at five remote locations. Likewise, the TP warm May temperature anomaly also produces June precipitation anomalies at these five locations. The effects of RM (cold) and TP (warm) temperature anomalies are consistent in the US South Coastal regions and the south Yangtze River Basin, yielding 49% (42%) of observed drought and 34% (44%) of observed flood, respectively. These LST/SUBT effects in RM and TP induce a global large-scale wave train linking North America with the TP, affecting the subtropical westerly jet and thereby modulating summer precipitation. Global SST effect is examined for comparison but does not yield statistically significant June precipitation anomalies in GFS/SSiB2. Furthermore, this study adds to evidence that high-mountain LST effects in the RM and TP are first-order sources of S2S precipitation predictability in summer months.

Nayak, Hara Prasad [University of California, Los ↗