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At least 307 records · Page 17

Nanoscale clustering and fission product segregation in irradiated annular U-10Zr fuel

Zirconium (Zr) is added to uranium (U) to improve the performance of metallic fuel for fast reactor applications. This study employs transmission electron microscopy (TEM) and atom probe tomography (APT) to investigate nanoscale clustering of U and Zr, as well as segregation of fission products (FPs), in annular U-10Zr (in weight) metallic fuel irradiated at the Advanced Test Reactor (ATR). The results reveal variations in the shape, size, and chemical composition of clusters at different radial locations within the irradiated fuel cross-section. Zr-rich clusters exhibit higher concentration of FPs compared to U-rich clusters, potentially due to the co-precipitation of Zr and FPs in the fuel matrix during cooling at the end-of-life. In conclusion, this work complements the study of fuel constituents and fission product distribution across multiple length scales in irradiated U-10Zr metallic fuel.

Atom probe tomography↗

Matrix Completion for Improved Observability in Low-Voltage Distribution Grids

This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.

low-rank matrix completion↗

Robust Matrix Completion State Estimation in Distribution Systems

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Equilibrium solute segregation to matrix- θ' precipitate interfaces in Al-Cu alloys from first principles

Particular combinations of solute atoms segregated to the interface of the Al and θ ' - Al 2 Cu in Al-Cu alloys can help stabilize θ ' precipitates at high temperatures. Stabilization of such precipitates is determined by a combination of thermodynamics (including driving forces for coarsening and transformation and solute segregation tendencies) and kinetic effects (including solute diffusion and interfacial mobility in the presence of interfacial solute segregation). For some alloys such as recent Al-Cu-based alloys, multiple solutes segregate in significant quantities to interfaces, and solute-solute interactions at the interface are important, with multiple types of solutes competing for similar interfacial sites. To treat this situation, we develop and apply a statistical mechanics approach to calculate the temperature-dependent equilibrium solute atoms distribution near the coherent and semicoherent interfaces between the Al matrix and the θ ' - Al 2 Cu precipitates. The developed approach is applied to the investigation of Si, Mn, and Zr segregation at the interface, as particular combinations of these elements affect the thermal stability of the θ ' precipitates. We demonstrate that because Si and Mn atoms segregate on the same semicoherent interface, the presence of Si reduces the concentration of Mn solutes at the interface. Si atoms preferably occupy the first layer of the interface and compete with Mn atoms for one type of particular sites in the layer. Mn atoms preferably occupy the second layer of the semicoherent interface, and the Mn-Mn interaction plays an important role in their distribution. Zr atoms mostly segregate on one of the two nonequivalent sites of the second layer of the coherent interface. Due to symmetry properties of the coherent interface, the calculations show that the segregation Zr of atoms to this interface will likely lead to the formation of L 1 2 ordered Al 3 Zr layer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Diagnostics for measuring 4D beam matrix [Slides]

Detailed knowledge on the particle distribution in accelerators can strongly benefit machine tuning and understanding of deleterious effects, which degrade beam quality. Properties of the beam downstream the beamline (i.e. 4D beam matrix) depend on beam properties upstream and parameters of the beamline. Measuring 2D x-y beam profile downstream provides limited information about the beam. Multiple measurements at different settings of the beamline (quadrupole scan) may provide enough information to recover original beam profile. Essentially, this concept is similar to tomography, when we need to reconstruct a higher dimension object from multiple low dimension projections.

43 PARTICLE ACCELERATORS↗

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Progress on the R-matrix Analysis for the n+ 181 Ta Evaluation [Slides]

This presentation discusses how nuclear data evaluations can influence the accuracy of computational nuclear design calculations. It also discusses the motivation for a new evaluation of 181 Ta. The goals of the evaluations are to generate a set of resonance parameters in the Resolved Resonance Region (RRR) that extends up to 2.6 keV, to generate a set of average resonance parameters in the Unresolved Resonance Region (URR) up to 100 keV (derived from the RRR parameters), and to generate covariance information for both RRR and URR. The presentation discusses how several different experimental data sets will be fit simultaneously in the evaluation of 181 Ta. It states that the level density of 181 Ta can make R-matrix fitting a challenge as the width of the levels increase with energy (as well as decreasing experimental resolution) and the measured resonances can overlap. The presentation concludes by discussing R-matrix analysis and covariance information as the latter is important when propagated to quantify the uncertainty on output responses of nuclear design calculations such as the multiplication factor k .

07 ISOTOPE AND RADIATION SOURCES↗

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

Nanostructural Analysis of Enzymatic and Non-enzymatic Brown Rot Fungal Deconstruction of the Lignocellulose Cell Wall†

Brown rot (BR) decay mechanisms employ carbohydrate-active enzymes (CAZymes) as well as a unique non-enzymatic chelator-mediated Fenton (CMF) chemistry to deconstruct lignocellulosic materials. Unlike white rot fungi, BR fungi lack peroxidases for lignin deconstruction, and also lack some endoglucanase/cellobiohydrolase activities. The role that the CMF mechanism plays in “opening up” the wood cell wall structure in advance of enzymatic action, and any interaction between CMF constituents and the selective CAZyme suite that BRs possess, is still unclear. Expression patterns for CMF redox metabolites and lytic polysaccharide monooxygenase (LPMO–AA9 family) genes showed that some LPMO isozymes were upregulated with genes associated with CMF at early stages of brown rot by Gloeophyllum trabeum. In the structural studies, wood decayed by the G. trabeum was compared to CMF-treated wood, or CMF-treated wood followed by treatment with either the early-upregulated LPMO or a commercial CAZyme cocktail. Structural modification of decayed/treated wood was characterized using small angle neutron scattering. CMF treatment produced neutron scattering patterns similar to that of the BR decay indicating that both systems enlarged the nanopore structure of wood cell walls to permit enzyme access. Enzymatic deconstruction of cellulose or lignin in raw wood samples was not achieved via CAZyme cocktail or LPMO enzyme action alone. CMF treatment resulted in depolymerization of crystalline cellulose as attack progressed from the outer regions of individual crystallites. Multiple pulses of CMF treatment on raw wood showed a progressive increase in the spacing between the cellulose elementary fibrils (EFs), indicating the CMF eroded the matrix outside the EF bundles, leading to less tightly packed EFs. Peracetic acid delignification treatment enhanced subsequent CMF treatment effects, and allowed both enzyme systems to further increase spacing of the EFs. Moreover, even after a single pulse of CMF treatment, both enzymes were apparently able to penetrate the cell wall to further increase EF spacing. The data suggest the potential for the early-upregulated LPMO enzyme to work in association with CMF chemistry, suggesting that G. trabeum may have adopted mechanisms to integrate non-enzymatic and enzymatic chemistries together during early stages of brown rot decay.

59 BASIC BIOLOGICAL SCIENCES↗

NXREFINE

NXRefine implements a complete workflow for both data acquisition and reduction of single crystal diffuse x-ray scattering collected as a series of area detector frames during continuous sample rotation. The data are stored in HDF5 files, which conform to the NeXus data format standard. These files contain a comprehensive set of metadata, including the incident wavelength, powder calibration scans used to define detector distances, beam centers, and yaw, pitch, and roll corrections. Automated peak searches of the three-dimensional data arrays define a set of Bragg peaks that are used to define an orientation matrix, defined according to Busing and Levy, which is then used to transform the data from angular coordinates to reciprocal space coordinates using the CCTW program. Multiple rotations at different detector translations and offset rotation axes are combined to ensure that there are no gaps in the reconstructed data, and allow the construction of masks to eliminate detector artifacts due to Compton scattering within the sensor layers. Finally, the data can be transformed into 3D-ΔPDF maps using the punch-and-fill method after symmetrization.

OSBORN, RAYMOND↗

Temporal Sampling of Enzymes from Live Cells by Localized Electroporation and Quantification of Activity by SAMDI Mass Spectrometry

Abstract Measuring changes in enzymatic activity over time from small numbers of cells remains a significant technical challenge. In this work, a method for sampling the cytoplasm of cells is introduced to extract enzymes and measure their activity at multiple time points. A microfluidic device, termed the live cell analysis device (LCAD), is designed, where cells are cultured in microwell arrays fabricated on polymer membranes containing nanochannels. Localized electroporation of the cells opens transient pores in the cell membrane at the interface with the nanochannels, enabling extraction of enzymes into nanoliter‐volume chambers. In the extraction chambers, the enzymes modify immobilized substrates, and their activity is quantified by self‐assembled monolayers for matrix‐assisted laser desorption/ionization (SAMDI) mass spectrometry. By employing the LCAD‐SAMDI platform, protein delivery into cells is demonstrated. Next, it is shown that enzymes can be extracted, and their activity measured without a loss in viability. Lastly, cells are sampled at multiple time points to study changes in phosphatase activity in response to oxidation by hydrogen peroxide. With this unique sampling device and label‐free assay format, the LCAD with SAMDI enables a powerful new method for monitoring the dynamics of cellular activity from small populations of cells.

Mukherjee, Prithvijit↗

Depletion capabilities in the OpenMC Monte Carlo particle transport code

A depletion solver has been implemented in OpenMC and is described herein. The depletion solver is implemented in Python and interfaces with OpenMC’s transport solver through a C++ application programming interface, which enables an in-memory transport-depletion coupling. Multiple integration methods for advancing in time have been implemented and exhibit tradeoffs in cost, accuracy, and memory use. For all time integration methods, evaluation of the matrix exponential is performed by using the incomplete partial fraction form of the Chebyshev rational approximation method. Simulations of a pressurized water reactor (PWR) pincell and a sodium-cooled fast reactor (SFR) assembly were carried out with OpenMC and Serpent. For both problems, the use of a high-fidelity depletion chain results in predictions of k eff that agree within 20–30 pcm between OpenMC and Serpent. Predicted actinide concentrations were found to agree to a fraction of a percent, and most fission product concentrations were found to agree within 1%. Here, the few cases where larger differences were observed can be attributed either to differences in how the energy dependence of fission product yields is handled or deficiencies in the nuclear data used. OpenMC simulations of the PWR and SFR problems using a simplified 228-nuclide depletion chain demonstrate that it achieves accuracy close to that of the full, high-fidelity depletion chain with respect to the studied responses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of the Higgs boson production rate in association with top quarks in final states with electrons, muons, and hadronically decaying tau leptons at $\sqrt{s} =$ 13 TeV

The rate for Higgs (${\mathrm{H}} $) bosons production in association with either one (${\mathrm{t}} {\mathrm{H}} $) or two (${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $) top quarks is measured in final states containing multiple electrons, muons, or tau leptons decaying to hadrons and a neutrino, using proton–proton collisions recorded at a center-of-mass energy of $13\,\text {Te}\text {V} $ by the CMS experiment. The analyzed data correspond to an integrated luminosity of 137$\,\text {fb}^{-1}$. The analysis is aimed at events that contain ${\mathrm{H}} \rightarrow {\mathrm{W}} {\mathrm{W}} $, ${\mathrm{H}} \rightarrow {\tau } {\tau } $, or ${\mathrm{H}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} $ decays and each of the top quark(s) decays either to lepton+jets or all-jet channels. Sensitivity to signal is maximized by including ten signatures in the analysis, depending on the lepton multiplicity. The separation among ${\mathrm{t}} {\mathrm{H}} $, ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $, and the backgrounds is enhanced through machine-learning techniques and matrix-element methods. The measured production rates for the ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $ and ${\mathrm{t}} {\mathrm{H}} $ signals correspond to $0.92 \pm 0.19\,\text {(stat)} ^{+0.17}_{-0.13}\,\text {(syst)} $ and $5.7 \pm 2.7\,\text {(stat)} \pm 3.0\,\text {(syst)} $ of their respective standard model (SM) expectations. The corresponding observed (expected) significance amounts to 4.7 (5.2) standard deviations for ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $, and to 1.4 (0.3) for ${\mathrm{t}} {\mathrm{H}} $ production. Assuming that the Higgs boson coupling to the tau lepton is equal in strength to its expectation in the SM, the coupling $y_{{\mathrm{t}}}$ of the Higgs boson to the top quark divided by its SM expectation, $\kappa _{{\mathrm{t}}}=y_{{\mathrm{t}}}/y_{{\mathrm{t}}}^{\mathrm {SM}}$, is constrained to be within $-0.9< \kappa _{{\mathrm{t}}}< -0.7$ or $0.7< \kappa _{{\mathrm{t}}}< 1.1$, at 95% confidence level. This result is the most sensitive measurement of the ${\mathrm{t}} {{\overline{{{\mathrm{t}}}}}} {\mathrm{H}} $ production rate to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗

Efficient Parallelization of Irregular Applications on GPU Architectures

With the enlarging computation capacity of general Graphics Processing Units (GPUs), leveraging GPUs to accelerate parallel applications has become a critical topic in academia and industry. However, a wide range of irregular applications with the computation-/memory-intensive nature cannot easily achieve high GPU utilization. The challenges mainly involve the following aspects: first, data dependence leads to coarse-grained kernel and inefficient parallelism; second, heavy GPU memory usage may cause frequent memory evictions and extra overhead of I/O; third, specific computation patterns produce memory redundancies; last, workload balance and data reusability conjunctly benefit the overall performance, but there may exist a dynamic trade-off between them. Targeting these challenges, this dissertation proposes multiple optimizations to accelerate two real-world applications: many-body correlation functions to simulate nuclear physics in a large-scale scientific system; the other is the eALS-based matrix factorization recommendation system. To accelerate the calculations of many-body correlation functions, this dissertation presents three frameworks in GPU memory management and multi-GPU scheduling. Firstly, an optimized systematic GPU memory management framework, MemHC, utilizes a series of new memory reduction designs in GPU memory allocation, CPU/GPU communications, and GPU memory oversubscription. Secondly, an enhanced multi-GPU scheduling framework, MICCO, particularly by taking both data dimension (e.g., data reuse and data eviction) and computation dimension into account. MICCO designs a heuristic scheduling algorithm and a machine learning-based regression model to generate the optimal settings of a proposed new concept to manage the trade-off. Thirdly, a locality-aware multi-GPU scheduling framework. This scheduler leverages pipeline batch generation with a looking-ahead strategy by building local dependency graphs for memory transfer reduction and better data reuse, achieving up to 79.92% memory cost reduction and 1.67x speedup. To parallelize the eALS-based recommendation system, this dissertation proposes an efficient CPU/GPU heterogeneous recommendation system, HEALS. HEALS employs newly designed architecture-adaptive data formats to achieve load balance and good data locality on CPU and GPU. To mitigate the data dependence, HEALS presents a CPU/GPU collaboration model for both task parallelism and data parallelism with multiple kernel computation optimizations. In summary, this dissertation efficiently accelerates two typical irregular applications on GPUs by building four frameworks, including CPU/GPU collaboration, GPU memory management, and multi-GPU scheduling.

Wang, Qihan↗

In Situ Scattering Studies of Crystallization Kinetics in a Phase-Separated Zr–Cu–Fe–Al Bulk Metallic Glass

In this work, thermal stability and the crystallization kinetics of a phase-separated Zr-Cu-Fe-Al bulk metallic glass were investigated using in situ high-energy synchrotron X-ray and neutron diffraction, as well as small-angle synchrotron X-ray scattering. It was revealed that this glass with excellent glass-forming ability possesses a two-step crystallization behavior. The crystalline products and their evolution sequence are more complicated than a homogeneous Zr-Cu-Al glass with average glass-forming ability. The experimental results indicate that a finely distributed nanometer-sized cubic Zr 2 Cu phase forms first and then transforms to a tetragonal Zr 2 Cu phase, while the matrix transforms to an orthorhombic Zr3Fe phase. The strength of the Zr-Cu-Fe-Al composite containing cubic Zr 2 Cu phase and glass matrix increases, and the plasticity also improves compared to the as-cast Zr-Cu-Fe-Al bulk metallic glass. Our results suggest that the formation of multiple and complex crystalline products would be the characteristics of the Zr-Cu-Fe-Al glass with better glass-forming ability. Our study may shed light on the synthesis of bulk-sized glass-nanocrystals composites of high strength and good plasticity.

36 MATERIALS SCIENCE↗

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel -statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion () with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

97 MATHEMATICS AND COMPUTING↗