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arXiv 2020年

作者： Meena, Chandrakala Hens, Chittaranjan Acharyya, Suman Haber, Simcha Boccaletti, Stefano Barzel, Baruch Department of Mathematics Bar-Ilan University Ramat-Gan Israel Gonda Multidisciplinary Brain Research Center Bar-Ilan University Ramat-Gan Israel Chemical Engineering and Process Development CSIR-National Chemical Laboratory Pune India Indian Institute of Science Education and Research Maruthamala P. O Vithura Kerala Thiruvananthapuram695551 India Physics and Applied Mathematics Unit Indian Statistical Institute Kolkata India Center for Computational Natural Sciences and Bioinformatics International Institute of Information Technology Gachibowli Telangana Hyderabad500032 India Cnr Institute of Complex Systems Florence Italy Moscow Russia Universidad Rey Juan Carlos calle Tulipán s/n Madrid Móstoles28933 Spain Network Science Institute Northeastern University BostonMA United States

The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, real world networks often appear random and highly irregular, raising the question of what are the naturally emerging organizing principles of complex system stability. The answer is encoded within the system's stability matrix - the Jacobian - but is hard to retrieve, due to the scale and diversity of the relevant systems, their broad parameter space, and their nonlinear interaction dynamics. Here, we introduce the dynamic Jacobian ensemble, which allows us to systematically investigate the fixed-point dynamics of a range of relevant network-based models. Within this ensemble, we find that complex systems exhibit discrete stability classes. These range from asymptotically unstable, where stability is unattainable, to sensitive, in which stability abides within a bounded range of the system's parameters. Alongside these two classes, we uncover a third asymptotically stable class, in which a sufficiently large and heterogeneous network acquires a guaranteed stability, independent of its microscopic parameters and of external perturbation. Hence, in this ensemble, two of the most ubiquitous characteristics of real-world networks - scale and heterogeneity - emerge as natural organizing principles to ensure fixed-point stability in the face of changing environmental conditions. © 2020, CC BY.

关键词： System stability

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EMPRESS. X. Spatially resolved mass-metallicity relation in extremely metal-poor galaxies: Evidence of episodic star-formation fueled by a metal-poor gas infall

arXiv

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arXiv 2024年

作者： Nakajima, Kimihiko Ouchi, Masami Isobe, Yuki Xu, Yi Ozaki, Shinobu Nagao, Tohru Inoue, Akio K. Rauch, Michael Kusakabe, Haruka Onodera, Masato Nishigaki, Moka Ono, Yoshiaki Sugahara, Yuma Hattori, Takashi Hirai, Yutaka Hashimoto, Takuya Kim, Ji Hoon Moriya, Takashi J. Yanagisawa, Hiroto Aoyama, Shohei Fujimoto, Seiji Fukushima, Hajime Fukushima, Keita Harikane, Yuichi Hatano, Shun Hayashi, Kohei Ishigaki, Tsuyoshi Kawasaki, Masahiro Kojima, Takashi Komiyama, Yutaka Koyama, Shuhei Koyama, Yusei Lee, Chien-Hsiu Matsumoto, Akinori Mawatari, Ken Motohara, Kentaro Murai, Kai Nagamine, Kentaro Nakane, Minami Saito, Tomoki Sasaki, Rin Shibuya, Takatoshi Suzuki, Akihiro Takeuchi, Tsutomu T. Umeda, Hiroya Umemura, Masayuki Watanabe, Kuria Yabe, Kiyoto Yajima, Hidenobu Zhang, Yechi National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Institute for Cosmic Ray Research The University of Tokyo 5-1-5 Kashiwanoha Chiba Kashiwa277-8582 Japan Osawa 2-21-1 Mitaka Tokyo181-8588 Japan University of Tokyo Chiba Kashiwa277-8583 Japan Kavli Institute for Cosmology University of Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Cavendish Laboratory University of Cambridge 19 JJ Thomson Avenue CambridgeCB3 0HE United Kingdom Waseda Research Institute for Science and Engineering Faculty of Science and Engineering Waseda University 3-4-1 Okubo Shinjuku Tokyo169-8555 Japan Department of Physics Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo Tokyo113-0033 Japan Department of Astronomy Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo Tokyo113-0033 Japan Research Center for Space and Cosmic Evolution Ehime University Bunkyo-cho 2-5 Ehime Matsuyama790-8577 Japan Department of Physics School of Advanced Science and Engineering Faculty of Science and Engineering Waseda University 3-4-1 Okubo Shinjuku Tokyo169-8555 Japan Observatories of the Carnegie Institution for Science 813 Santa Barbara St. PasadenaCA91101 United States Observatoire de Genève Université de Genève 51 Chemin de Pégase Versoix1290 Switzerland 650 North Aohoku Place HiloHI96720 United States Department of Physics and Astronomy University of Notre Dame 225 Nieuwland Science Hall Notre DameIN46556 United States Astronomical Institute Tohoku University 6-3 Aoba Aramaki Aoba-ku Miyagi Sendai980-8578 Japan Division of Physics Faculty of Pure and Applied Sciences University of Tsukuba Ibaraki Tsukuba305-8571 Japan Faculty of Pure and Applied Sciences University of Tsukuba Ibaraki Tsukuba305-8571 Japan Astronomy Program Department of Physics and Astronomy Seoul National University 1 Gwanak-ro Gwanak-gu Seoul08826 Korea Republic of SNU Astronomy Research Cent

Using the Subaru/FOCAS IFU capability, we examine the spatially resolved relationships between gas-phase metallicity, stellar mass, and star-formation rate surface densities (Σ★ and ΣSFR, respectively) in extremely metal-poor galaxies (EMPGs) in the local universe. Our analysis includes 24 EMPGs, comprising 9,177 spaxels, which span a unique parameter space of local metallicity (12 + log(O/H) 6.9 to 7.9) and stellar mass surface density (Σ★ ∼ 105 to 107 Mo kpc−2), extending beyond the range of existing large integral-field spectroscopic surveys. Through spatially resolved emission line diagnostics based on the [N ii] BPT-diagram, we verify the absence of evolved active galactic nuclei in these EMPGs. Our findings reveal that, while the resolved mass-metallicity relation exhibits significant scatter in the low-mass regime, this scatter is closely correlated with local star-formation surface density. Specifically, metallicity decreases as ΣSFR increases for a given Σ★. Notably, half of the EMPGs show a distinct metal-poor horizontal branch on the resolved mass-metallicity relation. This feature typically appears at the peak clump with the highest Σ★ and ΣSFR and is surrounded by a relatively metal-enriched ambient region. These findings support a scenario in which metal-poor gas infall fuels episodic star formation in EMPGs, consistent with the kinematic properties observed in these systems. In addition, we identify four EMPGs with exceptionally low central metallicities (12 + log(O/H) 7.2), which display only a metal-poor clump without a surrounding metal-rich region. This suggests that such ultra-low metallicity EMPGs, at less than a few percent of the solar metallicity, may serve as valuable analogs for galaxies in the early stages of galaxy evolution. Copyright © 2024, The Authors. All rights reserved.

关键词： Spectroscopic analysis

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Temperature-induced Lifshitz transition and possible excitonic instability in ZrSiSe

arXiv

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arXiv 2020年

作者： Chen, F.C. Fei, Y. Li, S.J. Wang, Q. Luo, X. Yan, J. Lu, W.J. Tong, P. Song, W.H. Zhu, X.B. Zhang, L. Zhou, H.B. Zheng, F.W. Zhang, P. Lichtenstein, A.L. Katsnelson, M.I. Yin, Y. Hao, Ning Sun, Y.P. Key Laboratory of Materials Physics Institute of Solid State Physics HFIPS Chinese Academy of Sciences Hefei230031 China University of Science and Technology of China Hefei230026 China Department of Physics Zhejiang University Hangzhou310027 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions High Magnetic Field Laboratory HFIPS Chinese Academy of Sciences Hefei230031 China College of Mathematics and Physics Beijing University of Chemical Technology Beijing100029 China School of Physics and Physical Engineering Qufu Normal University Qufu273165 China Institute for Theoretical Physics University Hamburg Jungiusstrasse 9 HamburgD-20355 Germany Theoretical Physics and Applied Mathematics Department Ural Federal University Mira Street 19 Ekaterinburg620002 Russia Institute for Molecules and Materials Radboud University Heijendaalseweg 135 NijmegenNL-6525AJ Netherlands Collaborative Innovation Center of Microstructures Nanjing University Nanjing210093 China

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy(spectroscopy)[STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 K and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a V-shape dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures. Copyright © 2020, The Authors. All rights reserved.

关键词： Selenium compounds

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2022 Review of Data-Driven Plasma Science

arXiv

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arXiv 2022年

作者： Anirudh, Rushil Archibald, Rick Asif, M. Salman Becker, Markus M. Benkadda, Sadruddin Bremer, Peer-Timo Budé, Rick H.S. Chang, C.S. Chen, Lei Churchill, R.M. Citrin, Jonathan Gaffney, Jim A. Gainaru, Ana Gekelman, Walter Gibbs, Tom Hamaguchi, Satoshi Hill, Christian Humbird, Kelli Jalas, Sören Kawaguchi, Satoru Kim, Gon-Ho Kirchen, Manuel Klasky, Scott Kline, John L. Krushelnick, Karl Kustowski, Bogdan Lapenta, Giovanni Li, Wenting Ma, Tammy Mason, Nigel J. Mesbah, Ali Michoski, Craig Munson, Todd Murakami, Izumi Najm, Habib N. Erik J. Olofsson, K. Park, Seolhye Peterson, J. Luc Probst, Michael Pugmire, David Sammuli, Brian Sawlani, Kapil Scheinker, Alexander Schissel, David P. Shalloo, Rob J. Shinagawa, Jun Seong, Jaegu Spears, Brian K. Tennyson, Jonathan Thiagarajan, Jayaraman Ticoş, Catalin M. Trieschmann, Jan van Dijk, Jan Van Essen, Brian Ventzek, Peter Wang, Haimin Wang, Jason T.L. Wang, Zhehui Wende, Kristian Xu, Xueqiao Yamada, Hiroshi Yokoyama, Tatsuya Zhang, Xinhua Lawrence Livermore National Laboratory LivermoreCA94550 United States Oak Ridge National Laboratory Oak RidgeTN37830 United States University of California Riverside RiversideCA92521 United States Felix-Hausdorff-Str. 2 Greifswald17489 Germany Aix Marseille University CNRS PIIM UMR 7345 Marseille France Department of Applied Physics Eindhoven University of Technology Netherlands Princeton Plasma Physics Laboratory Princeton NJ08540 United States Institute of Ion Physics and Applied Physics University of Innsbruck Technikerstrasse 25 Innsbruck6020 Austria DIFFER - Dutch Institute for Fundamental Energy Research Eindhoven Netherlands Science and Technology of Nuclear Fusion Group Eindhoven University of Technology Eindhoven Netherlands Department of Physics and Astronomy University of California Los AngelesCA90095 United States NVIDIA 2788 San Tomas Expressway Santa ClaraCA95051 United States Center for Atomic and Molecular Technologies Graduate School of Engineering Osaka University 2-1 Yamadaoka Suita Osaka Japan Department of Nuclear Sciences and Applications International Atomic Energy Agency Wagramer Strasse 5 PO Box 100 Vienna1400 Austria Center for Free-Electron Laser Science Department of Physics Universität Hamburg Luruper Chaussee 149 Hamburg22761 Germany Division of Information and Electronic Engineering Graduate School of Engineering Muroran Institute of Technology Hokkaido Muroran050-8585 Japan Seoul National University Seoul151-741 Korea Republic of Deutsches Elektronen-Synchrotron DESY Notkestr. 85 Hamburg22607 Germany Los Alamos National Laboratory Los AlamosNM87545 United States Center for Ultrafast Optical Science University of Michigan Ann ArborMI48109-2099 United States Department of Mathematics KULeuven University of Leuven Belgium Department of Physical Sciences The University of Kent CanterburyCT2 7NH United Kingdom Department of Chemical and Biomolecular Engineering University of California Berk

Data science and technology offer transformative tools and methods to science. This review article highlights latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS). A large amount of data and machine learning algorithms go hand in hand. Most plasma data, whether experimental, observational or computational, are generated or collected by machines today. It is now becoming impractical for humans to analyze all the data manually. Therefore, it is imperative to train machines to analyze and interpret (eventually) such data as intelligently as humans but far more efficiently in quantity. Despite the recent impressive progress in applications of data science to plasma science and technology, the emerging field of DDPS is still in its infancy. Fueled by some of the most challenging problems such as fusion energy, plasma-processing of materials, and fundamental understanding of the universe through observable plasma phenomena, it is expected that DDPS continues to benefit significantly from the interdisciplinary marriage between plasma science and data science into the foreseeable future. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

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β-decay of 61V and its role in cooling accreted neutron star crusts

arXiv

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arXiv 2021年

作者： Ong, W.-J. Brown, E.F. Browne, J. Ahn, S. Childers, K. Crider, B.P. Dombos, A.C. Gupta, S.S. Hitt, G.W. Langer, C. Lewis, R. Liddick, S.N. Lyons, S. Meisel, Z. Möller, P. Montes, F. Naqvi, F. Pereira, J. Prokop, C. Richman, D. Schatz, Hendrik Schmidt, K. Spyrou, A. Nuclear and Chemical Sciences Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States National Superconducting Cyclotron Laboratory East LansingMI48824 United States Joint Institute for Nuclear Astrophysics Center for the Evolution of the Elements Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Cylotron Institute Texas A&M University College StationTX77843 United States Department of Chemistry Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Mississippi State University Mississippi StateMS39762 United States Punjab140 001 India Department of Physics and Engineering Science Coastal Carolina University ConwaySC29528 United States Institute for Applied Physics Goethe-University Frankfurt a. M. Frankfurt am Main60438 Germany Department of Physics and Astronomy Ohio Univeristy AthensOH45701 United States Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States Department of Physics & Astrophysics University of Delhi Delhi110007 India Los Alamos National Laboratory Los AlamosNM87545 United States

The interpretation of observations of cooling neutron star crusts in quasi-persistent X-ray transients is affected by predictions of the strength of neutrino cooling via crust Urca processes. The strength of crust Urca neutrino cooling depends sensitively on the electron-capture and β-decay ground-state to ground-state transition strengths of neutron-rich rare isotopes. Nuclei with mass number A = 61 are predicted to be among the most abundant in accreted crusts, and the last remaining experimentally undetermined ground-state to ground-state transition strength was the β-decay of 61V. This work reports the first experimental determination of this transition strength, a ground-state branching of 8.1+2−2..20%, corresponding to a log ft value of 5.5+0−0..22. This result was achieved through the measurement of the β-delayed γ rays using the total absorption spectrometer SuN and the measurement of the β-delayed neutron branch using the neutron long counter system NERO at the National Superconducting Cyclotron Laboratory at Michigan State University. This method helps to mitigate the impact of the Pandemonium effect in extremely neutron-rich nuclei on experimental results. The result implies that A = 61 nuclei do not provide the strongest cooling in accreted neutron star crusts as expected by some predictions, but that their cooling is still larger compared to most other mass numbers. Only nuclei with mass numbers 31, 33, and 55 are predicted to be cooling more strongly. However, the theoretical predictions for the transition strengths of these nuclei are not consistently accurate enough to draw conclusions on crust cooling. With the experimental approach developed in this work all relevant transitions are within reach to be studied in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Cooling

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Manifold learning for organizing unstructured sets of process observations

arXiv

引用

arXiv 2018年

作者： Dietrich, Felix Kooshkbaghi, Mahdi Bollt, Erik M. Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Department of Electrical and Computer Engineering Clarkson Center for Complex Systems Science Clarkson University PotsdamNY13699-5815 United States

Data mining is routinely used to organize ensembles of short temporal observations so as to reconstruct useful, low-dimensional realizations of an underlying dynamical system. In this paper, we use manifold learning to organize unstructured ensembles of observations ("trials") of a system's response surface. We have no control over where every trial starts;and during each trial operating conditions are varied by turning "agnostic" knobs, which change system parameters in a systematic but unknown way. As one (or more) knobs "turn" we record (possibly partial) observations of the system response. We demonstrate how such partial and disorganized observation ensembles can be integrated into coherent response surfaces whose dimension and parametrization can be systematically recovered in a data-driven fashion. The approach can be justified through the Whitney and Takens embedding theorems, allowing reconstruction of manifolds/attractors through different types of observations. We demonstrate our approach by organizing unstructured observations of response surfaces, including the reconstruction of a cusp bifurcation surface for Hydrogen combustion in a Continuous Stirred Tank Reactor. Finally, we demonstrate how this observation-based reconstruction naturally leads to informative transport maps between input parameter space and output/state variable *** codes 37M20 Copyright © 2018, The Authors. All rights reserved.

关键词： Dynamical systems

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Stable super-resolution of images: A theoretical study

arXiv

引用

arXiv 2018年

作者： Eftekhari, Armin Bendory, Tamir Tang, Gongguo Institute of Electrical Engineering École Polytechnique Fédérale de Lausanne Program in Applied and Computational Mathematics Princeton University Department of Electrical Engineering Colorado School of Mines

We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a nonnegative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components, and if the translations of these components form a Chebyshev system, namely, a system of continuous functions that loosely behave like algebraic polynomials. Building upon recent results for one-dimensional signals [1], we prove that this super-resolution algorithm is stable (in the generalized Wasserstein metric) to model mismatch (namely, when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials, which are the main technical contribution of this paper, and partially resolve the question raised in [2] about the extension of the standard machinery to higher dimensions. Copyright © 2018, The Authors. All rights reserved.

关键词： Optical transfer function

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Communication-computation efficient gradient coding

arXiv

引用

arXiv 2018年

作者： Ye, Min Abbe, Emmanuel Department of Electrical Engineering Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University School of Mathematics Institute for Advanced Study PrincetonNJ08544 United States

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon EC2 clusters using Python with mpi4py package. Results show that the proposed scheme maintains the same generalization error while reducing the running time by 32% compared to uncoded schemes and 23% compared to prior coded schemes focusing only on stragglers (Tandon et al., ICML 2017). Copyright © 2018, The Authors. All rights reserved.

关键词： Python

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The implementation of K-Means clustering in kovats retention index on gas chromatography

引用

IOP Conference Series: Materials Science and engineering 2021年第1期1087卷

作者： T R Noviandy A Maulana N R Sasmita R Suhendra Muslem G M Idroes M Paristiowati Z Helwani E Yandri S Rahimah Muhammad Irvanizam R Idroes Department of Informatics Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Kopelma Darussalam Banda Aceh 23111 Indonesia Computational and Applied Statistics Research Group Department of Statistics Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Kopelma Darussalam Banda Aceh 23111 Indonesia Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Kopelma Darussalam Banda Aceh 23111 Indonesia Department of Chemical Engineering Faculty of Engineering Universitas Syiah Kuala Kopelma Darussalam Banda Aceh 23111 Indonesia Department of Chemistry Faculty of Mathematics and Sciences Universitas Negeri Jakarta Jl. Rawamangun Muka Jakarta 13220 Indonesia Department of Chemical Engineering Universitas Riau Pekanbaru 28293 Indonesia Graduate School of Renewable Energy Darma Persada University Jl. Radin Inten 2 Pondok Kelapa East Jakarta 13450 Indonesia Department of Food Industrial Technology Faculty of Agroindustrial Technology Universitas Padjadjaran Jatinangor 54363 Indonesia Faculty of Teacher Training and Education Abulyatama University Lampoh Keudee Aceh Besar 23372 Indonesia Department of Pharmacy Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Kopelma Darussalam Banda Aceh 23111 Indonesia

In this study, the retention index data of 146 compounds that are found in coal and petroleum-derived liquid fuels were grouped using the K-means clustering method, and the similarities between each cluster were analyzed. The psycho-chemical properties of each compound in the cluster were identified and compared with other clusters. Each compound's retention index is grouped based on the similarity between the column polarity and heating rate of one compound to another. Based on the results of tests carried out on nine differentk values, it is known that the grouping with the value of k = 3 is the best determined from the obtained silhouette score = 0.568, where this score is higher than the score obtained on the other k values. The results of clustering with k = 3 obtained three clusters, namely cluster C1, cluster C2, and cluster C3. Cluster C1 and cluster C2 consist of chemical compounds that have a relatively low carbon number and molecular mass, but in cluster C2 the molecular mass of the compound is lower than in cluster C1. In contrast, the C3 cluster consists of chemical compounds that have a relatively high carbon number and molecular mass.

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Estimation in the group action channel

arXiv

引用

arXiv 2018年

作者： Abbe, Emmanuel Pereira, João M. Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Electrical Engineering Department Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States

MSC Codes 94A15, 62B10We analyze the problem of estimating a signal from multiple measurements on a group action channel that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel is motivated by applications such as multi-reference alignment and cryoelectron microscopy. We focus on the large noise regime prevalent in these applications. We give a lower bound on the mean square error (MSE) of any asymptotically unbiased estimator of the signal's orbit in terms of the signal's moment tensors, which implies that the MSE is bounded away from 0 when N=σ2dis bounded from above, where N is the number of observations, σ is the noise standard deviation, and d is the so-called moment order cutoff. In contrast, the maximum likelihood estimator is shown to be consistent if N=σ2ddiverges. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean square error

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