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Existence of unbiased estimators in discrete quantum systems

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Physical Review Research 2025年第2期7卷 023060-023060页

作者： Javier Navarro Ricard Ravell Rodríguez Mikel Sanz Basque Center for Applied Mathematics Mazarredo 14 48009 Bilbao Spain and Department of Physical Chemistry University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain Basque Center for Applied Mathematics Mazarredo 14 48009 Bilbao Spain and Institute for Cross-Disciplinary Physics and Complex Systems UIB-CSIC Campus Universitat Illes Balears 07122 Palma de Mallorca Spain Basque Center for Applied Mathematics Mazarredo 14 48009 Bilbao Spain Department of Physical Chemistry University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain EHU Quantum Center University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain and IKERBASQUE Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Spain

The Cramér-Rao bound serves as a crucial lower limit for the mean square error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing the optimal unbiased estimator. In contrast, Bhattacharyya bounds offer a more robust estimation framework with respect to prior accuracy by introducing additional constraints on the estimator. In this work, we examine divergences that arise in the computation of these bounds and establish the conditions under which they remain valid. Notably, we show that when the number of constraints exceeds the number of measurement outcomes, an estimator with finite variance typically does not exist. Furthermore, we systematically investigate the properties of these bounds using paradigmatic examples, comparing them to the Cramér-Rao and Bayesian approaches.

关键词： Mean square error

Transmon probe for quantum characteristics of magnons in antiferromagnets

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arXiv 2023年

作者： Azimi-Mousolou, Vahid Bergman, Anders Delin, Anna Eriksson, Olle Pereiro, Manuel Thonig, Danny Sjöqvist, Erik Department of Applied Mathematics and Computer Science Faculty of Mathematics and Statistics University of Isfahan Isfahan81746-73441 Iran Department of Physics and Astronomy Uppsala University Box 516 UppsalaSE-751 20 Sweden Department of Applied Physics School of Engineering Sciences KTH Royal Institute of Technology AlbaNova University Center StockholmSE-10691 Sweden KTH Royal Institute of Technology StockholmSE-10044 Sweden School of Science and Technology Örebro University ÖrebroSE-701 82 Sweden

The detection of magnons and their quantum properties, especially in antiferromagnetic (AFM) materials, is a substantial step to realize many ambitious advances in the study of nanomagnetism and the development of energy efficient quantum technologies. The recent development of hybrid systems based on superconducting circuits provides the possibility of engineering quantum sensors that exploit different degrees of freedom. Here, we examine the magnon-photon-transmon hybridisation based on bipartite AFM materials, which gives rise to an effective coupling between a transmon qubit and magnons in a bipartite AFM. We demonstrate how magnetically invisible magnon modes, their chiralities and quantum properties such as nonlocality and two-mode magnon entanglement in bipartite AFMs can be characterized through the Rabi frequency of the superconducting transmon qubit. © 2023, CC BY.

关键词： Hybrid systems

Invariants and Reversibility In Polynomial Systems of Ode

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SSRN

SSRN 2024年

作者： Grašič, Mateja Jarrah, Abdul Salam Romanovski, Valery G. Faculty of Natural Science and Mathematics University of Maribor Koroška Cesta 160 MariborSI-2000 Slovenia Institute of Mathematics Physics and Mechanics Jadranska 19 LjubljanaSI-1000 Slovenia Department of Mathematics and Statistics American University of Sharjah Sharjah United Arab Emirates Faculty of Electrical Engineering and Computer Science University of Maribor Koroška cesta 46 MariborSI-2000 Slovenia Center for Applied Mathematics and Theoretical Physics Mladinska 3 MariborSI-2000 Slovenia

This paper explores a relationship between invariants of certain group actions and the time-reversibility of two-dimensional polynomial differential systems exhibiting a $1:-1$ resonant singularity. We focus on the connection of time-reversibility with the Sibirsky subvariety of the center variety, which encompasses systems possessing a local analytic first integral near the origin. An algorithm for generating the Sibirsky ideal for these systems is proposed and the algebraic properties of the ideal are examined. Furthermore, using a generalization of the concept of time-reversibility we study $n$-dimensional systems with a $1:\zeta:\zeta^2:\dots:\zeta^{n-1}$ resonant singularity, where $n$ is prime and $\zeta$ is a primitive $n$-th root of unity. We study the invariants of a Lie group action on the parameter space of the system, leveraging the theory of binomial ideals as a fundamental tool for the analysis. Our study reveals intriguing connections between generalized reversibility, invariants, and binomial ideals, shedding light on their complex interrelations. © 2024, The Authors. All rights reserved.

关键词： Choquet integral

Thermoelastic properties of bridgmanite using Deep Potential Molecular Dynamics

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arXiv 2023年

作者： Wan, Tianqi Luo, Chenxing Sun, Yang Wentzcovitch, Renata M. Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Physics Xiamen University Xiamen361005 China Department of Physics Iowa State University Ames50011 United States Department of Earth and Environmental Sciences Columbia University New YorkNY10027 United States Lamont–Doherty Earth Observatory Columbia University PalisadesNY10964 United States Data Science Institute Columbia University New YorkNY10027 United States

MgSiO3-perovskite (MgPv) plays a crucial role in the Earth’s lower mantle. This study combines deep-learning potential (DP) with density functional theory (DFT) to investigate the structural and elastic properties of MgPv under lower mantle conditions. To simulate complex systems, we developed a series of potentials capable of faithfully reproducing DFT calculations using different functionals, such as LDA, PBE, PBEsol, and SCAN meta-GGA functionals. The obtained predictions exhibit remarkable reliability and consistency, closely resembling experimental measurements. Our results highlight the superior performance of the DP-SCAN and DP-LDA in accurately predicting high-temperature equations of states and elastic properties. This hybrid computational approach offers a solution to the accuracy-efficiency dilemma in obtaining precise elastic properties at high pressure and temperature conditions for minerals like MgPv, which opens a new way to study the Earth’s interior state and related processes. Copyright © 2023, The Authors. All rights reserved.

关键词： Elasticity

Ground-based and additional science support for SMILE

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Earth and Planetary physics 2024年第1期8卷 275-298页

作者： J.A.Carter M.Dunlop C.Forsyth K.Oksavik E.Donovon A.Kavanagh S.E.Milan T.Sergienko R.C.Fear D.G.Sibeck M.Connors T.Yeoman X.Tan M.G.G.T.Taylor K.McWilliams J.Gjerloev R.Barnes D.D.Billet G.Chisham A.Dimmock M.P.Freeman D.-S.Han M.D.Hartinger S.-Y.W.Hsieh Z.-J.Hu M.K.James L.Juusola K.Kauristie E.A.Kronberg M.Lester J.Manuel J.Matzka I.McCrea Y.Miyoshi J.Rae L.Ren F.Sigernes E.Spanswick K.Sterne A.Steuwer T.Sun M.-T.Walach B.Walsh C.Wang J.Weygand J.Wild J.Yan J.Zhang Q.-H.Zhang Planetary Sciences Group School of Physics and AstronomyUniversity of LeicesterUniversity RoadLeicesterLE17RHUK Rutherford Appleton Laboratory Space Science Technology Facilities CouncilOxfordshireUK School of Space and Environment Beihang UniversityBeijing 100191China Key Laboratory of Space Environment Monitoring and Information Processing Ministry of Industry and Information TechnologyBeijing 100017China Department of Space and Climate Physics UCLMullard Space Science LaboratoryHolmbury St.MaryDorkingSurreyRH56NTUK Birkeland Centre for Space Science Department of Physics and Technology.University of BergenBergenNorway Department of Physics and Astronomy University of Calgary2500 University DriveCalgaryAlbertaCanada T2N 1N4 British Antarctic Survey CambridgeUK Swedish Institute of Space Physics KirunaSweden West Highfield Campus University of SouthamptonUniversity RoadSO171BJUK Goddard Space Flight Center NASAGreenbeltMarylandUSA Athabasca University AthabascaCanada ESTEC European Space AgencyNetherlands University of Saskatchewan SaskatoonCanada The Johns Hopkins University Applied Physics Laboratory LaurelMarylandUSA Swedish Institude of Space Physics UppsalaSE 75121Sweden Tongji University Shanghai 200092China Center for Space Plasma Physics Space Science Institute4765 Walnut Street Suite BBoulderColorado80301USA Polar Research Institute of China Shanghai 200136China Finnish Meteorological Institute(FMI) Finland Department of Earth and Environmental Sciences(Geophysics) Ludwig Maximilian University of Munich(LMU)MunichTheresienstr.41MunichD-80333Germany Canadian Space Agency MontrealCanada GFZ German Research Centre for Geosciences PotsdamGermany Nagoya University Institute for Space Earth Environment ResearchCenter for Integrated Data ScienceNagoyaAichiJP 464-8601 Northumbria University Newcastle upon TyneTyne and WearUK NE18ST National Space Science Center Chinese Academy SciencesBeijing 100190China Arctic Geophysics University Centre in Svalbard

The joint European Space Agency and Chinese Academy of sciences Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission will explore global dynamics of the magnetosphere under varying solar wind and interplanetary magnetic field conditions,and simultaneously monitor the auroral response of the Northern Hemisphere *** these large-scale responses with medium and fine-scale measurements at a variety of cadences by additional ground-based and space-based instruments will enable a much greater scientific impact beyond the original goals of the SMILE ***,we describe current community efforts to prepare for SMILE,and the benefits and context various experiments that have explicitly expressed support for SMILE can offer.A dedicated group of international scientists representing many different experiment types and geographical locations,the Ground-based and Additional science Working Group,is facilitating these *** include constructing an online SMILE data Fusion Facility,the discussion of particular or special modes for experiments such as coherent and incoherent scatter radar,and the consideration of particular observing strategies and spacecraft *** anticipate growing interest and community engagement with the SMILE mission,and we welcome novel ideas and insights from the solar-terrestrial community.

关键词： magnetosphere ionosphere magnetosphere-ionosphere coupling ground-based experimentation SMILE conjunctions missions

Dualband and Tripleband Metamaterial Absorber in Wr1 Band and Lower Terahertz Frequencies

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SSRN

SSRN 2023年

作者： Gharat, Sarvesh Kulkarni, Prutha Prabhu, Shriganesh Garde, Chandrashekhar Centre for Machine Intelligence and Data Science Indian Institute of Technology Bombay India Department of Electronics and Telecommunication Vishwakarma Institute of Information Technology Pune India Depatment of Engineering and Applied Sciences Vishwakarma Institute of Information Technology Pune India Department of Condensed Matter Physics and Materials Science Tata Institute of Fundamental Research Mumbai India

The frequency Band of 0.5 THz to 1.1 THz (WR1.5 and WR1) is one of the promising bands when it comes to 6G. In this paper, we propose a novel metamaterial absorber suitable to be used at lower WR1 frequencies in TE mode. Alternatively, the design can be used as a strong absorber at lower Terahertz frequencies. In addition, when used in TM mode the absorber works as a perfect absorber at a higher WR1 band. © 2023, The Authors. All rights reserved.

关键词： Metamaterials

CROSS-TARGET STANCE DETECTION BY EXPLOITING TARGET ANALYTICAL PERSPECTIVES

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arXiv 2024年

作者： Ding, Daijun Chen, Rong Jing, Liwen Zhang, Bowen Huang, Xu Dong, Li Zhao, Xiaowen Song, Ge College of Applied Science Shenzhen University Shenzhen China Shenzhen X-Institute Shenzhen China College of Big Data and Internet Shenzhen Technology University Shenzhen China Harbin Institute of Technology Shenzhen China Aoyama Gakuin University Tokyo Japan College of Mathematics and Informatics South China Agricultural University Guangzhou China

Cross-target stance detection (CTSD) is an important task, which infers the attitude of the destination target by utilizing annotated data derived from the source target. One important approach in CTSD is to extract domain-invariant features to bridge the knowledge gap between multiple targets. However, the analysis of informal and short text structure, and implicit expressions, complicate the extraction of domain-invariant knowledge. In this paper, we propose a Multi-Perspective Prompt-Tuning (MPPT) model for CTSD that uses the analysis perspective as a bridge to transfer knowledge. First, we develop a two-stage instruct-based chain-of-thought method (TsCoT) to elicit target analysis perspectives and provide natural language explanations (NLEs) from multiple viewpoints by formulating instructions based on large language model (LLM). Second, we propose a multi-perspective prompt-tuning framework (MultiPLN) to fuse the NLEs into the stance predictor. Extensive experiments results demonstrate the superiority of MPPT against the state-of-the-art baseline methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Natural language processing systems

Minimal Ternary Linear Codes from Vectorial Functions

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arXiv 2024年

作者： Li, Yanjun Kan, Haibin Liu, Fangfang Peng, Jie Zheng, Lijing Zhuo, Zepeng Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics Anhui Bengbu233030 China School of Computer Sciences Fudan University Shanghai200433 China Shanghai Key Laboratory of Intelligent Information Processing School of Computer Science Fudan University Shanghai Engineering Research Center of Blockchain Shanghai Institute for Advanced Communication and Data Science Shanghai200433 China School of Mathematics and Statistics Huaibei Normal University Anhui Huaibei235000 China Mathematics and Science College Shanghai Normal University Guilin Road #100 Shanghai200234 China The School of Mathematics and Physics University of South China Hunan Hengyang421001 China

The study on minimal linear codes has received great attention due to their significant applications in secret sharing schemes and secure two-party computation. Until now, numerous minimal linear codes have been discovered. However, to the best of our knowledge, no infinite family of minimal ternary linear codes was found from vectorial functions. In this paper, we present a necessary and sufficient condition for a large class of ternary linear codes from vectorial functions such that those codes are minimal. Based on that, we construct several minimal ternary linear codes with three-weight from vectorial regular plateaued functions, and determine their weight distributions. Moreover, we also give a necessary and sufficient condition for a large family of ternary linear codes from vectorial functions such that the codes are minimal and violate the AB condition simultaneously. According to this characterization, we find several minimal ternary linear codes violating the AB condition. Notably, our results show that our method can be applied to solve a problem on minimal linear codes proposed by Li et al. Copyright © 2024, The Authors. All rights reserved.

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LINSCAN - A Linearity Based Clustering Algorithm

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arXiv 2024年

作者： Dennehy, Andrew Zou, Xiaoyu Semnani, Shabnam J. Fialko, Yuri Cloninger, Alexander Committee on Computational and Applied Mathematics University of Chicago ChicagoIL United States Institute of Geophysics and Planetary Physics Scripps Institution of Oceanography University of California La Jolla San DiegoCA92093 United States Department of Structural Engineering University of California La Jolla San DiegoCA92093 United States Department of Mathematics Halcioglu Data Science Institute University of California La Jolla San DiegoCA92093 United States

DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN, designed to seek lineated clusters that are difficult to find and isolate with existing methods. In particular, by embedding points as normal distributions approximating their local neighborhoods and leveraging a distance function derived from the Kullback Leibler Divergence, LINSCAN can detect and distinguish lineated clusters that are spatially close but have orthogonal covariances. We demonstrate how LINSCAN can be applied to seismic data to identify active faults, including intersecting faults, and determine their orientation. Finally, we discuss the properties a generalization of DBSCAN and OPTICS must have in order to retain the stability benefits of these algorithms. © 2024, CC BY.

关键词： Normal distribution