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Tightness and equivalence of semidefinite relaxations for mimo detection

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arXiv 2021年

作者： Jiang, Ruichen Liu, Ya-Feng Bao, Chenglong Jiang, Bo Department of Electronic Engineering Tsinghua University Beijing100084 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Yau Mathematical Sciences Center Tsinghua University Beijing100084 China School of Mathematical Sciences Key Laboratory for NSLSCS of Jiangsu Province Nanjing Normal University Nanjing210023 China

The multiple-input multiple-output (MIMO) detection problem, a fundamental problem in modern digital communications, is to detect a vector of transmitted symbols from the noisy outputs of a fading MIMO channel. The maximum likelihood detector can be formulated as a complex least-squares problem with discrete variables, which is NP-hard in general. Various semidefinite relaxation (SDR) methods have been proposed in the literature to solve the problem due to their polynomial-time worst-case complexity and good detection error rate performance. In this paper, we consider two popular classes of SDR-based detectors and study the conditions under which the SDRs are tight and the relationship between different SDR models. For the enhanced complex and real SDRs proposed recently by Lu et al., we refine their analysis and derive the necessary and sufficient condition for the complex SDR to be tight, as well as a necessary condition for the real SDR to be tight. In contrast, we also show that another SDR proposed by Mobasher et al. is not tight with high probability under mild conditions. Moreover, we establish a general theorem that shows the equivalence between two subsets of positive semidefinite matrices in different dimensions by exploiting a special "separable" structure in the constraints. Our theorem recovers two existing equivalence results of SDRs defined in different settings and has the potential to find other applications due to its *** Codes 90C22, 90C20, 90C46, 90C27 Copyright © 2021, The Authors. All rights reserved.

关键词： Polynomial approximation

A well-conditioned direct PinT algorithm for first- And second-order evolutionary equations

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arXiv 2021年

作者： Liu, Jun Wang, Xiang-Sheng Wu, Shu-Lin Zhou, Tao Department of Mathematics and Statistics Southern Illinois University Edwardsville EdwardsvilleIL62026 United States Department of Mathematics University of Louisiana at Lafayette LafayetteLA70503 United States School of Mathematics and Statistics Northeast Normal University Changchun130024 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS ChineseAcademy of Sciences Beijing100190 China

In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method as the time integrator that leads to a tridiagonal time discretization matrix. Instead of solving the corresponding all-at-once system iteratively, we diagonalize the time discretization matrix, which yields a direct parallel implementation across all time levels. A crucial issue on this methodology is how the condition number of the eigenvector matrix V grows as n is increased, where n is the number of time levels. A large condition number leads to large roundoff error in the diagonalization procedure, which could seriously pollute the numerical accuracy. Based on a novel connection between the characteristic equation and the Chebyshev polynomials, we present explicit formulas for computing V and V −1, by which we prove that Cond2(V) = O(n2). This implies that the diagonalization process is well-conditioned and the roundoff error only increases moderately as n grows and thus, compared to other direct PinT algorithms, a much larger n can be used to yield satisfactory parallelism. Numerical results on parallel machine are given to support our findings, where over 60 times speedup is achieved with 256 *** Codes 65Y05, 65F05 Copyright © 2021, The Authors. All rights reserved.

关键词： Number theory

Chimera baryon spectrum in the Sp(4) completion of composite Higgs models 40

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Chimera baryon spectrum in the Sp(4) completion of composite...

40th International Symposium on Lattice Field Theory, LATTICE 2023

作者： Hsiao, Ho Bennett, Ed Hong, Deog Ki Lee, Jong-Wan Lin, C.-J. David Lucini, Biagio Piai, Maurizio Vadacchino, Davide Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Swansea Academy of Advanced Computing Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Extreme Physics Institute Pusan National University Busan46241 Korea Republic of Daejeon34126 Korea Republic of Center for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Park Campus Singleton Park Wales SwanseaSA2 8PP United Kingdom Centre for Mathematical Science University of Plymouth PlymouthPL4 8AA United Kingdom

In strongly coupled gauge theories that serve as completions of composite Higgs models, the fermionic bound states formed by fermions (hyperquarks) transforming in different representations, called chimera baryons, could serve as top partners, by embedding of the Standard Model appropriately. We report our results on the spectrum of chimera baryons in the Sp(4) gauge theory with hyperquarks transforming in fundamental and two-index antisymmetric representations. For this study, we adopt the quenched approximation. We investigate the mass hierarchy between the lightest chimera baryons with different quantum numbers, as a function of the lattice parameters. Inspired by baryon chiral effective field theory, and the Akaike Information Criterion, we perform a first extrapolation to the continuum and massless-hyperquark limit. © Copyright owned by the author(s) under the terms of the Creative Commons.

关键词： Gages

New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

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arXiv 2020年

作者： Zhao, Ting Liu, Hongwei Liu, Zexian School of Mathematics and Statistics Xidian University Xi’an710126 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing AMSS Chinese Academy of Sciences Beijing100190 China

In this paper, two new subspace minimization conjugate gradient methods based on p−regularization models are proposed, where a special scaled norm in p−regularization model is analyzed. Different choices for special scaled norm lead to different solutions to the p−regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions satisfying the sufficient descent condition. With a modified nonmonotone line search, we establish the global convergence of the proposed methods under mild assumptions. R−linear convergence of the proposed methods are also analyzed. Numerical results show that, for the CUTEr library, the proposed methods are superior to four conjugate gradient methods, which were proposed by Hager and Zhang (SIAM J Optim 16(1):170-192, 2005), Dai and Kou (SIAM J Optim 23(1):296-320, 2013), Liu and Liu (J Optim Theory Appl 180(3):879-906, 2019) and Li et al. (Comput Appl Math 38(1): 2019), respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： Conjugate gradient method

Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

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Science China(Physics,Mechanics & Astronomy) 2019年第6期62卷 13-20页

作者： Tao Xin Liang Hao Shi-Yao Hou Guan-Ru Feng Gui-Lu Long State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics Tsinghua University Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Center for Quantum Computing Peng Cheng Laboratory Shenzhen Key Laboratory of Quantum Science and Engineering Southern University of Science and Technology Institute of Applied Physics and Computational Mathematics Center for Computational Sciences Sichuan Normal University College of Physics and Electronic Engineering Sichuan Normal University Institute for Quantum Computing Waterloo Tsinghua National Laboratory of Information Science and Technology The Innovative Center of Quantum Matter

Quantum state preparation plays an equally important role as quantum operations and measurements in quantum information processing. The previous methods for initialization require either an exponential number of experiments, or cause signal reduction or place restrictions on molecular structures. In this study, we propose three types of quantum circuits for preparing the pseudo-pure states of(n-1) qubits in the n-coupled Hilbert space, which simply needs the assistance of one ancilla spin and two different experiments independent of n. Most importantly, our methods work well on homo-nuclear and hetero-nuclear molecules without the reduction of signals in the gradient field. As a proof-of-principle demonstration, we experimentally prepared the pseudo-pure states of heteronuclear 2-qubit and homonuclear 4-qubit molecules using a nuclear magnetic resonance quantum information processor.

关键词： quantum state preparation nuclear magnetic resonance quantum algorithms

MatterChat: A Multi-Modal LLM for Material Science

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arXiv 2025年

作者： Tang, Yingheng Xu, Wenbin Cao, Jie Gao, Weilu Farrell, Steven Erichson, Benjamin Mahoney, Michael W. Nonaka, Andy Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States NSF National AI Institute for Student-AI Teaming University of Colorado at Boulder Boulder United States Department of Electrical and Computer Engineering The University of Utah Salt Lake CityUT United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States International Computer Science Institute BerkeleyCA United States Department of Statistics University of California at Berkeley BerkeleyCA United States

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material structure data with language-based information through multi-modal large language models (LLMs) offers great potential to support these efforts by enhancing human–AI interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multi-modal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat employs a bridging module to effectively align a pretrained universal machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat significantly improves performance in material property prediction and human-AI interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis. © 2025, CC BY.

关键词： Structure (composition)

A MULTIFIDELITY MONTE CARLO METHOD FOR REALISTIC computational BUDGETS

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arXiv 2022年

作者： Gruber, Anthony Gunzburger, Max Ju, Lili Wang, Zhu Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseeFL32306 United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th Street AustinTX78712 United States Department of Mathematics University of South Carolina 1523 Greene Street ColumbiaSC29208 United States

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo *** Codes 62K05, 49M20 Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

Survey of physics reasoning on uncertainty concepts in experiments: an assessment of measurement uncertainty for introductory physics labs

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arXiv 2023年

作者： Vignal, Michael Geschwind, Gayle Pollard, Benjamin Henderson, Rachel Caballero, Marcos D. Lewandowski, H.J. JILA National Institute of Standards and Technology The University of Colorado BoulderCO80309 United States Department of Physics University of Colorado 390 UCB BoulderCO80309 United States Department of Physics Worcester Polytechnic Institute 100 Institute Road WorcesterMA01609 United States Department of Physics & Astronomy CREATE for STEM Institute Michigan State University East LansingMI48824 United States Department of Computational Mathematics Science & Engineering Michigan State University East LansingMI48824 United States Department of Physics Center for Computing in Science Education University of Oslo Oslo0315 Norway

Measurement uncertainty is a critical feature of experimental research in the physical sciences, and the concepts and practices surrounding measurement uncertainty are important components of physics lab courses. However, there has not been a broadly applicable, research-based assessment tool that allows physics instructors to easily measure students’ knowledge of measurement uncertainty concepts and practices. To address this need, we employed Evidence-Centered Design to create the Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE). SPRUCE is a pre-post assessment instrument intended for use in introductory (first- and second-year) physics lab courses to help instructors and researchers identify student strengths and challenges with measurement uncertainty. In this paper, we discuss the development of SPRUCE’s assessment items guided by Evidence-Centered Design, focusing on how instructors’ and researchers’ assessment priorities were incorporated into the assessment items and how students’ reasoning from pilot testing informed decisions around item answer options. We also present an example of some of the feedback an instructor would receive after implementing SPRUCE in a pre-post fashion, along with a brief discussion of how that feedback could be interpreted and acted upon. © 2023, CC BY.

关键词： Uncertainty analysis

A NITSCHE HYBRID MULTISCALE METHOD WITH NON-MATCHING GRIDS

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arXiv 2021年

作者： Ming, Pingbing Song, Siqi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic problem with bounded and measurable coefficients. The rate of convergence may be derived for coefficients with further structures such as periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions. Copyright © 2021, The Authors. All rights reserved.

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