检索结果-内蒙古大学图书馆

Exponential quantum advantages for practical non-Hermitian eigenproblems

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Zhang, Xiao-Ming Zhang, Yukun He, Wenhao Yuan, Xiao School of Physics South China Normal University Guangzhou510006 China Center on Frontiers of Computing Studies School of Computer Science Peking University Beijing100871 China Center for Computational Science and Engineering Massachusetts Institute of Technology CambridgeMA02139 United States School of Physics Peking University Beijing100871 China

While non-Hermitian physics has attracted considerable attention, current studies are limited to small or classically solvable systems. Quantum computing, as a powerful eigensolver, have predominantly been applied to Hermitian domain, leaving their potential for studying non-Hermitian problems largely unexplored. We extend the power of quantum computing to general non-Hermitian eigenproblems. Our approach works for finding eigenvalues without extra constrains, or eigenvalues closest to specified points or lines, thus extending results for ground energy and energy gap problems for Hermitian matrices. Our algorithms have broad applications, and as examples, we consider two central problems in non-Hermitian physics. Firstly, our approach is the first to offer an efficient quantum solution to the witness of spontaneous PT-symmetry breaking, and provide provable, exponential quantum advantage. Secondly, our approach enables the estimation of Liouvillian gap, which is crucial for characterizing relaxation times. Our general approach can also find applications in many other areas, such as the study of Markovian stochastic processes. These results underscore the significance of our quantum algorithms for addressing practical eigenproblems across various disciplines. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Fine-grained sentiment analysis using neural networks to identify guest preferences based on online reviews

学校读者我要写书评

暂无评论

Fine-grained sentiment analysis using neural networks to ide...

Computer, Power and Communications (ICCPC), International Conference on

作者： L. Antony Rosewelt Rajesh Kambattan Kovarasan Sridevi P. Ponmalar Computer Science and Engineering Sri Sai Ram Institute of Technology Chennai India Computer Science and Engineering Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai India Department of Computational Intelligence School of Computing SRM Institute of Science and Technology Chennai India

Online reviews are a sort of user-generated content that sway not only prospective guests' reservation decisions but also provide timely feedback to hotels on how to enhance their service offerings in response to guest feedback. Customer preferences can be inferred from online hotel evaluations by analysing the reviews for subtle indications of approval or disapproval of specific features. Sentiment component extraction, feature pair identification (FPI), and sentiment orientation analysis are all basic activities in fine-grained sentiment analysis. Yet, current fine-grained sentiment analysis techniques fail to identify FPIs reliably, particularly when dealing with review evaluations. To boost the efficiency of FPI detection, we develop a new convolutional neural network (i.e., CNN) model that can fully exploit unstructured and structured information. In addition, we present a modified fine-grained sentiment analysis methodology that integrates a term clustering algorithm for “aspect terms” to determine a correct “customer sentiment intensity value” for each evaluated aspect, rather than a simple “positive” or “negative” rating. At last, we undertake an empirical analysis of hotel web reviews to demonstrate the rationality and benefits of the suggested methodology. The empirical findings show that our suggested method can effectively identify consumer preferences from online evaluations of hotels and can enhance the effectiveness of FPI identification. Furthermore, we discover that different sorts of clients have distinct tastes in the amenities offered by hotels.

关键词： Sentiment analysis User-generated content Neural networks Clustering algorithms Companies Feature extraction Convolutional neural networks

Why is Grain Growth Not Curvature Flow?

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Qiu, Caihao Srolovitz, David J. Rohrer, Gregory S. Han, Jian Salvalaglio, Marco Department of Materials Science and Engineering City University of Hong Kong Hong Kong Department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong The University of Hong Kong Shenzhen China Department of Materials Science and Engineering Carnegie Mellon University PittsburghPA United States Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany

Grain growth describes the increase in the mean grain size with time during the annealing of a polycrystal;it is widely accepted that this is driven by capillarity (surface tension). Although classically modeled and interpreted as mean curvature flow, a growing body of evidence has demonstrated that this is overly simplistic and inconsistent with experimental observations. Despite many proposals for the source of this failure, it remains a subject of ongoing debate. By considering the fundamental microscopic mechanism of grain boundary (GB) migration, we demonstrate that internal stress (shear coupling) associated with GB motion is the primary factor causing deviations in grain growth from mean curvature flow. This is achieved through the application of a two-dimensional bicrystallography-respecting continuum model for GB migration to grain growth, implemented in a diffuse-interface approach. These results are validated by comparison with atomistic simulations and the scatter in the curvature-velocity relationship is shown to be in excellent agreement with experimental results for grain growth in 3D polycrystals (not possible based on other proposed explanations). This work also demonstrates how to account for the mechanical effects that are integral to grain growth in crystalline solids. Copyright © 2024, The Authors. All rights reserved.

关键词： Polycrystals

NEW C0 INTERIOR PENALTY METHOD FOR MONGE-AMPÈRE EQUATIONS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Chu, Tianyang Guo, Hailong Zhang, Zhimin LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematics and Statistics The University of Melbourne ParkvilleVIC3010 Australia Department of Mathematics Wayne State University DetroitMI48202 United States

Monge-Ampère equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the C0 interior penalty method to approximation the viscosity solution of the Monge-Ampère equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Ampère equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates. © 2024, CC BY.

关键词： Partial differential equations

Enhancing Older Adults’ Gesture Typing Experience Using the T9 Keyboard on Small Touchscreen Devices

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Kuang, Emily Chen, Ruihuan Fan, Mingming Golisano College of Computing and Information Sciences Rochester Institute of Technology United States School of Information Rochester Institute of Technology United States Computational Media and Arts Thrust The Hong Kong University of Science and Technology Guangzhou China Division of Integrative Systems and Design Department of Computer Science and Engineering The Hong Kong University of Science and Technology China

Older adults increasingly adopt small-screen devices, but limited motor dexterity hinders their ability to type effectively. While a 9-key (T9) keyboard allocates larger space to each key, it is shared by multiple consecutive letters. Consequently, users must interrupt their gestures when typing consecutive letters, leading to inefficiencies and poor user experience. Thus, we proposed a novel keyboard that leverages the currently unused key 1 to duplicate letters from the previous key, allowing the entry of consecutive letters without interruptions. A user study with 12 older adults showed that it significantly outperformed the T9 with wiggle gesture in typing speed, KSPC, insertion errors, and deletes per word while achieving comparable performance as the conventional T9. Repeating the typing tasks with 12 young adults found that the advantages of the novel T9 were consistent or enhanced. We also provide error analysis and design considerations for improving gesture typing on T9 for older adults. © 2023, CC BY-NC-ND.

关键词： Touch screens

Random ISAC Signals Deserve Dedicated Precoding

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Lu, Shihang Liu, Fan Dong, Fuwang Xiong, Yifeng Xu, Jie Liu, Ya-Feng Jin, Shi Southern University of Science and Technology Shenzhen518055 China The School of Information and Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Shenzhen518172 China The 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 National Mobile Communications Research Laboratory Southeast University Nanjing210096 China

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs. © 2023, CC BY.

关键词： Numerical methods

Crosslinker energy landscape effects on dynamic mechanical properties of ideal polymer hydrogels

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Khare, Eesha Alcantara, Amadeus Lee, Nic Skaf, Munir S. Buehler, Markus Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA United States Department of Materials Science and Engineering Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA United States Department of Computational Mechanics School of Mechanical Engineering University of Campinas - UNICAMP Campinas Sao Paulo Brazil Center for Computing in Engineering & Sciences CCES University of Campinas - UNICAMP Campinas Sao Paulo Brazil School of Architecture and Planning Media Lab Massachusetts Institute of Technology 75 Amherst Street CambridgeMA United States Institute of Chemistry School of Mechanical Engineering University of Campinas - UNICAMP Campinas Sao Paulo Brazil Center for Computational Science and Engineering Schwarzman College of Computing Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA United States

Reversible crosslinkers can enable several desirable mechanical properties, such as improved toughness and self-healing, when incorporated in polymer networks for bioengineering and structural applications. In this work, we performed coarse-grained molecular dynamics to investigate the effect of the energy landscape of reversible crosslinkers on the dynamic mechanical properties of crosslinked polymer network hydrogels. We report that, for an ideal network, the energy potential of the crosslinker interaction drives the viscosity of the network, where a stronger potential results in a higher viscosity. Additional topographical analyses reveal a mechanistic understanding of the structural rearrangement of the network as it deforms and indicate that as the number of defects increases in the network, the viscosity of the network increases. As an important validation for the relationship between the energy landscape of a crosslinker chemistry and the resulting dynamic mechanical properties of a crosslinked ideal network hydrogel, this work enhances our understanding of deformation mechanisms in polymer networks that cannot easily be revealed by experiment and reveals design ideas that can lead to better performance of the polymer network at the macroscale. © 2023, CC BY-NC-SA.

关键词： Hydrogels

A DISCONTINUOUS PLANE WAVE NEURAL NETWORK METHOD FOR HELMHOLTZ EQUATION AND TIME-HARMONIC MAXWELL'S EQUATIONS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Yuan, Long Hu, Qiya College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao266590 China LSEC Institute of Computational Mathematics and Scientic/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper we propose a discontinuous plane wave neural network (DPWNN) method with hp−refinement for approximately solving Helmholtz equation and time-harmonic Maxwell equations. In this method, we define a quadratic functional as in the plane wave least square (PWLS) method with h−refinement and introduce new discretization sets spanned by element-wise neural network functions with a single hidden layer, where the activation function on each element is chosen as a complex-valued exponential function like the plane wave function. The desired approximate solution is recursively generated by iteratively solving a quasi-minimization problem associated with the functional and the sets described above, which is defined by a sequence of approximate minimizers of the underlying residual functionals, where plane wave direction angles and activation coefficients are alternatively computed by iterative algorithms. For the proposed DPWNN method, the plane wave directions are adaptively determined in the iterative process, which is different from that in the standard PWLS method (where the plane wave directions are preliminarily given). Numerical experiments will confirm that this DPWNN method can generate approximate solutions with higher accuracy than the PWLS method. Copyright © 2023, The Authors. All rights reserved.

关键词： Wave propagation

Helmholtz Decomposition Based Windowed Green Function Methods for Elastic Scattering Problems on a Half-Space

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

作者： Yin, Tao Zhang, Lu Zheng, Weiying Zhu, Xiaopeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type $(\mathbb{I}+\mathbb{T})\bs\phi=\bs f$, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth ``slow-rise'' windowing function is introduced to truncate the boundary integral equations and a ``correction'' strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method. © 2023, The Authors. All rights reserved.

关键词： Boundary integral equations