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arXiv 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

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Chirped Bright and Kink Solitons in Nonlinear Optical Fibers with Weak Nonlocality and Cubic-Quantic-Septic Nonlinearity

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Chinese Physics Letters 2022年第4期39卷 12-16页

作者： Qin Zhou Yu Zhong Houria Triki Yunzhou Sun Siliu Xu Wenjun Liu Anjan Biswas Research Center of Nonlinear Science School of Mathematical and Physical SciencesWuhan Textile UniversityWuhan 430200China Radiation Physics Laboratory Department of PhysicsFaculty of SciencesBadji Mokhtar UniversityP.O.Box 1223000 AnnabaAlgeria School of Electronic and Information Engineering Hubei University of Science and TechnologyXianning 437100China State Key Laboratory of Information Photonics and Optical Communications School of ScienceBeijing University of Posts and TelecommunicationsBeijing 100876China Beijing University of Posts and Telecommunications Research Institute Shenzhen 518057China Department of Physics Chemistry and MathematicsAlabama A&M UniversityNormalAL 35762-4900USA Mathematical Modeling and Applied Computation(MMAC)Research Group Department of MathematicsKing Abdulaziz UniversityJeddah 21589Saudi Arabia

This work focuses on chirped solitons in a higher-order nonlinear Schrodinger equation,including cubic-quinticseptic nonlinearity,weak nonlocal nonlinearity,self-frequency shift,and self-steepening *** the first time,analytical bright and kink solitons,as well as their corresponding chirping,are *** influence of septic nonlinearity and weak nonlocality on the dynamical behaviors of those nonlinearly chirped solitons is thoroughly *** findings of the study give an experimental basis for nonlinear-managed solitons in optical fibers.

关键词： effect nonlinearity solitons

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MetaUE: Model-based Meta-learning for Underwater Image Enhancement

arXiv

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arXiv 2023年

作者： Zhang, Zhenwei Yan, Haorui Tang, Ke Duan, Yuping Center for Applied Mathematics Tianjin University Tianjin300072 China The Guangdong Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China The Research Institute of Trustworthy Autonomous Systems Southern University of Science and Technology Shenzhen518055 China

The challenges in recovering underwater images are the presence of diverse degradation factors and the lack of ground truth images. Although synthetic underwater image pairs can be used to overcome the problem of inadequately observing data, it may result in over-fitting and enhancement degradation. This paper proposes a model-based deep learning method for restoring clean images under various underwater scenarios, which exhibits good interpretability and generalization ability. More specifically, we build up a multi-variable convolutional neural network model to estimate the clean image, background light and transmission map, respectively. An efficient loss function is also designed to closely integrate the variables based on the underwater image model. The meta-learning strategy is used to obtain a pre-trained model on the synthetic underwater dataset, which contains different types of degradation to cover the various underwater environments. The pre-trained model is then fine-tuned on real underwater datasets to obtain a reliable underwater image enhancement model, called MetaUE. Numerical experiments demonstrate that the pre-trained model has good generalization ability, allowing it to remove the color degradation for various underwater attenuation images such as blue, green and yellow, etc. The fine-tuning makes the model able to adapt to different underwater datasets, the enhancement results of which outperform the state-of-the-art underwater image restoration methods. All our codes and data are available at https://***/Duanlab123/MetaUE. Copyright © 2023, The Authors. All rights reserved.

关键词： Image enhancement

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Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation

arXiv

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arXiv 2024年

作者： An, Dong Childs, Andrew M. Lin, Lin Ying, Lexing Beijing International Center for Mathematical Research Peking University China Joint Center for Quantum Information and Computer Science University of Maryland College Park United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Mathematics University of California Berkeley United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley United States Department of Mathematics Stanford University United States Institute for Computational and Mathematical Engineering Stanford University United States

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for non-normal matrices. We propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation (LCHS) method [An, Liu, Lin, Phys. Rev. Lett. 131, 150603, 2023;An, Childs, Lin, arXiv:2312.03916] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, A-k, and the exponential of the matrix inverse, e-A-1. The latter can be interpreted as the solution of a mass-matrix differential equation of the form Au′(t) = -u(t). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting A, reducing the computational complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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PCA: Semi-Supervised Segmentation with Patch Confidence Adversarial Training

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IEEE Transactions on Network Science and engineering 2025年

作者： Xu, Zhenghua Yang, Runhe Xu, Zihang Zhang, Shuo Yang, Yuchen Liu, Weipeng Xu, Weichao Chen, Junyang Lukasiewicz, Thomas Leung, Victor C. M. Hebei University of Technology State Key Laboratory of Reliability and Intelligence of Electrical Equipment School of Health Sciences and Biomedical Engineering Tianjin China The University of Hong Kong Department of Electrical and Electronic Engineering Hong Kong The Johns Hopkins University Department of Applied Mathematics and Statistic Baltimore United States Hebei University of Technology School of Artificial Intelligence Tianjin China Hebei Provincial Hospital of Traditional Chinese Medicine Digestive Disease Center Shijiazhuang China Shenzhen University College of Computer Science and Software Engineering Shenzhen China University of Oxford Department of Computer Science University of Oxford United Kingdom Department of Computer Science United Kingdom Vienna University of Technology institute of Logic and Computation nstitute of Logic and Computation Vienna Austria

Deep-learning-based semi-supervised learning (SSL) methods have achieved a strong performance in medical image segmentation, which can alleviate doctors' expensive annotation by utilizing a large amount of unlabeled data. Unlike most existing semi-supervised learning methods, adversarial training methods distinguish samples from different sources by learning the data distribution of the segmentation map, leading the segmenter to generate more accurate predictions. We argue that the current performance restrictions for such approaches are the problems of feature extraction and learning preferences. In this paper, we propose a new semi-supervised adversarial method called Patch Confidence Adversarial Training (PCA) for medical image segmentation. The PCA method's discriminator penalizes patch-level structures, guiding the generator to optimize different patch areas, by leveraging pixel context, the generator is driven to focus on high-frequency features, making it harder to deceive the discriminator and easy to converge to an ideal state, which more effectively guides the segmenter to generate high-quality pseudo-labels. Furthermore, at the discriminator's input, we supplement image information constraints, making it simpler to fit the expected data distribution. Extensive experiments on the Automated Cardiac Diagnosis Challenge (ACDC) 2017 dataset and the Brain Tumor Segmentation (BraTS) 2019 challenge dataset show that our method outperforms the state-of-the-art semi-supervised methods, which demonstrates its effectiveness for medical image segmentation. © 2025 IEEE. All rights reserved.

关键词： Adversarial machine learning

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On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them

arXiv

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arXiv 2024年

作者： Sroczynski, David W. Dietrich, Felix Koronaki, Eleni D. Talmon, Ronen Coifman, Ronald R. Bollt, Erik Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University PrincetonNJ United States School of Computation Information and Technology Technical University of Munich Munich Germany Faculty of Science Technology and Medicine University of Luxembourg Esch-sur-Alzette Luxembourg Viterbi Faculty of Electrical Engineering Technion Israel Institute of Technology Haifa Israel School of Engineering & Applied Science Yale University New HavenCT United States Electrical & Computer Engineering Clarkson University PotsdamNY United States Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Department of Urology Johns Hopkins University BaltimoreMD United States

Before we attempt to (approximately) learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of first deciding "the right quantities" to relate through such a function, and then proceeding to learn it. This is accomplished by first processing multiple simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: records of multiple observation processes of the system. We thus determine (a) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function);and (b) what information is unrelated to these common observables, and therefore particular to each observation process, and not contributing to the desired function. Any data-driven function approximation technique can subsequently be used to learn the input-output relation—from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular "twists" of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations from one process to entire level sets of measurements of the second process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures "now", while the second observation process measures "in the future", the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution. Copyright © 2024, The Authors. All rights reserved.

关键词： Nearest neighbor search

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Strong quantum entanglement based on two-mode photon-subtracted squeezed vacuum states

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Physical Review A 2023年第5期108卷 052420-052420页

作者： Hongbin Song Guofeng Zhang Hidehiro Yonezawa General Education Division and Shenzhen Key Laboratory of Semiconductor Lasers The Chinese University of Hong Kong Shenzhen Guang Dong 518116 China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon 999077 Hong Kong China and The Hong Kong Polytechnic University Shenzhen Research Institute Shenzhen Guang Dong 518057 China Centre for Quantum Computation and Communication Technology and School of Engineering and Information Technology The University of New South Wales Canberra ACT 2600 Australia

We present a strong quantum entanglement generation protocol based on two-mode photon-subtracted squeezed vacuum (TMPSSV) states. The generated entanglement shows higher entropy than those based on quantum catalysis, quantum scissors, photon-subtracted two-mode squeezed vacuum (PSTMSV) states, nonlocal PSTMSV states, and two-mode squeezed vacuum (TMSV) states in the ideal case. The impacts of experimental imperfections such as losses in the squeezed vacuum states and detection efficiency of single-photon detectors on the generated entanglement based on TMPSSV states are analyzed. When practical experimental imperfections are considered, higher logarithmic negativity than those of ideal PSTMSV states and ideal TMSV states are obtained for low initial squeezing level. Enhancement factor over 2 is obtained when the entanglement generated from imperfect non-Gaussian states passes through two lossy quantum channels in low initial squeezing level. Strong correlation is kept in lossy channels, which shows good robustness of the entanglement generation protocol based on TMPSSV states.

关键词： Entanglement production Quantum communication Quantum communication, protocols & technology Quantum correlations in quantum information Quantum protocols

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A phase-field model for non-small cell lung cancer under the effects of immunotherapy

arXiv

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arXiv 2023年

作者： Wagner, Andreas Schlicke, Pirmin Fritz, Marvin Kuttler, Christina Oden, J. Tinsley Schumann, Christian Wohlmuth, Barbara Computational Methods for PDEs Johann Radon Institute for Computational and Applied Mathematics Upper Austria Linz Austria School of Computation Information and Technology Technical University of Munich Bavaria Munich Germany Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX United States Clinic of Pneumology Thoracic Oncology Sleep and Respiratory Critical Care Klinikverbund Allgäu Bavaria Kempten Germany

Formulating tumor models that predict growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a simple Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simple nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. A single scalar value represents the immunotherapeutic agents in the entire lung, which decreases the proliferative cell concentration during therapy. An ordinary differential equation (ODE) model describes their evolution. Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to verify our model. For the reduced 1D model, we show that our model can qualitatively describe observations during immunotherapy by fitting our model parameters to existing patient data. Our model covers cases in which the immunotherapy is successful and limits the tumor size, as well as cases predicting a sudden relapse, leading to exponential tumor growth. We then move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we show the predictive benefits a more detailed patient-specific simulation including spatial information could yield in the future. © 2023, CC BY.

关键词： Nutrients

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Convergence, Consensus and Dissensus in the Weighted-Median Opinion Dynamics

arXiv

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arXiv 2022年

作者： Mei, Wenjun Hendrickx, Julien M. Chen, Ge Bullo, Francesco Dörfler, Florian The Department of Mechanics and Engineering Science Peking University China The Institute of Information and Communication Technologies Electronics and Applied Mathematics UCLouvain Belgium The Academy of Mathematics and Systems Science Chinese Academy of Sciences China The Center of Control Dynamical-Systems and Computation University of California Santa Barbara United States Automatic Control Laboratory ETH Zurich Switzerland

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any initial condition. Moreover, we prove a necessary and sufficient graph-theoretic condition for the almost-sure convergence to consensus, as well as a sufficient graph-theoretic condition for almost-sure persistent dissensus. It turns out that the weighted-median opinion dynamics, despite its simplicity in form, exhibit rich dynamical behavior that depends on some delicate network structures. To complement our sufficient conditions for almost-sure dissensus, we further prove that, given the influence network, determining whether the system almost surely achieves persistent dissensus is NP-hard, which reflects the complexity the network topology contributes to opinion *** Codes 93E03, 93A30, 91D30 Copyright © 2022, The Authors. All rights reserved.

关键词： Network topology

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Topology Optimization of Structures Using Higher Order Finite Elements in Analysis

Topology Optimization of Structures Using Higher Order Finit...

引用

International Conference on Modeling, Simulation and Optimization, CoMSO 2020

作者： Mukherjee, Sougata Lu, Dongcheng Dutta, Subhrajit Raghavan, Balaji Breitkopf, Piotr Xiao, Manyu Department of Civil Engineering National Institute of Technology Silchar Assam788010 India Xi’an Key Laboratory of Scientific Computation and Applied Statistics Department of Applied Mathematics School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710072 China Laboratoire de Genie Civil et Genie Mecanique EA 3913 Institut National des Sciences Appliquees de Rennes Rennes France Alliance Sorbonne Universites Universite de Technologie de Compiegne Laboratoire Roberval FRE UTC-CNRS 2012 Compiegne France

ISBN: (纸本)9789811598289

Topology optimization in general progresses with numerical instability i.e. checkerboard patterns if no filtering radius is used i.e. imposement of minimum length scale. Many studies are done in past decades to get rid of numerical instability or checkerboard pattern while optimizing the topology of mechanical structures. The proposed solution in this paper the structure is meshing structure twice (dual mesh) where first mesh defines the material distribution, and another mesh is utilized for computing the stress and displacement on an element which lets us to a stress-based refinement of mesh without modification of optimum design variables. Optimality criteria method is used for optimizing the design variable i.e. relative density over the domain. Another significance of this approach is that imposition minimum radius not needed to optimize design variables over the structural domain, instead the length scale is determined by the design mesh. A comparison is done between the topology obtained, compliance value and time taken after discretizing the structure with 4 noded element, 8 noded element and 9 noded quadrilateral element and a graph is also plotted to show the compliance value. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Topology

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