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arXiv 2025年

作者： Hwang, Chi-Chuan Su, Cheng-Fang Yang, Jung-Fan Department of Engineering Science National Cheng Kung University Tainan City701 Taiwan Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan Undergraduate Degree Program of Systems Engineering and Technology National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan Chung Cheng Institute of Technology National Defense University Taoyuan City33551 Taiwan

We present a hybrid quantum-classical computational framework for simulating relativistic quantum chemical systems using the variational quantum eigensolver (VQE). Our approach integrates relativistic electron integrals derived from the Dirac–Coulomb Hamiltonian with quantum circuit models constructed via Jordan–Wigner transformation. By employing both heuristic and chemistry-inspired ansätze, we compute ground-state energies and potential energy surfaces (PES) for benchmark molecules including H2, H2O, and H2S. Active-space reduction and Hartree–Fock embedding techniques are used to minimize the number of qubits and Pauli terms, enabling efficient simulation on near-term quantum devices. Our results demonstrate that VQE can reproduce classical full-configuration-interaction energies with millihartree-level accuracy, even under relativistic Hamiltonians. We observe consistent relativistic energy shifts and orbital contraction effects, particularly for the sulfur-containing H2S molecule. The constructed PES allow for equilibrium geometry prediction and activation energy analysis. This work highlights the feasibility and scalability of applying quantum algorithms to relativistic electronic structure problems, paving the way for future simulations of heavier-element systems in quantum chemistry. Copyright © 2025, The Authors. All rights reserved.

关键词： Molecular orbitals

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Comparative Analysis of Quantum Support Vector Machines and Variational Quantum Classifiers for B-cell Epitope Prediction in Vaccine Design

arXiv

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arXiv 2025年

作者： Hwang, Chi-Chuan Su, Cheng-Fang Hong, Yi-Ang Department of Engineering Science National Cheng Kung University Tainan City701 Taiwan Department of Applied Mathematics National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan Undergraduate Degree Program of Systems Engineering and Technology National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan Chung Cheng Institute of Technology National Defense University Taoyuan City33551 Taiwan

Quantum computing offers new opportunities for addressing complex classification tasks in biomedical applications. This study investigates two quantum machine learning models-the Quantum Support Vector Machine (QSVM) and the Variational Quantum Classifier (VQC)-in the context of B-cell epitope prediction, a key step in modern vaccine design. QSVM builds upon the classical SVM framework by using quantum circuits to encode nonlinear kernel computations, while VQC replaces the entire classification pipeline with trainable quantum circuits optimized variationally. A benchmark dataset from the Immune Epitope Database (IEDB) is used for model evaluation. Each epitope is represented by 10 physicochemical features, and dimensionality reduction via Principal Component Analysis (PCA) is applied to assess model performance across different feature spaces. We also examine the effect of sample size on prediction outcomes. Experimental results show that QSVM performs well under limited data conditions, while VQC achieves higher accuracy in larger datasets. These findings highlight the potential of quantum-enhanced models for bioinformatics tasks, particularly in supporting efficient and scalable epitope-based vaccine development. Copyright © 2025, The Authors. All rights reserved.

关键词： Epitopes

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Variable fidelity differential-algebraic equation model correlation

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MECHANICS OF STRUCTURES AND MACHINES 1997年第1期25卷 61-85页

作者： Haug, EJ Coroian, DI Serban, R [a] DEPARTMENT OF MECHANICAL ENGINEERING AND PROGRAM IN APPLIED MATHEMATICS THE UNIVERSITY OF IOWA IOWA CITY IOWA U.S.A

A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower fidelity model that is also governed by differential-algebraic equations of motion. An adjoint variable method for computing sensitivity of the error measure defined is derived and implemented in a nonlinear programming formulation that is suitable for iterative minimization of the error functional. A numerical example using a multibody mechanism is presented to demonstrate effectiveness of the method and provide insights into means for effectively formulating problems of model correlation and strategies for their solution.

关键词： Dynamics

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Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

arXiv

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arXiv 2025年

作者： Wei, Lu Jia, Zhian Wang, Yufeng Kaszlikowski, Dagomir Ling, Haibin Department of Applied Mathematics & Statistics Stony Brook University Stony BrookNY11794 United States Program of Data Science Stony Brook University Stony BrookNY11794 United States Centre for Quantum Technologies National University of Singapore SG 117543 Singapore Department of Physics National University of Singapore SG 117543 Singapore Department of Computer Science Stony Brook University Stony BrookNY11794 United States

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the transformer density operator ansatz for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state’s coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting steady states. © 2025, CC BY.

关键词： Hilbert spaces

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Harmonic analytic geometry on subsets in high dimensions - Empirical models

Harmonic analytic geometry on subsets in high dimensions - E...

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2018 International Congress of Mathematicians, ICM 2018

作者： Coifman, Ronald R. Department of Mathematics Program in Applied Mathematics Yale University United States

ISBN: (纸本)9789813272903

We describe a recent evolution of Harmonic Analysis to generate analytic tools for the joint organization of the geometry of subsets of Rn and the analysis of functions and operators on the subsets. In this analysis we establish a duality between the geometry of functions and the geometry of the space. The methods are used to automate various analytic organizations, as well as to enable informative data analysis. These tools extend to higher order tensors, to combine dynamic analysis of changing structures. In particular we view these tools as necessary to enable automated empirical modeling, in which the goal is to model dynamics in nature, ab initio, through observations alone. We will illustrate recent developments in which physical models can be discovered and modelled directly from observations, in which the conventional Newtonian differential equations, are replaced by observed geometric data constraints. This work represents an extended global collaboration including, recently, A. Averbuch, A. Singer, Y. Kevrekidis, R. Talmon, M. Gavish, W. Leeb, J. Ankenman, G. Mishne and many more. © ICM *** rights reserved.

关键词： Geometry

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Quantifying control measures for lumpy skin disease in cattle using a vector–host transmission model

Results in Control and Optimization

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Results in Control and Optimization 2025年 19卷

作者： Prathumwan, Din Numpanviwat, Nattakarn Trachoo, Kamonchat Chuchard, Pearanat Chaiya, Inthira Department of Mathematics Faculty of Science Khon Kaen University Khon Kean 40002 Thailand Applied Mathematics Program Faculty of Science and Technology Valaya Alongkorn Rajabhat University under the Royal Patronage Pathum Thani 13180 Thailand Department of Mathematics Faculty of Science Mahasarakham University Mahasarakham 44150 Thailand Department of Mathematics Faculty of Science Ramkhamhaeng University Bangkok 10240 Thailand

Purpose: This study aims to develop a mathematical model to understand and control the spread of lumpy skin disease in cattle populations, incorporating blood-sucking insects as vectors. Research Question: How can the interaction between cattle and vectors be effectively modeled to assess the impact of control strategies such as quarantine and treatment on the transmission of lumpy skin disease? Methodology: The population dynamics are modeled using the SLIQR-SL framework, categorizing cattle into six disease states and vectors into two states. Stability analysis is performed to identify equilibrium points, and the basic reproduction number (R₀) is calculated to evaluate disease persistence or eradication conditions. Numerical simulations are conducted to assess various control strategies. Validation: The model's predictions are validated through numerical examples, demonstrating its ability to replicate observed transmission patterns and evaluate control measures. Results: The analysis reveals that when R₀<1, lumpy skin disease can be eradicated, but when R₀>1, the disease persists. Numerical simulations highlight the critical role of quarantine and treatment in significantly reducing disease prevalence. Significance: The findings provide actionable insights for policymakers and veterinarians, emphasizing the importance of integrated control strategies in mitigating lumpy skin disease outbreaks and minimizing economic losses. © 2025 The Authors

关键词： Basic reproduction number Cattle population dynamics Compartmental model Control strategies Equilibrium analysis Lumpy skin disease Vector-borne transmission

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A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms 2

A Qualitative Study of the Dynamic Behavior for Adaptive Gra...

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2nd Mathematical and Scientific Machine Learning Conference, MSML 2021

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Stanford University United States Program in Applied and Computational Mathematics Princeton University United States Program in Applied and Computational Mathematics Department of Mathematics Princeton University United States

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial convergence, oscillations, and large spikes in the late phase. The sign gradient descent (signGD) flow, which is the limit of Adam when taking the learning rate to 0 while keeping the momentum parameters fixed, is used to explain the fast initial convergence. For the late phase of Adam, three different types of qualitative patterns are observed depending on the choice of the hyper-parameters: oscillations, spikes, and divergence. In particular, Adam converges much smoother and even faster when the values of the two momentum factors are close to each other. This observation is particularly important for scientific computing tasks, for which the training process usually proceeds into the high precision regime. © 2021 C. Ma, L. Wu & W. E.

关键词： Gradient methods

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Modeling Neural Activity with Conditionally Linear Dynamical Systems

arXiv

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arXiv 2025年

作者： Geadah, Victor Nejatbakhsh, Amin Lipshutz, David Pillow, Jonathan W. Williams, Alex H. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Center for Computational Neuroscience Flatiron Institute New York CityNY United States Department of Neuroscience Baylor College of Medicine HoustonTX United States Princeton Neuroscience Institute PrincetonNJ United States Center for Neural Science New York University New York CityNY United States

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task. © 2025, CC BY.

关键词： Neurons

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Preservation of Stochastic Orderings under Random Mapping by Point Processes

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Probability in the Engineering and Informational Sciences 1995年第4期9卷 563-580页

作者： Shaked, Moshe Wong, Tityik Department of Mathematics University of Arizona TucsonAZ85721 United States Applied Mathematics Program University of Arizona TucsonAZ85721 United States

Let N = [N(t), t ≥ 0] be a point process, and let T1 and T2 be two positive random variables that are independent of N. Define Mk = N(Tk), k = 1,2. In this paper we study conditions on the process N under which some stochastic orders between T1 and T2 are transformed into stochastic orders between M1 and M2. In some cases the converses are also shown to be true. Some applications and examples are given. Copyright © Cambridge University Press 1995.

关键词： Probability

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Overview of the Head and Neck Tumor Segmentation for Magnetic Resonance Guided Applications (HNTS-MRG) 2024 Challenge 1st

Overview of the Head and Neck Tumor Segmentation for Magneti...

引用

1st Challenge on Head and Neck Tumor Segmentation for MRI-Guided Applications, HNTS-MRG 2024, Held in Conjunction with 27th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2024

作者： Wahid, Kareem A. Dede, Cem El-Habashy, Dina M. Kamel, Serageldin Rooney, Michael K. Khamis, Yomna Abdelaal, Moamen R. A. Ahmed, Sara Corrigan, Kelsey L. Chang, Enoch Dudzinski, Stephanie O. Salzillo, Travis C. McDonald, Brigid A. Mulder, Samuel L. McCullum, Lucas Alakayleh, Qusai Sjogreen, Carlos He, Renjie Mohamed, Abdallah S. R. Lai, Stephen Y. Christodouleas, John P. Schaefer, Andrew J. Naser, Mohamed A. Fuller, Clifton D. Department of Radiation Oncology The University of Texas MD Anderson Cancer HoustonTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer HoustonTX United States Transitional Year Program Corewell Health Wiliam Beaumont Royal OakMI United States Department of Radiation Oncology University of Maryland School of Medicine BaltimoreMD United States Department of Clinical Oncology and Nuclear Medicine Faculty of Medicine Alexandria University Alexandria Egypt UT MD Anderson Cancer CenterUTHealth Houston Graduate School of Biomedical Sciences Houston United States Department of Radiation Oncology Baylor College of Medicine HoustonTX United States Department of Head and Neck Surgery The University of Texas MD Anderson Cancer HoustonTX United States Elekta AtlantaGA United States Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States

ISBN: (纸本)9783031832734

Magnetic resonance (MR)-guided radiation therapy (RT) is enhanc- ing head and neck cancer (HNC) treatment through superior soft tissue con- trast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)- driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto- segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2- weighted scans. The challenge provided 150 HNC cases for training and 50 for final testing hosted on *** using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Simi- larity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver vari- ability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC. © The Author(s) 2025.

关键词： Deep learning

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