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

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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

Estimation of mask effectiveness perception for small domains using multiple data sources

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arXiv 2021年

作者： Sen, Aditi Lahiri, Partha Applied Mathematics & Statistics and Scientific Computation University of Maryland College Park United States The Joint Program in Survey Methodology Department of Mathematics University of Maryland College ParkMD20742 United States

All pandemics are local;so learning about the impacts of pandemics on public health and related societal issues at granular levels is of great interest. COVID-19 is affecting everyone in the globe and mask wearing is one of the few precautions against it. To quantify people's perception of mask effectiveness and to prevent the spread of COVID-19 for small areas, we use Understanding America Study's (UAS) survey data on COVID-19 as our primary data source. Our data analysis shows that direct survey-weighted estimates for small areas could be highly unreliable. In this paper, we develop a synthetic estimation method to estimate proportions of mask effectiveness for small area using a logistic model that combines information from multiple data sources. We select our working model using an extensive data analysis facilitated by a new variable selection criterion for survey data and benchmarking ratios. We propose a jackknife method to estimate variance of our proposed estimator. From our data analysis, it is evident that our proposed synthetic method outperforms direct survey-weighted estimator with respect to commonly used evaluation measures. Copyright © 2021, The Authors. All rights reserved.

关键词： Data handling

Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

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Physical Review X 2023年第1期13卷 011038-011038页

作者： Oliver H. E. Philcox Salvatore Torquato Department of Astrophysical Sciences Princeton University Princeton New Jersey 08540 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Center for Theoretical Physics Department of Physics Columbia University New York New York 10027 USA Simons Foundation New York New York 10010 USA Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l

关键词： Large scale structure of the Universe

UV stability of 1-loop radiative corrections in higher-derivative scalar field theory

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arXiv 2024年

作者： Abe, Yugo Inami, Takeo Izumi, Keisuke Department of Pure and Applied Physics Kansai University Suita564-8680 Japan iTHEMS Program RIKEN Wako351-0198 Japan Yukawa Institute for Theoretical Physics Kyoto University Kitashirakawa Oiwakecho Sakyo-ku Kyoto606-8502 Japan Department of Mathematics Nagoya University Nagoya464-8602 Japan Kobayashi-Maskawa Institute Nagoya University Nagoya464-8602 Japan

We consider the theory of a higher-derivative (HD) real scalar field φ coupled to a complex scalar σ, the coupling of the φ and σ being given by two types, λσφσ†σφ2 and ξσφσ†σ (∂µφ)2. We evaluate φ one-loop corrections δV (σ) to the effective potential of σ, both the contribution from the positive norm part of φ and that from the negative norm part (ghost). We show that δV (σcl) at σcl → ∞, where σcl is a classical value of σ, is positive, implying the stability of δV (σcl) by the HD 1-loop radiative corrections at high energy. Copyright © 2024, The Authors. All rights reserved.

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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

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arXiv 2024年

作者： Wang, Haina Samajdar, Rhine Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to typical liquids, i.e., the structure factor obeys the scaling relation S(k) ∼ Bkα with B, α > 0 in the limit k → 0. Ground-state d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this work, we systematically address these questions by deriving the analytical small-k behaviors (and associatedly, α and B) of the total and spin-resolved structure factors of quasi-1D, 2D, and 3D electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our work thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple fermionic systems and paves the way for harnessing the unique hyperuniform

关键词： Density of liquids

Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability

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arXiv 2024年

作者： Hitin-Bialus, Adam Maher, Charles Emmett Steinhardt, Paul J. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Jefferson Physical Laboratory Harvard University CambridgeMA02138 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α > 0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wavenumber k ≡ |k| in the vicinity of the origin, e.g., S(k) ∼ |k|α in cases where S(k) varies continuously with k as k → 0. In this paper, we show that the spreadability is an effective method for determining α for quasiperiodic systems where S(k) is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Torquato, Phys. Rev. E 104, 054102 (2021)] that, for media with finite α, the long-time behavior of the excess spreadability S(∞) − S(t) can be fit to a power law of the form ∼ t−(d−α)/2, where d is the space dimension, to accurately extract α for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density χ˜V (k) of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract α for the 1D limit-periodic period doubling chain (α = 1) and the 1D quasicrystalline Fibonacci chain (α = 3) to within 0.02% of the analytically known exact results. Moreover, we obtain a value of α = 5.97 ± 0.06 for the 2D Penrose tiling, which had not been computed previously, and present plausible theoretical arguments strongly suggesting that α is exactly equal to 6. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-k region of the scattering information used to compute the spreadability and obtain an accurate value of α, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests t

关键词： Spectral density

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

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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

Generalized nonbacktracking bounds on the influence in independent cascade models

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 1112-1147页

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Princeton NJ Department of Electrical Engineering Princeton University Princeton NJ Program in Applied and Computational Mathematics Princeton University Princeton NJ

This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit r-nonbacktracking walks and Fortuin--Kasteleyn--Ginibre (FKG) type inequalities, and are computed by message passing algorithms. Further, we provide parameterized versions of the bounds that control the trade-off between efficiency and accuracy. Finally, the tightness of the bounds is illustrated on various network models.

关键词： influence estimation nonbacktracking walk message passing social networks independent cascade model

Artificial neural network approach for turbulence models: A local framework

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Physical Review Fluids 2021年第8期6卷 084612-084612页

作者： Chenyue Xie Xiangming Xiong Jianchun Wang Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China

A local artificial neural network (LANN) framework is developed for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms are reconstructed by the artificial neural network based on the local coordinate system which is orthogonal to the curved walls. We verify the proposed model in the flows over periodic hills. The correlation coefficients of the RANS unclosed terms predicted by the LANN model can be made larger than 0.96 in an a priori analysis, and the relative error of the unclosed terms can be made smaller than 18%. In an a posteriori analysis, detailed comparisons are made on the results of RANS simulations using the LANN, global artificial neural network (GANN), Spalart-Allmaras (SA), and shear stress transport (SST) k−ω models. It is shown that the LANN model performs better than the GANN, SA, and SST k−ω models in the prediction of the average velocity, wall-shear stress, and average pressure, which gives the results that are essentially indistinguishable from the direct numerical simulation data. The LANN model trained at low Reynolds number, Re=2800, can be directly applied to the cases of high Reynolds numbers, Re=5600, 10 595, 19 000, and 37 000, with accurate predictions. Furthermore, the LANN model is verified for flows over periodic hills with varying slopes. These results suggest that the LANN framework has a great potential to be applied to complex turbulent flows with curved walls.

关键词： Compressible boundary layers Turbulence Artificial neural networks