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6th IFIP TC 12 International Conference on Intelligence Science, ICIS 2024

作者： Chen, Ran Liu, Muhan Ma, Jinwen Department of Information and Computational Sciences School of Mathematical Sciences Peking University Beijing100871 China Department of Applied Mathematics China Agricultural University Beijing100083 China

ISBN: (纸本)9783031712524

Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for solving regression problems. Least Squares Support Vector Regression (LSSVR) has advantages in computing speed but can be prone to overfitting due to its sensitivity to noise and outliers. Additionally, Twin Support Vector Regression (TSVR) shows insufficient flexibility when dealing with large-scale data, and its robustness to noise could be improved. In response to these problems, this paper proposes an innovative solution: Twin Bounded Least Squares Support Vector Regression (TBLSSVR). This model combines the advantages of LSSVR and TSVR and introduces regularization terms to mitigate their limitations effectively. The regularization term helps minimize structural risk, reflecting the advantages of statistical learning theory and ensuring the stability of the solution. Experimental results demonstrate that TBLSSVR improves regression accuracy and significantly accelerates the solution speed, providing new directions and methods for future technology development. © IFIP International Federation for Information Processing 2025.

关键词： Vectors

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Numerical modeling of the ion-acoustic solitary waves arising in nonlinear dispersive system

Numerical modeling of the ion-acoustic solitary waves arisin...

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作者： Nikan, Omid Yang, Yin Avazzadeh, Zakieh School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Hunan Xiangtan411105 China Department of Mathematical Sciences University of South Africa Florida South Africa

This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains the water wave phenomena in nonlinear dispersive system. The solution of the ZK-BBME is discretized by using hybridization of the finite difference and localized radial basis function based on partition of unity method. The association of this hybridization leads to a meshless method and it does not requires any linearization. In the initial step, the PDE is converted into a nonlinear ODE system by making use of radial kernels. In the next step, the obtained nonlinear ODE system is solved based on an ODE solver of high order. The global collocation technique imposes a large computational cost because a dense algebraic system must be calculated. This proposed strategy is based on decomposing the initial domain into a number of sub-domains using kernel approximation on each sub-domain. Three numerical examples are illustrated to clarify the efficiency and accuracy of the proposed strategy. © 2023 John Wiley & Sons, Ltd.

关键词： Water waves

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Lawvere’s Frobenius Reciprocity, the Modular Connections of Grandis and Dilworth’s Abstract Principal Ideals

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applied Categorical Structures 2025年第3期33卷 1-8页

作者： Goswami, Amartya Janelidze, Zurab Manuell, Graham Department of Mathematics and Applied Mathematics University of Johannesburg Johannesburg South Africa National Institute for Theoretical and Computational Sciences (NITheCS) Stellenbosch South Africa Mathematics Division Department of Mathematical Sciences Stellenbosch University Stellenbosch South Africa

The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem.

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Accuracy Versus Predominance: Reassessing the Validity of the Quasi-Steady-State Approximation

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Bulletin of mathematical Biology 2025年第6期87卷 1-32页

作者： Srivastava, Kashvi Eilertsen, Justin Booth, Victoria Schnell, Santiago Department of Mathematics University of Michigan Ann Arbor USA Mathematical Reviews American Mathematical Society Ann Arbor USA Department of Biological Sciences and Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame USA

The application of the standard quasi-steady-state approximation to the Michaelis-Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, $$e_0$$ , to the Michaelis constant, $$K_M$$ , decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation as compared to other quasi-steady-state reductions in its proximity. Using standard tools from the analysis of ordinary differential equations, we show that while $$e_0/K_M$$ provides an indication of the standard quasi-steady-state approximation’s asymptotic accuracy, the standard quasi-steady-state approximation’s predominance relies on a small ratio of $$e_0$$ to the Van Slyke-Cullen constant, K. Here, we define the predominance of a quasi-steady-state reduction when it offers the highest approximation accuracy among other well-known reductions with overlapping validity conditions. We conclude that the magnitude of $$e_0/K$$ offers the most accurate measure of the validity of the standard quasi-steady-state approximation.

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Correction: Evaluation of beta integrals of Ramanujan type and integral representations for bilateral hypergeometric series

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The Ramanujan Journal 2025年第3期67卷 1-2页

作者： Cohl, Howard S. Volkmer, Hans Applied and Computational Mathematics Division National Institute of Standards and Technology Mission Viejo USA Department of Mathematical Sciences University of Wisconsin–Milwaukee Milwaukee USA

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Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

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Physical Review B 2025年第9期111卷 094113-094113页

作者： Pinchen Xie Yixiao Chen Weinan E Roberto Car Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA AI for Science Institute Beijing China and Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

关键词： Ferroelectricity

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THE NO-UNDERRUN SAMPLER: A LOCALLY ADAPTIVE, GRADIENT-FREE MCMC METHOD

arXiv

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arXiv 2025年

作者： Bou-Rabee, Nawaf Carpenter, Bob Liu, Sifan Oberdörster, Stefan Department of Mathematical Sciences Rutgers University United States Center for Computational Mathematics Flatiron Institute United States Institute for Applied Mathematics University of Bonn Germany

In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal’s funnel, a challenging multi-scale distribution from Bayesian hierarchical *** Codes 60J05, 65C05 Copyright © 2025, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Synergetic effects of multiple junction and surface hydroxyl in Cu/CuO/Cu2O/TiO2 heterostructures towards highly efficient photocatalysts for hydrogen generation

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Materials Science for Energy Technologies 2025年 8卷 131-142页

作者： Subagyo, Riki Anindika, Garcelina Rizky Aufkani, Afif Akmal Zhang, Lei Ardhyananta, Hosta Burhan, R.Y. Perry Nugraheni, Zjahra Vianita Akhlus, Syafsir Bahruji, Hasliza Prasetyoko, Didik Wellia, Diana Vanda Ivansyah, Atthar Luqman Arramel Kusumawati, Yuly Department of Chemistry Faculty of Science and Analytic Data Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Center of Excellence Applied Physics and Chemistry Nano Center Indonesia Jl PUSPIPTEK South Tangerang Banten15314 Indonesia Department of Physics National University of Singapore Singapore117551 Singapore Department of Materials and Metallurgical Engineering Faculty of Industrial Technology and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Centre of Advanced Material and Energy Science Universiti Brunei Darussalam Jalan Tungku Link BE 1410 Brunei Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Andalas Padang25163 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Science Institut Teknologi Bandung Jalan Ganesha No. 10 Bandung40132 Indonesia Instrumentation and Computational Physics Research Group Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesha No.10 West Java Bandung40132 Indonesia

The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide band gap of a photo-sensitive material of TiO2 are detrimental toward the targeted catalytical reaction. In this study, we present the rational design, fabrication, photocatalytic performance of TiO2-Cu/CuO/Cu2O heterostructures (CuTi) using viable chemical reduction method. The Z-scheme and S-scheme are succesfully generated across the TiO2/CuO/Cu2O interfaces, while the Schottky junction arises on the Cu perimeters. This is evidenced from the blue shifted about 0.3 eV of Cu 2p core level determined by using X-ray photoemission spectroscopy (XPS), in combination with the formation of inverse V-shape of the Mott-Schottky plots. In addition, we find that Cu/CuO/Cu2O facilitates photon absorption range up to the visible region. The multiple heterojunction and the large number of OHsurface enhanced charge carrier transfer are associated to the suppression of photoluminescence (PL) intensity, high surface hydroxyl (OHsurface) density in CuTi probed by XPS, and fast electron transfer based on the electrochemical measurements. The presence of OHsurface inhibits the recombination of electron. A significant H2 photogeneration rate enhancement is achieved when an optimized 5 wt% Cu/CuO/Cu2O concentration is used on TiO2 to achieve 7,157.19 μmol·g−1 (1,789.30 μmol·g−1·h−1). Based on this finding, zero emission energy innitiative could be materialized under multiple heterojunctions in photocatalytic process is beneficial for enhancing the H2 production. © 2025 The Authors

关键词： Titanium dioxide

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CONVERGENCE OF DISCONTINUOUS GALERKIN METHODS FOR QUASICONVEX AND RELAXED VARIATIONAL PROBLEMS

arXiv

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arXiv 2025年

作者： Grekas, Georgios Koumatos, Konstantinos Makridakis, Charalambo Vikelis, Andreas Computer Electrical Mathematical Sciences and Engineering Division KAUST Saudi Arabia Department of Mathematics University of Sussex United Kingdom Institute of Applied & Computational Mathematics Foundation for Research & Technology-Hellas Greece Department of Mathematics and Applied Mathematics University of Crete Greece Faculty of Civil Engineering Czech Technical University of Prague Czech Republic

In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential flexibility by removing inter-element continuity while also guaranteeing convergent approximations in the quasiconvex case. Notably, quasiconvexity is the weakest form of convexity pertinent to elasticity. Furthermore, we show that in the non-convex case discrete minimisers converge to minimisers of the relaxed problem. In this case, the minimisation problem corresponds to the energy defined by the quasiconvex envelope of the original energy. Our approach covers all discontinuous Galerkin formulations known to converge for convex energies. This work addresses an open challenge in the vectorial calculus of variations: developing and rigorously justifying numerical schemes capable of reliably approximating nonlinear energy minimization problems with potentially singular solutions, which are frequently encountered in materials science. © 2025, CC BY.

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Quantum Circuit for Non-Unitary Linear Transformation of Basis Sets

arXiv

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arXiv 2025年

作者： Zhu, Guorui Bierman, Joel Lu, Jianfeng Li, Yingzhou School of Mathematical Sciences Fudan University China Electrical and Computer Engineering North Carolina State University United States Department of Mathematics Department of Physics Department of Chemistry Duke University United States School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Key Laboratory of Computational Physical Sciences Ministry of Education China

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition (SVD) into the process, the method achieves an operational depth of O(n) with about n ancilla qubits, enhancing the computational capabilities for analyzing fermionic systems. The non-unitarity of the transformation allows us to transform a wave function from one basis to another, which can span different spaces. By this trick, we can calculate the overlap of two wavefunctions that live in different (but non-distinct Hilbert subspaces) with different basis representations. This provides the opportunity to use state specific ansatzes to calculate different energy eigenstates under orbital-optimized settings and may improve the accuracy when computing the energies of multiple eigenstates simultaneously in VQE or other framework. It allows for a deeper exploration of complex quantum states and phenomena, expanding the practical applications of quantum computing in physics and chemistry. © 2025, CC BY.

关键词： Wave functions

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