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Curve Classification Based onMean-Variance Feature Weighting and Its Application

Computers, Materials & Continua 2024年第5期79卷 2465-2480页

作者： Zewen Zhang Sheng Zhou Chunzheng Cao School of mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing210044China center for applied mathematics of Jiangsu Province Nanjing University of Information Science and TechnologyNanjing210044China

The classification of functional data has drawn much attention in recent years.The main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification accuracy.In this paper,we propose a mean-variance-based(MV)feature weighting method for classifying functional data or functional curves.In the feature extraction stage,each sample curve is approximated by B-splines to transfer features to the coefficients of the spline basis.After that,a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the coefficients.We also introduce a scaling parameter to adjust the gap between the weights of features.The new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing features.The algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both provided.Moreover,the new approach can be well integrated into existing functional data classifiers,such as the generalized functional linear model and functional linear discriminant analysis,resulting in a more accurate classification.The performance of the mean-variance-based classifiers is evaluated by simulation studies and real data.The results show that the newfeatureweighting approach significantly improves the classification accuracy for complex functional data.

关键词： Functional data analysis classification feature weighting B-splines

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Vanishing Viscosity Limits of a Chemotaxis-Navier-Stokes Model

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Acta Mathematicae Applicatae Sinica 2024年

作者： Ji-shan FAN Fu-cai LI Department of mathematics Nanjing University Department of applied mathematics Nanjing Forestry University

In this paper we prove vanishing viscosity limits of a coupled chemotaxis-fluid model in a bounded domain ??R3. The proof is based on the Banach’s fixed point theorem and the Lp-energy method. In addition,the L∞-est...

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Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

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Chinese Physics Letters 2024年第1期41卷 68-76页

作者：刘通夏旭 Department of applied Physics School of ScienceNanjing University of Posts and TelecommunicationsNanjing 210003China Academy of mathematics and System Sciences Chinese Academy of SciencesBeijing 100190China

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research interests.However,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical state.We propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier transform.With this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical states.Then,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state.Due to computational complexity,calculations are not performed for higher dimensional models.However,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal.Finally,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

关键词： state exponent critical

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Construction of conservation laws for the Gardner equation, Landau–Ginzburg–Higgs equation, and Hirota–Satsuma equation

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Communications in Theoretical Physics 2024年第5期76卷 51-59页

作者： Cheng Chen Faiza Afzal Yufeng Zhang School of mathematics China University of Mining and Technology Jiangsu center for applied mathematics (CUMT)

In this paper, two different methods for calculating the conservation laws are used, these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods, we obtain the conservation laws of the Gardner equation, Landau–Ginzburg–Higgs equation and Hirota–Satsuma equation, respectively.

关键词： conservation laws Gardner equation Hirota-Satsuma equation Landau-Ginzburg-Higgs equation

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Oscillatory Dynamics of Heterogeneous Stem Cell Regeneration

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Communications on applied mathematics and Computation 2024年第1期6卷 431-453页

作者： Xiyin Liang Jinzhi Lei School of Mathematical Sciences Center for Applied MathematicsTiangong UniversityTianjin300387China

Stem cell regeneration is an essential biological process in the maintenance of tissue homeostasis;dysregulation of stem cell regeneration may result in dynamic diseases that show oscillations in cell numbers.Cell heterogeneity and plasticity are necessary for the dynamic equilibrium of tissue homeostasis;however,how these features may affect the oscillatory dynamics of the stem cell regeneration process remains poorly understood.Here,based on a mathematical model of heterogeneous stem cell regeneration that includes cell heterogeneity and random transition of epigenetic states,we study the conditions to have oscillation solutions through bifurcation analysis and numerical simulations.Our results show various model system dynamics with changes in different parameters associated with kinetic rates,cellular heterogeneity,and plasticity.We show that introducing heterogeneity and plasticity to cells can result in oscillation dynamics,as we have seen in the homogeneous stem cell regeneration system.However,increasing the cell heterogeneity and plasticity intends to maintain tissue homeostasis under certain conditions.The current study is an initiatory investigation of how cell heterogeneity and plasticity may affect stem cell regeneration dynamics,and many questions remain to be further studied both biologically and mathematically.

关键词： Stem cell regeneration Heterogenous Hopf bifurcation Hematopoietic dynamical disease

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Revealing excited states of rotational Bose-Einstein condensates

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The Innovation 2024年第1期5卷 41-48页

作者： Jianyuan Yin Zhen Huang Yongyong Cai Qiang Du Lei Zhang School of Mathematical Sciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China Department of mathematics National University of SingaporeSingapore 119076Singapore Department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of applied Physics and applied mathematics and Data Science Institute Columbia UniversityNew YorkNY 10027USA Beijing International center for Mathematical Research Center for Quantitative BiologyCenter for Machine Learning ResearchPeking UniversityBeijing 100871China

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional.Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method.Four excitation mechanisms are identified:vortex addition,rearrangement,merging,and splitting.We demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.

关键词： method rotational excited

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Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

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Chinese Physics B 2024年第5期33卷 480-487页

作者：张树甜刘世鲲矫滕菲孙敏胡凤兰黄德财 Department of applied Physics Nanjing University of Science and TechnologyNanjing 210094China

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain(a nonintegrable system)and compares the simulation results with the theoretical results in fluid(an integrable system).Three stages(the pre-in-phase traveling stage,the central-collision stage,and the post-in-phase traveling stage)are identified to describe the nonlinear interaction processes in the granular chain.The nonlinear scattering effect occurs in the central-collision stage,which decreases the amplitude of the incident solitary waves.Compared with the leading-time phase in the incident and separation collision processes,the lagging-time phase in the separation collision process is smaller.This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage.We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain.The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude.The results are reversed in the fluid.An increase in solitary wave amplitude leads to decreased attachment,detachment,and residence times for granular chains and fluid.For the immediate time-phase shift,leading and lagging phenomena appear in the granular chain and the fluid,respectively.These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

关键词： integrable system nonintegrable system granular chain solitary wave

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Boosting Adversarial Training with Learnable Distribution

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Computers, Materials & Continua 2024年第3期78卷 3247-3265页

作者： Kai Chen Jinwei Wang James Msughter Adeke Guangjie Liu Yuewei Dai School of Electronics and Information Engineering Nanjing University of Information Science and TechnologyNanjing210044China Key Laboratory of Intelligent Support Technology for Complex Environments Ministry of EducationNanjing210044China School of Computer and Software Nanjing University of Information Science and TechnologyNanjing210044China Nanjing Center for Applied Mathematics Nanjing211135China

In recent years,various adversarial defense methods have been proposed to improve the robustness of deep neural networks.Adversarial training is one of the most potent methods to defend against adversarial attacks.However,the difference in the feature space between natural and adversarial examples hinders the accuracy and robustness of the model in adversarial training.This paper proposes a learnable distribution adversarial training method,aiming to construct the same distribution for training data utilizing the Gaussian mixture model.The distribution centroid is built to classify samples and constrain the distribution of the sample features.The natural and adversarial examples are pushed to the same distribution centroid to improve the accuracy and robustness of the model.The proposed method generates adversarial examples to close the distribution gap between the natural and adversarial examples through an attack algorithm explicitly designed for adversarial training.This algorithm gradually increases the accuracy and robustness of the model by scaling perturbation.Finally,the proposed method outputs the predicted labels and the distance between the sample and the distribution centroid.The distribution characteristics of the samples can be utilized to detect adversarial cases that can potentially evade the model defense.The effectiveness of the proposed method is demonstrated through comprehensive experiments.

关键词： Adversarial training feature space learnable distribution distribution centroid

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Empirical likelihood for spatial cross-sectional data models with matrix exponential spatial specification

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applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 125-139页

作者： LIU Yan RONG Jian-rong QIN Yong-song Nanning University Nanning 530200China center for applied mathematics of Guangxi and College of mathematics and Statistics Guangxi Normal UniversityGuilin 541004China

In this paper,we study spatial cross-sectional data models in the form of matrix exponential spatial specification(MESS),where MESS appears in both dependent and error terms.The empirical likelihood(EL)ratio statistics are established for the parameters of the MESS model.It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions,which are used to construct the confidence regions of model parameters.Simulation experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method.

关键词： MESS empirical likelihood con dence region

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Weak type(1, 1) of the Riesz transform on some direct product manifolds with exponential volume growth

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Science China mathematics 2024年第7期67卷 1599-1622页

作者： Hong-Quan Li Jie-Xiang Zhu 1.School of Mathematical Sciences, Fudan University 2.center for applied mathematics, Tianjin University School of Mathematical Sciences Fudan University center for applied mathematics Tianjin University

In this paper, we are concerned with the Riesz transform on the direct product manifold H~n× M,where H~n is the n-dimensional real hyperbolic space, and M is a connected complete non-compact Riemannian manifold satisfying the volume doubling property and generalized Gaussian or sub-Gaussian upper estimates for the heat kernel. We establish its weak type（1, 1） property. In addition, we obtain the weak type（1, 1） of the heat maximal operator in the same setting. Our arguments also work for a large class of direct product manifolds with exponential volume growth. Particularly, we provide a simpler proof of weak type（1, 1） boundedness of some operators considered in the work of Li et al.（2016）.

关键词： Riesz transform heat kernel direct product real hyperbolic space 42B20 58J35

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