作者：
He, Ying;Wang, Yan;Yang, Jerry Zhijian;Yin, Hongshuang
期刊：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2024年14(1):79-103 ISSN：2079-7362
通讯作者：
Wang, Y
作者机构：
[Yang, Jerry Zhijian; Yin, Hongshuang; He, Ying] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[He, Ying] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Global Science Press;EAJAM;East Asian Journal on Applied Mathematics;Nonlinear Dirac equation;uniformly accurate;finite difference method;time-splitting method;exponential integrator.
摘要：
Numerical methods for the nonlinear Dirac equation (NDE) in the massless nonrelativistic regime are considered. In this regime, the equation contains a small dimensionless parameter $0 <\varepsilon≤ 1,$ and its solution is highly oscillatory in time. We present and analyze traditional numerical schemes for the NDE, including finite difference methods, time-splitting methods and exponential integrators. Error analysis indicates that all these methods require an $\varepsilon$-dependent time-step size to achieve an optimal convergence order. Utilizing an operator splitting technique, we propose a uniformly accurate (UA) scheme. The scheme enables first-order convergence in time for all $\varepsilon ∈ (0, 1]$ without restrictions on time-step size. Error estimates for the UA scheme are rigorously established and numerical results confirm the properties of the method.
期刊：
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS,2023年27(6):3061-3071 ISSN：2168-2194
通讯作者：
Zhao, Weizhong;Shen, XJ
作者机构：
[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;[Sun, Han] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, WZ; Shen, XJ ] C;Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
关键词：
graph representation learning;heterogeneous information network;multi-head attention mechanism;Phage-host interactions prediction
摘要：
In the treatment of bacterial infectious diseases, overuse of antibiotics may lead to not only bacterial resistance to antibiotics but also dysbiosis of beneficial bacteria which are essential for maintaining normal human life activities. Instead, phage therapy, which invades and lyses specific pathogenic bacteria without affecting beneficial bacteria, becomes more and more popular to treat bacterial infectious diseases. For the effective phage therapy, it requires to accurately predict potential phage-host interactions from heterogeneous information network consisting of bacteria and phages. Although many models have been proposed for predicting phage-host interactions, most methods fail to consider fully the sparsity and unconnectedness of phage-host heterogeneous information network, deriving the undesirable performance on phage-host interactions prediction. To address the challenge, we propose an effective model called GERMAN-PHI for predicting Phage-Host Interactions via Graph Embedding Representation learning with Multi-head Attention mechaNism. In GERMAN-PHI, the multi-head attention mechanism is utilized to learn representations of phages and hosts from multiple perspectives of phage-host associations, addressing the sparsity and unconnectedness in phage-host heterogeneous information network. More specifically, a module of GAT with talking-heads is employed to learn representations of phages and bacteria, on which neural induction matrix completion is conducted to reconstruct the phage-host association matrix. Results of comprehensive experiments demonstrate that GERMAN-PHI performs better than the state-of-the-art methods on phage-host interactions prediction. In addition, results of case study for two high-risk human pathogens show that GERMAN-PHI can predict validated phages with high accuracy, and some potential or new associated phages are provided as well.
期刊：
MATHEMATICS OF COMPUTATION,2022年91(337):2215-2245 ISSN：0025-5718
通讯作者：
Wang, Y.
作者机构：
[WANG, Y. A. N.] CENT CHINA NORMAL UNIV, SCH MATH & STAT, Wuhan 430079, Peoples R China.;[WANG, Y. A. N.] CENT CHINA NORMAL UNIV, HUBEI KEY LAB MATH SCI, Wuhan 430079, Peoples R China.;[ZHAO, X. I. A. O. F. E. I.] WUHAN UNIV, SCH MATH & STAT & COMPUTAT SCI, HUBEI KEY LAB, Wuhan 430072, Peoples R China.
通讯机构：
School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
作者机构：
[Cai, Yongyong] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
摘要：
We propose a class of efficient and uniformly accurate nested Picard iterative integrators (NPI) for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime, and apply it to study the convergence rates of the NLDE to its limiting models, the dynamics of traveling waves, and the two-dimensional dynamics. The NLDE involves a dimensionless parameter epsilon is an element of (0, 1], and its solution is highly oscillatory in time with wavelength O(epsilon(2)) in the nonrelativistic regime. To gain uniform accuracies in time, the NPI method employs an operator decomposition technique for explicitly separating the highly oscillatory phases and utilizes exponential wave integrators for the time integrals. Moreover, with the help of nested Picard iterations, the NPI method could easily achieve uniform first- and second-order accuracies.
期刊：
Calculus of Variations and Partial Differential Equations,2022年61(6):1-18 ISSN：0944-2669
通讯作者：
Yuchen Wang
作者机构：
[Liu, Hui] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China.;[Wang, Yuchen] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yuchen Wang] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
Let
$$M=S^n/ \Gamma $$
and h be a nontrivial element of finite order p in
$$\pi _1(M)$$
, where the integer
$$n, p\ge 2$$
,
$$\Gamma $$
is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that for every irreversible Finsler compact space form (M,F) with reversibility
$$\lambda $$
and flag curvature K satisfying
$$\begin{aligned} \frac{4p^2}{(p+1)^2} \left( \frac{\lambda }{\lambda +1} \right) ^2< K \le 1,\;\;\lambda < \frac{p+1}{p-1}, \end{aligned}$$
there exist at least
$$n-1$$
non-contractible closed geodesics of class [h]. In addition, if the metric F is bumpy and
$$\begin{aligned} \left( \frac{4p}{2p+1}\right) ^2 \left( \frac{\lambda }{\lambda +1}\right) ^2< K \le 1,\;\;\lambda <\frac{2p+1}{2p-1}, \end{aligned}$$
then there exist at least
$$2\left[ \frac{n+1}{2}\right] $$
non-contractible closed geodesics of class [h], which is the optimal lower bound due to Katok’s example. For
$$C^4$$
-generic Finsler metrics, there are infinitely many non-contractible closed geodesics of class [h] on (M,F) if
$$\frac{\lambda ^2}{(\lambda +1)^2} < K \le 1$$
with n being odd, or
$$\frac{\lambda ^2}{(\lambda +1)^2}\frac{4}{(n-1)^2} < K \le 1$$
with n being even.
作者机构：
[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan 430079, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, Y ] C;Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Peoples R China.
摘要：
This paper is devoted to the construction and analysis of uniformly accurate (UA) nested Picard iterative integrators (NPI) for highly oscillatory second-order differential equations. The equations involve a dimensionless parameter ε ∈ (0,1], and their solutions are highly oscillatory in time with wavelength at
$\boldsymbol {\mathcal {O}}(\varepsilon ^{2})$
, which brings severe burdens in numerical computation when ε ≪ 1. In this work, we first propose two NPI schemes for solving a differential equation. The schemes are uniformly first- and second-order accurate for all ε ∈ (0,1]. Moreover, they are super convergent when the time-step size is smaller than ε2. Then, the schemes are generalized to a system of differential equations with the same uniform accuracies. Error bounds are rigorously established and numerical results are reported to confirm the error estimates.
期刊：
Communications in Statistics - Theory and Methods,2022年53(9):3350-3364 ISSN：0361-0926
通讯作者：
Luo, J
作者机构：
[Wang, Yuyun] Cent China Normal Univ, Dept Stat, Wuhan, Peoples R China.;[Xu, Zhimeng; Zhou, Lewei; Luo, Jing] South Cent MinZu Univ, Dept Math & Stat, Wuhan, Peoples R China.;[Luo, Jing] South Cent MinZu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.
通讯机构：
[Luo, J ] S;South Cent MinZu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.
摘要：
The Thurstone model is a common model for analyzing the paired comparison data. However, there is lack of asymptotic properties for the moment estimator of parameters in this model. Therefore, we prove uniform consistency and asymptotic normality of the moment estimator in the Thurstome model. Simulation studies and a data example illustrate the theoretical result.
摘要：
In this work, we consider the numerical integration of the nonlinear Dirac equation and the Dirac-Poisson system (NDEs) under rough initial data. We propose an ultra low-regularity integrator (ULI) for solving the NDEs which enables optimal first-order time convergence in H-r for solutions in H-r, i.e., without requiring any additional regularity on the solution. In contrast to classical methods, a ULI overcomes the numerical loss of derivatives and is therefore more efficient and accurate for approximating low regular solutions. Convergence theorems and the extension of a ULI to second order are established. Numerical experiments confirm the theoretical results and underline the favourable error behaviour of the new method at low regularity compared to classical integration schemes.
期刊：
SIAM JOURNAL ON NUMERICAL ANALYSIS,2019年57(4):1602-1624 ISSN：0036-1429
通讯作者：
Wang, Yan
作者机构：
[Cai, Yongyong] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Wang, Yan] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
This paper is devoted to the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit regime. In this regime, there is a dimensionless parameter ε ∈ (0, 1] inversely proportional to the speed of light and the equation admits propagating waves with O(1) wavelength in space and O(ε2) wavelength in time. To overcome the difficulty induced by the temporal ε dependent oscillation, we present the construction of several NPI methods which are uniformly first-, second-, and third-order convergent in time w.r.t. ε. The general idea is applying nested Picard iterations to the integral form of the Dirac equation and using exponential wave integrators to approximate the temporal integrals. Thanks to the nested Picard iterative idea, the NPI method can be extended to arbitrary higher-order in time with optimal and uniform accuracy. The implementation of the second-order in-time NPI method via Fourier pseudospectral discretization is clearly demonstrated, and the corresponding error bounds are rigorously established through the energy method as hm 0 + τ2, where h is the mesh size, τ is the time step, and m depends on the regularity of the solution. Numerical results are reported to confirm the error estimates for the second-order NPI method and show the uniform accurate properties (w.r.t. ε) for the first- and third-order NPI methods as well. 2019 Society for Industrial and Applied Mathematics
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2019年39(4):1745-1777 ISSN：1078-0947
通讯作者：
Yang, Jun
作者机构：
[Jiang, Ruiqi] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Wang, Youde] Guangzhou Univ, Coll Math & Informat Sci, Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China.;[Yang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Yang, Jun] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yang, Jun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
期刊：
IMA JOURNAL OF APPLIED MATHEMATICS,2018年83(2):283-301 ISSN：0272-4960
通讯作者：
Wang, Yan
作者机构：
[Wang, Yan] Hubei Univ Chinese Med, Informat Engn Coll, Wuhan 430065, Hubei, Peoples R China.;[Guo, Jun] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Wang, Yan] H;Hubei Univ Chinese Med, Informat Engn Coll, Wuhan 430065, Hubei, Peoples R China.
关键词：
the factorization method;inverse scattering problem;oblique derivative boundary condition
摘要：
We consider a direct and inverse problem for the scattering of an obstacle with a generalized oblique derivative and impedance boundary condition due to the incident plane wave, which arises in some scattering phenomenons such as the scattering of tidal waves by islands under suitable assumptions. The solvability of the direct scattering problem is proven by using the boundary integral equation method. A special technique is proposed in order to show the formulated boundary integral operator is Fredholm with index 0. Then the factorization method is established to reconstruct the shape of the obstacle. We note that the tangential derivative on the obstacle boundary leads to the difficulties on mathematical analysis. Finally, we present some numerical examples in 2D to show the feasibility and effectiveness of the factorization method.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2017年37(6):3161-3182 ISSN：1078-0947
通讯作者：
Fan, Shilei
作者机构：
[Fan, Aihua; Fan, Shilei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fan, Aihua] Univ Picardie Jules Verne, CNRS, LAMFA, UMR 7352, 33 Rue St Leu, F-80039 Amiens 1, France.;[Fan, Shilei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Liao, Lingmin] Univ Paris Est Creteil, LAMA, UMR 8050, CNRS, 61 Ave Gen Gaulle, F-94010 Creteil, France.;[Wang, Yuefei] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China.
通讯机构：
[Fan, Shilei] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
A rational map with good reduction in the field ℚp of p-adic numbers defines a 1-Lipschitz dynamical system on the projective line ℙ1(ℚp) over ℚp. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, ℙ1 (ℚp) is decomposed into three parts: Finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime p, a criterion of minimality for rational maps with good reduction is obtained. When p = 2, a condition in terms of the coefficients of the rational map is proved to be necessary for the map being minimal and having good reduction, and sufficient for the map being minimal and 1-Lipschitz. It is also proved that a rational map having good reduction of degrees 2, 3 and 4 can never be minimal on the whole space ℙ1 (ℚ1).
期刊：
Journal of Theoretical Biology,2016年390:40-49 ISSN：0022-5193
通讯作者：
Zhou, Da;Zhang, Xingan
作者机构：
[Zhang, Xingan; Chen, Xiufang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhou, Da] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;[Wang, Yue] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA.;[Feng, Tianquan] Nanjing Normal Univ, Sch Teachers Educ, Nanjing 210023, Jiangsu, Peoples R China.;[Yi, Ming] Huazhong Agr Univ, Dept Phys, Coll Sci, Wuhan 430070, Hubei, Peoples R China.
通讯机构：
[Zhou, Da] X;[Zhang, Xingan] C;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Cancer stem cell model;Cell plasticity;Multi-phenotypic model;Transient dynamics
摘要：
The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.
期刊：
Advances in Mathematics,2015年281:857-885 ISSN：0001-8708
通讯作者：
Feng, De-Jun
作者机构：
[Feng, De-Jun] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China.;[Rao, Hui] Cent China Normal Univ, Dept Math & Stat, Wuhan 430070, Hubei, Peoples R China.;[Wang, Yang] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China.;[Wang, Yang] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA.
通讯机构：
[Feng, De-Jun] C;Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China.
关键词：
Middle-third Cantor set;Self-similar subsets;Ternary expansions;Set of uniqueness
