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The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions:soliton resolution via the mixed■-Riemann-Hilbert problem

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Communications in Theoretical Physics 2024年第6期76卷 13-25页

作者： Minghe Zhang zhenya yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we investigate the Cauchy problem of the Sasa-Satsuma(SS)equation with initial data belonging to the Schwartz *** SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3×3 Lax *** the aid of the■nonlinear steepest descent method of the mixed■-Riemann-Hilbert problem,we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

关键词： Sasa-Satsuma equation inverse scattering ■-Riemann-Hilbert problem ■steepest descent method soliton resolution

Deep learning neural networks for the third-order nonlinear Schrodinger equation: bright solitons, breathers, and rogue waves

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Communications in Theoretical Physics 2021年第10期73卷 55-63页

作者： Zijian Zhou zhenya yan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The dimensionless third-order nonlinear Schrodinger equation(alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks(PINNs) deep learning method to explore the data-driven solutions(e.g. bright soliton,breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated(a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.

关键词： third-order nonlinear Schrodinger equation deep learning data-driven solitons data-driven parameter discovery

Data-driven parametric soliton-rogon state transitions for nonlinear wave equations using deep learning with Fourier neural operator

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Communications in Theoretical Physics 2023年第2期75卷 5-17页

作者： Ming Zhong zhenya yan Shou-Fu Tian KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Mathematics China University of Mining and TechnologyXuzhou 221116China

In this paper,we develop the deep learning-based Fourier neural operator(FNO)approach to find parametric mappings,which are used to approximately display abundant wave structures in the nonlinear Schr?dinger(NLS)equation,Hirota equation,and NLS equation with the generalized PT-symmetric Scarf-II ***,we analyze the state transitions of different types of solitons(*** solitons,breathers,peakons,rogons,and periodic waves)appearing in these complex nonlinear wave *** checking the absolute errors between the predicted solutions and exact solutions,we can find that the FNO with the Ge Lu activation function can perform well in all cases even though these solution parameters have strong influences on the wave ***,we find that the approximation errors via the physics-informed neural networks(PINNs)are similar in magnitude to those of the ***,the FNO can learn the entire family of solutions under a given distribution every time,while the PINNs can only learn some specific solution each *** results obtained in this paper will be useful for exploring physical mechanisms of soliton excitations in nonlinear wave equations and applying the FNO in other nonlinear wave equations.

关键词： deep learning Fourier neural operator solitonrogon state transition nonlinear Schrödinger equation hirota equation

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

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Communications in Theoretical Physics 2022年第9期74卷 6-22页

作者： Weifang Weng Guoqiang Zhang Shuyan Chen Zijian Zhou zhenya yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The Hirota equation can be used to describe the wave propagation of an ultrashort optical *** this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are *** employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(*** combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial *** the larger solution parameters,the first m(m

关键词： Multi-component Hirotaequations mixedbackgrounds modified Darbouxtransform semi-rational RWs and W-shaped solitons asymptotic analysis

Understanding and improving fairness in cognitive diagnosis

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Science China(Information Sciences) 2024年第5期67卷 99-114页

作者： Zheng ZHANG Le WU Qi LIU Jiayu LIU zhenya HUANG Yu YIN yan ZHUANG Weibo GAO Enhong CHEN Anhui Province Key Laboratory of Big Data Analysis and Application School of Computer Science and Technology& School of Data Science University of Science and Technology of China State Key Laboratory of Cognitive Intelligence School of Computer Science and Information Engineering Hefei University of Technology

Intelligent education is a significant application of artificial intelligence. One of the key research topics in intelligence education is cognitive diagnosis, which aims to gauge the level of proficiency among students on specific knowledge concepts(e.g., Geometry). To the best of our knowledge, most of the existing cognitive models primarily focus on improving diagnostic accuracy while rarely considering fairness issues; for instance, the diagnosis of students may be affected by various sensitive attributes(e.g., region). In this paper,we aim to explore fairness in cognitive diagnosis and answer two questions:(1) Are the results of existing cognitive diagnosis models affected by sensitive attributes?(2) If yes, how can we mitigate the impact of sensitive attributes to ensure fair diagnosis results? To this end, we first empirically reveal that several wellknown cognitive diagnosis methods usually lead to unfair performances, and the trend of unfairness varies among different cognitive diagnosis models. Then, we make a theoretical analysis to explain the reasons behind this phenomenon. To resolve the unfairness problem in existing cognitive diagnosis models, we propose a general fairness-aware cognitive diagnosis framework, FairCD. Our fundamental principle involves eliminating the effect of sensitive attributes on student proficiency. To achieve this, we divide student proficiency in existing cognitive diagnosis models into two components: bias proficiency and fair *** design two orthogonal tasks for each of them to ensure that fairness in proficiency remains independent of sensitive attributes and take it as the final diagnosed result. Extensive experiments on the Program for International Student Assessment(PISA) dataset clearly show the effectiveness of our framework.

关键词： fairness intelligent education cognitive diagnosis psychometrics adversarial learning

A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA■

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Journal of Systems Science & Complexity 2006年第3期19卷 301-306页

作者： zhenya yan Key Laboratory of Mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

在这篇论文，有五个潜力的一个 isospectral 问题在环代数学 A_2 被调查以便有五任意的功能的进化方程的一个新层次被获得。然后由修理五任意的功能是某些功能并且使用踪迹身份，进化方程的层次的概括 Hamiltonian 结构被给。方程的这... 详细信息

在这篇论文，有五个潜力的一个 isospectral 问题在环代数学 A_2 被调查以便有五任意的功能的进化方程的一个新层次被获得。然后由修理五任意的功能是某些功能并且使用踪迹身份，进化方程的层次的概括 Hamiltonian 结构被给。方程的这个层次是 Liouville integrable，这被显示出。最后， isospectral 问题的一些特殊情况也被给。

关键词：哈密尔敦函数结构积分环代数等光谱问题

Deep learning neural networks for the third-order nonlinear Schr?dinger equation: bright solitons, breathers, and rogue waves

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Communications in Theoretical Physics 2021年第10期73卷 57-65页

作者： Zijian Zhou zhenya yan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

The dimensionless third-order nonlinear Schr?dinger equation(alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks(PINNs) deep learning method to explore the data-driven solutions(e.g. bright soliton,breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated(a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.

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EXPLICIT EXACT SOLUTIONS FOR THE GENERALIZED COMBINED KdV AND MKdV EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2001年第2期16卷 156-160页

作者： yan zhenya Zhang HongqingDept.ofAppl.Math.,DalianUniv.ofTechnology,Dalian116024 Dept. of Appl. Math. Dalian Univ. of Technology Dalian

With the aid of Mathematica and Wu elimination method,via using a new generalized ansatz and well known Riccati equation,thirty two families of explicit and exact solutions for the generalized combined KdV and mKdV equation are obtained,which contain new solitary wave solutions and periodic wave *** approach can also be applied to other nonlinear evolution equations.

关键词： combined KdV and mKdV equation solitary wave solution periodic wave solution.

BLIND CHANNEL AND SYMBOL JOINT ESTIMATION IN COOPERATIVE MIMO FOR WIRELESS SENSOR NETWORK

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Journal of Electronics(China) 2008年第4期25卷 439-444页

作者： yan zhenya Zheng Baoyu Institute of Signal Processing ＆ Transmission Nanjing University of Posts and Telecommunications Nanjing 210003 China

In this paper,application of Sequential Quasi Monte Carlo(SQMC)to blind channel andsymbol joint estimation in cooperative Multiple-Input Multiple-Output(MIMO)system is proposed,which does not need to transmit training symbol and can save the power and channel ***,an improved version of SQMC algorithm by taking advantage of current received signal *** results show that the SQMC method outperforms the Sequential Monte Carlo(SMC)methods,and the incorporation of current received signal improves the performance of theSQMC obviously.

关键词：多输入多输出系统通信系统传感器网络连续拟蒙特卡洛法盲信道