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Number of Solitons Emerged in the Initial Profile of Shallow Water Using Convolutional Neural Networks

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Journal of Systems Science & Complexity 2024年第2期37卷 463-479页

作者： WANG Zhen CUI Shikun School of mathematical Sciences Dalian University of TechnologyDalian 116024China School of mathematical Sciences Beihang UniversityBeijing 100191China

The soliton resolution conjecture proposes that the initial value problem can evolve into a dispersion part and a soliton ***,the problem of determining the number of solitons that form in a given initial profile remains unsolved,except for a few specific *** this paper,the authors use the deep learning method to predict the number of solitons in a given initial value of the Korteweg-de Vries(KdV)*** leveraging the analytical relationship between Asech^(2)(x)initial values and the number of solitons,the authors train a Convolutional Neural Network(CNN)that can accurately identify the soliton count from spatio-temporal *** trained neural network is capable of predicting the number of solitons with other given initial values without any additional *** extensive calculations,the authors demonstrate the effectiveness and high performance of the proposed method.

关键词： Convolutional neural network deep learning method KdV equation soliton

RSPO2 as Wnt signaling enabler: Important roles in cancer development and therapeutic opportunities

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Genes & Diseases 2024年第2期11卷 788-806页

作者： Ankit Srivastava Deeksha Rikhari Sameer Srivastava Department of Biotechnology Motilal Nehru National Institute of TechnologyAllahabadUttar Pradesh 211004India

R-spondins are secretory proteins localized in the endoplasmic reticulum and Golgi bodies and are processed through the secretory *** the R-spondin family,RSPO2 has emanated as a novel regulator of Wnt signaling,which has now been acknowledged in numerous in vitro and in vivo *** is an abnormal growth of cells that proliferates and spreads uncontrollably due to the accumulation of genetic and epigenetic factors that constitutively activate Wnt signaling in various types of *** cancer (CRC) begins when cells in the colon and rectum follow an indefinite pattern of division due to aberrant Wnt activation as one of the key ***-long progress in research on R-spondins has demonstrated their oncogenic function in distinct cancer types,particularly *** a critical regulator of the Wnt pathway,it modulates several phenotypes of cells,such as cell proliferation,invasion,migration,and cancer stem cell ***,RSPO mutations,gene rearrangements,fusions,copy number alterations,and altered gene expression have also been identified in a variety of cancers,including *** this review,we addressed the recent updates regarding the recurrently altered R-spondins with special emphasis on the RSPO2 gene and its involvement in potentiating Wnt signaling in *** addition to the compelling physiological and biological roles in cellular fate and regulation,we propose that RSPO2 would be valuable as a potential biomarker for prognostic,diagnostic,and therapeutic use in CRC.

关键词： CRC Gene fusion R-Spondins RSPO2 Therapeutics Wnt signaling

Existence and asymptotics of normalized solutions for the logarithmic Schr?dinger system

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Science China Mathematics 2024年第9期67卷 2019-2048页

作者： Qian Zhang Wenming Zou Department of mathematical Sciences Tsinghua University

This paper is concerned with the following logarithmic Schr?dinger system:■where Ω=RNor Ω?RN（N≥3） is a bounded smooth domain,and ωi∈R,μi,ρi> 0 for i=1,***,p,q≥1,and 2≤p+q≤2*,where 2*:=2N/N-2. By using a Gagliardo-Nirenberg inequality and a careful estimation of u log u2,firstly,we provide a unified proof of the existence of the normalized ground state solution for all 2≤p+q ≤2*.Secondly,we consider the stability of normalized ground state ***,we analyze the behavior of solutions for the Sobolev-subcritical case and pass to the limit as the exponent p+q approaches 2*.Notably,the uncertainty of the sign of u log u2in（0,+∞） is one of the difficulties of this paper,and also one of the motivations we are interested *** particular,we can establish the existence of positive normalized ground state solutions for the Brézis-Nirenberg type problem with logarithmic perturbations（i.e.,p+q=2*）.In addition,our study includes proving the existence of solutions to the logarithmic type Bréis-Nirenberg problem with and without the *** ∫Ω|ui|2dx=ρi（i=1,2） by two different methods,*** results seem to be the first result of the normalized solution of the coupled nonlinear Schr?dinger system with logarithmic perturbations.

关键词： logarithmic Schrödinger system Brézis-Nirenberg problem normalized solution existence and stability behavior of solutions

Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems Science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong School of Physical and mathematical Sciences Nanjing Tech UniversityNanjing 211816China School of mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

Data-Driven Direct Adaptive Risk-Sensitive Control of Stochastic Systems

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Journal of Systems Science & Complexity 2024年第4期37卷 1446-1469页

作者： QIAO Nan LI Tao School of mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and mathematical Practice School of Mathematical SciencesEast China Normal UniversityShanghai 200241China

The authors propose a data-driven direct adaptive control law based on the adaptive dynamic programming(ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive *** authors use online data of the system to iteratively solve the generalized algebraic Riccati equation(GARE) and to learn the optimal control law *** the case with measurable system noises,the authors show that the adaptive control law approximates the optimal control law as time goes *** the case with unmeasurable system noises,the authors use the least-square solution calculated only from the measurable data instead of the real solution of the regression equation to iteratively solve the *** authors also study the influences of the intensity of the system noises,the intensity of the exploration noises,the initial iterative matrix,and the sampling period on the convergence of the ADP ***,the authors present two numerical simulation examples to demonstrate the effectiveness of the proposed algorithms.

关键词： Adaptive dynamic programming direct adaptive control generalized algebraic Riccati equation risk-sensitive control

Global well-posedness for 2D inhomogeneous asymmetric fluids with large initial data

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Science China Mathematics 2024年第3期67卷 527-556页

作者： Chenyin Qian Beibei He Ting Zhang School of mathematical Sciences Zhejiang Normal UniversityJinhua 321004China School of mathematical Sciences Zhejiang UniversityHangzhou 310058China

In this paper, by using time-weighted global estimates and the Lagrangian approach, we first investigate the global existence and uniqueness of the solution for the 2D inhomogeneous incompressible asymmetric fluids wi... 详细信息

关键词： inhomogeneous asymmetric fluids Littlewood-Paley theory Besov spaces global well-posedness

Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations

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Science China Mathematics 2024年第3期67卷 557-576页

作者： Jiaxiang Wang Bin Zhou Beijing International Center for mathematical Research Peking UniversityBeijing 100871China School of mathematical Sciences Peking UniversityBeijing 100871China

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity of the complex Hessian and Monge-Amp`ere equations with respect to a general nonnegative Borel measure. We obtain a quantitative characterization for these relations through the properties of the capacity-minimizing functions.

关键词： complex Monge-Ampère equations plurisubharmonic functions Sobolev inequality Moser-Trudinger inequality

Partial regularity and nonlinear potential estimates for Stokes systems with super-quadratic growth

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Science China Mathematics 2024年第7期67卷 1525-1554页

作者： Lingwei Ma Zhenqiu Zhang School of mathematical Sciences Tianjin Normal UniversityTianjin300387China School of mathematical Sciences and LPMC Nankai UniversityTianjin300071China

This paper builds a bridge between partial regularity theory and nonlinear potential theory for the following generalized stationary Stokes system with super-quadratic growth and continuous coefficients:-div A(x,Du)+■π=f,div u=0,where Du is the symmetric part of the gradient■*** first establish anε-regularity criterion involving both the excess functional of the symmetric gradient Du and Wolff potentials of the nonhomogeneous term f to guarantee the local vanishing mean oscillation(VMO)-regularity of Du in an open subset Ω_(u) of Ω with full *** anε-regularity criterion leads to a pointwise Wolff potential estimate of Du,which immediately infers that Du is partially C^(0)-regular under appropriate ***,we give a local continuous modulus estimate of Du.

关键词： nonlinear Stokes system partial regularity Wolff potential estimates continuous modulus estimates

A Novel Multi-objective Protection Coordination Scheme for a Microgrid with Optimal Deployment of Dual-setting ROCOV Based Relays

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Protection and Control of Modern Power Systems 2024年第4期9卷 23-38页

作者： Praveen Kumar Gupta Priyanshul Niranjan Niraj Kumar Choudhary Nitin Singh Ravindra Kumar Singh the Department of Electrical Engineering Motilal Nehru National Institute of Technology AllahabadPrayagraj 211004India

Relay coordination is crucial in electrical power systems to protect against malfunctions and damage caused by unexpected events like short *** address the challenge associated with the reverse direction of fault current,dual-setting(DS)directional over-current relays have evolved but failed to provide proper coordination during changes of load,generation,and *** the meantime,with the increasing number of DS relays,the total relay operating time tends to ***,this paper proposes a protection scheme based on the optimal deployment of conventional and dual-setting rate of change of voltage(DS-ROCOV)relays in distribution *** holds true for varying network topologies and is unaffected by variations in load and *** objective of the proposed scheme is to ensure reliable and efficient protection against faults in distribution systems by minimizing the overall operating time with the optimal number of DS-ROCOV *** proposed protection scheme’s performance is evaluated for different coordination time interval values as well as in different microgrid *** paper outlines the design and implementation of the proposed protection scheme which is validated on the modified IEEE 14-bus system using simulations in Matlab/Simulink.

关键词： Coordination time interval DS-ROCOV relay multi-objective optimization optimal-deployment protection coordination