Research Progress


  •    In this paper, noting that the prediction of time series follows the temporal order of data, we propose a frequentist model averaging method based on forward-validation. Our method also considers the uncertainty of the window size in estimation, i.e., we allow the sample size to vary among candidate models. We establish the asymptotic optimality of our method in the sense of achieving the lowest possible squared prediction risk. We also prove that if there exists one or more correctly specified models, our method will automatically assign all the weights to them. The promising performance of our method for finite samples is demonstrated by simulations and an empirical example of predicting the equity premium.
       Publication:
      Journal of Econometrics. Available online 21 May 2022
      Author:
       Xiaomeng Zhang
       Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
       University of Chinese Academy of Sciences, Beijing 100049, China
       Xinyu Zhang
       Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
       Beijing Academy of Artificial Intelligence, Beijing 100084, China
       Email: xinyu@amss.ac.cn

  •   Epigenetic information regulates gene expression and development. However, our understanding of the evolution of epigenetic regulation on brain development in primates is limited. Here, we compared chromatin accessibility landscapes and transcriptomes during fetal prefrontal cortex (PFC) development between rhesus macaques and humans. A total of 304,761 divergent DNase I-hypersensitive sites (DHSs) are identified between rhesus macaques and humans, although many of these sites share conserved DNA sequences. Interestingly, most of the cis-elements linked to orthologous genes with dynamic expression are divergent DHSs. Orthologous genes expressed at earlier stages tend to have conserved cis-elements, whereas orthologous genes specifically expressed at later stages seldom have conserved cis-elements. These genes are enriched in synapse organization, learning and memory. Notably, DHSs in the PFC at early stages are linked to human educational attainment and cognitive performance. Collectively, the comparison of the chromatin epigenetic landscape between rhesus macaques and humans suggests a potential role for regulatory elements in the evolution of differences in cognitive ability between non-human primates and humans.
      Publication:
       Nature Communications, (2022) 13:3883.
       Author:
      Xuelong Yao
      CAS Key Laboratory of Genome Sciences and Information, Collaborative Innovation Center of Genetics and Development, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, 100101 Beijing, China
      University of Chinese Academy of Sciences, 100049 Beijing, China
      Guangzhou Nvwa Life Technology Co., Ltd, Guangzhou 510535, China
      Zongyang Lu
      University of Chinese Academy of Sciences, 100049 Beijing, China
      School of Life Science and Technology, Shanghai Tech University, 100 Haike Rd., Pudong New Area, Shanghai 201210, China
      Shanghai Institute of Biochemistry and Cell Biology, Chinese Academy of Sciences, 320 Yueyang Road, Shanghai 200031, China
      Zhanying Feng
      University of Chinese Academy of Sciences, 100049 Beijing, China
      CEMS, NCMIS, MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
      Lei Gao
      CAS Key Laboratory of Genome Sciences and Information, Collaborative Innovation Center of Genetics and Development, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, 100101 Beijing, China
      Xin Zhou
      State Key Laboratory of Brain and Cognitive Science, CAS Center for Excellence in Brain Science and Intelligence Technology, Institute of Brain-Intelligence Technology (Shanghai), Institute of Biophysics, Chinese Academy of Sciences, 100101 Beijing, China
      Min Li
      University of Chinese Academy of Sciences, 100049 Beijing, China
      State Key Laboratory of Brain and Cognitive Science, CAS Center for Excellence in Brain Science and Intelligence Technology, Institute of Brain-Intelligence Technology (Shanghai), Institute of Biophysics, Chinese Academy of Sciences, 100101 Beijing, China
      Suijuan Zhong
      State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, 100875 Beijing, China
      IDG/McGovern Institute for Brain Research, Beijing Normal University, 100875 Beijing, China
      Qian Wu
      State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, 100875 Beijing, China
      IDG/McGovern Institute for Brain Research, Beijing Normal University, 100875 Beijing, China
      Zhenbo Liu
      CAS Key Laboratory of Genome Sciences and Information, Collaborative Innovation Center of Genetics and Development, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, 100101 Beijing, China
      Haofeng Zhang
      Obstetrics and Gynecology Medical Center of Severe Cardiovascular of Beijing Anzhen Hospital, Capital Medical University, 100029 Beijing, China
      Zeyuan Liu
      University of Chinese Academy of Sciences, 100049 Beijing, China
      State Key Laboratory of Brain and Cognitive Science, CAS Center for Excellence in Brain Science and Intelligence Technology, Institute of Brain-Intelligence Technology (Shanghai), Institute of Biophysics, Chinese Academy of Sciences, 100101 Beijing, China
      Lizhi Yi
      CAS Key Laboratory of Genome Sciences and Information, Collaborative Innovation Center of Genetics and Development, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, 100101 Beijing, China
      University of Chinese Academy of Sciences, 100049 Beijing, China
      Tao Zhou
      School of Life Science and Technology, Shanghai Tech University, 100 Haike Rd., Pudong New Area, Shanghai 201210, China
      Shenzhen Key Lab of Drug Addiction; The Brain Cognition and Brain Disease Institute (BCBDI), Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences; Shenzhen-Hong Kong Institute of Brain Science-Shenzhen Fundamental Research Institutions, Shenzhen 518055, China
      Xudong Zhao
      Kunming Primate Research Center, Key Laboratory of Animal Models and Human Disease Mechanisms of Chinese Academy of Sciences, Kunming Institute of Zoology, Chinese Academy of Sciences, 650223 Kunming, China
      Jun Zhang
      Obstetrics and Gynecology Medical Center of Severe Cardiovascular of Beijing Anzhen Hospital, Capital Medical University, 100029 Beijing, China
      Yong Wang
      University of Chinese Academy of Sciences, 100049 Beijing, China
      CEMS, NCMIS, MDIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
      Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences, Kunming 650223, China
      Email: yongwang@amss.ac.cn
      Xingxu Huang
      School of Life Science and Technology, Shanghai Tech University, 100 Haike Rd., Pudong New Area, Shanghai 201210, China
      Zhejiang Provincial Key Laboratory of Pancreatic Disease, The First Affiliated Hospital, and Institute of Translational Medicine, Zhejiang University School of Medicine, Hangzhou, Zhejiang 310058, China
      Xiaoqun Wang
      University of Chinese Academy of Sciences, 100049 Beijing, China
      State Key Laboratory of Brain and Cognitive Science, CAS Center for Excellence in Brain Science and Intelligence Technology, Institute of Brain-Intelligence Technology (Shanghai), Institute of Biophysics, Chinese Academy of Sciences, 100101 Beijing, China
      Institute for Stem Cell and Regeneration, Chinese Academy of Sciences, 100101 Beijing, China
      Beijing Institute for Brain Disorders, 100069 Beijing, China
      Jiang Liu
      CAS Key Laboratory of Genome Sciences and Information, Collaborative Innovation Center of Genetics and Development, Beijing Institute of Genomics, Chinese Academy of Sciences and China National Center for Bioinformation, 100101 Beijing, China
      University of Chinese Academy of Sciences, 100049 Beijing, China
      Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences, Kunming 650223, China

  •   Consider the inverse acoustic scattering of time-harmonic point sources by a locally perturbed interface with buried obstacles in the lower half-space. A novel version of the sampling method is proposed to simultaneously reconstruct the local perturbation of the rough interface and buried obstacles by constructing a modified near-field equation associated with a special rough surface, yielding a fast imaging algorithm. Numerical examples are presented to illustrate the effectiveness of the inversion algorithm.
      Publication:
       Journal of Computational Physics. Volume 464, 1 September 2022, 111338
       Author:
      Jianliang Li
      School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
      Jiaqing Yang
      School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
      Bo Zhang
      LSEC and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
      School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
      Email: b.zhang@amt.ac.cn 

  •   The Cauchy problem for the barotropic compressible Navier--Stokes equations on the whole two-dimensional space with vacuum as far field density is considered. When the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds, the global existence and uniqueness of strong and classical solutions is established. It should be remarked that there are no restrictions on the size of the data.
      Publication:
      SIAM Journal on Mathematical Analysis. Vol. 54, Iss. 3, pp: 3192-3214.
       
      Author:
      Xiangdi Huang
      Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China
      Email: xdhuang@amss.ac.cn
      Jing Li
      Department of Mathematics, and Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, P. R. China
      Institute of Applied Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, P.R. China
      School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
      Email: ajingli@gmail.com

  •    Designing privacy-preserving distributed algorithms for stochastic aggregative games is urgent due to the privacy issues caused by information exchange between players. This paper proposes two differentially private distributed algorithms seeking the Nash equilibrium in stochastic aggregative games. By adding time-varying random noises, the input and output-perturbation methods are given to protect each player’s sensitive information. For the case of output-perturbation, utilizing mini-batch methods, the algorithm’s mean square error is inversely proportional to the privacy level ε and the number of samples. For the case of input-perturbation, a differentially private distributed stochastic approximation-type algorithm is developed to achieve almost sure convergence and (ε,δ)-differential privacy. Under suitable consensus time conditions, the algorithm’s convergence rate is rigorously presented for the first time, where the optimal convergence rate O(1/k) in a mean square sense is obtained. Then, utilizing mini-batch methods, the influence of added privacy noise on the algorithm’s performance is reduced, and the convergence rate of the algorithm is improved. Specifically, when the batch sizes and the number of consensus times at each iteration grow at a suitable rate, an exponential rate of convergence can be achieved with the same privacy level. Finally, a simulation example demonstrates the algorithms’ effectiveness.
       Publication:
      Automatica. Volume 142, August 2022, 110440.
       
      Author:
       Jimin Wang
       School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China
       Email: jimwang@ustb.edu.cn
       Ji-Feng Zhang
       Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
       School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
       Email: jif@iss.ac.cn
       Xingkang He
       Department of Electrical Engineering, University of Notre Dame, IN 46556, USA
       Email: xhe9@nd.edu

  •   This article presents a new study on adaptive control of multi-input and multi-output (MIMO) discrete-time nonlinear systems with a noncanonical form involving parametric uncertainties. The adaptive control scheme employs a vector relative degree formulation to reconstruct the noncanonical system dynamics and derives a normal form. Then, a new matrix decomposition-based adaptive control scheme is proposed for the controlled plant with a vector relative degree [1, 1, …, 1] under some relaxed design conditions. In particular, the matrix decomposition technique is adopted to overcome the singularity problem during the adaptive estimation of an uncertain high-frequency gain matrix. The adaptive control scheme ensures closed-loop stability and asymptotic output tracking. An extension to the adaptive control of general canonical-form MIMO discrete-time nonlinear systems is also presented. Finally, through simulations, the effectiveness of the proposed control scheme is verified.
      Publication:
      IEEE Transactions on Automatic Control. Volume: 67, Issue: 8, pp: 4330-4337.
       
      Author:
      Yanjun Zhang
      School of Automation, Beijing Institute of Technology, Beijing 100081, China
      Email: yanjun@bit.edu.cn
      Ji-Feng Zhang
      Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
      School of Mathematics Sciences, University of Chinese Academy of Sciences, Bejing 100149, China
      Email: jif@iss.ac.cn
      Xiao-Kang Liu
      School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
      Email: xiaokangliu@hust.edu.cn

  •   In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. We first show the existence of the density function of the numerical solution by proving its exponential integrability property, Malliavin differentiability and the almost surely non-degeneracy of the associated Malliavin covariance matrix. Then the smoothness of the density function is obtained through a lower bound estimate of the smallest eigenvalue of the corresponding Malliavin covariance matrix. Meanwhile, we derive the optimal strong convergence rate in every Malliavin–Sobolev norm of the numerical solution via Malliavin calculus. Combining the strong convergence result and the smoothness of the density functions, we prove that the convergence order of the density function of the numerical scheme coincides with its strong convergence order.
      Publication:
       Mathematics of Computation, Volume 91 (2022), pp: 2283-2333.
       
      Author:
      Jianbo Cui
      Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Republic of China
      Email address: jianbo.cui@polyu.edu.hk
      Jialin Hong
      LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China; and School of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
      Email address: hjl@lsec.cc.ac.cn
      Derui Sheng
      LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China; and School of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
      Email address: sdr@lsec.cc.ac.cn 

  •   We study the steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions, we establish the existence of a boundary layer solution for both linear and nonlinear Boltzmann equations in half-space with diffusive reflection boundary condition in $L^\infty_{x,v}$ when the far-field Mach number of the Maxwellian is zero. The continuity and the spacial decay of the solution are obtained. The uniqueness is established under some constraint conditions.   Publication:  SIAM Journal on Mathematical Analysis. Volume. 54, Issue. 3, pp: 3480-3534.     Author:  Feimin Huang  Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  Email: fhuang@amt.ac.cn  Yong Wang  Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  Email: yongwang@amss.ac.cn

  •   The gravitational collapse of an isolated self-gravitating gaseous star for $\gamma$-law pressure $p(\rho)=\rho^\gamma$ ($1<\gamma<\frac43$) in the mass-supcritical case is investigated. It was first shown in [Y. Guo, M. Had?i?, and J. Jang, Arch. Rational Mech. Anal., 239 (2021), pp. 431--552] that there exists a kind of continued gravitational collapse, and the collapse is based on a special solution of the pressureless Euler--Poisson system. In this paper, all spherically symmetric solutions of the pressureless Euler--Poisson system are classified. Precisely speaking, for fixed radius $r$, there exists a unique critical velocity $v^*(r)>0$ depending on the mean density in the ball $B(0,r)$ for the pressureless Euler--Poisson system such that if the initial velocity $\chi_1(r)\geq v^*(r)$ (escape case), then the dust runs away from the gravitational force forever along an escape trajectory, and if the initial velocity $\chi_1(r)< v^*(r)$ (collapse case), then the dust collapses at the origin in a finite time $t^*(r)$ even if it expands initially, i.e., $\chi_1(r)>0$. Moreover, it is proved that there exists a class of spherically symmetric solutions of a gaseous star, which formulates a continued gravitational collapse in finite time, based on the background of the pressureless solutions if $\chi_1(r)< v^*(r)$ for all $r\in[0,1]$. It is noted that $\chi_1(r)$ could be positive; that is, the star might expand initially but finally collapse.     Publication:  SIAM Journal on Mathematical Analysis. Volume. 54, Issue. 3, pp: 3139-3160.     Author:  Feimin Huang  Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  Email: fhuang@amt.ac.cn  Yue Yao  Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  Email: yaoyue17@mails.ucas.ac.cn

  •   Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating polar decomposition method (APD). In this paper, an improved version iAPD of the classical APD is proposed. For the first time, all of the following four fundamental properties are established for iAPD: (i) the algorithm converges globally and the whole sequence converges to a KKT point without any assumption; (ii) it exhibits an overall sublinear convergence with an explicit rate which is sharper than the usual O(1/k) for first order methods in optimization; (iii) more importantly, it converges R-linearly for a generic tensor without any assumption; (iv) for almost all LROTA problems, iAPD reduces to APD after finitely many iterations if it converges to a local minimizer.
       
      Publication:
      Mathematical Programming, 30 July 2022
       
       Author:
       Shenglong Hu
       Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China
      Ke Ye
      KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
      Email: keyk@amss.ac.cn

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