为了更好地开展数学与统计学最新研究成果的学术交流，促进数学、统计学交叉研究，北京理工大学数学与统计学院和中国科学院应用数学研究所联合举办2019年学术年会。大会于12月13日至14日在北方温泉会议中心召开。大会邀请国内外4位学者做50分钟大会报告，邀请北京理工大学数学与统计学院、中国科学院应用数学研究所18位教师做25分钟邀请报告。希望通过年会，进一步加强交流与合作，促进产生更多优秀创新成果。

欢迎感兴趣的老师莅临现场，具体报告摘要如下：

12月14日上午举行大会报告

地点：第六会议室

8:00-8:10 田玉斌 院长讲话

8:10-8:20 骆顺龙 所长讲话

 

大会报告主持人：骆顺龙 研究员

8:20-9:10

曹道民 研究员

报告题目：不可压欧拉方程的定常涡环解

 

9:10-10:00

房军生 教授

报告题目：Operators in Type II1 factors

 

10:00-10:20

茶歇

 

大会报告主持人：陈振庆 教授

10:20-11:10

张土生 教授

报告题目：Stochastic reaction diffusion equations

 

11:10-12:00

王启华 研究员

报告题目：Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random

 

12:10-13:20

午餐（地点：一楼中餐厅）

 

14日中午举办教学会议报告

主持人：李炳照 教授

地点：第六会议室

 

13:20-13:50

林海 教授

报告题目：教学成果与课程改革

 

 

14日下午三场分会场报告

 

量子计算与代数分会场

主持人：万金奎 教授

地点：第一会议室

 

2：00-2：25

骆顺龙：Gaussian states as minimum uncertainty states

2：25-2：50

胡  峻：Symmetric structure on the endomorphism algebra of projective and injective modules

2：50-3：15

李楠：Monotonicity of quantumness of ensembles under commutativity-preserving channels

3：15-3: 40

谢  迅：Conjectures P1-P15 for Coxeter groups with complete graph

 

3:40-4:00

茶歇

 

统计与概率分会场

主持人： 席福宝 教授

4：00-4：25

王典朋：Change-point detection of the failure mechanism for electronic devices based on Arrhenius model

4：25-4：50

张让让：Large deviation principles for first-order scalar conservation laws with stochastic forcing

方程理论分会场

主持人：王一夫 教授

地点：第三会议室

 

2：00-2：25

黄飞敏：Thermal creep flow in gas motion(气体运动中的热蠕变流动)

2：25-2：50

王博：On the /sigma_{k}-Nirenberg problem

2：50-3：15

杨建伟：Blowup, scattering and invariant manifolds: longtime dynamics of nonlinear wave equations of energy super-critical growth

3：15-3: 40

郑涛：The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds

 

3:40-4:00

茶歇

 

优化分会场

主持人：熊黎明 教授

4：00-4：25

丁超：Matrix optimization in statistical learning with outliers

4：25-4：50

李庆娜：An Efficient Semismooth Newton’s Method for  Support Vector Machine

 

 

 

计算数学与人工智能分会场

主持人：姜海燕 副教授

地点：第五会议室

 

2：00-2：25

张世华：Towards Understanding Residual and Dilated Dense Neural Networks

2：25-2：50

张波：The PML method for time-domain electromagnetic scattering problems

2：50-3：15

刘晓东：Inverse scattering with phaseless far field data

3：15-3: 40

陈伟坤：Combinatorial separation algorithms for the continuous knapsack polyhedra with divisible capacities

 

3:40-4:00

茶歇

计算与模糊分会场

主持人： 史福贵 教授

4：00-4：25

巫文婷：On greedy randomized coordinate descent methods for solving large linear least-squares problems

4：25-4：50

庞斌：Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces

6：00-8：00

晚餐（一楼中餐厅）

2019年数学与统计学学术年会组委会

                                                 2019．12．10

 

报告摘要

 

曹道民 广州大学教授、研究员

题目： 不可压欧拉方程的定常涡环解

摘要： 报告人将报告近年来在不可压欧拉方程定常涡解方面的研究，特别地要介绍在二维时涡补丁解（vortex patch)和 三维时涡环解（vortex ring）存在性和唯一性方面的结果。报告人将讲述涡补丁解的存在唯一性与Kirchhoff - Routh 函数临界点之间的联系，而Kirchhoff - Routh 临界点又与方程所在区域的几何性质密切相关。  报告人主要介绍的结果是来源于和郭玉霞、彭双阶、严树森合作的论文及和王国栋、万杰、詹伟城合作的论文。

 

 

房军生 河北师范大学数学科学学院教授

题目：  operators in type II1 factors

摘要：  I will talk about some open problems related to operators in type II1 factors, which include the invariant subspace problem, the strongly irreducible operators, irreducible operators and reducible operators in type II1 factors.

 

 

张土生 英国曼彻斯特大学教授

题目:    Stochastic reaction diffusion equations

 摘要 :   The first half of the talk is  a brief introduction to  stochastic reaction diffusion equations  and in the second part of the talk I will present a recent result on  the existence and uniqueness of solutions to stochastic reaction diffusion equations with logarithmic nonlinearity on a bounded domain in the setting  of square integrable functions.

 

 

王启华 中国科学院数学研究院研究员

题目： Bias-corrected Kullback-Leibler distance criterion based model selection with covariables missing at random          

摘要：Let $Y$ be the response variable, and $(X,Z)$ the covariable vector. We consider the model selection problem for $f_{Y|X,Z}(y|x,z)$ with $X$ missing at random, where $f_{Y|X,Z}(y|x,z)$ is the conditional probability function of $Y$ given $(X,Z)$. Two novel model selection criteria are suggested. One is called bias-corrected Kullback-Leibler distance (BCKL) criterion and another one is called empirical-likelihood-based bias-corrected Kullback-Leibler distance (ELBCKL) criterion. Both the criteria  specify a parametric model, which do not need to be correct,  for $f_{X|Y,Z}(x|y,z)$,  the conditional probability function of the missing covariates given the observed variables.  It is shown, however,  that the model selection by both the proposed criteria is consistent and that the population parameter estimators, corresponding to the selected model, are also consistent and asymptotically normal even if the parametric model for $f_{X|Y,Z}(x|y,z)$ is misspecified. This is a remarkable superiority of our proposed criteria to some existing model selection strategies. Extensive simulation studies are conducted to investigate the finite-sample performances of the proposed two criteria and a thorough comparison is made with some related model selection methods. The simulation results show that our proposals perform competitively especially when the conditional distribution of the missing covariates given the observed variables is misspecified. Supplementary materials for this article are available online.

 

骆顺龙 中科院应用数学研究所 研究员

题目： Gaussian states as minimum uncertainty states

摘要：In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this talk, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation  established in [S. Luo, Phys. Rev. A 72, 042110 (2005)]. This characterization puts Gaussian states on a novel basis of physical significance.

 

 

胡峻 北京理工大学教授

题目： Symmetric structure on the endomorphism algebra of projective and injective modules

摘要：The existence of symmetric structure on the endomorphism algebra of projective and injective modules over some finite dimensional algebras arising in Lie theory have attracted a lot of attention in recent years. In this talk, I will discuss some recent work by N. Lam and myself, as well as by M. Fang and myself on the endomorphism algebra of projective and injective modules in (parabolic) BGG category O of semisimple Lie algebras and of quantum groups, and projective and injective modules over cyclotomic Schur algebras.

 

 

李楠 中科院应用数学研究所副研究员

题目：  Monotonicity of quantumness of ensembles under commutativity-preserving channels

摘要：  A quantum channel (operation) is commutativity-preserving if it maps commutating states to commutating states. We show that commutativity-preserving channels cannot increase quantumness of ensembles, as quantified in terms of the commutator of square roots of constituent states in a quantum ensemble recently introduced [Phys. Rev. A 96, 022132 (2017)].

 

谢迅 北京理工大学特别副研究员

题目： Conjectures P1-P15 for Coxeter groups with complete graph

摘要： We prove  Lusztig's conjectures P1-P15   for  Coxeter groups with complete graph, using deceasing induction on a-values  and a kind of decomposition formula of Kazhdan-Lusztig basis elements. As a byproduct, we give a description of the left, right, and two-sided cells. In the appendix, we prove P1-P15 for right-angled Coxeter groups by the same methods.

 

王典朋 北京理工大学特别副研究员

题目：Change-point detection of the failure mechanism for electronic devices based on Arrhenius model

摘要: In accelerated life tests, the reliability of electronic devices is always predicted by using extrapolation based on the common failure mechanism assumption at different accelerating stresses. In the literature, few works have been proposed to detect the change-point of failure mechanism based on exact lifetimes. However, censored data is common in accelerated life tests due to the limits of test time and test cost, which would make the detection of failure mechanism to be difficult. In this paper, two types of change-point of failure mechanism, abrupt change-point and continuous change-point are considered and the corresponding detection methods based on Weibull distribution and Arrhenius model are proposed with censored data. The simulation studies and real data examples both show the superior performances of the proposed methods.

 

张让让 北京理工大学特别副研究员

题目: Large deviations for quasilinear parabolic stochastic partial differential equations

摘要: Since the coefficients of quasilinear parabolic stochastic partial differential equations are neither monotone nor locally monotone, a family of heat kernels is introduced for the well-posedness problem. We prove that the Freidlin-Wentzell type large deviation principles are valid for this model by utilizing the weak convergence method. In this talk, I will show you a brief proof. This is a joint work with Zhao Dong and Tusheng Zhang.

黄飞敏 中科院应用数学研究所研究员

题目：Thermal creep flow in gas motion(气体运动中的热蠕变流动)

摘要：In this lecture, I will present my recent works on the thermal creep flow phenomenon on the gas motion.

 

王博 北京理工大学特别副研究员

题目: On the /sigma_{k}-Nirenberg problem

摘要: In this talk, I will present some recent results concerning the /sigma_{k}-Nirenberg problem in the study of conformal geometry, including existence and compactness. This is a joint work with YanYan Li and Luc Nguyen.

 

  杨建伟  北京理工大学特别副研究员

题目: Blow-up, scattering and invariant manifolds: long-time dynamics of nonlinear wave equations of energy super-critical growth

摘要:  We study the focusing nonlinear wave equation (NLW) outside a ball subject to the Dirichlet boundary condition with energy super-critical nonlinearity. This equation admits finite-time blow- up solutions and a countable sequence of radial stationary solutions. We classify all radial stationary solutions and prove that all radial global solutions of  NLW are asymptotically the sum of a stationary solution and a radiation term. We shall also study the local dynamics around a stationary solution: construct centerstable manifolds close to every stationary solutions and show that the solutions scattering to the stationary solution in question weave out a Lipschitz manifold of finite time blowup solutions is open, whose boundary coincides with the invariant manifolds, which separates $/mathcal  O$ away from the open set of scattering solutions. This work is joint with Thomas Duyckaerts (LAGA (UMR 7539), Université Paris 13).

 

 

 

郑涛 北京理工大学特别副研究员

题目：The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds

摘要：We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori $C^2$ estimates which depend on the initial data on manifolds, the admissible subsolutions and the upper bound of the gradients of the solutions. In some special cases, we also obtain the gradient estimates, and hence we can solve the corresponding Dirichlet problem with admissible subsolutions, which is mainly motivated by our alternative proof of the upper bound of the gradients of the solutions to the equations related to the $(m-1)$-plurisubharmonic functions solved by Tosatti /&  Weinkove and to the Gauduchon conjecture solved by Sz/'ekelyhidi, Tosatti /& Weinkove on the compact Hermitian manifolds without boundary.This is a joint work with Dr. Ke Feng and Professor Huabin Ge.

 

丁超  中科院应用数学研究所 副研究员

题目：Matrix optimization in statistical learning with outliers

摘要：In this talk, we propose a matrix optimization based statistical learning model with outliers. A non-asymptotic error bound for the proposed model is established. We prove that the matrix optimization model produces a high accuracy estimator with high probability, when the order of the sample size is roughly the degree of freedom of a low-rank matrix up to a logarithmic factor. Moreover, we show that the proposed model can identify the outliers without any prior information with high probability, when the number of outliers is small.  Finally, numerical experiments show that the matrix optimization-based model can produce configurations of high quality on large data points that the classical approach would struggle to cope with and significantly outperforms the existing methods.

 

 

 

李庆娜 北京理工大学副教授

题目：An Efficient Semismooth Newton’s Method for  Support Vector Machine
摘要: Support Vector Machine(SVM) is an important and fundamental technique in machine learning. In this talk, we apply a semismooth Newton method to solve two typical SVM models: the L2-loss SVC model and the $/epsilon$-L2-loss SVR model. A common belief on the semismooth Newton method is its fast convergence rate as well as high computational complexity. Our contribution is that by exploring the sparse structure of the models, we significantly reduce the computational complexity, meanwhile keeping the quadratic convergence rate. Extensive numerical experiments demonstrate the outstanding performance of the method.

 

张世华 中科院应用数学研究所研究员

题目：Towards Understanding Residual and Dilated Dense Neural Networks

摘要：Convolutional Neural Network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, Multi-Layer Convolutional Sparse Coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Inspired by this scheme, we propose the Residual Convolutional Sparse Coding (Res-CSC) model and Mixed-Scale Dense Convolutional Sparse Coding (MSD-CSC) model, which have close relationship with the Residual neural network (ResNet) and Mixed-Scale (Dilated) Dense neural network (MSDNet), respectively. Mathematically, both the ResNet and MSDNet are special cases of Res-CSC and MSD-CSC, respectively. Moreover, we also find a theoretical interpretation of the dilated convolution and dense connection operations in the MSDNet by analyzing the MSD-CSC model, which gives a clear mathematical understanding about them. We implement the Iterative Soft Thresholding Algorithm (ISTA) and its fast version to solve Res-CSC and MSD-CSC without adding extra parameters. At last, extensive numerical experiments and comparison with competing methods demonstrate their effectiveness.

 

张波 中科院应用数学研究所研究员

题目：The PML method for time-domain electromagnetic scattering problems

摘要: In this talk, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coordinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Green's function for the Maxwell equations in the free space. This is a joint work with Changkun Wei and Jiaqing Yang.

 

刘晓东 中科院应用数学研究所副研究员

题目： Inverse scattering with phaseless far field data

摘要:The well known translation invariance property of the phaseless far field patterns with incident plane waves make it is impossible to reconstruct the location of the underlying scatterers even for multiple incident directions and frequencies. To overcome this difficulty, a fast and stable phase retrieval approach is proposed based on a simple geometrical result which provides a stable reconstruction of a point in the plane from three distances to the given points. Both the uniqueness and direct sampling methods will also be mentioned in this talk.

 

陈伟坤 北京理工大学特别副研究员

题目：Combinatorial separation algorithms for the continuous knapsack polyhedra with divisible capacities

摘要：We consider the separation problems of the two continuous knapsack polyhedra with divisible capacities. These two polyhedra are the convex hulls of the sets which consist of $ n $ nonnegative integer variables, one unbounded continuous, $ m $ bounded continuous variables, and one linear constraint in either $ /geq $ or $ /leq $ form where the coefficients of integer variables are integer and divisible. Wolsey and Yaman (Math Program 156: 1--20, 2016) have shown that these two polyhedra can be described by two closely related families of partition inequalities. However, no polynomial-time combinatorial separation algorithm for the two polyhedra, or equivalently, the two related families of partition inequalities, is known until now. In this talk, for each polyhedron, we provide a combinatorial separation algorithm with the complexity of $ /mathcal{O}(nm+m/log m ) $. In particular, we solve the separation problem for the continuous $ /geq $-knapsack polyhedron by presenting a polynomial-time combinatorial separation algorithm for the family of $ /geq  $-partition inequalities. For the continuous $ /leq $-knapsack polyhedron, we derive the complemented partition inequalities which dominate the $ /leq $-partition inequalities. The continuous $ /leq $-knapsack polyhedron is completely described with the addition of the proposed inequalities. We again show that the family of the proposed inequalities can be separated in polynomial time.   

 

巫文婷 北京理工大学特别副研究员

题目：On greedy randomized coordinate descent methods for solving large linear least-squares problems

摘要：For solving large scale linear least-squares problem by iteration methods, inspired by the work of Strohmer and Vershynin who gave a bound for the convergence rate of the randomized Kaczmarz method in terms of a natural linear-algebraic condition measure, Leventhal and Lewis found that by choosing a unit coordinate direction as a search direction randomly according to an appropriate probability distribution, a convergence rate for the resulting randomized coordinate descent method can be obtained in terms of the scaled or the relative condition number.

In this talk we introduce a probability criterion for selecting the working columns from the coefficient matrix and construct a greedy randomized coordinate descent method. Theoretical analysis shows that this method possesses faster convergence rate than the randomized coordinate descent method in terms of natural linear-algebraic condition measures. Numerical results show that the greedy randomized coordinate descent method is more efficient than the randomized coordinate descent method.

 

庞斌：北京理工大学特别副研究员

题目：Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces

摘要：Hull operators and interval operators are basic tools in the theory of convex spaces. In his talk, fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces are investigated. Firstly, the concept of L-hull operators is introduced and the resulting category is shown to be isomorphic to that of L-convex spaces. Secondly, considering the graded inclusions of L-subsets, the notion of L-ordered hull operators is presented, which is shown to be categorically isomorphic to strong L-convex structures. Finally, the concept of L-interval operators is introduced and it is shown that there is a Galois correspondence between the category of L-interval spaces and that of L-convex spaces. In particular, the category of arity 2 L-convex spaces can be reflectively embedded into that of L-interval spaces.