為了更好地開展數(shù)學(xué)與統(tǒng)計學(xué)最新研究成果的學(xué)術(shù)交流，促進(jìn)數(shù)學(xué),、統(tǒng)計學(xué)交叉研究，北京理工大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院和中國科學(xué)院應(yīng)用數(shù)學(xué)研究所聯(lián)合舉辦2019年學(xué)術(shù)年會,。大會于12月13日至14日在北方溫泉會議中心召開。大會邀請國內(nèi)外4位學(xué)者做50分鐘大會報告,，邀請北京理工大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院,、中國科學(xué)院應(yīng)用數(shù)學(xué)研究所18位教師做25分鐘邀請報告。希望通過年會,，進(jìn)一步加強(qiáng)交流與合作,，促進(jìn)產(chǎn)生更多優(yōu)秀創(chuàng)新成果。

歡迎感興趣的老師蒞臨現(xiàn)場,，具體報告摘要如下：

12月14日上午舉行大會報告

地點：第六會議室

8:00-8:10 田玉斌 院長講話

8:10-8:20 駱順龍 所長講話

 

大會報告主持人：駱順龍 研究員

8:20-9:10

曹道民 研究員

報告題目：不可壓歐拉方程的定常渦環(huán)解

 

9:10-10:00

房軍生 教授

報告題目：Operators in Type II1 factors

 

10:00-10:20

茶歇

 

大會報告主持人：陳振慶 教授

10:20-11:10

張土生 教授

報告題目：Stochastic reaction diffusion equations

 

11:10-12:00

王啟華 研究員

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

 

12:10-13:20

午餐（地點：一樓中餐廳）

 

14日中午舉辦教學(xué)會議報告

主持人：李炳照 教授

地點：第六會議室

 

13:20-13:50

林海 教授

報告題目：教學(xué)成果與課程改革

 

 

14日下午三場分會場報告

 

量子計算與代數(shù)分會場

主持人：萬金奎 教授

地點：第一會議室

 

2：00-2：25

駱順龍：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

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

 

3:40-4:00

茶歇

 

統(tǒng)計與概率分會場

主持人： 席福寶 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

張讓讓：Large deviation principles for first-order scalar conservation laws with stochastic forcing

方程理論分會場

主持人：王一夫 教授

地點：第三會議室

 

2：00-2：25

黃飛敏：Thermal creep flow in gas motion(氣體運(yùn)動中的熱蠕變流動)

2：25-2：50

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

2：50-3：15

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

3：15-3: 40

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

 

3:40-4:00

茶歇

 

優(yōu)化分會場

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

李慶娜：An Efficient Semismooth Newton’s Method for  Support Vector Machine

 

 

 

計算數(shù)學(xué)與人工智能分會場

主持人：姜海燕 副教授

地點：第五會議室

 

2：00-2：25

張世華：Towards Understanding Residual and Dilated Dense Neural Networks

2：25-2：50

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

2：50-3：15

劉曉東：Inverse scattering with phaseless far field data

3：15-3: 40

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

 

3:40-4:00

茶歇

計算與模糊分會場

主持人： 史福貴 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

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

6：00-8：00

晚餐（一樓中餐廳）

2019年數(shù)學(xué)與統(tǒng)計學(xué)學(xué)術(shù)年會組委會

                                                 2019．12．10

 

報告摘要

 

曹道民 廣州大學(xué)教授,、研究員

題目： 不可壓歐拉方程的定常渦環(huán)解

摘要： 報告人將報告近年來在不可壓歐拉方程定常渦解方面的研究，特別地要介紹在二維時渦補(bǔ)丁解（vortex patch)和 三維時渦環(huán)解（vortex ring）存在性和唯一性方面的結(jié)果,。報告人將講述渦補(bǔ)丁解的存在唯一性與Kirchhoff - Routh 函數(shù)臨界點之間的聯(lián)系,，而Kirchhoff - Routh 臨界點又與方程所在區(qū)域的幾何性質(zhì)密切相關(guān)。  報告人主要介紹的結(jié)果是來源于和郭玉霞,、彭雙階,、嚴(yán)樹森合作的論文及和王國棟、萬杰,、詹偉城合作的論文,。

 

 

房軍生 河北師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授

題目：  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.

 

 

張土生 英國曼徹斯特大學(xué)教授

題目:    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.

 

 

王啟華 中國科學(xué)院數(shù)學(xué)研究院研究員

題目： 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.

 

駱順龍 中科院應(yīng)用數(shù)學(xué)研究所 研究員

題目： 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 北京理工大學(xué)教授

題目： 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 中科院應(yīng)用數(shù)學(xué)研究所副研究員

題目：  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)].

 

謝迅 北京理工大學(xué)特別副研究員

題目： 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 北京理工大學(xué)特別副研究員

題目：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.

 

張讓讓 北京理工大學(xué)特別副研究員

題目: 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.

黃飛敏 中科院應(yīng)用數(shù)學(xué)研究所研究員

題目：Thermal creep flow in gas motion(氣體運(yùn)動中的熱蠕變流動)

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

 

王博 北京理工大學(xué)特別副研究員

題目: 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.

 

  楊建偉  北京理工大學(xué)特別副研究員

題目: 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).

 

 

 

鄭濤 北京理工大學(xué)特別副研究員

題目：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  中科院應(yīng)用數(shù)學(xué)研究所 副研究員

題目：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.

 

 

 

李慶娜 北京理工大學(xué)副教授

題目：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.

 

張世華 中科院應(yīng)用數(shù)學(xué)研究所研究員

題目：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.

 

張波 中科院應(yīng)用數(shù)學(xué)研究所研究員

題目：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.

 

劉曉東 中科院應(yīng)用數(shù)學(xué)研究所副研究員

題目： 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.

 

陳偉坤 北京理工大學(xué)特別副研究員

題目：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 北京理工大學(xué)特別副研究員

題目：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.

 

龐斌：北京理工大學(xué)特別副研究員

題目：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.