《系统科学与复杂性》（英文版）编辑部  主办

中国科学院数学机械化重点实验室 承办

 

 

 

报告1：朱春钢（大连理工大学）9:10-9:35

报告题目：Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain

【摘要】 Inspired by the r-refinement method in isogeometric analysis, in this paper, the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information, which is more straightforward and effective. The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee. Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.

 

【报告人简介】  朱春钢，大连理工大学数学科学学院教授，博士生导师。2000年于山东大学获信息与计算科学专业学士学位，2005年于大连理工大学获计算数学专业博士学位，2005年至今在大连理工大学数学科学学院工作。现任中国工业与应用数学学会常务理事，辽宁省计算数学与数据智能重点实验室副主任，计算科学研究所所长。目前主要从事计算几何与计算机辅助几何设计方向的研究工作，发表多篇论文，出版教材2部，主持多项国家自然科学基金项目。个人主页: http://faculty.dlut.edu.cn/zhu。

 

报告2：蔺宏伟（浙江大学）9:35-10:00

报告题目：Isogeometric Analysis-Based Topological Optimization for Heterogeneous Parametric Porous Structures

【摘要】 Porous structures widely exist in nature and artifacts, which can be exploited to reduce structural weight and material usage or improve damage tolerance and energy absorption. In this study, the authors develop an approach to design optimized porous structures with Triply Periodic Minimal Surfaces (TPMSs) in the framework of isogeometric analysis (IGA)-based topological optimization. In the developed method, by controlling the density distribution, the designed porous structures can achieve the optimal mechanical performance without increasing the usage of materials. First, the implicit functions of the TPMSs are adopted to design several types of porous elements parametrically. Second, to reduce the cost of computation, the authors propose an equivalent method to forecast the elastic modulus of these porous elements with different densities. Subsequently, the relationships of different porous elements between the elastic modulus and the relative density are constructed. Third, the IGA-based porous topological optimization is developed to obtain an optimal density distribution, which solves a volume constrained compliance minimization problem based on IGA. Finally, an optimum heterogeneous porous structure is generated based on the optimized density distribution. Experimental results demonstrate the effectiveness and efficiency of the proposed method.

 

【报告人简介】 蔺宏伟，浙江大学数学科学学院教授，博士生导师。1996年于浙江大学应用数学系获学士学位，后在国企工作三年，2004年于浙江大学数学系获博士学位。主持或参与国家自然科学基金、重点研发计划等项目若干项。近年来，从事计算机辅助几何设计、计算机辅助拓扑设计、量子图形学等方面的研究工作，发表或录用论文80余篇。曾获得陆增镛CAD&CG高科技一等奖、国家自然科学奖二等奖等学术荣誉。

 

报告3：雷娜（大连理工大学）10:00-10:25

报告题目：基于计算共形几何的结构化网格生成

【摘要】  CAD、CAE是实现智能制造的关键软件，网格生成是CAD/CAE的核心基础技术，是CAD/CAE一体化的桥梁。结构化网格具有存储资源省，计算精度高，数值计算收敛速度快等优点，但其自动化生成一直是领域中的难题。在这个报告中将介绍基于计算共形几何的结构化网格自动生成的前沿进展，并提出需要进一步探索研究的问题和潜在的发展方向。

 

【报告人简介】  雷娜，大连理工大学国际信息与软件学院党总支书记，教授，博士生导师。研究方向主要聚焦于计算共形几何、计算拓扑、计算机数学算法及其在人工智能、计算机图形学、几何建模和医学图像中的应用。主持国家杰出青年科学基金、国家重点研发计划课题、国家自然科学基金重点项目、面上项目以及中央部委创新项目等。学术成果多次被菲尔兹奖获得者或美国科学院院士等在国际会议上介绍；获得的知识产权在工业界成功应用，开发的软件被应用单位评价“超过商业软件”。担任网格生成领域国际顶会IMR 唯一亚洲committee member。获得世界华人数学家大会最佳论文奖。

 

报告4：于立佳（中国科学院数学与系统科学研究院）10:35-11:00

报告题目：鲁棒神经网络的逼近定理

【摘要】 神经网络的逼近定理保证了神经网络强大的拟合能力，让神经网络可以被应用到各种场合。但是，现在的神经网络仍然存在一些问题，比如说神经网络的鲁棒性仍然有待提高。我们从理论的角度出发，给出了神经网络鲁棒逼近所需要的参数数量，论证了如何提升网络的鲁棒性是最优的，并解决了相关的一些问题。

 

【报告人简介】 于立佳、2018年进入中国科学院数学与系统科学研究院攻读硕士学位，并于2020年继续攻读博士学位。从入学至今一直在研究神经网络的对抗攻击，防御以及数据投毒，并在高小山老师的指导下完成了数篇论文，获得了两次奖学金。

 

报告5：潘彦斌（中国科学院数学与系统科学研究院）11:00-11:25

报告题目：Polynomial-Time Key-Recovery Attacks against NTRUReEncrypt from ASIACCS’15

【摘要】  In ASIACCS 2015, Nuuez, Agudo, and Lopez proposed a proxy re-encryption scheme, NTRUReEncrypt, based on NTRU. Because of the potential resistance to quantum algorithm, high efficiency and various applications in real life, its security has been widely discussed and analyzed. In PQCrypto2019, Liu et al. proposed two key recovery attacks against NTRUReEncrypt. However, their attack are unrealistic. In this talk, inspired by the broadcast attack against NTRU, we find out that the an adversary can recover the  private key in the communication in polynomial time, which means we break the scheme. In addition, we construct an altered version of NTRUReEncrypt to resist our attacks.

 

【报告人简介】  潘彦斌，中国科学院数学与系统科学研究院副研究员，博士生导师。2005年6月获南京大学学士学位，2010年7月获中国科学院数学与系统科学研究院博士学位。2018年至2019年任美国俄克拉荷马大学访问学者。研究兴趣主要包括格算法与格密码的安全性分析，计算数论等。目前在EUROCRYPT，CRYPTO, ASIACRYPT，PKC, IEEE Trans. on Information Theory等会议期刊发表学术论文多篇；曾担任ISC，Africacrypt等国际会议程序委员会委员，《密码学报》编委，《Journal of Systems Science and Complexity》青年编委；主持国家自然科学基金项目2项，参与国家重点研发计划，国家自然科学基金重点项目等多项。

 

报告6：林昌露（福建师范大学）11:25-11:50

报告题目：Ramp Scheme Based on CRT for Polynomial Ring over Finite Field

【摘要】Chinese Reminder Theorem (CRT) for integers has been widely used to construct secret sharing schemes for different scenarios, but these schemes have lower information rates than that of Lagrange interpolation-based schemes. In ASIACRYPT 2018, Ning, et al. constructed a perfect (r, n)-threshold scheme based on CRT for polynomial ring over finite field, and the corresponding information rate is one which is the greatest case for a (r, n)-threshold scheme. However, for many practical purposes, the information rate of Ning, et al. scheme is low and perfect security is too much security. In this work, the authors generalize the Ning, et al. (r, n)-threshold scheme to a (t, r, n)-ramp scheme based on CRT for polynomial ring over finite field, which attains the greatest information rate (r ？ t) for a (t, r, n)-ramp scheme. Moreover, for any given 2 ≤ r1 < r2 ≤ n, the ramp scheme can be used to construct a (r1, n)-threshold scheme that is threshold changeable to (r, n)-threshold scheme for all r’ ∈ {r1 + 1, r1 + 2, · , r2}. The threshold changeable secret sharing (TCSS) scheme has a greater information rate than other existing TCSS schemes of this type.

 

【报告人简介】 林昌露，现为福建师范大学数学与统计学院教授、博士生导师。中国密码学会（CACR）组织工作委员会委员、区块链专委会委员，中国工业与应用数学学会（CSIAM）编码密码及相关组合理论专业委员会委员，全国密码数学挑战赛竞赛组织委员会委员，中国计算机学会（CCF）区块链专委会执行委员。中国科学院大学（原中国科学院研究生院）国家信息安全重点实验室博士毕业，曾访问英国、新加坡、加拿大、台湾及大陆部分高校。主要研究兴趣包括秘密分享与安全多方计算、公钥密码及在区块链等应用；在IEEE Trans. IT、 DCC、密码学报，ProvSec 2020等国内外学术刊物及会议上发表论文70余篇。先后主持国家自然科学基金项目3项，福建省自然科学基金项目3项；参与国家自然科学基金3项；福建省自然科学基金项目2项。授权发明专利1项。

 

报告7：张 彪（天津师范大学）14:00-14:25

报告题目：The Log-Concavity of Kazhdan-Lusztig Polynomials of Uniform Matroids

【摘要】Elias, Proudfoot, and Wakefield conjectured that the Kazhdan-Lusztig polynomial of any matroid is log-concave. Inspired by a computer proof of Moll's log-concavity conjecture given by Kauers and Paule, we use a computer algebra system to prove the conjecture for arbitrary uniform matroids.

 

【报告人简介】张彪，天津师范大学副教授。研究方向为组合数学，主要从事对称函数理论和单峰型理论方面的研究工作。2015年6月博士毕业于南开大学。2018年8月至2019年8月赴美国宾夕法尼亚大学访问。在《Journal of Combinatorial Theory, Series A》、《Advances in Applied Mathematics》、《SIAM Journal on Discrete Mathematics》等期刊发表学术论文20余篇，主持国家自然科学基金项目3项。

 

报告8：王 瑾（浙江师范大学）14:25-14:50

报告题目：Nonlinear Inverse Relations of the Bell Polynomials via the Lagrange Inversion Formula (II)

【摘要】By means of the classical Lagrange inversion formula, the authors establish a general nonlinear inverse relation as the solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell polynomials via the Lagrange inversion formula, J. Integer Seq., Vol. 22 (2019), Article 19.3.8]. As applications of this inverse relation, the authors not only find a short proof of another nonlinear inverse relation due to Birmajer, et al. (2012), but also set up a few convolution identities concerning the Mina polynomials.

 

【报告人简介】王瑾，讲师，现任职于浙江师范大学，研究方向为组合反演，q-级数。本科毕业于浙江师范大学，后保送到苏州大学攻读硕博士学位。目前主持国家自然科学基金青年基金一项，主持省自然科学基金一项，到目前为止，在Advances in Applied Mathematics、Proceedings of the American Mathematical Society、The Ramanujan Journal等本领域知名期刊上发表论文10余篇。

 

报告9：吴弢（湖南科技大学）14:50-15:15

报告题目：Smith Form of Triangular Multivariate Polynomial Matrix

【摘要】  The Smith form of a matrix plays an important role in the equivalence of matrix. It is known that some multivariate polynomial matrices are not equivalent to their Smith forms. In this paper, the authors investigate mainly the Smith forms of multivariate polynomial triangular matrices and testify two upper multivariate polynomial triangular matrices are equivalent to their Smith forms respectively.

 

【报告人简介】  2015年9月-2019年6月，湖南科技大学数学与计算科学学院，数学与应用数学，本科

2019年9月-2021年6月，湖南科技大学数学与计算科学学院，数学，硕士

2021年9月至今，湖南科技大学计算机科学与工程学院，软件工程，在读博士

 

报告10：鲁东（西南交通大学）15:15-15:40

报告题目：New Results on the Equivalence of Bivariate Polynomial Matrices

【摘要】  The equivalence of multivariate polynomial matrices is an important aspect in the theory of multidimensional systems with wide applications in areas of image processing, multidimensional signal analysis, iterative learning control systems, and so on. In this talk, we will introduce some new results on the equivalence of bivariate polynomial matrices. For example, a necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is proposed. Meanwhile, we present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms. In addition, we generalize the main result to the non-square case. This is a joint work with Dingkang Wang, Fanghui Xiao and Xiaopeng Zheng.

 

【报告人简介】  鲁东，副教授。2019年6月于中国科学院数学与系统科学研究院获得理学博士学位，博士导师是王定康研究员；2019年7月在北京航空航天大学数学科学学院从事博士后研究工作，合作导师是王东明教授；2021年7月入职西南交通大学数学学院。研究领域为符号计算，主要涉及多项式系统的符号求解方法、多元多项式矩阵的分解与等价问题研究，与国内外学者合作发表论文十余篇，现主持国家自然科学基金青年项目一项。