题目一：Reconstruction of Bandlimited Graph Signals from Random Local Sampling

内容简介：In this talk, we will present random sampling and reconstruction for bandlimited graph signals. The random sampling of signals residing on graphs is one of the fundamental topics in graph signal processing.  On the other side，we consider the random sampling of k-bandlimited signals from the local measurements and show that no more than O(k log k) samples taken with replacement are sufficient to ensure the accurate and stable recovery of all k-bandlimited graph signals.

报告人：冼军

报告人简介：中山大学数学学院教授、博士生导师、中国数学会理事、广东省数学会理事、广东省工业与应用数学学会副理事长。2004年毕业于中山大学获理学博士学位, 同年进入浙江大学数学博士后流动站, 2006年博士后出站至今在中山大学数学学院工作。主要研究方向为小波分析与应用调和分析、采样理论及其在信号处理中的应用。在Appl. Comput. Harmon. Anal., Inverse Probl., J. Fourier Anal. Appl., Proc. Amer. Math. Soc., J. Approx. Theory等国内外主流专业期刊发表多篇关于信号的采样与重构的理论及其应用的论文, 部分结果获得同行们的关注。曾作为项目负责人主持多项国家级和省部级基金项目。

题目二：MSR codes with linear field size and smallest sub-packetization for any number of helper nodes

内容简介：The sub-packetization $\ell$ and the field size $q$ are of paramount importance in the MSR array code constructions. For optimal-access MSR codes, Balaji \emph{et al.} proved that $\ell\geq s^{\left\lceil n/s \right\rceil}$, where $s = d-k+1$.Rawat \emph{et al.} showed that this lower bound is attainable for all admissible values of $d$ when the field size is exponential in $n$. After that, tremendous efforts have been devoted to reducing the field size. However, till now, reduction to linear field size is only available for $d\in\{k+1,k+2,k+3\}$ and $d=n-1$. In this work, we construct the first class of explicit optimal-access MSR codes with the smallest sub-packetization $\ell = s^{\left\lceil n/s \right\rceil}$ for all $d$ between $k+1$ and $n-1$,resolving an open problem in the survey (Ramkumar \emph{et al.}, Foundations and Trends in Communications and Information Theory: Vol. 19: No. 4). We further propose another class of explicit MSR code constructions (not optimal-access) with even smaller sub-packetization $s^{\left\lceil n/(s+1)\right\rceil }$ for all admissible values of $d$, making significant progress on another open problem in the survey. Previously, MSR codes with $\ell=s^{\left\lceil n/(s+1)\right\rceil }$ and $q=O(n)$ were only known for $d=k+1$ and $d=n-1$.The key insight that enables a linear field size in our construction is to reduce $\binom{n}{r}$ global constraints of non-vanishing determinants to $O_s(n)$ local ones, which is achieved by carefully designing the parity check matrices. This is a joint work with Guodong Li, Ningning Wang, and Min Ye.

报告人：胡思煌

报告人简介：山东大学网络空间安全学院教授，目前主要研究方向是通信与存储编码理论。在组合数学与信息论期刊和会议上发表20余篇论文，主持国家重点研发计划青年科学家项目、基金委青年项目和CCF-华为胡杨林基金。

题目三：Propagation Dynamics in Diffusion Equations with degenerate nonlinearities

内容简介：This talk is concerned with the traveling wave solutions and asymptotic spreading for a class of diffusion equations with degenerate nonlinearities. The influence of degeneracy on the propagation threshold and complete spreading or vanishing is explored. We first study the existence of traveling wave solutions by constructing proper super-solutions and show the monotonicity, asymptotic behavior, uniqueness up to translation and stability of traveling wave solutions. Then some sufficient conditions on the complete spreading or vanishing are given by using suitable super- and sub-solutions, which depend on the degeneracy of nonlinearity as well as the initial value. To illustrate our results, several degenerate equations are investigated, which shows that the degeneracy could slow down the propagation threshold.

报告人：薄伟健

报告人简介：西安电子科技大学，讲师，2016-2020年就读于兰州大学并获得理学博士学位，师从林国教授；2018-2020年在美国中佛罗里达大学做访问学者，师从齐远伟教授；2022年至今在西安电子科技大学数学流动站从事博士后研究，师从吴事良教授。研究领域为微分方程与动力系统、生物数学，特别关注一些经典模型的空间传播理论。已在JDDE、JMB、DCDS等SCI杂志正式发表论文10余篇。获得甘肃省自然科学二等奖1项（排名2/2），主持国家自然科学基金青年项目、澳门青年学者项目、第72批中国博士后面上项目各1项，参与国家自然科学基金面上项目3项。

时  间：2024年1月1日（周一）上午8：00 开始

地  点：腾讯会议889-509-851

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信息科学技术学院/网络空间安全学院

2023年12月29日