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

内容簡介：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.

報告人：冼軍

報告人簡介：中山大學數學學院教授、博士生導師、中國數學會理事、廣東省數學會理事、廣東省工業與應用數學學會副理事長。2004年畢業于中山大學獲理學博士學位, 同年進入浙江大學數學博士後流動站, 2006年博士後出站至今在中山大學數學學院工作。主要研究方向為小波分析與應用調和分析、采樣理論及其在信号處理中的應用。在Appl. Comput. Harmon. Anal., Inverse Probl., J. Fourier Anal. Appl., Proc. Amer. Math. Soc., J. Approx. Theory等國内外主流專業期刊發表多篇關于信号的采樣與重構的理論及其應用的論文, 部分結果獲得同行們的關注。曾作為項目負責人主持多項國家級和省部級基金項目。

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

内容簡介：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.

報告人：胡思煌

報告人簡介：山東大學網絡空間安全學院教授，目前主要研究方向是通信與存儲編碼理論。在組合數學與信息論期刊和會議上發表20餘篇論文，主持國家重點研發計劃青年科學家項目、基金委青年項目和CCF-華為胡楊林基金。

題目三：Propagation Dynamics in Diffusion Equations with degenerate nonlinearities

内容簡介：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.

報告人：薄偉健

報告人簡介：西安電子科技大學，講師，2016-2020年就讀于蘭州大學并獲得理學博士學位，師從林國教授；2018-2020年在美國中佛羅裡達大學做訪問學者，師從齊遠偉教授；2022年至今在西安電子科技大學數學流動站從事博士後研究，師從吳事良教授。研究領域為微分方程與動力系統、生物數學，特别關注一些經典模型的空間傳播理論。已在JDDE、JMB、DCDS等SCI雜志正式發表論文10餘篇。獲得甘肅省自然科學二等獎1項（排名2/2），主持國家自然科學基金青年項目、澳門青年學者項目、第72批中國博士後面上項目各1項，參與國家自然科學基金面上項目3項。

時  間：2024年1月1日（周一）上午8：00 開始

地  點：騰訊會議889-509-851

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太阳集团1088vip/網絡空間安全學院

2023年12月29日