題目一：Maximum principles for P1-P0 weak Galerkin finite element approximations of quasi-linear Second order elliptic equations

内容簡介：In this talk, designing recovery algorithms for generalized linear models (GLMs) using approximate standard Bayesian inference algorithms (approximate message passing (AMP), vector approximate message passing (VAMP), sparse Bayesian learning (SBL), variational Bayesian inference (VBI)) will be presented. Substantial examples such as image classification, parameter estimation from quantized data and phase retrieval can be formulated as a GLM problem. Compared to the standard linear models (SLMs), solving the GLMs is more challenging because of the coupling of the linear and nonlinear transforms. Although the generalized approximate message passing (GAMP) algorithm has been proposed to solve the GLMs, it does not provide any insight into the relationship between the SLMs and GLMs. According to expectation propagation (EP), the GLM can be iteratively approximated as a sequence of SLM subproblems, and thus the standard Bayesian algorithm can be easily extended to solve the GLMs.

報告人：吉林大學  張然  教授

報告人簡介：博士生導師。主要從事非标準有限元方法、随機微分方程數值解、多尺度分析及應用、金融衍生産品的數值計算等課題研究。在包括計算數學領域的重要期刊《SIAM J Numerical Analysis》、《SIAM J Scientific Computing》、《Mathematics of Computation》、《IMA J Numerical Analysis》等上發表學術論文50餘篇。2013年，入選教育部新世紀人才獎勵計劃；2016年，入選“長江學者獎勵計劃”青年學者；2018年獲國務院政府特殊津貼。

題目二：Relevant sampling in finitely generated shift-invariant spaces (II)

内容簡介：We consider random sampling in finitely generated shift-invariant spaces $V(/Phi) /subset {/rm L}^2(/mathbb{R}^n)$ generated by a vector $/Phi = (/varphi_1,/ldots,/varphi_r) /in ( {/rm L}^2(/mathbb{R}^n))^r$. Following the approach introduced by Bass and Gr/"ochenig, we consider certain relatively compact subsets $V_{R,/delta}(/Phi)$ of such a space, defined in terms of a concentration inequality with respect to a cube with side lengths $R$. Under very mild assumptions on the generators, we show that for $R$ sufficiently large, taking $O(R^n log(R))$ many  random samples (taken independently uniformly distributed within $C_R$) yields  a sampling set for $V_{R,/delta}(/Phi)$ with high probability. We give explicit estimates of all involved constants in terms of the generators $/varphi_1, /ldots, /varphi_r$.

報告人：中山大學  冼軍  教授

報告人簡介：博士生導師、廣東省千百十人才工程入選者、國家優秀青年基金獲得者。2004年畢業于中山大學數學系獲理學博士學位，同年進入浙江大學博士後流動站，2006年返回中山大學數學學院任副教授、教授、碩士研究生導師、博士研究生導師。主要研究方向為應用調和分析、采樣理論及其在信号處理中的應用。2004年至今訪問過美國耶魯大學、美國中佛羅裡達大學、加拿大Alberta大學，德國亞琛工業大學、法國馬賽大學、新加坡國立大學、香港城市大學等高校，相關論文發表在APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS，JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS，BMC BIOINFORMATICS，SIGNAL PROCESSING，PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY，JOURNAL OF APPROXIMATION THEORY等國内外核心期刊。

時  間：2018年11月17日（周六）上午8：00始

地  點：南海樓330室

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