报告一：Complete Solution to the Most General Nonlinear Filtering Problems and Its Implementation

摘要: The famous filtering problem of estimating the state of a stochastic dynamical system from noisy observations is of central importance in engineering. The problem is reduced to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time. The difficulty is that DMZ equation is a parabolic equation with coefficients in observations. This means that the DMZ equation is not available until in the application. In this lecture we shall show that this problem can be solved in real time theoretically. We present numerical algorithms for low dimensional problems implementation. Numerical simulations show the efficiency of our solutions.

报告二：Real time virus classification by natural vector method

摘要: The International Committee on Taxonomy of Viruses authorizes and organizes the taxonomic classification of viruses. However, the detailed classifications for all viruses are neither complete nor free from dispute. Using our proposed Natural Vector representation, all referenced viral genomes (including single-segmented and multiple-segmented) in GenBank can be embedded in . Unlike other approaches, this allows us to determine phylogenetic relations for all viruses at any level (e.g., Baltimore class, family, subfamily, genus, and species) in real time. Additionally, the proposed graphical representation for virus phylogeny provides a visualization of the distribution of viruses in . Our approach is successfully used to predict and correct viral classification information, as well as to identify viral origins. We further construct a virus database and an online inquiry system to server people who are interested in viral classification and prediction.

报告三：Protein universe and its applications

报告摘要：Current methods cannot tell us what the nature of the protein universe is concretely. Here we develop a novel method to realize the nature of protein universe. We show the protein universe can be realized as a protein space in 60-dimensional Euclidean space by using the distribution information of each amino acid within the protein. Every protein is in one-to-one correspondence with a point in protein space, where proteins with similar properties stay close together. Thus the distance between two points in protein space represents the biological distance of the corresponding two proteins. We also propose a natural graphical representation for inferring phylogeny. The representation is natural and unique based on the biological distances of proteins in protein space. This will solve the fundamental question of how proteins are distributed in the protein universe.

As an application, we shall answer the following fundamental question. What kinds of amino acid sequences could possibly be protein sequences? From all existing databases that we can find, known proteins are only a small fraction of all possible combinations of amino acids. Here we show that when the collection of arbitrary amino acid sequences is viewed in an appropriate geometric context, the protein sequences cluster together. This leads to a new computational test, described here, that has proved to be remarkably accurate at determining whether an arbitrary amino acid sequence can be a protein. Even more, if the results of this test indicate that the sequence can be a protein, and it is indeed a protein sequence, then its identity as a protein sequence is uniquely defined.

报告人简介：丘成栋，现任清华大学数学科学系教授。1976年毕业于美国纽约州立大学石溪分校，获理学博士学位。1980年加入伊利诺伊大学芝加哥分校工作。2011年辞去美国伊利诺伊大学教授职位，全职回到清华大学数学系科学系从事科研教学等一线工作。国际顶尖数学专业杂志《Journal of Algebraic Geometry》创始人与主编、应用数学杂志《Communications in Information and Systems》创始人与主编。已在国际期刊 Invert. Math.、Ann. of Math.、Automatica、IEEE Trans. Automat. Control、PloS ONE、Scientific Reports等上发表论文340余篇。主持国家自然科学基金面上项目2项，重点项目1项，重大研究计划1项。荣获美国数学学会Fellow(2013)，美国伊利诺伊大学杰出教授 (2005)，IEEE Fellow（2003），John Simon Guggenheim Fellowship（2000），Alfred P. Sloan Research Fellowship（1980）等奖项。

目前主要研究领域为代数几何、奇点理论；复几何；非线性滤波理论；生物信息学。现已在清华大学数学系创立了三个方向的研究团队：纯数学团队、生物信息学团队、控制论团队。欢迎热爱科研工作的优秀学生加入。