摘要：We identify two fractals if and only if they are bilipschitz equivalent. Fix a ratior, for dust-like graph-directed sets with ratio r and integer characteristic, we obtain a rigid theorem that these graph-directed sets are uniquely determined by their Hausdorff dimension (or integer characteristic) in the sense of bilipschitz equivalence. Using this rigidity theorem, we show that in a suitable class of self-similar sets, two totally disconnected self-similar sets without complete overlaps are bilipschitz equivalent. We also provide an algorithm to test complete overlaps in polynomial time.
题目：Identification of pre-microRNAs by characterizing their sequence order evolution information and secondary structure graphs
摘要：Distinction between pre-microRNAs (precursor microRNAs) and length-similar pseudo pre-microRNAs can reveal more about the regulatory mechanism of RNA biological processes. Machine learning techniques have been widely applied to deal with this challenging problem. However, most of them mainly focus on secondary structure information of pre-microRNAs, while ignoring sequence-order information and sequence evolution information.
We use new features for the machine learning algorithms to improve the classification performance by characterizing both sequence order evolution information and secondary structure graphs. We developed three steps to extract these features of pre-microRNAs. We first extract features from PSI-BLAST profiles and Hilbert-Huang transforms, which contain rich sequence evolution information and sequence-order information respectively. We then obtain properties of small molecular networks of pre-microRNAs, which contain refined secondary structure information. In total, our feature space covers 591 features. The maximum relevance and minimum redundancy (mRMR) feature selection method is adopted before support vector machine (SVM) is applied as our classifier. The constructed classification model is named MicroRNA-NHPred. The performance of MicroRNA-NHPred is high and stable, which is better than that of those state-of-the-art methods, achieving an accuracy of up to 94.83% on same benchmark datasets.
个人简介：喻祖国，湘潭大学二级教授，博导，博士。1997年于复旦大学数学系获博士学位。湖南省“芙蓉学者计划”特聘教授、湖南省首届享受政府特殊津贴专家、“智能计算与信息处理”教育部重点实验室副主任，教育部“长江学者和创新团队发展计划”创新团队和湖南省高校科技创新团队负责人、教育部“新世纪人才计划”人选, 澳大利亚昆士兰理工大学兼职教授 (Adjunct Professor, 2014-2016)、湖南省统计学会副会长、湖南省数学会及计算数学与应用软件学会常务理事。担任国际期刊Pacific J. Appl. Math.、Commun. Frac. Calc.、Chin. J. Biol.、Austin J. Comput. Biol. Bioinform. 的编委 。其主要从事分形和相关方法, 及在生物与环境数据分析、复杂网络分析中的应用研究。先后获得中国高校科学技术二等奖（2001年）、湖南省自然科学二等奖（2009、2016年，均排名第1）和湖南青年科技创新奖杰出奖（2009年，单独）等科研奖励。
题目：Some new results in complex differential and difference equations主讲：廖良文
摘要：In this talk, we will give some new results in complex differential equations and difference equations