报告题目： 有限域上迹的研究

摘要： 有限域的迹(trace)，是一个常见的概念，在理论上和应用上都有相当的重要性。由于对平方剩余码译码的需要，我们对有限域的迹做了一些研究。从去年八月份开始，我们全力投入这项研究，研究室的三十几部计算机，每部计算机上安装两个Mathematica软件，24小时不停地计算，提供相关数据。最近我们完成了主要定理的证明，算是阶段性地完成了理论部分的工作。

　　在这个报告中，我们将对整个研究工作的始末做一个介绍。

报告题目： Numerical Sparsity? Determination and Early Termination

摘要：Ankur Moitra in his paper at STOC 2015 has given an in-depth analysis of how oversampling improves the conditioning of the arising Prony systems for sparse interpolation and signal recovery from numeric data. Moitra assumes that oversampling is done for a number of samples beyond the actual sparsity of the polynomial/signal. We give an algorithm that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation. The early termination strategy of polynomial interpolation has been incorporated in the algorithm: by oversampling at a small number of extra sample points we can diagnose that the sparsity has not been reached.Our algorithm still has to make a guess of the number s of oversamples, and we show by example that if s the number is guessed too small, premature termination can occur, but our criterion is numerically more accurate than that by Kaltofen, Lee and Yang (Proc. SNC 2011, ACM) but not as efficiently computable. For heuristic justification ne has available the multivariate early termination theorem by Kaltofen and Lee (JSC vol. 36(3-4) 2003) for exact arithmetic, and the numeric Schwartz-Zippel Lemma by Kaltofen, Yang and Zhi (Proc. SNC 2007, ACM). A main contribution here is a modified proof of the Theorem by Kaltofen and Lee that permits starting the sequence at the point (1,...,1), for scalar fields of characteristic not equal 2(in characteristic 2 counter-examples are given).
Joint work with Erich Kaltofen and Zhiwei Hao. 

报告题目： 基于影像数据的智能医疗决策

摘要： 面对资源紧张且分布不均的公共医疗卫生服务，智能医疗决策支持系统应运而生。智能医疗决策是现代健康信息系统的新型特征，如何实现智能决策是其关键。我们初步探讨了智能医疗决策问题，通过构建基于影像数据的深度学习网络模型，实现皮肤病智能预测分类的方法框架。实际数据验证结果表明，皮肤病智能决策方法能够学习医生的经验并达到预期的实用目标，从而有效缩减医生的重复劳动和提高工作效率。