Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of works on SGD, much less is known about the statistical inferential properties of predictions based on SGD solutions. In this talk, we introduce a novel procedure termedHiGrad to conduct statistical inference for online learning, without incurring additional computational cost compared with the vanilla SGD. The HiGrad procedure begins by performing SGD iterations for a while and then split the single thread into a few, and this procedure hierarchically operates in this fashion along each thread. With predictions provided by multiple threads in place, a t-based confidence interval is constructed by decorrelating predictions using covariance structures given by the Ruppert–Polyak averaging scheme.

The Mullineux conjecture is about computing the p-regular partition associated with the tensor product of an irreducible representation of a symmetric group with the sign representation. Since being formulated in 1979, the conjecture attracted a lot of attention and was not settled until 1997 when B. Ford and A. Kleshchev first proved it in a paper over a hundred pages. The proof was soon been shorten and, at the same time, its quantum version was also settled. The main ingredient of the proof is the modular branching rules.

In this talk, I will introduce an estimation methodology for a semiparametric quantile factor panel model. I will also talk about our proposed tools for inference that are robust to the existence of moments and to the form of weak cross-sectional dependence in the idiosyncratic error term. Specifically, we use sieve techniques to obtain preliminary estimators of the nonparametric beta functions, and use these to estimate the factor return vector at each time period. We then update the loading functions and factor returns sequentially.

题目：关于弦弧曲线的若干问题报告人：沈玉良 教授（苏州大学太平洋在线会员登录）时间：2018年7月6日（周五）下午14：30-15:30地点：宁静楼104室欢迎广大师生参加

Ramsey theory dates back to the 1930's and computing Ramsey numbers is a notoriously difficult problem in combinatorics. We study Ramsey numbers of graphs in Gallai colorings, where a Gallai coloring is a coloring of the edges of a complete graph such that no triangle has all its edges colored differently. Given an integer $k/ge1$ and ``forbidden" graphs $H_1, /ldots, H_k$, the Gallai-Ramsey number $GR(H_1, /ldots, H_k)$ is the least integer $n$ such that every Gallai coloring of the complete graph $K_n$ using $k$ colors contains a monochromatic copy of $H_i$ in color $i$ for some $i /in /{1, /ldots, k/}$. Gallai-Ramsey numbers are more well-behaved, though computing them is far from trivial.

A number of ion channels are observed to be sensitive to the temperature changes. These temperature-gated ion channels can detect the temperature thus regulate the internal homoeostasis and disease-related processes such as the thermal adaptation and the fever response. In order to understand how the temperature affects the ion channel mechanics, we develop a Poisson--Nernst--Planck--Fourier (PNPF) system through the energetic variational approach. With given form of the free energy functional and the entropy production, we achieve the mechanical equations and a temperature equation, which satisfy the laws of thermodynamics automatically. From the energy point of view, we also develop the numeric scheme which satisfy the discrete energy dissipation.

Let A be a sequence of complex numbers. In this talk we present a new family of asymptotic formulas for of digamma function of sequence A. Then we apply it and use residue theorem to obtain a new family of identities for Dirichlet series. As applications of these relations, we establish some relations of Euler sums and hyperbolic series. Moreover, we give many explicit formulas for non-alternating Euler sums with weight ≤ 6 in terms of Riemann zeta values, and for alternating Euler sums with weight ≤ 10 in terms of Riemann zeta values and polylogarithms.

题目：数学的意义报告人：席南华 院士地点：综合楼410室时间：2018年7月1日 14：30-15:30报告人简介：席南华，中国科学院院士，现任中科院数学与系统科学研究院院长；曾获国家自然科学奖二等奖、陈省身数学奖、首届国家杰出青年基金等。主要从事代数群与量子群领域研究，并取得了一系列突出的研究结果，对仿射A型Weyl群证明了Lusztig关于基环的猜想，成为国际上很多后续工作的基础之一，对代数群理论有重要贡献。欢迎各位参加