杜克大学和清华大学构建了以研究生助教教学能力提升证书项目为核心的助教培养体系.杜克大学的证书项目包含了丰富的学习课程、多样的教学实践、双向的教学观摩、深度的教学研讨和全面的教学辅助等内容;清华大学的证书项目包含了有层次的课程学习、有梯度的岗位实践和有节奏的教学研讨等内容.基于此,本文得出了重视助教在教育教学中的作用、构建系统化的助教培养体系、打通助教工作与求职间的通路等重要启示.

面向第四次产业革命,培养能够实现"从0到1"范式突破的创新人才,并建立高质量创新人才培养的长效机制,不仅是关系到"两个大局"如何破局的关键问题,更是关系到中华民族百年大计甚至千年大计的重大命题.清华大学钱学森力学班(以下简称"清华钱班")经过10年的探索,初步实现了对上述命题的"点"突破.在此基础之上,清华钱班与深圳有关部门经过近1年的共同探索,共同构建了体现我国制度和文化优势的创新人才培养机制——"零一学院".相信沿着这个方向坚持10年,一定可以初步建立一个以深圳为起点,辐射全国的创新人才培养体系,为高等教育提供一个拔尖创新人才培养的新范式.

A fullerene graph is a planar cubic graph with only pentagonal and hexagonal faces. It has been proved that fullerene graphs have exponentially many perfect matchings. The lower bound for this number has been studied in the last 20 years. The best known result is 2(n-380/61), which is given in [13] by using the four color theorem. We generalize the structure using in [13] and obtain the improved lower bound 2(n-1820/47.29).

在大部分高中学生要进入大学学习的今天,更好地衔接中学与大学的数学教育,是非常值得关注的课题,特别针对中学生的以团队方式解决问题的综合训练,对提升人才培养质量、培养提高学生的创新能力都是至关重要的.全国大学生数学建模竞赛经过二十多年的建设与发展,已经进入了健康有序的发展阶段,并拥有一支一流的专家团队.为进一步强化数学建模在人才培养中的地位和作用,基于全国大学生数学建模竞赛多年的经验,在中国教师发展基金会的大力资助下,在清华大学教育研究院等单位的协调、支持、配合下,首届“登峰杯”全国中学生数学建模竞赛及夏令营圆满结束.全国大学生数学建模竞赛组委会及专家组的多位专家承担了出题和各项评阅工作.

"清华学堂人才培养计划"作为国家"拔尖计划"的组成部分,经历了7年的改革与实践,"领跑者"理念初见成效。但同时也需要探索进一步上升和提高的空间,激励和引导学生追求卓越、超越自我。本文在简要分析国际上高水平大学荣誉学位项目经验的基础上,对清华荣誉学位的定位与钱学森力学班荣誉学位项目构建的指导原则、荣誉学位方案设计和实施等进行了较为详细的阐述。荣誉学位是对"领跑者"理念的深化。

The permanental polynomial of IPR fullerene C-70(D-5h) is computed with quadruple precision arithmetic based on sparse graph on PC in acceptable time. The computing adopts 128 bits to store one float and works well for C-70, while the largest fullerene computed before is C-60, which can be easily obtained now. Some properties of the coefficients and zeroes of the permanental polynomials of IPR fullerenes C-60 and C-70 are also investigated. Computational results show the quadruple precision method can handle permanental polynomial of C-70 and even larger fullerenes, which are of interest in applications.

Advertisement (ad) selection plays an important role in sponsored search, since it is an upstream component and will heavily influence the effectiveness of the subsequent auction mechanism. However, most existing ad selection methods regard ad selection as a relatively independent module, and only consider the literal or semantic matching between queries and keywords during the ad selection process. In this paper, we argue that this approach is not globally optimal. Our proposal is to formulate ad selection as such an optimization problem that the selected ads can work together with downstream components (e.g., the auction mechanism) to achieve the maximization of user clicks, advertiser social welfare, and search engine revenue (we call the combination of these objective functions as the marketplace objective for ease of reference). To this end, we 1) extract a bunch of features to represent each pair of query and keyword, and 2) train a machine learning model that maps the features to a binary variable indicating whether the keyword is selected or not, by maximizing the aforementioned marketplace objective. This formalization seems quite natural; however, it is technically difficult because the marketplace objective is non-convex, discontinuous, and indifferentiable regarding the model parameter due to the ranking and second-price rules in the auction mechanism. To tackle the challenge, we propose a probabilistic approximation of the marketplace objective, which is smooth and can be effectively optimized by conventional optimization techniques. We test the ad selection model learned with our proposed method using the sponsored search log from a commercial search engine. The experimental results show that our method can significantly outperform several ad selection algorithms on all the metrics under investigation.

数据分割研究的基本内容是数据的分类和聚类,是数据挖掘的核心问题之一,在实际问题中应用广泛.特别是针对有向网络数据的研究更是学科发展的前沿.但由于这类问题结构的非对称性,使得模型与算法的构建存在本质困难,因此相应的研究结果较少.本文借鉴分子动力学方法的思想,提出了一类新的网络数据半监督分类模型及算法.该算法不仅适用于关系对称的无向网络数据,而且适用于关系非对称的有向网络.最后针对期刊引用网络数据进行了数值实验,结果表明了模型及算法的可行性和有效性.

Jones and Nachtsheim (2011) propose a new class of designs for definitive screening. These designs have very nice properties for practical use. Their construction approach requires a computerized search. This short note provides a theoretical basis for design construction, making use of conference matrices. The design construction is straightforward, and the resulting design is always a global optimum definitive screening design. The proposed method only works when the number of factors is even, however.

SUMMARYThe research in parallel machine scheduling in combinatorial optimization suggests that the desirable parallel efficiency could be achieved when the jobs are sorted in the non‐increasing order of processing times. In this paper, we find that the time spending for computing the permanent of a sparse matrix by hybrid algorithm is strongly correlated to its permanent value. A strategy is introduced to improve a parallel algorithm for sparse permanent. Methods for approximating permanents, which have been studied extensively, are used to approximate the permanent values of submatrices to decide the processing order of jobs. This gives an improved load balancing method. Numerical results show that the parallel efficiency is improved remarkably for the permanents of fullerene graphs, which are of great interests in nanoscience. Copyright © 2012 John Wiley & Sons, Ltd.

Several relations between the coefficients of the permanental and characteristic polynomials were given by Gutman and Cash [MATCH Commun. Math. Comput. Chem. 45 (2002) 55-70]. In this paper, some more and general connections between those coefficients are presented.

Two-state spin system is a classical topic in statistical physics. We consider the problem of computing the partition function of the system on a bounded degree graph. Based on the self-avoiding tree, we prove the system exhibits strong correlation decay under the condition that the absolute value of inverse temperature is small. Due to strong correlation decay property, an FPTAS for the partition function is presented and uniqueness of Gibbs measure of the two-state spin system on a bounded degree infinite graph is proved, under the same condition. This condition is sharp for Ising model.

We propose an improved algorithm for counting the number of Hamiltonian cycles in a directed graph. The basic idea of the method is sequential acceptance/rejection, which is successfully used in approximating the number of perfect matchings in dense bipartite graphs. As a consequence, a new ratio of the number of Hamiltonian cycles to the number of 1-factors is proposed. Based on this ratio, we prove that our algorithm runs in expected time of O(n^8^.^5) for dense problems. This improves the Markov chain Monte Carlo method, the most powerful existing method, by a factor of at least n^4^.^5(logn)^4 in running time. This class of dense problems is shown to be nontrivial in counting, in the sense that they are #P-Complete.

The state equations of stochastic control problems, which are controlled stochastic differential equations, are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved. Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk. This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.

Query suggestion algorithms, which aim to suggest a set of similar but independent queries to users, have been widely studied to simplify user searches. However, in many cases, the users will accomplish their search tasks through a sequence of search behaviors instead of by one single query, which may make the classical query suggestion algorithms fail to satisfy end users in terms of task completion. In this paper, we propose a quantum path integral inspired algorithm for personalized user search behavior prediction, through which we can provide sequential query suggestions to assist the users complete their search tasks step by step. In detail, we consider the sequential search behavior of a user as a trajectory of a particle that moves in a query space. The query space is represented by a graph with each node is a query, which is named as query-path graph. Inspired by the quantum theorems, each edge in query-path graph is represented by both amplitude and phase respectively. Using this graph, we modify the quantum path integral algorithm to predict a user’s follow-up trajectory based on her behavioral history in this graph. We empirically show that the proposed algorithm can well predict the user search behavior and outperform classical query suggestion algorithms for user search task completion using the search log of a commercial search engine.

Fowler-Manolopoulos criterion, that is defined as the second moment of the hexagon neighbor signature, is one of the most powerful predictors for fullerene stability. In this note, we present a relationship between Fowler-Manolopoulos predictor and another hexagonal parameter, which could give Fowler-Manolopoulos predictor a graphical explanation. This result can be regarded as an understanding of Fowler-Manolopoulos criterion.

Stochastic action integral and Lagrange formalism of stochastic Hamiltonian systems are written through construing the stochastic Hamiltonian systems as nonconservative systems with white noise as the nonconservative 'force'. Stochastic Hamilton's principle and its discrete version are derived. Based on these, a systematic approach of producting symplectic numerical methods for stochastic Hamiltonian systems, i.e., the stochastic variational integrators are established. Numerical tests show validity of this approach.

Brégman-Minc theorem gives the best known upper bound of the permanent of (0, 1)-matrices. A new proof of the theorem is presented in this paper, using an unbiased estimator of permanent [L.E. Rasmussen, Approximating the permanent: a simple approach, Random Structures Algorithms 5 (1994), p. 349]. This proof establishes a connection between the randomized approximate algorithm and the bound estimation for permanents.

For a periodic optimal control problem, the midpoint rule is proposed to discretize the state equation for the Markov chain approximation method, to produce and improve the numerical feedback solutions. Symplec-tic methods are applied to the controlled Hamiltonian system related to the maximum principle to give better open-loop solutions than non-symplectic method.