khKm,n的K1,k-因子分解

给出了多重完全二部图khKm,n具有K1,k-因子分解的必要条件及一个充分条件,其中k是质数,h是正整数.     

一类S~(φ*)图的补图的等价性分析

通过研究一类Sφ*图的伴随多项式的因式分解,证明了这类图的补图的色等价图的结构性质。     

中学数学里不定方程的解法

介绍二元一次不定方程和可分解因式的二元二次不定方程的初等解法。     

A novel recommendation method based on social network using matrix factorization technique

The rapid development of information technology and the fast growth of Internet have facilitated an explosion of information which has accentuated the information overload problem. Recommender systems have emerged in response to this problem and helped users to find their interesting contents. With increasingly complicated social context, how to fulfill personalized needs better has become a new trend in personalized recommendation service studies. In order to alleviate the sparsity problem of recommender systems meanwhile increase their accuracy and diversity in complex contexts, we propose a novel recommendation method based on social network using matrix factorization technique. In this method, we cluster users and consider a variety of complex factors. The simulation results on two benchmark data sets and a real data set show that our method achieves superior performance to existing methods.     

Realization of Shor's algorithm on an optical quantum computer

Aresearch team led by Prof.PAN Jianwei with the University of Science and Technology of China(USTC),CAS has been successful in performing Shor's algorithm,a quantum algorithm for factorization,in an optical quantum computer.The feat is also independently made by another team led by Andrew White from the University of Queensland in Brisbane,Australia.Both results were published in the 19 December,2007 issue of Physics Review Newsletters.     

基于丰度分布约束的NMF端元生成方法

非负矩阵分解（non-negative matrix factorization,NMF）端元生成方法可以同时获得端元和丰度,且支持乘式迭代实现目标函数优化,处理效率高,因此受到越来越多的关注。由于目标函数非凸,基于NMF的端元提取方法容易陷入局部极值。尽管采用增加约束的方式可以缓解局部极值问题,但往往会破坏NMF乘式迭代规则,从而降低NMF方法的处理效率。提出一种基于丰度分布约束的方法,利用矩阵迹运算实现目标函数乘式迭代优化。实验结果表明,该方法既能估计出准确的端元,又能提高端元生成的效率。     

一种基于因数分解的动态密钥分存方案研究

本文给出了一种基于因数分解的动态（t,n）-门限方案,该方案具有如下特点：（1）系统在更新系统密钥时,无须更改每个成员的子密钥;（2）当某个成员的子密钥泄密时,系统只须为该成员重新分配子密钥而不必更改其他成员的子密钥;（3）当新成员加入时,系统只须为新成员分配一个子密钥,而其他成员不受任何影响;（4）子密钥可无限制地多次使用;（5）恢复系统密钥时,采用并行过程。     

广义系统 Bezout 恒等式分析(英文)

讨论了广义系统Ｂｅｚｏｕｔ恒等式的状态空间实现问题,用更为简明的方式表述和证明了Ｗａｎｇ和Ｂａｌａｓ给出的结果,并分析了Ｗａｎｇ和Ｂａｌａｓ结果的物理意义．     

Modeling user preferences using neural networks and tensor factorization model

With the expansion of information on the web, recommendation systems have become one of the most powerful resources to ease the task of users. Traditional recommendation systems (RS) suggest items based only on feedback submitted by users in form of ratings. These RS are not competent to deal with definite user preferences due to emerging and situation dependent user-generated content on social media, these situations are known as contextual dimensions. Though the relationship between contextual dimensions and user’s preferences has been demonstrated in various studies, only a few studies have explored about prioritization of varying contextual dimensions. The usage of all contextual dimensions unnecessary raises the computational complexity and negatively influences the recommendation results. Thus, the initial impetus has been made to construct a neural network in order to determine the pertinent contextual dimensions. The experiments are conducted on real-world movies data-LDOS CoMoDa dataset. The results of neural networks demonstrate that contextual dimensions have a significant effect on users’ preferences which in turn exerts an intense impact on the satisfaction level of users. Finally, tensor factorization model is employed to evaluate and validate accuracy by including neural network’s identified pertinent dimensions which are modeled as tensors. The result shows improvement in recommendation accuracy by a wider margin due to the inclusion of the pertinent dimensions in comparison to irrelevant dimensions. The theoretical and managerial implications are discussed.     

一种基于隐式信任感知的MOOCs推荐方法

[目的/意义]随着MOOCs迅猛发展和普及,如何利用智能推荐技术为学习者从海量的MOOC中"寻找最佳课程"成为MOOC发展中需要解决的重要课题。[方法/过程]基于自我知觉理论和学习行为投入框架,充分利用学习行为日志和评分数据挖掘学习者之间的隐式信任关系,并通过信任传播建立MOOC社区信任网络,从而构建动态结合兴趣和隐式信任感知的混合推荐方法。为解决数据稀疏问题,提出基于信任的联合概率矩阵分解模型(TA-PMF),将课程评分矩阵、信任关系矩阵的分解相结合来挖掘用户及课程潜在特征,进而实现评分预测。[结果/结论]真实数据集测试结果表明,与显性评分值相比,学习行为投入信息对信任度构建贡献权重达到0.7;TA-PMF方法对MOOC推荐具有较好的适用性,且能在一定程度上缓解冷启动问题。