关于实对称矩阵的惯性定理

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度,介绍实对称矩阵的惯性定理的三种证明,以期加深对实对称矩阵的惯性定理的理解.     

长沙市近10年土地利用变化过程与未来趋势分析

为真实地刻画和揭示长沙市土地利用变化的过程与趋势,利用HJ-CCD及 ETM遥感影像获得长沙市2000—2010年的土地利用变化信息.利用变化幅度和动态度、土地利用转移矩阵和变化趋势指数,定量分析过去10年土地利用空间变化,预测各土地利用类型的变化趋势.结果表明：人工表面空间位置转移不频繁,未来变化趋势为强劲的涨势,扩张可能来自耕地、湿地以及未利用土地的系统性转入;耕地和林地的空间位置转移频繁;耕地的变化趋势为落势,未来流失方向是人工表面;林地变化趋势为落势,流失方向是人工表面和草地,转化为人工表面的可能性更大;草地以净增加为主,来自未利用土地转入的可能性更大;未利用土地以净流失为主特征,流失方向是人工表面.     

基于弹性大挠度理论的幕墙玻璃设计

根据弹性薄板大挠度理论,运用加权残值法分析计算幕墙玻璃的挠度和应力,并与幕墙玻璃规范设计进行比较,结果表明,基于非线性理论的设计计算是可行的.     

社会资本视阈下转型村庄的社会建设

社会资本是在社会建设反思阶段发展起来的理论概念,并成为当代社会建设的主题.村庄社会资本关注的是村民之间相互关系所构成的行动能力,与村庄公共物品生产具有密切关系.在传统社会向现代社会转型的过程中,作为村落资本的社会关系在属性、范围和结构方面发生了一些适应性的演变.村庄社会关系的"圈子性"特征所造成的网络封闭性,以及关系的变动性和理性化引起合作关系的不确定性,构成了资本运作的功能边界,也限制了社会合作的规模和能力.在社会资本的再生产过程中,包括家族、姻亲、拟亲缘关系在内的制度资源需要得到挖掘和重视,农民自治组织的培育是资本再生产的关键手段.     

基于矩阵划分和兴趣方差的协同过滤算法

数据稀疏性是协同过滤系统面临的一个巨大挑战。本文提出了一种新的推荐算法———基于矩阵划分和兴趣方差的协同过滤算法。该算法采用矩阵分块的思想来缩小最近邻搜索的范围。矩阵分块时,采用聚类的方法,大大降低了矩阵的维度和稀疏等级。同时引入兴趣方差的概念,提高了计算最近邻的准确度。实验证明,本文提出的过滤算法在预测精度上较传统的推荐算法有很大的提高。     

矩阵幂级数的收敛性质

根据矩阵幂级数的定义和数学分析中幂级数的收敛性质,运用类比的推理法,得到并验证了矩阵幂级数的部分相应的收敛性质。     

多变量系统状态反馈型的闭型解

基于广义逆矩阵的理论和Bellman最优性原理,给出了多输入多输出(MIMO)系统状态反馈型闭型解。对最优终端控制问题作了进一步的详细研究,导出了终端控制误差和控制能量与控制时间的关系。     

Search result diversification on attributed networks via nonnegative matrix factorization

Search result diversification is an effective way to tackle query ambiguity and enhance result novelty. In the context of large information networks, diversifying search result is also critical for further design of applications such as link prediction and citation recommendation. In previous work, this problem has mainly been tackled in a way of implicit query intent. To further enhance the performance on attributed networks, we propose a novel search result diversification approach via nonnegative matrix factorization. Our approach encodes latent query intents as well as nodes as representation vectors by a novel nonnegative matrix factorization model, and the diversity of the results accounts for the query relevance and the novelty w.r.t. these vectors. To learn the representation vectors of nodes, we derive the multiplicative updating rules to train the nonnegative matrix factorization model. We perform a comprehensive evaluation on our approach with various baselines. The results show the effectiveness of our proposed solution, and verify that attributes do help improve diversification performance.     

Aspect-based sentiment analysis with alternating coattention networks

Aspect-based sentiment analysis aims to predict the sentiment polarities of specific targets in a given text. Recent researches show great interest in modeling the target and context with attention network to obtain more effective feature representation for sentiment classification task. However, the use of an average vector of target for computing the attention score for context is unfair. Besides, the interaction mechanism is simple thus need to be further improved. To solve the above problems, this paper first proposes a coattention mechanism which models both target-level and context-level attention alternatively so as to focus on those key words of targets to learn more effective context representation. On this basis, we implement a Coattention-LSTM network which learns nonlinear representations of context and target simultaneously and can extracts more effective sentiment feature from coattention mechanism. Further, a Coattention-MemNet network which adopts a multiple-hops coattention mechanism is proposed to improve the sentiment classification result. Finally, we propose a new location weighted function which considers the location information to enhance the performance of coattention mechanism. Extensive experiments on two public datasets demonstrate the effectiveness of all proposed methods, and our findings in the experiments provide new insight for future developments of using attention mechanism and deep neural network for aspect-based sentiment analysis.     

正交矩阵的反问题及其最佳逼近

本文解决以下两个问题:问题1,给定X,B∈R~(n×m),寻找A∈H,使得AX=B,其中H表示所有n阶正交矩阵组成的集合,这样的A组成集合S,研究集S非空的充分必要条件,给出集S元素的通式表示。问题2,给定■∈R~(n×n),求■∈S使得■