Realizing Enveloping Algebras via Varieties of Modules

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L（A） generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R（A） of L（A）, this generalizes the main result of Riedtmann. We also obtain Green＇s formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R（A）.

Constructive Sets in Computable Sets

The original interpretation of the constructive set theory CZF in Martin-Lof's type theory uses the 'extensional identity types'. It is generally believed that these 'types' do not belong to type theory. In this paper it will be shown that the interpretation goes through without identity types. This paper will also show that the interpretation can be given in an intensional type theory. This reflects the computational nature of the interpretation. This computational aspect is reinforced by an w-Set model of CZF

Linear algorithm for lexicographic enumeration of CFG parse trees

We study CFG parse tree enumeration in this paper. By dividing the set of all parse trees into infinite hierarchies according to height of parse tree, the hierarchical lexicographic order on the set of parse trees is established. Then grammar-based algorithms for counting and enumerating CFG parse trees in this order are presented. To generate a parse tree of height n, the time complexity is O（n）. If τ is a lowest parse tree for its yield, then O（n） =O（｜｜τ｜｜ ＋ 1）, where ｜｜τ｜｜ is the length of the sentence （yield） generated by τ. The sentence can be obtained as a by-product of the parse tree. To compute sentence from its parse tree （needn＇t be lowest one）, the time complexity is O（node）＋O（｜｜τ｜｜ ＋ 1）, where node is the number of non-leaf nodes of parse tree τ. To generate both a complete lowest parse tree and its yield at the same time, the time complexity is O（｜｜τ｜｜ ＋ 1）.

AOL4PS:A Large-scale Data Set for Personalized Search

Personalized search is a promising way to improve the quality of Websearch,and it has attracted much attention from both academic and industrial communities.Much of the current related research is based on commercial search engine data,which can not be released publicly for such reasons as privacy protection and information security.This leads to a serious lack of accessible public data sets in this field.The few publicly available data sets have not become widely used in academia because of the complexity of the processing process required to study personalized search methods.The lack of data sets together with the difficulties of data processing has brought obstacles to fair comparison and evaluation of personalized search models.In this paper,we constructed a large-scale data set AOL4 PS to evaluate personalized search methods,collected and processed from AOL query logs.We present the complete and detailed data processing and construction process.Specifically,to address the challenges of processing time and storage space demands brought by massive data volumes,we optimized the process of data set construction and proposed an improved BM25 algorithm.Experiments are performed on AOL4 PS with some classic and state-of-the-art personalized search methods,and the experiment results demonstrate that AOL4 PS can measure the effect of personalized search models.