We consider the Whitehead problem for principal ideal domains of large size. It is proved, in ZFC, that some p.i.d.’s of size ≥ א2 have nonfree Whitehead modules even though they are not complete discrete valuation rings. A module M is a Whitehead module if ExtR(M,R) = 0. The second author proved that the problem of whether every Whitehead Z-module is free is independent of ZFC + GCH (cf. [5], ...

In this paper we present the Unison-CF algorithm, which provides an efficient way to combine multiple collaborative filtering approaches, drawing advantages from each one of them. Each collaborative filtering approach is treated as a separate component, allowing the Unison-CF algorithm to be easily extended. We evaluate the Unison-CF algorithm by applying it on three existing filtering approach...

We describe how we build the system for NTCIR-13 Short Text Conversation (STC) Chinese subtask. In our system, we use the retrieval-based method and the generationbased method respectively. For the retrieval-based method, we develop several features to match the candidates and then apply a learning to rank algorithm to get properly ranked results. For the generation-based method, we first gener...

There are many algorithms for optimizing the search engine results, ranking takes place according to one or more parameters such as; Backward Links, Forward Links, Content, click through rate and etc. The quality and performance of these algorithms depend on the listed parameters. The ranking is one of the most important components of the search engine that represents the degree of the vitality...

A key challenge of the collaborative filtering (CF) information filtering is how to obtain the reliable and accurate results with the help of peers’ recommendation. Since the similarities from small-degree users to large-degree users would be larger than the ones opposite direction, the large-degree users’ selections are recommended extensively by the traditional second-order CF algorithms. By ...

An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...

We develop a new collaborative filtering (CF) method that combines both previously known users’ preferences, i.e. standard CF, as well as product/user attributes, i.e. classical function approximation, to predict a given user’s interest in a particular product. Our method is a generalized low rank matrix completion problem, where we learn a function whose inputs are pairs of vectors – the stand...

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