Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses

A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses

Multi-breathers and high order rogue waves for the nonlinear Schr\"odinger equation on the elliptic function background

We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The dynamics of the breathers in the presence of various kinds of backgrounds such as dn, cn, and non-trivial phase-modulating elliptic solutions are presented, and their behaviors dependent on the effect of backgrounds are elucidated. We also determine the asymptotic behaviors for the multi-breather solutions with different velocities in the limit $t\to\pm\infty$, where the solution in the neighborhood of each breather tends to the simple one-breather solution. Furthermore, we exactly solve the linearized NLSE using the squared eigenfunction and determine the unstable spectra for elliptic function background. By using them, the Akhmediev breathers arising from these modulational instabilities are plotted and their dynamics are revealed. Finally, we provide the rogue-wave and higher-order rogue-wave solutions by taking the special limit of the breather solutions at branch points and the generalized Darboux transformation. The resulting dynamics of the rogue waves involves rich phenomena: depending on the choice of the background and possessing different velocities relative to the background. We also provide an example of the multi- and higher-order rogue wave solution.Comment: 45 pages, 16 figure

Dual-reference Face Retrieval

Face retrieval has received much attention over the past few decades, and many efforts have been made in retrieving face images against pose, illumination, and expression variations. However, the conventional works fail to meet the requirements of a potential and novel task --- retrieving a person's face image at a specific age, especially when the specific 'age' is not given as a numeral, i.e. 'retrieving someone's image at the similar age period shown by another person's image'. To tackle this problem, we propose a dual reference face retrieval framework in this paper, where the system takes two inputs: an identity reference image which indicates the target identity and an age reference image which reflects the target age. In our framework, the raw images are first projected on a joint manifold, which preserves both the age and identity locality. Then two similarity metrics of age and identity are exploited and optimized by utilizing our proposed quartet-based model. The experiments show promising results, outperforming hierarchical methods.Comment: Accepted at AAAI 201