Invertibility of symmetric random matrices

We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the spectrum of H is delocalized on the optimal scale o(n^{-1/2}). These results improve upon a polynomial singularity bound due to Costello, Tao and Vu, and they generalize, up to constant factors, results of Tao and Vu, and Erdos, Schlein and Yau.Comment: 53 pages. Minor corrections, changes in presentation. To appear in Random Structures and Algorithm

Optimal Information Retrieval with Complex Utility Functions

Existing retrieval models all attempt to optimize one single utility function, which is often based on the topical relevance of a document with respect to a query. In real applications, retrieval involves more complex utility functions that may involve preferences on several different dimensions. In this paper, we present a general optimization framework for retrieval with complex utility functions. A query language is designed according to this framework to enable users to submit complex queries. We propose an efficient algorithm for retrieval with complex utility functions based on the a-priori algorithm. As a case study, we apply our algorithm to a complex utility retrieval problem in distributed IR. Experiment results show that our algorithm allows for flexible tradeoff between multiple retrieval criteria. Finally, we study the efficiency issue of our algorithm on simulated data

Will New Trends in Foreign Direct Investment Change the Structure of Intra-industry Trade between China and Japan?

It is generally believed that Japan's cost-oriented and export-oriented direct investment has introduced a bilateral intra-industry trade pattern in ChinaJapan trade through which China imports accessories from Japan, processes them and exports the product to Japan. Based on investment and trade data in the machinery sector, this paper discusses whether Japan's market-oriented investment in China since 2000 has changed the structure of the trade between two countries. We conclude that the vertical division of labour, as described by the flying-geese model and applied to the machinery industry, is gradually disappearing. In its place, no stereotypical East Asian vertical division of labour has been formed in transport machinery industry, despite it being the sector into which investment has grown fastest since 2000. Rather, factor endowment is the main determinant of intra-industry trade in the machinery industry between the two countries.trade, foreign direct investment, Japan, China, Intra-industry trade