Examples of quasitoric manifolds as special unitary manifolds

This note shows that for each $n\geq 5$ with only $n\not= 6$, there exists a $2n$-dimensional specially omnioriented quasitoric manifold $M^{2n}$ which represents a nonzero element in $\Omega_*^U$. This provides the counterexamples of Buchstaber--Panov--Ray conjecture.Comment: 10 pages, v3: final versio

Multi-View Active Learning in the Non-Realizable Case

The sample complexity of active learning under the realizability assumption has been well-studied. The realizability assumption, however, rarely holds in practice. In this paper, we theoretically characterize the sample complexity of active learning in the non-realizable case under multi-view setting. We prove that, with unbounded Tsybakov noise, the sample complexity of multi-view active learning can be $\widetilde{O}(\log\frac{1}{\epsilon})$, contrasting to single-view setting where the polynomial improvement is the best possible achievement. We also prove that in general multi-view setting the sample complexity of active learning with unbounded Tsybakov noise is $\widetilde{O}(\frac{1}{\epsilon})$, where the order of $1/\epsilon$ is independent of the parameter in Tsybakov noise, contrasting to previous polynomial bounds where the order of $1/\epsilon$ is related to the parameter in Tsybakov noise.Comment: 22 pages, 1 figur

The Chinese Export Bundles - Patterns, Puzzles and Possible Explanations

Chinas exports have become increasingly sophisticated. This has generated anxiety in developed countries as the competitive pressure may be increasingly felt outside labor-intensive industries. Using product-level data on exports from different cities within China, this paper investigates the contributing factors to the rising export sophistication. Somewhat surprisingly, neither processing trade nor foreign invested firms are found to play an important role in generating the increased overlap in the export structure between China and high-income countries. Instead, improvement in human capital and government policies in the form of tax-favored high-tech zones appear to be the key in the countrys evolving export structure. On the other hand, processing trade, foreign invested firms, and government-sponsored high-tech zones all have contributed significantly to raising the unit values of Chinas exports within a given product category.China, India, Export sophistication, Export structure, high-tech zones, Human Capital