Examples of Matrix Factorizations from SYZ

We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger-Yau-Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori-Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy $(1,-1)$ and $(-1,1)$ in the Fukaya category of ${\mathbb C}P^1 \times {\mathbb C}P^1$, which was predicted by Kapustin and Li from B-model calculations

Memory-Efficient Query Processing over XML Fragment Stream with Fragment Labeling

The portable/hand-held devices deployed in mobile computing environment are mostly limited in memory. To make it possible for them to locally process queries over a large volume of XML data, the data needs to be streamed in fragments of manageable size and the queries need to be processed over the stream with as little memory as possible. In this paper, we report a considerable improvement of the state-of-the-art techniques of query processing over XML fragment stream in memory efficiency. We use XML fragment labeling (XFL) as a method of representing XML fragmentation, and show that XFL is much more effective than the popular hole-filler (HF) model employed in the state-of-the-art in reducing the amount of memory required for query processing. The state-of-the-art with the HF model requires more memory as the stream size increases. With XFL, we overcome this fundamental limitation, proposing the techniques to make query processing scalable in the sense that memory requirement is not affected by the size of the stream as long as the stream is bounded. The improvement is verified through implementation and a detailed set of experiments

THE BEGINNING OF THE PATH TO SELF-DISCOVERY: A STUDY ON LIANG QICHAO'S CONCEPT OF NATION

In this thesis, I will analyze how Liang Qichao’s idea of nation played a role in the emergence of national identity in China in the late nineteenth and early twentieth century. The concept of nation in China didn’t emerge from the bottom-up spontaneously. Rather, I will argue, the emergence of Chinese national identity can largely be explained as an imported ideology pursued by Chinese elites. In the formation of the concept of nation in China, not only the contact with the West but also interactions and tensions among the East Asian countries were crucial. This thesis is divided into two interdependent parts. The first part deals with theoretical studies of nationalism and national identity, and it will provide a general picture of the major theoretical trend in nationalism. This part will explore three major perspectives: the primordialist perspective that describes ethnic identities as something fixed and unchanging; the ethno-symbolist perspective that argues that pre-modern ethnic ties are important in understanding the formation of modern nations and nationalism; and the modernist perspective that treats nationalism as a recent phenomenon. Through a critical evaluation of theories of nationalism and national identity, I will begin to discern the contours of how Liang Qichao’s concept of nation was formed. In the second part, by way of introducing nationalist discourses in China, I will explore historical concepts of nation and its boundaries. Since his arrival in Japan, Liang immersed himself in Western political theory and read Japanese authors broadly, and his thoughts changed accordingly. As a result, Liang advocated great nationalism that would awaken a sense of belonging to China in all the peoples of the Qing Empire. In this regard, the introduction of Liang’s borrowed concept of nation to China was a transformative event for Chinese national self-perception

Atrial fibrillation detection by heart rate variability in Poincare plot

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