Randomness Extraction in AC0 and with Small Locality

Randomness extractors, which extract high quality (almost-uniform) random bits from biased random sources, are important objects both in theory and in practice. While there have been significant progress in obtaining near optimal constructions of randomness extractors in various settings, the computational complexity of randomness extractors is still much less studied. In particular, it is not clear whether randomness extractors with good parameters can be computed in several interesting complexity classes that are much weaker than P. In this paper we study randomness extractors in the following two models of computation: (1) constant-depth circuits (AC0), and (2) the local computation model. Previous work in these models, such as [Vio05a], [GVW15] and [BG13], only achieve constructions with weak parameters. In this work we give explicit constructions of randomness extractors with much better parameters. As an application, we use our AC0 extractors to study pseudorandom generators in AC0, and show that we can construct both cryptographic pseudorandom generators (under reasonable computational assumptions) and unconditional pseudorandom generators for space bounded computation with very good parameters. Our constructions combine several previous techniques in randomness extractors, as well as introduce new techniques to reduce or preserve the complexity of extractors, which may be of independent interest. These include (1) a general way to reduce the error of strong seeded extractors while preserving the AC0 property and small locality, and (2) a seeded randomness condenser with small locality.Comment: 62 page

Weak Measurement of Qubit Oscillations with Strong Response Detectors: Violation of the Fundamental Bound Imposed on Linear Detectors

We investigate the continuous weak measurement of a solid-state qubit by single electron transistors in nonlinear response regime. It is found that the signal-to-noise ratio can violate the universal upper bound imposed quantum mechanically to any linear response detectors. We understand the violation by means of the cross-correlation of the detector currents.Comment: 4 pages, 4 figure

The Impact of Monetary Policy Shocks on Stock Prices: Evidence from Canada and the United States

monetary policy shocks; stock prices; open economy; structural vector autoregressive model

Confucianism and capitalist development in the East Asian newly industrialised societies

The immediate concern of this thesis is to understand the role played by Confucianism in the capitalist development of the East Asian NISs. In pursuit of this aim, it focuses on the relationship between Confucian political philosophy and state intervention in economic activities, on Confucian family practice and its links to modem organisations, on the Confucian emphasis on frugality and hard work and the work ethic, and on the Confucian stress on knowledge and high level modem education. It contends that through these mechanisms contemporary Confucian values have helped to facilitate the development of capitalist order and economic growth in the East Asian NISs. The thesis also explores the Confucian tradition and its modern transformations. It traces the historical evolution of Confucianism and shows how, more recently, it has changed in response to the challenge of capitalist development. It further identifies the contemporary forms of Confucian values and illustrates their variations across different East Asian societies. This line of enquiry is pursued empirically through an analysis of the development of Confucian themes in one of the principal spaces for public commentary and debate on economic, social and political issues - the popular press. The present analysis is one of the first to investigate the practical deployment of Confucian themes in everyday public discourse. The thesis approaches the questions in a Weberian tradition, which takes culture as an explanatory variable in social change, and recognises the influence of socioeconomic conditions on cultural change at the same time. It believes that change is an integrated process which involves all sectors of society. During this process cultural, social, political and economic forces compete and interact with each other within the specific contexts that conditioned the change. The capitalist development in the East Asian NISs is a process which involves the interaction between Confucianism and capitalism. Capitalism failed to develop in the Far East when it first emerged, due to the inhibitions of traditional Confucianism. But after it had triumphed in the West and been introduced to these societies by the colonisers, Confucianism could no longer resist the force of capitalist modernity, it had no choice but to adapt to the new situations. As a result, Confucian culture absorbed the idea of profit seeking, competition and rationalisation of economic activity, but retained its emphasis on collectiveness, family, and harmony. Combined with the continuing Confucian emphasis on education, merit, hard work, discipline and high achievement motivation, these values form a potent underpinning for economic growth. And this force has given rise to a special kind of capitalism in the East Asian NISs

Synthetic studies of natural compounds and their analogues

A83586C, a novel cyclodepsipeptide isolated from Streptomyces Kamatakensis, exhibits antitumour properties in vitro against a CCRF-CEM human T-cell Leukaemia line (IC50 = 0.0135 μg/mL). The strategy for synthesis of the peptide portion of A83586C can, in principle, be divided into three parts. First, the asymmetric synthesis of 3S- or 3R-piperazic acids via the Evans-Vederas alkylation procedure. Second, the formation of the linear hexapeptide Third, the intramolecular coupling to form the cyclic depsipeptide. The problem of N,O-acyl shifts during the cyclization of depsipeptides occurs when serine or threonine residues are present. It was therefore decided to form the lactone bond between (2S,3S)-3-hydroxyleucine and threonine in the last step. Three types of fragment condensations were employed in an attempt to synthesis the linear hexapeptide. The successful synthesis used a "1+2+3" condensation procedure. Synthesis of the linear hexapeptide was achieved by coupling specific amino acids using DCC or BOP-CI. 4-Methyl-2-E-pentenic acid was used inplace of (2S,3S)-3- hydroxyleucine in the coupling reaction. The Fmoc group was employed to protect the amino function of N-Me-(R)-alanine. The Z and Bn permanent protecting groups were employed to protect the amine of 3S- or 3R-piperazic acids and the hydroxyl group of N-hydroxylalanine. The carboxylic acid of threonine was protected by formation of the methyl ester. The 4-methyl-2-E-pentenic acid derivative could potentially be converted to the (2S,3S)-3-hydroxyleucine derivative by a Sharpless asymmetric epoxidation procedure from the linear pseudo-hexapeptide