Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot

In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with a fixed limiting ratio, $s$, of $M$ and $(N+1/2)$. We find out the asymptotic expansion formula (AEF) of the colored Jones polynomials of the figure eight knot with $s$ close to $1$. Nonetheless, we show that the exponential growth rate of the colored Jones polynomials of the figure eight knot with $s$ close to $1/2$ is strictly less than those with $s$ close to $1$. It is known that the Turaev Viro invariant of the figure eight knot can be expressed in terms of a sum of its colored Jones polynomials. Our results show that this sum is asymptotically equal to the sum of the terms with $s$ close to 1. As an application of the asymptotic behavior of the colored Jones polynomials, we obtain the asymptotic expansion formula for the Turaev-Viro invariants of the figure eight knot. Finally, we suggest a possible generalization of our approach so as to relate the AEF for the colored Jones polynomials and the AEF for the Turaev-Viro invariants for general hyperbolic knots.Comment: 40 pages, 0 figure

The housing ladder and Hong Kong housing market\u27s boom and bust cycle

This paper presents evidence, based on the recent Hong Kong experience, for the existence of a “housing ladder effect.” An increase of housing equity at the bottom of the ladder tends to translate into a trading up activity that will both increase housing market turnover and buoy up the entire housing market. Based on a natural experiment through the introduction of a public housing privatization scheme, this papers presents evidence supporting this story using a logit model and a price-volume causality test

Knowledge Sources of Innovation in a Small, Open Economy: The Case of Singapore

By tracing the flows of patent citation of prior patents and scientific journal articles, we investigate the sources of knowledge for innovation output in Singapore, a small, highly open economy that has traditionally been significantly dependent on foreign multinational corporations (MNCs). We found that the local production of new knowledge by indigenous Singaporean firms depends disproportionately on technological knowledge produced by MNCs with operational presence in Singapore and scientific knowledge generated by foreign universities. Locally produced new knowledge by indigenous firms and local universities constitute an insignificant, albeit rapidly growing, source for innovation in Singapore.innovation system, patent citation, Singapore, knowledge sources

Availability of Financing, Regulatory Business Costs and National Entrepreneurial Propensity

In this paper, we focus on two barriers to entry that may hinder the formation of new firms: capital requirements and regulatory business cost. The contribution of this paper is twofold: we compare the availability of different types of financing sources to address the issue of capital requirement and we utilise a new measure of business cost by constructing a composite index using data from the World Bank’s Doing Business Database. Using cross-sectional data on 37 countries that participated in the 2002 Global Entrepreneurship Monitor, we examine the effect of availability of financing and regulatory business costs on the propensity of three different types of entrepreneurial activity:opportunity-driven, necessity driven and high-growth potential new firm formation. The availability of three types of financing sources is analysed: traditional debt financing, venture capital financing, and informal investments. The findings show that only informal investments significantly influence the propensity to be entrepreneurs. Regulatory business costs were found to deter opportunity driven entrepreneurship, but had no impact on other types of entrepreneurial activity.entrepreneurial activity, financing, venture capital, informal investment, business cost

Towards a transparent, credible, evidence-based decision-making process of new drug listing on the Hong Kong Hospital Authority Drug Formulary: challenges and suggestions

The aim of this article is to describe the process, evaluation criteria, and possible outcomes of decision-making for new drugs listed in the Hong Kong Hospital Authority Drug Formulary in comparison to the health technology assessment (HTA) policy overseas. Details of decision-making processes including the new drug listing submission, Drug Advisory Committee (DAC) meeting, and procedures prior to and following the meeting, were extracted from the official Hong Kong Hospital Authority drug formulary management website and manual. Publicly-available information related to the new drug decision-making process for five HTA agencies [the National Institute of Health and Care Excellence (NICE), the Scottish Medicines Consortium (SMC), the Australia Pharmaceutical Benefits Advisory Committee (PBAC), the Canadian Agency for Drugs and Technologies in Health (CADTH), and the New Zealand Pharmaceutical Management Agency (PHARMAC)] were reviewed and retrieved from official documents from public domains. The DAC is in charge of systemically and critically appraising new drugs before they are listed on the formulary, reviewing submitted applications, and making the decision to list the drug based on scientific evidence to which safety, efficacy, and cost-effectiveness are the primary considerations. When compared with other HTA agencies, transparency of the decision-making process of the DAC, the relevance of clinical and health economic evidence, and the lack of health economic and methodological input of submissions are the major challenges to the new-drug listing policy in Hong Kong. Despite these challenges, this review provides suggestions for the establishment of a more transparent, credible, and evidence-based decision-making process in the Hong Kong Hospital Authority Drug Formulary. Proposals for improvement in the listing of new drugs in the formulary should be a priority of healthcare reforms

Singapore as an innovative city in East Asia : an explorative study of the perspectives of innovative industries

The city-state of Singapore has achieved rapid economic development in the past by its positioning as an efficient business hub in Asia. To remain competitive in the global knowledge economy, however, Singapore needs to move beyond efficiency by developing a strong"innovative"edge as well. This paper examines the challenges that Singapore faces in seeking to do so through an explorative survey of 40 firms from three innovative sectors: high-tech manufacturing industries, knowledge-intensive business services (KIBS), and creative content industries. Overall, while the survey confirms Singapore's continuing competitive strength in efficiency infrastructure, it also finds a favorable perception of Singapore as an innovative city. Indeed, many of the industry actors indicated that an efficient business infrastructure is a prerequisite for locating their innovative activities in Singapore, suggesting that the relationship between innovation and efficiency is complementary, rather than substitutional. While the study found that intellectual property and its protection are widely recognized by actors in all three sectors, interesting differences exist. In particular, intellectual property protection appears to be of greater concern to the high-tech research and development-intensive manufacturing sector and the creative contents sector than to the KIBS sector. Another interesting difference is that while competition in high-tech innovation tends to be global, competition in creative content tends to have a stronger local or regional dimension. Public policy in East Asia has traditionally emphasized the development of technological innovation capabilities in the manufacturing sector. In light of the findings, public policymakers may need to be more sensitive to the nuanced differences in policies needed to promote the new creative content industries and the associated supporting KIBS.ICT Policy and Strategies,Health Monitoring&Evaluation,Economic Theory&Research,Health Economics&Finance,Environmental Economics&Policies