Gyuchang Lim

Statistical Analysis of Fluorescence Correlation Spectroscopy of Ultra Low Concentration Molecules with a Confocal Microscope

In this study, we simulated a statistical model of FCS (fluorescence correlation spectroscopy) based on a Poisson process to understand and explain observations of the experiment performed on molecules of ultra-low concentration by the home-built laser- scanning confocal microscope. The statistical model confirmed that the relative mean square amplitude of fluctuations is shown to be inversely proportional to the average number of molecules, even in the ultra-low concentration, if some conditions are satisfied. Signal-to-noise ratio and the variability of dwelling time under the confocal volume were found to be effective conditions for the experiment.

MULTIFRACTAL BEHAVIORS IN FOREIGN EXCHANGE MARKETS

A two-phase phenomenon in three financial exchange prices is studied. To understand the underlying mechanism for the formation of market prices, we perform the multifractal analysis and the detrended fluctuation analysis in terms of time series of market prices. We also examine higher order temporal correlations for the market price. Although the multifractal properties of market prices are obtained, it cannot be reproduced the binomial multiplicative process through that was used to understand fully developed turbulence.

Information of group-correlations in Korean financial market

We study two sides of the KOSPI, classified as an emerging market. First, the evolutionary property is examined in terms of overlapping matrix and survival ratios. To this end, we apply the random matrix theory (RMT) and the one-factor model to analyzing correlation matrix and finding business clusters. Second, we examine the relations between the market capitalization and the business. For the well-developed markets such as NYSE, the contribution of the firms to the second-largest eigenvector shows an exponential function of the market capitalizations while no clue is observed for the KOSPI. We confirm that the market capitalization is distributed in a power-law with the exponent 1.2 like a Paretos distribution. Particulary, the KOSPI shows a different behavior compared to the mature market, that is, one or two companies lead a number of companies with the little money and big companies competed to win each other. The clusters also represent by largest eigenstates show a weak affiliation compared to smaller ones. These results imply that the KOSPI is the target for the short-positioned investors.

Dynamical models of high-frequency data analysis

To treat with social phenomena, statistical and mathematical physics provides a powerful and rigorous method [1], and several papers have studied the models of social phenomena based on stochastic processes. Many researchers in econometrics or biometrics have proposed that the discrete choice including binary analysis may be formulated as the AR (autoregressive), logit, and probit models [2]. In this paper, we present the future predictability of the AR and logit models, by using the tick data analysis of the KOSPI. We consider two delivery periods of the KOSPI: Data A (B) was from January 1997 to December 1998 (January 2004 to December 2004). Data A (B) contains 133,823 (86,561) items of minutely data. In our calculations, to determine the minimized order k of AR and logit models, we define the Akaike information criterion (AIC) as AIC = 2 T [− lnMl + lnMp] for the sample size