Thesis Defense

Honors Thesis Defense

Title:  Thesis Defense/presentation session
Speaker: Shigeng Sun, GWU

Shigeng Sun Senior Honor Thesis Project Abstracts:

Part I. MODELING THE INTERNATIONAL LINKS BETWEEN INTERBANK OFFERED RATES AMONG DIFFERENT MARKETS THROUGH A WAVELET ANALYSIS APPROACH 

SHIGENG SUN    SVETLANA ROUDENKO

Abstract. This project investigates the links and interactions of the interbank offered lending rates among different types markets, through the implementation of a wavelet multi-scale approach. The data used includes USD-Libor rate, which is long been well established, CHYShibor rate and RUB-Mosprime rate. The latter two are relatively new, but already have close interactions with the USD counterpart because of the globalization of the money and financial markets. In our studies, we employ the wavelet multi-scale approach, which has various advantages over a direct application of the traditional econometrics methods. The wavelet approach allows us to decompose the data into multiple (specific) time scales instead of being limited to only the short-run and the long-run scales. The wavelet method provides the unique versatile ability to separate the local dynamics from the global one. We fully exploit in this study the fact that different participants of the market react to changes diversely, however, persistently (within themselves) in terms of time. We perform the wavelet transform on the data using various Daubechies bases that have different lengths of oscillations. As a result, we decompose the data into different time scales and then perform the Granger Causality Test. This provides the evidence of causality across different time scales. The wavelet variances are computed in turn to show that the short-term rates are more volatile than the longer-term rates. We also discuss causality between the offered rates from different types of markets, how it varies across different time scales, among other results. 

Part II. NUMERICAL STUDY OF PERIODIC MIGRATION OF ONE DIMENSIONAL CELL 

SHIGENG SUN   YANXIANG ZHAO

Abstract. In this project, we study the one-dimensional cell migration on micro- patterned substrates. This work is an extension of the study proposed in a paper of Camley et.al, in which the proposed model (later referred as ‘the model’) couples cell morphology with the polarizations of actin and myosin molecules. In this project, we use the model to study the effects of system parameters on the cell migration periodicity. More specifically, we study the protrusion and contraction forces and their effects on the amplitude and frequency of the periodical migration behaviors. For the numerical simulations, we show that periodic motion emerges naturally from the coupling of cell polarization and cell shape by running simulations with different values of system parameters. Both parameters are determined by different sharp interface results. We also show via simulations that there are important bifurcation points resulted from difference in protrusion and contraction forces. Furthermore, we have discovered an emergent phenomenon from our simulation, which shown that the protrusion stress increase resulted in an abrupt change on the amplitude of the periodic migration. 

The George Washington University    Department of Mathematics