Publication Date

2012-06-13

Availability

Embargoed

Embargo Period

2013-12-05

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Physics (Arts and Sciences)

Date of Defense

2012-05-09

First Committee Member

Neil F. Johnson

Second Committee Member

Joshua Cohn

Third Committee Member

Luca Mezincescu

Fourth Committee Member

Douglas Emery

Abstract

This thesis is an interdisciplinary work under the heading of complexity science which focuses on an arguably common "hard" problem across physics, finance and biology [1], to quantify and mimic the macroscopic "emergent phenomenon" in largescale systems consisting of many interacting "particles" governed by microscopic rules. In contrast to traditional statistical physics, we are interested in systems whose dynamics are subject to feedback, evolution, adaption, openness, etc. Global financial markets, like the stock market and currency market, are ideal candidate systems for such a complexity study: there exists a vast amount of accurate data, which is the aggregate output of many autonomous agents continuously competing with each other. We started by examining the ultrafast "mini flash crash (MFC)" events in the US stock market. An abrupt system-wide composition transition from a mixed human machine phase to a new all-machine phase is uncovered, and a novel theory developed to explain this observation. Then in the study of FX market, we found an unexpected variation in the synchronicity of price changes in different market subsections as a function of the overall trading activity. Several survival models have been tested in analyzing the distribution of waiting times to the next price change. In the region of long waiting-times, the distribution for each currency pair exhibits a power law with exponent in the vicinity of 3.5. By contrast, for short waiting times only, the market activity can be mimicked by the fluctuations emerging from a finite resource competition model containing multiple agents with limited rationality (so called El Farol Model). Switching to the biomedical domain, we present a minimal mathematical model built around a co-evolving resource network and cell population, yielding good agreement with primary tumors in mice experiment and with clinical metastasis data. In the quest to understand contagion phenomena in systems where social group structures evolve on a similar timescale to individual level transmission, we investigated the process of transmission through a model population comprising of social groups which follow simple dynamical rules for growth and break-up, and the profiles produced bear a striking resemblance to empirical data obtained from social, financial and biological systems. Finally, for better implementation of a widely accepted power law test algorithm, we have developed a fast testing procedure using parallel computation.

Keywords

Complex System; Finance; Network; Minority Game; Tumor Growth

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