Real-world data often behaves different as its collection of partial information, which is called emergence. Due to long-range correlation, the local fluctuation drives whole system and produces distinct features. Such systems are referred as Complex Systems, where long-range correlation is shown by several aspects in temporal, spatial and internal degrees of the randomness. This thesis discusses a few systems which exhibits complex behavior.
Chapter 2 discusses emergence of long-term memory in popularity dynamics, using ranking chart of western popular music, the Billboard Hot 100 chart. Using simple spreading model with long-term memory kernel, we found the rise and fall of popularity is influenced under long-term memory. Also, the memory effect becomes greater in recent, which means different type of popularity dynamics is emerging.
Chapter 3 discusses quantitative evidence of industry convergence. Interaction between companies is quantified by co-mention frequency, and the convergence can be represented by weakening community structure between community of companies. As a result, mesoscopic scale dynamics of community composition showed industry convergence.
Chapter 4 discusses totally asymmetric simple exclusion process (TASEP) on one-dimensional system with a defect. The discrepancy between numerical and analytical solution have different opinion on localization of a defect. Scaling analysis of the finite-size effect of a defect shows there is a crossover from localized phase to bulk phase.
Chapter 5 discusses spreading impact of local defect in one-dimensional body-centered solid-on-solid (BCSOS) surface growth. The universal class of growing surface is shown by fluctuation structure, known as Kardar-Parisi-Zhang (KPZ) class. Numerical simulation shows that local defect breaks surfaces' fluctuation universality class with the impact spreading.
Chapter 6 discusses generalization of TASEP dynamics which can change localization of the defect. Using zero-range process (ZRP) type attraction/repulsion to the particles, condensation due to attraction and jamming caused by local defect competes and produces rich phase structure. Using extension of defect mean-field, we obtained marginal critical defect strength, as well as phase diagram. Also, condensation of the vacancies affected by local defect is discussed.