本論文在分析 SP500 指數其中交易最為頻繁的 345 家公司在 1996 年各月份的股票數據，相關係數與時間尺度間的關聯已經被證實出來， 而我們利用 K − L 展開來分解股價對數報酬的時間序列，特徵成份的時間部分基底對時間尺度有顯著的依賴特性。我們對每個特徵成份計算持續性時間的量(switch time)和參與率(participation ratio)，並仔細分析它們與特徵值之間的關聯，做為特徵成份分類的參考，而在較小的時間尺度底下大部份的特徵成份的特徵值與持續性時間呈線性關係。這些訊息可以用來補充先前對股市對數報酬率所呈現粒子特性所做的分析。

The quantitative measurement of structural alterations at the nanoscale level is important for understanding the physical states of weakly disordered optical mediums such as cells/tissues. Progress in certain diseases, such as cancer or abnormalities in the brain, is associated with the nanoscale structural alterations at basic building blocks of the cells/tissues. Elastic light scattering, especially at visible wavelengths range provides non-invasive ways to probe the cells/tissues up to nanoscale level. Therefore, a mesoscopic physics-based open light scattering technique with added finer focusing, partial wave spectroscopy (PWS), is developed to probe nanoscale changes. Then, molecular-specific light localization technique, a close scattering approach called inverse participation ratio (IPR) is proposed that is sensitive to nano to microstructural cell/tissue alterations. In this dissertation, we have introduced the further engineered PWS system with the finer focus for precise volume scattering and molecular-specific light localization IPR techniques. As an application of PWS, we first probe precise scattering volume in commercially available tissue microarrays (TMA) tissue samples to standardize the existing cancer diagnostic methods by distinguishing the cancer stages. We also apply the PWS technique to probe chemotherapy drug-treated metastasizing cancer patients by xenografting prostate cancer cells using a mouse model and identify drug-sensitive and drug-resistance treatment cases. On the other hand, as an illustration of another mesoscopic physics-based molecular specific light localization technique, Confocal-IPR, we study the effects of a probiotic on chronic alcoholic mice brains by targeting the molecular specific alteration in glial cells, astrocytes and microglia, and chromatin of the brain cells through staining with appropriate dyes/proteins. Using structural disorder of IPR as a biomarker, the results show that probiotics in the presence of alcohol are beneficial and help overall brain health. Finally, a TEM-IPR study was performed using nanoscale resolution TEM imaging to support the optical IPR method by studying the anti-cancerous drug effect in ovarian cancer cells. The result shows that we can quantitatively measure the effect of anti-cancerous drugs in cancer treatment and the level of tumorigenicity far below the diffraction limit, and it has a similar effect and supports the optical IPR method.

Optical scattering techniques are suitable probes for studying weak disordered refractive index media such as biological cells and tissues. Several brain diseases accompany the nano-to-submicron scales’ structural alterations of the basic building blocks of cells/tissues in the brain and skin fibroblasts. For example, several molecular modifications such as DNA methylation, and histone degradation occur in cells earlier than morphological changes detectable at a microscopic level. These alterations also change the refractive index structures of the cells/tissues at the nano-to-submicron scales. Unfortunately, traditional methods do not allow the detection of these alterations in the early stages of diseases. Recent developments in mesoscopic optical physics-based techniques can probe these alterations. Particularly, mesoscopic light transport and localization approaches enable the measurements and quantifications of the degree of structural alterations in the cells/tissues and unprecedented information on progressive brain diseases. This dissertation provides a detailed study of the structural changes at nano-to-submicron levels in human brain cells/tissues and human skin fibroblasts in two major neurodegenerative diseases, Alzheimer’s disease (AD) and Parkinson's disease (PD), using dual spectroscopic imaging techniques, namely partial wave spectroscopy (PWS) for light transport and inverse participation ratio (IPR) for weak light localization. In particular, a nanoscale-sensitive advanced PWS technique is used to quantify the structural alterations in cells/tissues. Further, the IPR technique is used to quantify molecular-specific mass density alterations within cells using their light localization properties via confocal imaging. These dual optical scattering techniques were utilized to measure the degree of structural disorders, termed ‘disorder strength’, by distinguishing the diseased cells/tissues from normal ones in the human brain and human skin fibroblasts due to neurodegenerative diseases. Our results show that the degree of structural disorder (����) increases in the affected cells and tissues relative to the normal, both at the cellular/tissue level and in the DNA molecular mass density structural levels. The results of the studies strongly reveal that the degree of structural disorder strength (����) is an effective biomarker/numerical indicator for brain disease diagnostics.