臺灣博碩士論文加值系統

內外噪聲常同時存在於生物系統中，如典型的DNA轉錄轉譯問題，因此過去有許多分解這兩種效應的工作。有別於過去Swain生物角度的內外噪聲定義，本研究採van Kampen的物理角度定義，對chemical master equation做微擾，推導出物理版本的內外噪聲分解公式。我們將理論應用在Yi-Der Chen的網路模型，藉由解析解推導及電腦模擬證實存在“外噪聲壓抑內噪聲隨機性”的可能性，並在低維系統推導出該可能性出現的條件。此種兩噪聲加成後漲落減小的現象，有違直覺。我們將此物理版分解公式跟Swain的生物版分解公式做比較，分析他們的相似與相異性。

It is rather often that intrinsic and extrinsic noises coexist in a biological system. A typical example is the transcription and translation of DNA. This raises numerous works devoting to decomposing these two effects. Apart from the previous definition of intrinsic and extrinsic noises from biological aspect, this work adopts the definition of van Kampen from physical aspect. Based on that definition, we perturb the chemical master equation and derive a physical version of decomposition formula for intrinsic and extrinsic noises. We apply this theory to the network model of Yi-Der Chen. The derived exact solutions and numerical studies on that model reveal the possibility of “suppressing intrinsic noise induced stochasticity by extrinsic noises”. The condition for this possibility is derived in a low dimensional network. This suppression indicates that the fluctuations could decline when intrinsic and extrinsic noises are added together, which is a bit counter-intuition. We compare this physical version of decomposition formula with the biological version of formula derived by Swain and analyze the common and distinct features between these two formulas.

中文摘要.............................................i
Abstract.............................................ii
誌謝.................................................iii
圖目錄...............................................v
第一章 歷史回顧與動機................................1
第二章 隨機過程的漲落................................3
2.1 Random walk model的漲落..........................3
2.2 兩態系統的漲落...................................4
第三章 內外噪聲分解理論..............................6
3.1 純內噪聲系統的漲落...............................6
3.1.1 Chemical master equation.......................6
3.1.2 聯合機率函數的解...............................10
3.2 內外噪聲共存系統的漲落...........................16
3.2.1 微擾chemical master equation...................16
3.2.2 微擾聯合機率函數...............................21
3.2.3 內外噪聲拆解公式...............................29
3.3 內外噪聲共存的網路模型...........................33
3.3.1 微擾chemical master equation的應用.............33
3.3.2 外噪聲對內噪聲隨機性的影響.....................36
3.3.3 外噪聲壓抑內噪聲隨機性的條件...................39
第四章 物理版與生物版噪聲分解公式比較................42
第五章 結論與展望....................................46
附錄一...............................................47
附錄二...............................................48
參考文獻.............................................49

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