The emergence of complex diseases resulting from abnormal cell-cell signaling and the spread of infectious diseases caused by pathogens are significant threats to humanity. Unraveling the dynamic... Show moreThe emergence of complex diseases resulting from abnormal cell-cell signaling and the spread of infectious diseases caused by pathogens are significant threats to humanity. Unraveling the dynamic mechanisms underlying cell-cell signaling and infectious disease spreading is crucial for effective disease prevention and treatment. As science and technology advance, the availability and diversity of observational and experimental data related to these biological processes continue to grow. In this thesis, we integrate multisource data with dynamic modeling to investigate the biological mechanisms of Notch signaling in biological development and to develop prevention and control strategies for infectious diseases. Show less
This dissertation consists of two parts, each of which considers a different research area related to random interval maps. In the first part we are interested in random interval maps that are... Show moreThis dissertation consists of two parts, each of which considers a different research area related to random interval maps. In the first part we are interested in random interval maps that are critically intermittent. In Chapter 2 we consider a large class of such systems and demonstrate the existence of a phase transition, where the absolutely continuous invariant measure changes between finite and infinite. For a closely related class we derive in Chapter 3 statistical properties like decay of correlations and the Central Limit Theorem. In Chapter 4 we investigate whether a similar phase transition remains to exist when the critical behaviour is toned down. Random interval maps can also be used to generate number expansions, which will be the main object of study in the second part. In Chapter 5 we generalize Lochs’ Theorem, which compares the efficiency between representing real numbers in decimal expansions and regular continued fraction expansions, to a wide class of pairs of random interval maps that produce number expansions. Closely related to this result, we study in Chapter 6 the efficiency of beta-encoders as a potential source for pseudo-random number generation by comparing the output of a beta-encoder with its corresponding binary expansion. Show less
The main topic of this PhD thesis is the Arakelov ray class group of a number field, an algebraic object that contains both the ideal class group structure and the unit group structure. The main... Show moreThe main topic of this PhD thesis is the Arakelov ray class group of a number field, an algebraic object that contains both the ideal class group structure and the unit group structure. The main result consists of the fact that certain specific random walks on the Arakelov ray class group result in a target point that is uniformly distributed on this group, under the assumption of an extended version of the Riemann Hypothesis. Almost all other results of this work are consequences of this fact. Show less
