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
Inverse problems are problems where we want to estimate the values of certain parameters of a system given observations of the system. Such problems occur in several areas of science and... Show moreInverse problems are problems where we want to estimate the values of certain parameters of a system given observations of the system. Such problems occur in several areas of science and engineering. Inverse problems are often ill-posed, which means that the observations of the system do not uniquely define the parameters we seek to estimate, or that the solution is highly sensitive to small changes in the observation. In order to solve such problems, therefore, we need to make use of additional knowledge about the system at hand. One such prior information is given by the notion of sparsity. Sparsity refers to the knowledge that the solution to the inverse problem can be expressed as a combination of a few terms. The sparsity of a solution can be controlled explicitly or implicitly. An explicit way to induce sparsity is to minimize the number of non-zero terms in the solution. Implicit use of sparsity can be made, for e.g., by making adjustments to the algorithm used to arrive at the solution.In this thesis we studied various inverse problems that arise in different application areas, such as tomographic imaging and equation learning for biology, and showed how ideas of sparsity can be used in each case to design effective algorithms to solve such problems. Show less
