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Intracellular protein gradients serve a variety of functions, such as the establishment of cell polarity or to provide positional information for gene expression in developing embryos. Given that cell size in a population can vary considerably, for the protein gradients to work properly they often have to be scaled to the size of the cell. Here, we examine a model of protein gradient formation within a cell that relies on cytoplasmic diffusion and cortical transport of proteins toward a cell pole. We show that the shape of the protein gradient is determined solely by the cell geometry. Furthermore, we show that the length scale over which the protein concentration in the gradient varies is determined by the linear dimensions of the cell, independent of the diffusion constant or the transport speed. This gradient provides scale-invariant positional information within a cell, which can be used for assembly of intracellular structures whose size is scaled to the linear dimensions of the cell, such as the cytokinetic ring and actin cables in budding yeast cells. 

Self-driving autonomous vehicles (AVs) have recently gained popularity as a research topic. The safety of AVs is exceptionally important as failure in the design of an AV could lead to catastrophic consequences. AV systems are highly heterogeneous with many different and complex components, so it is difficult to perform end-to-end testing. One solution to this dilemma is to evaluate AVs using simulated racing competition. In this thesis, we present a simulated autonomous racing competition, Generalized RAcing Intelligence Competition (GRAIC). To compete in GRAIC, participants need to submit their controller files which are deployed on a racing ego-vehicle on different race tracks. To evaluate the submitted controller, we also developed a testing pipeline, Autonomous System Operations (AutOps). AutOps is an automated, scalable, and fair testing pipeline developed using software engineering techniques such as continuous integration, containerization, and serverless computing. In order to evaluate the submitted controller in non-trivial circumstances, we populate the race tracks with scenarios, which are pre-defined traffic situations commonly seen in the real road. We present a dynamic scenario testing strategy that generates new scenarios based on results of the ego-vehicle passing through previous scenarios.