We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been...
Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...
"What’s wrong with this AI?" Explainable AI (XAI) researchers are moving beyond explaining an AI’s actions, to helping users detect an AI’s failures. However this detection may not be enough—for actionability, we often need to pinpoint which part failed. We investigate how AAR/AI, a structured assessment process, supports users with...
With continuing improvements in performance and capability, GPU processing has gained significant and growing interest across science and industry. With this interest, research has increasingly focused upon methods of processing algorithms with stochastic, non-uniform branching while maintaining low divergence. Central among these methods is thread-data remapping (TDR), whereby data is...
When studying robot systems, it is common to ask about optimal approaches to accomplish a given task. In the context of mobile systems, particularly biomimetic systems, optimization tasks are closely related to the relevant dynamics of locomotion. In this thesis, building on prior work from the geometric mechanics community, we...
Real-world datasets are dirty and contain many errors. Examples of these issues are violations of integrity constraints, duplicates, and inconsistencies in representing data values and entities. Applying machine learning on dirty databases may lead to inaccurate results. Users have to spend a lot of time and effort repairing data errors...
Causal inference is an important analytical tool to bridge the gap between prediction and decision-making. However, learning a causal network solely from data is a challenging task. In this work, various techniques have been explored for a better and improved causal network learning from data. Firstly, the problem of learning...
An important problem in computer graphics is to determine where contour lines and ridges appear in a surface constructed from a triangle mesh. In this presentation we will investigate a new answer to this problem – the horizon measure. The horizon measure determines the likelihood of contour lines to appear...