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- Creators: School of Mathematical and Statistical Sciences
- Status: Published
Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.
2D fetal echocardiography (ECHO) can be used for monitoring heart development in utero. This study’s purpose is to empirically model normal fetal heart growth and function changes during development by ECHO and compare these to fetuses diagnosed with and without cardiomyopathy with diabetic mothers. There are existing mathematical models describing fetal heart development but they warrant revalidation and adjustment. 377 normal fetuses with healthy mothers, 98 normal fetuses with diabetic mothers, and 37 fetuses with cardiomyopathy and diabetic mothers had their cardiac structural dimensions, cardiothoracic ratio, valve flow velocities, and heart rates measured by fetal ECHO in a retrospective chart review. Cardiac features were fitted to linear functions, with respect to gestational age, femur length, head circumference, and biparietal diameter and z-scores were created to model normal fetal growth for all parameters. These z-scores were used to assess what metrics had no difference in means between the normal fetuses of both healthy and diabetic mothers, but differed from those diagnosed with cardiomyopathy. It was found that functional metrics like mitral and tricuspid E wave and pulmonary velocity could be important predictors for cardiomyopathy when fitted by gestational age, femur length, head circumference, and biparietal diameter. Additionally, aortic and tricuspid annulus diameters when fitted to estimated gestational age showed potential to be predictors for fetal cardiomyopathy. While the metrics overlapped over their full range, combining them together may have the potential for predicting cardiomyopathy in utero. Future directions of this study will explore creating a classifier model that can predict cardiomyopathy using the metrics assessed in this study.
Over the years, advances in research have continued to decrease the size of computers from the size of<br/>a room to a small device that could fit in one’s palm. However, if an application does not require extensive<br/>computation power nor accessories such as a screen, the corresponding machine could be microscopic,<br/>only a few nanometers big. Researchers at MIT have successfully created Syncells, which are micro-<br/>scale robots with limited computation power and memory that can communicate locally to achieve<br/>complex collective tasks. In order to control these Syncells for a desired outcome, they must each run a<br/>simple distributed algorithm. As they are only capable of local communication, Syncells cannot receive<br/>commands from a control center, so their algorithms cannot be centralized. In this work, we created a<br/>distributed algorithm that each Syncell can execute so that the system of Syncells is able to find and<br/>converge to a specific target within the environment. The most direct applications of this problem are in<br/>medicine. Such a system could be used as a safer alternative to invasive surgery or could be used to treat<br/>internal bleeding or tumors. We tested and analyzed our algorithm through simulation and visualization<br/>in Python. Overall, our algorithm successfully caused the system of particles to converge on a specific<br/>target present within the environment.
}}=\tau$. This research will focus on improving approximations on the lower bound of $\tau$. Toward this end we will examine algorithmic enumeration, and series analysis for self-avoiding polygons.
This thesis intends to show that the diversity of algorithmic choreography can be reduced into more specific categories. As algorithmic choreography is fundamentally intertwined with the concept of computation, it is natural to propose that algorithmic choreography works be separated based on a spectrum that is defined by the extent of the involvement of computation within each piece.
This thesis seeks to specifically outline three primary categories that algorithmic works can fall into: pieces that involve minimal computational influence, entirely computationally generated pieces, and pieces that lie in between. Three original works were created to reflect each of these categories. These works provide examples of the various methods by which computation can influence and enhance choreography.
The first piece, entitled Rαinwater, displays a minimal amount of computational influence. The use of space in the piece was limited to random, computationally generated paths. The dancers extracted a narrative element from the random paths. This iteration resulted in a piece that explores the dancers’ emotional interaction within the context of a rainy environment. The second piece, entitled Mymec, utilizes an intermediary amount of computation. The piece sees a dancer interact with a projected display of an Ant Colony Optimization (ACO) algorithm. The dancer is to take direct inspiration from the movement of the virtual ants and embody the visualization of the algorithm. The final piece, entitled nSkeleton, exhibited maximal computational influence. Kinect position data was manipulated using iterative methods from computational mathematics to create computer-generated movement to be performed by a dancer on-stage.
Each original piece was originally intended to be presented to the public as part of an evening-length show. However, due to the rise of the COVID-19 pandemic caused by the novel coronavirus, all public campus events have been canceled and the government has recommended that gatherings with more than 10 people be entirely avoided. Thus, the pieces will instead be presented in the form of a video published online. This video will encompass information about the creation of each piece as well as clips of choreography.