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- All Subjects: Algorithms
- Creators: School of Mathematical and Statistical Sciences
- Creators: Kosut, Oliver
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
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.
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.
Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.
}}=\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.