Mathematics & Statisticshttp://hdl.handle.net/10211.3/1224902018-09-21T13:24:25Z2018-09-21T13:24:25ZOn Deep Learning and Neural NetworksLyche, Samuelhttp://hdl.handle.net/10211.3/2058072018-08-24T22:52:49Z2018-08-24T00:00:00ZOn Deep Learning and Neural Networks
Lyche, Samuel
This thesis gives an introductory overview of neural networks and deep learning. A new wave of computational power has brought about a fundamental change in the way that software is written. Only recently have machines become powerful enough to efficiently implement these algorithms. Due also to the massive increase in data storage capabilities and data production, artificial intelligence, of which neural networks form part of the foundation, will soon be affiliated with nearly every industry in the world. We give a high-level overview of the mathematical machinery necessary to implement neural networks, as well as the Python code to actually run the algorithms. Finally, we will show an example of how neural networks can be used to find cell nuclei in medical images as we compete in the 2018 Kaggle Data Science Bowl.
Ch1: History of neural networks. Ch2: Mathematics of perceptrons, convolutional networks, activation functions, etc. Ch3: Intro to programming perceptrons and convolutional networks in Python with Keras and TensorFlow. Ch4: Competing in the 2018 Kaggle Data Science Bowl using U-net for cell nuclei segmentation.
2018-08-24T00:00:00ZMetric Dimension of Cayley Graphs Symmetric Groups and Their TranspositionsHomier, Samanthahttp://hdl.handle.net/10211.3/2055312018-08-17T20:55:28Z2018-08-17T00:00:00ZMetric Dimension of Cayley Graphs Symmetric Groups and Their Transpositions
Homier, Samantha
Pretend that you cannot remember where you parked your car in the parking lot of the grocery store, but you do remember some of the cars parked near you. One could construct a graph based on your memory of the cars and then use the idea of the metric dimension to find your car. The metric dimension was introduced by PJ Slater in 1975 and has since been applied in fields such as chemistry, optimization, navigation, and more. There is no general/standard metric dimension for every graph, however, there are known metric dimensions for families of graphs. In this paper we study the metric dimension of Cayley graphs, which are graphs based on groups that have convenient algebraic properties. Our main goal is to find the metric dimension of the Cayley graph associated with the symmetric group $S_4$ and its set of transpositions $T_4$.
2018-08-17T00:00:00ZHow Bipartite Are You?Florido, Gabrielahttp://hdl.handle.net/10211.3/2052652018-07-26T22:14:51Z2018-07-26T00:00:00ZHow Bipartite Are You?
Florido, Gabriela
Facebook. Twitter. American Airlines.
Can you determine if these networks are bipartite?
Given a network an adjacency matrix can be created. This powerful matrix allows us to make incredible discoveries about our networks. We will discover the influences of the adjacency matrix in finding properties for bipartite graphs. The adjacency matrix in addition with the diagonal matrix create a normal matrix that also has beneficial proper- ties of bipartivity. In addition, we will use these properties to create different measures of nonbipartitvity. These measures will allow us to determine how close our networks are to being bipartite. Using Mathematica code we will be able to easily calculate the measure values not only for specific adjacency matrices but also for randomly generated graphs. Moreover, we will discuss real life applications by looking into different networks on the Koblenz Network Collection. Lastly, we will explore properties of bipartite graphs and use the complement and clustering algorithms to find a potential method of finding frustrated edges.
2018-07-26T00:00:00ZDimension of Strictly Self Similar SetsEcheverria, Santiagohttp://hdl.handle.net/10211.3/2045812018-07-12T22:17:22Z2018-07-12T00:00:00ZDimension of Strictly Self Similar Sets
Echeverria, Santiago
In this paper, many concepts and ideas will be presented about fractals and their dimension. There will be a over look of a few definitions which classify fractals and what type of dimension they possess. The types of fractals which will be covered are sets which we will classify as strictly and non-strictly self similar sets. Also there will be a comparison of two different dimensions on a strictly self similar set.
2018-07-12T00:00:00Z