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27 Graves Place, Holland, MI 49423-3617
Jiyi Jiang: Classifying Handwritten Digits Without Seeing an Image
Digital images of handwritten digits are high dimensional and vary with writing style. This work presents a method to per-
form classification on one of handwritten digits database, MNIST, and enable visualization in low dimensional space. To address the handwritten digit variation issue, the edges of each digit in an image are firstly highlighted by gradient feature extraction. Then, the curse of high dimension is broken by t-SNE algorithm, which constructs a certain “lens” so that one can visualize MNIST on two or three coordinates. The “lens” also helps trace from low dimension back to the high dimension in which clustering is applied to assigned level sets and form a more explicit visible structure among all data points. The last process is done by Mapper algorithm.
Tae Hyun Choi: Examining the effects of heavily-censored survival data on quantile estimation and precision
The analysis of survival data (time to event data) is frequently complicated due the occurrence of right-censored obser-
vations. Many methods for dealing with this have been proposed, encompassing non-, semi- and parametric models for the data. In this talk, we explore the effects heavily-censored data have on quantile estimation as well as estimation precision. Comparisons will be made across methods and differences, advantages as well as disadvantages of these methods will be discussed.
Aaron Green & Cole Watson: Graph Pebbling and Graham’s Conjecture
Graph pebbling is a game on a connected graph G in which pebbles are placed on the vertices of G. A pebbling move consists of removing two pebbles from vertex and adding one to an adjacent vertex. A configuration of pebbles is rsolvable if for a given target vertex r, there is a sequence of pebbling moves so that at least one pebble can be placed on r. The pebbling number of a graph G is the smallest integer π(G) such that any configuration that uses π(G) pebbles is r-solvable for any r in V (G). A long standing conjecture in graph pebbling is Graham’s Conjecture. It states that given any two graphs G and H, π(G□H) ≤ π(G)π(H), where G□H is the Cartesian product of graphs. A graph G satisfies the two-pebbling property if two pebbles can be placed on any vertex v in V (G) given any configuration of 2π(G)-q+1 pebbles, where q is the number of vertices that have at least one pebble. The smallest known graph that does not satisfy the two-pebbling property is called the Lemke graph (L). We will show that Graham’s conjecture holds for such families as L□Kn and several others.
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