The set of subsets {1, 3}, {1, 3, 4}, {1, 3, 4, 6} is a symmetric chain in the partially ordered set (poset) of subsets of {1,...,6}. It is a chain, because each of the subsets is a subset of the next one. It is symmetric because the collection has as many subsets with less […]
Title: Using Stitching for faster sampling Speaker: Mark Huber, Department of Mathematics, Claremont McKenna College Abstract: Point processes are used to model location data, such as the locations of trees in a forest, or cities in a plain. Repulsive point processes modify the basic model in order to obtain points that are farther apart from each other than would […]
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed k, the method finds a convex polytope with k vertices, called archetype points, such that the polytope is contained in the convex hull of the data and the mean squared distance between the data and the polytope […]
A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d. Power permutations are used in cryptography, and the exponent d must be chosen so that the permutation is highly nonlinear, that is, not easily approximated by linear functions. The Walsh spectrum […]
Title: Exploiting metric structure for more accurate classification Speaker: Mike Izbicki, Department of Mathematical Sciences, Claremont McKenna College Abstract: Classification problems often have many semantically similar classes. For example, the famous ImageNet dataset contains classes for 80 different dog breeds, 40 different bird species, and 25 types of vehicles. This semantic structure can be formalized using a metric […]
