In 2005, Vikas Sindwani and the University of Chicago team proposed a new semi-supervised kernel-based SVM algorithm in the paper Beyond the Point Cloud: from Transductive to Semi-supervised Learning. In this algorithm, instead of Euclidean geometry, they utilized the unlabeled data to understand the underlying geometry and construct a Deformed Kernel to encode the information of the deformed geometry. However, the computational time complexity of construction of the Deformed Kernel is cubic. Consequently, the algorithm failed to scale. Our goal is to improve the algorithm and eventually construct a deformed kernel within quadratic computation time complexity.
The Jones polynomial is an important knot invariant introduced in 1984 by Vaughn Jones. There are multiple ways to compute the Jones polynomial and in this paper we will explore a technique introduced by L. Zulli using trip matrices. In particular, we will focus on using trip matrices to compute the Jones polynomial of T(2,n) torus knots. Jones proved an explicit formula for the Jones Polynomial of all torus knots, but the proof relies on heavy machinery from Abstract Algebra. We provide a more elementary proof of this formula for T(2, n) knots using trip matrices and basic Linear Algebra.
An empirical climate model (ECM) takes a statistics-based approach in modelling the global Earth temperature as dependent on various forcings, such as the levels of greenhouse gases and solar radiation. Our web application visualizes such a model. Specifically, through an interactive interface, the application enables users to directly explore how four forcings can account for the variation and change in Earth’s mean global temperature record. The application is intended to be used in educational settings. For instance, it will be part of an online curriculum developed by the Biological Sciences Curriculum Study (BSCS). It is live at https://ecm.coloradocollege.edu/.
Our project aims to streamline the workflow for making course proposals at Colorado College. Currently, in order to create a course proposal, professors need to go through a tedious and time consuming process, following specific formatting rules and manually retrieving existing course data to add to their proposals. Our web application offers a more efficient way to generate course proposal documents.
We describe homophily as the tendency of people to connect with others who share similar socio-cultural traits. Homophily affects social networks across industries and communities, and increasing or decreasing the homophily within a network can help us predict the evolution of connections over time. By building a network based on measured characteristics, we will further dissect the impacts of homophily on a model network and explore the implications of these network formations.