Santa Clara University Math/CS Colloquium Series

Fall 2007

October 2: Don Albers, SCU, on Routine and Tough Calculus Problems Made Easy

O’Connor 107

Abstract: Employing a relatively unknown, but powerful visual method, some easy and not-so-easy calculus problems will be dispatched. Little or no knowledge of calculus will be needed to understand the problems or solutions. First-term calculus students might enjoy challenging (or tormenting) students of advanced calculus with some of the problems, and then demonstrating solutions understandable to pre-calculus students.

October 9: No colloquium scheduled.

October 16: Aaron Diaz, SCU, on Computing Eigenvalues of Perturbed Matrices

O'Connor 107

Abstract: The problem of efficiently updating the eigenspace associated with an eigenvalue or set of eigenvalues after a perturbation to the underlying matrix is important to many applications including analysis of nano systems and signal processing. In this talk we describe a novel algorithm for performing this computation. This method is based on a directed search of a suitably chosen subspace. This is a general talk and will not assume a specialized background.

October 23: Rebecca Glover, SCU, on Growth Series for Right-Angled Coxeter Groups

O'Connor 107

Abstract: The growth series for a right-angled Coxeter group is an infinite power series whose coefficients represent the number of elements of the group of a certain length. In this talk, I examine two generating sets and the growth series they form, called the standard and the automatic growth series. I will explore the relationships between these growth series, discuss how they can be calculated, and examine how well they represent the corresponding Coxeter group. This talk will cover the research I worked on with Professor Rick Scott this past summer.

October 30: Keith Devlin, Executive Director, CSLI Stanford University

O'Connor 206

Title: Math 20-20 Vision

Abstract: By the year 2020, we are likely to have seen two major revolutions in mathematics education. Videogame technology will bring an understanding of mathematics to children in the affluent western societies who do not respond to current teaching methods. At the other end of the economic spectrum, cheap mobile phones will deliver instruction in basic quantitative skills to the millions in the developing world for whom the mobile phone is the only programmable computing device in the home. Both revolutions require taking a fresh look at the nature of mathematics and how it can be taught.

November 8: (Note that this is a Thursday.) Benjamin Ragan-Kelley, Graduate Program in Applied Science & Technology, College of Engineering, University of California, Berkeley, CA

Title: Design and Analysis of a Watermarking System for Care Labels

Abstract: We propose a watermarking system for embedding textile care labels directly onto fabric design, and analyze its stochastic properties. Under the assumption that pixel values are independently and identically distributed with finite mean and variance, we derive
i) the expected mean squared error between the original and watermarked images (transparency); and
ii) an upper bound on the average absolute change to DCT coefficients of the watermarked image after one application of simulated fading (robustness).

Experimental results demonstrate that the proposed scheme preserves image fidelity well and is very robust under simulated fading.

This is joint work with Nicholas Tran, supported in part by NSF Grant IIS-0242435.

November 13: Giovanni Seni, SCU

O'Connor 206

Title: Introduction to Ensemble Methods for Data Mining

Abstract: Ensemble methods are one of the most influential developments in Machine Learning over the past decade. They perform extremely well in a variety of problem domains, have desirable statistical properties, and scale well computationally. By combining competing models into a committee, they can strengthen `weak' learning procedures.

This presentation provides an introduction to `classic' ensemble methods--bagging, random forests, and boosting--using Importance Sampling as a unifying framework. We begin with an overview of regression trees which allow us to introduce many of the key issues in predictive (machine) learning. Following the material on trees, is a consideration of regularization, a technique to control model complexity to avoid over-fitting. Finally, we'll provide a summary of ensemble procedures. Time permitting, an analysis of real data from a manufacturing domain will be also shown.

November 27: Ginger Myles, Research Staff Member at the IBM Almaden Research Center

O'Connor 206

Title: Software-Based Approaches to Software Protection

The problem of protecting software from illegal copying and redistribution has been the focus of considerable research motivated by billions of dollars in lost revenue each year. Currently, there are three major threats recognized against the intellectual property contained in software: software tampering, malicious reverse engineering, and software piracy. A variety of mechanisms have been explored to prevent these threats through legal, ethical, and technical means, yet no single mechanism has been successful at preventing all three threats. The legal approach relies on a variety of laws such as copyrights, patents, trademarks, and trade secrets, which offer limited effectiveness by relying on the fear of consequences. Because the legal protections have limited effectiveness, a variety of technical approaches have been proposed to prevent and detect individual cases of attack. In this talk we will discuss the three major threats and explore the legal and technical approaches used to address them.