Edward Aboufadel

A New Method for Computing the Mean Center of Population of the United States

Abstract The mean center of population of the United States is a convenient location used to summarize the population distribution of the United States and how it changes over time. As computed by the U.S. Census Bureau, the center depends on an arbitrary choice of a map projection. We feel that this location should depend only on the population distribution and not on any choices made in representing the data of the distribution. This note discusses a method for computing this location that does not depend on any choices made and describes how the results of this method differ from those of the Census Bureau.

Breaking the Holiday Inn Priority Club CAPTCHA

Edward Aboufadel (aboufade@gvsu.edu; Grand Valley State University, Allendale, MI 49401) received his B.S. from Michigan State University in 1986, and his Ph.D. from Rutgers University in 1992. He is now an Associate Professor at Grand Valley State University. He became interested in wavelets in the early 1990s, upon learning that the Federal Bureau of Investigation had adopted a wavelet-based method to compress fingerprint images. nese days, his time at work is devoted to teaching, departmental service, research with undergraduates, and day trading his CREF account.

Quantification of the Variability of Continuous Glucose Monitoring Data

Several measurements are used to describe the behavior of a diabetic patient’s blood glucose. We describe a new, wavelet-based algorithm that indicates a new measurement called a PLA index could be used to quantify the variability or predictability of blood glucose. This wavelet-based approach emphasizes the shape of a blood glucose graph. Using continuous glucose monitors (CGMs), this measurement could become a new tool to classify patients based on their blood glucose behavior and may become a new method in the management of diabetes.

Digital creation of Chuck Close block-style portraits using wavelet filters

Chuck Close is an American artist who paints large ‘block portraits,’ which are a type of mosaic where the tiles are small rotated squares which contain abstract shapes. Despite the drastic change in fine details compared to a photograph, all of the abstract marks work together to create a realistic looking portrait. There is a certain duality: viewed up close, the paintings are flat and obscured, but from afar they seem to pop out into three dimensions. This article presents a new method to digitally create portraits in the block style of Chuck Close. The work described in this article is novel in three ways: (1) wavelets filters are used to determine the shapes in the marks, (2) the colour-picking algorithm leads to a more natural colouring than previous work in this area and (3) tiles other than squares are used.

Imitating the Shazam App with Wavelets

Summary With the Shazam smartphone app, a listener captures a short excerpt of a recorded song with the smartphones microphone, and in a matter of moments the app reports the name of the song and the artist. Fourier analysis is a key mathematical tool that powers the app. In this paper, we describe a wavelet-based method that captures the basic process used by the Shazam app to search a database of number sequences (signals) to find those that are similar to a test signal. We will describe our implementation with a different source of signals: continuous glucose monitor data from the management of type-1 diabetes.