Dr. John Kern II

Chair, Associate Professor of Statistics
Department of Mathematics and Computer Science
440 College Hall McAnulty College
600 Forbes Ave
Pittsburgh , PA 15282
Email: mathchair@duq.edu
Phone: 412.396.6467

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Fa12 Seminar List

All the past Fall 2012 Seminars are listed below with the most recent at the top.

 Dr. Brad Lucier | Dr. Tony Shaska | Mr. Glenn Sidle | Dr. Hayley Iben

Mr. Brad Lucier

When: Wednesday 11/12 at 2:00 PM

Where: 447 College Hall

Speaker: Dr. Brad Lucier, Purdue University

Title: The Nature of Numbers: Real Computing

God made the integers; all else is the work of man: Leopold Kronecker (1823-1891)

Abstract: In elementary school, children are taught about numbers in a concrete way-numbers consist first of single digits, then finite strings of digits. Children are shown how to add, subtract, multiply, and divide these representations of numbers. Rational numbers are introduced, and it is shown that they can be represented by (possibly repeating) finite strings of digits.

Later on, the concept of number gets a bit fuzzy. Square roots are introduced, and although a student's calculator will give the first few digits of the square root of 2, for example, many students don't know how to get more digits if they need them. The number π appears, with a vague geometric definition and a few starting digits. Students begin to compute things without knowing how many correct digits are in the answers they get.

What happens if you continue with the constructive approach to numbers and operations on numbers that began in elementary school? Can you compute as many digits as you like of π, e, √2? What about functions on numbers, such as x^2, e^x, or sin⁡(x)? More generally, what is a computable number or function? You can look at these questions from the viewpoint of real analysis, mathematical logic, or computer science; the answers might surprise you.

All are welcome. Snacks will be provided.

Dr. Tony Shasha 

When: Thursday 9/27 at 4:30 PM

225 College Hall

Dr. Tony Shaska Oakland University

Some Remarks on Binary Octavics.

Finding invariants of binary forms has was a classical problems of 19th century mathematics. Bolza determined the ring of invariants for binary sextics in 1897.In 1967, in a paper published in the American J. Math., Shioda determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined by Shioda are incorrect. In this talk, we will compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field k, of characteristic not equal to 2, 3, 5, 7. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants. The talk will be intended for a general audience.

All are welcome. Snacks will be provided.  

Mr. Glenn Sidle

Tuesday 9/18 at 4:30 PM

222 College Hall

Glenn Sidle, Duquesne University

Modeling HIV Infection with Data Mining Techniques

Many models of HIV infection require an underlying assumption about the biological mechanisms of infection, and simple statistical techniques often struggle to capture the nonlinear dynamics of this system. In order to capture these dynamics without impressing assumptions on the system, we will examine the use of data mining. The techniques we use are artificial neural networks, a type of generalized nonlinear regression modeled after biological neural networks, and regression trees, a type of data mining procedure modeled after a decision flow chart. We will use the techniques based on past patient CD-4 count, CD-8 count, viral load and drug adherence to predict future patient health. We will describe techniques for creating both patient-specific models and a model created for all patients. After analyzing the model's ability to predict both short and long term patient health, we will describe how we can use the techniques to create a "virtual" clinical cohort on which we can evaluate the impact of clinical trials. Finally, we will show how this model can be used to understand how to optimally treat each patient.

All are welcome. Snacks will be provided.

Dr. Hayley Iben

Title: Curls Gone Wild: Hair Simulation in Brave

Speaker: Hayley Iben from Pixar Animation Studios
(Duquesne University class of 2001)

When: Tuesday September 4th 4:30-5:30 PM

Where: 446 College Hall

Abstract: In Pixar's recent feature film Brave, Merida's hair is an important extension of her character. Like Merida, it is fierce, tempestuous, and unpredictable. We were tasked with the challenge of creating hair that possesses its own dramatic and expressive personality, but still appears realistic and physically convincing. To accomplish this, we engineered a hair system that produces believable, natural movement while providing simulation artists with tools to direct the hair's motion as the story demanded. This talk will discuss the novel hair simulator we developed and the new techniques developed in production to utilize it.

Bio: Hayley Iben earned a B.S. in computer science from Duquesne University in 2001 and a M.S. and Ph.D. in computer science with an emphasis in computer graphics from the University of California, Berkeley in 2005 and 2007, respectively. Hayley joined Pixar Animation Studios in 2006 as an intern with the Research group and transitioned to full-time position with the Studio Tools group in 2007. She then worked on proprietary software tools for character articulation and animation with a particular focus on inverse kinematics. In 2010, Hayley transitioned to a position with both research and development and has since been splitting her time between improving simulation algorithms and transferring that new technology into production. Her work has been used in the production of Pixar's recent feature film, "Brave," released on June 22, 2012.

All are welcome. Snacks will be provided.