WIT Math Club
Wednesdays 5:30-6:30PM
Beatty 401


4/3/12 (Next Week):

Lorenz Attractors,
Chaotic Systems
Modeling Cancer

Outreach at the
Tobin Middle School



Presenters:  Shayna Jackson and Matthew Shakespeare

Abstract:  Chaotic systems have been a difficult area of study.  While they are deterministic in nature (not stochastic), their trajectories are complicated and oftentimes have a fractal dimension.  Because of the complex nature of the system there are few single-valued invariants that can be used to describe them; namely Lyapunov exponents (which describe the divergence/convergence of the trajectories) and a few other notions of dimensions. One  such notion of dimensions is Omega-Complexity.  This is a novel notion of associating a number with a fractal trajectory that gives a quantitative measure of something qualitative about its behavior, that is, is there a dominant component or direction in which the fractal develops.  We have written various Mathematica programs to test the properties of Omega-Complexity on 2D systems (Henon) and 3D systems (Lorenz) along with a few variations of Henon time delay embedding up to the 4th dimension.  We have found experimentally that Omega-Complexity will vary with the number of points but appears to stabilize as the number of points increases. Also the Omega Complexity for x time delay coordinates is equal to the Omega Complexity for y time delay coordinates. We are now using these programs to test multiple systems and determine if any version of multi-dimensional visibility will detect Omega-Complexity of the underling system.

Cancer is a widespread disease that emerges in a variety of ways, and its count is only growing with more and more subcategories entering into study. Each type of cancer requires its own approach and because of that cancer becomes harder and harder to cure. Many institutions have backed researchers and published documentation of the great strides in understanding cancer and its growth, and this key process of any research has been done over and over again, producing a variety of results from numerous perspectives to study as many forms of cancer as possible, with more still in development. With a great deal of the study work finished, the processes of application and interpretation become the playgrounds for breakthroughs in the field. Through the combination of fields, such as biology and chemistry, scientists have developed a wealth of knowledge for just what this disease is and how it works. By applying methodology from chaos theory to study the growth patterns of cancer a more accurate model for their growth patterns may be found. The aim is to develop a general model that can be fitted across many forms of cancer, and may even provide the doorway for new methods and approaches to be developed.

Presenter:  Wentworth Math Club

Abstract:  During this Math Club meeting, we will be headed to the Tobin Middle School in Mission Hill to discuss visual cryptography and how to encode/decode some basic cyphers.

The Wentworth Institute of Technology Applied Mathematics Department has a Facebook Page.  Feel free to visit!

Previous Meetings
The Mathematics of Cribbage
Sam Irwin
The Central Limit Theorem, Normal Distributions and Plinko
John Haga
Modeling Mesoscale Structure in Comb Polymer Materials for Anhydrous Proton Transport
Barry Husowitz
BBC Special:  Fermat's Last Theorem

The Mathematics of SET
Aisha Arroyo, Nora Shea
Connections Between Mathematics and Art
Marty Kemen
Lorenz Attractors, Chaotic Systems and Modeling Cancer
Shayna Jackson and
Matthew Shakespeare

Fall Semester 2012
Donald in Mathemagic Land and the Golden Ratio
John Haga
Handshaking and Chaos
Georgi Gospidinov
Phylogenetic Trees
Amanda Hattaway
Pick's Theorem John Haga
An Introduction to Graph Theory
Georgi Gospidinov
The Birthday Paradox and Monte Carlo Simulations
Barry Husowitz
An Introduction to Constructions with Compass and Ruler
John Haga
Trisecting an Angle Using Origami
Ophir Feldman
The Game of Go
David Ferrone

Questions or Comments can be emailed to mathclub@wit.edu.  This page is maintained by John Haga.