How to measure a Cantor set?

Speaker: 

Anton Gorodetski

Institution: 

UC Irvine

Time: 

Monday, February 7, 2011 - 6:00pm

Location: 

RH 306

Topologically all Cantor sets are the same. Nevertheless, thee are many ways to assign a quantitative characteristic to Cantor sets, and these notions play important role in applications to dynamical systems, number theory, spectral theory, and other areas of mathematics. We will describe some of the characteristics (e.g. fractal dimentions, thickness) of Cantor sets and the ways one can calculate and use them.

* Pizza and Soda to be served!

Cramer-Rao Bound for Estimating Non-linear Parameters in a Model for Chemical Species Separation using Magnetic Resonance Imaging

Speaker: 

Emily Bice

Institution: 

UC Irvine

Time: 

Monday, January 31, 2011 - 6:00pm

Location: 

RH 306

Magnetic resonance images typically contain signals from multiple chemical species such as water and fat. The diagnostic information in the image can be improved by separating the components of the signal coming from individual chemical species. The model that describes the signal generation includes non-linear parameters which arise from imperfections in the magnetic field and signal decay. The Cramer-Rao Bound is the minimum variance of an unbiased estimator of a parameter. In this work, we use the Cramer-Rao Bound to optimize the data acquisition for the non-linear inverse problem of estimating the magnetic field inhomogeneities and signal decay.

Feedback, lineages and cancer

Speaker: 

Prof. John Lowengrub

Institution: 

UCI

Time: 

Monday, November 29, 2010 - 5:30pm

Location: 

RH 306

A multispecies continuum model is developed to simulate the dynamics of cell lineages in solid tumors. The model accounts for spatiotemporally varying cell proliferation and death mediated by the heterogeneous distribution of oxygen and soluble chemical factors. Together, these regulate the rates of self-renewal and differentiation of the different cells within the lineages. As demonstrated in the talk, the feedback processes are found to play a critical role in tumor progression and the development of morphological instability.

*Pizza and soda will be served!

Cryptography and Counting Points on Elliptic Curves

Speaker: 

Nick Alexander

Institution: 

UCI

Time: 

Monday, November 8, 2010 - 5:30pm

Location: 

RH 306

In 2003, the National Security Agency (NSA) payed Certicom, a small Canadian security company, 25 million dollars for the right to use Certicom's elliptic curve cryptography technology. We will introduce elliptic curves and their applications to cryptography and computer security, and suggest why the NSA paid so much. Then we will describe the computationally important "point counting problem", which is necessary for efficient elliptic curve cryptography. We will survey some recent research that "counts points" on certain elliptic curves.

Mathematical Models of Flames

Speaker: 

Joanna Bieri

Institution: 

University of Redlands

Time: 

Monday, October 25, 2010 - 5:30pm

Location: 

RH 306

Many of the mechanisms that govern flame dynamics are complicated and not well understood. Even simple models can give us a lot of information about the stability, shape and location of flames. The goal of this talk will be to discuss the model of an edge-flame in a confined space, or narrow channel. We will begin by talking about the heat equation, a diffusion-type partial differential equation, and the possible boundary conditions for such an equation. Then we will develop a model for a flame in a narrow channel and discuss how we can use numerical methods to find solutions for this system.

*Pizza and soda served!

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