Plenary Lecture I:

Waves in Plane Hydrodynamics
 

Dr. Nabil Moussa,
Professor of Mathematics,
The American University in Cairo,
P.O.Box 2511,
Cairo, Egypt

moussan@aucegypt.edu
 

Abstract: In this lecture a survey of the constructive existence proof of solutions of a comrehensive class of nonlinear free boundary value problems of plane hydrodynamics, given by Eberhard Zeidler, based on the method of Dubreil-Jacotin for formulating the boundary value problem, conformal mapping and a functional analytical version of Liapunov-Schmidt, will be given.  Two general computational methods for solving several cases numerically, like for example, permanent heavy waves and permanent capillar-heavy waves of one liquid as well as of two liquides flowing one upon the other with different boundary conditions, will also be given.

Plenary Lecture II:

Bioinformatics: From Sequences to Imaging
 

Tuan Pham, PhD
Associate Professor
School of Information Technology
James Cook University
Townsville, QLD 4811, Australia
tuan.pham@jcu.edu.au

Abstract: Some challenging problems encountered in molecular biology and biomedicine whose promising solutions require the applications of computational methods will be briefly introduced. Following are the discussions of some recent results of our research into biological (DNA and protein) sequence comparisons and bio-imaging. For sequence comparisons, we have applied stochastic and fuzzy-set methods for computing the similarities between whole mtDNA genomes, which can overcome some limitations of  conventional alignment-based methods. We have recently developed a numerical model for protein sequence comparison based on the framework of linear predictive coding. For bio-imaging, we have successfully developed a fuzzy clustering model for segmenting cell puncta, whose solution is superior to an adaptive thresholding method which was implemented in the widely and freely distributed NIH software known as ImageJ. A current collaborative project on bio-imaging with the Harvard Medical School will also be briefly presented.

Plenary Lecture II:

Mathematical models of tumor angiogenesis

Akisato Kubo(*)
[joint work with Takashi Suzuki(**)]

* Department of mathematics, School of Health Sciences,
Fujita Health University, Toyoake, 470-1192 Aichi,
Japan
akikubo@fujita-hu.ac.jp

** Division of Mathematical Sciences, Graduate School of Engineering Science,
Osaka University, Toyonaka, 560-8531, Japan

Abstract: In this talk we deal with well konwn two mathematical models of tumor angiogenesis. We first study a parabolic ODE system modeling tumor angiogenesis proposed by Othmer and Stevens. In use of the transformation of Levine and Sleeman, we reduce it to a hyperbolic equation with strong dissipation. Then, we show the existence of collapse in arbitrary space dimension by the method of energy. On the other hand, Anderson and Chaplain proposed a mathematical model of tumor angiogenesis independently of Othmer and Stevens. However they presented only numerical computations of their model. Secondarily we deal with Anderson and Chaplain model mathematically based on our approach used in Othmer-Stevens model. In fact, developing Levine and Sleeman’s transformation it can be reduced to a hyperbolic equation with strong dissipation. Finally we discuss the relationship among these models.