Seminars, 2005
Lectures:
• 2.11.2005
Prof. A. Korol, Institute of Evolution, University of Haifa, Haifa.
Some problems of multilocus genetics: Mathematical & computer modeling

Abstract
To a large extent, the activity of laboratory of mathematical & populations genetics can be considered as evolutionary genetics/genomics and bioinformatics. A short outline of main objectives and results of these studies is presented below:

1. Evolution of sex and recombination: Building and testing theoretical models
aimed to explain the factors responsible for evolution of sex and recombination; role of sex and recombination in population adaptation and genome organization; adaptive value of major properties of recombination and mutation systems; ecological-genetic regulation of recombination and mutation. Our results include formal explanation (modifier models) of recombination/mutation properties, and demonstration of dynamic complexity (dynamic chaos) in simple population-genetic models with panimixia and partial sexual reproduction.
2. Genome sequence organization on the above-gene level: New measures
(compositional spectra based on fuzzy linguistics) for sequence comparisons on
the whole genome level. “Genome dialect” concept.
3. Genome mapping: Multilocus mapping allowing reliable ordering of DNA markers and genes (by reduction to “traveling salesman problem” - TSP). As a tool of discrete optimization for this challenging problem with complexity ~ n! (where n ~102-103) new heuristics for Evolution Strategy algorithms are developed in our lab. Even more challenging is mapping based on parallel data from different labs (synchronous TSP).
4. Genetic architecture of complex (quantitative) traits: Methods for genetic
mapping of quantitative traits loci (QTL), joint analysis of multiple trait complexes across the genome, using data scored in different ecological conditions. Multiple-trait QTL analysis for revealing genomic determinants of microarray expression patterns.
5. Structural genomics: New algorithms and tools for hierarchical clustering of microarray expression arrays based on novel highly efficient heuristics for Evolution Strategy algorithms (by reduction of the phylogeny problem to TSP). Evolutionary tree reconstruction for multi-site sequence data in challenging situations of many hundreds (thousands) of genotypes or species in the presence of recombination.

• 20.06.2005
Dr. E. Braverman, University of Calgary, Canada
On stability of equations with several delays and Mackey Glass equation with variable coefficients

Abstract
In the first part of the talk, some new results on stability of linear delay equations with several delays and variable delays and coefficients are presented. These results can be applied to the local stability of nonlinear equations. As an example, we consider the Mackey-Glass equation with variable coefficients and a non constant delay $N = [(r(t)N(g(t)))/(1+(N(g(t))^g)] - b(t)N(t)$ which models white blood cell production. Other qualitative properties of this equation, such as boundedness of solutions, persistence and oscillation, are also discussed. It is also demonstrated that with two delays the equation does not keep the persistence property.

• 02.06.2005
Prof. S. Schochet, Tel-Aviv University Israel
Are scalar viscous traveling waves still interesting?

Abstract
Three problems not covered by the standard theory for scalar viscous traveling waves will be discussed:

1) Global stability in higher dimensions:
2) Saturating viscosity:
3) Non-integrable perturbations:
The results presented are joint work with Shoshana Kamin (1) and with Shlomo Engelberg (2-3).

• 23.05.2005
Dr. B. Abramovitz & Dr. M. Berezina, ORT Braude College, Israel
Some Remarks on Open and Multiple Choice Tests

Abstract
This lecture is based on a joint work with Prof. Abraham Berman which is currently in publication process in “International Journal of Mathematical Education in Science and Technology”.. We discus some of the shortcomings of multiple choice tests in Mathematics given to undergraduate engineering students. Examples are presented, where the disadvantages of a multiple choice test are given.

• 05.05.2005
Prof. V. Ryazanov, Inst. Appl. Math. & Mech. NASU, Ukraine
Mappings with finite distortion

Abstract
Various classes of mappings with finite distortion like finite length and finite area distortion mappings are considered. Such classes are intensively studied during the last decade by many leading experts in the mapping theory as Frederick Gehring, Karri Astala, Tadeush Iwaniec, Pekka Koskela, Olli Martio, Gaven Martin, Juha Heinonen, Uri Srebro, Eduard Yakubov and others.

• 10.04.2005
Prof. D. Shoikhet, ORT Braude College, Israel
A Flower Structure of Backward Flow Invariant Domains for Semigroups of Holomorphic Function

Abstract

• 03.02.05
Prof. G. Weinstein, University of Alabama at Birmingham, U.S.A.
A Counter-Example to a Penrose Inequality for Charged Black Holes

Abstract
We construct a time-symmetric asymptotically flat initial data set to the Einstein -Maxwell Equations which satisfies $$m-1/2(R+\frac {Q^2}}R})<0$$ where m is the total mass, $R=\sqrt{\frac A {4\pi}}$ is the area radius of the outermost horizon and Q is the total charge. This yields a counter-example to a natural extension of the Penrose Inequality to charged black holes.

• 11.01.05
Dr. V. Turetsky, Technion, Israel
A Priori Estimates for Elliptic Systems in Fractional Sobolev Spaces with Applications to Geometry

Abstract
We will present a priori estimates for systems with coefficients in Bessel potential spaces. These results have applications to Riemanian geometry, where the Riemanian metric $g$ belongs to a certain Bessel potential space. Our motivation to deal with elliptic systems arises from the studying of Cauchy problem for Einstein Equations.