December 24, 2012
Electrokinetic phenomena
Professor Ehud Yariv, Department of Mathematics, Technion

Abstract

Electrokinetic phenomena are ubiquitous in numerous engineering applications. In this talk I will review the governing equations and underlying concepts, discuss the thin-double-layer limit, and elaborate on surface-conduction effects.

December 17, 2012
A Toy Model of Fractal Glioma Development Under RF Electric Field Treatment
Dr. Iomin Alexander, Department of Physics, Technion

Abstract

A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating-field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.

November 19, 2012
The String Topology Category of Special Unitary Groups
Dr. Shoham Shamir

Abstract

The space of free loops on a compact manifold M, denoted LM, has been of major interest in topology for the last decade.
One reason for this interest is the discovery, by Chas and Sullivan, of a rich structure on the homology of LM - which is sometimes called the string homology of M. In particular, the string homology of M is a commutative ring, and the space of paths between any two submanifolds of M gives rise to a module over this ring. All this information can be neatly packaged into a construct called: the string topology category of M. Blumberg, Cohen and Teleman, who invented the string topology category, posed the following question: for which submanifolds N of M can we reconstruct the entire string homology of M using only the paths from N to itself? I will give an answer to this question when M is a special unitary group. Along the road we will meet novel techniques from algebra, and also a little bit of algebraic geometry. I will try to keep the talk as elementary as possible.

November 12, 2012
Mathematical Modeling of Ultrasound-Induced Drug Release from Liposome
Dr. Giora Enden, Department of Biomedical Engineering, Ben-Gurion University of the Negev

Abstract

Controlled, targeted and non-invasive drug release is highly desirable for attaining high efficacy in treatment of tumors and inflamed tissues. It has been shown in previous studies that exposure of 100nm diameter liposomes to low frequency ultrasound (LFUS) irradiation has a twofold effect: a) it causes the impermeable liposome membrane to become permeable and b) it induces liposome disintegration. When LFUS irradiation is stopped the liposome membrane immediately resumes its impermeable state and liposome disintegration is terminated. This suggests that LFUS irradiation can be used to remotely and non-invasively trigger drug release from liposomes at desired sites. A mathematical model may provide a better quantitative and qualitative understanding of this phenomenon. Here it is shown that the time-dependent non-dimensional volume of the liposome compartment can be accurately approximated by the sum of a single exponential and a constant. This is sufficient to provide a closed-form solution for the liposome drug-content and evaluate the relative contributions of the diffusion and disintegration factors to the overall drug release.

November 5, 2012

July 16, 2012
On the spectral properties of operators of the quantum mechanics and limit operators
Professor Vladimir Rabinovich, Instituto Politécnico Nacional, Mexico

Abstract

We will discuss the applications of the limit operators method for a description of the essential spectra of the Schrödinger and Dirac operators and for estimates of a behavior of eigenfunctions of the discrete spectrum of these operators at infinity.

June 18, 2012
Enzymatic degradation of polymers: mathematical modeling and analysis of reaction pathways
Professor Rosa Azhari, Department of Biotechnology Engineering, ORT Braude College

Abstract

Natural polymers (polysaccharides, proteins, DNA) undergo degradation by specific enzymes. Each enzyme is cleaving the polymeric chain via a unique pathway. Unlike low molecular weight substrates, polymers usually contain many sites that are susceptible to enzymatic attack. Therefore, enzymatic degradation of a certain polymer may proceed in different patterns that depend on the enzyme-polymer interactions, as well as on the probabilities for cleavage of bonds located at different positions in the polymeric chain. The degradation pathway determines the dynamic changes in the size distribution of the oligomeric fragments produced.  In our study, a unified model for analysis of different enzyme-promoted homopolymer degradation processes was developed and used for determination of mechanisms pursued in enzymatic hydrolysis of polysaccharides. We wish to extend the model to the description of enzymatic degradation of copolymers and seek collaborations for assistance with the development of the mathematical model and the numerical tools needed for its use in analyzing experimental data.

May 28, 2012
Terminal Cost Distribution in Uncertain Controlled Systems with Imperfect Information

Professor Valery Glizer, Associate Professor Vladimir Turetsky,
Department of Mathematics, ORT Braude College

Abstract

Recursive formula for the terminal cost distribution in a scalar linear discrete-time system with disturbance and noise corrupted measurements is obtained. The system is subject to a linear saturated control strategy. The distributions of the initial state
and the estimator error are assumed to be known. The disturbance is independent of the state/control and its distribution is known. The general result is applied to an interception problem with different types of disturbance. Illustrative numerical examples confirm that the analytical method can replace extensive Monte Carlo simulations.