Seminars 2008-2009

 Date  Lecturer  Topic
28/06/2009 tatiana Savina

Ohio University, Israel

Reflections: from functional equations to integro-differential operators

In this talk we will discuss some classical statements of the continuation problem for elliptic equations and derive non-local reflection formulas generalizing the celebrated Schwarz symmetry principle

11/06/2009 Dr. Nir Shvalb

Ariel University, Israel

The configuration spaces of graphs and their topological singularities.


Configuration space of a graphs is defined as the totality of all
embeddings of the underlying geometric structure of a given graph in
the Euclidian space. For Example two rods concatenated and fixed to
the ground by a rotational joints constraint to the plane have a
2-torus as it configuration space, that is the multiplication S\up{1}
x S\up{1}.These are of importance for motion planning problem and
singularity analysis in Robotics. Usually having dimension >2,
configuration spaces of mechanisms are generally out of hand, and most
of the research is focused on finding topological constants such as
connectivity and topological groups. We will take a closer look at
what had been achieved till now in this field.
And will present a new peeling procedure for identifying topological
singularities of a c-space of graphs.

19/04/2009 Prof. Alexander Domoshnistky, Abraham Maghakyan, Roman Shklyar

Ariel University, Israel

maximum principles and boundary value problems for first order neutral functional differential equations


In this paper we obtain the maximum principles for the first order neutral functional differential equation

02/04/2009 A.JKanel-Belov

Moscow Center of Continous Mathematical education, Russia

2-dimentional problems of statistical geometry

The talk is devoted to the following problem.
Consider random set of lines. They divide plane into polygonal parts. Find distributionlaw  of this parts by arrears, perimeters, etc. The similar problems get rise to Voronoi mosaics.
We suggest the general method to express these distributions in terms of solutions of some PDE systems, sometimes they can be reduced to the ordinary differentional equtions. In particular, perimeter distributions can be expressed via Ricatty equations.

26/03/2009 Wojciech Czernous

Insitute of mathematics, University of Gdansk, Poland

Infinite systems of first order PFDEs with mixed conditions
19/03/2009 Wojciech Czernous

Insitute of mathematics, University of Gdansk, Poland

generalized solutions of mixed problems for first-order partial functional differential equations


12/03/2009 Dror Tobi

Ariel University, Israel

Development of improved potentials for protein docking and interface recognition


Understanding protein-protein interactions is fundamental to our ability to understand and control cell function. Protein-protein interactions provide an underlying framework through which cell activities such as enzymatic reactions are executed. The molecular mechanism of interaction between protein-protein complexes is usually characterized by structure determination methods such as X-ray crystallography, NMR spectroscopy, and cryo-electron microscopy. However, many complexes are too transient to lend themselves to experimental characterization.  Docking simulations have recently gained importance as possible means of predicting the quaternary structures of protein-protein complexes. Yet, these algorithms generate a large number of false-positive and false-negatives, mainly due to the inaccuracy of scoring functions (docking potentials) used for evaluating the docked conformations. We propose a novel way to construct docking potentials using a Linear Programmingtechnique. The technique has two major advantages over the statistical approaches used so far. (i) It enables us to train the scoring function from a large set of non-native protein-protein conformations. The inclusion of a wealth of information on non-native complexes states in building scoring functions enable us to overcome the problem of limited data, and to train our potentials using knowledge extracted from transient complexes

19/02/2009 Abraham Maghakyan

Ariel University, Israel

About generalized Burger’s Equation
08/01/2009 Prof. Leonid Berezansky

Ben-Gurion University, Israel

Nicholson Blowflies Differential Equations Revisited


Immunotherapy treatment of Bladder Cancer:  A mathematical model

AUTHORS: Svetlana Bunimovich-Mendrazitsky, Israel Chaskalovic, Eliezer Shochat, Jean Claude Gluckman and Lewi Stone

AFFILIATIONS: Biomathematics Unit, Faculty of Life Science, Tel-Aviv University

We present a modeling study of bladder cancer growth and its treatment via immunotherapy with Bacillus Calmette-Gue´rin (BCG) – an attenuated strain of Mycobacterium bovis (M. bovis). BCG immunotherapy is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite extensive biological research. The mathematical model presented here attempts to gain insights into the different dynamical outcomes arising from tumor-immune interactions in the bladder. We studied two types of the treatment: continuous and pulsed BCG therapy. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. A mathematical analysis of the differential equations identifies multiple equilibrium points, their stability properties, and bifurcation points.  Intriguing regimes of bistability are identified in which treatment has the potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. In the case of continuous therapy, the model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient. The model predicts i) regimes in which immunotherapy cannot help; ii) the optimal BCG dosage. Intense therapy can incur damage and side effects via the immune system; iii) quantitative relationships between BCG dosage, the cancer’s initial condition and tumour growth rate that can be calculated prior to treatment.

Next research that we examine is analyzing the expression of interleukin-2 (IL-2) with a course of treatment with BCG. IL-2 causes inflammation, which is the reason that it has been tried as a therapeutic to augment the function of the immune system. The mathematical analysis of the seven ODE equations explains the conditions for successful bladder cancer treatment.

The final goal in this work is to determine the applicable treatment regime that prevents the immune system destructive side effects (caused by BCG + IL-2) and enhances tumor eradication.

17/12/2008 Robert Hackl

Institute of Mathematics, Academy of Sciences of the Czech Republic

Periodic Boundary Value Problem for Linear Functional Differential Equations of Higher Order
11/12/2008 Robert Hackl

Institute of Mathematics, Academy of Sciences of the Czech Republic

Periodic Boundary Value Problem for Linear Functional Differential Equations of Higher Order