BULGARIAN ACADEMY OF SCIENCES

INSTITUTE OF MATHEMATICS AND INFORMATICS

ACTIVITY REPORT

2000

DEPARTMENT OF BIOMATHEMATICS

Acad. G. Bonchev str. block 8, Sofia, Bulgaria

http://www.math.bas.bg/~bio/

CONTENTS

STAFF

· GENERAL INFORMATION

· MOST IMPORTANT SCIENTIFIC RESULTS

· PUBLICATIONS AND THESES

· PROJECT CONTRACTS/GRANTS

· LECTURE COURSES

· SEMINARS, WORKSHOPS, CONFERENCES, LECTURES

· MISSIONS

· MEMBERSHIP IN SCIENTIFIC SOCIETIES, EDITORIAL BOARDS, ETC

· VISITORS

STAFF


Svetoslav Markov	Associate Professor	PhD

Mikhail Krastanov	Associate Professor	PhD

Neli Dimitrova	Assistant Professor	PhD

Evgenia Popova	Assistant Professor	PhD

Dessislava Vassileva	Specialist

Nadejda Grigorova	PhD student

GENERAL INFORMATION

Research topics

The Department (section) of Biomathematics of IMI-BAS is generally concerned with research and education in the field of mathematical modelling in biology under uncertainty, dynamical models of ecological, physiological, biochemical and other processes, scientific computations, numerical methods and algorithms with result verification, methods of operations research, error analysis and interval analysis, computer arithmetic, programming languages and systems of computation, esp. computer algebra systems, computer graphics.

The major research efforts are currently focused on the following areas:

· mathematical models of enzyme kinetic and fermentation processes;

· algebraic properties of intervals and convex bodies;

· linear algebraic equations whose coefficients and right-hand sides depend on uncertain parameters;

· stability and controllability of nonlinear control systems;

· interval computer algebra (application of computer algebra methods to interval computations);

· verification algorithms for nonlinear problems.

Lecture courses/educational programs

The Department of Biomathematics of IMI-BAS offers permanently the following lecture courses for master and PhD programs:

Mathematical modelling in biology; one semester (15 weeks, 2+2 hours weekly (total 30+30).

The lecture course is intended for students of the 3rd up to the 5th year of the speciality ``Applied Mathematics'' of the Faculty of Mathematics and Informatics at the University of Sofia. The course is devoted to i) basic principles of the mathematical modelling and contemporary methods for modelling of biological processes; ii) particular models of mathematized biological areas, such as population dynamics, mathematical ecology, enzyme kinetics, bioreactors and chemostats, transmission of nerve signals, kinetics of chemical synapses, mathematical epidemiology etc. The models are constructed under a detailed motivation of the biological hypotheses, a systematic mathematical analysis is performed and specific case studies are considered with a respective biological interpretation.

· Introduction to mathematical modelling, one semester (15 weeks, 2+2 hours weekly (total 30+30).

The lecture course is intended for students of the 3rd up to the 5th year. An emphasize is made on the algebraical properties of computational errors, the error analysis and the usage of contemporary computational and programming tools. Some aspects of the treatment of mathematical problems under uncertain input date are considered. Such problems arise often in the course of mathematical modelling of biological processes, as the latter usually involve short and unrepeatable experimental series of input data, containing thereby considerable inaccuracies, and moreover, the formulated mathematical problems are often very sensitive. The numerical methods with result verification automatically provide guaranteed results and a possibility for a strict distinction between the model predictions and the experimentally observed data.

· Interval analysis

· Convex analysis

· Numerical methods with verification

· Computer arithmetic

MOST IMPORTANT SCIENTIFIC RESULTS 2000

The space of errors (symmetric intervals on the real line) has been fully investigated with respect to the operations addition and multiplication and the ordering inclusion using the axiomatic approach. The results are used to represent the interval space as a direct sum of the space of errors and the real ordered field;

· Investigated are properties of local variations of higher order for nonlinear controllable systems related to small-time local controllability with respect to a set;

· Constructed is a bounded feedback for an automatic stabilization of a control system (modelling the continuous process of methan fermentation under uncertainty) in a neighborhood of a set of optimal points with regard to a suitable criteria.

· A mathematical model describing biochemical processes in an organism has been further elaborated and numerically experimented using the computer algebra system Maple (collaborative work with the Center of Mathematical Biology, Oxford);

· A method of Gauss-Seidel type has been proposed for the enclosure of the set of solutions of parametric interval linear systems; the method has been applied for the parameter estimation when simulating linear electric circuits under uncertainty (collaborative work with the IEEE of U. of Kyoto).

PUBLICATIONS AND THESES 2000

1. N. Ribarska, Ts. Tsachev, M. Krastanov: A note on: Ön a critical point theory for multivalued functionals and application to partial differential inclusions", Nonlinear Anal. 43, no. 2, Ser. A: Theory Methods, pp. 153-158, 2000.

2. S. Markov: On the Algebraic Properties of Convex Bodies and Some Applications, Journal of Convex Analysis 7 (2000), 129-166.

3. N. Ognjanova-Rumenova, M. Filipova-Marinova, E. Popova: Environmental history and human influence at coastal wetlands in the Bay of Sozopol, Bulgarian Black sea coast. Acta Palaeobotanica Suppl. EPPC 2, 1999, pp. 589-593.

4. M. Krastanov, M. Quincampoa: Local small-time controllability and attainability of a set for nonlinear control systems, Prepublications du Departement de Mathematique de l'Universite de Bretagne Occidentale, No. 7, 2000.

5. S. Markov: On the Algebra of Errors and Intervals. Preprint IMI - BAS, Sofia, 2000, No. 2.

6. S. Markov: On the Solution of Linear Tight Interval Systems. 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation.

CD:Sessions/121-5.pdf

7. N. Dimitrova, I. Simeonov: Advanced Sensitivity Analysis of a Nonlinear Model of the Methane Fermentation. Proc. Automatics and Informatics Conf., October 24-26, 2000, Sofia, pp. 80-83.

8. M. Krastanov, N. Dimitrova: Feedback Control of an Anaerobic Fermentation Process Under Uncertain Data. Mathematics and Education in Mathematics, Proc. 29th Spring Conf. of UBM, 2000, pp. 184-191.

9. S. Markov: Mathematical Modelling of Dieting. Mathematics and Education in Mathematics, Proc. 29th Spring Conf. of UBM, 2000, pp. 119-127.

10.N. Grigorova, S. Markov: Mathematical Modelling and Numerical Simulation of Metabolic Processes, Proc. BioPS'2000, Sofia, 11-13 September 2000, II.17-II.20.

11.E. Popova: Generalized Interval Arithmetic - Properties and Implementation. Inst. of Mathematics & Informatics, Bulgarian Academy of Sciences, Sofia, 2000 (Ph D Thesis).

12.S. Kambitov: Packages for Interval Arithmetic & Simplification of Interval Expressions in CAS Mathematica. Faculty of Mathematics & Informatics, Sofia University, Sofia, 2000 (M Sc Thesis; supervisor: E. Popova).

PROJECT CONTRACTS/GRANTS 2000

National

Bulgarian NSF Project contract No. I-903/99: Interval Computer Algebra (1999-2002).

International

Bilateral Study Agreement between DFG-Germany and BAS: Multiaspect Data Types in the Implementation of a New Hierarhy of Numerical Spaces having a Reach Algebraic Structure; jointly with Lehrstuhl fuer Informatik II, Universitaet Wuerzburg, Germany (1998-2000).

· Bilateral Study Agreement between CNRS-France and BAS: Reliability of Numerical Software; jointly with CHPV Team at LIP6, University Paris-VI, France (1998-2001).

· Bilateral Study Agreement between TUBUTAK, Turkey and BAS: Verification Algorithms for Computer Algebra Systems; jointly with Bosphorus University, Istanbul, Turkey (2000-2002).

· Bilateral Study Agreement between PAS, Poland and BAS: Interval Analysis and Diagramatic Presentation; jointly with Institute of Fundamental Technological Research of PAS (2000-2002).

· Direct contract between IMI-BAS and PUCRS, Brasil: Numerical Analysis for Problems Involving Uncertainties.

· NATO Linkage Grant: Functional analysis of the peroxisomal protein import machinery Univ. of Groningen, Netherlands; Inst. of Molecular Biology, BAS; IMI, BAS.

Grants

Three DFG Travel Grants for SCAN2000, Karlsruhe, Germany. Sept 19-22, 2000

· One travel grant for EUROATTRACTOR'2000 at the Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, 6-15 June 2000.

LECTURE COURSES 2000

S. Markov: Mathematical Modelling in Biology, Lecture course for students of the 3rd up to the 5th year of the speciality ``Applied Mathematics'' of the Faculty of Mathematics and Informatics at the University of Sofia. Horarium: one semester, 3+3 hours weekly.

SEMINARS, WORKSHOPS, CONFERENCES 2000

Seminars

Interdisciplinary Seminar on Biomathematics and Scientific Computations;

· Weekly Seminar of the Dept. of Biomathematics of IMI-BAS;

· Annual report session of section "Biomathematics" at IMI-BAS, 15 December 2000:


10:00 - 10:30:	S. Markov, Algebraic theory of errors, intervals and convex bodies;
10:30 - 11:00:	M. Krastanov, On the small-time local controllability of a set;
11:00 - 11:30:	E. Popova, Quality of the solution set of parameter-dependent interval
	linear systems;
11:30 - 12:00:	N. Dimitrova, Investigation of biotechnological processes under uncertainties;
12:00 - 12:30:	N. Grigorova, On some mathematical models based on enzyme kinetic;
12:30 - 13:00:	A. Alexandrov, High frequency oscillatory pattern in LH and FSH response;
13:00 - 13:30:	A. Popov, On the estimation of the fractal dimension of surfaces.

List of public lectures 2000

S. Markov:

- Mathematical Modelling of Dieting. 4 April 2000, 29th Spring Conf. of UBM, Lovech;

- On the algebraic properties of interval and stochastic numbers, 23 May 2000, University Paris 6, LIP6;

- Mathematical modelling of metabolic processes in relation to nutrition, 28 May 2000, University Paris 6, LIP6;

- Reducing Linear Interval Systems to Systems of Coordinates, 21 September 2000, Karlsruhe, SCAN 2000; http://www.scan2000.de

- On the Algebraic Properties of Stochastic Arithmetic, 21 September 2000, Karlsruhe, SCAN 2000, (jointly with R. Alt);

- On the algebraic properties of convex bodies, 20 September 2000, Institute of Economy and Statistics, University Karlsruhe, Seminar of Prof. D. Pallaschke;

- On the Algebra of Convex Bodies, Errors and Intervals, 25.09.2000, University of Wuerzburg, Lehrstuhl fuer Informatik;

- On the Algebra of Convex Bodies and Errors, 30 September 2000, University of Hamburg, International Colloquium on Applications of Mathematics in memoriam Lothar Collatz (1910-1990);

- Algebraic Theory of Errors, 19 December 2000, Annual Seminar on ``Algorithms for Scientific Computations'' organized by CLPP-BAS and IMI-BAS;

· M. Krastanov:

- Small-time local controllability and weak invariance, 4 April 2000, University Bretagne Occidentale, France;

- Small-time local controllability with respect to a set, 16 May 2000, Seminar of the department of the Operations Research, IMI-BAS;

· E. Popova

- On the Solution of Parametrised Linear Systems, 21 September 2000, Karlsruhe, SCAN 2000;

- The Impact of Computer Algebra on Interval Computations, 26 September 2000, Informatics Colloquium, Univ. of Wuerzburg, Germany;

· N. Dimitrova

- Feedback Control of an Anaerobic Fermentation Process Under Uncertain Data, 5 April 2000, 29th Spring Conf. of UBM, Lovech (jointly with M. Krastanov);

- Stabilizing Control Design of a Nonlinear Process Involving Uncertainties, 19 September 2000, University of Karlsruhe, SCAN 2000 (jointly with M. Krastanov);

· N. Grigorova

- Mathematical Modelling of Metabolic Processes in Relation to Nutrition, 10 June 2000, EUROATTRACTOR'2000, Institute of Biocybernetics and Biomedical Engineering, PAS, Warsaw;

- Mathematical Modelling and Numerical Simulation of Metabolic Processes, 11 September 2000, BioPS'2000, Sofia (jointly with S. Markov).

MISSIONS

M. Krastanov: visiting professor in the University Bretagne Occidentale, France, March 6 - May 5, 2000;

· S. Markov: visiting professor in University Paris-VI, LIP6, May 4-June 2;

· N. Grigorova: participation at EUROATTRACTOR'2000, organized by the Institute of Biocybernetics and Biomedical Engineering, PAS, Warsaw, 6-15 June 2000;

· N. Dimitrova, E. Popova, S. Markov: participation at the GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2000), jointly with: International Conference on Interval Methods in Science and Engineering (Interval 2000), 19-22 September 2000, http://www.scan2000.de ;

· E. Popova, S. Markov: University of Wuerzburg, Germany, September 23-28 2000;

· S. Markov: participation at International Colloquium on Applications of Mathematics in memoriam Lothar Collatz (1910-1990), University of Hamburg, 29.09.00-30.09.00.

MEMBERSHIP IN SOCIETIES, BOARDS, ETC

S. Markov: member of UMB (president of section ``Biomathematics and Scientific Computa- tion''); member of GAMM (president of the Bulgarian section of GAMM); member of the European Society for Mathematical and Theoretical Biology (ESMTB); member of the Union of Automatics and Informatics; reviewer of Zentralblatt; member of the Editorial Board of Reliable Computing (a Kluwer Journal);

· M. Krastanov: member of UMB (section ``Biomathematics and Scientific Computation''); member of GAMM (Bulgarian section of GAMM); member of the Americam Mathematical Society (AMS); reviewer of Mathreview and Zentralblatt;

· N. Dimitrova: member of UMB (secretary of section ``Biomathematics and Scientific Computation''); member of GAMM (Bulgarian section of GAMM); reviewer of Zentralblatt;

· E. Popova: member of UMB (``Biomathematics and Scientific Computation''); member of GAMM (secretary of the Bulgarian section of GAMM); member of the European Society for Mthematical and Theoretical Biology (ESMTB);

· D. Vassiliva: member of UMB (section ``Biomathematics and Scientific Computation'');

· N. Grigorova: member of UMB (section ``Biomathematics and Scientific Computation'');

VISITORS

15-19 August 2000, Prof. Ph. Maini, Center for Mathematical Biology, Oxford, UK; Lecture on 17 August 2000, at the joint Seminar of the Departments on Biomathematics and Mathematical Modelling: Applications of Chemotactic Models in Biomedicine.

· 13-21 November 2000, Prof. Rene Alt, University Paris-6, France;
Lecture on November 16, 2000 (14:00) at the joint Seminar of the Departments on Biomathe- matics and Probabilities and Statistics: On the Algebraic Properties of Stochastic arithmetic. Comparison with Interval Arithmetic.

· 13-21 November 2000, Assist. Prof. J.-L. Lamotte, University Paris-6, France.