BULGARIAN ACADEMY OF SCIENCES

INSTITUTE OF MATHEMATICS AND INFORMATICS

 

ACTIVITY REPORT

2001

 

DEPARTMENT OF BIOMATHEMATICS

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

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

 

CONTENTS

·  STAFF

·  RESEARCH TOPICS

·  PUBLICATIONS

·  PROJECT CONTRACTS

·  RESEARCH, TRAVEL AND CONFERENCE GRANTS

·  SEMINARS, WORKSHOPS, CONFERENCES

·  VISITORS FROM ABROAD

·  LECTURE COURSES AND PUBLIC LECTURES

·  MISSIONS

·  MOST IMPORTANT SCIENTIFIC RESULTS

·  ANNUAL REPORT SESSION

·  FORTHCOMING CONFERENCES

·  MEMBERSHIP IN SCIENTIFIC SOCIETIES, EDITORIAL BOARDS, ETC
 

STAFF

Svetoslav Markov    Associate Professor  PhD 
Mikhail Krastanov    Associate Professor  PhD 
Neli Dimitrova          Assistant Professor   PhD 
Evgenia Popova        Assistant Professor    PhD
Nadejda Grigorova   PhD student                     
Krassimir Yanchev    Specialist                         
Dessislava Vassileva  Specialist                        
Katja Dimova            Specialist                        
Ivac Dakov               Specialist                        

                                                                RESEARCH TOPICS

The Department (section) of Biomathematics of IMI--BAS is generally concerned
with research and education in the field of mathematical modeling 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;

 PUBLICATIONS
 


1. Markov, S.: On the Algebraic Properties of Intervals and Some Applications, Reliable Computing 7, 2, 2001, pp.~113--127.

2. Markov, S., Computation of Algebraic Solutions to Interval Systems via Systems of Coordinates, Scientific Computing, Validated Numerics, Interval Methods (Eds. W. Kraemer, J. Wolff von Gudenberg), Kluwer, 2001, 103--114.

3. Alt, R., Markov, S., On the Algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic, Scientific Computing, Validated Numerics, Interval Methods (Ed. W. Kraemer, J. Wolff von Gudenberg), Kluwer, 2001, 331--341.

4. Markov, S. On the Algebraic Properties of Errors, Proc. Appl. Math. Mech. 1 (2001), WileyInterscience (www.interscience.wiley.com -- electronic journal).

5. Grigorova, S. Markov: Numerical Comparison Between Two Enzyme-kinetik Models, In: Proc.Intern. Symposium and Young Scientists' school on Bioprocess Systems (BioPS'2001), ed. S. Tsonkov, pp. I.45--I.48.

6. Krastanov, M. and M. Quincampoix, Local small-time controllability and attainability of a set for nonlinear control systems, ESAIM: Control. Optim. Calc. Var. 6, 2001, 499--516.

7. Krastanov, M. and N. Dimitrova, Stabilizing control design of nonlinear process involving uncertainties, Scientific Computing, Validated Numerics, Interval Methods (Eds. W. Kraemer, J. Wolff von Gudenberg), Kluwer, 2001, 255-266.

8. Krastanov, M. and M. Quincampoix, Hoelder continuity of the minimal time to reach a set for nonlinear control, published in the Proc. of the International Program Committee of the 6th European Control Conference, ECC 01, Porto, Portugal.

9. Dimitrova, N., P. Zlateva: Steady States Analysis of the Yeast Strain Saccharomyces cerevisiae Involving Uncertain Data. Proc. Int. Symp. and Young Scientists' School on Bioprocess Systems (BioPSAE2001), ed. S. Tsonkov, Sofia, October 1-3, 2001,
I.21--I.24.

10. Popova, E.: On the Solution of Parametrised Linear Systems. In W. Kraemer, J. Wolff von Gudenberg (Eds.): Scientific Computing, Validated Numerics, Interval Methods, Kluwer, 2001, 127--138.

11. Popova, E.: Multiplication Distributivity of Proper and Improper Intervals, Reliable Computing 7, 2, 2001, 129-140.

12. Popova, E.: Quality of the Solution Sets of Parameter-Dependent Interval Linear Systems. To appear in ZAMM.

13. Ognjanova-Romenova, N., M. Filipova-Marinova, E. Popova: Enviromental history and human influence at coastal wetlands in the bay of Sosopol, Bulgarian Black sea cost, to appear in Acta Paleobotanica Suppl. EPPC.


PROJECT CONTRACTS

 National

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

Bulgarian NSF Project contract No. NZ-903/99: Model of evolution of agila (1999--2002);

Bulgarian NSF Project contract No. MM-807/99: Reachable sets of differential inclusions (1998--2001);

BAS Project contract ``Mathematical Modelling in Biology''

Modelling and control of microbiological processes -- between the Institutes of Mathematics and Informatics and the Institute of Microbiology of BAS.
 

 International

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 TUBITAK, 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, 1999--2001.

GRANTS

One travel grant from GAMM for the GAMM 2001 Annual Scientific Conference, February 12--15, 2001, ETH Zuerich;

Two travel grants from the Institute for Informatics at PMF-UKIM for the II Conference on Informatics, December 20--23, Hotel Molika Bitola;

 

SEMINARS, WORKSHOPS, CONFERENCES

·  Interdisciplinary Seminar on Biomathematics and Scientific Computations;

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

·  Annual Seminar of the Dept. of Biomathematics of IMI--BAS.

·  International Minisymposium on Mathematical Modelling and Scientific Computing (MMSC'2001), April 10, 2001 (in the frames of the 30th Spring UBM Conference (8--11.04.2001, Borovets,
http://www.math.bas.bg/\~bio/mmsc/mm.htm).
The minisymposium comprised the following presentations:

1. A. Alexandrov: A mathematical model of tubulin pulse generator.

2. C. Christov and N. Papanicolaou: Galerkin spectral methods for higher-order boundary value problems arising in fluid mechanics.

3. F. Jezequel: Numerical accuracy of converging sequences.

4. N. Nedialkov and K. Jackson: Some recent advances in validated methods for IVP's for ODE's.

5. E. Neuwirth: Visualizing recursion and difference equations using spreadsheets.

6. A. Popov: On some imprecise geometrical computations based on morphological techniques.

7. S. Yanchuk and T. Kapitaniak: Modelling chaos-hyperchaos transition in coupled R\"ossler systems.

The presentations at MMSC'2001 are published in:

Mathematics and Education in Mathematics, Union of Bulgarian Mathematicians, Proc. 30-th Spring
Conference of UMB, Borovets, April 8--11, 2001, 432--467.


VISITORS FROM ABROAD

·  Prof. E. Spedicato from Dept. Math. at Univ. of Bergamo; Lecture on 19.02.2001 at joint seminar of Sections IO and BM: ABS methods for optimization.

·  08--18 April 2001, Dr. Fabienne Jezequel, Laboratory of Informatics of University Paris-6, France; Lecture on 10.04.2001 at MMSC'2001 and lecture on 17.04.2001 at the Interdisciplinary seminar on Scientific Computation and Mathematical Biology: Numerical Accuracy of convergent sequences;

·  Prof. Ch. I. Christov from the U. of Louisiana (Lecture on 10.04.2001 at MMSC'2001): Galerkin spectral methods for higher-order BVP arising in fluid mechanics (jointly with N. Papanicolau);

·  Prof. T. Kapitaniak from the Technical University of Lodz (Division of Dynamics), Poland (Lecture on 10.04.2001 at MMSC'2001): Modelling chaos-hyperchaos transition in coupled Roesler systems (jointly with S. Yanchuk);

·  Prof. N. S. Nedialkov from McMaster University (Dept. Computing and Software), Ontario, Canada (Lecture on 10.04.2001 at MMSC'2001): Some recent advances in validated methods for IVP's for ODE's (jointly with K. Jackson).
 

LECTURE COURSES AND PUBLIC LECTURES

LECTURE COURSES

·  S. Markov: Mathematical Modeling 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, 30+30 (2+2 hours weekly, 15 weeks).

·  E. Popova: Computer Arithmetic.  Mathematica as an Environment for Modelling and Scientific Computations. Lecture course for PhD students and scientific staff of the Institute for Space Research at BAS. Horarium: 30 hours.
 

PUBLIC LECTURES

S. Markov:

15.02.2001, Algebraic Properties of Errors; ETH Zuerich, GAMM'2001 Annual Conference.

3.05.2001, "Arithmetic properties of intervals" at the seminar on Approximation Theory chaired by Prof. Bl.
Sendov;

06.06.2001, On the Probability of a Certain Relations Between Two Given Intervals on the Real Line. Seminar at LIP6, Paris (joinly with K. Dimova);

13.06.2001, On the Models of Enzyme Kynetic and Biotechnological Processes Seminar at LIP6, Paris;

17.12.2001, Quasilinear Spaces of Convex Bodies, Lecture at the annual report session of section ``Biomathematics'' at IMI--BAS;

22.12.2001, ``On some Spaces Used in Interval Computations'', 2nd Conference on Informatics and Information Technology, 20--23.12.2001, Bitola (Hotel Molika), Macedonia; organised by the Institute of Informatics, PMF--UKIM (Skopie).

M. Krastanov:

On the small-time local controllability, 11 September 2001, Warsaw, Poland, VIII European Workshop on ``Well-posedness in optimization and related topics'', September 10 -14, 2001;

On the small-time local controllability with respect to a set, 8 September, 2001, Seminar of the Department of the Mathematics, Polytechnic of Torino, Italy;

Stabilization of a model of methan fermentation, December 17, 2001, report at the annual scientific session of
the Department of Biomathematics, IMI, BAS.

On the small-time local controllability, December 18, 2001, report at the annual scientific session of the Department of Operation Research, IMI, BAS.

E. Popova

22.12.2001, ``Establishing CSE in BGand MK'', 2nd Conference on Informatics and Information Technology, 20--23.12.2001, Bitola (Hotel Molika), Macedonia; organised by the Institute of Informatics, PMF--UKIM (Skopie).


Neli Dimitrova

Studying Fermentation Processes Under Uncertainties, Seminar at LIP6, Paris, 13.06.2001 (jointly with M. Krastanov);

 Maple -- Program System for Computer Algebra, Research Summer School for High School Students, 07.08.2001, Uzana, Gabrovo.

N. Grigorova

17.12.2001: N. Grigorova, Numerical Comparison of Two Models of enzyme kinetic; ann. session of IMI--BAS.
 


 MISSIONS

·  S. Markov: participation at the GAMM Board Meeting (11.02.2001) and the Annual Scientific Conference of GAMM, 12--15.02.2001, ETH Zuerich

·  S. Markov: visiting professor in University Paris-VI, LIP6, June 2 -- June 30;

·  M. Krastanov: participation at the VIII European Workshop on ``Well-posedness in optimization and related topics'', September 10 -14, 2001, Warsaw, Poland;

·  M. Krastanov: visiting professor at the University of Genoa, November, 4 - 16, 2001;

·  N. Dimitrova: visit in University Paris-VI, LIP6, May 29 -- June 28;

·  E. Popova, S. Markov: 2nd Conference on Informatics and Information Technology, 20--23.12.2001, Bitola (Hotel Molika), Macedonia; organised by the Institute of Informatics, PMF--UKIM (Skopie).

·  K. Dimova: visit in University Paris-VI, LIP6, June 2 -- June 12;
 

MOST IMPORTANT SCIENTIFIC RESULTS

 

a) theoretical achievements:

·  The space of intervals and convex bodies has been investigated. A full characterization of the space of symmetric elements has been found;

·  A sufficient condition of a high order for the local controllability of a set with respect to a generalized control system;

·  Necessary and sufficient conditions for the coincidence of the bounds for the solutions of a parametric interval linear system and the bounds for the solution of the corresponding nonparametric system, for which there exist
methods for the determination of the exact hull, have been obtained; a computational analogue of these conditions has been found.
 

b) theoreticaly-applicable achievements:

·  Investigated is a 2D dynamical model of methan fermentation under uncertainties. Determined is the set of optimal stationary points under appropriate criteria. Constructed is a stabilizing feed-back in a neighbourhood
of this set. Performed are numerical experiments in CAS Maple.

·  Developed is a MATHEMATICA package for solving interval linear systems. The package contains optimized implementations of all known methods for parametric interval linear systems, as well as some methods for general (nonparametric) systems.


c) theoreticaly-applicable achievements as result of international collaboration:

·  diagrammatical presentation of multiplication (set-theoretic and centered) of intervals (within PAS/BAS agreement);

·  comparison of certain probability distributions (Gausian and Beta-distribution).


ANNUAL REPORT SESSION

of section ``Biomathematics'' at IMI, 17 December 2001


13:15 - 13:30:   S. Markov, Opening;
13:30 - 13:45:   I. Simeonov, Modelling of Methan Fermentation of organic waste via adding stimulators;
13:45 - 14:00:   M. Krastanov, Stabilization of a Model of Methan Fermentation;
14:00 - 14:15:   N. Grigorova, Numerical Comparison of Two Models of enzyme kinetic;
14:15 - 14:30:   P. Zlateva, Investigation of the Statistic Characteristics of a class of Fermentation Processes        under Uncertainties;
14:30 - 14:45   R. Ivanova, G. Simeonov, Parameter Identification of the Michaelis-Menten Model of Oxigen Consumption, Based on Data for the Breath of a Tissue Plate.
14:45 -- 15:00  Coffee break
15:00 -- 15:15  S. Markov, Quasilinear Spaces of Convex Bodies;
15:15 -- 15:30  E. Popova, Exact Bounds for the Solutions of Parametric Linear Systems with Uncertain data;
15:30 -- 15:45  Sv. Margenov, Optimal Iteration Methods;
15:45 -- 16:00  N. Dimitrova, Numerical Integration with Error Control;
16:00 -- 16:15  D. Nikolova, Computer Systems in Algebra, Oriented Towards Group Theory;
16.15 -- 16:30  E. Popova, S. Markov, The Project ``Establishing CSE in BG and MK''.
 

FORTHCOMING CONFERENCES

The Department of Biomathematics of IMI--BAS is a co-organizer of a Minisymposium on Mathematical Modelling and Scientific Computations to be held on the 4-th of April 2002 within the frames of the 31-st Spring Conference of the Union of Mathematicians in Bulgaria, see

URL: http://www.math.bas.bg/\~bio/mmsc/mm.html

Members of the Department of Biomathematics of IMI--BAS will participate in the following forthcoming events:

·  GAMM annual meeting 2002 in Augsburg, 25--28.03.2002, see:
http://gamm2002.uni-augsburg.de

·  MMSC'2002 at the Spring UMB Conference, April 2001, see:
URL: http://www.math.bas.bg/\~{}bio/mmsc/mm.htm

·  International Conference on Construction Function Theory, June 19--23, 2002, Varna, Golden Sands, see:
http://www.varna2002.com

·  International Conference on Numerical Methods and Applications, August 20--24, 2002, Borovets, see:
http://www.bas/clpp/nmao2.html

·  SCAN 2002 Conference in Paris, September 2002 see:
http://scan2002.lip6.fr
 

 MEMBERSHIP IN SCIENTIFIC SOCIETIES, EDITORIAL 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); on 11.02.2001 participation at the meeting of the board 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 American Mathematical Society (AMS); reviewer of Mathreview and Zentralblatt;

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

·  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 Mathematical and Theoretical Biology (ESMTB); Member of the Bulgarian Statistical Association;

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

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

·  I. Dakov: member of UMB (section ``Biomathematics and Scientific Computation''); member of GAMM (Bulgarian section of GAMM);

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

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


On 14.03.2001 a Bulgarian National section of GAMM (GAMM-BG) was established with the active participation of the members of section ``Biomathematics'' at IMI--BAS. The official address of GAMM-BG is:

GAMM-BG
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
"Acad. G. Bonchev" str, block 8
BG-1113 Sofia, Bulgaria

tel. +3592 9793704
fax: +3592 9713649
e-mail: gamm-bg@math.bas.bg
URL: www.math.bas.bg/\~{}gamm-bg