BULGARIAN ACADEMY OF SCIENCES
INSTITUTE OF MATHEMATICS AND INFORMATICS
ACTIVITY REPORT - 2002
Acad. G. Bonchev str. block 8, Sofia Bulgaria
CONTENTS :
MISSIONS, RESEARCH VISITS, TRAVEL AND CONFERENCE GRANTS
SEMINARS, WORKSHOPS, CONFERENCES, PUBLIC LECTURES
MEMBERSHIP IN SCIENTIFIC SOCIETIES, EDITORIAL BOARDS, ETC
Svetoslav Markov Associate
Professor PhD
Mihail Krastanov Associate
Professor PhD
Neli
Dimitrova
Associate Professor PhD
Evgenia Popova Assistant
Professor PhD
Nagejda Grigorova PhD
Student
Krassimir
Yanchev Specialist
Petko
Alov
Specialist
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, convex and interval analysis, abstract spaces of errors, intervals, zonotopes, convex bodies, stochastic numbers, etc., computer arithmetic, programming languages and systems of computation, esp. computer algebra systems, computer graphics and web accessible mathematical computations. The major research efforts are currently focused on the following areas :
· Mathematical modeling of enzyme kinetic and fermentation processes;
· Algebraic properties of errors, intervals, zonotopes, convex bodies, stochastic numbers;
· Linear algebraic equations whose coefficients and right-hand sides depend on uncertain parameters;
· Stability and controllability of nonlinear control systems; sensitivity analisis of input-output static characteristics of biotechnological processes;
· Computer algebra methods applied to computations with intervals, zonotopes, etc. (incl. relevant visualization techniques);
· Verification algorithms under uncertainties for a) linear and nonlinear problems, b) dynamical models in enzyme kinetics, biology and ecology;
· Web accessible mathematical computations.
· Statistical analysis of biological data.
Published papers:
Dimitrova, N. and 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.
Markov, S. On the Algebraic Properties of Errors, Proc. Appl. Math. Mech . 1 (2002), 1, 506-507.
Akyldiz, Y., D. Claudio, S. Markov : On the Linear Combinations of Symmetric Segments, Mathematics & Education in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.& Informatics, BAS, 321-326.
Dimitrova, N. S. : Numerical integration with error control, Mathematics and Education in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.& Informatics, BAS, 338-343, 2002.
Dimitrova, N. S., M. I. Krastanov : Stabilizing feedback design of a class of fermentation processes involving uncertanties. Proc. of Int. Conf. "Automatics and Informatics:, Nov. 5-6, 2002, Sofia, 253-256.
Grigorova N. : Numerical Comparsion between two Enzyme-kynetik Models, Mathematics & Education in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.& Informatics, BAS, 332-337.
Krastanov M. I. : A sufficient condition for small-time local attainability of a set, Control and Cybernetics, vol. 31, No. 3, 1-11, 2002.
Krastanov, M. I. : On the Stabilizing Feedback Control, Mathematics & Education in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.& Informatics, BAS, 356-361.
Popova E. : Quality of the Solution Sets of Parameter-Dependent Interval Linear systems. ZAMM 82 (2002), 10, 723-727 (pdf file).
Popova E. : Solving Parametric Interval Linear Systems by Mathematica. Mathematics & Education in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.& Informatics, BAS, 391-396.
Papers accepted for publication:
Krastanov M. I., N. S. Dimitrova : Stabilizing feedback of a nonlinear process involving uncertain data, Bioprocess and Biosystems Engineering, Springer.
Krastanov M. I., V. M. Veliov : On the stabilizability of control constrained linear systems, Springer Lecture Notes in Computer Science.
Krastanov M. I., N. S. Dimitrova : Stabilizing control design of a nonlinear process involving uncertainties, Springer Lecture Notes in Computer Science.
Markov S. : On Quasilinear Spaces of Convex Bodies and Intervals. J. Comp. Appl. Math., Special issue ed. N. Revol.
Markov S. : On Some Spaces Used in Convex and Interval Analysis , Proc. 2 Conf. on Informatics, UKIM - Skopie.
Alt R., S. Markov : Stochastic and Interval Arithmetic: A comparative Study. Reliable Computing.
Papers submitted for publication:
Markov, S., R. Alt, On the Algebraic Properties of Stochastic Numbers: Addition and Multiplication by Scalars. Numerical Algorithmes.
Kulpa, Z., S. Markov, On the inclusion properties of interval multiplication: A diagrammatic study, BIT.
Markov, S., On Quasivector Spaces of Convex Bodies and Zonotopes, Numerical Algorithms, Special issue - Proc. of SCAN-2002 (Paris, 24-27 Sept.2002).
Popova, E.: Parametric Linear Solver, Numerical Algorithmes, Special issue - Proc. of SCAN-2002 (Paris, 24-27 Sept.2002).
National:
Bulgarian NSF Project contract No. I-903/99: Interval Computer Algebra
(1999-2002), head: S. Markov;
Bulgarian NSF Project contract No. NZ-903/99: Model of the evolution of
agila and colonization of Lacustrine diatoms in continental basins in SW
Bulgaria during the miocene (1999-2004), head N. Ognjanova-Rumenova;
BAS Project contract "Mathematical Modelling in Biology'' , head S.
Markov;
Interinstitutional project: Modelling and control of microbiological processes
-- between the Institutes of Mathematics and Informatics and the Institute of
Microbiology of BAS, heads: I. Simeonov and S. Markov;
MM-1104/01 Modelling and control of biotechnological processes using mathematical methods for processing uncertain information (2001-2003), head M. Krastanov;
MM-807/98 Reachable sets of differential inclusions (1998-2002), head N. Kirov;
BAS project contract: Scientific support of competitions in mathematics: strategies and educational materials, head O. Mushkarov.
International:
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 (1998-2002).
Direct contract between IMI-BAS and Swiss NSF SCOPES 7 IP 65642, Swiss
(2002-2004).
MISSIONS, RESEARCH
VISITS, TRAVEL
AND CONFERENCE GRANTS :
Fall 2002 SCOPES IP Meeting, Zuerich, Switzerland - S. Markov, E. Popova.
SCAN 2002 Symposium, Paris, France - S. Markov, E. Popova.
U. of Paris 6, Lip6-ANP-CHPV, Paris, France - S. Markov, 30 days (May 2002).
SEMINARS, WORKSHOPS, CONFERENCES, PUBLIC LECTURS :
· Interdisciplinary Seminar
on Biomathematics and Scientific Computations;
· Weekly Seminar
of the Dept. of Biomathematics of IMI-BAS;
· ANNUAL
REPORT SESSION of the Dept. of Biomathematics of IMI--BAS.
Workshop "CSE: Education & Research", February 27, 2002, Sofia (organized by: E. Popova, S. Markov, W. Gander, P. Arbenz). Lectures by MB/IMI members delivered at the workshop:
E. Popova: Mathematica Tools for Analysis of Uncertain Linear Problems.
N. Dimitrova: Computation and Visualization of Fast-Decreasing Polynomials Using Maple
M. Krastanov: On the Small-Time Local Controllability of a Set.
N. Grigorova: Study of Enzyme-Kynetic Models Using Mathematica
S. Markov: Algebraic Computations with Convex Bodies.
Minisymposium on Mathematical Modelling and Scientific Computations, 4.04. 2002, Borovets, within the frames of the 31-st Spring Conference of the Union of Mathematicians in Bulgaria (organizers: M. Krastanov and S. Markov).
For the publications of the presentations see: Mathematics & Education
in Mathematics, 2002, (Eds. E. Kelevedziev, P. Boyvalenkov), Inst. Math.&
Informatics, BAS, 321-396. Lectures delivered at the minisymposium:
V. Goranko. Algebraic models for two-player games with iterations. T. Magyla, O. Svegzda. Application
of the Subjective Quantitative Criteria
Method for Operational Prognosis. Y. Akyildiz,
D. Claudio, S. Markov. On the Linear Combinations of
Symmetric Segments. A. Poceski.
Numerical Solution of
Differential Equations. C. Popa.
Some Developments of Kovarik’s
Approximate Ortogonalization
Methods R. Marinova, H. Aiso, T. Takahashi. Some Requirements Regarding Difference Schemes for Incompressible Navier-Stokes Equations. N. Dimitrova. Numerical Integration with Error Control. W. Krämer. Advanced Software Tools for Validated Computing. E. Popova.
Solving Parametric Interval Linear Systems by Mathematica.
N. Grigorova. Numerical Comparison Between Two Enzyme-Kinetic
Models. M. Krastanov.
On the Stabilizing Feedback Controls. Minisymposium on "Control
and Uncertain Systems", August 20, 2002, Borovets, within the frames of the Fifth International Conference on Numerical
Methods and Applications NM&A 02, August
20-24, 2002, Borovets (organizers: M. Krastanov, V. Veliov and S.
Markov). Lectures delivered at the minisymposium: P. Sain-Pierre, Evaluation of
Crisis, Reversibility, Alert Management for Constrained Dynamical Systems Using
Impulse Dynamical Systems and Numerical Issues U. Felgenhauer, Optimality and
Stability of Bang-Bang Type Controls I.
Chryssoverghi, Discrete Methods for Optimal Control Problems E.
Farkhi, Convexification Rates for Minkowski Averages of Compact Sets I. Gruene, P. Kloeden, Numerical Schemes
of Higher Order for a Class of Nonlinear Control Systems E. Crueck, P. Sain-Pierre,
Numerical Schemes for Nonlinear Impulse Target Problems under State Constraint
Approximationof the Minimum Time Function M.
Konstantinov, P. Petkov,
Sensitivity Analysis of Unitary Matrix Decomposition N.
Nedialkov, An Introduction to Validated Methods for Initial Value
Problems for Ordinary Differential Equations A. Piazzi, A. Visioli, An Interval Analysis Based
Algorithm for Computing the Stability Margin of Uncertain Systems M.
Krastanov, N. Dimitrova, A Stabilizing Feedback for an Uncertain Control
System G. Grammel, Strong Elastic
Constraints in Mechanics and Averaging J.
Hernandez, A Size Distribution Model Applied to Fish Farming M. Krastanov, V. Veliov, On the Stabilizability of
Control Constrained Linear Systems Ts. Donchev, Approximation of the Solution Set
of of a Nonconvex-Valued Differential Inclusion SCAN 2002 Conference in Paris, September 2002 see: S. Markov: Quasivector Spaces. S. Markov, N. Grigorova: Numerical Comparison
of Two Enzyme-kynetic Models. R. Alt, S. Markov: On the Algebraic Properties
of Stochastic Numbers. E. Popova: Parametric Linear Solver. Fall 2002
SCOPES IP Meeting, Zuerich, Switzerland, Sept. 30, 2002. The following
lectures have been delivered by IMI/BM members: Popova, E.: Solving Linear Parametric Problems
Involving Uncertainties. Markov, S.: Algebraic Computation with
Certain Nonnumeric Objects. Public lectures held by members of the department: S. Markov: Algebraic Computations with Convex
Bodies, Workshop "CSE: Education &
Research", 27.02.2002. S. Markov (with Y. Akyildiz and
D. Claudio). On the Linear Combinations of
Symmetric Segments, Minisymposium Mathematical Modelling and
Scientific Computations, 4.04. 2002, Borovets. S. Markov, G. Mitov: On the order of
distributions, 10.04.2002, seminar on Probability and statistics. S. Markov: Algebraic properties of
stochastic numbers, 17.04.2002, seminar on Probability and statistics. S. Markov: Algebraic operations with sets,
14.11.2002, joint seminar of Algebra and Coding Theory. S. Markov: Quasivector Spaces, 25 Sept. 2002,
SCAN 2002 Conference in Paris, September 2002. S. Markov, N. Grigorova: Numerical Comparison
of Two Enzyme-kynetic Models, 26 Sept. 2002, SCAN 2002 Conference in Paris,
September 2002. R. Alt, S. Markov: On the Algebraic Properties
of Stochastic Numbers, 27 Sept. 2002, SCAN 2002 Conference in Paris, September
2002. E. Popova: Mathematica Tools for Analysis of
Uncertain Linear Problems, Workshop "CSE: Education &
Research", 27.02.2002. E. Popova. Solving Parametric Interval Linear Systems by Mathematica,
Minisymposium Mathematical Modelling and
Scientific Computations, 4.04. 2002, Borovets E. Popova: Parametric Linear Solver, 26 Sept.
2002, SCAN 2002 Conference in Paris, September 2002 N. Dimitrova: Computation and Visualization
of Fast-Decreasing Polynomials Using Maple, Workshop "CSE: Education &
Research", 27.02.2002. N. Dimitrova. Numerical Integration with Error Control, Minisymposium Mathematical Modelling and
Scientific Computations, 4.04. 2002, Borovets N. Dimitrova: Linear transformations in the
extended complex plane. Demonstrative examples within Maple. Lecture at the 2nd
Research Summer School of the High School Students Inst. of Mathematics and
Informatics, 4-23 August 2002, Varna. M. Krastanov: On the Small-Time Local
Controllability of a Set, Workshop "CSE: Education &
Research", 27.02.2002. M. Krastanov. On
the Stabilizing Feedback Controls,
Minisymposium Mathematical
Modelling and Scientific Computations, 4.04. 2002, Borovets M.
Krastanov ( with N. Dimitrova), A Stabilizing Feedback for an Uncertain
Control System, Minisymposium on "Control and Uncertain Systems",
August 20, 2002, Borovets M. Krastanov, V. Veliov, On the Stabilizability of
Control Constrained Linear Systems, Minisymposium on "Control and Uncertain Systems",
August 20, 2002, Borovets N. Grigorova: Study of Enzyme-Kynetic Models
Using Mathematica, Workshop "CSE: Education &
Research", 27.02.2002. N. Grigorova. Numerical Comparison Between Two Enzyme-Kinetic Model, Minisymposium Mathematical Modelling and Scientific
Computations, 4.04. 2002, Borovets.
V. Goranko
(SA)
T. Magyla (LT)
A. Poceski
(MK)
C. Popa (RO)
E. Farkhi (IZ, BG)
I. Chryssoverghi (GR)
U. Felgenhauer (DE)
G. Grammel (DE)
E. Cruck (FR) J.
Patric Sain-Pierre (FR)
Hernandez (ES)
P. Kloeden (DE)
N. Nedialkov (CA)
V. Veliov (AT, BG)
A. Visioli
(IT)
S. Simov (AU, BG) PhD Students: N. Grigorova (supervisor S. Markov) Diploma students: Josif Kolev, Desislava Nikolcheva, Jordan
Jordanov (supervisor E. Popova) Lecture courses: S. Markov: Mathematical Modeling in Biology, Lecture course for students of
the Faculty of Mathematics and Informatics at the University of Sofia.
Horarium: one semester, 30+30. M. Krastanov: Linear Optimization, Lecture course for students of the
Faculty of Mathematics and Informatics at the University of Sofia. Horarium:
one semester, 30+0. M. Krastanov: Mathematical optimization, Lecture course for students of the
Faculty of Mathematics and Informatics at the University of Sofia. Horarium:
one semester, 30+0. M. Krastanov: Games Theory, Lecture course for students of the Faculty of
Mathematics and Informatics at the University of Sofia. Horarium: one semester,
45+0. M. Krastanov: Optimal Control, Lecture course for students of the Faculty of
Mathematics and Informatics at the University of Sofia. Horarium: one semester,
45+0. Theoretical achievements: Theoreticaly-applicable achievements: Theoreticaly-applicable achievements as result of international
collaboration: Further development of diagrammatic presentations of
the operation for multiplication (set-theoretic and centered) of intervals. By the financial aid of SCOPES 7IP 65642
Project, some multi-user client-server applications were developed and a web
service, called webComputing,
was founded to offer interactive (dynamic) mathematical computations and
visualization over the web. A detailed
program in Bulgarian Lectures delivered at the session (a detailed
program in English, PDF format) G. Dimitrov.
Establishment of research group "Automation of biological experiment and
mathematical modelling" at the Center of Biology of BAS. I. Pazheva.
Quantitative relations chemical structure - biological activity (QSAR). I. Cakovska. QSAR and
molecule modelling of a class of substances, overcoming drug resistence. A. Dimitrov. A method
for computation of processes running in multicable structures. N. Dimitrova, G.
Dimitrov. Mathematical modelling of potentials generated from nerve muscle
fibres and motor units --- fundamentals for a correct
interpretation of changes in electromiographic signals. T. Arabadzhiev.
Simulator of electromiographic signals. R. Rajkova, H.
Aladzhov. (Motco.dir.bg) - a simulator of control of motor units upon
realisation of given contraction. C. Ostromski.,
I Dimov. Application of the Danish Eulerian Model for estimation of
agricultural losses due to high ozon concentrations in the air. N. Dimitrova, M.
Krastanov. Stabilizing feed back of nonlinear biotechnological process
under uncertainty. P. Zlateva, N.
Dimitrova. Sensitivity analysis of a nonlinear model of the yeast strain
Saccharomyces cerevisiae. E. Popova.
Finite element modelling under uncertainties - new computational tools
and Web-based resources. S. Nikolov, S. Stoychev, J. Nieto, G. Torres.
Mathematical model of the intracranial aneurism hemodynamics. A. Alexandrov.
Chronoendocrinology as part of chronobiology. N. Neykov, P.
Neychev. Statistical modelling in biology and meteorology N. Pencheva, P. Milanov. Drug design via
artificial neuron nets. S. Simov. Curious
negotiator. S. Markov, N.
Grigorova. On the matematical modelling of enzyme-kinetic processes. MEMBERSHIP
IN SCIENTIFIC SOCIETIES, EDITORIAL BOARDS, ETC : S. Markov: member of UMB (president of section ``Biomathematics and
Scientific Computation''); 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);
http://scan2002.lip6.fr S.
Markov was a member of the Scientific Committee. The following lectures have
been delivered by IMI/BM members:
Using local variations of higher order a discontinuous stabilizing
feedback for a class of nonlinear systems in the neighbourhood of a closed set
has been constructed. A stabilizing partially linear feedback for the case
of locally controllable automatic linear system with controls bounded in
a convex cone has been constructed. Proposed is an algorithm for finding outer
approximation of a zonotope in the plane by means of zonotopes from
a given class.
For a dynamical model of methane fermentation under uncertainties a
continuous feedback with respect to the measurable state variables
has been constructed, which stabilizes the system in the
neighbourhood of a set, which is optimal with respect to a suitable criteria,
characterizing the process; numerical simulations in the computer algebra
system Maple have been performed. The theory of quasivector spaces has
been applied for zonotopes in the plane, as well as for stochastic numbers.
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 (secterary of UMB, secretary of section ``Biomathematics
and Scientific Computation'' at UMB); member of GAMM (Bulgarian section of
GAMM); reviewer of Zentralblatt; member of the European Society for
Mathematical and Theoretical Biology (ESMTB);
E. Popova: member of UMB (``Biomathematics and Scientific Computation'');
member of SIAM; 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'');
K. Yanchev: member of UMB (section ``Biomathematics and Scientific
Computation''); member of GAMM (Bulgarian section of GAMM);