In order to deal with real life applications stability and fast convergence of numerical methods have to be provided. However, research in this field is very much in progress, and many problems concerning both the theoretical foundations and practical issues remain open: existence of optimizers for underlying continuous problem and necessary optimality conditions, questions of stability and convergence for numerical methods, the interplay between discretization and optimization, etc.

These issues require a wide range of mathematical disciplines (e.g. optimal control theory, functional analysis, numerical analysis, etc.) as well as engineering understanding in order to choose the appropriate mathematical model for the problem at hand. The goal of this session is to bring together mathematicians and engineers, who develop or use algebraic and numerical methods, to exchange ideas and views, and to present both original research results involving computer algebra as well as challenging directions and industrial applications.

Possible topics for this session include (but are not limited to):

• numerical simulation for engineering design using computer algebra systems
• symbolic-numerical methods for (global) optimization
• handling constraints given by differential, differential-algebraic, and difference equations
• (computational) optimal control
• (non)linear programming
• complexity considerations
• applications:
  • mechanism design and robotics
  • manufacturing
  • nanotechnology
  • medical devices
  • molecular biology
  • etc.

Here is the link to the web-page for our session at ACA 2007.

The organizers will invite the speakers maintain a web page describing the session with talk abstracts provided.

The session will be held in three hour blocks of time, with nine 1/2 hour talks.

Prospective and interested invited speakers could be (among others):

• Iwan M. Duursmaa, University of Illinois at Urbana-Champaign, USA
• Michael E. O'Sullivan, San Diego State University
• María Bras-Amorós, Autonomous University of Barcelona
• Olav Geil, Aalborg University
• Ferruh Özbudak, Middle East Technical University, Turkey
• John B. Little, Holy Cross Mathematics and Computer Science, USA
• Judy Walker, Katherine Bartley Department of Mathematics,University of Nebraska - Lincoln
• Jose-Angel Dominguez, José María Muñoz Porras, G. Serrano Sotelo Univ. de Salamanca.
• Jon-Lark Kim, Department of Mathematics, University of Louisville
• Patrick Fiztpatrick, University College, Cork
• Edgar Martínez-Moro, Universidad de Valladolid
• Diego Ruano, Technical University of Denmark
• Fernando Hernando, University College, Cork

The goal of this session is to exchange ideas and experiences, to hear about classroom experiments, and to discuss all issues related with the use of computer algebra tools in classroom (such as assessment, change of curricula, new support material, ...)

If you are interested in presenting a paper, please contact one of the organizers.

The following topics, among others, will be considered:

1. Stability and bifurcation analysis of dynamical systems
2. Construction and analysis of the structure of integral manifolds
3. Symplectic methods.
4. Symbolic dynamics.
5. Normal forms and programs for their computations.
6. Deterministic chaos in dynamical systems.
7. Families of periodic solutions.
8. Perturbation theories.
9. Exact solutions and partial integrals.
10. Analysis of singularities of equations by Power Geometry algorithms.
11. Computation of asymptotic forms and asymptotic expansions of solutions and its program implementation.
12. Integrability and Nonintegrability of ODEs.
13. Computation of formal integrals.
14. Computer Algebra for Celestial Mechanics and Stellar Dynamics.
15. Specialized Computer Algebra software for Celestial Mechanics.
16. Topological structure of phase portraits and computer visualization.

The art of compact computer algebra is becoming again increasingly important. New directions for symbolic computing include the migration from workstations to handheld devices and the changing role from standalone applications to lightweight services within integrated systems. Whether running on a graphing calculator or as support of a client-side web application, certain applications of computer algebra require compact data representation, space-efficient algorithms and effective memory management.

The purpose of this session is to communicate efforts in research, design, development and application of compact computer algebra. We invite contributions in all aspects of this area, including, but not limited to

• math education tools (eg. Derive, TI-Nspire, Class-Pad, HP 50g),
• portable and Internet-accessible symbolic calculators (eg. Mate, Symbolic Calculator),
• CAS for personal digital assistants (eg. AzirPad).
• "spell checkers" for math content in document processing software
• validators for online and offline mathematical recognizers
• backend engines to pen-computing interfaces
• math editing components for 2D expressions

In this session, we would like to examine various relations between differential and integral operators. To this end, we want to bring together the following topics and communities:

• Factorization of Differential/Integral Operators
• Constructive Methods for D-Modules
• Linear Initial/Boundary Value Problems and Green's Operators
• Rota-Baxter Algebras
• Symbolic Computation with Differential Polynomials
• Initial/Boundary Value Problems for Nonlinear Differential Equations

For the current list of speakers, please refer to the session webpage.

This session is intended to discuss recent theoretical and practical developments in the theory of Gröbner bases as well as applications of Gröbner bases to other fields. Research contributions as well as expository papers are solicited. For more information and/or to present a paper at the session, please contact the session organizers by e-mail.

This session is a continuation of a series of sessions on the theory of Gröbner bases and its applications organized at previous ACA conferences and other workshops.

Session Topics inlcude (but are not limited to):

• elimination theory
• computational commutative algebra
• multivariate polynomial ideal theory
• solving systems of algebraic equations
• Algorithms for computing GB's
• GB for improving oil drilling platforms
• GB for guessing "missing links" in palaeontology
• GB in cryptography (code breaking)
• GB in software engineering (automated inductive assertion generation)
• GB for sudoku
• GB in origami
• GB in combinatorial design theory
• GB in computer aided design
• GB in solid modeling
• GB in mathematics
• GB in logic
• GB in education
• GB in geometrical theorem proving
• GB in integer programming
• GB in sciences and engineering

This special session continues the tradition established by previous conferences and special sessions (including e.g. the conferences Interval-xx, ACA 2000, ACA 2003 and ACA 2006 sessions) on interval and computer-algebraic methods in science and engineering. The aim is to bring together participants from diverse areas of mathematics, computer science, various life & engineering/science disciplines that will demonstrate the progress in the interaction between symbolic- algebraic and result-verification methods. The meeting goal is to stimulate the communication, coordination, integration, and cross- fertilization of ideas capable to meet the research challenges.

SCOPE

For this special session, we invite survey papers, presentations of some recent developments, application case studies and research challenges. The topics include but are not limited to:

• Algebraic approach to interval mathematics; theoretical foundations for combining interval and symbolic-algebraic techniques; formalisms for presentation of interval knowledge in CA; usage of analytical transformations and other techniques from computer algebra in interval computations;
• Exact methods, computer aided proofs, computational complexity analysis of symbolic computation problems with interval uncertainty;
• Verified multiple-precision computation of special functions
• Bugs in current CA systems
• Development and implementation of symbolic-numeric methods for problems involving interval data;
• (Interval) Taylor models
• Embedding of interval data structures, hybrid and result- verification algorithms in CA systems and specialized software;
• Applications of combined interval-analytical techniques in science, biology, engineering, control and other areas;
• Interval mathematics on the Internet: the use of web and grid service infrastructures, and semantic web technologies for identifying and describing web-based interval resources;
• Interval Software Interoperability: interoperability between computing systems (like Mathematica, Maple, Matlab, etc.) and languages for dynamic applications (Java, JavaScript, C, C++, ...) that support interval computations aiming at an increased functionality and effectiveness;
• CA in interval education and online interval knowledge (e-Learning).

DEADLINES

If you are interested in participation, please send your name, email and approximate title to kraemer@math.uni-wuppertal.de or epopova@bio.bas.bg or fill in the form available at http://www.math.bas.bg/~epopova/ACA2008/.

Submission of talk title - April 15, 2008
Submission of abstract - May 15, 2008.

PUBLICATIONS

Papers presented at the special session will be proposed for post- conference publication in "Serdica Journal of Computing" or another specialised journal.

MOTIVATION

In the last years, interest in applying methods from computer algebra to various problems in system design, verification and control has increased. Precise symbolic computation techniques are needed e.g. in order to properly handle parameters in parametric descriptions of systems. In particular, parametric/non-convex constraint solving and optimization methods are used in plant design.

In fact, numerous problems in science and engineering, in particular problems which occur in the verification of parametric reactive and hybrid systems, can be reduced to reasoning in complex theories – typically combinations of concrete theories (e.g. theories of integers or reals) and abstract theories (e.g. theories of data structures). Therefore, finding methods for efficiently combining deductive techniques with symbolic computation techniques and devising parametric variants of computer algebra and deduction algorithms will have a significant impact in these areas.

The goal of this session is to enhance the interaction between the symbolic computation, automated reasoning and verification communities.

The session is devoted to research on

• mathematical theories, which have a direct practical application,
• algorithms (symbolic, symbolic-numeric),
• software libraries/packages,
• applications in science and engineering

for efficiently solving (parametric) problems in verification.

AIMS

The main aim of this session is to encourage discussions and to stimulate collaborations among researchers working in

• symbolic computation (e.g. comprehensive Gröbner bases, quantifier elimination);
• deduction and automated reasoning, in particular in theorem proving over complex domains, which explicitly make use of computer algebra methods;
• SAT-checking – including methods that go beyond traditional SAT-checking (e.g. QSAT, parametric SAT, SAT modulo theories);
• the design, verification, and control of real time and hybrid systems.

as well as among researchers interested in using symbolic computation systems and systems for automated deduction for solving concrete problems in verification and control.

This will help in

• investigating computational issues in the control design methodology yielding parametric optimization,
• identifying interesting problems in deduction and symbolic computation stemming from the verification of reactive and hybrid systems, and
• clarifying the expectations and wishes the users from verification and control have from symbolic computation systems or from systems which combine deduction and computation.

The ultimate aim is to expand the horizons of this area of research, deepen the interactions, sensibilize researchers from the symbolic computation and deduction community to the problems occurring in verification, and, conversely, the researchers in verification to the newest symbolic computation systems and methods and — last but not least — offer persons working in research and development centers of software companies the possibility to get an overview of the problems and their solutions.

TOPICS

Topics of interest are those at the borderline between theoretical research in symbolic computation and deduction and applications. These include, but are not restricted to:

• Deductive verification and symbolic computation.

  Of particular interest are examples from verification of reactive and hybrid systems which illustrate the type of deductive problems appearing in relationship with verification tasks: symbolic computation, decision procedures for numerical (or possibly mixed) domains, deduction, SAT checking, quantifier elimination, interpolation.

• Integration of deduction and computation.

  Of particular interest are possibilities of combining decision procedures or of combining deductive techniques with symbolic computation techniques.

• Parametric verification vs parametric deduction and computation.

  Devising parametric variants of computer algebra and deduction algorithms will have a significant impact on applications. In particular, effective parametric/non-convex constraint solving and optimization methods (possibly combined with methods for reasoning in more complex domains) are strongly required in wide areas of industrial manufacturing and science. This includes but is not limited to:

  • loop parallelization,
  • software verification,
  • analysis and design of differential equations,
  • system design in control, signal processing etc.
• Parametric optimization and optimization over parameters

  Current computation in modern control is based almost exclusively on standard numerical linear algebra routines. However, computer algebra is gaining importance as a computational tool due to its capability of dealing with parameters, since many problems in practical applications can be reduced to parameter optimization problems.

• Applications to:
  • verification of real time and hybrid systems,
  • control system design and verification,
  • manufacturing design and design automation.

This session will emphasize methods in verification that combine the use of computer algebra techniques — such as Gröbner bases or quantifier elimination — with methods for reasoning in complex domains (hierarchical and modular reasoning, DPLL reasoning modulo theories).

Mostly independent of these developments, algorithms for symbolic summation and integration have ever since been subject to research in computer algebra. Today, a fairly far developed algebraic summation and integration theory is available which gives rise to algorithms applicable to to a wide class of problems. Implementations of these algorithms are also available and these have been able to discover and/or prove many deep identities in special functions and combinatorics in the past. It turns out that the more general algorithms arising from this research can also be successfully applied in particle physics.

In the session, we want to bring together people from both sides, to present the different techniques, and to discuss possible combinations that may help in handling challenging problems from quantum field theory.

Research contributions as well as expository papers are welcomed. For more information please contact the session organizers by email.

This session covers the following topics, but is not restricted to these.

1. Approximate GCD and approximate factorization.
2. Approximate computation of Groebner bases.
3. Algebraic computation using floating-point numbers and numeric algorithms.
4. Approximate computation by series expansion.
5. Error analysis and stabilization of algorithms.
6. Validation of approximate algebraic computation.
7. Computation of bounds for roots of polynomials
8. Isolation of polynomial roots
9. Software for solving hyperbolic polynomials
10. Computation of bounds for polynomial divisors
11. Symbolic-numerical methods of finding roots of polynomial systems
12. Software for solving polynomial systems
13. New algorithms suited to approximate algebraic computation.
14. Model construction by approximate algebraic algorithms.
15. Applications to science and technology.

SESSION TOPICS

The session topics include but not restricted to:

• reinvention and adaption of existing highly sophisticated symbolic algorithms to a parallel setting
• computer algebra systems specifically designed to exploit and operate in multiprocessor environment
• parallel methods for solving systems of differential equations
• parallel methods for Groebner basis computations
• parallel algorithms for solving linear and polynomial systems

For suggesting a talk, please contact the session organizers until May 30.

TALKS

• Gennadi Malaschonok, Mikhail Zueyv (Tambov State University, Tambov, Russia): Two recursive pivot-free algorithms for parallel matrix inversion
• Alkiviadis Akritas (Phessaly University, Volos, Greece): Parallel implementation of Sendov's real root approximation method
• Natasha Malaschonok (Tambov State University, Tambov, Russia): Solving differential equations by parallel Laplace method with assured accuracy

Several highly efficient specialised systems have been created and group-theory oriented packages within general purpose CAS have been developed over the last years.

The purpose of the section is to exchange ideas and experience and discuss recent progress in applying computer tools to the study of deep and difficult problems of group theory, representation theory and Lie theory. In fact, applications to group theory and representation theory are (alongside with algebraic geometry and commutative algebra, and number theory), among the most significant applications of computers in mathematics.

Computer algebra aspects of the following topics, among others, will be considered:

1. Finite groups of Lie type
2. Sporadic simple groups
3. Algebraic simple groups
4. Finite subgroups of algebraic groups
5. Arithmetic and related groups
6. Representations of finite groups
7. Representations of algebraic groups
8. Efficient generation of groups
9. Classification of maximal subgroups
10. Group cohomology
11. Conjugacy classes and their products
12. Group related geometries and graphs
13. Laws defining various classes of groups
14. Finite and pro-finite p-groups
15. Groups of small orders
16. Classification of perfect groups

Submission of talk title and abstract: June 15, 2008.