The Mathematical Foundations of Computer Science Laboratory does research related to
mathematics of computation and computer-aided teaching of mathematics. This includes
- an interactive email-based teaching system under UNIX;
- the theoretical foundations of genetic algorithms and genetic programming;
- applications of genetic algorithms such as optimizing shapes of vehicles in a virtual
wind tunnel or optimizing game code;
- fuzzy logic systems and generalizations;
- theory of quantum computers;
- numerical and other applications of matrix methods.
|Professor Schmitt’s major research fronts may be described as follows:|
- Teaching System. The Mathematical Foundations of Computer Science Laboratory
continuously keeps developing an interactive email-based teaching system
under UNIX. This system started as a teaching system for English Composition
for Japanese students of The University of Aizu (see [L.M. Schmitt, K.T. Christianson,
Pedagogical aspects of a UNIX-based network management system for
English instruction, System 26 (1998), 567–589]). This research has been continued
and further applications have been developed. These are: (i) introduction of
attendance checks and (ii) static/randomized quizzes.
(i) In today’s educational environment where motivation of students is low, the
instructor must make an extra effort to have students attend class since only in
class can under regular circumstance knowledge be communicated. One necessary
inconvenience for students in this regard are attendance checks which are mandated
by university regulations. The above mentioned teaching system generates
a receipt containing a 10-digit random number which the student obtains in class
and returns via email to the computer. The computer verifies the random code
and automatically prepares statistics about attendance for the instructor which is
used to limit admission to exams.
(ii) The second new module in regard to the teaching system allows development
of quizzes using typesetting with LATEX. Typesetting with LATEX is important for
the representation of mathematical content. The quizzes are developed through a
special file format which can be best described as a slight LATEX-extension. These
contain in separate units the LATEX-source to prepare a task-sheet with questions,
the answer to questions (fixed strings of characters) which are used to automatically
generate a homework checking program, and special comment which is used to give
hints to students about the solution after evaluation. The new module is designed
in such a way that students can, based upon a graded computer-generated report
including individualized solution-hints, resubmit their work for multiple evaluation.
The ensueing amount of machine-generated feedback is impossible to achieve by
human work alone.
The quiz module which has a dedicated development-interface for the instructor
has been further generalized to include randomized quizzes such that every student
in class obtains a different homework task.
L.M. Schmitt. An Email-based LearningManagement System forMathematics. In:
M. Osano et al (eds.), Proc. HC 2008, 11th International Conference on Humans
and Computers, The University of Aizu (2008)
L.M. Schmitt. Email-based Mathematics Teaching Tools. In: J. Brine & D. Roy
(eds.), Proc. Elearning and Usability Technical Meeting at The University of Aizu:
Oct 31st 2009, to appear
L.M. Schmitt. Course Materials (quiz series) for four Undergraduate Courses at
The University of Aizu. The University of Aizu (2008–2010)
- Genetic Algorithms and Genetic Programming Applications. Genetic algorithms
and genetic programming are by now well-established optimization techniques.
Currently, there are two lines of applied research persued in this direction which
both use a genetic algorithm setting with paralled fitness evaluation on the Mathematical
Foundations of Computer Science Laboratory’s own Linux-PC/Mac network:
(i) optimization of vehicle shapes in a virtual wind tunnel in regard to the
wind resistance force (with S. Takako and Y. Takemura) and (ii) optimization (improvement)
of a chess program (GNU chess) using a dedicated genetic algorithm
(with T. Mitsuta).
(i) We have developed and continue to develop a Linux-PC/Mac network on which
a parallel genetic algorithm runs which optimizes vehicles shapes (cars, trucks) in a
virtual wind tunnel in regard to the wind resistance force. This requires installation
and use of specialized software for meshing and solution of the three-dimensional
Navier-Stokes equation. This project has thus far included the following activities:
generation of a stochastic model for the real-valued genetic algorithm with parallel
fitness evealuation along the lines of [L.M. Schmitt. Theory of Genetic Algorithms.
Theoretical Computer Science 259 (2001), 1–61]. Optimization of a car shape
which gives a realistic impression and reduces the wind resistance force compared
to standard triangalar or rectangular shapes considerably. Optimization of the
shape of a truck’s shield on top of the drivers cabin. Also here, the wind resistance
force compared to standard triangalar, parabolic or rectangular shapes is reduced considerably.
And the shapes obtained in the latter experiemtn seem to be new.
(ii) As an application in the field of Artificial Intelligence, it is also attempted to
find a better-playing variation of the GNU-chess program using a genetic algorithm
where the fitness functions is measured against the original GNU-chess program.
This is work in progress.
S. Takako, Y. Takemura & L.M. Schmitt. Minimizing Wind resistance of Vehicles
with a Parallel Genetic Algorithm. Preprint in preparation, The University of Aizu
|Professor Yamakami’s major research fronts may be described as follows:|
- Quantum Computing Applications. Professor Yamakami persued research in
Quantum Computation, Information Theory and Quantum Cryptography. Quantum
Computation seeks to exploit quantum mechanical phenomena, such as superposition
and entanglement, to perform operations on data. If large-scale quantum
computers can be constructed, then such machines will solve certain problems much
faster than any of our current classical computers. Such ultra-fast computational
methods would also allow applications in Cryptography namely the cracking of
previously unbreakable encryption codes or the design of newer much more secure
|Professor Asai’s major research fronts may be described as follows:|
- Matrix Methods and Applications. Matrix-theoretic high-performance algorithm
construction with application to the numerical computation of critically important
quantities associated with difficult special functions occurring from 3-D wave equations
such as regular Coulomb wave functions, Mathieu functions, spheroidal wave
functions, Lame functions and ellipsoidal wave functions. The Bessel function of
the first kind, an easier function serves as a model case where two types of computational
problems were solved in the complex domain as well as real domain:
given a complex order Bessel function, compute a given number of zeros closest
to the origin to a specified accuracy; and given a complex number find a specified
number of orders of Bessel functions closest to the origin, to a specified accuracy.
There are no comparable algorithms known elsewhere which give as accurate an
error estimate as ours.
- Construction of Dictionaries. Construction of hyper English word study dictionary:
it is available at http://hidic.u-aizu.ac.jp/. This represents a longrange
project, aiming at compiling a database for the study of English words for
Japanese students. The main feature is that the dictionary is organized to bring
out the best fruits of comparative linguistics in the past century: the usefulness of
Indo-European roots as presented in the wonderful book by Calvert Watkins, The
American Heritage Dictionary of Indo-European Roots, Second Edition, Houghton
Mifflin, 2000. Example: The organizing principle of the dictionary will tell you that
the following words are best studied as a group: riddle, garble, crime, decree, discern,
secret, hypocrisy (they are all derivatives from the same Indo-European root
krei-, meaning ”to sieve”, indicating that a group of seemingly unrelated words
come from the same notion ”to sieve”). Another example: the usage of the socalled
synonyms ”anger, rage and wrath” can be clearly explained by tracing them
back to their respective Indo-European root: anger to angh-, meaning painful, rage
to rebh-, meaning violent, impetuous, and wrath to wreit-, meaning to turn, twist
(anger is akin to angst, angina, rage is akin to rabid, rabies, and wrath is akin to