Monday, April 28, 2003
| Title |
Morphisms and Continuous Maps on the Space of Formal Languages
|
| Speaker |
Daniela Genova |
| Time |
2:00-3:00 p.m. |
| Place |
PHY 109 |
Abstract
The set of all languages consisting of finite words over a finite alphabet
equipped with the standard language metric is homeomorphic to the Cantor space. We
characterize the continuous morphisms on this space and discuss morphic properties
of forbidding-enforcing families.
Monday, April 21, 2003
| Title |
An Introduction to Back-Circulant Graphs |
| Speaker |
Nathan Chau |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
We will look at some basic properties and examples of “back-circulant&rdquo
graphs, which are defined as follows:
Let S be a subset of Zn, the group
of integers mod n. The back-circulant graph
BC(S,n) has vertex set Zn,
and vertex u is adjacent to vertex v iff u
+ v is in S and u is not equal to v.
(The restriction u not equal to v is necessary to avoid
loops in BC(S,n)).
Theorems involving the connectivity, degree sequence, and (partial)
classification of these graphs will be discussed.
Monday, April 14, 2003
| Title |
Languages From and for DNA Sequences |
| Speaker |
Kalpana Mahalingam |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
In DNA nanotechnology and DNA based computations the design of DNA sequences
that are error resistant is of essential importance. The set of all sequences that
are generated by a biomolecular protocol forms a language over the four letter
alphabet DELTA = {A, G, C, T}. This
alphabet is associated with a natural involution mapping A ↦
T, G ↦ C, which is an antimorphism of
DELTA*. In order to avoid undesirable Watson-Crick bonds between the words
(undesirable hypridizaation), the language has to satisfy certain coding
properties. In particular for DNA, no involution of a word is a subword of another
word, or no involution of a word is a subword of a composition of two words. The
set of code words that satisfy these properties forms a language. We give
necessary and sufficient conditions for a finite set of code words to generate
(through concatenation) an infinite set of code words with the same properties.
Monday, April 7, 2003
| Title |
Modular Leonard Triples |
| Speaker |
Dr. Brian Curtin |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
Let V denote a vector space of finite positive dimension. A Leonard
triple is a triple A, A*, A# of linear operators
on V such that for each choice of A, A*, and
A#, there is a basis for V such that the matrix representing
the chosen operator is diagonal and the matrices representing the other two
are irreducible tridiagonal. A Leonard triple A, A*, A#
is called modular when for each choice A, A*, and A#,
there is an antiautomorphism of End(V) which fixes the chosen operator
and swaps the other two.
We describe a complete charaterization of modular Leonard triples which gives
the entries of the matrices representing the three operators with respect to
one of the above mentioned bases. We also discuss how instances of modular Leonard
triples arise from distance-regular graph which support a spin model.
Monday, March 31, 2003
| Title |
Leonard Pairs, II |
| Speaker |
Hassan Al-Najjar |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Monday, March 24, 2003
| Title |
Leonard Pairs |
| Speaker |
Hassan Al-Najjar |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
Let F denote a field, and let V denote a vector space
over F with finite positive dimension. We consider a pair of
F-linear maps (A,B) from V to
V satisfying the following conditions:
- there exists a basis for V with respect to which the matrix
representing A is diagonal, and the matrix representing B
is irreducible tridiagonal.
- there exists a basis for V with respect to which the matrix
representing B is diagonal, and the matrix representing A
is irreducible tridiagonal. We call such a pair a leonard pair on V.
Monday, February 10, 2003
| Title |
Cographic Excluded Minors for the Classes of Gain-Graphic
Matroids |
| Speaker |
Dr. Hongxun Qin
Department of Mathematics
Ohio State University |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Dr. Stephen Suen |
| Note |
Speaker is a candidate for Asst. Prof. in Algebra. |
Abstract
A gain graph is a graph with edges labeled by elements of a group. A matroid
can then be defined on its edge set. For a finite group A, the class of
gain-graphic matroids Z(A) forms a minor-closed class. Hence
a natural problem is to determine the excluded minors for the class. We
characterize the graphs whose dual matroids are excluded minors for
Z(A). Let G be a 2-connected graph and let
N be the dual of its cycle matroid. If the order of A is
odd, then N belongs to Z(A) if and only if
G is planar; if the order of A is even, then N
belongs to Z(A) if and only if G is projective
planar.
This is joint work with Thomas Dowling.
Monday, January 27, 2003
| Title |
Negation and Failure, Part III |
| Speaker |
Professor Greg McColm |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
In first order logic, negation is effected by plopping a negation sign in front
of a formula. In infinitary (game-theoretic) logics, things are not so simple.
We look at a fragment of least fixed point logic: the logic where all but a
fixed number of moves is made by Player E. (This logic is commonly called
“Existential Fixed Point logic”.) We look at what Immerman's theorem
says — and does not say — about negation in this logic.
Friday, January 24, 2003
| Title |
Negation and Failure, Part II |
| Speaker |
Professor Greg McColm |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Note: There will be another organizational meeting prior to the talk.
Friday, January 17, 2003
| Title |
Negation and Failure |
| Speaker |
Professor Greg McColm |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 108 |
Abstract
In first order logic, negation is effected by plopping a negation sign in front
of a formula. In infinitary (game-theoretic) logics, things are not so simple.
We start with a game-theoretic view of Least Fixed Point logic, and find that
just because a relation can be expressed in that logic doesn't mean that its
negation can be so expressed.
NOTE: There will be an organizational meeting prior to the talk.
Wednesday, January 8, 2003
| Title |
Orbits of Acyclic Group and the q-binomial Coefficient |
| Speaker |
Professor Dennis Stanton
University of Minnesota |
| Time |
3:00-4:00 p.m. |
| Place |
CHE 203 |