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27 Aug 2006 |
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Dr Jeremy Kaminski, Holon Institute of Technology |
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Sunday 15:00 |
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Room 330/5 |
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COMPUTATIONAL
ALGEBRAIC GEOMETRY- II |
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We present a series of lectures on Computational Algebraic Geometry.
The purpose is to introduce the basic concepts of algebraic geometry
and so the basic tools for computations. The program includes, among
others, the following subjects: affine and projective varieties,
primary decomposition, Groebner bases, dimension and degree of a
variety, Hilbert function and polynomial, zero-dimensional algebra,
resultants (univariate and multivariate), toric resultant, bezoutian,
dual affine algebra, Gorenstein algebras, algebraic residues. |
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13 Aug 2006 |
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Dr Jeremy Kaminski, Holon Institute of Technology |
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Sunday 15:00 |
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Room 330/5 |
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COMPUTATIONAL
ALGEBRAIC GEOMETRY- I |
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We present a series of lectures on Computational Algebraic Geometry.
The purpose is to introduce the basic concepts of algebraic geometry
and so the basic tools for computations. The program includes, among
others, the following subjects: affine and projective varieties,
primary decomposition, Groebner bases, dimension and degree of a
variety, Hilbert function and polynomial, zero-dimensional algebra,
resultants (univariate and multivariate), toric resultant, bezoutian,
dual affine algebra, Gorenstein algebras, algebraic residues. |
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22 Feb 2006 |
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Dr Jeremy Kaminski, Holon Institute of Technology |
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Wednesday 14:00 |
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Room 330/5 |
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INTRODUCTION TO
TROPICAL CONVEXITY - II |
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The lecture will
continue the first presentation and introduce further developments.
We will focus on tropical polytopes and cell complexes. In
particular, we will show that several classical results on ordinary
polytopes also hold in the tropical framework. |
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16 Feb 2006 |
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Dr Jeremy Kaminski, Holon Institute of Technology |
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Wednesday 14:00 |
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Room 330/5 |
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INTRODUCTION TO
TROPICAL CONVEXITY - I |
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The lecture will
introduce the basic concepts of tropical geometry and in particular
the basis of tropical convexity. The definitions are basically the
same than in the classical setting. However the set of scalar is now
the real line endowed by two new operations, making it a semi-ring.
The lecture includes the following issues: the tropical semi-ring
and the tropical projective space, tropically convex sets, tropical
polytopes and cell complexes. |
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04 Jan 2006 |
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Dr Yulia Kempner, Holon Academic Institute of Technology |
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Wednesday 12:00 |
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Room 330/5 |
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A GEOMETRIC
CHARACTERISATION OF POLY-ANTIMATROIDS |
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The notion of "antimatroid
with repetition" was invented by Bjorner, Lovasz and Shor in 1991 as
an extension of the notion of antimatroid in the framework of
non-simple languages. There are many equivalent ways to define
antimatroids. They may be separated into two categories:
antimatroids defined as set systems and antimatroids defined as
languages. In our research we emphasize the set system approach, and
we extend it to multisets systems. As a result, we define poly-antimatroids
and prove the equivalence between poly-antimatroids and antimatroids
with repetition. Our main observation is a geometric
characterization of poly-antimatroids in terms of abstract
convexity. |
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14 Dec 2005 |
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Professor Yuval Roichman, Bar Ilan University |
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Wednesday 13:00 |
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STATISTICS OF
PERMUTATION GROUPS, CANONICAL WORDS, |
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Room 330/5 |
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AND PATTERN
AVOIDANCE |
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The number of
left to right minima of a permutation is generalized to Coxeter (and
closely related) groups, via an interpretation as the number of
"long factors" in canonical expressions of elements in the group.
This statistic is used to determine a covering map, which "lifts"
identities on the symmetric group S_n to the alternating
group A_{n+1}. The covering map is then extended to "lift"
known identities on
S_n to new identities on S_{n+q-1} for every positive
integer q, thus yielding q-analogues of the known
S_n identities. Equi-distribution identities on certain families
of pattern avoiding permutations follow. The cardinalities of
subsets of permutations avoiding these patterns are given by
extended Stirling and Bell numbers. The dual systems (determined by
matrix inversion) have combinatorial realizations via statistics on
coloured permutations. |
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07 Dec 2005 |
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Dr Danny Hermelin, University of Haifa |
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Wednesday 13:00 |
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FIXED-PARAMETER
ALGORITHMS FOR PROTEIN SIMILARITY |
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Room 330/5 |
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SEARCH UNDER RNA
STRUCTURE CONSTRAINTS |
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In the context of protein engineering, we
consider the problem of computing an mRNA sequence of maximal codon-wise
similarity to a given mRNA (and consequently, to a given protein)
that additionally satisfies some secondary structure constraints,
the so-called MRSO problem. Since the MRSO problem is known to be
APX-hard, Bongartz proposed to attack the problem using the concept
of parameterized complexity. In this paper we follow this suggested
approach by devising fixed-parameter algorithms for several
interesting parameters of MRSO. We believe these algorithms to be
relevant for practical applications today, as well as for several
future applications. Furthermore, our results extend the known
tractability borderline of MRSO, and provide new research horizons
for further improvements of this sort. |
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16 Nov 2005 |
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Dr David Garber, Holon Academic Institute of
Technology |
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Wednesday 13:00 |
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Room 330/5 |
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EXCEDANCE NUMBERS
OF SOME COLOURED PERMUTATION GROUPS |
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We generalize
the results of Ksavrelof and
Zeng about the
multidistribution of the excedance
number of S_n with some natural parameters to
the colored
permutation group and to the Coxeter
group of type D. We define two different orders on these groups
which induce two different excedance
numbers. Surprisingly, in the case of the
colored permutation group,
we get the same generalized formulas for both orders. |
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