Mathematical Application Seminar*
Fall 2008
Tuesdays 11:10 –
Monroe Hall,
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Speaker: Yang Huang, NIH/NLM/NCBI
Title: Galois lattice and its application in gene
expression analysis
Place: Monroe Hall,
Abstract:
As an important discrete
mathematics tool, Galois lattice recently
found its applications in gene-expression analysis, which is an active
research area in bioinformatics. There are numerous methods available
for analyzing the large volume of gene-expression data. Among those,
the method involving Galois lattice shows some unique advantages. In
this talk, I will introduce the definition and basic properties of
Galois lattice. Then I will discuss some of our own work in applying
Galois lattice to distinguish gene-expression vectors and
gene-expression matrices obtained at different conditions. The basic idea was
to
represent gene-expression data with binary matrices and construct a Galois
lattice
for each binary matrix. The difference between gene expression data was
measured by the distance between lattices. The method has been applied
to time series gene-expression data obtained from smoking mouse and human
drug response.
Reference can be found on
http://www.ncbi.nlm.nih.gov/
1. Martin Farach-Colton and Yang Huang, A linear delay algorithm for
building concept lattices, 19th Symposium on Combinatorial Pattern
Matching (CPM'08), 2008.
2. Yang Huang and Martin Farach-Colton, Lattice based clustering of
temporal gene-expression matrices, 7th SIAM International Conference
on Data Mining (SDM'07), 2007.
3. Vicky Choi, Yang Huang, Vy Lam, Dustin Potter, Reinhard Laubenbacher
and Karen Duca, Using formal concept analysis for microarray data
comparison, 5th Asia Pacific Bioinformatics Conference (APBC'07),
Hong Kong, 2007, p57-66.
Speaker: Elena Rivas, Janelia Farm Research
Campus, Howard Hughes Medical Institute,
Title: RNA structure prediction including pseudoknots: A transformational
grammar interpretation.
Place: Monroe Hall,
Abstract:
I will
describe a dynamic programming algorithm for predicting optimal RNA secondary
structure,
including
pseudoknots. The algorithm has a worst case complexity of O(L^6) in time and
O(L^4)
in memory for
a sequence of length L. The description of the algorithm is complex, which led
us to
adopt a
useful graphical representation (Feynman diagrams) borrowed from quantum field
theory. I will present
an
implementation of the algorithm that generates the optimal minimum energy
structure for a single
RNA sequence,
using standard RNA folding thermodynamic parameters augmented by a few
parameters
describing
the thermodynamic stability of pseudoknots. The general unrestricted RNA
folding problem
is NP-complete.
I will show how this algorithm avoids the full NP-complete problem by
considering a
subclass of
all possible RNA pseudoknots.
I will also
show a one-to-one correspondence between the pseudoknot algorithm (PKNOTS) and
a
formal
transformational grammar. Not-pseudoknoted RNA structures (nested structures)
are well represented
by the so
called context-free grammars (that can deal with palindroms for instance). The
pseudoknot
grammar class
encompasses the context-free grammars and goes beyond to generate pseudoknotted
structures.
The pseudoknot grammar avoids the use of general context-sensitive rules by
introducing a
small number
of auxiliary symbols used to reorder the strings generated by an otherwise
context-free
grammar.
Everyone is welcome to
participate the
Fifth Symposium on
Frontiers of Statistical, Mathematical and Computational Sciences (
Contact
Dr. Jagdish Chandra, at
Speaker: Yongwu Rong, George Washington University
Title: Dynamics of Boolean networks
Place: Monroe Hall, 2115 G Street, Room 267
Abstract:
Networks have been of great interests lately in many disciplines including mathematics,
computer science, biology, social studies and more. One specific problem is the so-called
reverse engineering problem, which asks for the interaction between units in the network
given its dynamics. Various models have been proposed and studied.
I will discuss a specific Boolean network model proposed by GWU colleagues
Rahul Simha (computer science), Guanyu Wang, and Chen Zeng (both bio physics),
which relates naturally to the Satisfiability Problem in logic. Connections with mathematical
work by R. Laubenbacher (Virginia Tech) and his collaborators will be discussed.
November 11, 2008. Tuesday, 11:10 – 12:00 noon
Speaker: Jianjun Paul Tian, College of William and Mary.
Title: Introduction
to evolution algebras
Place: Monroe Hall, 2115 G Street, Room 267
Abstract:
Behind the neutral Wright-Fisher models in population genetics, asexual reproduction or
generally non-Mendelian inheritance including intracellular population genetics,
there exists an intrinsic and general mathematical structure. We defined it as a new type of algebra –
evolution algebras. In this talk, I will introduce basic concepts in evolution algebras,
and describe the structure theorem. I will also describe how to apply evolution algebras
to the study of Markov chains, and other mathematical subjects such as graph theory and knot theory.
November 18, 2008. Tuesday, 11:10 – 12:00 noon
Speaker: Thomas Wanner, George
Mason University
Title: Homological Analysis of Complicated Random Patterns
Place: Monroe Hall, 2115 G Street, Room 267
Abstract:
Many partial differential equation models arising in applications generate
complex time-evolving patterns which are hard to quantify due to the lack of
any underlying regular structure. Such models may include some element of
stochasticity which leads to variations in the detail structure of the
patterns and forces one to concentrate on rougher common geometric features.
In many of these instances, such as for example in phase-field type models
in materials science, one is interested in the geometry of sublevel sets of
a function in terms of their topology, in particular, their homology.
Recent computational advances make it possible to compute the homology of
discrete structures efficiently and fast. Such methods can be applied to the
above situation if the sublevel sets of interest are approximated using an
underlying discretization of the considered partial differential equation.
Yet, this method immediately raises the question of the accuracy of the
resulting homology computation. In this talk, I will present a probabilistic
approach which gives insight into the suitability of the above method in the
context of random fields. We will obtain explicit probability estimates for
the correctness of the homology computations, which in turn yield a-priori
bounds for the suitability of certain grid sizes.
December 2, 2008. No
seminar is scheduled for the week.
Everyone is welcome to attend the Biophysics Seminar on
Wendesday, December 3, 1:30pm, Corcoran 104, with the talk
Formation of new
patterns by programming cell motility
By Professor Jiandong Huang of Biochemistry Department of Hong Kong University.
Contact Chen Zeng at chenz@ gwu.edu
December 9, 2008. Tuesday, 11:10 – 12:00 noon
Speaker: Jie Zheng, NIH/NLM/NCBI
Title: Coalescent-based Statistical Modeling of Meiotic Recombination Hotspots
Place: Monroe Hall, 2115 G Street, Room 267
Abstract:
Meiotic
recombination plays important roles in both physiology and evolution.
Recombination events tend to cluster into narrow spans of a few kilo bases
long, called recombination hotspots. Recombination hotspots are not conserved
between human and chimpanzee and vary between different human ethnic groups. At
the same time, recombination hotspots are inheritable. Previous studies showed
instances where differences in recombination rate could be associated with
sequence polymorphism. In this work we provided the first look at the large
scale association of recombination hotspots with genetic polymorphism, based on
coalescent modeling and analysis of population genetic data. We demonstrated
that, for a significant fraction of hotspots, there is an association between
variation in intensity of recombination and variation in genotype.
Interestingly, a significant fraction of associated single nucleotide
polymorphisms (SNPs) is positioned more than 50kb
from hotspots. The existence of such SNPs would be
consistent with models that propose to resolve the hotspot paradox through the
existence of trans-acting hotspot regulators. Importantly, our computational
approach was able to correctly predict the association of SNP FG11 with the
hotspot DNA2 in the MHC class II region (Jeffreys and
Neumann 2002). Such association is known to exist based on sperm typing
experiments. This demonstrates that computational approaches as the one
proposed in this work are likely to be more powerful than previously
anticipated.
In
this talk, I will also describe how mathematical modeling can help elucidate
mechanisms in genetics and molecular biology. This work is in collaboration
with Teresa M. Przytycka from NCBI, NLM, NIH, and Pavel P. Khil and Rafael Daniel Camerini-Otero from NIDDK, NIH.
Hungry for talks in January? Consider
AMS Special Session on
Topological Methods in Applied Mathematics
January
5-6, 2009. Details at
http://www.ams.org/amsmtgs/2110_program_ss56.html#title
Still hungry? consider more
talks at the Joint Annual Mathematics Meetings:
http://www.ams.org/amsmtgs/2110_intro.html
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Previous Seminars
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* The Mathematical Application
Seminar is currently sponsored by the
George Washington University Seminars program.
It also received support the Department of Mathematics at the George
Washington University.
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