Graduate Seminar Series — Fall 2012
Location: Haag Hall, room 307 (Unless otherwise noted)
Day & Time: Fridays, 3:00-4:00 pm (Unless otherwise noted)
Campus Map for Talks (PDF Format)
Organizer: Dr. Majid Bani-Yaghoub, 235-2845
Dates, Titles, Speakers (with Abstracts as available)
Friday, Sep. 7
Mechanisms of actomyosin ring contraction for budding yeast cell division
Stowers Institute for Medical Research
Actin filaments and myosin-II are evolutionarily conserved force
generating components of the contractile ring during cytokinesis.
We show that in budding yeast actin filament depolymerization plays a
major role in actomyosin ring constriction. Cofilin mutation or
chemically stabilizing actin filaments attenuates actomyosin ring
constriction. Deletion of myosin II motor domain or the myosin
regulatory light chain reduced the contraction rate and also the rate
of actin depolymerization in the ring. We constructed a quantitative
microscopic model of actomyosin ring constriction via filament sliding
driven by both actin depolymerization and myosin II motor activity.
Model simulations based on experimental measurements supports the notion
that actin depolymerization is the predominant mechanism for ring
constriction. The model predicts invariability of total contraction
time irrespective of the initial ring size as originally reported for
embryonic cells. This prediction was validated in yeast
cells of different sizes due to having different ploidies.
Friday, Sep. 14
Challenges in computation of basic and type- reproduction numbers for disease models with free-living pathogen
UMKC Department of Mathematics and Statistics
The basic reproduction number R0 is a threshold quantity
that is used to measure the intensity of disease spread in a community.
The Next Generation Matrix (NGM) approach is often used to calculate a
unique R0 expression. This study shows that the uniqueness
of R0 expression is lost when a disease model includes
growth and survival of free-living pathogen. Consequently, the R0
values related to an infection can be substantially different. The issue
of multiple R0 Expressions is partly resolved when the type
reproduction number T is used. However, the T expression related to the
infected host population is meaningful only when the net growth rate of
free-living pathogen is negative. These results are shown by considering
model with free-living pathogen. Furthermore, the conditions for global
stability of the endemic and disease-free equilibria are established via
LaSalle's invariance principle and the method of Lyapunov function.
Friday, Sep. 21
Statistical Methods for Tissue Images:
Algorithmic Scoring, Data Contamination, and Blessings of Dimensionality
UMKC Department of Mathematics and Statistics
Tissue microarray (TMA) technology allows one to evaluate large
numbers of immunohistochemically-stained tissue images and has been
successfully used in many applications, such as clinical outcome analysis,
tumor progression analysis, identification of risk factors, validation of
biomarkers etc. In response to concerns about the subjectivity and
variability of pathologist-based TMA evaluation, we develop the TACOMA
algorithm to automatically score TMAs in an efficient and objective manner.
The statistical regularity in TMAs are effectively captured by statistics
related to the transition of gray levels. A few "representative" image
patches allow TACOMA to focus on biologically relevant features and score
in a similar way as the pathologists. Experiments with TMA images for
different biomarkers show that TACOMA rivals pathologists in terms of
accuracy and reproducibility. Moreover, it is able to reveal salient
pixels in an image most relevant to scoring. There are two particular
challenges in the training of TACOMA, label noise (scores by pathologists
often different from the "truth") and the small training sample size.
Co-training allows us to substantially boost performance for a small
training sample. Theoretical insights are given to the success of
thinning-based co-training, which is particularly relevant to
high-dimensional settings with "sufficient" redundancy among features.
Time permitting, I will discuss a recent work on data contamination,
motivated by the image mis-registration problem and the observed label
noise during TMA image scoring. In particular, the impact of data
contamination to classification will be discussed, for which a sharp
asymptotic data contamination bound is established.
Friday, Oct. 5
The Hot Spots Conjecture and its Discrete Analogue
Department of Mathematics, U of MO
The hot-spots conjecture was proposed by Jeffery Rauch in 1974 and
roughly conjectures the following: Consider a 2-dimensional connected
insulated piece of metal. If the metal is given an initial heat
distribution and the heat is then allowed to flow, eventually the
hottest and coldest points will lie on the boundary. Mathematically, the
conjecture concerns the second eigenfunction of the Neumann-Laplacian on
a connected 2-dimensional domain D. Since its statement, the hot-spots
conjecture has been proven for some domains and counter-examples have
been exhibited for others. In particular, while the conjecture is known
to be true for obtuse triangles, the conjecture has not yet been proven
for general triangles!
I will give an overview of what is known about the hot-spots conjecture
and show how coupled reflected Brownian motion can be used to give an
elegant proof in some domains. I will then also discuss the discrete
analogue of the conjecture and explain a result of mine where I exhibit
a counter example to a related conjecture of Moo Chung in the discrete case.
Friday, Oct. 12
On Personalized Information Filtering
University of Minnesota
Personalized information filtering extracts the information specifically
relevant to a user, based on the opinions of users who think alike or the
content of the items that a specific user prefers. In this presentation,
I will introduce partial latent models to utilize additional user-specific
and content-specific predictors, for personalized prediction. In particular,
we factorize a user-over-item preference matrix into a product of two
matrices, each representing a user's preference and item preference by
users. On this basis, we seek a sparsest latent factorization from a
class of overcomplete factorizations, possibly with a high percentage of
missing values. A likelihood approach will be discussed, with an emphasis
on scalable computation. Examples will be given to contrast with popular
methods for collaborative filtering and contented-based filtering.
Friday, Oct. 19
Spatial Spread and Front Propagation Dynamics
of Nonlocal Monostable Equations in Periodic Habitats
Department of Mathematics, The
University of Kansas.
This talk is concerned with the spatial spread and front propagation
dynamics of monostable equations with nonlocal dispersal in spatially
periodic habitats. Such equations arise in modeling the population
dynamics of many species which exhibit nonlocal internal interactions
and live in spatially periodic habitats. Firstly, we establish a general
principal eigenvalue theory for spatially periodic nonlocal dispersal
operators. Secondly, applying such theory and comparison principle for
sub- and super-solutions, we obtain the existence, uniqueness, and
global stability of spatially periodic positive stationary solutions and
the existence of a spatial spreading speed in any given direction of a
general spatially periodic nonlocal equation. Such features are generic
for nonlocal monostable equations in the sense that they are independent
of the assumption of the existence of the principal eigenvalue of the
linearized nonlocal dispersal operator at 0. Finally, under the above
assumption we also investigate the front propagation feature for
monostable equations with non-local dispersal in spatially periodic
habitats. It remains open whether this feature is generic or not for
spatially periodic nonlocal monostable equations.
Friday, Oct. 26
Objective Bayesian Analysis of Vector Smoothing Spline
Shawn Xiaoguang Ni,
Department of Economics,
University of Missouri
We consider a multivariate smoothing problem with
correlated error components (noise) and correlated derivatives of the vector
components (signals). We relate the vector smoothing spline to a multivariate
Bayesian Gaussian linear mixed model. We conduct full Bayesian inference on the
smoothing spline and the unknown covariance matrices associated with the noise
and signal components. We propose informative and objective priors under
different parameterizations, provide conditions for posterior propriety under
objective priors, and develop Markov Chain Monte Carlo (MCMC) algorithms for
Bayesian computation. We show in numerical simulations that vector smoothing
spline outperforms univariate smoothing splines.
I will also present related topics on filtering time series data in
Friday, Nov. 2
Restricted Partitions and Bernoulli Polynomials
Stowers Institute for Medical Research
The problem of the partition of an
integer number into a set of smaller integers has a long history starting from
Leonhard Euler. The solution can be presented as
a sum of the so-called Sylvester waves each corresponding to the divisor of the
partition integers set. We present an explicit formula for the arbitrary
Sylvester wave through the generalized Bernoulli and Euler polynomials.
We also show that this formula can be written using the Bernoulli polynomials
Friday, Nov. 9
4:00 pm (note different time)
An Introduction to Algebraic Methods for the Stochastic Shortest Path
Department of Mathematics, University of Missouri
Operations research (OR) is an applied area of mathematics
that can be thought of as the “theory of optimization.”
A well-studied problem in OR is the
shortest path problem, in which goal of the shortest path problem is to find the
length of a shortest path between two specified locations.
It is typically formulated on a network where nodes represent an
abstraction of a set of elements and the connecting edges/arcs indicate the
relationship between these elements.
In most real-world applications the “costs” of these relationships (edge/arc
weights) are not known explicitly and are often modeled using random variables,
thus giving rise to a stochastic
network. The goal of the stochastic
shortest path problem is to find the
probability distribution of the shortest path length.
In this talk, we will introduce the stochastic shortest
path problem as well as some of its applications.
A new algebraic approach for solving the stochastic shortest path problem
will then be presented and we will discuss an exact solution algorithm.
We will also discuss approximate algorithms that can be employed using
this algebraic technique to obtain bounding distributions.
Lastly, we will examine the results obtained using these exact and
approximating algorithms in two test networks.
Wednesday, Nov. 14 —
Weller Overstreet Lectures in Science
Identifying Separated Time-scales in Stochastic
Models of Cellular Reaction Networks
Department of Mathematics / Department of Statistics,
University of Wisconsin—Madison
Continuous time Markov chains have become a standard
way of modeling chemical reaction networks in biological cells.
The talk will begin with a review of some of the basic approaches
for specifying and analyzing these models. In these models,
reaction rates and chemical species numbers may vary over several
orders of magnitude. Combined, these large variations can lead to
subnetworks operating on very different time-scales. This
separation of time-scales has been exploited in many contexts as a
basis for reducing the complexity of dynamic models, but the
interaction of the rate constants and the species numbers makes
identifying the appropriate time-scales tricky at best. Some
systematic approaches to this identification will be discussed and
illustrated by application to one or more reaction network models.
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