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Upcoming Seminars
MONDAY, September 17, 2007
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 304 1:40 p.m.
Moderators: Slim Ibrahim, Svetlana Roudenko, Sergei Suslov,
Department of Mathematics and Statistics
"Local and Global Analysis of Nonlinear Dispersive Equations"
ABSTRACT: We study in details modern approaches in Analysis and
Nonlinear PDEs based on the book from CBMS series by Terence
Tao (Field's Medalist 2006). Graduate students and postdocs are
especially welcome.
COLL0QUIUM (FACULTY CANDIDATE) PSA 206 1:40 p.m.
Rodrigo Platte, Department of Mathematics and Statistics
"Radial Basis Function Methods for Solving Partial
Differential Equations"
ABSTRACT: Spectral methods are usually based on polynomial or
trigonometric expansions and are known for their fast
convergence (exponential for smooth problems). Solutions can be
efficiently computed through fast Fourier transforms, making
them popular in the study of turbulent flows, meteorological
simulations, and imaging. Conventional spectral methods,
however, have limitations which have prevented them from being
used in many applications where finite differences and finite
elements are predominant. One obstacle is the need of special
nodal sets for accurate approximations. In this talk we will
explore three viable alternatives to circumvent this
difficulty: radial basis function, hybrid, and underdetermined
methods. Of particular interest is how the accuracy and
stability of these schemes depend on node location and the
geometry of the problem. Adaptive implementations will also be
considered.
Refreshments will be served in PSA 206 at 1:15 p.m.
TUESDAY, September 18, 2007
MATHEMATICS AND COGNITION SEMINAR ISTB1 401 12:15 p.m.
Marco Santello, Department of Kinesiology
"Grasping Uncertainty: Planning Contact Points and Forces in
Multi-Digit Manipulation"
ABSTRACT: Humans use anticipatory mechanisms to scale fingertip
forces when grasping an object. The sensory feedback signaling
object properties acquired through repeated manipulations of
the same object allows subjects to generate sensorimotor
memories associating digit forces with the object. We have
recently provided evidence for anticipatory control mechanisms
in the kinematic domain by showing that subjects change the
spatial distribution of their digits on an object when its
center of mass (CM) can be anticipated ('Predictable'
condition; Lukos et al., 2007). However, when object CM - hence
digit forces - could not be predicted on a trial-to-trial basis
('Unpredictable' condition), subjects used a 'default'
distribution of contact points on the object and performance
was characterized by significantly larger object rolls than in
the 'Predictable' condition (Lukos et al., 2007).
The present study was designed to quantify the extent to
which these effects of sensorimotor memories on movement
planning could be mimicked by providing subjects with verbal
or visual cues about CM location. This question was addressed
by providing these cues (declarative knowledge) while changing
object CM location from trial to trial, hence depriving
subjects from developing sensorimotor memories through
practicing manipulation over consecutive trials (procedural
learning). We found that declarative knowledge of object CM
enabled subjects to modulate contact points but not to
anticipate forces to the same extent associated with procedural
learning. These findings suggest that effect of sensorimotor
memories - generated by procedural learning - on movement
planning cannot be fully substituted by declarative knowledge
of object properties. These results emphasize the critical role
of tactile feedback for grasp planning and execution.
For additional information e-mail tom.taylor@asu.edu
WEDNESDAY, September 19, 2007
ANALYSIS/PDE SEMINAR PSA 306 1:40 p.m.
Fernando Carreon, Department of Mathematics and Statistics
"Singular Limits of a RDE of KPP Type in an Infinite Cylinder"
ABSTRACT: The limit of a scaled reaction diffusion equation of
KPP type on an infinite cylinder is analyzed using viscosity
solution methods. We show that the solutions of the scaled
equation converge locally uniformly to piecewise constant
function that attains the two equilibria of the equation, as
the scale parameter goes to zero. The regions where the
solutions converge to each equilibrium state are characterized
through the viscosity solution of a variational inequality. The
coefficients of the variational inequality are obtained using
concepts from homogenization of elliptic operators.
COMPRESSIVE SENSING SEMINAR ECA 225 4:00 p.m.
(In cooperation with Department of Electrical Engineering)
Video Lecture by Emmanuel J. Candes,
California Institute of Technology
"Sparsity and Incoherence - Part II"
ABSTRACT: Compressed sensing essentially relies on two tenets:
the first is that the object we wish to recover is
compressible in the sense that it has a sparse expansion in a
set of basis functions; the second is that the measurements we
make (the sensing waveforms) must be incoherent with these
basis functions. This video lecture introduces key results in
the field such as a new kind of sampling theorem which states
that one can sample a spectrally sparse signal at a rate close
to the information rate.
FRIDAY, September 21, 2007
DISSERTATION DEFENSE PSA 206 8:45 a.m.
Muhammad Dur-e-Ahmad, Department of Mathematics and Statistics
"Structural Plasticity of Dendritic Spines: A Computational
Study"
ABSTRACT: Recent evidence indicates that the morphology and
density of dendritic spines are regulated during synaptic
plasticity. High-frequency stimuli that induce long-term
potentiation (LTP) have been associated with increases in the
number and size of spines. In contrast, low-frequency stimuli
that induce long-term depression (LTD) are associated with
decreases in the number and size of spines. Decreases in
spine density also occur due to excitotoxicity associated with
very high levels of activity such as during seizures.
In this work, we use continuum models to investigate the
calcium dependent morphology and density of dendritic spines.
The models are based on the standard dimensionless cable
equation for the changes in membrane potential in a passive
dendrite. Additional equations characterize the change in
potential in the spine head, calcium dynamics in the spine head
and calcium-dependent changes in spine structure and density
along the dendrite. Based on the conceptual model proposed by
Segal et. al (TIN 2000), when the level of calcium in the spine
head is in the medium range, elongation of existing spine and
formation of new spines occurs, while very low or very high
calcium concentrations lead to spine shrinkage and pruning. In
contrast, a prolonged low-frequency stimulation paradigm that
would typically induce LTD results in a decrease in stem
resistance (correlated with spine shortening) and an eventual
decrease in spine density.
On the computational side, we introduce two new algorithms
based on the Chebyshev spectral collocation methods and compare
the results with the finite difference scheme. We find that
these algorithms are about fifteen times more efficient than
the finite difference approach in spite of the fact that
spectral collocation requires more steps and more function
evaluations.
MATH BIOLOGY SEMINAR PSA 102 3:40 p.m.
Stephen A. Wirkus, Mathematical Sciences & Applied Computing
Department, ASU West Campus
"Gene Regulatory Network: A Continuous Nonlinear Model"
ABSTRACT: Gene expression is the process by which a gene makes
its effect on a cell or organism. Linear differential equations
have been explored as a model for gene expression. We discuss
the shortcomings of this model, and we propose a system of
nonlinear differential equations to mathematically model gene
expression in prokaryotes, such as bacteria, and simple
eukaryotes, such as yeast. We investigate this biological
system using explicit functions that describe the processes of
protein synthesis which includes transcription, translation,
degradation, and feedback in hope of shedding light on their
associated rates. We analyze the transient and steady state
solutions of the model and give a biological interpretation of
these results. We briefly mention some possible extensions
using networks.
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