TALKS GIVEN
MATH BIOLOGY/DIFFERENTIAL EQUATIONS SEMINAR PSF 208
2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Frank Hoppensteadt, Department
of Mathematics and SSERC
"Some uses of
Electronic Circuit Analogs in Neuroscience"
ABSTRACT: Some decisive
uses of electronic circuits in studies
of neurons and networks
of them from Lapicque (1907) to phase
locked loops (1999) will
be described.
TUESDAY, September 7, 1999
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MATH BIOLOGY/DIFFERENTIAL
EQUATIONS SEMINAR PSF 208 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Steve Baer, Department of
Mathematics
"Modeling Spatially
Clustered Synaptic Inputs in Nerve and Muscle"
ABSTRACT: Many neurons have
their dendritic cables studded with
thousands of dendritic spines,
which are small (1-2 micron)
thornlike protuberances
from the dendritic surface. Various
hypotheses regard spines
as possible loci for synaptic
plasticity. Since
a single neuron may have as many as 10^5
spines, Baer and Rinzel
(1991) formulated a continuum cable
theory to model large populations
of spines. We present a new
variation of this model
to investigate spatially clustered
synaptic inputs in both
nerve and muscle fibers.
FRIDAY, September 17, 1999
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NONLINEAR
DYNAMICS/MATH BIOLOGY SEMINAR GWC 604
10:40 a.m.
(Co-sponsor:
Systems Science and Engineering Research Center)
Eugene
Izhikevich, Department of Mathematics
"Bifurcations in Neuron Dynamics"
ABSTRACT:
Bifurcation mechanisms involved in the generation of
action
potentials (spikes) by neurons are reviewed here. We
show
how the type of bifurcation affects the neuro-computational
properties
of the cells. For example, when the rest state is
near
a saddle-node bifurcation, the cell can fire all-or-none
spikes
with an arbitrary low frequency, it has a well-defined
threshold
manifold, and it acts as an integrator; i.e., the
higher
the frequency of incoming pulses, the sooner it fires.
In
contrast, when the rest state is near an Andronov-Hopf
bifurcation,
the cell fires in a certain frequency range, its
spikes
are not all-or-none, it does not have a well-defined
threshold
manifold, and it acts as a resonator; i.e., it
responds
preferentially to a certain (resonant) frequency of
the
input. Increasing the input frequency may actually delay
or
terminate its firing.
TUESDAY, September 21, 1999
MATHEMATICAL
BIOLOGY SEMINAR
PSF 208 2:40 p.m.
(Co-sponsor:
Systems Science and Engineering Research Center)
Gregory
D. Smith, Department of Mathematics
"The Buffered Diffusion of Intracellular Ca2+ near an open Ca2+
Channel: Derivation of Second-Order 'Excess Buffer,' 'Rapid
Buffer,' and 'Nearly Immobile Buffer' Approximations."
ABSTRACT:
The 'domain' Ca2+ concentration near an open Ca2+ channel
can
be estimated by obtaining hemispherically symmetric
steady-state
solutions to a reaction-diffusion formulation for the
buffered
diffusion of intracellular Ca2+. After nondimensionalizing
these
equations and scaling space so that both reaction terms and
the
source amplitude are O(1), we identify two dimensionless
parameters
(eps_c and eps_b) that correspond to the scaled mobility
of
dimensionless Ca2+ and buffer, respectively.
Using perturbation methods, we derive second order approximations
for
the Ca2+ and buffer profiles in three asymptotic limits. 1) An
'excess
buffer approximation' (EBA), where the mobility of buffer
exceeds
that of Ca2+ (eps_b >> eps_c), and the fast diffusion of
buffer
toward the Ca2+ channel prevents buffer saturation (cf.
Neher,
1986). 2) A 'rapid buffer approximation' (RBA), where the
diffusivetime
scale for Ca2+ and buffer are comparable, but slow
compared
toreaction [eps_c << 1, eps_b << 1, and epc_c/eps_b = O(1)],
resulting
in saturation of buffer near the Ca2+ channel (cf. Wagner
and
Keizer,1994; Smith, 1996). 3) A recently identified (nearly)
'immobile
buffer approximation' (IBA), where the diffusion of Ca2+
is
fast compared to buffer (eps_c >> eps_b). [In collaboration
with
L Dai, R Miura, and A Sherman].
TUESDAY, September 28, 1999
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Joint
MATHEMATICAL BIOLOGY SEMINAR(Math) and
LSE 106 4:00 p.m.
BIOLOGY SEMINAR(Biology
department)
(Co-sponsors: Systems Science
and Engineering Research Center
and Department of Biology)
James Elser, Department
of Biology
"Biological
Stoichiometry from Genes to Ecosystems"
TUESDAY, October 5, 1999
MATHEMATICAL BIOLOGY SEMINAR
PSF 208 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Mustafa Erdem, Department
of Mathematics
"Pseudo-State
Inhalation Model for Soluble Gases and Vapors"
ABSTRACT: An important issue
arising in the field of toxicology
is the rate at which gases
and vapors are taken up by the body.
We study a physicologically-based
pharmacokinetic model for
which monkeys were the subject.
Gases introduced into the
respiratory cycle are absorbed
in the alveolar region of the
lungs. Furthermore, gases
with a high solubility will also be
absorbed into the tissue
of the conducting airways during
inhalation and desorbed
upon exhalation: this is called a 'wash
in-wash out' effect.
To analyze these processes, a pseudo-state
model is developed. The
absorption of gas is described by an
algebraic expression, which
depends essentially on a function
of H=H(x) modeling the spatial
distribution of the uptake of
the gases.
TUESDAY, October 19, 1999
MATHEMATICAL BIOLOGY SEMINAR
PSF 208 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Philip Sabes, Department
of Chemical/Bio & Materials Engineering
"Planning Object-Based
Eye Movements: Recordings from
Parietal Cortex"
TUESDAY, October 26, 1999
MATHEMATICAL BIOLOGY SEMINAR
PSF 208 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Edward Castaneda, Departmentof
Psychology
"Understanding
Parkinson's Disease: Harnessing Endogenous
Compensatory
Brain Mechanisms and Nudging Recovery of Function
with Genetic
Interventions"
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TUESDAY, November 2, 1999
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MATHEMATICAL BIOLOGY SEMINAR
PSF 208 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Konstantin V. Baev, Division
of Neurological Surgery, Barrow
Neurological Institute
"Principals
of Organization of Biological Neural Networks"
ABSTRACT: Novel conceptual
framework for neurobiology achieved
by the application of control
theory will be presented. This new
paradigm provides unifying
principles for understanding the
functional construction
of the brain. As an example, the
functions of the cortico
- basal ganglia - thalamocortical loops
are analyzed within this
framework. Clinical applications include
an original explanation
of Parkinson's disease and suggested
mechanisms of alleviating
its symptoms by conducting
neurosurgical procedures.
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TUESDAY, November 9,1999
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MATHEMATICAL BIOLOGY SEMINAR
MU 226B (Ventana) 4:00 p.m.
BIOLOGY SEMINAR
John Jungck, Department
of Biology, Benoit College
"Ten Equations
That Changed Biology and Could Change Biology
Education"
ABSTRACT: Mathematics
has played exceptionally important
roles throughout the history
of biology. Too frequently, these
roles have been unappreciated
in biology curricula because
textbook authors assume
that biology students have an
inadequate mathematical
preparation. This practice:
(1) deskills many
biology students, (2) is inconsistent
with our requirements, (3)
misrepresents contemporary
biological research, and,hence,
(4) underprepares students
to read much of the biological
research literature or to
contribute in many areas
of biology. However, the recent
calculus reform movement
has empowered thousands of American
undergraduate biologists
to become proficient in the use of
mathematical software packages
that could be used to
investigate the behavior
of many famous mathematical models
in biology. But where
can they look? There are numerous
recent texts in mathematical
biology, research journals, web
sites, and some advanced
biological texts which are replete
with numerous models.
However, there is a need to identify a
succinct list of achievements
that represent the power of
mathematics in biology.
The BioQUEST Curriculum Consortium has
instantiated many of these
mathematical models in computer
simulations designed to
help students develop long-term
strategies of research.
Hence, ten equations, a brief
description of their historical
importance, and investigative
laboratory activities will
be presented in order to draw
students' and faculty's
attention to a variety of mathematical
models that have been intrinsic
to many of the significant
discoveries in biology in
the twentieth century and which could
provide a foundation for
a more conceptual approach to biology
education.
TUESDAY, November 16, 1999MONDAY,
PET SEMINAR (Mathematical
and Computational Aspects of Neuroimaging)
GWC 302 3:45 p.m.
Allen Kaplan, Director
of Child Neurology, Phoenix Children's
Hospital
"Overview of
Neuroimaging"
ABSTRACT: Historical review,
specific neuroimaging techniques
including ultrosound, computed
tomography (CT), Magnetic Resoance
Imaging (MRI), MR spectroscopy
and especially Positron Emission
Tomography (PET), and the
future of neuroradiology
TUESDAY, November 30, 1999
PET SEMINAR (Mathematical
and Computational Aspects of Neuroimaging)
Room to be announced 4:00 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Michael Miller, Johns Hopkins
University
"Image Understanding,
Deformable Templates, and Computational
Anatomy"
ABSTRACT: We examine
image understanding from the classical
source-channel point of
view of statistical communications. The
space of images corresponding
to the source is a Grenander
deformable template, an
orbit under the group action of
diffeomorphisms of a prototype.
The prior distribution on the
source is induced through
a distribution on the group. The
channel corresponding to
the remote sensor generates the
observable images reflecting
projection and noise which is
statistically modeled via
a conditional probability density,
the likelihood function.
Minimum-risk and MAP estimation are
examined by introducing
a distance between images via a
distance on the group. Examples
are examined, both for finite
and infinite dimensional
groups associated with object
recognition in computer
vision and anatomical shape
representation in Computational
Anatomy
Refreshments will be served at 2:30 p.m. in PSA 206.
Fall, 1997 talks
Spring, 1998 talks,
Fall, 1998
talks
Spring, 1999