Dendritic properties can have substantial effects on the
dynamics of single neurons and the activity in neuronal
networks. For instance, the architecture of the
dendritic tree can alter the firing pattern of a neuronal
oscillator, and dendritic filtering can change the
phase-locking behavior in networks of neuronal
oscillators. From a more basic standpoint, dendritic
properties can affect the firing rates of neuronal
oscillators in response to constant input. Even when
considering passive dendrites, these effects are not as
easy to understand as it might seem. That is, the
dendritic "load" can have surprising effects on a
neuron.s firing frequency. Kepler et al. 1990 found that
coupling a somatic oscillator to a passive neuronal
compartment can sometimes increase or decrease the firing
frequency. However, their explanation was specific to a
two variable piecewise linear relaxation oscillator.
Thus, the general mechanisms by which dendritic
properties affect frequency remain to be clarified.
Primary growth is characterized by cell expansion
facilitated by water uptake generating hydrostatic
(turgor) pressure to inflate the cell, stretching the
rigid cell walls. The multiple source theory of root
growth is based on the proposal that phloem and
protophloem transport water into the growth zone from the
mature tissue higher in the root. Here protophloem water
sources are used as boundary conditions in a generalized
three-dimensional model of growth sustaining water
potentials in primary roots. The model predicts small
radial gradients in water potential, with a significant
longitudinal gradient. The results improve the agreement
of theory with empirical studies for water potential in
the primary growth zone of roots of Zea mays. A
sensitivity analysis quantifies the functional importance
of small root diameter and apical phloem differentiation
in permitting growth under water stress. This
presentation will complete the 4 year presentation series
that I've presented for the RMA and will provide the
conclusion of my thesis work.
In the field of cancer research, proteomic techniques
have been applied to identify and characterize the
protein signatures of human cancer cells and tissues for
patient diagnosis, toxicity monitoring, and therapeutic
intervention. Two-dimensional gel electrophoresis (2DGE)
is a principle technique in proteomics. The objective of
differential analysis of protein expression data
generated by 2DGE is to identify the protein expression
that is changed between biological samples taken under
differing conditions. A case study on the effect to human
cells of combined exposures of low dose arsenic and low
dose ionizing radiation is used to present our
statistical differential analysis, which includes data
preprocessing, analysis of variance, adjustment for
multiple comparisons and chi-square test. Several
statistical methods were compared. ANOVA using empirical
Bayesian estimate of protein-specific variance combined
with pFDR adjustment gave the highest yield of
differential protein expression while minimizing the
false discovery rate.
A circle packing is a configuration of circles with
prescribed tangencies corresponding to a given
triangulation. In fact, given a triangulation, there is a
well-established algorithm for creating its associated
circle packing. In this project, we will describe circle
packings defined by triangulations that arise from
Penrose tilings. Penrose tilings are interesting because,
though lacking translational symmetry, they are highly
ordered through a process known as inflation. This
presentation will describe a gluing process which
explains how the geometry of Penrose tilings is reflected
in the corresponding circle packings at high levels of
inflation.
Population dynamics can drastically affect an
individual.s decision to forage for resources within a
given region or relocate to an area with higher rate of
net energy gain, resulting in higher fitness.
Ecologists have analyzed foraging behavior using
various mathematical models and computer simulations.
Organisms can distribute randomly or make a conscious
choice between two locations by weighing costs and
benefits, with the latter potentially resulting in an
ideal free distribution (IFD). The IFD model predicts
that, at equilibrium, organisms will optimally
distribute themselves in proportion to the net amount
of resources available between a number of locations.
We used a genetic algorithm (GA) simulation to predict
distributions of organisms in two scenarios: one
consisting of a constant return rate and the other with
a variable return rate. The GA served to predict an
optimal foraging strategy regarding distribution
between two patches with differing rates of energy
return over many generations. Experimentally, we
tested our predictions against populations of mallard
ducks (Anas platyrhynchos). We found that fewer ducks
stayed in the high return rate patch relative to the
prediction made by our GA. We hypothesize that ducks in
a wild population, unlike those living within a park,
as was used for our study, would exhibit distributions
more consistent with our predictions.
Anesthetics are believed to modulate activity of a
variety of voltage-gated and ligand-gated ion channels.
However, the exact biophysical mechanisms underlying
anesthesia remain unclear. Recent experimental evidence
suggests that the volatile anesthetic isoflurane targets
the TREK and TASK two-pore potassium conductances and the
persistent sodium conductance (Jinks et al. unpublished
results). Furthermore, recent data indicate that
volatile anesthetics produce immobility, a fundamental
element of anesthesia, predominantly through direct
action at the level of the spinal cord.
A stylized compressed sensing radar is proposed in which
the time-frequency plane is discretized into an N by N
grid. Assuming the number of targets K is small (i.e., K
is much less than N^2), then we can transmit a
sufficiently ``incoherent'' pulse and employ the
techniques of compressed sensing to reconstruct the
target scene. A theoretical upper bound on the sparsity
$K$ is presented. Numerical simulations verify that even
better performance can be achieved in practice. This
novel compressed sensing approach offers great potential
for better resolution over classical radar.
One of the greatest challenges in conservation biology is
assessing the impacts of habitat loss and fragmentation
on population viability. These challenges are especially
relevant to vernal pools, fragmented seasonal wetlands,
because they contain many rare and endemic species.
Although, vernal pools once occupied a large portion of
the California landscape, increasing agricultural and
suburban development has caused habitat loss and
fragmentation. However, there has been no theoretical
framework to guide conservation efforts. Here, we
developed a mathematical model and computer simulations
to describe the population dynamics of an endangered
vernal pool plant. We used analytical techniques to
determine general persistence conditions for the plant
population and used the computer simulations to determine
the effect of the pools’ spatial configuration on the
plant’s population dynamics. The simulation results
suggest that pool size has a larger influence on
population persistence than the distance between pools.
Furthermore, when the total area of pool coverage is
fixed, a landscape consisting of a few large pools
increases the population’s abundance and the likelihood
of persistence more effectively than one with many small
pools.
Convex polyhedra are sets of feasible solutions to linear optimization problems. The graph of a polytope is intimately connected to Dantzig's simplex family of methods for solving linear programs. A simplex pivot rule resolves ambiguities when an iteration of the simplex method presents multiple choices. Bounding the diameters of the graphs of polytopes is particularly interesting since the diameter of the graph is a lower bound on the number of iterations required for the simplex method using any pivot rule. The Hirsch Conjecture asserts that the diameter of polytope has a linear upper bound.
To probe this issue further, we model a neuron as a thin
passive dendritic cable attached to an isopotential
somatic oscillator, i.e. a "ball and stick" model. We
then use the theory of weakly perturbed oscillators to
derive an equation for the change in frequency of the
oscillator due to the perturbation resulting from the
presence of the dendrite. Intuitively, if the reversal
potential of the dendrite is lower (higher) than the
average voltage of the somatic oscillations, then the
firing frequency of the somatic oscillator will decrease
(increase) as the radius of the dendrite increases. We
show that this is indeed the case when the phase response
curve of the somatic oscillator has a positive average
value. However, when the average value of the phase
response curve is negative, our equation shows that the
intuitive prediction described above would be reversed:
the firing frequency of the oscillator increases as the
radius of the dendrite increases (at least initially).
Curiously, for values of the dendritic reversal potential
close to the average voltage of the somatic oscillations,
there is a non-monotonic dependence of the firing
frequency on the dendritic radius. We confirm these
results using direct numerical simulations.
Our results show that the addition of a passive dendrite
to a neuronal oscillator can sometimes have
counter-intuitive effects on firing frequency.
Furthermore, we show that these results can be understood
in terms of the somatic oscillator.s phase response curve.
Modeling the Hydraulics of Root Growth in Three-Dimensions with Internal Water Sources
Brandy Wiegers, Angela Y. Cheer, Wendy K. Silk
Proteomic Aanalysis by 2-D PAGE for Response to Low Dose Ionizing Radiation and Arsenic Exposure
Dan Li, Susanne R. Berglund, Alison Santana, Zelanna Goldberg
Circle Packings and Penrose Tilings
Matthew Stamps
Distribution Modeling of Anas platyrhynchos Under Ideal Free and Variable Conditions
Matthew Reed, Dai-Ying Wu, Andy Huang
Co-authors (in alphabetical order): Tania Gonzalez,
Andy Huang, Mary Jacklin, Michelle Jensen, Christopher
Mosser, Matthew Reed, Tushar Rawat, Daniel Suderow,
Dai-Ying Wu
Faculty Advisors:
Carole Hom
Richard McElreath
Andy Sih
Mathematical Modeling of Isoflurane Action on Lamprey Spinal Neurons
Tamara J Schlichter, Anne C Smith, Steven L Jinks, Timothy J Lewis
We use mathematical modeling and experiments on the
lamprey spinal cord to study the effects of isoflurane on
neuronal activity. Our experimental results on the
disinhibited spinal cord preparation suggest that the
excitatory interneurons of the CPG are the main target of
isoflurane. As the anesthetic concentration increases,
ventral root activity (assumed to be representative of
the activity of spinal cord excitatory interneurons)
transitions from bursting to silent. However, in some
animals the activity transitions directly from bursting
to silent where in others it transitions from bursting to
a brief period of tonic firing before falling silent.
We incorporate the anesthetic-sensitive TREK, TASK and
persistent sodium conductances into a preexisting
detailed biophysical model of the lamprey excitatory
interneuron, and a canonical bursting model. We then
perform a thorough bifurcation analysis on these models.
Our results suggest that the anesthetic effects of TREK,
TASK and persistent sodium currents alone are sufficient
to account for the transition from bursting to silent,
but are not sufficient to account for a robust transition
from bursting to tonic to silent.
High-Resolution Radar via Compressed Sensing
Matthew Herman, Thomas Strohmer
The Population Dynamics of a Vernal Pool Plant: The Effect of Habitat Fragmentation and Restoration on Population Persistence and Abundance
Matthew Holden, Lauren Lui, Motoki Wu, Margot Wood, Vivian Tang, Shabnam Yekta, Pak Kwong
Multi-index Transportation Polytopes
Edward Kim, Jesứs De Loera, Shmuel Onn, Francisco Santos
In this poster, we consider the graphs of multi-index transportation polytpes. Transportation polytopes are well-known objects in operations research and mathematical programming. We discuss a computer implementation to systematically enumerate all combinatorial types of non-degenerate multi-index transportation polytopes. Our exhaustive lists helped us answer some conjectures of Yemelichev et al. (1984). We give a quadratic upper bound for the diameter of the one-skeleton graph for triply-indexed axial transportation polytopes.