**REPORT 0405-1: **
Effectiveness of numerical techniques for calculating the quantity of calcium
ion species during calcium sparksin heart muscle

D. A. Lott,
M. Li and
J. R. Berlin

An efficient numerical algorithm based on the convolution of functions and on
finite difference approximations for the diffusion equation is utilized to
determine the quantity of calcium ionsparticipating in unitary calcium ions
release events, termed "calcium ions sparks," in heart muscle. Output images of
localized increases in cytosolic calcium ion concentration, due predominantly to
calcium ions release from intracellular storage sites, are obtained using
fluorescent calcium indicators and confocal microscopy. To obtain the quantity
of calcium ions underlying these localized increases of cytosolic calcium ion
concentration, one-dimensional output images are deconvolved with a point spread
function that describes the optical properties of the microscope. The resulting
input image is then reconstructed assuming symmetry, in a three-dimensional
image of calcium ion concentration and all calcium ion-bound species. Temporal
information about

free and bound calcium ions species can be obtained by performing convolutions
on a series of output images recorded in time and then accounting for the
kinetics of calcium ions interactions with the fluorescent calcium indicator and
other calcium ion binding species. The effect of microscope imaging properties
on

measurements of local calcium ion concentration and the ability to reconstruct
the underlying changes in calcium ions species during a calcium ions spark are
presented.

**REPORT 0405-2: ** Time delay
and amplitude estimation in underwater acoustics: a Gibbs Sampling approach

Zoi-Heleni Michalopoulou and
Michele Picarelli

Multipath arrivals of a signal at a receiving sensor are frequently encountered
in many areas of signal processing, including sonar, radar, and communication
problems. In underwater acoustics, numerous approaches to source localization,
geoacoustic inversion, and tomography rely on accurate multipath arrival
extraction. In this work, a novel method for estimation of time delays and
amplitudes of arrivals with Maximum A Posteriori (MAP) estimation is presented.
MAP estimation is optimal if appropriate statistical models are selected for the
received data; implementation, requiring maximization of a multi-dimensional
function, is computationally demanding. Gibbs Sampling is proposed as an
efficient means for estimating the necessary posterior probability
distributions, bypassing analytical calculations. The Gibbs Sampler estimates
posterior distributions through an iterative process and includes as unknowns
noise variance and number of arrivals as well as time delays and amplitudes of
multipaths. Through Monte Carlo simulations, the method is shown to have a
performance very close to that of analytical MAP estimation. The method is shown
to be superior to Expectation-Maximization, which is often applied to time delay
estimation. The Gibbs Sampling - MAP approach is demonstrated to be more
informative than other time delay and amplitude estimation methods, providing
complete posterior probability distributions compared to just point estimates;
the probability distributions illustrate the uncertainty in the problem,
presenting likely values of the unknowns that are different from simple point
estimates.

**REPORT 0405-3:**
Existence of traveling wave solutions for Ginzburg-Landau-type problems in
infinite cylinder

M. Lucia,
C. B. Muratov and
M. Novaga

We study a class of systems of reaction-diffusion equations in infinite
cylinders. These systems of equations arise within the context of Ginzburg-Landau
theories and describe the kinetics of phase transformation in second-order or
weakly first-order phase transitions with non-conserved order parameter. We use
a novel variational characterization to study existence of traveling wave
solutions under very general assumptions on the nonlinearities. These solutions
are a special class of the traveling wave solutions which are characterized by a
fast exponential decay in the direction of propagation. Our main result is a
simple verifiable criterion for existence of these traveling waves. We also
prove boundedness, regularity, and some other properties of the obtained
solutions, as well as several sufficient conditions for existence or
non-existence of such traveling waves, and give rigorous upper and lower bounds
for their speed. In addition, we prove that the speed of the obtained solutions
gives a sharp upper bound for the propagation speed of a class of disturbances
which are initially sufficiently localized. We give a sample application of our
results using a computer-assisted approach.

**REPORT 0405-4:**
On undercompressive shocks and flooding in countercurrent two-layer flows

T. M. Segin,
B. S. Tilley and
L. Kondic

We consider the countercurrent flow of two incompressible immiscible viscous
fluids in an inclined channel. This configuration may lead to the phenomena of
"flooding", i.e. the transition from a countercurrent regime to a cocurrent
regime. This transition is marked by a variety of transient behavior, such as
the development of large-amplitude waves that impede the flow of one of the
fluids to the reversal of the flow of the denser fluid. From a lubrication
approximation based on the ratio of the channel height to the downstream
disturbance wavelength, we derive a nonlinear system of evolution equations that
govern the interfacial shape separating the two fluids and the leading-order
pressure. This system, which assumes fluids with disparate density and dynamic
viscosity ratios, includes the effects of viscosity stratification, inertia,
shear, and capillarity. Since the experimental constraints for this effective
system are unclear, we consider two ways to drive the flow: either by fixing the
volumetric flow rate of the gas phase or by fixing the total pressure drop over
a downstream length of the channel. The latter forcing results in a single
evolution equation whose dynamics depends nonlocally on the interfacial shape.
From both of these driven systems, admissible criteria for Lax shocks,
undercompressive shocks and rarefaction waves are investigated. Interestingly,
these criteria, through a numerical verification, do not depend significantly on
the inertial effects within the more dense layer. The choice of the local/nonlocal
constraints appears to play a role in the transient growth of undercompressive
shocks, and may relate to the phenomena observed near the onset of flooding.

**REPORT 0405-5:**
Bursting in 2-compartment neurons: A case study of the Pinsky-Rinzel model

Amitabha Bose and
Victoria Booth

The two-compartment Pinsky-Rinzel model of a hippocampal CA3pyramidal neuron
consists of electrically coupled soma and dendritic compartments, each with
active ionic conductances. This model has been widely used in a variety of
contexts, but little analysis has been performed on its bursting solutions. In
this chapter, we provide a geometric framework to study the Pinsky-Rinzel model.

Using a combination of analysis and simulations, we identify neuronal mechanisms
responsible for certain salient features of the model such as burst initiation
and somatic-dendritic ping-pong.

Some of these mechanisms are then demonstrated in a conceptually simpler,
two-compartment Morris-Lecar model.

**REPORT 0405-6:** On the
Blaschke Conjecture for 3-Webs

Vladislav V. Goldberg and Valentin V. Lychagin

We find relative differential invariants of orders eight and nine for a planar
nonparallelizable 3-web such that their vanishing is necessary and sufficient
for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs.
As a side result, we show that the number of linearizations in the Gronwall
conjecture does not exceed fifteen and give criteria for rigidity of 3-webs.

**REPORT 0405-7:** A
computational model of electrically coupled, intrinsically distinct pacemaker
neurons

Cristina Soto-Treviņo, Pascale Rabbah, Eve Marder and Farzan Nadim

Electrical coupling between neurons with similar properties is often studied.
Nonetheless, the role of electrical coupling between neurons with widely
different intrinsic properties also occurs, but is less well-understood.
Inspired by the pacemaker group of the crustacean pyloric network, we developed
a multi-compartment, conductance-based model of a small network of intrinsically
distinct, electrically coupled neurons. In the pyloric network, a small
intrinsically bursting neuron, through gap-junctions, drives two larger,
tonically spiking neurons to reliably burst in-phase with it. Each model neuron
has two compartments, one responsible for spike-generation and the other for
producing a slow, large amplitude oscillation. We illustrate how these
compartments interact, and determine the dynamics of the model neurons. Our
model captures the dynamic oscillation range measured from the isolated and
coupled biological neurons. At the network level, we explore the range of
coupling strengths for which synchronous bursting oscillations are possible.
The spatial segregation of ionic currents significantly enhances the ability of
the two neurons to burst synchronously, and the oscillation range of the model
pacemaker network depends not only on the strength of the electrical synapse but
also on the identity of the neuron receiving inputs. We also compare the
activity of the electrically coupled, distinct neurons with that of a network of
coupled identical bursting neurons. For small to moderate coupling strengths,
the network of identical elements, when receiving asymmetrical inputs, can have
a smaller dynamic range of oscillation than that of its constituent neurons in
isolation.

**REPORT 0405-8:** Effect of
electrical coupling on ionic current and synaptic potential measurements

Pascale Rabbah, Jorge Golowasch and Farzan Nadim

Recent studies have found electrical coupling to be more ubiquitous than
previously thought, and coupling through gap junctions is known to play a
crucial role in neuronal function and network output. In particular, current
spread through gap junctions may affect the activation of voltage-dependent
conductances as well as chemical synaptic release. Using voltage-clamp
recordings of two strongly electrically coupled neurons of the lobster
stomatogastric ganglion and conductance-based models of these neurons, we
identified effects of electrical coupling on the measurement of leak and
voltage-gated outward currents, as well as synaptic potentials. Experimental
measurements showed that both leak and voltage-gated outward currents are
recruited via gap junctions from neurons coupled to the clamped cell.
Nevertheless, in spite of the strong coupling between these neurons (~23%), the
errors made in estimating voltage-gated conductance parameters were relatively
minor (<10%). Thus, in many cases isolation of coupled neurons may not be
required if a small degree of measurement error of the voltage-gated currents or
the synaptic potentials is acceptable.

Modeling results show, however, that such errors may be as high as 20% if the
gap junction position is near the recording site or as high as 90% when
measuring smaller voltage-gated ionic currents. Paradoxically, improved space
clamp increases the errors due to electrical coupling because voltage control
across gap junctions is poor for even the highest realistic coupling
conductances.

Furthermore, the common procedure of leak subtraction can add an extra error to
the conductance measurement, the sign of which depends on the maximal
conductance.

**REPORT 0405-9:**
Target-specific short-term dynamics are important for the function of synapses
in an oscillatory neural network.

Akira Mamiya and Farzan Nadim

Short-term dynamics such as facilitation and depression are present in most
synapses and are often target-specific, even for synapses from the same type of
neuron. We examine the dynamics and possible functions of two synapses from the
same presynaptic neuron in the rhythmically active pyloric network of the spiny
lobster. Using simultaneous recordings, we show that the synapses from the
lateral pyloric (LP) neuron to the pyloric dilator (PD) and the pyloric
constrictor (PY) neurons both show short-term depression. However, the
postsynaptic potentials produced by the LP to PD synapse are larger in
amplitude, depress less and recover faster than those produced by the LP to PY
synapse. We show that the synapse from the LP neuron to the PD neuron, the
latter a member of the pyloric pacemaker ensemble, functions to slow down the
pyloric rhythm when it is fast and to speed it up when it is slow. In contrast,
the synapse from the LP neuron to the PY neuron functions to delay the activity
phase of the PY neuron at all cycle periods. Using a computational model of the
pyloric network, we show that the short-term dynamics of synaptic depression
observed for each of these synapses are tailored to their individual functions
and that replacing the dynamics of either synapse with the other would disrupt
these functions.

Together, the experimental and modeling results suggest that the target-specific
features of short-term synaptic depression are functionally important for
synapses efferent from the same presynaptic neuron.

**REPORT 0405-10:** Postural
Stability Index is a More Valid Measure of Stability Than Equilibrium Score

Hans Chaudhry, Thomas Findley, Karen S. Quigley, Zhiming Ji, Miriam Maney,
Tiffany Sims, Bruce Bukiet, and Richard Foulds

Researchers, therapists and physicians often use Equilibrium Score (ES) from the
Sensory Organization Test (SOT), a key test in the NeuroCom dynamic
posturography system, to assess stability. ES reflects the overall coordination
of the visual, proprioceptive, and vestibular systems for maintaining standing
posture. In our earlier paper, we proposed a new measure of postural stability,
the Postural Stability Index (PSI), which takes into account more biomechanical
aspects than ES. In that paper, it was shown that PSI provides a clinically
important adjunct to ES. In this paper, we show that PSI can provide an
acceptable index even if a person falls during the trial, whereas ES assigns a
zero score for any fall.

We also show that PSI is more closely related to ankle stiffness than ES, which
is generally recognized as in indicator of postural stability. These results
suggest that PSI is a more valid measure of stability than ES.

**REPORT 0405-11:**
Relationship Among Postural Stability, Weight, Height and Moment of Inertia of
Normal Adults

Hans Chaudhry, Thomas Findley, Zhiming Ji, Bruce Bukiet, Richard Foulds, and
Miriam Maney

Using the definition of postural stability index (PSI) developed by the authors
in their earlier work, and the experimental results on 22 normal adults
employing the Neurocom Equitest device, we demonstrate in this paper, that there
is little correlation among postural stability, weight, height, the product of
weight and height, and moment of inertia of a subject about the ankle joint.
However, we observe, that there is a slight tendency for PSI and therefore
stability to decrease as the height increases.

**REPORT 0405-12**: The
effects of varying the timing of inputs on a conditional oscillator

Christina Ambrosio, Farzan Nadim, Amitabha Bose

A conditional oscillator is one that requires input to oscillate. An example of
such is the gastric mill network of the stomatogastric ganglion of the crab
Cancer borealis which requires a modulatory input from outside the
stomatogastric ganglion and input from the pyloric network of the animal in
order to oscillate.

Here we study how the frequency of the gastric mill network is determined when
it is receives rhythmic input from two different sources but where the timing of
these inputs may differ. We find that over a certain range of the time
difference one of the two rhythmic inputs plays no role what so ever in
determining the network frequency, while in another range, both inputs work
together to determine the frequency. The existence and stability of periodic
solutions to model sets of equations are obtained analytically using geometric
singular perturbation theory. The results are validated through numerical
simulations. Comparisons to experiments are also presented.

**REPORT 0405-13:** Predictive
Inference for Future Responses Given a Doubly Censored Sample from a Two
Parameter Exponential Distribution

Hafiz M. R. Khan, M. Safiul Haq, and Serge B. Provost

In this paper, we derive the predictive distributions of one and several future
responses including their average, on the basis of a type II doubly censored
sample from a two parameter exponential life testing model. We also determine
the highest predictive density interval for a future response. A numerical
example is provided to illustrate the results.

**REPORT 0405-14:** Predictive
Inference for Future Responses from Two Component Systems

Hafiz M. R. Khan, M. Safiul Haq, and Serge B. Provost

Predictive distributions for bivariate future responses are derived for systems
whose components are connected in parallel or in series under the assumption
that the lifetimes of the components are exponentially distributed. The
predictive reliability, moment generating and hazard rate functions are derived
for the former case. Illustrative examples are provided for each type of system.

**REPORT 0405-15:** Matching
reflectances for the estimation of inherent optical properties

Zoi-Heleni Michalopoulou, Sima Bagheri, Lisa Axe

A novel approach based on an analytical bio-optical model is developed for the
retrieval of Inherent Optical Properties, from which the water quality
constituent concentrations can be obtained. The proposed method generates
synthetic (sub)surface irradiance reflectances (R(0)) for different values of
the unknown parameters and matches them to the measured reflectances; the values
of the parameters that generate the best match are taken to be the parameter
estimates. Through Monte Carlo simulations the method is shown to be superior to
linear matrix inversion, consistently producing estimates very close to the true
values of absorption and backscattering.

**REPORT 0405-16:** Vector-soliton
collision dynamics in nonlinear optical fibers

Roy H. Goodman and Richard Haberman

We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schrodinger equations. We study a
low-dimensional model system of Hamiltonian ordinary differential equations (ODEs)
derived by Ueda and Kath and also studied by Tan and Yang. We derive a further
simplified model which has similar dynamics but is more amenable to analysis.
Sufficiently fast solitons move by each other without much interaction, but
below a critical velocity the solitons may be captured. In certain bands of
initial velocities the solitons are initially captured, but separate after
passing each other twice, a phenomenon known as the two-bounce or two-pass
resonance. We derive an analytic formula for the critical velocity. Using
matched asymptotic expansions for separatrix crossing, we determine the location
of these resonance windows. Numerical simulations of the ODE models show they
compare quite well with the asymptotic theory.

**REPORT 0405-17:** Bayesian
prediction for the log-normal model under Type II censoring

Hafiz M. R. Khan, M. Safiul Haq, and Serge B. Provost

Given a Type II censored sample and a Type II `median censored' sample from the
two parameter log-normal distribution, we have derived the predictive
distribution of future responses assuming a non-informative prior as well as an
informative prior distribution for the parameters. We have also obtained various
types of estimates of reliability functions. A numerical example illustrates the
results.

**REPORT 0405-18:** Strong
Versions of the DFR Property

M.C. Bhattacharjee

This paper investigates two distinct subclasses of DFR distributions that
exhibit strong forms of anti-aging behavior. Our results characterize such
distributions through several representation theorems and consider associated
consequences such as closure properties and reliability bounds for distributions
which are DFR in the strong sense considered. The usefulness and prevalence of
strong DFR properties are illustrated by examples and several applications.

**REPORT 0405-19:** A
simulation study of a Bayesian Hierarchical Changepoint Model with Covariates

Wonsuk Yoo and Elizabeth H. Slate

This paper presents a simulation study to investigate the behavior of estimates
of covariate effects in a Bayesian hierarchical changepoint model. The model is
a segmented linear regression model with one changepoint within a fully Bayesian
framework. We introduce covariate effects into the model in three ways: as an
affect on the interaction term, an affect on the slope after the changepoint, or
as an affect on the timing of the changepoint. We estimate all parameters using
Markov chain Monte Carlo and compute bias, relative bias and average mean square
error of the posterior means of the parameters capturing the covariate effects.
We also investigate the effects of model misspecification on the characteristics
of the effect of using an inappropriate fitted model.

**REPORT 0405-20:**
Hyperpolarizabilities for the one-dimensional infinite single-electron periodic
systems: I. Analytical solutions under dipole-dipole correlations

Shidong Jiang and Minzhong Xu

The analytical solutions for the general-four-wave-mixing hyperpolarizabilities
on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki
models of trans-polyacetylene are obtained through the scheme of dipole-dipole
correlation. Analytical expressions of DC Kerr effect, DC-induced second
harmonic generation, optical Kerr effect and DC-electric-field-induced optical
rectification are derived. By including or excluding the gradient terms in the
calculations, comparisons show that the intraband contributions dominate the
hyperpolarizabilities if they are included. The intraband transition leads to
the break of the overall permutation symmetry in hyperpolarizabilities even for
the low frequency and non-resonant regions. Hence it breaks the Kleinman
symmetry that is directly based on the overall permutation symmetry. Our
calculations provide a clear understanding of the Kleinman symmetry breaks that
are widely observed in many experiments. Finally, we also suggest a feasible
experiment on hyperpolarizabilities to test the validity of overall permutation
symmetry and our theoretical prediction.

**REPORT 0405-21:**
Hyperpolarizabilities for the one-dimensional infinite single-electron periodic
systems: II. Dipole-dipole versus current-current correlations

Minzhong Xu and Shidong Jiang

Based on Takayama-Lin-Liu-Maki model, analytical expressions for the
third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical
Kerr effect, optical Kerr effect or intensity-dependent index of refraction and
DC-electric-field-induced optical rectification are derived under the static
current-current correlation for one-dimensional infinite chains. The results of
hyperpolarizabilities under the current-current correlation are then compared
with those obtained using the dipole-dipole correlation. The comparison shows
that the conventional current-current correlation, albeit quite successful for
the linear case, is incorrect for studying the nonlinear optical properties of
periodic systems.

**REPORT 0405-22:** Breaking of
the overall permutation symmetry in nonlinear optical susceptibilities of
periodic systems

Minzhong Xu and Shidong Jiang

Abstract:

Based on infinite one-dimensional periodic chain models (Su-Shrieffer-Heeger and
Takayama-Lin-Liu-Maki) of trans-polyacetylene, we show analytically that the
overall permutation symmetry of nonlinear optical susceptibilities is, albeit
preserved in the molecular systems with only bound states, no longer generally
held for the periodic systems. Hence it breaks the Kleinman symmetry in the
off-resonant regions. Our theory qualitatively explain the widely observed
deviations of Kleinman symmetry in experiments. New nonlinear optical
experiments are proposed to verify the overall symmetry break.

**REPORT 0405-23:** Preclinical
Cardiac Safety Assessment of Pharmaceutical Compounds Using an Integrated
Systems-Based Computer Model of the Heart

Dean Bottino, Chrstian Penland, Andrew Stamps, Martin Traebert, Berengere
Dumotier, Anna Georgieva, Gabriel Helmlinger and Scott Lett

Blockade of the delayed rectifier potassium channel current,IKr, has been
associated with drug-induced QT prolongation in the ECG and life-threatening
cardiac arrythmias. However, it is increasingly clear that compound-induced
interactions with multiple cardiac ion channels may significantly affect QT
prolongation that would result from inhibition of only IKr (Redfern, Carlsson et
al, 2003). Such an assessment may not be feasible in vitro, due to
multi-factorial processes that are also time-dependent and highly non-linear.
Limited preclinical data, IKr hERG assay and canine Purkinje fiber action
potentials (Gintant, Limberis et al. 2001), were used for two test compounds in
a systems-based modeling platform of cardiac electrophysiology (Muzikant and
Penland 2002) to (i) convert a canine myocyte model to a Purkinje fiber model by
training functional current parameters to the action potential data; (ii)
reverse-engineer the compounds’ effects on five channel currents other than IKr,
predicting significant IC50 values for INa+,sustained and ICa2+, L-type , which
were subsequently experimentally validated; (iii) ICa2+use the predicted (INa+,sustained
and ICa2+, L-type) and measured (IKr) IC50 values to simulate dose-dependent
effects of the compounds on action potentials in Endo-, M-, and Epi-cardiac
ventricular cells; and (iv) integrate the three types of cellular responses into
a tissue-level spatial model, which quantifiably predicted no potential for the
test compounds to induce either QT prolongation or increased transmural
dispersion of repolarization in a dose-dependent and reverse rate-dependent
fashion, despite their inhibition of IKr in vitro.

**REPORT 0405-24:** Some
generalizations of the First Fredholm Theorem to Hammerstein Equations and the
Number of Solutions

P.S. Milojevic

We prove some generalizations of the First Fredholm theorem for Hammerstein
operator equations in Banach spaces and study the number of their solutions
using a projection like method. The linear part is assumed to be either
selfadjoint or nonselfadjoint while the nonlinearities are such that the
corresponding map is ( pseudo) approximation proper. In particular, the
nonlinearities can be either of monotone type, or of type (S+), or condensing,
or the sum of such maps.

**REPORT 0405-25:** The "exact"
confidence limits for unknown probability in Bernoulli models.

R.I. Andrushkiw, D.A. Klyushin, Yu.I. Petunin and M.Yu. Savkina,

The application of mathematical-statistical models in medical diagnostics often
requires the construction of an "exact" confidence interval for the unknown
probability p of success in Bernoulli models (so called binomial proportion, or
proportion of population). This problem was considered in a number of papers
(for example, see [1-5] and references cited). The web-site BioMed Central gives
more than 200 citations devoted to this theme. The purpose of our paper is to
construct an "exact" confidence interval for unknown probability p of success in
classical and generalized Bernoulli models.

**REPORT 0405-26:** An Embedded
Network Approach for Scale-Up of Fluctuation-driven Systems with Preservation of
Spike Information

David Cai, Louis Tao and David McLaughlin

To address computational "scale-up" issues in modeling of large regions of the
cortex, many coarse-graining procedures have been invoked to obtain effective
descriptions of neuronal network dynamics. However, because of local averaging
in space and time, these methods do not contain detailed spike information, and,
thus, cannot be used to investigate, e.g., cortical mechanisms which are encoded
through detailed spike-timing patterns. To retain spike information, we develop
a hybrid theoretical framework which embeds a sub-network of point neurons
within, and fully interacting with, a coarse-grained network of dynamical
background. We employ our newly developed kinetic theory for the description of
the coarse-grained background, in combination of a Poisson spike reconstruction
procedure to ensure that our method works for the fluctuation-driven regime as
well as the mean-driven regime. This embedded network approach is verified to be
dynamically accurate and numerically efficient. As an example, we use this
embedded representation to construct "reverse-time correlations" as
spiked-triggered averages in a ring model of orientation tuning dynamics.

**REPORT 0405-27:** Orientation
Selectivity in Visual Cortex by Fluctuation-Controlled Criticality

Louis Tao, David Cai, David McLaughlin, Robert Shapley and Michael Shelley

We examine how synaptic fluctuations modify the effects of strong recurrent
network amplification to produce orientation selectivity in a large-scale
neuronal network model of the macaque primary visual cortex. Previously, we
showed that the model reproduces many of the experimentally observed properties
of simple and complex cells, through a balance between feedforward and recurrent
excitation. However, strong cortical amplification leads to network
instabilities, unrealistically high firing rates and complex cells that are not
orientation selective, even in the presence of strong cortical inhibition. In
this paper, we show that large fluctuations in the cortico-cortical conductances
can stabilize the network, allowing strong cortical gain and the emergence of
orientation selective complex cells. By increasing the strength of synaptic
fluctuations, say, through sparsifying the network connectivity, we identify a
transition between two types of dynamics, mean- and fluctuation-driven. In a
network with strong recurrent excitation, this fluctuation-controlled transition
is signified by a near hysteretic behavior and a rapid rise of network firing
rates as the synaptic drive or stimulus input is increased. We discuss the
connection between this transition and orientation selectivity in our model of
primary visual cortex.

**REPORT 0405-28:** Stratified
Kolmogorov flow. Part 2.

N. J. Balmforth and Y.-N. Young

Forced stratified flows are shown to suffer two types of linear long-wave
instability: a 'viscous'

instability which is related to the classical instability of Kolmogorov flow,
and a 'conductive instability', with the form of a large-scale, negative thermal
diffusion. The nonlinear dynamics of both instabilities is explored with weakly
nonlinear theory and numerical computations. The introduction of stratification
arises with stronger stratification and creates a prominent staircase in the
buoyancy field; the steps of the staircase evolve over long timescales by
approaching one another, colliding and merging (coarsening the staircase).

**REPORT 0405-29:**
Registration-based morphing of active contours for segmentation of CT scans

Y.-N. Young and D. Levy

We present a new algorithm for segmenting organs in CT scans for radiotherapy
treatment planning. Given a contour of an organ that is segmented in one image,
our algorithm proceeds to segment contours that identify the same organ in the
consecutive images. Our technique combines partial differential equations-based
morphing active contours with algorithms for joint segmentation and
registration. The coupling between these different techniques is done in order
to deal with the complexity of segmenting ``real" images, where boundaries are
not always well defined, and the initial contour is not an isophote of the
image.

**REPORT 0405-30:** Long-wave
linear stability theory for two-fluid channel flow

Tetyana M. Segin, Lou Kondic and Burt S. Tilley

We present the linear stability of the laminar flow of an immiscible system of a
compressible gas and incompressible liquid separated by an interface with large
surface tension in a thin inclined channel. The flow is driven by an applied
pressure drop and gravity. Following the air-water case, which is found in a
variety of engineering systems, the ratio of the characteristic values of the
gas and liquid densities and viscosities are assumed to be disparate. Under
lubrication approximation, and assuming ideal gas behavior and isothermal
conditions, this approach leads to a coupled nonlinear system of partial
differential equations describing the evolution of the interface between the gas
and the liquid and the streamwise density distribution of the gas. This system
also includes the effects of viscosity stratification, inertia, shear, and
capillarity. A linear stability analysis that allows for physically relevant
nonzero pressure-drop base state is then performed. In contrast to zero-pressure
drop case which is amenable to the classical normal-mode approach, this
configuration requires solving numerically a nonautonomous boundary-value
problem for the gas density and interfacial deviations from the base state in
the streamwise coordinate. We find that the effect of gas compressibility on the
interfacial stability in the limit of vanishingly small wavenumber is
destabilizing, even for Stokes flow in the liquid. However, for finite
wavenumber disturbances, compressibility may have stabilizing effects. In this
regime, sufficient shear is required to destabilize the flow.

**REPORT 0405-31:** Velocity
Profiles in Repulsive Athermal Systems under Shear

Ning Xu, Corey S. O'Hern and Lou Kondic

We conduct molecular dynamics simulations of athermal systems undergoing
boundary-driven planar shear flow in two and three spatial dimensions. We find
that these systems possess nonlinear mean velocity profiles when the velocity
$u$ of the shearing wall exceeds a critical value $u_c$. Above $u_c$, we also
show that the packing fraction and mean-square velocity profiles become
spatially-dependent with dilation and enhanced velocity fluctuations near the
moving boundary. In systems with overdamped dynamics, $u_c$ is only weakly
dependent on packing fraction $\phi$. However, in systems with underdamped
dynamics, $u_c$ is set by the speed of shear waves in the material and tends to
zero as $\phi$ approaches $\phi_c$. In the small damping limit, $\phi_c$
approaches values for random close-packing obtained in systems at zero
temperature. For underdamped systems with $\phi<\phi_c$, $u_c$ is zero and thus
they possess nonlinear velocity profiles at any nonzero boundary velocity.

**REPORT 0405-32:** Dopamine
Modulation of Phasing of Activity in a Rhythmic Motor Network: Contribution of
Synaptic and Intrinsic Modulatory Actions

Bruce R. Johnson, Lauren Schneider, Farzan Nadim, Ronald M. Harris-Warrick

The phasing of neuronal activity in a rhythmic motor network is determined by a
neuron's intrinsic firing properties and synaptic inputs; these could vary in
their relative importance under different modulatory conditions. In the lobster
pyloric network, the firing of eight follower PY neurons is shaped by their
intrinsic rebound after pacemaker inhibition and by synaptic input from the LP
neuron, which inhibits all PY neurons and is electrically coupled to a subset of
them. Under control conditions, LP inhibition is weak and has little influence
on PY firing. We examined modulation that could theoretically enhance the LP's
synaptic contribution to PY firing. We measured the effects of dopamine (DA) on
LPaPY synapses, driving the LP neuron with trains of realistic waveforms
constructed from prerecorded control and DA LP oscillations, which differed in
shape and duration. Under control conditions, chemical inhibition underwent
severe depression and disappeared; in the mixed synapses, electrical coupling
dominated. Switching between control and DA LP waveforms (with or without DA
present) caused only subtle changes in synaptic transmission. DA markedly
enhanced synaptic inhibition, reduced synaptic depression and weakened
electrical coupling, reversing the sign of the mixed synapses. Despite this,
removal of the LP from the intact network still had only weak effects on PY
firing. DA also enhances PY intrinsic rebound properties, which still control
the onset of PY firing. Thus, in a rhythmic network, the functional importance
of synaptic modulation can only be understood in the context of parallel
modulation of intrinsic properties.

**REPORT 0405-33:** Integrated
Data Analysis for Genotyping Microarrays

Kai Zhang, Marc Q. Ma, Hui-Yun Wang, Yu Wang, Frank Shih

We present TIMDA (a Toolkit for Integrated Microarray Data Analysis), a Matlab-based
software framework designed for spotted single nucleotide polymorphism (SNP)
genotyping microarray data analysis. TIMDA features seamlessly integration of
numerical computation, analysis, visualization and algorithms as well as
excellent extensibility and maintainability. The framework consists of modules
designed for image processing, intermediate data conversion, genotype calling,
and loss-of-heterozygosity (LOH) study with text or graphics output. Each of
these modules can work smoothly with others or independently from each other.
Meanwhile, data from other software also can be integrated into TIMDA.

**REPORT 0405-34:** Modeling
and Simulation of Soluble Guanylyl Cyclase

Yu Wang, Kentaro Sugino, Marc Q. Ma, Annie V. Beuve

Soluble guanylyl cyclase (sGC) is a heterodimeric enzyme that catalyzes the
formation of cGMP from GTP. The mechanisms regulating the catalytic activity of
sGC still remain unclear despite extensive experimental studies. We detail the
steps used in homology modeling for constructing the 3D structure of sGC's
catalytic core region. Many homology-based models are obtained, and their
quality is evaluated using various programs including PROCHECK. Based on our
homology models, we perform classical molecular dynamics (MD) simulations to
study the conformational changes of the protein complex during the allosteric
regulation, and a tentative mechanism is established, which can be used to guide
the screening and design of new vasodilation drugs.

**REPORT 0405-35:** Variable
Selection of a Bayesian hierarchical changepoint Model for longitudinal
biomarkers of Prostate Cancer

Wonsuk Yoo, Elizabeth H. Slate

Prostate specific antigen (PSA) is a common biomarker used to aid detection of
prostate cancer (PCa). This research aims to develop and implement models for
longitudinal biomarkers for prostate cancer, and to use these models to develop
a diagnostic rule for early detection. We generalize a fully Bayesian
hierarchical changepoint model, similar to that proposed by Slate and Clark
(1999), by incorporating risk factors for prostate cancer as covariates. The
changepoint, which is specific to each individual, represents the age of PCa
onset. Our model permits the covariates to affect an individual's PSA three
ways: the overall level, the age at which cancer initiates (changepoint), and
the growth rate following the changepoint. We use Markov chain Monte Carlo (MCMC)
to estimate all model parameters, including, especially, the subject-specific
changepoints. Using data obtained from the Nutritional Prevention of Cancer
Trial (Clark et al, 1996), we investigate the effects of smoking status, alcohol
consumption and body mass index (BMI) on PSA growth. Moreover, we consider
whether PSA velocity varies with the stage of prostate cancer at diagnosis.

We select the most useful combination of covariates in the model by examining
the Bayesian credible intervals for the associated parameters, by computing
conditional predictive ordinate (CPO) values (Gelfand et al., 1992) and pseudo
Bayes factors. A retrospective receiver operating characteristic (ROC) curve
method is applied to verify a potential best model.

**REPORT 0405-36:** Signal
transmission between gap-junctionally coupled passive cables occurs at an
optimal cable diameter

Farzan Nadim, Jorge Golowasch

Theoretical studies have shown that gap junctional coupling can lead to complex
network activity. We examine the consequences of current flow between two
passive cables coupled by gap junctions at one end and derive analytical
solutions for the steady state case. This architecture could represent gap-junctionally
coupled processes of two neurons or coupling between two muscle fibers. We find
that the transfer of electrical signals across the gap junction between two
coupled cables does not always increase with increased cable diameter as
expected from the increase in length constants, but that an optimal diameter
exists. The optimal cable diameter arises because the gap junction acts as a
current limiter. As current flows from one cable to the second, voltage
attenuation along the latter follows two opposing rules. At low diameters,
voltage attenuation along cable 2 decreases with increasing diameter, while at
high diameters, it increases. This is due to an increase in leak conductance in
cable 2 and the limited current flow through the gap junction. This optimal
diameter depends on the gap junction resistance as well as the membrane
properties and lengths of the cables. Moreover, in branched cables dependence on
diameter is local and thus may serve to functionally compartmentalize branches
that are independently coupled to other cells. Such compartmentalization may be
important when periodic signals or action potentials cause the current flow
across gap junctions. We predict that, in biological networks, coupled processes
may have optimal diameters that maximize signal transfer between cells.

**REPORT 0405-37:** Analysis of
Equivalent Distorted Ratchet Potentials

Yiming Cheng, Robert M. Miura

Different kinds of charged particles undergoing Brownian motion can be separated
by subjecting them periodically to an asymmetrical spatially periodic electric
field, sometimes referred to as a Brownian ratchet. It has been found
numerically that equal fluxes of particles can be obtained from two different
potentials under special distortions. Although a simple physical explanation for
this equivalency can be given, there is no corresponding mathematical proof.
Here, we pose the mathematical problem and discuss the difficulty in carrying
out the analytical proof.