# Reception and Poster Session

Monday, March 4, 2013 - 4:20pm - 6:00pm

Lind 400

**Change point analysis for standard Skew Normal Distribution****An interesting family of polynomials in Z_2[x]**

in TeX: An interesting family of polynomials in $mathbb{Z}_2[x]$

Katherine Anders (University of Illinois at Urbana-Champaign)

I describe a sequence of polynomials $p_n(x)inmathbb{Z}_2[x]$ such that the order of $p_n(x)=d_n$ and $p_n(x)q_n(x)=1+x^{d_n}$ with the property that the proportion of $1$'s among the coefficients of $q_n(x)$ goes to 1 as $ntoinfty$.**Tate Cohomology Relation for Finite Dimensional Hopf Algebras**

Van Nguyen (Texas A & M University)

I show that the Tate cohomology ring of a finite dimensional Hopf algebra A is a direct summand of its Tate-Hochschild cohomology ring. This result extends the analogous cohomology relation of A to negative degrees. I will provide a computational example for the Sweedler algebra H_4. As an application, I will describe the decomposition of the Tate-Hochschild cohomology of a finite group algebra and introduce a product formula with respect to this decomposition. All necessary definitions will be given in the poster.**A minimal complexity model analyzing dominant processes in sea-ice algal growth.**

Samantha Oestreicher (University of Minnesota, Twin Cities)

Sea-ice algae is a prominent part of ice-covered ecosystems. Alterations to the arctic algal life cycle, due to changes in annual ice patterns, has uncertain consequences. Understanding how algae is best modeled leads to further understanding, and eventually prediction, of the physical system. Additionally, a conceptual understanding of the small and large scale processes which control algal growth/death is vital to interpreting and validating larger models and limited observations.

A minimal complexity conceptual model of sea-ice algae is derived and analyzed. The model incorporates sea ice concentration, light, nutrients and ice-ocean brine dynamics. The model arises directly from conservation equations which allows direct analysis of individual components. The model is optimized over a large parameter space. We consider the relative merits of several alternative modeling choices, parameter values, and nutrient levels.**Categorification in topology and algebra**

Radmila Sazdanović (University of Pennsylvania)

We will introduce the notion of categorification and discuss several examples. In particular, we will focus on Khovanov homology and chromatic homology theories categorifying the chromatic polynomial for graphs and relations between them. We develop a diagrammatic categorification of the polynomial ring Z[x], based on a geometrically defined algebra and show how to lift various operations on polynomials to the categorified setting. This construction generalizes to categorification of orthogonal polynomials, including Chebyshev polynomials and the Hermite polynomials**A class of integral operators on spaces of analytic functions**

Snehalatha Ballamoole (Mississippi State University)

We determine the spectrum and essential spectrum as well as resolvent estimates for a class of integral operators $T_{mu,nu}f(z)=z^{mu-1}(1-z)^{-nu}int_{0}^{z}f(w)w^{-mu}(1-w)^{nu-1}dw$ acting on either analytic besov spaces or other Banach spaces of analytic functions on the unit disk, including the classical Hardy and weighted Bergman spaces as well as certain generalized Bloch spaces.**The Benjamin-Ono equation in weighted Sobolev spaces**

Cynthia Flores (University of California)

The Benjamin-Ono equation describes long internal waves in a stratified medium of infinite depth. In this work we investigate unique continuation properties of solutions to the initial value problem associated to the Benjamin-Ono equation in weighted Sobolev spaces. More precisely, we prove that the uniqueness property based on a decay requirement at three times cannot be lowered to two times even by imposing stronger decay on the initial data.**Algebras Counting Intersections and Self-Intersections of Loops**

Patricia Cahn (University of Pennsylvania)

Goldman and Turaev defined a Lie bialgebra structure on the vector space generated by nontrivial free homotopy classes of loops on an oriented surface. The Goldman bracket and Turaev cobracket give lower bounds on the minimal intersection and self-intersection numbers of loops in given free homotopy classes, respectively. Chas showed that these bounds are not equalities in general. Andersen, Mattes, and Reshetikhin defined a Lie bracket that generalizes Goldman's. We show that their bracket gives a formula for the minimal intersection number. We also define an operation that generalizes Turaev's cobracket in the same way that the Andersen-Mattes-Reshetikhin bracket generalizes Goldman's bracket, and show this operation gives a formula for the minimal self-intersection number.**Developing a Math Problem Solving Course for Future Educators**

Casey Monday (University of Kentucky)

While content courses for future educators can be some of the most intimidating to develop, they greatly benefit both student and instructor. This presentation focuses on the creation, implementation, reflection and revision of a problem solving course for future middle grades educators at the University of Kentucky. In addition to the course’s structure and content, student feedback, examples of student work, motivation for each task and lessons learned by the instructor are presented.**A numerical study on vorticity-enhanced heat transfer**

Xiaolin Wang (Georgia Institute of Technology)

The Glezer lab at Georgia Tech has found that vorticity produced by vibrated reeds can improve heat transfer in electronic hardware. Vortices enhance forced convection by boundary layer separation and thermal mixing in the bulk flow. In this work, we propose a simplified model by simulating flow and temperature in a 2-D channel. We simulate periodically steady-state solutions. We classify three types of the vortex street and determine how the global Nusselt number is increased, depending on the vortices' strengths and spacings, in the parameter space of Reynolds and Peclet numbers. We find a surprising spatial oscillation of the local Nusselt number due to the vortices.**Stability of Eigenvalues on a Quantum Graph**

A quantum graph is a metric graph along with a differential

operator defined on edges and matching conditions defined at vertices. We

analyze the quantum graph equipped with the magnetic Schrodinger operator.

We consider the eigenvalues of this graph as functions of magnetic

potential (or equivalently, magnetic flux) and look for critical points, as

well as the corresponding Morse indices. We will prove that zero magnetic

flux is a critical point whose Morse index is directly related to the

number of zeros of the corresponding eigenfunction. A main tool in this

proof is cutting each cycle of the graph and analyzing the critical points

(and corresponding Morse indices) on the resulting tree. These will then

be related to eigenvalues on our original graph via an intermediate (third)

quantum graph which has imaginary magnetic flux.**Effects of variability and noise on synchrony between reciprocally pulse coupled oscillators with delays**

The mechanism by which stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical (using mathematical neuronal models) methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only for delays greater than half a network period. At these delays, each neuron receives an input late in its firing cycle and almost immediately fires an action potential. We call the region of the PRC corresponding to immediate spike initiation the causal-limit region. Synchronization at locking points approaching the causal-limit region was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast with excitatory coupling, inhibitory coupling led to near-synchrony for short delays. PRC-based methods predicted an early region comprised of either unstable synchrony or bistability between synchrony and antiphase, with noise favoring antiphase at the shortest delays but increasingly favoring synchrony for a wide range of delays. Hence, PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity.**Community Profile of Low Income Women's Utilization of Prevention and Treatment of General &Breast Health Services**

Juliet Ndukum (Visionserve Associates LLC)

Breast cancer is one of the most common types of cancer among women in the world and one of the primary causes of death. Black women below 40years have higher incidence and lower 5-year mortality rates than white women. Low income African American women without health insurance and those with no usual source of health care have lowest screening rates; are less likely to screen repeatedly.

Eligible study participants were African American, Hispanic and Caucasian low income adult women who attend local churches, health fairs, and other gatherings in their local communities who agree to participate, as well as women who belong to not-for-profit organizations that provide breast health outreach education and screening services. The self-administered survey consists of approximately 50 questions the major themes being general health and utilization of health care for prevention, screening and health care; knowledge, attitudes and behavior with regard to breast health and breast cancer screening among others.

Of the respondents, 50% had family history of breast cancer, about 9% of which have the disease. More than 80% of respondents believe mammogram is important and have considered having one. Knowledge of breast self-exam is significantly (p less than 0.05) associated with doing the exam.

Our findings suggest the importance in understanding more carefully the link between knowledge, attitudes and behaviors as well as behavioral intentions with regards to breast health and their perceptions and utilization of screening and preventive health care in general and breast health in particular.**Modeling Building Evacuation**

Olive Mbianda (Southern Illinois University)

Evacuation process is a set of actions, engaged to ensure human safety in an emergency situations. The main purpose of evacuation is to have people moved from risky locations to safe ones, in a minimum amount of time. Since catastrophes cannot be predicted, the challenge is in anticipating problems that may occur, especially those related to human behavior. Many evacuation models have been developed, in order to help minimize the evacuation time and maximize the number of rescues. To reach these goals, there are many factors that should be taken into account when developing such models. Among these factors are occupant’s characteristics and types of relation among them, building architecture (characteristics) and nature or type of emergency. We will see how a variation on one (or many) of these factors would affect the outcome of the evacuation (evacuation time, number of rescues). Therefore, it will help us to develop suitable evacuation models for a variety of buildings.

Joint work with Henry Hexmoor**A Fast Algorithm To Solve The Biharmonic Equation With Application To Slow Viscous Flow**

Aditi Ghosh (Texas A & M University)

We present here a very accurate fast algorithm to solve the inhomogeneous

Biharmonic equation with different boundary conditions in the interior of a

unit disk of the complex plane. The fast algorithm is based on the

representation of the solution in terms of Green functions, fast Fourier

transform and some recursive relation derived in the Fourier space. The fast solver is derived through exact analyses and properties of convolution of

integrals using Greens function and hence is very accurate.

The numerical evaluation of the double integrals has been optimized giving

an asymptotic operation count $O(ln N)$ per point on the average and

requires no additional memory storage except the initial data. It has been

implemented, validated and applied to solve several interesting applied

problems from fluid mechanics and electrostatics.**Existence of Alternate Steady States in a Phosphorus Cycling Model**

Dagny Butler (University of North Carolina, Greensboro)

We analyze the positive solutions to a steady state reaction diffusion equation with Dirichlet boundary conditions on a bounded domain. In particular, we consider a model which describes the steady states of phosphorus cycling in stratified lakes. It can also describe the colonization of barren soils in drylands by vegetation. We discuss the existence of multiple positive solutions for certain parameter ranges leading to the occurrence of an S-shaped bifurcation curve. We outline the proof of our results using the method of sub-super solutions. Also, we look at the one-dimensional case using the quadrature method.**Feedback-Mediated Dynamics in a Model of Coupled Nephrons**

Hwayeon Ryu (Duke University)

The nephron in the kidney regulates its fluid capacity, in part, by a

negative feedback mechanism known as the tubuloglomerular feedback (TGF)

that mediates oscillations in tubular fluid pressure and flow, and NaCl

concentration. Single-nephron tubular flow oscillations found in

spontaneously hypertensive rats (SHR) can exhibit highly irregular

resembling deterministic chaos. In this study, we developed a mathematical

model of short-looped nephrons coupled through their TGF system to study

the extent to which internephron coupling contributes to the emergence of

regular or irregular flow oscillations. For a bifurcation analysis, we

derived a characteristic equation obtained via linearization from the TGF

model equations. An analysis of that characteristic equation revealed a

number of parameter regions, indicating the potential for different model

dynamic behaviors. The model results suggest that internephron coupling

tends to increase the likelihood of LCO. Some model behaviors exhibit a

degree of complexity that is consistent with our hypothesis for the

emergence of irregular oscillations in SHR.**Myxococcus xanthus Cluster Formation**

Amy Buchmann (University of Notre Dame)

The bacteria, Myxococcus xanthus, are known to exhibit collective motion, but the details of their organized motility is not fully understood. Mathematical modeling can be used to understand complex biological processes such as bacteria swarming. I will present a parallel implementation of a subcellular element model of M. Xanthus. The parallelization of this model allows for thousands of bacteria cells to be modeled so questions pertaining to collective motion may now be studied. This model is used to analyze the clusters of bacteria that form when M. Xanthus swarm in a vegetative state. In particular, we investigate how a cell’s flexibility, adhesive properties, and reversal period contribute to cluster formation. These findings lead to predictions that can be tested experimentally.**A novel shock-capturing scheme for multimaterial compressible flows and its application to industrial aerospace**

Mona Karimi (Texas A & M University)

This study focuses on the simulation of compressible multifluid flows with strong shocks. To solve the hyperbolic-elliptic Euler equations for compressible flows, quasi-BGK scheme is suggested. The proposed scheme can be oscillation-free through material interfaces. The scheme is applied to typical shock flows and the results are compared with exact solutions. These demonstrate that the gas-kinetic BGK scheme is an excellent shock-capturing method for supersonic flows in aerospace applications such as scramjets and re-entry vehicles.**Learning the Association of Multiple Inputs in a Recurrent Network**

Jeannine Abiva (The University of Iowa)

We investigate the dynamic response of a recurrent neural network to inputs under reward modulated learning rules. The inputs combine distinct features (A, B and X, Y respectively) of the stimulus, and are grouped in pairs (A, X), (A, Y), (B, X), (B, Y). The learning task is defined by a pair-association paradigm. It leads to specific changes in the synaptic weight connectivity matrix that further influences the recurrent network internal dynamics.**Toroidal fluid structures created by slender rods precessing cones in a viscous fluid**

Longhua Zhao (University of Minnesota, Twin Cities)

Motile cilia play a large role in fluid motion across the surface of ciliated tissue. We present an experimental and theoretical study involving a single rigid cilium rotating in a viscous fluid about one of its ends in contact with a horizontal no-slip plane. Experimentally tracked three dimensional Lagrangian trajectories are compared with theoretical trajectories computed using a properly imaged slender body theory. The addition of planar bend to the rod geometry is shown to break symmetry and create large scale nested tori in the Lagrangian particle trajectories. Three dimensional PIV measurements are presented which help to explain the origin of the large scale tori and compared directly with the slender body theory.**The Economic Gains of Alternative Markowitz Portfolios in the Foreign Exchange Market**

Weiye (Betty) Chen (University of Notre Dame)

Recently there have been a lot of modifications to the classic Markowitz mean-variance analysis for finance portfolio constructions. Among which those methods, the methods introduce estimator shrinkage, although introduce some bias at the same time, deliver lower out-of-sample portfolio variance and higher Sharpe ratios in the U.S. equity market. However it is unclear if similar shrinkage can improve portfolio performance in foreign exchange market. We apply the newly developed inverse covariance matrix shrinkage method, graphical lasso, to the portfolio construction in currency market and examine if these shrinkage would improve the behavior of portfolios based on Sharpe ratio. We take a look at the out-of-sample performance of minimum-variance portfolios and the out-of-sample performance of portfolios based on economic utility function.