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«Strengthening the Nation through Diversity, Innovation & Leadership in STEM San Antonio,Texas · October 3-6, 2013 Get Connected! Connect with the ...»

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in the synapse. The expression of LTD is described in our model by a calcium-dependent positive-feedback loop involving the activation of PKC and subsequent AMPAR phosphorylation. We modeled the intracellular volume and plasma membrane of a single Purkinje cell dendritic spine. The model tracked the position and biochemical state of all molecules involved in cerebellar LTD after the release of calcium ions (Ca2+). Our MC model replicated the observed Ca2+ dependence of cerebellar LTD and exhibited LTD initiation after PKC activation. To simulate crowding, we then implemented the presence of large concentrations of non-reactive macromolecules. A classical approach would suggest that the presence of crowding would result in an increase in the amount of Ca2+ needed to induce LTD, producing a rightward shift of the LTD curve. Instead, our simulations showed an increase in maximal LTD, earlier LTD, and a steepening of the sigmoidal curve that replicates experimental results. Overall, our results show that there is a strong influence of molecular crowding in the activation of biochemical signals in synapses. (Partially funded by NIGMS MBRS-RISE GM060655, NSF HRD-0932339, and EF 1137897.) FRI-390



Javier Tapia Jr.1, Krystal Blanco2, Andrea Steele3, Aida Briceno4, Carlos Castillo-Chavez5.

St. Mary’s University, San Antonio, TX, 2Boston University, Boston, MA, 3Medgar Evers College, The City University 1 of New York, Brooklyn, NY, 4Columbia College, Columbia, SC, 5Arizona State University, Tempe, AZ.

The 21st century has redefined the way we communicate, our concept of individual and group privacy, and the dynamics of acceptable behavioral norms. The messaging (tweets) dynamics on Twitter, an important internet social network, has opened new ways/modes of spreading information and, as a result, cyberbullying or the spread of offensive messages has become a growing, persistent, and prevalent problem. The aim of the analysis carried out in this project is to identify and evaluate conditions that would dampen the role of small-group (tweeters) cyber bullying dynamics on Twitter. This is explored by the introduction of a rating system that may help hinder the spread of offensive messages. A discrete-time nonlinear compartmental model is introduced. We examine the stability of the equilibrium solutions and measure the interactions between communities and their change of status from unaware of the impact of a negative tweet (ignorant), to that of an offender, or indifferent to the posting of an offensive message.

We hope that the analysis of this dynamic model will shed some insights into the viability of new models of selfsustaining methods of reducing cyberbullying in public social networks.



Leonila Lagunes, Charles Lee.

California State University, Fullerton, Fullerton, CA.

Biomimetic pattern recognition (BPR) is a classification process using a constructed biological structure. BPR is derived from the Principle of Homology-Continuity, which assumes members of the same class are biologically evolved and continuously connected. Recently, BPR has been successfully used in voice, facial, and iris recognition.

In our study, we develop two BPR algorithms using proximity extension and two classification schemes. We investigate the performance of the proposed BPR methods to detect cancer using DNA microarray data. A sample, normal or cancerous, consists of thousands of expressed genes which are regarded as single nodes in a hyperdimensional space. Assuming the PHC, nodes of the same class can be topologically assembled into a complex skeleton-like structure and can be further covered with a tissue-layer to form a biological body. The resulting product can subsequently be used for classification. Performance for the algorithms are studied based on leukemia, bladder, liver, and colon cancers. Our results indicate that the proposed BPR has an increase in recognition rate when compared to previous techniques. BPR has shown to be a promising approach for cancer detection using DNA microarray data.



Ramon Miranda1, Lora Harris2, Javier Parapar1.

Universidad Metropolitana de Cupey, San Juan, PR, 2University of Maryland Center for Environmental Science, 1 Chesapeake Biological Laboratory, Solomons, MD.

Puerto Rico has 3 of the 10 most famous permanent bioluminescent bays in the world. These bioluminescent bays represent important ecological and socio-economic resources to the local economy and are associated with dense

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aggregations of the dinoflagellate Pyrodinium bahamense. Dynamic nutrient-phytoplankton-zooplankton-detritus (NPZD) models are important tools to help us understand the relative roles of nutrients and food web dynamics to system productivity. The goal of this study is to adapt a NPZD model to predict Pyrodinium bahamense biomass changes through time, within the specific environmental conditions of the Laguna Grande coastal lagoon. This dynamic model is parameterized with measurements of primary and secondary production, grazing rates, and nutrients fluxes determined during 2012 and 2013. To describe and explore the dynamics of P. bahamense, we established two size classes of phytoplankton, assuming the larger size class is dominated by the bioluminescent dinoflagellate. Because the lagoon has a persistent bioluminescent bloom, we used assumptions of steady-state conditions in our model to explore the factors that might contribute to a system where P. bahamense biomass is optimized. This model could be a very useful tool to monitor and manage this lagoon’s unique natural resource.



Valerie Cheathon1, Octavious Talbot2, Victor Suriel3, Agustin Flores4, Luis Melara Jr.5.

Arizona State University, West Campus, Phoenix, AZ, 2Morehouse College, Atlanta, GA, 3State University of New 1 York at Stony Brook, Stony Brook, NY, 4Northeastern Illinois University, Chicago, IL, 5Shippensburg University, Shippensburg, PA.

This project is motivated by the costs associated with travel and international trade which come from the documented risks associated with the accidental and/or deliberate introduction of non-native invasive species of plants, animals, or pathogens into regions where they have no natural enemies. The spatiotemporal dynamics related to the invasion and spread of Nylanderia fulva, commonly known as the rasberry crazy ant, are explored via the use of models that focus on the reproduction of ant colonies. The impact of spatial correlations on the dynamics of invasion is investigated numerically and analytically with the aid of a mean field (MF) model and a pair approximation (PA) model, the latter of which accounts for adjacent cell level effects. The PA model approach considers the limited mobility range of N.

fulva; that is, the grid cell dynamics are not strongly influenced by non-adjacent cells. Geographical heterogeneity

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Joan Ponce1, Matthew Jastrebski2.

University of Florida, Gainesville, FL, 2Northeastern Illinois University, Chicago, Chicago, IL.

1 Borrelia burgdorferi is a spirochete bacteria which causes Lyme disease, a common arthropod-borne disease that infects mammals such as mice, deer, and humans. It is especially prevalent in the Northeastern United States. It is spread by Ixodes Scapularis, a species of tick that feeds primarily on deer and mice. These ticks, in turn, bite humans, thereby spreading the infection and causing significant health problems among the general population. Reducing the population of ticks feeding on both large mammals and small mammals would reduce the spread of Lyme disease to the human population. A 2-patch model is used to describe the dynamics of the spread in 2 generic adjoining regions/states. One region does not allow hunting of deer, whereas the other permits regulated harvesting. In order to feasibly arrive at this solution, we modeled the spread of Lyme disease through 2 populations on separate patches with varying hunting restrictions using a 6-dimensional, 2-patch SI model. We then performed stability analysis and determined the sensitivity and bifurcation of equilibrium points in order to find the ideal hosts on which to introduce restrictions to tick proliferation.

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Lynesia Taylor1, Alicia Arrua2, Rosa Orellana3, Gustavo Melendez Rios4, Samuel Ivy5.

Spelman College, Atlanta, GA, 2California State Polytechnic University Pomona, Pomona, CA, 3Dartmouth College, 1 Hanover, NH, 4University of Puerto Rico at Mayagüez, Mayagüez, PR, 5North Carolina State University, Raleigh, NC.

Consider the sequence [x; f(x); f(f(x)) = f2(x); ::: ; f(n-1)(x)] where f is a real-valued function and n ≥ 2. We can associate a permutation to every such sequence by comparing it with x1 x2... xn, where xi =f(j-1)(x) for some j = 1, 2,..., n.

Permutations that arise from these sequences are called allowed permutations, and those that do not are called forbidden permutations. For example, the logistic map, f : [0; 1] → [0; 1] is denied by f(x) = rx(1-x), where 0 ≤ r ≤ 4, for any x. We focus on enumerating the number of forbidden permutations for the logistic map and other functions, including trigonometric functions. For example, for the n = 3 case, we have found that the one-line permutation (321) is a forbidden permutation for the function sin(πx).



Alicia Ricci, Tuncay Aktosun.

University of Texas at Arlington, Arlington, TX.

We analyze certain exact solutions to the Korteweg-de Vries equation, which is a nonlinear partial differential equation with important applications in propagation of surface water waves in shallow and long canals and acoustic waves in ionized gases. We present a formula for the so-called n-soliton solution, the solution containing n solitary wave components (solitons) interacting with each other only when they are close to each other. The n-soliton solution formula uses as input 3 constant matrices A, B, C with sizes n × n, n × 1, and 1 × n, respectively. It is expressed in terms of matrix exponentials, and it is valid for any positive integer n. We relate the mathematical parameters in the n-soliton solution to the velocities and widths of individual solitons and to the eigenvalues of the matrix A. We further analyze solitons and their interactions by using Mathematica animations. Exact solutions such as multisoliton solutions are important not only physically but also mathematically, as they may be used to test the accuracy of computational methods developed for solving nonlinear differential equations numerically.



Dallas Albritton1, Justin Peters2.

Emory University, Atlanta, GA, 2Iowa State University, Ames, IA.

1 Consider an infinite exponential in the complex plane defined to be the limit of a sequence of exponential towers with finitely many exponents. We know that if the exponents are equal and within a region known as the BakerRippon region, then this infinite exponential converges. This poster presentation will show generalizations of previous results characterizing the convergence of exponential towers in the complex plane. Specifically, we are investigating the domain of convergence of the tower with nonconstant exponents, a question which is closely related to the stability of fixed points. We also hypothesize that in the case of constant exponents, uniform convergence occurs on any compact set within the Baker-Rippon region. Lastly, we are exploring the relationship between the rate of convergence of the tower and the rate of convergence of the exponents in special cases. We investigate these problems numerically using Matlab and then provide proofs. Note that this investigation constructs the tower “topdown” (changing the base of the tower) while others construct it “bottom-up.” It appears that this approach has not been thoroughly explored.



Aracely Alcala, Evan Breikss, Cristina Retamoza, Javier Rojo.

Rice University, Houston, TX.

In survival analysis the Kaplan-Meier estimator takes into account censored data. Censored data can result from a subject leaving a study before its completion or the inability to record the desired outcome during the length of the study. As Kaplan-Meier takes into account subjects that may have once been entirely excluded, much more information seems to be retrieved from the experiment. Our research examines the operating characteristics


presented by the Kaplan-Meier estimator. For instance, when the last data point of a study is censored, the survival curve will come to a halt. Literature proposes various methods for retrieving information that may lie beyond the last given point. Thus, we compared the various methods proposed by R.D Gill, B. Efron, and Brown et al. Then, we explored the possibility of changing the initial starting time of our Kaplan-Meier distributions; that is squaring or applying a function to the distributions and noticing if any major changes occurred to its properties. Lastly, we compared the Kaplan-Meier estimator to the empirical estimator, which entirely excludes censored data, in order to determine the difference in bias and variance.



Francis Castro1, Jose Pastrana Chiclana2, Rita Zevallos3, Rosa Orellana4, Alexander Diaz Lopez5.

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