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Preterm infants are at risk for multiple morbidities, including motor, cognitive, and behavioral deficits. Investigation of long-term outcomes of brain structure in preterm infants who receive red blood cell transfusion in the neonatal period may increase understanding of the developing brain in association with anemia and its treatment. The objective of this study was to compare the brain structure of preterm females, at an average age of 13 years, who were randomized at birth to receive either a liberal or restrictive transfusion threshold for anemia of prematurity. This study was designed as a long-term follow-up supplemental study to the Iowa trial for anemia of prematurity. As neonates, participants were randomized to receive either a liberal or restrictive transfusion threshold. Quantitative structural magnetic resonance imaging scans for 44 of the original 100 subjects were obtained. Only the female infants of each transfusion group were included. Main outcome measures were volumes of multiple brain areas. General white-matter volumes were significantly decreased in females randomized to the liberal transfusion threshold, including total white and cerebral white volumes; total cerebral volume was also decreased in liberal females. Regional white matter volumes for all cerebral lobes were not different between the 2 transfusion groups though all measures were lower in the liberal group.
MATHEMATICS & STATISTICS
APPLIED MATHEMATICSRoom 214C
SEMIGROUPS OF MAPS AND HIGHER DIMENSIONAL PERIODIC DIFFERENCE EQUATIONS: AN
APPLICATION TO A 2-STAGE POPULATION MODEL WITH MIGRATIONSelenne Garcia-Torres, Robert Sacker.
University of Southern California, Los Angeles, CA.
We study a class of monotone mappings from Rn to Rn motivated by applications from population dynamics. Monotone maps have received much attention in the field of dynamical systems because of their applications to finding fixed points but have not been applied to the study of periodic systems in higher dimensions. We define monotonicity and concavity with respect to a cone and show that such a mapping satisfying certain conditions has a globally asymptotically stable fixed point. Moreover, this class of mappings forms a semigroup under composition. Thus, we are able to show that a periodic solution is obtained by finding the fixed point of the composition of the various maps.
We apply this to a multidimensional, nonlinear discrete system that describes the dynamics of a 2-stage population model with migration. A structured population is one with consistent differences among the members of the population as a function of some attribute such as age, size, or physiological condition as they develop. Here, we partition the population by reproductive maturity. We take 2 such populations of the same species in adjacent locations and consider migration between the 2 locations. When constant breeding and migration are considered, we propose simple conditions under which the model has a unique globally attracting periodic state. These conditions are much
simpler than those given by other authors. We apply our theory to a generalized version of the model with a larger number of patches and a periodically varying environment and under different, but still simple, conditions, reach the same conclusion.
MODELING THE EFFECTS OF THE INTRODUCTION OF A UNIVERSAL VACCINE FOR INFLUENZAJorge A. Alfaro-Murillo1, David Durham2, Zhilan Feng1, Alison Galvani2, Carlos Castillo-Chavez3.
Purdue University, West Lafayette, IN, 2School of Public Health, Yale University, New Haven, CT, 3Computational and 1 Modeling Sciences Center, Arizona State University, Tempe, AZ.
Influenza represents a high burden for the population worldwide; annual epidemics produce up to 5 million cases of severe illness, and cause between 250 to 500 thousand deaths per year. Vaccines against flu are produced every year and are considered the best way to prevent or reduce the chances of infection. Nevertheless, the influenza virus is constantly mutating, and current vaccines only offer partial protection against the disease or no protection at all in the case of a pandemic. Yet, the picture for the future is encouraging. Several novel approaches are on the way to develop an influenza vaccine that offers long-term protection for several years against any strain of influenza. In this study we develop a model, in which 2 types of vaccines are available: seasonal and universal, for the dynamics of influenza during several seasons. Our model assumes that individuals may obtain different levels of immunity from the seasonal or universal vaccines, or from an infection, and that the immunity wanes at different rates in each case.
The strain that the population confronts changes each year and is determined with a stochastic parameter that also accounts for the possibility of the appearance of a completely new strain. Finally, we provide a cost-effectiveness analysis of several strategies of vaccination. The outcomes of this study could help public health authorities design optimal vaccination strategies when the universal flu vaccine becomes available.
AN EXACT SOLUTION FORMULA FOR THE KADOMTSEV-PETVIASHVILI EQUATIONAlicia Machuca, Tuncay Aktosun.
University of Texas at Arlington, Arlington, TX.
The study of integrable nonlinear partial differential equations (NPDEs) is interesting to mathematicians, engineers, and physicists because they have physically important solutions that can be expressed in terms of elementary functions. In general, NPDEs do not yield exact solutions and are solved using numerical methods. The goal of this research is to find nontrivial explicit solutions to an integrable NPDE, the Kadomtsev-Petviashvili equation, expressed in terms of elementary functions. Taking advantage of the well-known inverse scattering theory for NPDEs of one spatial dimension and one temporal dimension, we have been able to extend the theory to an NPDE with more than 1 spatial dimension. A study of the associated Marchenko integral equation reveals an explicit formula of exact solutions in terms of matrix exponentials. This systematic method is generalizable to integrable NPDEs with an associated Marchenko integral equation and produces exact solutions dependent on a quadruplet of constant matrices.
MODELING DNA UNKNOTTING BY XERCD-FTSK ENZYMES USING THE TANGLE METHODCrista Moreno, Mariel Vazquez.
San Francisco State University, San Francisco, CA.
Simplifying the topology of DNA is vital to the health of a cell. Knotted and linked DNA causes complications during DNA replication and transcription. DNA topology simplification is usually mediated by enzymes. Research on the unknotting of DNA by enzymes, like topoisomerases, has led to the development of anticancer drugs. In Escherichia coli, in the absence of the topoisomerase IV, the XerCD-FtsK complex has been found to effectively unlink replication links. By observing changes in DNA topology (knotting and linking) we can characterize the local enzymatic action through the use of knot theory and tangle calculus. The tangle method models the enzyme together with the bound Graduate
knot types of the DNA substrates and products, the tangle method constructs a system of tangle equations. One of these tangles represents the region of DNA bound to the enzyme and another tangle represents the action of the enzyme. Using tangle calculus we can solve for the unknown tangles. We aim to incorporate new results in tangle theory into the tangle method and its computer implementation TangleSolve. Then, we will use these tools to study DNA unknotting by XerCD-FtsK. We will give an overview of both the mathematical and computational methods used in the analysis of XerCD-FtsK.
RESONANT SPATIAL INSTABILITY AND NONLINEAR WAVE INTERACTIONS IN ELECTRICALLY FORCEDJETS Saulo Orizaga1, Daniel N. Riahi2, L. Steven Hou1.
Iowa State University, Ames, IA, 2University of Texas-Pan American, Edinburg, TX.
1 We investigate the problem of linear spatial instability of the modes that satisfy the dyad resonance conditions and the associated nonlinear wave interactions in jets driven by either a constant or a variable external electric field. A mathematical model based on the governing equations of electro-hydrodynamics, which is developed and used for the spatially growing modes with resonance and their nonlinear wave interactions in electrically driven jet flows, leads to equations for the unknown amplitudes of such waves. These equations are solved for both a water-glycerol mixture and glycerol jet cases, and the expressions for the dependent variables of the corresponding modes are determined.
The results of the generated data for these dependent variables versus spatial direction indicate, in particular, that the instability that is generated by the nonlinear wave interactions of such modes is mostly of amplifying effect. The energy exchanged during the interaction is very strong and for most cases the domain of the dependent variables was significantly reduced. The amplified instability was also found to provide a significant reduction in the jet radius, which is a favorable result for practical applications.
CONTROLLABILITY AND REGULARITY OF SOME 1-DIMENSIONAL THERMAL SYSTEMS WITH INTERNAL
POINT MASSESJose de Jesus Martinez, Scott W Hansen.
Iowa State, Ames, IA.
We investigate the controllability and regularity of coupled systems of partial differential equations describing heat flow across interior point masses. First, we describe a possible model for heat flow between 2 chambers divided by a thin wall that acts as a thermal barrier between them. In the idealized 1-dimensional model, 2 heat equations on respective domains (-a, 0) and (0, b) are coupled through a differential equation that describes the temperature of the thermal barrier at x = 0. For this system, we show that by controlling the temperature at one end, for any T 0, any initial state can be controlled to the zero temperature state in time T. Our approach is based on the moment method.
Then, we consider other possible models. For example, we consider the case in which there is more than one thin wall acting as a thermal barrier. Results about controllability and regularity are then discussed.
A FIRST MATHEMATICAL MODEL FOR THE DYNAMICS OF SOLUBLE REACTIVE PHOSPHORUS IN LAGUNA
CARTAGENA USING ORDINARY DIFFERENTIAL EQUATIONS AND SOFTWARE STELLA (V8)Brenda C. Torres-Velasquez, Yashira Sánchez-Colón, Marlio Paredes-Gutiérrez, Fred Schaffner.
Universidad del Turabo, Gurabo, PR.
Laguna Cartagena (LC) is a tropical freshwater wetland located in southwestern Puerto Rico and impacted by unnaturally high nutrient loading, particularly phosphorus, since the latter half of the 20th century. Eutrophication leads to excessive plant productivity that contributes to wildlife habitat degradation and enhanced greenhouse gas (methane) emissions. The main objectives of the research project were to develop a mathematical model to reproduce the dynamics of phosphorus inside Laguna Cartagena and to predict future behavior of soluble, reactive phosphorous (SRP) using the model developed. A first step in this analysis was the documentation of phosphorous dynamics within the lagoon using field and laboratory data. The primary variable is SRP concentration taken from samples of water entering and exiting LC at its inlet and outlet points and at 3 locations in the western, eastern, and center sectors of the lagoon. Samples for all 5 sites were collected in triplicate on 18 occasions from August 2010 to September 2011.
STELLA (v8) was used to model SRP dynamics based on the net amount of SRP (μg/L) in the system. An ordinary differential equations system (ODES) was developed and solved. Simulations were run for n = 17, 50, and 100 days.
The ODES solution was the logistic function with estimated parameters M = 16.78 g/L and r = -0.15. Results show that SRP flow going in and out of Laguna Cartagena occurs in cycles. Even in periods when SRP concentrations at the inlet canal are less than SRP concentrations at the outlet canal, Laguna Cartagena’s SRP stock concentrations increase over time.
ORAL ABSTRACTSSTATISTICS Room 205
THE OBJECTIVE AND ROBUST BAYESIAN STUDENT T TESTIsrael Almodovar-Rivera1, Luis Pericchi2.
Iowa State University, Ames, IA, 2University of Puerto Rico, San Juan, PR.