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## Applied Mathematics

- Kelly Buch ;
- Abena Annor ;
- Daniel Rodriguez Pinzon ;
- Benjamin Morin ;

THU-803

FEMALE-CENTERED MATE SELECTIONS AS AN EXPLANATORY MECHANISM FOR DIMORPHIC SOLUTIONS IN A ROCK-PAPER-SCISSORS GAME

__Kelly Buch__^{1}, Abena Annor^{2}, Daniel Rodriguez Pinzon^{3}, Benjamin Morin^{4}.

^{1}*Southern Illinois University, Edwardsville, Edwardsville, IL, ^{2}University of Florida, Gainesville, FL, ^{3}Universidad de Los Andes, Bogotá, CO, ^{4}Global Institute of Sustainability, Arizona State University, Tempe, AZ.*

Side-blotched lizards, *Uta stansburiana*, exhibit trimorphic male throat-colors (orange, blue, or yellow). In terms of mating, the males participate in an apparent game of rock-paper-scissors determined by throat color (i.e., a cyclic dominance chain). Mathematical models of this behavior predict stable monomorphic and trimorphic populations. However, researchers have observed stable dimorphic populations of orange and blue males. Furthermore, it is postulated that the only large-scale, long-term, stable solutions exclude the yellow throat type. We propose a new mathematical model accounting for the female population available for mating that may exhibit such behavior. We discuss the conditions under which particular population configurations are stable and flow attractive. We use these results to motivate conservative methods that may mitigate biodiversity loss by preventing the decline of a particular monomorphic or dimorphic population.

THU-807 MODELING AND ANALYSIS OF A TWO-PATCH POPULATION WITH ALLEE EFFECTS

- Luis Mestre ;
- Richard Rebarber ;

THU-807

MODELING AND ANALYSIS OF A TWO-PATCH POPULATION WITH ALLEE EFFECTS

__Luis Mestre__^{1}, Richard Rebarber^{2}.

^{1}*Universidad Metropolitana, San Juan, PR, ^{2}University of Nebraska-Lincoln, Lincoln, NE.*

A metapopulation is a collection of subpopulations of the same species living in separated habitats (called patches) coupled by migration. We will consider a metapopulation for which each subpopulation has a carrying capacity and an Allee threshold. An Allee threshold for a patch is a population under which the species is not viable in the patch. Other parameters needed for the model are migration probability and migration survival. We developed a model for such a metapopulation in an arbitrary number of patches, and studied the dynamics in 2 patches in detail. We were especially interested in conservation, so we studied which combination of parameters and initial populations lead to persistence of the population. Using detailed simulations in MATLAB, Python, and Sage, we described the basin of attraction for the zero population; that is, the range of initial conditions for which the population goes extinct. These are the initial conditions we want to avoid and, if there are too many of them, the population is more likely to go extinct. We studied this for a deterministic model, and then studied a stochastic model which takes into account the fact that the model parameters are uncertain.

FRI-806 MATHEMATICAL MODEL FOR TIME TO NEURONAL APOPTOSIS DUE TO ACCRUAL OF DNA DOUBLE-STRAND BREAKS

- Jennifer Rodriguez ;
- Chindu Mohanakumar ;
- Annabel Offer ;
- Carlos Castillo-Garsow ;

FRI-806

MATHEMATICAL MODEL FOR TIME TO NEURONAL APOPTOSIS DUE TO ACCRUAL OF DNA DOUBLE-STRAND BREAKS

__Jennifer Rodriguez__^{1}, Chindu Mohanakumar^{2}, Annabel Offer^{3}, Carlos Castillo-Garsow^{4}.

^{1}*California State University, Channel Islands, Camarillo, CA, ^{2}University of Florida, Gainesville, FL, ^{3}Texas Tech University, Lubbock, TX, ^{4}Eastern Washington University, Cheney, WA.*

We propose a mechanism to explain neuronal aging by tracking the number of non-transient DNA double-strand breaks (DSBs) and repairs over time that may lead to apoptosis. Neuronal apoptosis depends on the amount of space between DSBs as well as time. We derived 3 models to track the effects of neurodegeneration: a system of autonomous ordinary differential equations (ODEs), a probability model to track the spatial requirement, and a stochastic model that incorporates both the ODE temporal dynamics and a spatial probability model. Using these models, we estimated a distribution for the lifespan of a neuron and explored the effects of parameters on time to death. We identified 3 possible causes of premature neuron apoptosis: problems with coding critical repair proteins, issues with the neuron detecting DSBs, and issues with the neuron responding to DSBs.

FRI-808 BREAKING DOWN THE POWER GRID

- Michael Briden ;
- Alaina Gibbons ;
- Javier Rojo ;

FRI-808

BREAKING DOWN THE POWER GRID

__Michael Briden__^{1}, Alaina Gibbons^{2}, Javier Rojo^{2}.

^{1}*Pacific Lutheran University, Tacoma, WA, ^{2}University of Nevada, Reno, Reno, NV.*

Power grids with radial topologies are susceptible to many types of failures. Failures may occur for any number of reasons. Examples include weather-related events, age-related failure, distance from urban centers, and geographical features. Often, these effects are localized to smaller areas, and therefore may affect different parts of the power grid in various ways, if at all, for some parts. In addition, different component types are more important to the overall stability of the grid than others, and susceptibility of these components to geographical effects causes concern as well. This study presents a closed-form probabilistic model for a radial topology power grid that can allow for inclusion of regional effects when determining the reliability of a grid. The measure of reliability used is customer service availability (CSA), which is the percentage of customers in the grid that are receiving power. In order to create the CSA-probability mass function, a convolution product is performed using probabilities from smaller sections of the grid for which such geospatial effects can be superimposed. Probabilities of failure for grid components are then varied to analyze which component types have the greatest effect on the reliability of the grid as a whole. We additionally propose methods that may prove effective in modeling how weather and geography affect reliability when applied to our system.

FRI-816 DYNAMIC ANALYSIS OF GRAPH THEORETIC FUNCTIONAL CONNECTIVITY IN THE HUMAN BRAIN

- Roger Vargas Jr. ;
- Darren Narayan ;

FRI-816

DYNAMIC ANALYSIS OF GRAPH THEORETIC FUNCTIONAL CONNECTIVITY IN THE HUMAN BRAIN

__Roger Vargas Jr.__^{1}, Darren Narayan^{2}.

^{1}*Williams College, Williamstown, MA, ^{2}Rochester Institute of Technology, Rochester, NY.*

The human brain is a dynamic network of firing neurons and continuously changing oxygen levels. To accurately and precisely model this network, it is not sufficient to use a single static network, but rather a time varying aggregate of hundreds or thousands of networks. The sequence of networks obtained over the time course of a functional magnetic resonance imaging (fMRI) scan provides valuable information regarding the dynamic functional and structural connectivity of the human brain. Using data from experiments where subjects were asked to pantomime and view several objects, we used degree centrality to analyze dynamic changes in the network over time. We also analyzed the strength of various connections in the brain and how they differed by treating various regions of the brain as a network and measuring connections with betweenness centrality when subjects were asked to pantomime versus when they were simply asked to view objects. We expect to find that certain connections are stronger under pantomiming whereas others are stronger under viewing. Finally, we investigated the leverage centrality of a vertex, which compares the degree of a vertex with the degrees of its neighbors. This property is used to analyze fMRI data of the brain. We explored this property from a mathematical perspective and determined the leverage centrality for several families of graphs. In particular, we show the number of distinct leverage centralities in the Cartesian product of path powers has a surprising link to the triangular and figurate numbers.

FRI-818 DYNAMIC SAMPLE SPACE TRANSFORMATIONS FOR NONLINEAR DATA ASSIMILATION

- Michael Lopez ;
- Mesa Walker ;
- Juan Restrepo ;

FRI-818

DYNAMIC SAMPLE SPACE TRANSFORMATIONS FOR NONLINEAR DATA ASSIMILATION

__Michael Lopez__, Mesa Walker, Juan Restrepo.

*Oregon State University, Corvallis, OR.*

Data assimilation refers to the use of dynamics models and observations to improve predictions. Traditional Bayesian methods often fail when the dynamics are nonlinear and the inherent uncertainties are non-Gaussian. The path integral formulation for data assimilation yields predictions on these challenging problems; however, the method is very inefficient. We demonstrate how adaptive dynamic deformations of the sampling space significantly improve the efficiency of the path integral strategy. Homotopy also imparts robustness of the numerical implementation of the assimilation method. These improvements lead to the practical application of the path integral formulation for data assimilation on challenging prediction problems in meteorology, climatology, robotics, and guidance that are not amenable to conventional data assimilation.

THU-805 MATHEMATICAL MODELING OF THE NF & KAPPAB-SIGNALING PATHWAY USING PYSB

- Geena Ildefonso ;
- Carlos Lopez ;

THU-805

MATHEMATICAL MODELING OF THE NF & KAPPAB-SIGNALING PATHWAY USING PYSB

__Geena Ildefonso__, Carlos Lopez.

*Vanderbilt University, Nashville, TN.*

Nuclear factor-KappaB (NF-κB) is a signal transduction pathway centering around transcription factors that regulate gene expression in response to environmental stimuli. Aberrant activation of NF-κB has been linked to inflammation, autoimmune diseases, and improper immune development. In addition, NF-κB has a pivotal role in the initiation and progression of several cancers. The importance of NF-κB to these pathologies has led to the development of many mathematical models over the past decade, motivated by the need to gain a detailed quantitative, and, ideally, predictive understanding of biological systems. In particular, Tay et al.'s, model successfully recapitulates key aspects of NF-κB signaling and, in turn, has yielded insights into the pathway's structure, dynamics, and function. Recently, modeling frameworks such as PySB, which construct mathematical rule-based models of biochemical systems as computer programs have emerged. PySB facilitates reusable, shareable, and transparently developed biological models. Here, we implement Tay et al.'s model of NF-κB signaling in PySB and examine the pathway's ability to control programmed cell death through regulation of anti-apoptotic signals. We also intend to link the model with other models of apoptosis and necrosis to better understand cell fate outcomes in cancers.

- Jessica Conrad ;
- Genesis Islas ;
- Adrien Bossogo-Egoume ;
- Marco Hamins-Puertolas ;
- Maryam Khan ;

THU-804

MINIMIZING RECIDIVISM BY OPTIMIZING PROFIT: A THEORETICAL CASE STUDY OF INCENTIVIZED REFORM IN A LOUISIANA PRISON

__Jessica Conrad__^{1}, Genesis Islas^{2}, Adrien Bossogo-Egoume^{3}, Marco Hamins-Puertolas^{4}, Maryam Khan^{5}.

^{1}*Tulane University, New Orleans, LA, ^{2}California State University, Long Beach, Long Beach, CA, ^{3}University of Wisconsin-Madison, Madison, WI, ^{4}St. Mary's College of Maryland, St. Mary’s City, MD, ^{5}Arizona State University, Tempe, AZ.*

Recidivism is the phenomenon whereby an individual returns to criminal activity after being released from prison. Many prisoners in the U.S. end up back in jail within 5 years. Using Louisiana as a case study, we show that prison management can minimize recidivism by subsidizing reform programs in for-profit prisons. Accounting for such an incentive program allows us to observe alterations in prison profit optimization. Within the model, the prison alters the proportion of time each inmate spends in the reform program. The incarceration dynamics respond to the average proportion of time that prisoners spend in reform. We determined that the prison's profit is most sensitive to the value of the incentive, the fixed cost per prisoner, the effectiveness of the instated reform program, the number of first-time offenders currently in the prison, and the *per diem* rate per prisoner the prison receives from the state. Prisons with higher initial incomes require a larger incentive to obtain the same results as their less profitable neighbors. The reduction in recidivism has diminishing returns as the incentive is increased.

THU-808 NUMERICAL RESULTS FOR THE IVP TO THE BURGER'S EQUATION WITH EXTERNAL FORCES

- Crystal Mackey ;
- Alejandra Castillo ;
- Armando Morales ;
- Julio César Enciso Alva ;
- Cynthia Flores ;

THU-808

NUMERICAL RESULTS FOR THE IVP TO THE BURGER'S EQUATION WITH EXTERNAL FORCES

__Crystal Mackey__^{1}, Alejandra Castillo^{2}, Armando Morales^{3}, Julio César Enciso Alva^{4}, Cynthia Flores^{3}.

^{1}*Youngstown State University, Youngstown, OH, ^{2}Pomona College, Claremont, CA, ^{3}California State University, Channel Islands, Camarillo, CA, ^{4}Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, MX.*

In this project, we use Burger's equation to study traffic flow, including shock and rarefaction waves, where traffic density, traffic flow, and velocity are the main variables expressed as functions of position and time. The derivation of the conservation law from physical principles can be reduced to Burger's equation. The initial value problem (IVP) of Burger's equation is a partial differential equation with an initial condition. Our objective is to numerically approximate solutions to the IVP for Burger's equation with external forces. After deriving the Lax-Wendroff method and modifying it to improve numerical approximations, adaptations were made to include an external force term. External forces may help to capture physical traffic interpretations such as traffic lights, driver interactions, multiple lanes, or on and off ramps on a highway. Our goal is to approximate solutions to the IVP for Burger's equation with external forces and compare our numerical simulations to real data. In this poster, we compare our numerical simulations to real data and present the methods used.

FRI-805 STOCHASTIC DELAY DIFFERENTIAL EQUATIONS FOR CORAL REEF DYNAMICS

- Valerie Carrasquillo ;
- Claudia Guerrero ;
- Kyle McGrath ;
- Michael Law ;
- Kelly Black ;

FRI-805

STOCHASTIC DELAY DIFFERENTIAL EQUATIONS FOR CORAL REEF DYNAMICS

__Valerie Carrasquillo__^{1}, Claudia Guerrero^{2}, Kyle McGrath^{3}, Michael Law^{4}, Kelly Black^{5}.

^{1}*Universidad Metropolitana, San Juan, PR, ^{2}Universidad Autonoma del Estado de Hidalgo, Pachuca, Hidalgo, MX, 3The State University of New York at Potsdam, Potsdam, NY, ^{4}University of Florida, Gainesville, FL ^{5}The University of Georgia, Athens, GA.*

Coral reefs are one of the most diverse ecosystems of marine biomes. However, they are globally threatened due to their sensitivity to dramatic physical changes. Other researchers have proposed deterministic models to analyze coral reef dynamics. For example, X. Li et al., constructed a mathematical model with delay differential equations for macro algae, corals, and alga turfs. Equilibria and stability analyses for this system were found considering variations in the grazing intensity and the time delay. In this investigation, we extended the model of X. Li et al., by adding noise via scarid feeding mechanisms. We explored the effects of the delay and noise using numerical approximations for the stochastic differential equation model implemented using Milstein’s method. Data analysis showed that noise has an influence on coral population stability.

- Armando Morales ;
- Cynthia Flores ;

FRI-803

TRAFFIC SIMULATIONS IN SANTA BARBARA COUNTY, CALIFORNIA USING MODIFIED NUMERICAL METHODS AND BURGER'S EQUATION

__Armando Morales__, Cynthia Flores.

*California State University, Channel Islands, Camarillo, CA*.

The goal of this research project is to develop a mathematical model for traffic simulation. The classical Burger's equation ut + uux = 0 is used as our model and is derived by assuming the traffic’s velocity and density are continuous functions. It also captures the phenomenon of shock and rarefaction wave formation. Numerical methods were investigated and applied to linear and non-linear partial differential equations (PDEs). Presented in this poster are the modified numerical methods that were the key to approximating solutions to Burger's equation and the numerical outcome in a traffic flow model. The traffic simulation takes place on the northbound US 101 freeway from Camarillo, California, to Santa Barbara County on approximately 11 miles of highway. Data from the Caltrans Performance Measurement System, coming from different sensors along the highway, collect information such as traffic flow, velocity, and occupancy. We were able to compare the numerical results from our simulations to the known data and improve the classical Lax-Wendroff method to approximate solutions to Burger's equation.

THU-819 GROUND WATER FLOW TO A WELL MODELING IN SMALL SCALE

- Ying Liu ;
- Ross Rueger ;
- Larry Owens ;

THU-819

GROUND WATER FLOW TO A WELL MODELING IN SMALL SCALE

__Ying Liu__, Ross Rueger, Larry Owens.

*College of the Sequoias, Visalia, CA.*

Studies show that water flow from the aquifer to a well being pumped forms a conical shape known as the cone of depression, which affects the water table of nearby wells. Using the Theis equation and Jacob analysis, hydrologists can approximate the shape of the cone and investigate its effect on well drawdowns. The hypothesis of this research is that the conical pattern of the water flow should exist in any scale and the mathematical model of the Theis equation and Jacob analysis should apply to a small-scale physical model. An experiment was designed to simulate an aquifer of 18 inches in diameter and 17.7 inches in thickness with 1 main well and 12 observation wells. Two types of soil were tested and 1 was suitable to be a confined aquifer. Drawdowns of the observation wells were recorded continuously during 30-minute pumping of the main well. Data were plotted using Mathematica and Excel. Due to leveling issues and boundary effect, some data were considered inconclusive; however, the results suggest that the conical pattern can be duplicated in a small-scale model and the data can fit in a logarithmic model. With more precise equipment, research can be done on a small-scale model without digging wells in the field.

THU-817 APPROXIMATING SOLUTIONS FOR CONSERVATION LAWS USING MODIFIED NUMERICAL METHODS

- Alejandra Castillo ;
- Julio César Enciso Alva ;
- Crystal Mackey ;
- Armando Morales ;
- Cynthia Flores ;

THU-817

APPROXIMATING SOLUTIONS FOR CONSERVATION LAWS USING MODIFIED NUMERICAL METHODS

__Alejandra Castillo__^{1}, Julio César Enciso Alva^{2}, Crystal Mackey^{3}, Armando Morales^{4}, Cynthia Flores^{4}.

^{1}*Pomona College, Claremont, CA, ^{2}Universidad Autónoma del Estado de Hidalgo, Pachuca, Hidalgo, MX, ^{3}Youngstown State University, Youngstown, OH, ^{4}California State University, Channel Islands, Camarillo, CA.*

Burger's equation is a non-linear conservation law that is used to model traffic flow, hydrostatics, gas dynamics, and serves as a simplification of the Navier-Stokes equation. Paired with an initial condition, Burger's equation becomes a partial differential equation known as the Burger's equation initial value problem (IVP), which can be solved analytically, though these solutions limit the physical applications of exact solutions. This motivated the use of numerical simulations to approximate exact solutions. Using difference methods, we ran numerical simulations to approximate exact solutions of the Burger's equation IVP. We carefully derived the Backward Euler and Lax-Wendroff difference methods for linear and nonlinear conservation laws. This allowed us to make original modifications to the Lax-Wendroff difference method thus improving our numerical results when comparing them to real data.

- Wayne Harvey ;
- Oleksandr Makeyev ;
- Quan Ding ;
- Walter Besio ;

FRI-817

DERIVING ANALYTIC LAPLACIAN ESTIMATES FOR MULTIPOLAR CONCENTRIC RING ELECTRODES USING INVERSE VANDERMONDE MATRIX

__Wayne Harvey__^{1}, Oleksandr Makeyev^{1}, Quan Ding^{2}, Walter Besio^{3}.

^{1}*Diné College, Tsaile, AZ, ^{2}University of California, San Francisco, CA, ^{3}University of Rhode Island, Kingston, RI. *

Concentric ring electrodes (CRE) have shown great promise in non-invasive electrophysiology. Tripolar CREs are successfully used in a wide range of applications including brain-computer interface and seizure onset detection, among others. They have demonstrated their superiority to conventional disc electrodes, in particular, in the accuracy of Laplacian estimation. Recently, we proposed a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This allows cancellation of all the truncation terms up to the order of 2n. This has been shown to be the highest order achievable for a CRE with n rings. This increase in accuracy of Laplacian estimation due to a decrease in truncation error associated with an increase in n for novel multipolar CREs has been confirmed using finite element method modeling. The drawback of the proposed general approach was that for any n ≥ 2, the Laplacian estimates in the form of the null space vectors could be calculated numerically using, for example, Gaussian elimination, but no analytic formula for Laplacian estimate as a function of n was derived. The goal of this study was to derive the explicit formula for a multipolar Laplacian. This derivation was accomplished based on the inversion of a square Vandermonde matrix completing the proposed general approach for estimation of multipolar Laplacian and making it more efficient in terms of computation. This work is a part of our continued effort to improve the electrode design for non-invasive electrophysiology via multipolar CREs.

FRI-804 DEVELOPMENT OF A COMPUTATIONAL MODEL OF GLUCOSE TOXICITY IN THE PROGRESSION OF DIABETES MELLITUS

- Danilo Perez Jr. ;
- Veronica Torres ;
- Abraham Torres Maytee Cruz Aponte ;

FRI-804

DEVELOPMENT OF A COMPUTATIONAL MODEL OF GLUCOSE TOXICITY IN THE PROGRESSION OF DIABETES MELLITUS

__Danilo Perez Jr.__, Veronica Torres, Abraham Torres Maytee Cruz Aponte.

*University of Puerto Rico in Cayey, Cayey, PR.*

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual’s blood glucose levels, and its main regulator, insulin. These complications can vary largely from person to person depending on their current biophysical state. Biomedical research day-by-day makes strides to impact the lives of patients of a variety of diseases, including diabetes. One large stride that is being made is the generation of techniques to assist physicians to personalize medicine. From genetics to biophysics, more information is supporting physicians in interpreting and deciding with their patients what will impact the patients’ condition. Nonetheless, frameworks that integrate all of this information have not been consistently engineered as to truly be able to project and predict how a specific patient’s condition will progress under a specific treatment plan. Therefore, we developed a simple mathematical model to accurately simulate dynamics between glucose, insulin, and pancreatic β-cells throughout disease progression, adhering to constraints that maintain biological relevance. Our future work will focus on our mathematical model evolving into a model capable of tracking not only the patient’s current progress through the disease, but also how effective a given plan of treatment would be at returning the patient to a desirable biophysical state.

THU-816 BUILDING A FITNESS PROFILE FOR NEUROSPORA CRASSA

- Linda Ma ;
- Boya Song ;
- Marcus Roper ;

THU-816

BUILDING A FITNESS PROFILE FOR *NEUROSPORA CRASSA*

__Linda Ma__, Boya Song, Marcus Roper.

*University of California, Los Angeles, Los Angeles, CA.*

Filamentous fungi such as *Neurospora crassa* are capable of proliferating indefinitely. Their growth is limited only by space and resources. *Armillaria solidipes*, also known as the humongous fungus, is considered the world’s largest living organism, covering 2,385 acres of Oregon’s Malheur National Park. However, should the edge of this fungus be considered to be the same individual as its center? Each fungus contains millions of totipotent, genetically diverse, and potentially selfish nuclei. Interactions between nuclei are mapped by removing single nuclei from the colony and measuring their fitness against wild type. To build a fitness profile with *N. crassa*, we seek to determine whether competitive interactions exist between nuclei, and how these impact the overall fitness of the fungus. Further, we seek to learn the role that spore size and germination rate play in fitness and growth rate. We measure fitness changes with colony size by isolating single GFP-tagged spores from different parts of a 30 cm-long colony. By confronting individual GFP-tagged spores with wild-type DsRed-tagged spores we can measure fitness changes during growth. Spores isolated from the first few centimeters of the colony outcompete the wild-type, but spores from the end are outcompeted by wild-type. Our preliminary data suggest that initial proliferation favors the fastest growing nuclei, but that over time, and despite intense competition between nuclei, deleterious mutations are accumulated and start to reduce overall nuclear fitness within the mycelium. That fungal growth rate itself is not affected suggests that cellular mechanisms exist to prevent tragedies of the common between these competitive nuclei.

THU-818 DEVELOPING SUPPORT FOR 3D DATA IN OPEN MSI

- Natalie Azevedo ;
- Benjamin Bowen ;
- Curt Fischer ;

THU-818

DEVELOPING SUPPORT FOR 3D DATA IN OPEN MSI

__Natalie Azevedo__^{1}, Benjamin Bowen^{2}, Curt Fischer^{2}.

^{1}*University of California, Merced, Merced, CA, ^{2}Lawrence Berkeley National Laboratory, Berkeley, CA.*

Mass spectrometry imaging (MSI) is an emerging technology with potential to revolutionize disease diagnosis among other biological applications, but there are limited resources to view and analyze this data. OpenMSI is a web-based platform for viewing, analysis, and sharing of MSI data for 2D datasets of varying file formats. We focused on extending OpenMSI to support processed mode imzML files and 3D imzML files. The imzML spectral data is stored in either continuous or processed form. In continuous mode, all spectra share an m/z (mass/charge) axis while in processed mode each spectrum has a different m/z array. Continuous mode data is compatible with the existing framework; therefore, we are able to extend compatibility to processed mode data by converting it into continuous mode. To achieve this, a logarithmically spaced m/z axis is created that can be shared by every scan in a file. To accommodate 3D data, which is a series of aligned 2D image slices, a datacube (x, y, m/z) is created for each z position. Each datacube is then stacked to create a 3D image. The integration of processed and 3D imzML data with OpenMSI expands the availability of useful data to the mass spectrometry community.

FRI-807 MATHEMATICAL MODELING, ANALYSIS, AND CONTROL OF CARBAPENEM-RESISTANT ENTEROBACTERIACEAE INFECTIONS

- Jorge Flores Ortega ;
- Mohammed Yahdi ;

FRI-807

MATHEMATICAL MODELING, ANALYSIS, AND CONTROL OF CARBAPENEM-RESISTANT ENTEROBACTERIACEAE INFECTIONS

__Jorge Flores Ortega__, Mohammed Yahdi.

*Hartnell College, Salinas, CA.*

Drug resistance is a serious and growing threat to hospitalized patients. It is implicated in 700,000 deaths each year, and is predicted to become a global crisis, killing 10 million people a year worldwide by 2050 unless action is taken. With limited treatment options and the scarcity of new antibiotics in the pharmaceutical industry's pipeline, examining strategies to efficiently prevent and control those infections is becoming critically urgent. This project uses robust mathematical tools to determine and simulate efficient and cost effective control strategies, focused on special preventive measures for carbapenem-resistant enterobacteriaceae (CRE) infections. CRE have been associated with high mortality rates (30% to 72%), have demonstrated resistance to numerous classes of antibiotics, and are listed by the CDC as an immediate health threat that requires urgent and aggressive action. The mathematical model we developed is based on clinical data, up-to-date special preventive measures that have shown to reduce or clear other antibiotic resistant infections, and distinctions among susceptible, colonized, and infected patients either in a short- or long-term hospital stay. After validation of the model and identification of critical parameters, results from the basic reproduction number and the optimal control analyses show that special preventive measures, used as main controls, have greater impact in reducing the outbreak risk of CRE infections in various ICU scenarios. Mathematical concepts used include a system of 6 non-linear differential equations, next-generation matrix, optimal control theory, Pontryagin’s minimum principle, Hamiltonian, Runge-Kutta methods, and MatLab for numerical solutions and simulations.

THU-806 Q-ANALOGS OF SOME EQUATIONS FROM PHYSICS AND NUCLEAR PHYSICS

- Huy Bui ;
- Plamen Simeonov ;

THU-806

Q-ANALOGS OF SOME EQUATIONS FROM PHYSICS AND NUCLEAR PHYSICS

__Huy Bui__, Plamen Simeonov.

*University of Houston-Downtown, Houston, TX.*

We construct q-analogues of several important equations from nuclear physics. This is done by first defining 2q-versions of a power series, and then defining the q-versions of the exponential, sine, and cosine functions through the q-versions of their power series. Then we write the q-analogs of equations from nuclear physics that use these standard mathematics functions by replacing these functions with their q-analogues. The action of the q-derivative on the 2q-analogues of a power series is also explored.

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### Event Sponsors

Conference Grant Funders

- National Institute of General Medical Sciences – National Institute of Health
- National Security Agency (NSA) - Department of Defense

Platinum Sponsors

- Central Intelligence Agency
- National Geospatial-Intelligence Agency (NGA)
- National Security Agency (NSA) - Department of Defense

Gold Sponsors

Silver Sponsors

Bronze Sponsors

- Genentech
- National Aeronautics and Space Administration (NASA) - Minority University Research and Education Project (MUREP)
- Texas A&M University-Corpus Christi (TAMUCC) - College of Science & Engineering
- Texas A&M University - Graduate and Professional Studies
- University of Southern California - Keck School of Medicine, Department of Preventive Medicine

Student Presentations Sponsors

- American Chemical Society
- American Society for Biochemistry and Molecular Biology
- Biophysical Society
- Botanical Society of America
- Genetics Society of America
- Maryland Sea Grant
- Society for Industrial and Applied Mathematics
- St. Jude Children’s Research Hospital
- The University of Kansas-Department of Geology