Matching Items (25)
Filtering by
- Creators: Barrett, The Honors College
- Creators: Kostelich, Eric
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Pharmacokinetics describes the movement and processing of a drug in a body, while Pharmacodynamics describes the drug's effect on a given subject. Pharmacokinetic/Pharmacodynamic(Pk/Pd) models have become a fundamental tool when predicting bacterial behavior and drug development. In November of 2009, Katsube et al. published their paper detailing their Pk/Pd model for the drug Doripenem and the bacteria P. aeruginosa. In their paper, they determined that there is a dependent relationship between the drug's effectiveness and the dosing strategy of the drug. Therefore, this thesis has applied optimal control in order to optimize the drug's effectiveness, while not burdening the subject with the side effects of the drug. Optimal Control is a mathematical tool used to balance two competing factors. As a result, it has become a useful tool used to make decisions involving complex behavior. By using Optimal Control, the model will maximize the drug's effect on the bacterial population of P. aeruginosa, while minimizing the drug concentration of Doripenem. In doing so, our research will enable doctors and clinicians to maximize a drug's effectiveness on the body, while minimizing side effects.
ContributorsSawkins, Bryan Thomas (Author) / Camacho, Erika (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
Morphine is a commonly used analgesic in pain management. Opioid administration to a patient after surgery, such as spinal decompression surgery, can lead to adverse side effects. To demonstrate these adverse side effects could be decreased we created a model of how morphine and its metabolites are transported and excreted from the body. Using the of morphine and a standard compartment approach this thesis aimed at projecting pharmacokinetics trends of morphine overtime. A Matlab compartment model predicting the transport of morphine through the body can contribute to a better understanding of the concentrations at the systemic level, specifically with respect to a CSF, and what happens when you compare an intravenous injection to a local delivery. Other studies and models commonly utilized patient data over small periods of time2,3,5. An extended period of time will provide information into morphine’s time course after surgery. This model focuses on a compartmentalization of the major organs and the use of a simple Mechalis-Menten enzyme kinetics for the metabolites in the liver. Our results show a CSF concentration of about 1.086×〖10〗^(-12) nmol/L in 6 weeks and 1.0097×〖10〗^(-12) nmol/L in 12 weeks. The concentration profiles in this model are similar to what was expected. The implications of this suggest that patients who reported effects of morphine paste, a locally administered opioid, weeks after the surgery were due to other reasons. In creating a model we can determine important variables and dosage information. This information allows for a greater understanding of what is happening in the body and how to improve surgical outcomes. We propose this study has implications in general research in the pharmacokinetics and dynamics of pharmacology through the body.
ContributorsJacobs, Danielle Renee (Author) / Caplan, Michael (Thesis director) / Giers, Morgan (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05
Description
Monatomic gases are ideal working mediums for Brayton cycle systems due to their favorable thermodynamic properties. Closed Brayton cycle systems make use of these monatomic gases to increase system performance and thermal efficiency. Open Brayton cycles, on the other hand, operate with primarily diatomic and polyatomic gases from air and combustion products, which have less favorable properties. The focus of this study is to determine if monatomic gases can be utilized in an open Brayton cycle system, in a way that increases the overall performance, but is still cost effective.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
ContributorsBernaud, Ryan Clark (Author) / Dahm, Werner (Thesis director) / Wells, Valana (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Predicting the binding sites of proteins has historically relied on the determination of protein structural data. However, the ability to utilize binding data obtained from a simple assay and computationally make the same predictions using only sequence information would be more efficient, both in time and resources. The purpose of this study was to evaluate the effectiveness of an algorithm developed to predict regions of high-binding on proteins as it applies to determining the regions of interaction between binding partners. This approach was applied to tumor necrosis factor alpha (TNFα), its receptor TNFR2, programmed cell death protein-1 (PD-1), and one of its ligand PD-L1. The algorithms applied accurately predicted the binding region between TNFα and TNFR2 in which the interacting residues are sequential on TNFα, however failed to predict discontinuous regions of binding as accurately. The interface of PD-1 and PD-L1 contained continuous residues interacting with each other, however this region was predicted to bind weaker than the regions on the external portions of the molecules. Limitations of this approach include use of a linear search window (resulting in inability to predict discontinuous binding residues), and the use of proteins with unnaturally exposed regions, in the case of PD-1 and PD-L1 (resulting in observed interactions which would not occur normally). However, this method was overall very effective in utilizing the available information to make accurate predictions. The use of the microarray to obtain binding information and a computer algorithm to analyze is a versatile tool capable of being adapted to refine accuracy.
ContributorsBrooks, Meilia Catherine (Author) / Woodbury, Neal (Thesis director) / Diehnelt, Chris (Committee member) / Ghirlanda, Giovanna (Committee member) / Department of Psychology (Contributor) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Traumatic brain injury (TBI) is a major concern in public health due to its prevalence and effect. Every year, about 1.7 million TBIs are reported [7]. According to the According to the Centers for Disease Control and Prevention (CDC), 5.5% of all emergency department visits, hospitalizations, and deaths from 2002 to 2006 are due to TBI [8]. The brain's natural defense, the Blood Brain Barrier (BBB), prevents the entry of most substances into the brain through the blood stream, including medicines administered to treat TBI [11]. TBI may cause the breakdown of the BBB, and may result in increased permeability, providing an opportunity for NPs to enter the brain [3,4]. Dr. Stabenfeldt's lab has previously established that intravenously injected nanoparticles (NP) will accumulate near the injury site after focal brain injury [4]. The current project focuses on confirmation of the accumulation or extravasation of NPs after brain injury using 2-photon microscopy. Specifically, the project used controlled cortical impact injury induced mice models that were intravenously injected with 40nm NPs post-injury. The MATLAB code seeks to analyze the brain images through registration, segmentation, and intensity measurement and evaluate if fluorescent NPs will accumulate in the extravascular tissue of injured mice models. The code was developed with 2D bicubic interpolation, subpixel image registration, drawn dimension segmentation and fixed dimension segmentation, and dynamic image analysis. A statistical difference was found between the extravascular tissue of injured and uninjured mouse models. This statistical difference proves that the NPs do extravasate through the permeable cranial blood vessels in injured cranial tissue.
ContributorsIrwin, Jacob Aleksandr (Author) / Stabenfeldt, Sarah (Thesis director) / Bharadwaj, Vimala (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
Food safety is vital to the well-being of society; therefore, it is important to inspect food products to ensure minimal health risks are present. A crucial phase of food inspection is the identification of foreign particles found in the sample, such as insect body parts. The presence of certain species of insects, especially storage beetles, is a reliable indicator of possible contamination during storage and food processing. However, the current approach to identifying species is visual examination by human analysts; this method is rather subjective and time-consuming. Furthermore, confident identification requires extensive experience and training. To aid this inspection process, we have developed in collaboration with FDA analysts some image analysis-based machine intelligence to achieve species identification with up to 90% accuracy. The current project is a continuation of this development effort. Here we present an image analysis environment that allows practical deployment of the machine intelligence on computers with limited processing power and memory. Using this environment, users can prepare input sets by selecting images for analysis, and inspect these images through the integrated pan, zoom, and color analysis capabilities. After species analysis, the results panel allows the user to compare the analyzed images with referenced images of the proposed species. Further additions to this environment should include a log of previously analyzed images, and eventually extend to interaction with a central cloud repository of images through a web-based interface. Additional issues to address include standardization of image layout, extension of the feature-extraction algorithm, and utilizing image classification to build a central search engine for widespread usage.
ContributorsMartin, Daniel Luis (Author) / Ahn, Gail-Joon (Thesis director) / Doupé, Adam (Committee member) / Xu, Joshua (Committee member) / Computer Science and Engineering Program (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Compressed sensing magnetic resonance spectroscopic imaging (MRSI) is a noninvasive and in vivo potential diagnostic technique for cancer imaging. This technique undersamples the distribution of specific cancer biomarkers within an MR image as well as changes in the temporal dimension and subsequently reconstructs the missing data. This technique has been shown to retain a high level of fidelity even with an acceleration factor of 5. Currently there exist several different scanner types that each have their separate analytical methods in MATLAB. A graphical user interface (GUI) was created to facilitate a single computing platform for these different scanner types in order to improve the ease and efficiency with which researchers and clinicians interact with this technique. A GUI was successfully created for both prospective and retrospective MRSI data analysis. This GUI retained the original high fidelity of the reconstruction technique and gave the user the ability to load data, load reference images, display intensity maps, display spectra mosaics, generate a mask, display the mask, display kspace and save the corresponding spectra, reconstruction, and mask files. Parallelization of the reconstruction algorithm was explored but implementation was ultimately unsuccessful. Future work could consist of integrating this parallelization method, adding intensity overlay functionality and improving aesthetics.
ContributorsLammers, Luke Michael (Author) / Kodibagkar, Vikram (Thesis director) / Hu, Harry (Committee member) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05