Mountain Scholar :: Browsing by Author "Shipman, Patrick, committee member"

Browsing by Author "Shipman, Patrick, committee member"

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Open Access
A new approach to addressing two problems in pharmacokinetics and pharmacodynamics using machine learning
(Colorado State University. Libraries, 2020) Habib, Sohaib, author; Reisfeld, Brad, advisor; Munsky, Brian, committee member; Shipman, Patrick, committee member
In this work, machine learning was applied to develop solutions for two problems related to drug pharmacokinetics (PK) and pharmacodynamics (PD). The first problem was finding a way to easily predict important pharmacological measures accurately representative of those from simulation results computed via a sophisticated model for drug absorption via oral dosing. This model (OpenCAT: Open source Compartmental And Transit model) comprises a system of differential equations describing the absorption of drugs into the gastrointestinal tract, including such factors as drug dissolution and spatially-distributed absorption, metabolism, and transport. For this problem, a machine learning framework was built to develop a self-contained random forest representation of the model predictions that could be queried for critical PK parameters such as maximum plasma concentration (Cmax), time at which the maximum concentration occurs (tmax), and the area under the concentration-time curve (AUC). The random-forest representation was able to generate predictions for the targeted PK parameters close to the solution of the original OpenCAT model over a wide range of drug characteristics. The second problem involved predicting the pharmacodynamics (cholinesterase reactivation) of antidotes for nerve agents. In this case, a machine learning framework was built to use experimental data and corresponding theoretically-derived chemical descriptors to predict the pharmacodynamics of new candidate antidotes against both tested and untested nerve agents. Overall, this project has demonstrated the utility of machine learning approaches in the fields of drug pharmacokinetics and pharmacodynamics.
Open Access
A non-invasive Hall current distribution measurement system for Hall effect thrusters
(Colorado State University. Libraries, 2015) Mullins, Carl Raymond, author; Williams, John, advisor; Shipman, Patrick, committee member; Yalin, Azer, committee member
A direct, accurate method to measure thrust produced by a Hall Effect thruster on orbit does not currently exist. The ability to calculate produced thrust will enable timely and precise maneuvering of spacecraft—a capability particularly important to satellite formation flying. The means to determine thrust directly is achievable by remotely measuring the magnetic field of the thruster and solving the inverse magnetostatic problem for the Hall current density distribution. For this thesis, the magnetic field was measured by employing an array of eight tunneling magnetoresistive (TMR) sensors capable of milligauss sensitivity when placed in a high background field. The array was positioned outside the channel of a 1.5 kW Colorado State University Hall thruster equipped with a center-mounted electride cathode. In this location, the static magnetic field is approximately 30 Gauss, which is within the linear operating range of the TMR sensors. Furthermore, the induced field at this distance is greater than tens of milligauss, which is within the sensitivity range of the TMR sensors. Due to the nature of the inverse problem, the induced-field measurements do not provide the Hall current density by a simple inversion; however, a Tikhonov regularization of the induced field along with a non-negativity constraint and a zero boundary condition provides current density distributions. Our system measures the sensor outputs at 2 MHz allowing the determination of the Hall current density distribution as a function of time. These data are shown in contour plots in sequential frames. The measured ratios between the average Hall current and the discharge current ranged from 0.1 to 10 over a range of operating conditions from 1.3 kW to 2.2 kW. The temporal inverse solution at 2.0 kW exhibited a breathing mode of 37 kHz, which was in agreement with temporal measurements of the discharge current.
Open Access
A numerical model for the determination of biomass ignition from a hotspot
(Colorado State University. Libraries, 2015) McArdle, Patrick, author; Williams, John, advisor; Gao, Xinfeng, committee member; Shipman, Patrick, committee member
The determination of biomass ignition from an inert spherical hotspot using a fourth-order finite-volume method is presented. The transient ignition-combustion system is modeled by two coupled reaction-diffusion equations. One equation governs the heating characteristics of the biomass while the other governs the mass loss of the biomass. The combustion assumes a one-step, 1st-order Arrhenius reaction. This work is motivated and funded by the Department of Defense Legacy Program to create a munition specific fire danger rating system. Improving fire danger rating systems on military lands would minimize the economic and environmental impact of soldiers training on protected habitats. A better understanding of these ignition characteristics would also improve current fire spread models. Our result shows that given the ignition criteria derived from a simplified non-dimensional model and specifying critical values found by Gol'dshleger et al., an ignition probability can be established by varying the biomass properties based on moisture content. Following the procedure developed in this thesis, the computed ignition probabilities correlate well with experimental ignition data that was obtained at the Center for Environmental Management of Military Lands. Moreover, numerically solving the coupled reaction-diffusion system provides additional insight into more realistic ignition criteria involving mass loss. The numerical solution suggests more sources of heat loss, in addition to convection, must be considered for a more realistic ignition model.
Open Access
An integrated mathematics/science activity for secondary students: development, implementation, and student feedback
(Colorado State University. Libraries, 2016) Gentry, Abigail Rose, author; Pilgrim, Mary, advisor; Shipman, Patrick, committee member; Gloeckner, Gene, committee member
Mathematics teachers are often challenged by their students to give reasoning for why learning mathematics is necessary. An approach to address this question is to show students the value in learning mathematics by enlightening them on the connections that mathematics has with other disciplines and the real-world applications of mathematics. Integration is a method of teaching that can be used to give students insight as to how mathematics is useful in a variety of different fields. In addition to engaging students with relevant curriculum, leading students to discover the connections between mathematics and science (among other fields) is helpful in showing students why learning mathematics is valuable. This thesis reports on my experiences in developing and implementing an integrated mathematics/science activity in a STEM Technology class at a local high school as well as discusses student feedback about the activity, about their interdisciplinary STEM Technology class, and about the integration of mathematics and science in the classroom.
Open Access
An inverse problem and multi-compartment lung model for the estimation of lung airway resistance throughout the bronchial tree
(Colorado State University. Libraries, 2022) Heavner, Emily, author; Mueller, Jennifer, advisor; Shipman, Patrick, committee member; Cheney, Margaret, committee member; Rezende, Marlis, committee member
Mechanical ventilation is a vital treatment for patients with respiratory failure, but mechanically ventilated patients are also at risk of ventilator-induced lung injury. Optimal ventilator settings to prevent such injury could be guided by knowledge of the airway resistance throughout the lung. While the ventilator provides a single value estimating the total airway resistance of the patient, in reality the airway resistance varies along the bronchial tree. Multiple literature sources reveal a wide range of clinically used values for airway resistance along the bronchial tree, motivating an investigation to estimate the values of airway resistance in the alveolar tree and the relationship to disease state. In this work, we introduce a multi-compartment asymmetric lung model based on resistor-capacitor circuits by using an analogy between electric circuits and the human lungs. A method for solving the inverse problem of computing the vector of airway resistance values in the alveolar tree is presented. The method uses a linear least squares optimization approach with several constraints. First, a symmetric lung model that makes use of parameters supplied by the mechanical ventilator of patients with acute respiratory distress syndrome (ARDS) is used. We then generalize the model to an asymmetric lung model. The asymmetric model takes regional information data from electrical impedance tomography, a medical imaging technique, and converts them to time dependent lung airway volumes. The linear least squares optimization inverse problem is embedded in an iterative method to update unknown parameters of the forward problem for the asymmetric case.
Open Access
An investigation of the Novikov-Veselov equation: new solutions, stability and implications for the inverse scattering transform
(Colorado State University. Libraries, 2012) Croke, Ryan P., author; Mueller, Jennifer, advisor; Bradley, Mark, committee member; Shipman, Patrick, committee member; Zhou, Yongcheng, committee member
Integrable systems in two spatial dimensions have received far less attention by scholars than their one--dimensional counterparts. In this dissertation the Novikov--Veselov (NV) equation, a (2+1)--dimensional integrable system that is a generalization of the famous Korteweg de--Vreis (KdV) equation is investigated. New traveling wave solutions to the NV equation are presented along with an analysis of the stability of certain types of soliton solutions to transverse perturbations. To facilitate the investigation of the qualitative nature of various types of solutions, including solitons and their stability under transverse perturbations, a version of a pseudo-spectral numerical method introduced by Feng [J. Comput. Phys., 153(2), 1999] is developed. With this fast numerical solver some conjectures related to the inverse scattering method for the NV equation are also examined. The scattering transform for the NV equation is the same as the scattering transform used to solve the inverse conductivity problem, a problem useful in medical applications and seismic imaging. However, recent developments have shed light on the nature of the long-term behavior of certain types of solutions to the NV equation that cannot be investigated using the inverse scattering method. The numerical method developed here is used to research these exciting new developments.
Open Access
Analysis and modeling of cells, cell behavior, and helical biological molecules
(Colorado State University. Libraries, 2011) Benoit, Steven Richard, author; Putkaradze, Vakhtang, advisor; Shipman, Patrick, committee member; Estep, Don, committee member; Marconi, Mario, committee member; Tobet, Stuart, committee member
Mathematical models of biological systems have evolved over time and through the introduction and growth of computer simulation and analysis. Models have increased in sophistication and power through the combination of multi-scale approaches, molecular and granular dynamics simulations, and advances in parallelization and processing speed. However, current cell models cannot accurately predict behaviors at the whole-cell scale, nor can molecular models predict accurately the complex shape assumed by large biological molecules including proteins, although significant progress is being made toward this goal. The present work introduces new models in three domains within biological systems modeling. We first discuss a phenomenological model of observed cell motions in developing tissue that characterizes cells according to a best-fit generalized diffusion model and combines this data with Voronoi diagrams to effectively visualize patterns of cell behavior in tissue. Next, we present a series of component models for cells and cell structure that support simulations involving tens to hundreds of cells in a way that captures behaviors ignored by existing models, including pseudopod formation, membrane mechanics, cytoskeletal polymerization / depolymerization, and chemical signal transduction. The resulting models exhibit many of the behaviors of real-world cells including polarization and chemotaxis. Finally, we present a method for analysis of biological molecules that form helical conformations that includes long-range electrostatic interactions as well as short-range interactions to prevent self-intersections. We consider the stability of molecules with repeating monomers that include off-axis charge concentrations and derive energy landscapes to identify stable conformations, then analyze helical stability using geometric methods.
Open Access
Automated methods for quantifying the tortuosity of microvascular networks
(Colorado State University. Libraries, 2012) Dodd, Melody, author; Putkaradze, Vakhtang, advisor; Tobet, Stuart, committee member; Shipman, Patrick, committee member
Networks of microscopic blood vessels can be studied for changes in morphology that correlate with biological abnormalities. Tortuosity, or vessel twistiness, is one of these morphological properties, and it can be surprisingly difficult to quantify. The purpose of this thesis is to present the development, testing, and analysis of new automated methods to measure and quantify the tortuosity of microvascular networks. We will explain necessary automated image processing techniques and background information before presenting our new metrics for measuring network tortuosity. Experiments using the methods will be presented, including a full analysis of the results. We will use the results from these experiments to justify our final conclusions and recommendations regarding the performance of the methods.
Open Access
Computational feasibility of simultaneous analysis and design in interior point topology optimization
(Colorado State University. Libraries, 2023) O'Connor, Justin, author; Bangerth, Wolfgang, advisor; Weinberger, Chris, committee member; Shipman, Patrick, committee member; Liu, James, committee member; Weinberger, Chris, committee member
Topology optimization is a class of algorithms designed to optimize a design or structure to accomplish some goal. It is part of a process of computer generated design that allows engineers to design better products faster. One such algorithm that has piqued the imagination of developers is called Simultaneous Analysis and Design (SAND), especially in the context of Interior Point Optimization (IPO). This method is known to generate extremely optimal designs, and is good at avoiding local minima. However, this method is not used in practice, due to its computational cost. This thesis examines the SAND IPO method, and develops an effective algorithm to generate a design using it. I begin by discussing nonlinear optimization algorithms, selecting pieces that work together for this problem, to generate a cohesive algorithm for the whole process. Inside this developed algorithm, as with most nonlinear optimization algorithms, the most ex- pensive part is a linear solve. In my case, it is a linear solve of a block system. I develop and implement a multi-tier preconditioning approach to solve this system in a reasonable amount of time. Finally, I present a large topology optimization problem presented in three dimensions that has been solved using IPO and SAND, demonstrating the usability of the implemented algorithm.
Open Access
Computational modeling of the pharmacokinetics and pharmacodynamics of selected xenobiotics
(Colorado State University. Libraries, 2016) Zurlinden, Todd J., author; Reisfeld, Brad, advisor; Hays, Sean, committee member; Shipman, Patrick, committee member; Munsky, Brian, committee member
The determination of important endpoints in toxicology and pharmacology continues to involve the acquisition of large amounts of data through resource-intensive experimental studies involving a large number of resources. Because of this, only a small fraction of chemicals in the environment and marketplace can reasonably be evaluated for safety, and many promising drug candidates must be eliminated from consideration based on inadequate evaluation. Promisingly, advances in biologically-based computational models are beginning to allow researchers to estimate these endpoints and make useful extrapolations using a limited set of experimental data. The work described in this dissertation examined how computational models can provide meaningful insight and quantitation of important pharmacological and toxicological endpoints related to toxicity and pharmacological efficacy. To this end, physiologically-based pharmacokinetic and pharmacodynamic models were developed and applied for several pharmaceutical agents and environmental toxicants to predict significant, and diverse, biological endpoints. First, physiologically-based modeling allowed for the evaluation of various dosing regimens of rifapentine, a drug that is showing great promise for the treatment of tuberculosis, by comparing lung-specific concentration predictions to experimentally-derived thresholds for antibacterial activity. Second, physiologically-based pharmacokinetic modeling, coupled with Bayesian inference, was used as part of a methodology to characterize genetic differences in acetaminophen pharmacokinetics and also to help clinicians predict an ingested dose of this drug under overdose conditions. Third, a methodology for using physiologically-based pharmacokinetic modeling to predict health-based cognitive endpoints was demonstrated for chronic exposure to chlorpyrifos, an organophosphorus insecticide. The environmental public health indicators derived from this work allowed for biomarkers of exposure to be used to predict neurobehavioral changes following long-term exposure to this chemical. Finally, computational modeling was used to develop a mechanistically-plausible pharmacodynamic model for hepatoprotective and pro-inflammatory events to relate trichloroethylene dosing conditions to observed pathologies associated with auto-immune hepatitis.
Open Access
Constrained dynamics of rolling balls and moving atoms
(Colorado State University. Libraries, 2011) Kim, Byungsoo, author; Putkaradze, Vakhtang, advisor; Tavener, Simon, committee member; Shipman, Patrick, committee member; Marconi, Mario C., committee member
This dissertation is devoted to the study of the dynamics, conservation laws and symmetries of rolling spheres, with special attention to applications to atomic and molecular systems. Previously known conservation laws of the rolling motion are associated with the nonholonomic version of Noether's theorem. Moreover, the conservation laws are related to the reduction by Lie symmetries of the dynamic equations of motion. Symmetries in the Noether's theorem and in the reduction by Lie symmetries are compared in their applications. In addition, we analyze the collective motion of the system of rolling particles for its statistical quantities under the constraint condition of rolling without slipping motion. The numerical simulations revealed some of qualitative characteristics in the statistical mechanics of the rolling-constrained system. As a separate topic, the study of the molecular dynamics is discussed in relation to the results of recent experimental achievements with the non-contact atomic force microscopy. We propose a novel scenario explaining the process of single-atom manipulation in terms of the classical resonance effect.
Open Access
Data analysis and predictive modeling for synthetic and naturally occurring biological switches
(Colorado State University. Libraries, 2016) Schaumberg, Katherine A., author; Prasad, Ashok, advisor; Medford, June, advisor; Shipman, Patrick, committee member; Antunes, Mauricio, committee member; Krapf, Diego, committee member
Biological switches are biochemical network motifs responsible for determining the chemical state of cells, and are a key part of every biological system. The impact of these biological switches on cell behavior is broad. For example, many diseases such as cancer are thought to be caused by a misregulation of the bio-chemical state in a cell or group of cells. Also cell fates in differentiating stem cells are controlled by biological switches. Because of their general importance the synthetic biology community has also constructed synthetic biological switches in living organisms. While there are different kinds of possible switches, in my thesis I study switches capable of stably generating two unique molecular states, also called bi-stable switches. Here these switches are studied from two perspectives. In Chapters 1-4 I present theoretical and experimental work on analysis of specific circuits that act like biological switches. In Chapter 5 I employ a data mining perspective to identify gene expression signatures of switches that are sensitive to cytotoxic cancer drugs. This dissertation starts with a computational analysis of the effect of leaky promoter expression on bi-stable biological switches. In several biological and synthetic systems gene transcription is never completely off, even when repressed. This residual expression is referred to here as leaky expression. Bi-stable systems would be expected to have some amount of leaky expression in their off state. However, the impact of leaky expression on the functioning and properties of biological switches has not been well studied. To help fill this gap we conducted a theoretical analysis of leaky expression’s effect on biological switches. Two switches, a positive feedback and negative inhibition-based switch were studied. We found that the different circuit topologies showed different advantages in terms of their ability to handle leaky expression. Next this dissertation describes work done in collaboration with the Medford lab at Colorado State University, to construct and characterize a library of genetic plant parts. These parts would later be used in construction of perhaps the first synthetic bi-stable toggle switch in a plant. As part of this study, experiments were designed and conducted for finding the nature of the experimental noise associated with the assays used to test these plant parts. A mathematical normalization was developed to estimate quantitative information on the performance of each part. Validation experiments were done to assess the usefulness of this method for predicting the behavior of stably transformed plants from higher throughput transient assays. In the end a library of over one hundred quantitatively characterized plant parts in both Arabidopsis and Sorghum was constructed. The quantitative parameters of this library of genetic parts were then used in combination with a probabilistic bootstrap method we developed to predict optimal part combinations for construction of a bi-stable switch in Arabidopsis. The dissertation concludes with a study of biological networks in cancer cells from a data mining perspective. A large amount of data exists in the public domain on the sensitivity of cancer cell lines to cytotoxic drugs. Some cancers appear to be in a "sensitive state" while others are in a "resistant state". We would like to be able to know the gene expression signatures of these two states in order to predict cancer drug sensitivity from gene expression data. As a first step towards this goal we assessed the repeatability of predictions between the two standard databases of cancer cell lines, the NCI60 and the GDSC. This lead to identification of a preprocessing method needed to combine data from multiple databases. This was then followed up with the development of a comparative analysis platform. This platform was used to test the accuracy of models designed to predict drug sensitivity, when different model construction methods were used.
Open Access
Determination of reliable minimum, disproof-based particle formation mechanisms: investigation of a second-generation Ir(0)n nanoparticle system
(Colorado State University. Libraries, 2021) Whitehead, Christopher Breck, author; Finke, Richard, advisor; Neilson, Jamie, committee member; Van Orden, Alan, committee member; Shipman, Patrick, committee member
A long-sought goal in particle formation is an understanding of the chemical reaction mechanism. The complete understanding of the associated processes (nucleation, growth, and agglomeration) will yield particle size and distribution control. Mechanistic control and knowledge will yield improvements in the development of renewable energy and catalytic materials. The current state of chemical reaction mechanisms and the direct methods to study them are presented in an in-depth literature review in Chapter II. The best, state-of-the-art case studies are examined and the minimum criteria for a reliable, disproof-based chemical mechanism are presented. The experimental work presented in this dissertation centers on a second-generation {[(1,5-COD)IrI•HPO4]2}2– precursor to Ir(0)~150(HPO42–)x nanoparticle system. The exhaustive investigation of the reaction speciation and the dependence of IrI and HPO42– concentrations on the reaction kinetics are presented in Chapter III. Based on the reaction kinetics and there experimentally determined nucleation step, the molecular mechanism of Ir(0)~150(HPO42–)x nanoparticle formation is elucidated. Next, in Chapter IV, the second-generation {[(1,5-COD)IrI•HPO4]2}2– precursor to Ir(0)~150(HPO42–)x nanoparticle system is monitored directly by X-ray absorption spectroscopy and small-angle X-ray scattering and indirectly by in-house cyclohexene reporter reaction, gas-liquid chromatography, proton nuclear magnetic resonance, and transmission electron microscopy. A total of 6 physical methods are used to follow the particle formation kinetics. Finally, mechanism-enabled population balance modeling is applied as a final test of the proposed mechanism.
Open Access
Determining driving forces for small molecule aggregation using computational and theoretical methods
(Colorado State University. Libraries, 2022) Anderson, Jakob Edward, author; Rappé, Anthony, advisor; McCullagh, Martin, advisor; Kennan, Alan, committee member; Chen, Eugene, committee member; Shipman, Patrick, committee member
Molecular aggregation is largely dictated by noncovalent interactions and is a phenomenon found in a broad list of disciplines. Computational and theoretical methods, such as molecular dynamics simulations and Quantum Mechanical calculations, are well suited techniques to study the noncovalent association of various systems as they provide atomistic resolution and experimentally comparable results for the timescales on which association occurs. The studies found in this dissertation are introduced in the first chapter and are put in the context of using computational methods to study the noncovalent association and aggregation of small molecules. Chapters two, three, and four provide a foundation for the rational design of dipeptides for a given application. A wide range of potential applications for diphenylalanine (FF) have been proposed which would benefit from the development of design principles. Chapter two discusses the complexity of the noncovalent interactions at multiple stages in the FF self-assembly process. Specifically, we suggest the initial aggregation of FF is predominantly driven by electrostatics, and after a reorientation event, nanotube growth is suggested to be driven by solvent mediated forces. The results from this chapter use an array of generalized analyses enabling quantitative comparisons to future dipeptide studies. The impact of sidechain modification for either FF residue is studied in chapter three by considering valine-phenylalanine (VF) and phenylalanine-valine (FV). While the monomeric conformations are shown to sample the same states for these two dipeptides, the probabilities for state sampling as well as the water dynamics around the peptide bond are shown to differ. Chapter four connects chapters two and three by considering both the behavior of sequence dependence and dimerization of VF, FV, isoleucine-phenylalanine, and phenylalanine-isoleucine relative to that of FF. The modification of the C-terminus of FF to a smaller hydrophobic sidechain is hypothesized to enable tighter packing from this study. Additionally, N-terminus FF modification is hypothesized to increase the solvent mediated forces during dimerization in agreement with the results from chapter three. While not a completed study, chapter four provides a foundation for the continued development of design principles for FF-derivatives. A novel approach to computing the free energy of association from Quantum Mechanical calculations is then described in chapter five. Due to the treatment of low energy frequencies as harmonic and a lack of temperature dependence, calculations of the entropy of associating molecules is inaccurate. The rigid-rotor-Gaussian-oscillator approximation proposed addresses these issues by treating low lying modes with anharmonic Gaussian potentials and wave functions as well as adding a temperature dependence to the partitioning between vibrational and translational/rotational modes. This approximation significantly reduces the error in computing the entropy of associating molecules resulting in a more accurate calculation of the total free energy. The results from these studies as well as future studies based on the work in this dissertation are then summarized in the final chapter.
Open Access
Exploiting noise, non-linearity, and feedback to differentially control multiple different cells using a single optogenetic input
(Colorado State University. Libraries, 2023) May, Michael P., author; Munsky, Brian, advisor; Stasevich, Tim, advisor; Krapf, Diego, committee member; Shipman, Patrick, committee member
Motivated by Maxwells-Demon, we propose and solve a cellular control problem in which the exploitation of stochastic noise can break symmetry between two cells and allow for specific control of multiple cells using a single input signal. We find that a new type of noise-exploiting controllers are effective and can remain effective despite coarse approximations to the model's scale or extrinsic noise in key model parameters, and that these controllers can retain performance under substantial observer-actuator time delays. We also demonstrate how SIMO controllers could drive two-cell systems to follow different trajectories with different phases and frequencies by using a noise-exploiting controller. Together, these findings suggest that noise-exploiting control should be possible even in the case where models are approximate, and where parameters are uncertain. Having demonstrated the potential of noise-enhanced feedback control through computational modeling, we have also begun the next steps toward automating microscopy to implement this potential in experimental practice. Specifically, we demonstrate a new integrated pipeline to automate the image collection including: (i) quickly search in two-dimensions to find fields of view with cells of desired phenotypes, (ii) targeted collection of three-dimensional image data for these chosen fields of view, and (iii) streamlined processing of the collected images for rapid segmentation, spot detection and tracking, and cell/spot phenotype quantification.
Open Access
Flux balance analysis of metabolic models: a review of recent advances and applications
(Colorado State University. Libraries, 2016) Estep, Forrest Earnest, author; Peebles, Christie, advisor; Shipman, Patrick, committee member; Snow, Chris, committee member
Genome-level reconstructions of metabolic networks have provided new insight into the cellular functions of many organisms. These metabolic models are massive constructs, often including thousands of metabolic and transport reactions and metabolite species for even the most basic organisms. Construction of these models has typically involved an initial genomic analysis to identify known genes or genes with homologous structures for which the function may be inferred, followed by an intensive process of literature searching and experimental validation to refine the model. A number of automated algorithms have been developed to assist with this process. Once the model has been constructed, optimization techniques are applied to predict the distribution of fluxes through the reaction network. The systems then studied by FBA are generally static systems, assumed to be operating at a steady state, and thus constrained by the stoichiometries of the reactions rather than the kinetics. While these assumptions have shown to be valid under select laboratory conditions, evidence indicates that most organisms are not always at this steady state. A number of model improvements have been considered to bring predicted results more in line with experimental data, including the addition of regulatory controls, more detailed incorporation of thermodynamics, and the consideration of metabolite pool and flux data from metabolomics and labeled carbon studies, respectively. The improved predictive capabilities of these models readily find application in metabolic engineering in the custom strain design of organisms. Often this purpose is the production of some valuable bioproduct. This review seeks to give overview the advances made on both the model construction and application ends, with particular emphasis on model improvements via more complex constraints and the incorporation of experimental data.
Open Access
Gale duality, decoupling, parameter homotopies, and monodromy
(Colorado State University. Libraries, 2014) Niemerg, Matthew E., author; Bates, Daniel J., advisor; Shipman, Patrick, committee member; Peterson, Christopher, committee member; Lee, Chihoon, committee member
Numerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy.
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Generic support vector machines and Radon's theorem
(Colorado State University. Libraries, 2019) Carr, Brittany M., author; Adams, Henry, advisor; Shipman, Patrick, committee member; Fremstad, Anders, committee member
A support vector machine, (SVM), is an algorithm which finds a hyperplane that optimally separates labeled data points in Rn into positive and negative classes. The data points on the margin of this separating hyperplane are called \emph{support vectors}. We study the possible configurations of support vectors for points in general position. In particular, we connect the possible configurations to Radon's theorem, which provides guarantees for when a set of points can be divided into two classes (positive and negative) whose convex hulls intersect. If the positive and negative support vectors in a generic SVM configuration are projected to the separating hyperplane, then these projected points will form a Radon configuration.
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HIV-1 Gag trafficking and assembly: mathematical models and numerical simulations
(Colorado State University. Libraries, 2013) Munoz-Alicea, Roberto, author; Liu, Jiangguo, advisor; Tavener, Simon, advisor; Chen, Chaoping, committee member; Mueller, Jennifer, committee member; Shipman, Patrick, committee member
AIDS (acquired immune deficiency syndrome) is an infectious disease that takes away many people's lives each year. Group-specific antigen (Gag) polyprotein precursor is the major structural component of HIV, the causing agent of AIDS. Gag is essential and sufficient for the formation of new HIV virus-like particles. The late stages of the HIV-1 life cycle include the transport of Gag proteins towards the cell membrane, the oligomerization of Gag near the cell membrane during the budding process, and core assembly during virion maturation. The mechanisms for Gag protein trafficking and assembly are not yet fully understood. In order to gain further insight into the mechanisms of HIV-1 replication, we develop and analyze mathematical models and numerical algorithms for intracellular Gag protein trafficking, Gag trimerization near the cell membrane, and HIV-1 core assembly. Our preliminary results indicate that active transport plays an important role for Gag trafficking in the cytoplasm. This process can be mathematically modeled by convection-diffusion equations, which can be solved efficiently using characteristic finite element methods. We employ differential dynamical systems to model Gag trimerization and HIV-1 core assembly. For the Gag trimerization model, we estimate relationships between the association and dissociation parameters as well as the Gag arrival and multimerization parameters. We also find expressions for the equilibrium concentrations of the monomer and trimer species, and show that the equilibrium is asymptotically stable. For HIV-1 core assembly, we first consider a model developed by Zlonick and others, which regards assembly as a polymerization reaction. We utilize theoretical and numerical tools to confirm the stability of the equilibrium of CA intermediates. In addition, we propose a cascaded dynamical system model for HIV-1 core assembly. The model consists of two subsystems: one subsystem for nucleation and one for elongation. We perform simulations on the nucleation model, which suggests the existence of an equilibrium of the CA species.
Open Access
Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces
(Colorado State University. Libraries, 2012) Brake, Daniel Abram, author; Putkaradze, Vakhtang, advisor; Maciejewski, Tony, advisor; Marconi, Mario, committee member; Bates, Dan, committee member; Shipman, Patrick, committee member
This dissertation considers three topics that are united by the theme of application of geometric and nonlinear mechanics to practical problems. Firstly we consider the parallel implementation of numerical solution of nonlinear polynomial systems depending on parameters. The program written to do this is called Paramotopy, and uses the Message Passing Interface to distribute homotopy continuation solves in another program called Bertini across a supercomputer. Paramotopy manages writing of Bertini input files, allows automatic re-solution of the system at points at which paths failed, and makes data management easy. Furthermore, parameter homotopy nets huge performance gains over fresh homotopy continuation runs. Superlinear speedup was achieved, up to hard drive throughput capacity. Various internal settings are demonstrated and explored, and the User's Manual is included. Second, we apply nonlinear theory and simulation to nanomechanical sensor arrays. Using vibrating GaAs pillars, we model Intrinsic Localized Modes (ILMs), and investigate ILM-defect pinning, formation, lifetime, travel and movement, and parameter dependence. Intrinsic Localized Modes have been analyzed on arrays of nonlinear oscillators. So far, these oscillators have had a single direction of vibration. In current experiments for single molecule detection, arrays made of Gallium Arsenide will be innately bidirectional, forced, dissipative. We expand previous full models to bidirectionality, and simulate using ODE solvers. We show that small regions of a very large parameter space permit strong ILM formation. Additionally, we use Hamiltonian mechanics to derive new simplified models for the monodirectional ILM travel on an infinite array. This monodirectional ILMs of constant amplitude have unrealistic behavior. Permitting the amplitude of the ILM to vary in time produces much more realistic behavior, including wandering and intermittent pinning. The final set of problems concerns the application of numerical algebraic geometric methods to untangle the phase space of cooperating robots, and optimize configuration for fault tolerance. Given two robots in proximity to each other, if one experiences joint failure, the other may be able to assist, restoring lost workspace. We define a new multiplicity-weighted workspace measure, and use it to solve the optimization problem of finding the best location for an assistance socket and separation distance for the two robots, showing that the solution depends on robot geometry, which link is being grasped, and the choice of objective function.