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Mathematical modeling

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Articles 61 - 69 of 69

Full-Text Articles in Mathematics

Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan Apr 2010

Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.

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Coenzyme Q1 Redox Metabolism During Passage Through The Rat Pulmonary Circulation And The Effect Of Hyperoxia, Said H. Audi, Marilyn P. Merker, Gary S. Krenz, Taniya Ahuja, David L. Roerig, Robert D. Bongard Oct 2008

Coenzyme Q1 Redox Metabolism During Passage Through The Rat Pulmonary Circulation And The Effect Of Hyperoxia, Said H. Audi, Marilyn P. Merker, Gary S. Krenz, Taniya Ahuja, David L. Roerig, Robert D. Bongard

Mathematics, Statistics and Computer Science Faculty Research and Publications

The objective was to evaluate the pulmonary disposition of the ubiquinone homolog coenzyme Q1 (CoQ1) on passage through lungs of normoxic (exposed to room air) and hyperoxic (exposed to 85% O2 for 48 h) rats. CoQ1 or its hydroquinone (CoQ1H2) was infused into the arterial inflow of isolated, perfused lungs, and the venous efflux rates of CoQ1H2 and CoQ1 were measured. CoQ1H2 appeared in the venous effluent when CoQ1 was infused, and CoQ1 appeared when CoQ1H2 was infused. In normoxic lungs, CoQ …

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At Least Four Distinct Circadian Regulatory Mechanisms Required For All Phases Of Rhythms In Mrna Amount, Sigrid Jacobshagen, Bruce Kessler, Claire Rinehart Jul 2008

At Least Four Distinct Circadian Regulatory Mechanisms Required For All Phases Of Rhythms In Mrna Amount, Sigrid Jacobshagen, Bruce Kessler, Claire Rinehart

Mathematics Faculty Publications

Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA abundance have been reported. These rhythms generally differ in amplitude and phase. First studies on circadian rhythms of transcription on a large scale are also emerging. We investigated to what extent the same circadian regulatory mechanism of transcription can give rise to rhythms in RNA amount that differ in phase solely based on a parameter that is not regulated by the circadian clock. Using a discrete-time approach, we modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. We …

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Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng May 2007

Prediction Of Mrna Polyadenylation Sites In The Human Genome And Mathematical Modeling Of Alternative Polyadenylation, Yiming Cheng

Dissertations

Messenger RNA (mRNA) polyadenylation plays many important roles in the cell, such as transcription termination, mRNA stability and transportation, and mRNA translation in eukaryotic cells. A large number of human and mouse genes have multiple polyadenylation sites (referred to as poly(A) sites) that lead to variable transcripts, some of which are translated into various protein products with different functions. However, the details about when and where the polyadenylation occurs, and how pre-mRNA switches from one poly(A) site to another are still unknown. This kind of 3 '-end processing can be regulated by the cell environment, cell cycle stage, and tissue …

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Modeling Projection Neuron And Neuromodulatory Effects On A Rhythmic Neuronal Network, Nicholas Kintos Jan 2007

Modeling Projection Neuron And Neuromodulatory Effects On A Rhythmic Neuronal Network, Nicholas Kintos

Dissertations

Projection neurons shape the activity of many neural networks. In particular, neuromodulatory substances, which are often released by projection neurons, alter the cellular and/or synaptic properties within a target network. However, neural networks in turn influence projection neuron input via synaptic feedback. This dissertation uses mathematical and biophysically-realistic modeling to investigate these issues in the gastric mill (chewing) motor network of the crab, Cancer borealis. The projection neuron MCN1 elicits a gastric mill rhythm in which the LG neuron and INTl burst in anti-phase due to their reciprocal inhibition. However, bath application of the neuromodulator PK elicits a similar gastric …

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Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore Jan 2006

Optimal Therapy Regimens For Treatment-Resistant Mutations Of Hiv, Weiqing Gu, Helen Moore

All HMC Faculty Publications and Research

In this paper, we use control theory to determine optimal treatment regimens for HIV patients, taking into account treatment-resistant mutations of the virus. We perform optimal control analysis on a model developed previously for the dynamics of HIV with strains of various resistance to treatment (Moore and Gu, 2005). This model incorporates three types of resistance to treatments: strains that are not responsive to protease inhibitors, strains not responsive to reverse transcriptase inhibitors, and strains not responsive to either of these treatments. We solve for the optimal treatment regimens analytically and numerically. We find parameter regimes for which optimal dosing …

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A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu Apr 2005

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

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Coffee To Go! Modeling Thermoclines In Multivariable Calculus, Andrea Bruder, Brynja R. Kohler Jan 2005

Coffee To Go! Modeling Thermoclines In Multivariable Calculus, Andrea Bruder, Brynja R. Kohler

Mathematics and Statistics Faculty Publications

While mathematical modeling is an integral process in applied mathematics, students rarely encounter genuine modeling opportunities in their calculus courses. Here we introduce a laboratory experience as a natural starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data. We require students to write a report about their findings. This …

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A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya Jan 2001

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

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