Applied Mathematics Commons^™

Effects Of An Inserted Endoscope On Chyme Movement In Small Intestine – A Theoretical Model, V. P. Srivastava

Applications and Applied Mathematics: An International Journal (AAM)

The effects of an inserted endoscope on chyme movement in small intestine (gastrointestinal tract) have been investigated. The flow of chyme is induced by a progressive wave of area contraction along the length of intestinal wall under long wavelength approximation. It is found that the chyme movement is significantly influenced due to the presence of the endoscope. The pressure drop assumes lower values for higher values of the endoscope radius for small flow rates but the property reverses with increasing flow rates. The friction forces at intestinal wall and endoscope possess character similar to the pressure drop for any given …

Age-Structured Population Model With Cannibalism, Mmohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An age-structured population model with cannibalism is investigated. We determine the steady states and study the local asymptotic stability as well as the global stability. The results in this paper generalize previous results.

Stability Analysis For The Gurtin-Maccamy’S Age-Structured Population Dynamics Model, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of the Gurtin-MacCamy’s age-structured population dynamics model is investigated. We determine the steady states and study their stability. The results in this paper generalize previous results.

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

An Age-Structured Resource-Consumer Dynamical Model, Jean M. Tchuenche

Applications and Applied Mathematics: An International Journal (AAM)

Many dynamical systems in population biology in which agents compete for resources may exhibit chaotic fluctuations. This short letter develops Gamarra and Solé's previous work. We briefly review a classical model of population with complex dynamics, and proceed to study the dynamics of an age-structured resource-consumer model, in which the fertility coefficients are density independent. Implicit or first integral solutions of the model are obtained, and conditions for which they are stable given. It is observed that resource availability at any time depends on the number of potential consumers present.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng

Department of Mathematics: Faculty Publications

Sexual reproduction in nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.

An Epidemiological Model Of Rift Valley Fever, Holly D. Gaff, David M. Hartley, Nicole P. Leahy

Biological Sciences Faculty Publications

We present and explore a novel mathematical model of the epidemiology of Rift Valley Fever (RVF). RVF is an Old World, mosquito-borne disease affecting both livestock and humans. The model is an ordinary differential equation model for two populations of mosquito species, those that can transmit vertically and those that cannot, and for one livestock population. We analyze the model to find the stability of the disease-free equlibrium and test which model parameters affect this stability most significantly. This model is the basis for future research into the predication of future outbreaks in the Old World and the assessment of …

Spatial Ecology Of The Coachwhip, Masticophis Flagellum (Squamata: Colubridae), In Eastern Texas, Richard W. Johnson, Robert R. Fleet, Michael B. Keck, D. Craig Rudolph

Faculty Publications

We radio-tracked nine Masticophis flagellum (Coachwhips) to determine home range, habitat use, and movements in eastern Texas from April to October 2000. Home ranges of Coachwhips contained more oak savanna macrohabitat than early-successional pine plantation or forested seep, based on the availability of these three macrohabitats in the study area. Likewise, within their individual home ranges, Coachwhips used oak savanna more than the other two macrohabitats, based on availability. An analysis of microhabitat use revealed that, relative to random sites within their home range, Coachwhips were found at sites with fewer pine trees and more herbaceous vegetation taller than 30 …

Multiple Mixed-Type Attractors In A Competition Model, J. M. Cushing, Shandelle M. Henson, Chantel C. Blackburn

Faculty Publications

We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages. © 2007 Taylor & Francis Group, LLC.

Analysis Of An Sirs Age-Structured Epidemic Model With Vaccination And Vertical Transmission Of Disease, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIRS age-structured epidemic model for a vertically as well as horizontally transmitted disease under vaccination is investigated when the fertility, mortality and removal rates depend on age and the force of infection of proportionate mixing assumption type, and vaccination wanes over time. We prove the existence and uniqueness of solution to the model equations, and show that solutions of the model equations depend continuously on the initial age-distributions. Furthermore, we determine the steady states and obtain an explicitly computable threshold condition, in terms of the demographic and epidemiological parameters of the model; we then study the stability of the …

Remarks On The Stability Of Some Size-Structured Population Models I: Changes In Vital Rates Due To Population Only, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We consider a size-structured population model that has been studied in Calsina et al. (2003). We propose a different approach that provides direct stability results, and we correct a stability result given therein. In addition, we obtain global stability results that have not been given in Calsina et al. (2003).

Development Of An Unbiased Statistical Method For The Analysis Of Unigenic Evolution, Colleen D. Behrsin, Chris J. Brandl, David W. Litchfield, Brian H. Shilton, Lindi M. Wahl

Biochemistry Publications

Background: Unigenic evolution is a powerful genetic strategy involving random mutagenesis of a single gene product to delineate functionally important domains of a protein. This method involves selection of variants of the protein which retain function, followed by statistical analysis comparing expected and observed mutation frequencies of each residue. Resultant mutability indices for each residue are averaged across a specified window of codons to identify hypomutable regions of the protein. As originally described, the effect of changes to the length of this averaging window was not fully eludicated. In addition, it was unclear when sufficient functional variants had been examined …

An Optimal Brain Can Be Composed Of Conflicting Agents, Adi Livnat, Nicholas Pippenger

All HMC Faculty Publications and Research

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve “selfish” agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only.

Why Is The Number Of Dna Bases 4?, Bo Deng

Department of Mathematics: Faculty Publications

In this paper we construct a mathematical model for DNA replication based on Shannon’s mathematical theory for communication. We treatDNAreplication as a communication channel. We show that the mean replication rate is maximal with four nucleotide bases under the primary assumption that the pairing time of the G–C bases is between 1.65 and 3 times the pairing time of the A–T bases.

Using Domination To Analyze Rna Structures., Travis Reves Coake

Electronic Theses and Dissertations

Understanding RNA molecules is important to genomics research. Recently researchers at the Courant Institute of Mathematical Sciences used graph theory to model RNA molecules and provided a database of trees representing possible secondary RNA structures. In this thesis we use domination parameters to predict which trees are more likely to exist in nature as RNA structures. This approach appears to have promise in graph theory applications in genomics research.

Cluster Analysis Of Genomic Data With Applications In R, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper, we provide an overview of existing partitioning and hierarchical clustering algorithms in R. We discuss statistical issues and methods in choosing the number of clusters, the choice of clustering algorithm, and the choice of dissimilarity matrix. In particular, we illustrate how the bootstrap can be employed as a statistical method in cluster analysis to establish the reproducibility of the clusters and the overall variability of the followed procedure. We also show how to visualize a clustering result by plotting ordered dissimilarity matrices in R. We present a new R package, hopach, which implements the hybrid clustering method, …

A Bayesian Method For Finding Interactions In Genomic Studies, Wei Chen, Debashis Ghosh, Trivellore E. Raghuanthan, Sharon Kardia

The University of Michigan Department of Biostatistics Working Paper Series

An important step in building a multiple regression model is the selection of predictors. In genomic and epidemiologic studies, datasets with a small sample size and a large number of predictors are common. In such settings, most standard methods for identifying a good subset of predictors are unstable. Furthermore, there is an increasing emphasis towards identification of interactions, which has not been studied much in the statistical literature. We propose a method, called BSI (Bayesian Selection of Interactions), for selecting predictors in a regression setting when the number of predictors is considerably larger than the sample size with a focus …

Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh

The University of Michigan Department of Biostatistics Working Paper Series

One of the benefits of profiling of cancer samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Such subgroups have typically been found in microarray data using hierarchical clustering. A major problem in interpretation of the output is determining the number of clusters. We approach the problem of determining disease subtypes using mixture models. A novel estimation procedure of the parameters in the mixture model is developed based on a combination of random projections and the expectation-maximization algorithm. Because the approach is probabilistic, our approach provides a measure for the number of true clusters …

Differential Expression With The Bioconductor Project, Anja Von Heydebreck, Wolfgang Huber, Robert Gentleman

Bioconductor Project Working Papers

A basic, yet challenging task in the analysis of microarray gene expression data is the identification of changes in gene expression that are associated with particular biological conditions. We discuss different approaches to this task and illustrate how they can be applied using software from the Bioconductor Project. A central problem is the high dimensionality of gene expression space, which prohibits a comprehensive statistical analysis without focusing on particular aspects of the joint distribution of the genes expression levels. Possible strategies are to do univariate gene-by-gene analysis, and to perform data-driven nonspecific filtering of genes before the actual statistical analysis. …

A Graph Theoretic Approach To Testing Associations Between Disparate Sources Of Functional Genomic Data, Raji Balasubramanian, Thomas Laframboise, Denise Scholtens, Robert Gentleman

Bioconductor Project Working Papers

The last few years have seen the advent of high-throughput technologies to analyze various properties of the transcriptome and proteome of several organisms. The congruency of these different data sources, or lack thereof, can shed light on the mechanisms that govern cellular function. A central challenge for bioinformatics research is to develop a unified framework for combining the multiple sources of functional genomics information and testing associations between them, thus obtaining a robust and integrated view of the underlying biology.

We present a graph theoretic approach to test the significance of the association between multiple disparate sources of functional genomics …

Statistical Analyses And Reproducible Research, Robert Gentleman, Duncan Temple Lang

Bioconductor Project Working Papers

For various reasons, it is important, if not essential, to integrate the computations and code used in data analyses, methodological descriptions, simulations, etc. with the documents that describe and rely on them. This integration allows readers to both verify and adapt the statements in the documents. Authors can easily reproduce them in the future, and they can present the document's contents in a different medium, e.g. with interactive controls. This paper describes a software framework for authoring and distributing these integrated, dynamic documents that contain text, code, data, and any auxiliary content needed to recreate the computations. The documents are …

Miscellaneous Publication 8/2004 - Midas User Manual. Version 1, Ross Kingwell, Felicity Flugge, Emma Kopke, Michael O'Connell

Farm Systems and Economics published reports

What is MIDAS?

It's a computer model of dryland farming in Western Australia. MIDAS is an acronym (Model of an Integrated Dryland Agricultural System). Currently there are five versions of MIDAS, each describes a representative farm in a particular farming region of Western Australia. Versions exist for the following regions (see Figure 1):

• the Eastern Wheatbelt;
• the Central Wheatbelt;
• the West Midlands;
• the Great Southern; and,
• the South Coast.

Each of these versions is a mathematical programming model of a representative farm.

Bioconductor: Open Software Development For Computational Biology And Bioinformatics, Robert C. Gentleman, Vincent J. Carey, Douglas J. Bates, Benjamin M. Bolstad, Marcel Dettling, Sandrine Dudoit, Byron Ellis, Laurent Gautier, Yongchao Ge, Jeff Gentry, Kurt Hornik, Torsten Hothorn, Wolfgang Huber, Stefano Iacus, Rafael Irizarry, Friedrich Leisch, Cheng Li, Martin Maechler, Anthony J. Rossini, Guenther Sawitzki, Colin Smith, Gordon K. Smyth, Luke Tierney, Yee Hwa Yang, Jianhua Zhang

Bioconductor Project Working Papers

The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. We detail some of the design decisions, software paradigms and operational strategies that have allowed a small number of researchers to provide a wide variety of innovative, extensible, software solutions in a relatively short time. The use of an object oriented programming paradigm, the adoption and development of a software package system, designing by contract, distributed development and collaboration with other projects are elements of this project's success. Individually, each of these concepts are useful and important but when combined they have …

Diel Activity Patterns Of The Louisiana Pine Snakes (Pituophis Ruthveni) In Eastern Texas, Marc J. Ealy, Robert R. Fleet, D. Craig Rudolph

Faculty Publications

This study examined the diel activity patterns of six Louisiana pine snakes in eastern Texas using radio-telemetry. snakes were monitored for 44 days on two study areas from May to October 1996. Louisana pine snakes were primarily diurnal with moderate crepuscular activity, spending the night within pocket gopher burrows or inactive on the surface. During daylight hours, snakes spent approximately 59% of their time underground within gopher burrows, burned out/rotten stumps, or nine-branded armadillo (Dasypus novemcinctus) burrows. Remaining time was spent on the surface either close to subteranean refuge, or in long distance movements that generally terminet at …

Computational Protein Biomarker Prediction: A Case Study For Prostate Cancer, Michael Wagner, Dayanand N. Naik, Alex Pothen, Srinivas Kasukurti, Raghu Ram Devineni, Bao-Ling Adam, O. John Semmes, George L. Wright Jr.

Mathematics & Statistics Faculty Publications

Background: Recent technological advances in mass spectrometry pose challenges in computational mathematics and statistics to process the mass spectral data into predictive models with clinical and biological significance. We discuss several classification-based approaches to finding protein biomarker candidates using protein profiles obtained via mass spectrometry, and we assess their statistical significance. Our overall goal is to implicate peaks that have a high likelihood of being biologically linked to a given disease state, and thus to narrow the search for biomarker candidates.

Results: Thorough cross-validation studies and randomization tests are performed on a prostate cancer dataset with over 300 patients, obtained …

Simple Parallel Statistical Computing In R, Anthony Rossini, Luke Tierney, Na Li

UW Biostatistics Working Paper Series

Theoretically, many modern statistical procedures are trivial to parallelize. However, practical deployment of a parallelized implementation which is robust and reliably runs on different computational cluster configurations and environments is far from trivial. We present a framework for the R statistical computing language that provides a simple yet powerful programming interface to a computational cluster. This interface allows the development of R functions that distribute independent computations across the nodes of the computational cluster. The resulting framework allows statisticians to obtain significant speed-ups for some computations at little additional development cost. The particular implementation can be deployed in heterogeneous computing …

Literate Statistical Practice, Anthony Rossini, Friedrich Leisch

UW Biostatistics Working Paper Series

Literate Statistical Practice (LSP, Rossini, 2001) describes an approach for creating self-documenting statistical results. It applies literate programming (Knuth, 1992) and related techniques in a natural fashion to the practice of statistics. In particular, documentation, specification, and descriptions of results are written concurrently with writing and evaluation of statistical programs. We discuss how and where LSP can be integrated into practice and illustrate this with an example derived from an actual statistical consulting project. The approach is simplified through the use of a comprehensive, open source toolset incorporating Noweb, Emacs Speaks Statistics (ESS), Sweave (Ramsey, 1994; Rossini, et al, 2002; …

Stochastic Intra-Cellular Modeling, Thomas E. Hopkins

Theses and Dissertations

Air Force personnel may sometimes come into contact with potentially harmful chemicals while performing their duties. Of course the Air Force desires to keep any potential health risks to its members to a minimum. To this end the Air Force would like to identify which chemicals are toxic, their level of toxicity, and the processes by which these chemicals disrupt normal biological activities at the cellular level. The development of mathematical models can be of great benefit to toxicity studies. Because real world systems involve randomness, that is noise, and the desire is to create mathematical models to represent those …

Comparing Clustering Algorithms For Use With Genomic And Proteomic Data, Rebecca A. Olson

Theses and Dissertations

The Human Genome Project and related projects have resulted in the development of a number of new experimental and analytic tools for use in genomic and proteomic research. In the area of toxicogenomics, researchers are concerned with how genes react to exposure to certain chemicals. The United States Air Force is interested in the effect of exposure to mission-essential chemicals. Although military personnel may come into contact with chemicals such as hydrazine, risk assessment is usually very limited. On the genomic level, risk assessment is a multi-stop and multi-disciplinary process. The process begins with an experiment that exposes cells to …