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Full-Text Articles in Applied Mathematics

Mutation Size Optimizes Speciation In An Evolutionary Model, Nathan Dees, Sonya Bahar Aug 2010

Mutation Size Optimizes Speciation In An Evolutionary Model, Nathan Dees, Sonya Bahar

Physics Faculty Works

The role of mutation rate in optimizing key features of evolutionary dynamics has recently been investigated in various computational models. Here, we address the related question of how maximum mutation size affects the formation of species in a simple computational evolutionary model. We find that the number of species is maximized for intermediate values of a mutation size parameter μ; the result is observed for evolving organisms on a randomly changing landscape as well as in a version of the model where negative feedback exists between the local population size and the fitness provided by the landscape. The same result …

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Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine Aug 2010

Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine

Mathematical Sciences Technical Reports (MSTR)

Proteins are a primary functional component of organic life, and understanding their function is integral to many areas of research in biochemistry. The three-dimensional structure of a protein largely determines this function. Protein structure alignment compares the structure of a protein with known function to that of a protein with unknown function. A protein’s three-dimensional structure can be transformed through a smooth piecewise-linear sigmoid function to a real symmetric contact matrix that represents the functional significance of certain parts of the protein. We address the protein alignment problem as a minimization of the 2-norm difference of two proteins’ contact matrices. …

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Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas Hanes Jul 2010

Symmetries Of The Central Vestibular System: Forming Movements For Gravity And A Three-Dimensional World, Gin Mccollum, Douglas Hanes

Mathematics and Statistics Faculty Publications and Presentations

Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

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Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper May 2010

Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper

Mathematical Sciences Technical Reports (MSTR)

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …

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Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul May 2010

Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

Masters Theses & Specialist Projects

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus …

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Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of Long-Term Viabilities Of Annuals And Perennials, Anthony Delegge Apr 2010

Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of Long-Term Viabilities Of Annuals And Perennials, Anthony Delegge

Department of Mathematics: Dissertations, Theses, and Student Research

In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present …

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Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal Feb 2010

Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal

Ocean Engineering and Marine Sciences Faculty Publications

We test whether the phenotypic variance of symbionts (Symbiodinium) in corals is closely related with the capacity of corals to acclimatize to increasing seawater temperatures. Moreover, we assess whether more specialist symbionts will increase within coral hosts under ocean warming. The present study is only applicable to those corals that naturally have the capacity to support more than one type of Symbiodinium within the lifetime of a colony; for example, Montastraea annularis and Montastraea faveolata. Methodology/Principal Findings: The population dynamics of competing Symbiodinium symbiont populations were projected through time in coral hosts using a novel, discrete time optimal-resource model. Models …

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Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz Feb 2010

Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz

Mathematical Sciences Technical Reports (MSTR)

We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.

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Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng Jan 2010

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

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Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman Jan 2010

Sex, Mixability, And Modularity, Adi Livnat, Christos Papadimitriou, Nicholas Pippenger, Marcus W. Feldman

All HMC Faculty Publications and Research

The assumption that different genetic elements can make separate contributions to the same quantitative trait was originally made in order to reconcile biometry and Mendelism and ever since has been used in population genetics, specifically for the trait of fitness. Here we show that sex is responsible for the existence of separate genetic effects on fitness and, more generally, for the existence of a hierarchy of genetic evolutionary modules. Using the tools developed in the process, we also demonstrate that in terms of their fitness effects, separation and fusion of genes are associated with the increase and decrease of the …

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From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng Jan 2010

From Energy Gradient And Natural Selection To Biodiversity And Stability Of Ecosystems, Bo Deng

Department of Mathematics: Faculty Publications

The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and …

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Remarks On The Stability Of Some Size-Structured Population Models V: The Case When The Death Rate Depends On Adults Only And The Growth Rate Depends On Size Only, M. El-Doma Dec 2009

Remarks On The Stability Of Some Size-Structured Population Models V: The Case When The Death Rate Depends On Adults Only And The Growth Rate Depends On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (To appear). We concentrate our efforts in the special case when the death rate depends on adults only, the growth rate depends on size only and the maximum size for an individual in the population is infinite. Three demographic parameters are identified and are shown to determine conditions for the (in)stability of a nontrivial steady state. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. …

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Pulsatile Flow Of Blood In A Constricted Artery With Body Acceleration, Devajyoti Biswas, Uday Shankar Chakraborty Dec 2009

Pulsatile Flow Of Blood In A Constricted Artery With Body Acceleration, Devajyoti Biswas, Uday Shankar Chakraborty

Applications and Applied Mathematics: An International Journal (AAM)

Pulsatile flow of blood through a uniform artery in the presence of a mild stenosis has been investigated in this paper. Blood has been represented by a Newtonian fluid. This model has been used to study the influence of body acceleration and a velocity slip at wall, in blood flow through stenosed arteries. By employing a perturbation analysis, analytic expressions for the velocity profile, flow rate, wall shear stress and effective viscosity, are derived. The variations of flow variables with different parameters are shown diagrammatically and discussed. It is noticed that velocity and flow rate increase but effective viscosity decreases, …

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Remarks On The Stability Of Some Size-Structured Population Models Iv: The General Case Of Juveniles And Adults, M. El-Doma Dec 2009

Remarks On The Stability Of Some Size-Structured Population Models Iv: The General Case Of Juveniles And Adults, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models is investigated when the population is divided into adults and juveniles. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El-Doma (2006), Farkas, et al. (2008), and El-Doma (2008 a).

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Two-Layered Model Of Blood Flow Through Composite Stenosed Artery, Padma Joshi, Ashutosh Pathak, B. K. Joshi Dec 2009

Two-Layered Model Of Blood Flow Through Composite Stenosed Artery, Padma Joshi, Ashutosh Pathak, B. K. Joshi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a steady, axisymmetric flow, with a constricted tube has been studied. The artery has been represented by a two-layered model consisting of a core layer and a peripheral layer. It has been shown that the resistance to flow and wall shear stress increases as the peripheral layer viscosity increases. The results are compared graphically with those of previous investigators. It has been observed that the existence of peripheral layer is useful in representation of diseased arterial system.

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Remarks On The Stability Of Some Size-Structured Population Models Vi: The Case When The Death Rate Depends On Juveniles Only And The Growth Rate Depends On Size Only And The Case When Both Rates Depend On Size Only, M. El-Doma Dec 2009

Remarks On The Stability Of Some Size-Structured Population Models Vi: The Case When The Death Rate Depends On Juveniles Only And The Growth Rate Depends On Size Only And The Case When Both Rates Depend On Size Only, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

We continue our study of size-structured population dynamics models when the population is divided into adults and juveniles, started in El-Doma (to appear 1) and continued in El-Doma (to appear 2). We concentrate our efforts in two special cases, the first is when the death rate depends on juveniles only and the growth rate depends on size only, and, the second is when both the death rate and the growth rate depend on size only. In both special cases we assume that the maximum size for an individual in the population is infinite. We identify three demographic parameters and show …

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Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis Aug 2009

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis

Masters Theses & Specialist Projects

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between …

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Modeling And Analysis Of Biological Populations, Joan Lubben Jul 2009

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

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Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey Jun 2009

Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model for the spread of Japanese Encephalitis, caused by infected mosquito feeding on susceptible human population incorporating demographic and environmental factors is proposed and analyzed. In the modeling process, it is assumed that the growth rates of reservoir animal population and vector mosquito population are enhanced due to environmental discharges caused by human population related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is found that whenever the disease-free equilibrium is locally asymptotically stable, the endemic …

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Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi Jun 2009

Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi

Applications and Applied Mathematics: An International Journal (AAM)

The flow of blood through a stenosed catheterized artery has been studied. To observe the effects of hematocrit, blood has been represented by a two-phase macroscopic model (i.e., a suspension of red cells in plasma). It is found that for any given catheter size, the impedance increases with hematocrit and also for a given hematocrit, the same increases with the catheter size. In the stenotic region, the wall shear stress increases in the upstream of the stenosis throat and decreases in the downstream in an uncatheterized artery but the same possesses an opposite character in the case of a catheterized …

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Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon Jun 2009

Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the paper is to develop a simple model for capillary tissue fluid exchange system to study the effect of glycocalyx layer on the single file flow of red cells. We have considered the channel version of an idealized Krogh capillary-tissue exchange system. The glycocalyx and the tissue are represented as porous layers with different property parametric values. Hydrodynamic Lubrication theory is used to compute the squeezing flow of plasma within the small gap between the cell and the glycocalyx layer symmetrically surrounded by the tissue. The system of non linear partial differential equations has been solved using …

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Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang Jun 2009

Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang

Applications and Applied Mathematics: An International Journal (AAM)

We study an age-structured SEIR epidemic model with infectivity in the latent period. By using the theory and methods of Differential and Integral Equations, the explicit expression for the basic reproductive number R0 is first derived. It is shown that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1. It is then proved that only one endemic equilibrium exists if R0 > 1 and its stability conditions are also given.

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Biology In Mathematics At The University Of Richmond, Lester Caudill Jan 2009

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

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Habitat Selection By Anolis Carolinensis (Green Anole) In Open Pine Forests In Eastern Texas, Richard R. Schaefer, Robert R. Fleet, D. Craig Rudolph, Nancy E. Koerth Jan 2009

Habitat Selection By Anolis Carolinensis (Green Anole) In Open Pine Forests In Eastern Texas, Richard R. Schaefer, Robert R. Fleet, D. Craig Rudolph, Nancy E. Koerth

Faculty Publications

We initiated a mark-recapture study to determine the effects of shrub density on Anolis carolinensis (Green Anole) populations. Green Anole perch site, shrub species, and shrub volume preferences were also examined. We established two study plots of different shrub densities in open pine forests on the Angelina National Forest in eastern Texas. In late spring, the Green Anole population at the higher shrub-density plot was estimated to be 16 times greater than the population at the lower shrub-density plot. Green Anoles most commonly perched on live shrubs, but exhibited very little preference or avoidance of any particular species of live …

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Conceptual Circuit Models Of Neurons, Bo Deng Jan 2009

Conceptual Circuit Models Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …

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Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma Dec 2008

Remarks On The Stability Of Some Size-Structured Population Models Iii: The Case Of Constant Inflow Of Newborns, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El- Doma (2006) and El-Doma (2008).

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Model-Based Clustering Of Methylation Array Data: A Recursive-Partitioning Algorithm For High-Dimensional Data Arising As A Mixture Of Beta Distributions, E. Andres Houseman, Brock C. Christensen, Ru-Fang Yeh, Carmen J. Marsit, Margaret R. Karagas, Margaret Wrensch, Heather H. Nelson, Joseph Wiemels, Shichun Zheng, John K. Wiencke, Karl T. Kelsey Jun 2008

Model-Based Clustering Of Methylation Array Data: A Recursive-Partitioning Algorithm For High-Dimensional Data Arising As A Mixture Of Beta Distributions, E. Andres Houseman, Brock C. Christensen, Ru-Fang Yeh, Carmen J. Marsit, Margaret R. Karagas, Margaret Wrensch, Heather H. Nelson, Joseph Wiemels, Shichun Zheng, John K. Wiencke, Karl T. Kelsey

Harvard University Biostatistics Working Paper Series

No abstract provided.

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Remarks On The Stability Of Some Size-Structured Population Models Ii: Changes In Vital Rates Due To Size And Population Size, Mohammed El-Doma Jun 2008

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

Applications and Applied Mathematics: An International Journal (AAM)

The stability of some size-structured population dynamics models are investigated. We determine the steady states and study their stability. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003) and El-Doma (2006).

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Neural Network Models For Solving The Maximum Flow Problem, S. Effati, M. Ranjbar Jun 2008

Neural Network Models For Solving The Maximum Flow Problem, S. Effati, M. Ranjbar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, two new neural network models for solving the maximum flow problem are presented. The maximum flow problem in networks is formulated as a special type of linear programming problem and it is solved by appropriately defined neural networks. The nonlinear neural networks are able to generate optimal solution for maximum flow problem. We solve neural network models by one of the numerical method. Finally, some numerical examples are provided for the sake of illustration.

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Use Of Trees By The Texas Ratsnake (Elaphe Obsoleta) In Eastern Texas, Josh B. Pierce, Robert R. Fleet, Lance Mcbrayer, D. Craig Rudolph Jan 2008

Use Of Trees By The Texas Ratsnake (Elaphe Obsoleta) In Eastern Texas, Josh B. Pierce, Robert R. Fleet, Lance Mcbrayer, D. Craig Rudolph

Faculty Publications

We present information on the use of trees by Elaphe obsoleta (Texas Ratsnake) in a mesic pine-hardwood forest in eastern Texas. Using radiotelemetry, seven snakes (3 females, 4 males) were relocated a total of 363 times from April 2004 to May 2005, resulting in 201 unique locations. Snakes selected trees containing cavities and used hardwoods and snags for a combined 95% of arboreal locations. Texas Ratsnake arboreal activity peaked during July and August, well after the peak of avian breeding activity, suggesting arboreal activity involves factors other than avian predation.

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