Applied Mathematics Commons^™

Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer

Mathematical Sciences Technical Reports (MSTR)

Flux Balance Analysis (FBA) is a widely used computational model for studying the metabolic pathways of cells and the role individual metabolites and reactions play in maintaining cell function. However, the successes of FBA have been limited by faulty biological assumptions and computational imperfections. We introduce Robust Analysis of Metabolic Pathways (RAMP) to provide a more theoretically sound and computationally accurate model of cellular metabolism. RAMP overcomes the faulty assumptions of traditional FBA by allowing deviation from steady-state and accounting for variability across a cellular culture. Computationally, RAMP more successfully predicts the lethality of gene knockouts and reduces degeneracy in …

Quantitative Reasoning And Sustainability, Corrine H. Taylor

Numeracy

Quantitative Reasoning and Sustainability have much in common. Both are complex, nuanced concepts with rather long definitions that have evolved over time. Both subjects are “everybody’s business” on college campuses, and must be approached in courses across the curriculum, not merely in one course on QR or in one course on Sustainability. The growing, wider presence of both QR and Sustainability on college campuses is due to their applicability in individuals’ personal, professional, and public lives. Moreover, QR and Sustainability support and enhance each other in and out of the classroom. Sustainability is an important, authentic, relevant context for lessons …

Parameter Estimation And Uncertainty Quantication For An Epidemic Model, Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd

Mathematics and Computer Science Faculty Publications

We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )—an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications …

Parameter Estimation And Uncertainty Quantication For An Epidemic Model, Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun Lloyd

Mathematics and Statistics Faculty Publications

We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )—an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications …

Half-Life Learning Curves In The Defense Acquisition Life Cycle, Adedeji B. Badiru

Faculty Publications

Learning curves are useful for assessing performance improvement due to the positive impact of learning. In recent years, the deleterious effects of forgetting have also been recognized. Workers experience forgetting or decline in performance over time. Consequently, contemporary learning curves have attempted to incorporate forgetting components into learning curves. An area of increasing interest is the study of how fast and how far the forgetting impact can influence overall performance. This article introduces the concept of half-life analysis of learning curves using the concept of growth and decay, with particular emphasis on applications in the defense acquisition process. The computational …

Numerical Analysis For Interface Problems, Lin Mu

Theses and Dissertations

A large number of partial differential equations in geoscience and engineering can be described as interface problems. Three interface models will be considered in this dissertation. They are elliptic interface problems, Stokes interface problems, and Brinkman problems. The purpose of the dissertation is to develop and analyze robust finite element methods and finite volume methods for solving these problems. Firstly, we report the a posteriori error estimate for interface problems by conforming finite volume methods, nonconforming finite volume methods, and discontinuous finite volume methods. Recovery-based and residual-based a posteriori error estimators are constructed by using computable quantities. Secondly, we develop …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah

Applications and Applied Mathematics: An International Journal (AAM)

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …

A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal

Applications and Applied Mathematics: An International Journal (AAM)

In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …

Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.

Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study a boundary stabilization of the torsional vibrations of a solar panel. The panel is held by a rigid hub at one end and is totally free at the other. The dynamics of the overall system leads to hybrid system of equations. It is set to a certain initial vibrations with a control torque as a stabilizer at the hub end only. Taking a non-linear damping as boundary stabilizer, a uniform exponential energy decay rate is obtained directly. Thus an explicit form of uniform stabilization of the system is achieved by means of the exponential energy …

Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …

Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

In this article an efficient modification of the variational iteration method (VIM) is presented using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The new modification is tested for some examples to demonstrate reliability and efficiency of the proposed method. A comparison of our numerical results those of the conventional numerical method, the fourth-order Runge-Kutta method (RK4) are given. The comparison shows that the solution using our modification is fast-convergent and is in excellent conformance with the exact solution. Finally, we conclude that the proposed method can be applied to a large class of …

Distal Fuzzy Dynamical Systems, Y. Sayyari, M. R. Molaei

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the t-distal notion is extended for fuzzy dynamical systems on fuzzy metric spaces. A method for constructing fuzzy metric spaces is studied. The product of t-distal fuzzy dynamical systems is considered. It is proved that: a product of fuzzy dynamical systems is t- distal if and only if its components are t-distal. The persistence of the t-distal property up to a fuzzy factor map is proved.

A New Four Point Circular-Invariant Corner-Cutting Subdivision For Curve Design, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A 4-point nonlinear corner-cutting subdivision scheme is established. It is induced from a special C-shaped biarc circular spline structure. The scheme is circular-invariant and can be effectively applied to 2-dimensional (2D) data sets that are locally convex. The scheme is also extended adaptively to non-convex data. Explicit examples are demonstrated.

Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper.

Commutativity Results In Non Unital Real Topological Algebras, M. Oudadess, Y. Tsertos

Applications and Applied Mathematics: An International Journal (AAM)

We give conditions entailing commutativity in certain non unital real topological algebras. Several other results of complex algebras are also examined for real ones.

Oscillation Of Neutral Partial Dynamic Equations, Deniz Uçar, Yaşar Bolat

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the oscillation of solutions of a certain more general neutral type dynamic equation. We establish within the necessary and sufficient conditions for the oscillation of its solutions.

A New Cg-Algorithm With Self-Scaling Vm-Update For Unconstraint Optimization, Abbas Y. Al-Bayati, Ivan S. Latif

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new combined extended Conjugate-Gradient (CG) and Variable-Metric (VM) methods is proposed for solving unconstrained large-scale numerical optimization problems. The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by Al-Bayati's SCVM-method to fit a new step-size parameter using Armijo Inexact Line Searches (ILS). This method is based on the ILS and its numerical properties are discussed using different non-linear test functions with various dimensions. The global convergence property of the new algorithm is investigated under few weak conditions. Numerical experiments show that the …

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

Analysing Domestic Electricity Smart Metering Data Using Self Organising Maps, Fintan Mcloughlin, Aidan Duffy, Michael Conlon

Conference Papers

This paper investigates a method of classifying domestic electricity load profiles through Self Organising Maps (SOMs). Approximately four thousand customers are divided into groups based on their electricity demand patterns. Dwelling and occupant characteristics are then investigated for each group. The results show that SOMs are an effective way of classifying customers into groups in terms of their electrical load profile and that certain dwelling and occupant characteristics are significant factors in determining which group they end up in.

A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the determination of an unknown radiation term in the nonlinear boundary condition of a linear heat equation from an overspecified condition. First we study the existence and uniqueness of the solution via an auxiliary problem. Then a numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving the inverse heat conduction problem (IHCP) using temperature data containing significant noise is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. Some numerical experiments confirm the …

New Explicit Solutions For Homogeneous Kdv Equations Of Third Order By Trigonometric And Hyperbolic Function Methods, Marwan Alquran, Roba Al-Omary, Qutaibeh Katatbeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study two-component evolutionary systems of the homogeneous KdV equation of the third order types (I) and (II). Trigonometric and hyperbolic function methods such as the sine-cosine method, the rational sine-cosine method, the rational sinh-cosh method, sech-csch method and rational tanh-coth method are used for analytical treatment of these systems. These methods, have the advantage of reducing the nonlinear problem to a system of algebraic equations that can be solved by computerized packages.

A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.

Enacting Clan Control In Complex It Projects: A Social Capital Perspective, Cecil Eng Huang Chua, Wee-Kiat Lim, Christina Soh, Siew Kien Sia

CCX Research

The information technology project control literature has documented that clan control is often essential in complex multistakeholder projects for project success. However, instituting clan control in such conditions is challenging as people come to a project with diverse skills and backgrounds. There is often insufficient time for clan control to develop naturally. This paper investigates the question , "How can clan control be enacted in complex IT projects? " Recognizing social capital as a resource , we conceptualize a clan as a group with strong social capital (i.e., where its members have developed their structural, cognitive, and relational ties to …

Higher Homotopy Operations And André-Quillen Cohomology, David Blanc, Mark W. Johnson, James M. Turner

University Faculty Publications and Creative Works

There are two main approaches to the problem of realizing a Π-algebra (a graded group Λ equipped with an action of the primary homotopy operations) as the homotopy groups of a space X. Both involve trying to realize an algebraic free simplicial resolution G . of Λ by a simplicial space W ., and proceed by induction on the simplicial dimension. The first provides a sequence of André-Quillen cohomology classes in H n+2(Λ;Ω nΛ) (n≥1) as obstructions to the existence of successive Postnikov sections for W . (cf. Dwyer et al. (1995) [27]). The second gives a sequence of geometrically …

Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined …

The First Integral Method To Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh, A. S. Paghaleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we show the applicability of the first integral method for obtaining exact solutions of some nonlinear partial differential equations. By using this method, we found some exact solutions of the Landau-Ginburg-Higgs equation and generalized form of the nonlinear Schrödinger equation and approximate long water wave equations. The first integral method is a direct algebraic method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra.