Browsing Department of Mathematics and Statistics by Issue Date
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Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
(Journal of Differential Equations (Elsevier Science), 2002)In this paper we prove finite cyclicity of several of the most generic graphics through a nilpotent point of saddle or elliptic type of codimension 3 inside C . families of planar vector fields. In some cases our results ... 
Bifurcation Analysis of a PredatorPrey System With Nonmonotonic Function Response
(SIAM Journal on Applied Mathematics, 2002)We consider a predatorprey system with nonmonotonic functional response: p(x) = mx /(ax2 +bx+1) . By allowing b to be negative (b > −2√a), p(x) is concave up for small values of x > 0 as it is for the sigmoidal functional ... 
The CourantHerrmann conjecture
(Journal of Applied Mathematics and Mechanics, 2003)The Courant‐Herrmann Conjecture (CHC) concerns the sign properties of combinations of the Dirichlet eigenfunctions of elliptic pde's, the most important of which is the Helmholtz equation for $D \in \mathbb{R}^N$. If the ... 
Metapopulation Dynamics with Migration and Local Competition
(American Mathematical Society, 2003)Many patchbased metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We study a metapoulation model which explicitly incorporates ... 
PPgraphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem
(Journal of Differential Equations (Elsevier Science), 2004)This paper is part of the program launched in (J. Differential Equations 110(1) (1994) 86) to prove the finiteness part of Hilbert’s 16th problem for quadratic system, which consists in proving that 121 graphics have finite ... 
Fast and slow dynamics of malaria and the Sgene frequency.
(Journal of Dynamics and Differential Equations (Springer), 2004)A mathematical model incorporating both malaria epidemics and human population genetics of the sicklecell gene is studied. Singular perturbation techniques are used to separate the dynamics of the model into two timescales ... 
Removal of phase artifacts from fMRI data using a Stockwell transform filter improves brain activity detection
(Magnetic Resonance in Medicine, 2004)A novel and automated technique is described for removing fMRI image artifacts resulting from motion outside of the imaging field of view. The technique is based on the Stockwell transform (ST), a mathematical operation ... 
Asymptotic Properties of Weighted Likelihood Estimators
(Journal of Statistical Planning and Inference, 2004)The relevance weighted likelihood method was introduced by Hu and Zidek (Technical Report No. 161, Department of Statistics, The University of British Columbia, Vancouver, BC, Canada, 1995) to formally embrace a variety ... 
A Mathematical Model for Assessing Control Strategies Against West Nile Virus
(Bulletin of Mathematical Biology, Society for Mathematical Biology, 2005)Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and ... 
Distributed Vector Processing of A New Local Multiscale: Fourier Transform for Medical Imaging Applications
(IEEE Transactions on Medical Imaging, 2005)The recently developed Stransform (ST) combines features of the Fourier andWavelet transforms; it reveals frequency variation over both space and time. It is a potentially powerful tool that can be applied to medical image ... 
From the PPgraphics to the finiteness part of Hilbert's 16th problem for quadratic systems
(World Scientific Publishing, 2005)This is part of the effort, the program launched by Dumortier, Roussarie and Rousseau, in proving the finiteness part of Hilbert’s 16th problem. In this paper, we highlight the ideas of proving the finite cyclicity of ... 
Derivation of Mixture Distribution and Weighted Likelihood as minimizers of KLdivergence subject to constraints
(Annals  Institute of Statistical Mathematics, 2005)In this article, mixture distributions and weighted likelihoods are derived within an informationtheoretic framework and shown to be closely related. This surprising relationship obtains in spite of the arithmetic form ... 
Nonparametric tests for differential gene expression and interaction effects in multifactorial microarray experiments
(BioMed Central, 20050721)Background Numerous nonparametric approaches have been proposed in literature to detect differential gene expression in the setting of two userdefined groups. However, there is a lack of nonparametric procedures to analyze ... 
Multiple Focus and Hopf Bifurcations in a PredatorPrey System with Nonmonotonic Functional Response
(SIAM Journal on Applied Mathematics, 2006)In this paper, we develop a criterion to calculate the multiplicity of a multiple focus for general predator prey systems. As applications of this criterion, we calculate the most multiplicity of a multiple focus in a ... 
An Iterative Nonparametric Clustering Algorithm Based on Local Shrinking
(Computational Statistics and Data Analysis, 2006)In this paper, we propose a new nonparametric clustering method based on local shrinking. Each data point is transformed in such a way that it moves a specific distance toward a cluster center. The direction and the ... 
A Derivative Free Optimization Algorithm based on Conditional Moments
(Journal of Mathematical Analysis and Applications, 2006)In this paper we propose a derivativefree optimization algorithm based on conditional moments for finding the maximizer of an objective function. The proposed algorithm does not require calculation or approximation of any ... 
Linear grouping using orthogonal regression
(Computational Statistics and Data Analysis, 2006)A new method to detect different linear structures in a data set, called Linear Grouping Algorithm (LGA), is proposed. LGA is useful for investigating potential linear patterns in data sets, that is, subsets that follow ... 
Clustering Large Software Systems at Multiple Layers
(Information and Software Technology, 2006)Software clustering algorithms presented in the literature rarely incorporate in the clustering process dynamic information, such as the number of function invocations during run time. Moreover, the structure of a software ... 
The Loop Quantities and Bifurcations of Homoclinic Loops
(Journal of Differential Equations (Elsevier Science), 20070131)The stability and bifurcations of a homoclinic loop for planar vector fields are closely related to the limit cycles. For a homoclinic loop of a given planar vector field, a sequence of quantities, the homoclinic loop ... 
Efficient algorithmic implementation of the Voigt/complex error function based on exponential series approximation
(Elsevier, Applied Mathematics and Computation, 20111101)We show that a Fourier expansion of the exponential multiplier yields an exponential series that can compute highaccuracy values of the complex error function in a rapid algorithm. Numerical error analysis and computational ...