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Articles 1 - 8 of 8
Full-Text Articles in Mathematics
An Image Segmentation Technique With Statistical Strategies For Pesticide Efficacy Assessment, Steven B. Kim, Dong Sub Kim, Xiaoming Mo
An Image Segmentation Technique With Statistical Strategies For Pesticide Efficacy Assessment, Steven B. Kim, Dong Sub Kim, Xiaoming Mo
Mathematics and Statistics Faculty Publications and Presentations
Image analysis is a useful technique to evaluate the efficacy of a treatment for weed control. In this study, we address two practical challenges in the image analysis. First, it is challenging to accurately quantify the efficacy of a treatment when an entire experimental unit is not affected by the treatment. Second, RGB codes, which can be used to identify weed growth in the image analysis, may not be stable due to various surrounding factors, human errors, and unknown reasons. To address the former challenge, the technique of image segmentation is considered. To address the latter challenge, the proportion of …
A Posteriori Error Estimates For Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques, Stefano Giani, Luka Grubišić, Harri Hakula, Jeffrey S. Ovall
A Posteriori Error Estimates For Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques, Stefano Giani, Luka Grubišić, Harri Hakula, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate …
A Tutorial Of Bland Altman Analysis In A Bayesian Framework, Krissina M. Alari, Steven B. Kim, Jeffrey O. Wand
A Tutorial Of Bland Altman Analysis In A Bayesian Framework, Krissina M. Alari, Steven B. Kim, Jeffrey O. Wand
Mathematics and Statistics Faculty Publications and Presentations
There are two schools of thought in statistical analysis, frequentist, and Bayesian. Though the two approaches produce similar estimations and predictions in large-sample studies, their interpretations are different. Bland Altman analysis is a statistical method that is widely used for comparing two methods of measurement. It was originally proposed under a frequentist framework, and it has not been used under a Bayesian framework despite the growing popularity of Bayesian analysis. It seems that the mathematical and computational complexity narrows access to Bayesian Bland Altman analysis. In this article, we provide a tutorial of Bayesian Bland Altman analysis. One approach we …
Robust Estimates For Hp-Adaptive Approximations Of Non-Self-Adjoint Eigenvalue Problems, Stefano Giani, Luka Grubišić, Agnieszka Międlar, Jeffrey S. Ovall
Robust Estimates For Hp-Adaptive Approximations Of Non-Self-Adjoint Eigenvalue Problems, Stefano Giani, Luka Grubišić, Agnieszka Międlar, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experiments demonstrate the efficiency and reliability of our approach.
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
The P-P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P?P order based on P-P plots. For a pair of random variables (X 1, Y1) and (X 2, Y 2) one can see the relative precedence of Y 2 over X 2 versus that of Y 1 over X 1 using P-P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the …
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc
Mathematics and Statistics Faculty Publications and Presentations
We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Benchmark Results For Testing Adaptive Finite Element Eigenvalue Procedures Ii (Cluster Robust Eigenvector And Eigenvalue Estimates), Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
As a model benchmark problem for this study we consider a highly singular transmission type eigenvalue problem which we study in detail both analytically as well as numerically. In order to justify our claim of cluster robust and highly accurate approximation of a selected groups of eigenvalues and associated eigenfunctions, we give a new analysis of a class of direct residual eigenspace/vector approximation estimates. Unlike in the first part of the paper, we now use conforming higher order finite elements, since the canonical choice of an appropriate norm to measure eigenvector approximation by discontinuous Galerkin methods is an open problem.
Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.