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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas
Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas
Mathematics and Statistics Faculty Publications and Presentations
This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.
Spatial Factor Models For High-Dimensional And Large Spatial Data: An Application In Forest Variable Mapping, Daniel Taylor-Rodríguez, Andrew O. Finley, Abhirup Datta, Chad Babcock, Hans-Erik Andersen, Bruce D. Cook, Douglas C. Morton, Sudipto Banerjee
Spatial Factor Models For High-Dimensional And Large Spatial Data: An Application In Forest Variable Mapping, Daniel Taylor-Rodríguez, Andrew O. Finley, Abhirup Datta, Chad Babcock, Hans-Erik Andersen, Bruce D. Cook, Douglas C. Morton, Sudipto Banerjee
Mathematics and Statistics Faculty Publications and Presentations
Gathering information about forest variables is an expensive and arduous activity. As such, directly collecting the data required to produce high-resolution maps over large spatial domains is infeasible. Next generation collection initiatives of remotely sensed Light Detection and Ranging (LiDAR) data are specifically aimed at producing complete-coverage maps over large spatial domains. Given that LiDAR data and forest characteristics are often strongly correlated, it is possible to make use of the former to model, predict, and map forest variables over regions of interest. This entails dealing with the high-dimensional (∼102 ) spatially dependent LiDAR outcomes over a large number …
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.
Connection And Curvature In Crystals With Non-Constant Dislocation Density, Marek Z. Elźanowski, Gareth P. Parry
Connection And Curvature In Crystals With Non-Constant Dislocation Density, Marek Z. Elźanowski, Gareth P. Parry
Mathematics and Statistics Faculty Publications and Presentations
Given a smooth defective solid crystalline structure defined by linearly independent ‘lattice’ vector fields, the Burgers vector construction characterizes some aspect of the ‘defectiveness’ of the crystal by virtue of its interpretation in terms of the closure failure of appropriately defined paths in the material and this construction partly determines the distribution of dislocations in the crystal. In the case that the topology of the body manifold M is trivial (e.g., a smooth crystal defined on an open set in R2), it would seem at first glance that there is no corresponding construction that leads to the notion of a …
Reconsidering The Foundations Of Thermodynamics From An Engineering Perspective, Terry Bristol
Reconsidering The Foundations Of Thermodynamics From An Engineering Perspective, Terry Bristol
Mathematics and Statistics Faculty Publications and Presentations
Currently, there are two approaches to the foundations of thermodynamics. One, associated with the mechanistical Clausius-Boltzmann tradition, is favored by the physics community. The other, associated with the post-mechanical Carnot tradition, is favored by the engineering community. The bold hypothesis is that the conceptual foundation of engineering thermodynamics is the more comprehensive. Therefore, contrary to the dominant consensus, engineering thermodynamics (ET) represents the true foundation of thermodynamics. The foundational issue is crucial to a number of unresolved current and historical issues in thermodynamic theory and practice. ET formally explains the limited successes of the ‘rational mechanical’ approaches as idealizing special …
A New Method For Multi-Bit And Qudit Transfer Based On Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman
A New Method For Multi-Bit And Qudit Transfer Based On Commensurate Waveguide Arrays, Jovan Petrovic, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The faithful state transfer is an important requirement in the construction of classical and quantum computers. While the high-speed transfer is realized by optical-fibre interconnects, its implementation in integrated optical circuits is affected by cross-talk. The cross-talk between densely packed optical waveguides limits the transfer fidelity and distorts the signal in each channel, thus severely impeding the parallel transfer of states such as classical registers, multiple qubits and qudits. Here, we leverage on the suitably engineered cross-talk between waveguides to achieve the parallel transfer on optical chip. Waveguide coupling coefficients are designed to yield commensurate eigenvalues of the array and …
Clustering And Multifacility Location With Constraints Via Distance Function Penalty Methods And Dc Programming, Mau Nam Nguyen, Thai An Nguyen, Sam Reynolds, Tuyen Tran
Clustering And Multifacility Location With Constraints Via Distance Function Penalty Methods And Dc Programming, Mau Nam Nguyen, Thai An Nguyen, Sam Reynolds, Tuyen Tran
Mathematics and Statistics Faculty Publications and Presentations
This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given set constraints. We also provide different numerical examples to test our method.
On The Girth And Diameter Of Generalized Johnson Graphs, Louis Anthony Agong, Carmen Amarra, John Caughman, Ari J. Herman, Taiyo S. Terada
On The Girth And Diameter Of Generalized Johnson Graphs, Louis Anthony Agong, Carmen Amarra, John Caughman, Ari J. Herman, Taiyo S. Terada
Mathematics and Statistics Faculty Publications and Presentations
Let v > k > i be non-negative integers. The generalized Johnson graph, J(v,k,i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever |A∩B|= i. In this article, we derive general formulas for the girth and diameter of J(v,k,i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection.
Bootcmatch: A Software Package For Bootstrap Amg Based On Graphweighted Matching, Pasqua D'Ambra, Salvatore Filipone, Panayot S. Vassilevski
Bootcmatch: A Software Package For Bootstrap Amg Based On Graphweighted Matching, Pasqua D'Ambra, Salvatore Filipone, Panayot S. Vassilevski
Mathematics and Statistics Faculty Publications and Presentations
This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the …
Intensity Inhomogeneity Correction Of Sd-Oct Data Using Macular Flatspace, Andrew Lang, Aaron Carass, Bruno M. Jedynak, Sharon D. Solomon, Peter A. Calabresi, Jerry L. Prince
Intensity Inhomogeneity Correction Of Sd-Oct Data Using Macular Flatspace, Andrew Lang, Aaron Carass, Bruno M. Jedynak, Sharon D. Solomon, Peter A. Calabresi, Jerry L. Prince
Mathematics and Statistics Faculty Publications and Presentations
Images of the retina acquired using optical coherence tomography (OCT) often suffer from intensity inhomogeneity problems that degrade both the quality of the images and the performance of automated algorithms utilized to measure structural changes. This intensity variation has many causes, including off-axis acquisition, signal attenuation, multi-frame averaging, and vignetting, making it difficult to correct the data in a fundamental way. This paper presents a method for inhomogeneity correction by acting to reduce the variability of intensities within each layer. In particular, the N3 algorithm, which is popular in neuroimage analysis, is adapted to work for OCT data. N3 works …
High-Order Method For Evaluating Derivatives Of Harmonic Functions In Planar Domains, Jeffrey S. Ovall, Samuel E. Reynolds
High-Order Method For Evaluating Derivatives Of Harmonic Functions In Planar Domains, Jeffrey S. Ovall, Samuel E. Reynolds
Mathematics and Statistics Faculty Publications and Presentations
We propose a high-order integral equation based method for evaluating interior and boundary derivatives of harmonic functions in planar domains that are specified by their Dirichlet data.