Random effects diagonal metric multidimensional scaling models

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45758/1/11336_2005_Article_BF02295730.pd

Modeling full PCSELs and VCSELs using modified rigorous coupled-wave analysis

An integrated rigorous coupled-wave analysis (RCWA) algorithm is presented in this paper, which can simulate full vertical-cavity surface-emitting laser (VCSEL) and photonic crystal surface-emitting laser (PCSEL) structures. A classic RCWA can only analyze a structure when the light source is incident from the top, bottom, or both sides of the device. However, for VCSEL applications, the light source is generated in the middle and propagates in both directions. A bidirectional scattering matrix method and doubling algorithm are implemented in RCWA. The resonant wavelength and Q factor of a VCSEL can then be found in the output spectrum. The accuracy and execution speed are compared with those of the Lumerical finite-difference time-domain (FDTD) method for several VCSEL and PCSEL designs. The results show that the maximum discrepancy between RCWA and FDTD is less than 3 nm, and the difference in the far-field divergence angle is less than 0.5°. The speed of RCWA also outperforms FDTD simulation significantly

Estimating Local Apparent Conductivity with a 2-D Electrophysiological Model of the Heart

Abstract. In this article we study the problem of estimating the parameters of a 2-D electrophysiological model of the heart from a set of temporal recordings of extracellular potentials. The chosen model is the reaction-diffusion model on the action potential proposed by Aliev and Panfilov. The strategy consists in building an error criterion based upon a comparison of depolarization times between the model and the measures. This error criterion is minimized in two steps: first a global and then a local adjustment of the model parameters. The feasibility of the approach is demonstrated on real measures on canine hearts, showing also the necessity to introduce anisotropy and probably a third spatial dimension in the model.