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We develop an empirical model for measured frequency-dependent insertion loss ( $\vert {S}_{{21}}\vert $ ). The model parameters are determined with a stochastic optimization implementation of the Levenberg–Marquard method. We compare measured $\vert {S}_{{21}}\vert $ on through silicon via (TSV)-interconnects, from two different providers, as a function of the extent of thermal annealing. The frequency-dependent changes in the electrical characteristics of the interconnect are attributed to silanol (Si-OH) and other dangling bond polarizations at the Si–SiO interface between the silicon substrate and the lateral silicon oxide that isolates the coaxial metal core from the silicon substrate. The changes in the polarizations are traceable to changes in the chemistry of the isolation dielectric during thermal annealing. The data also suggest that the evolution of the chemical defects inherent in the “as-manufactured” products may be responsible for some of the signal integrity degradation issues and other early reliability failures observed in TSV-enabled 3-D devices.

To calibrate an optical transition edge sensor, for each pulse of the light source (e.g., pulsed laser), one must determine the ratio of the expected number of photons that deposit energy and the expected number of photons created by the laser. Based on the estimated pulse height generated by each energy deposit, we form a pulse height spectrum with features corresponding to different numbers of deposited photons. We model the number of photons that deposit energy per laser pulse as a realization of a Poisson process, and the observed pulse height spectrum with a mixture model method. For each candidate feature set, we determine the expected number of photons that deposit energy per pulse and its associated uncertainty based on the mixture model weights corresponding to that candidate feature set. From training data, we select the optimal feature set according to an uncertainty minimization criterion. We then determine the expected number of photons that deposit energy per pulse and its associated uncertainty for test data that are independent of the training data. Our uncertainty budget accounts for random measurement errors, systematic effects due to mismodeling feature shapes in our mixture model, and possible imperfections in our feature set selection method.

Steady-state laminar flow through single rock fractures is predicted in terms of spatial statistics computed from the arrangement of voids and contact areas within the fracture. Within the voids, aperture is assumed to be constant. One statistic measures how often pixels alternate from void to contact area in the rows parallel to the flow direction. Two others measure the dispersion of voids in the rows and columns of the pattern. Fractures with complexity typical of observed data are simulated. Flow through patterns with 80% voids is predicted in terms of a linear combination of the three statistics. Using an extended model involving one of the three statistics, flow through patterns with other void fractions is predicted.

To determine the magnetic resonance imaging (MRI) characteristics of pilocytic astro-cytomas and to correlate them with the histopathologic findings.