- Supplementary Content
- 10.2139/ssrn.6104626
The Geography of Billionaires in the United States
- Jan 01, 2026
- SSRN Electronic Journal
- Philip Obazee
Publications from 2021 to 2026
Showing 10 of 25 papers
The Geography of Billionaires in the United States
An Empirical Bayesian Approach for Testing the Fairness of Automated Scoring
This study proposes an empirical Bayesian approach with loss functions for testing the fairness of an automated scoring algorithm. The proposed method outperforms traditional approaches by (1) being robust to small samples, (2) incorporating parameter uncertainty, and (3) balancing the loss of keeping versus flagging items. The impact of flagging potentially unfair items on the classification of examinees is investigated. The effectiveness of the proposed method is illustrated through simulations and an application to language assessment data.
Read moreNanorobotics for Neurosurgery
Low coherence interferometry for mid-infrared precision optics manufacturing
We report on an optical, non-contact, thickness measurement system for materials that are opaque in the Near infrared (NIR) through ultraviolet (UV) wavelength range. While measurement options do exist, they must either physically touch the sample or rely on an assumed bulk distribution of material. In addition, optical and semiconductor materials are often highly sensitive to contamination and greatly benefit from noncontact metrology. The authors have adapted techniques used for the Lumetrics Optigauge 2000 low coherence interferometry (LCI) system to build a 2.8 μm LCI system using non-silica optical fibers to direct the probe signal. A (100) Silicon (Si) test sample was selected as a control because it can be measured by both an Optigauge II and the MIR-LCI system. In this work, the authors successfully measured materials that are transparent in the midinfrared (MIR) range, such as Germanium. The authors speculate that MIR-LCI will enable wedge, thickness, flatness, and other measurements performed using an Optigauge II system for MIR transparent materials.
Read moreMultimodal characterization of contact lenses
A table top instrument has been designed, constructed and tested to characterize all of the primary optical and physical properties of contact lenses. Measured optical properties include base power, cylinder power, cylindrical axis, prism, refractive index and wavefront aberrations. Measured physical properties include center thickness, lens diameter and lens sagittal depth. The instrument combines a Shack-Hartmann wavefront sensor (SHWS), a machine vision sensor, and a low coherence light interferometer (LCI) all coaxially aligned into a single tabletop unit. The unit includes a cuvette, mounted in a translatable sample chamber for holding the contact lens under test, and it can be configured to measure wet or dry contact lenses. During operation, the vision sensor measures the diameter of the lens, and locates the center of the lens. The lens is then aligned for other measurements. The vision sensor can also measure various alignment marks on the lens, as well as identify any alpha numerical features, which can be used to associate the lens orientation with the measured aberrations. The LCI measures the center thickness, sagittal depth and index of refraction of the contact lens. The base radius of curvature is then calculated using these measured parameters. The SHWS measures the lenses prescription power, including spherical, cylinder, prism, and higher order wavefront aberrations. NIST traceable calibration artifacts are used to calibrate the SHWS, machine vision and LCI modalities. Repeatability measurements on a contact lens in a saline solution are presented.
Read moreSpherical aberration standards and measurement system stability over time
A Shack-Hartmann wave-front sensor system has been used to measure a set of plano-convex lenses at two different times, separated by almost 2 years. The plano-convex lenses were selected to cover a range of powers and apertures relevant to intraocular lenses, and were measured at two different orientations. The results demonstrate the high temporal stability of the measurement system, as well as of the glass standard. In addition, both times the effective focal lengths of the standards were measured using a NIST traceable nodal slide bench, and the center thicknesses were measured using low-coherence interferometer. The spherical aberration and the effective focal length results are analyzed for statistically significant changes. The results are also compared to the Zemax models of the standards.
Read moreComputation of Fresnel Integrals. II
This paper describes an improved method for computing Fresnel integrals with an error of less than 1 × 10−9. The method is based on a known approximate formula for a different integral which is due to Boersma and referenced by Abramowitz and Stegun.
Read moreComparison of Motored and Fired Velocities in a Two Stroke Engine
<div class="htmlview paragraph">Measurements were made of the in-cylinder fluid velocities in a crankcase compression, piston ported two-stroke engine under both motored and fired operating conditions to investigate the effect of combustion on the scavenging process. The engine was modified to allow optical access to the clearance volume and was operated in a burst fired manner, where the firing sequence was controlled by modulating the fuel delivered to the crankcase. The burst fired sequence consisted of 30 cycles, of which there were twelve consecutive cycles where fuel was injected into the crankcase. The engine was operated at a speed of 500 RPM, with a delivery ratio of 0.54, and a fuel-air equivalence ratio of 1.28. Laser Doppler Velocimetry was used to measure two components of the in-cylinder fluid velocity at five locations in the cylinder head cup during the burst fired operation of the engine. These measurements were sorted into groups representative of the motored and fired operation of the engine based on the cycle number within the burst fired sequence in which the measurements were taken. The groupings were based on an analysis of cylinder, crankcase, and exahust port pressure measurements made while the engine was being operated in the burst fired mode.</div> <div class="htmlview paragraph">The velocity measurements show a significant increase in the peak velocity of the scavenging flows under fired conditions when compared to the scavenging flows under motored conditions. These results indicate that under motored conditions the backflow from the exhaust system into the cylinder at the time of exhaust port opening retards the incoming jets from the intake ports. Under firing conditions, the flow out of the cylinder does not impede the incoming fresh charge, and the momentum of this outflow may help draw the fresh charge into the cylinder. A comparison of the RMS velocities under both motored and fired conditions indicated that for the period between bottom dead center and ignition both components of the RMS velocities were equal. This result indicates that the main effect of firing on the scavenge flow was to induce mean flow patterns which purge the burned gases, as opposed to enhancing in-cylinder mixing.</div>
Read moreA ground test application of laser Doppler velocimetry to aircraft gas turbine engine inlet flow
Engine inlet velocity flow fields are important for determining inlet flow distortion, optimizing inlet design, and understanding high angle of attack operation. We show that laser Doppler velocimetry (LDV) offers high spatial and temporal resolution for the case of a ruggedized LDV system incorporating a high-bandwidth real-time signal processor. An inlet duct with optical access and seeding methodology were developed. One-component axial mean and rms velocity profiles were successfully determined under steady state and transient engine run conditions from idle to maximum afterburner. Time-velocity correlations during transient engine maneuvers and an estimate of LDV data rate vs. laser power were also obtained. The results show that LDV may be applied to full-scale engine inlets both with and without seeding. Data rates in most cases would be adequate for active feedback control of the engine. The results of this work will be used to guide the development of an in-flight instrument. (Author)
Read moreApplication of an integrated phase doppler interferometer/ rainbow thermometer/point-diffraction interferometer for characterizing burning droplets