The Mathematical Association of America Maryland-District of Columbia-Virginia Section

Transmitting electrical power without the use of cables is a modern convenience that we currently experience. This engineering breakthrough is called wireless power transmission (WPT), the most basic setup of which involves two RLC-circuits that are coupled with mutual inductance. An RLC circuit is an electrical circuit in series or parallel, consisting of a resistor, inductor, and a capacitor. The key component in WPT is the mutual inductance, this piece connects the two circuits together allowing power to be moved from one circuit to the other and then back. In this project, we derive a mathematical model of an equivalent circuit of a two-coil WPT. The model involves a system of two linear second-order ordinary differential equations with constant coefficients, one of which is non-homogeneous while the other one is homogeneous. We apply elementary methods to derive closed-form general solutions of the system. Then, using specific parameters, we solve the system using various methods: analytical solutions via the Laplace Transform, numerical simulation via Matlab, circuit simulation via MultiSim and then from the data obtained from our simulated circuit in Multisim, we conduct parameter estimation via Excel. While the implementation of Laplace Transforms by hand computations require carefully chosen parameters, using the Matlab, Multisim, and Excel allowed us to analyze the solutions of the system over a larger interval of parameters to include realistic values for the RLC components. Finally, we perform a local sensitivity analysis of the system with respect to the parameters using direct differentiation. Sensitivity analysis is a systematic investigation of the behavior of the dependent variables of a system with respect to perturbation in its parameters. In particular, we produce evolution curves of the rate of change of each of the dependent variables with respect to each of the parameters and compute their 2-norms in order to measure and compare the sensitivities.

Friedrich Oliver Vechs is surely one of the most enigmatic figures in the history of mathematics. Ann Dalmak, whose 2015 account in Math Horizons brought his story to popular notice, has recently disclosed an exciting new discovery: a hitherto unknown account Vechs wrote of his early struggles to find a thesis topic. The original manuscript, found hidden in a clothes cabinet in the private chambers of one of Vechs' closest confidantes, only came to light last year when that person moved into a retirement community. By a strange string of circumstances, this boudoir armoire memoir of Friedrich Oliver Vechs came into the possession of Dalmak, who is giving it the rigorous study that it deserves. The purpose of this presentation is to provide a preview of some of Dalmak's findings.

NOTE: This talk was originally planned before the rescheduling of the section meeting, under the assumption that it would be presented much closer to April first. Whether it is still appropriate this late in the month, or indeed at any time at all, is left to the judgment of the listener.

Sallie Pero Mead (1893-1981) is a figure that should be better known in the Mathematics community. Her work in industrial mathematics had an impact, in particular in the lead-up to World War II. In 1915, when she was hired by AT&T, women were not considered for jobs as professional mathematicians or engineers. They were not expected to stay at a firm for more than a year or two. Mead's 43-year career began with a short stint as a human computer; through her professionalism and her credentials (she had Mathematics degrees from Barnard and Columbia), she quickly became a professional Mathematician, ultimately joining Thornton Fry's Mathematical Research department at AT&T. This talk will discuss her education and her contributions.

The first decade of the new millennium is often called the "dawn of the --omics era" Suddenly biomedical studies were capturing tens of thousands of measurements per patient. A common goal was to use these measurements to predict class membership or determine who would respond well to a particular treatment. Typically dimension reduction would be required to reduce the dimensionality of the prediction space to a level less than the number of participants in the study. The oldest tool, Bonferroni adjustment, was quickly deemed much too conservative for --omics. Luckily, 5 years earlier, Benjamini and Hochberg (BH) introduced their procedure which offered much less stringency by introducing a new paradigm. Rather than controlling the family wise error rate, or probability of one or more false positives, their procedure controls the expected proportion of false discoveries or false discovery rate (FDR). This quickly gained popularity and widespread use to such an extent that it became a knee-jerk choice for ensuring validity in biomarker studies. However, a given experiment produces an (unobserved) instance of the false discovery proportion (FDP) while the BH-FDR procedure only guarantees control of its expected value (FDR = E[ FDP ] ). This is adequate if the distribution of the FDP is highly spiked at its mean. Unfortunately, the BH-FDR procedure gets used regularly in situations when this distribution is not at all spiked. In this talk we will discuss a procedure introduced by Lehmann and Romano in 2008 which controls the probability that the FDP exceeds a threshold, or FDX, but this procedure is only slightly less restrictive than Bonferroni adjustment. We present an alternative less restrictive procedure which controls the FDX based on asymptotic approximation and discuss domains of appropriate application of these various procedures.