Abstract-The ability to determine the characteristics of peripheral nerve fiber size distributions would provide additional information to clinicians for the diagnosis of specific pathologies of the peripheral nervous system. Investigation of these conditions, using electro-diagnostic techniques, is advantageous in the sense that such techniques tend to be minimally invasive yet provide valuable diagnostic information. One of the principal electro-diagnostic tools available to the clinician is the nerve conduction velocity test. While the peripheral nerve conduction velocity test can provide useful information to the clinician regarding the viability of the nerve under study, it is a single parameter test that yields no detailed information about the characteristics of the functioning nerve fibers within the nerve trunk. In this study we present a technique based on a decomposition of the maximal compound evoked potential and subsequent determination of the group delay of the contributing nerve fibers. The fiber group delay is then utilized as an initial estimation of the nerve fiber size distribution and the concomitant temporal propagation delays of the associated single fiber evoked potentials to a reference electrode. Subsequently the estimated single fiber evoked potentials are optimized against the template maximal compound evoked potential using a simulated annealing algorithm. Simulation studies, based on deterministic single fiber action potential functions, are used to demonstrate the robustness of the proposed technique in the presence of noise associated with variations in distance between the nerve fibers and the recording electrodes between the two recording sites.

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Abstract. In abstract algebra courses, teachers are often confronted with the task of drawing subgroup lattices. For purposes of instruction, it is usually desirable that these lattices be planar graphs (with no crossings). We present a characterization of abelian groups with this property. We also resolve the following problem in the abelian case: if the subgroup lattice is required to be drawn hierarchically (that is, in monotonic order of index within the group), when is it possible to draw the lattice without crossings?

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This paper describes a model for high-school teacher professional development and student learning that can be readily adapted by other universities seeking meaningful partnerships with K-12 schools. In this program, university engineering and science faculty work collaboratively with high school teachers to present challenging engineering design projects to high school students.Our program consists of a series of Teacher Workshops for high school teachers, each followed by a Discovery Weekend with their students, and culminating in a challenge weekend. Each project includes a thorough integration of mathematics, science and engineering, thereby leading to a much deeper understanding of how the mathematics and science topics taught in high school are related to engineering design. This approach has led to increased confidence in the high school teachers, increased interest in STEM topics among the students, and a heightened awareness of the role engineering can play in meeting the challenges facing our society. The collaboration between university faculty and high school teachers maximizes the benefit to the students by having both their regular teachers and university faculty directly involved in their projects. It also effectively demonstrates to the students how diverse teams can often provide better solutions to problems.