Pi Mu Epsilon - Mathematical Association of America

Thursday MAA Session #7 August 2, 2012
MAA Session #7
Room: Meeting Room K
2:00P.M. – 3:55P.M.
2:00–2:15
Characterization of Melanoma and Moles using Signature Curves, Invariant
Histograms and Fractal Dimension
Jack Stangl, Aaron Rodriguez, and Rimi Bhowmik
University of St. Thomas
This presentation focuses on the mathematical detection and analysis of border irregularity in skin
lesions, for the purpose of identifying malignant melanoma amongst benign moles. In particular, it
utilizes three different methods. The method of Signature Curves is based upon the curvature and
the derivative of curvature for a given skin lesion, the method of Fractal Dimension is based upon
the box counting method, and the method of Invariant Histograms is based upon cumulative distance
histograms. The border irregularity of known malignant melanoma samples are compared to
the border of known nevi, or common moles. We propose that melanoma possess distinguishable
border differences from nevi, often undetectable to the human eye. We utilize these mathematical
methods to detect and quantize this difference for diagnosis.
2:20–2:35
Modeling Spiking in Neurons with a Poisson Process
Peter Wiese
Augustana College
In the nervous system, nerve cells communicate through changes in ion concentrations called action
potentials, or spikes. These spikes have been recorded and studied to understand the change in
their distribution due to the presentation of a stimulus. By using a Poisson process, it is possible to
model the distribution of spikes in time. Based on physiological properties, changes in the model
are made to account for both the absolute refractory period and bursting of spikes. We will present
several different models implemented on a spread sheet, both of a single neuron and of small systems
of neurons.
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