@article{arthur_burton_ermentrout_2013, title={Stimulus features, resetting curves, and the dependence on adaptation}, volume={34}, ISSN={["0929-5313"]}, DOI={10.1007/s10827-012-0433-5}, abstractNote={We derive a formula that relates the spike-triggered covariance (STC) to the phase resetting curve (PRC) of a neural oscillator. We use this to show how changes in the shape of the PRC alter the sensitivity of the neuron to different stimulus features, which are the eigenvectors of the STC. We compute the PRC and STC for some biophysical models. We compare the STCs and their spectral properties for a two-parameter family of PRCs. Surprisingly, the skew of the PRC has a larger effect on the spectrum and shape of the STC than does the bimodality of the PRC (which plays a large role in synchronization properties). Finally, we relate the STC directly to the spike-triggered average and apply this theory to an olfactory bulb mitral cell recording.}, number={3}, journal={JOURNAL OF COMPUTATIONAL NEUROSCIENCE}, author={Arthur, Joseph G. and Burton, Shawn D. and Ermentrout, G. Bard}, year={2013}, month={Jun}, pages={505–520} }
 @article{veliz-cuba_arthur_hochstetler_klomps_korpi_2012, title={On the Relationship of Steady States of Continuous and Discrete Models Arising from Biology}, volume={74}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-012-9778-1}, abstractNote={For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.}, number={12}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Veliz-Cuba, Alan and Arthur, Joseph and Hochstetler, Laura and Klomps, Victoria and Korpi, Erikka}, year={2012}, month={Dec}, pages={2779–2792} }