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Theory of the Snowflake Plot and Its Relations to Higher-Order Analysis Methods

gabriela{at}neurostat.mgh.harvard.edu, Neuroscience Statistics Research Laboratory, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, U.S.A.

Sonja Grün

gruen{at}neurobiologie.fu-berlin.de, Institute for Biology–Neurobiology, Free University, Berlin, 14195, Germany

Satish Iyengar

si{at}stat.pitt.edu, Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

The snowflake plot is a scatter plot that displays relative timings of three neurons. It has had rather limited use since its introduction by Perkel, Gerstein, Smith, and Tatton (1975), in part because its triangular coordinates are unfamiliar and its theoretical properties are not well studied. In this letter, we study certain quantitative properties of this plot: we use projections to relate the snowflake plot to the cross-correlation histogram and the spike-triggered joint histogram, study the sampling properties of the plot for the null case of independent spike trains, study a simulation of a coincidence detector, and describe the extension of this plot to more than three neurons.