 
Summary: A PDF Model of Populations of Purkinje Cells:
NonLinear Interactions and High Variability.
Shahin Hakimian, Charles H. Anderson, W. Thomas Thach
Department of Anatomy and Neurobiology, Washington University School of Medicine
Abstract:
While the Marr/Albus cerebellar model expects Purkinje cells to behave linearly and have noise
free outputs, physiological studies suggest otherwise. A cerebellar model based on ensembles of neurons
encoding Probability Density Functions (PDF's) described here may resolve these contradictions. Our
simulations show that a PDF based model can describe the noisy output of these cells, and more
importantly, efficiently compute the complex nonlinear functions necessary for the cerebellar
computations, such as for the control of arm movement (Bastian et al 1996). We further intend to simulate
the computation of more complex functions using similar methods.
Keywords: Cerebellum, Modeling, Simulation, Nonlinear, Noisy.
Introduction:
The Marr/Albus (Marr 1969 and Albus 1971) cerebellar model predicted the role of Purkinje cells
to be primarily lookuptables that compute linear sums of their inputs, and to have noise free outputs.
Experimentally, however, the cerebellar inputoutput relationships seem to be complex nonlinear
functions, and the Purkinje cell outputs seem to be very noisy. Work of Bastian et al (Bastian 1996), for
example, suggests that the cerebellum computes complex nonlinear functions needed for control of arm
movement. Calculations of these nonlinear equations based on the linear Marr/Albus model seems highly
