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Summary: Supplemental Materials for "Balanced amplification: a
new mechanism of selective amplification of neural
activity patterns"
Brendan K. Murphy and Kenneth D. Miller
February 18, 2009
Contents
S1 Mathematical Solutions and Analysis of the Models Studied in the Main
Text 2
S1.1 Two-Population Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
S1.1.1 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
S1.1.2 Applications to Results in the Main Text . . . . . . . . . . . . . . . . 4
S1.1.3 Paradoxical Effects of Input to Inhibitory Cells . . . . . . . . . . . . 6
S1.2 Multi-Neuron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
S2 Amplification in the Data and the Models 9
S2.1 Relationship Between Transient Response to an Initial Condition and Sus-
tained Response to Onset of a Steady-State Stimulus . . . . . . . . . . . . . 9
S2.2 Amplification in the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
S2.3 Amplification in Linear Models . . . . . . . . . . . . . . . . . . . . . . . . . 11
S3 Non-normal matrices, Neurobiological Connection Matrices, and the Schur
Decomposition 15
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