Developed and taught by John S Butler
This is a very short introduction into simple mathematical functions that are used in behavourial and neurophysiolgical papers. The python code below is motivated by data and plots from papers to illusrate the use and power of the line, sigmoid function, and sinewaves to analyse and interpret data.
Applying simple examples of the line and a psychometric function used Behavioural and Clinical Neuroscience to illustrate python functions.
- Tutorial 1 Plotting the line [1].
- Tutorial 2 Two lines [1].
- Tutorial 3 The Psychometric Function [2].
- Tutorial 4 The Psychometric function for multisensory integration [2].
Using python to implement simple examples of Spike train analysis, tuning functions, frequencies and fast fourier transform.
- Tutorial 1 Single Spike Train [3].
- Tutorial 2 Multiple Spike Trains [3].
- Tutorial 3 The Tuning Function [4].
- Tutorial 4 Frequencies [5].
- Tutorial 5 Fourier Transform [5].
The sound of different spike patterns [6]
[1] Butler, John S., et al. "Non-parametric bootstrapping method for measuring the temporal discrimination threshold for movement disorders." Journal of neural engineering 12.4 (2015): 046026.
[2] Ernst, Marc O., and Martin S. Banks. "Humans integrate visual and haptic information in a statistically optimal fashion." Nature 415.6870 (2002): 429-433.
[3] Meredith, M. A., & Stein, B. E. (1986). Visual, auditory, and somatosensory convergence on cells in superior colliculus results in multisensory integration. Journal of neurophysiology, 56(3), 640-662.
[4] Britten, Kenneth H., et al. "The analysis of visual motion: a comparison of neuronal and psychophysical performance." Journal of Neuroscience 12.12 (1992): 4745-4765.
[5] Fiebelkorn, I. C., Foxe, J. J., Butler, J. S., Mercier, M. R., Snyder, A. C., & Molholm, S. (2011). Ready, set, reset: stimulus-locked periodicity in behavioral performance demonstrates the consequences of cross-sensory phase reset. Journal of Neuroscience, 31(27), 9971-9981.
[6] Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on neural networks, 14(6), 1569-1572.
Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience: computational and mathematical modeling of neural systems. Computational Neuroscience Series.
Mathematical Tools for Neuroscience by Ella Batty
Neuromatch Academy 't Hart, B. M., Achakulvisut, T., Blohm, G., Kording, K., Peters, M. A. K., Akrami, A., Alicea, B., et al. (2021, February 15). Neuromatch Academy: a 3-week, online summer school in computational neuroscience. OSF Preprints. Retrieved from [https://osf.io/9fp4v/]
Neuromatch Academy GitHub Repository
Lindsay, G. (2021). Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain. Bloomsbury Publishing.
Strogatz, S. (2004). Sync: The emerging science of spontaneous order. Penguin UK.
Humphries, M. (2021). The Spike. In The Spike. Princeton University Press.