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“In The Name of God”

“In The Name of God”. An Introduction to Information Theory. Presented by: Yoosef Najian. Claude Shanon (1916-2001). A classic book: “The mathematical theory of communication” 1949. Entropy (H) = Uncertainty. Before Uncertainty (Hb) Measurement After Uncertainty (Ha)

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“In The Name of God”

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  1. “In The Name of God” An Introduction to Information Theory Presented by: Yoosef Najian

  2. Claude Shanon (1916-2001) A classic book: “The mathematical theory of communication” 1949

  3. Entropy (H) = Uncertainty Before Uncertainty (Hb) Measurement After Uncertainty (Ha) Information = Hb - Ha

  4. Uncertainty = 3 Symbol Uncertainty = 2 Symbol

  5. Uncertainty = 3 Symbol Uncertainty = 2 Symbol Uncertainty = 6 Symbol

  6. Uncertainty = Log 3 Uncertainty = Log 2 Uncertainty = Log 6

  7. Unit of Uncertainty Uncertainty = Log (M)M = The Number of Symbols • Base of Logarithm 2 bits 10 digits e nits

  8. Very Surprised Not Surprised

  9. Uncertainty is the mean surprisal for different symbols

  10. Question : Bit Bit Bit Bit Bit

  11. Information = Decrease in Uncertainty Information=Hb - Ha If There wasn’t any noise, Ha Should be Zero (Ha = 0), So Information=Hb

  12. 0 0 1 1 0 1 0 1 P=0.99 P=0.01 P=0.01 P=0.99 Bit Bit Bit

  13. Mutual Information is the information of a neuron about a set of stimuli. is the difference between total response entropy and mean response entropy of each repeating stimulus.

  14. image presnum Average SD CV Latency Sig • 25040000 6 29.76 20.91 0.70 80.0 1 • 2 7.14 3 28.57 4 42.86 6 64.29 7 14.29 9 21.43 • 05100000 7 26.53 24.30 0.92 80.0 0 • 71.43 2 21.43 3 7.14 4 0.00 7 14.29 8 42.86 • 9 28.57 • 57210000 8 25.89 15.71 0.61 80.0 1 • 0.00 2 21.43 3 14.29 4 42.86 6 21.43 7 50.00 • 8 28.57 9 28.57 • 59640000 7 25.51 14.20 0.56 80.0 1 • 21.43 2 7.14 3 21.43 4 50.00 5 14.29 7 35.71 • 8 28.57 • 55730000 9 25.40 18.25 0.72 80.0 1 • 7.14 2 7.14 3 28.57 4 57.14 5 21.43 6 50.00 • 7 28.57 8 21.43 9 7.14 • 59570000 8 23.21 13.09 0.56 80.0 1 • 7.14 2 14.29 3 14.29 4 35.71 6 42.86 7 35.71 • 8 21.43 9 14.29

  15. Mutual Information total response entropy: response entropy of one repeating stimulus: mean response entropy of each repeating stimulus:

  16. Mutual Information

  17. image presnum Average SD CV Latency Sig • 25040000 6 29.76 20.91 0.70 80.0 1 • 2 7.14 3 28.57 4 42.86 6 64.29 7 14.29 9 21.43 • 05100000 7 26.53 24.30 0.92 80.0 0 • 71.43 2 21.43 3 7.14 4 0.00 7 14.29 8 42.86 • 9 28.57 • 57210000 8 25.89 15.71 0.61 80.0 1 • 0.00 2 21.43 3 14.29 4 42.86 6 21.43 7 50.00 • 8 28.57 9 28.57 • 59640000 7 25.51 14.20 0.56 80.0 1 • 21.43 2 7.14 3 21.43 4 50.00 5 14.29 7 35.71 • 8 28.57 • 55730000 9 25.40 18.25 0.72 80.0 1 • 7.14 2 7.14 3 28.57 4 57.14 5 21.43 6 50.00 • 7 28.57 8 21.43 9 7.14 • 59570000 8 23.21 13.09 0.56 80.0 1 • 7.14 2 14.29 3 14.29 4 35.71 6 42.86 7 35.71 • 8 21.43 9 14.29

  18. Network: Computation in Neural Systems 7 (1996) 87–107. Printed in the UK Analytical estimates of limited sampling biases in different information measures Stefano Panzeri and Alessandro Treves S=Number of Stimuli R=Number of Rates N=Number of Presentation for each Stimulus

  19. The End

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