1. A computational paradigm for dynamic logic-gates in neuronal activity Sander Vaus 15.10.2014

2. Background “A logical calculus of the ideas immanent in nervous activity” (Mcculloch and Pitts, 1943)

3. Background “A logical calculus of the ideas immanent in nervous activity” (Mcculloch and Pitts, 1943) Neumann’s generalized Boolean framework (1956)

4. Background “A logical calculus of the ideas immanent in nervous activity” (Mcculloch and Pitts, 1943) Neumann’s generalized Boolean framework (1956) Shannon’s simplification of Boolean circuits (Shannon, 1938)

5. Problems Static logic-gates (SLGs)

6. Problems Static logic-gates (SLGs) – Influencial in developing artificial neural networks and machine learning

7. Problems Static logic-gates (SLGs) – Influencial in developing artificial neural networks and machine learning – Limited influence on neuroscience

8. Problems Static logic-gates (SLGs) – Influencial in developing artificial neural networks and machine learning – Limited influence on neuroscience Alternative: – Dynamic logic-gates (DLGs)

9. Problems Static logic-gates (SLGs) – Influencial in developing artificial neural networks and machine learning – Limited influence on neuroscience Alternative: – Dynamic logic-gates (DLGs) Functionality depends on history of their activity, the stimulation frequencies and the activity of their interconnetcions

10. Problems Static logic-gates (SLGs) – Influencial in developing artificial neural networks and machine learning – Limited influence on neuroscience Alternative: – Dynamic logic-gates (DLGs) Functionality depends on history of their activity, the stimulation frequencies and the activity of their interconnetcions Will require new systematic methods and practical tools beyond the methods of traditional Boolean algebra

11. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike

12. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike – Typically in the order of several milliseconds

13. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike – Typically in the order of several milliseconds – Repeated stimulations cause the delay to stretch

14. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike – Typically in the order of several milliseconds – Repeated stimulations cause the delay to stretch – Three distinct states/trends

15. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike – Typically in the order of several milliseconds – Repeated stimulations cause the delay to stretch – Three distinct states/trends – The higher the stimulation rate, the higher the increase of latency

16. Elastic response latency Neuronal response latency – The time-lag between a stimulation and its corresponding evoked spike – Typically in the order of several milliseconds – Repeated stimulations cause the delay to stretch – Three distinct states/trends – The higher the stimulation rate, the higher the increase of latency – In neuronal chains, the increase of latency is cumulative

17. (Vardi et al., 2013b)

18. Δ

19. Experimentally examined DLGs Dyanamic AND-gate

20. (Vardi et al., 2013b)

21. Experimentally examined DLGs Dyanamic AND-gate Dynamic OR-gate

22. (Vardi et al., 2013b)

23. Experimentally examined DLGs Dyanamic AND-gate Dynamic OR-gate Dynamic NOT-gate

24. (Vardi et al., 2013b)

25. Experimentally examined DLGs Dyanamic AND-gate Dynamic OR-gate Dynamic NOT-gate Dynamic XOR-gate

26. (Vardi et al., 2013b)

28. Theoretical analysis A simplified theoretical framework

29. Theoretical analysis A simplified theoretical framework l(q) = l 0 + qΔ(1) l 0 – neuron’s initial response latency q – number of evoked spikes Δ – constant (typically in range of 2-7 μs

30. Theoretical analysis A simplified theoretical framework l(q) = l 0 + qΔ(1) τ(q) = τ 0 + nqΔ(2) τ 0 – initial time delay of the chain n – number of neurons in the chain

31. Theoretical analysis A simplified theoretical framework l(q) = l 0 + qΔ(1) τ(q) = τ 0 + nqΔ(2) Simplifying assumption: The number of evoked spikes of a neuron is equal to the number of its stimulations

32. Theoretical analysis Dynamic AND-gate

33. (Vardi et al., 2013b)

34. Theoretical analysis Dynamic AND-gate – Generalized AND-gate

35. (Vardi et al., 2013b)

36. Theoretical analysis Dynamic AND-gate – Generalized AND-gate – number of intersections of k non-parallel lines: 0.5k(k – 1)

37. (Vardi et al., 2013b)

38. Theoretical analysis Dynamic AND-gate – Generalized AND-gate – number of intersections of k non-parallel lines: 0.5k(k – 1) Dynamic XOR-gate

39. (Vardi et al., 2013b)

40. Theoretical analysis Dynamic AND-gate – Generalized AND-gate – number of intersections of k non-parallel lines: 0.5k(k – 1) Dynamic XOR-gate Transitions among multiple modes

41. (Vardi et al., 2013b)

42. Theoretical analysis Dynamic AND-gate – Generalized AND-gate – number of intersections of k non-parallel lines: 0.5k(k – 1) Dynamic XOR-gate Transitions among multiple modes Varying inputs

43. (Vardi et al., 2013b)

44. Multiple component networks and signal processing Basic edge detector: (Vardi et al., 2013b)

45. Suitability of DLGs to brain functionality Short synaptic delays

46. Suitability of DLGs to brain functionality Short synaptic delays – The examined cases set the synaptic delays to a few tens of milliseconds, as opposed to those of several milliseconds in the brain

47. Suitability of DLGs to brain functionality Short synaptic delays – The examined cases set the synaptic delays to a few tens of milliseconds, as opposed to those of several milliseconds in the brain Can be remedied with the help of long synfire chains

48. (Vardi et al., 2013b)

49. Suitability of DLGs to brain functionality Short synaptic delays – The examined cases set the synaptic delays to a few tens of milliseconds, as opposed to those of several milliseconds in the brain Can be remedied with the help of long synfire chains Population dynamics – DLGs assume

50. (Vardi et al., 2013b)

51. References 1. Goldental, A., Guberman, S., Vardi, R., Kanter, I. (2014). “A computational paradigm for dynamic logic-gates in neuronal activity,” Frontiers in Computational Neuroscience, Volume 8, Article 52, pp. 1-16. 2. Vardi, R., Guberman, S., Goldental, A., Kanter, I. (2013b). “An experimental evidence-based computational paradigm for new logic-gates in neuronal activity,” EPL 103:66001 3. Mcculloch, W. S., Pitts, W. (1943). “A logical calculus of the ideas immanent in nervous activity,” Bull. Math. Biophys., 5: 115-33. 4. Shannon, C. (1938). “A symbolic analysis of relay and switching circuits,” Trans. AIEE 57: 713-23.