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A computational paradigm for dynamic logic-gates in neuronal activity

A computational paradigm for dynamic logic-gates in neuronal activity. Sander Vaus 15.10.2014. Background. “A logical calculus of the ideas immanent in nervous activity” ( Mcculloch and Pitts, 1943). Background.

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A computational paradigm for dynamic logic-gates in neuronal activity

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  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 (Vardi et al., 2013b)

  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)

  27. (Vardi et al., 2013b)

  28. Theoretical analysis • A simplified theoretical framework

  29. Theoretical analysis • A simplified theoretical framework l(q) = l0 + qΔ(1) l0– 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) = l0 + qΔ (1) τ(q) = τ0 + nqΔ(2) τ0 – initial time delay of the chain n –number of neurons in the chain

  31. Theoretical analysis • A simplified theoretical framework l(q) = l0 + qΔ (1) τ(q) = τ0 + 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)

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