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A computational paradigm for dynamic logic-gates in neuronal activity

This paper explores the shift from static logic gates to dynamic logic gates (DLGs) for modeling neuronal activity. Traditional static logic gates, while influential in machine learning and artificial neural networks, have limitations in reflecting the complexities of neuronal behavior. DLGs, which depend on historical activity, stimulation frequencies, and interconnections, present a more accurate framework. The work builds on foundational theories by McCulloch and Pitts, Neumann, and Shannon, proposing new systematic methods for understanding neural dynamics and their latency responses.

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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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