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

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

• Neumann’s generalized Boolean framework (1956)

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)

Problems

• Static logic-gates (SLGs)

Problems

• Static logic-gates (SLGs)– Influencial in developing artificial neural networks

and machine learning

Problems

• Static logic-gates (SLGs)– Influencial in developing artificial neural networks

and machine learning

– Limited influence on neuroscience

Problems

• Static logic-gates (SLGs)– Influencial in developing artificial neural networks

and machine learning

– Limited influence on neuroscience

• Alternative:– Dynamic logic-gates (DLGs)

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

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

Elastic response latency

• Neuronal response latency– The time-lag between a stimulation and its

corresponding evoked spike

Elastic response latency

• Neuronal response latency– The time-lag between a stimulation and its

corresponding evoked spike

– Typically in the order of several milliseconds

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

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

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

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

(Vardi et al., 2013b)

(Vardi et al., 2013b)

Δ

Experimentally examined DLGs

• Dyanamic AND-gate

(Vardi et al., 2013b)

Experimentally examined DLGs

• Dyanamic AND-gate

• Dynamic OR-gate

(Vardi et al., 2013b)

Experimentally examined DLGs

• Dyanamic AND-gate

• Dynamic OR-gate

• Dynamic NOT-gate

(Vardi et al., 2013b)

Experimentally examined DLGs

• Dyanamic AND-gate

• Dynamic OR-gate

• Dynamic NOT-gate

• Dynamic XOR-gate

(Vardi et al., 2013b)

(Vardi et al., 2013b)

Theoretical analysis

• A simplified theoretical framework

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

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

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

Theoretical analysis

• Dynamic AND-gate

(Vardi et al., 2013b)

Theoretical analysis

• Dynamic AND-gate– Generalized AND-gate

(Vardi et al., 2013b)

Theoretical analysis

• Dynamic AND-gate– Generalized AND-gate

– number of intersections of k non-parallel lines: 0.5k(k – 1)

(Vardi et al., 2013b)

Theoretical analysis

• Dynamic AND-gate– Generalized AND-gate

– number of intersections of k non-parallel lines: 0.5k(k – 1)

• Dynamic XOR-gate

(Vardi et al., 2013b)

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

(Vardi et al., 2013b)

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

(Vardi et al., 2013b)

Multiple component networks and signal processing

Basic edge detector:

(Vardi et al., 2013b)

Suitability of DLGs to brain functionality• Short synaptic delays

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

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

(Vardi et al., 2013b)

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

(Vardi et al., 2013b)

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.