a computational paradigm for dynamic logic-gates in neuronal activity sander vaus 15.10.2014
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A computational paradigm for dynamic logic-gates in neuronal activity
Sander Vaus
15.10.2014
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Background
• “A logical calculus of the ideas immanent in nervous activity” (Mcculloch and Pitts, 1943)
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Background
• “A logical calculus of the ideas immanent in nervous activity” (Mcculloch and Pitts, 1943)
• Neumann’s generalized Boolean framework (1956)
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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)
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Problems
• Static logic-gates (SLGs)
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Problems
• Static logic-gates (SLGs)– Influencial in developing artificial neural networks
and machine learning
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Problems
• Static logic-gates (SLGs)– Influencial in developing artificial neural networks
and machine learning
– Limited influence on neuroscience
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Problems
• Static logic-gates (SLGs)– Influencial in developing artificial neural networks
and machine learning
– Limited influence on neuroscience
• Alternative:– Dynamic logic-gates (DLGs)
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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
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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
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Elastic response latency
• Neuronal response latency– The time-lag between a stimulation and its
corresponding evoked spike
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Elastic response latency
• Neuronal response latency– The time-lag between a stimulation and its
corresponding evoked spike
– Typically in the order of several milliseconds
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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
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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
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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
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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
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(Vardi et al., 2013b)
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(Vardi et al., 2013b)
Δ
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Experimentally examined DLGs
• Dyanamic AND-gate
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(Vardi et al., 2013b)
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Experimentally examined DLGs
• Dyanamic AND-gate
• Dynamic OR-gate
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(Vardi et al., 2013b)
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Experimentally examined DLGs
• Dyanamic AND-gate
• Dynamic OR-gate
• Dynamic NOT-gate
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(Vardi et al., 2013b)
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Experimentally examined DLGs
• Dyanamic AND-gate
• Dynamic OR-gate
• Dynamic NOT-gate
• Dynamic XOR-gate
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(Vardi et al., 2013b)
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(Vardi et al., 2013b)
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Theoretical analysis
• A simplified theoretical framework
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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
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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
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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
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Theoretical analysis
• Dynamic AND-gate
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(Vardi et al., 2013b)
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Theoretical analysis
• Dynamic AND-gate– Generalized AND-gate
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(Vardi et al., 2013b)
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Theoretical analysis
• Dynamic AND-gate– Generalized AND-gate
– number of intersections of k non-parallel lines: 0.5k(k – 1)
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(Vardi et al., 2013b)
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Theoretical analysis
• Dynamic AND-gate– Generalized AND-gate
– number of intersections of k non-parallel lines: 0.5k(k – 1)
• Dynamic XOR-gate
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(Vardi et al., 2013b)
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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
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(Vardi et al., 2013b)
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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
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(Vardi et al., 2013b)
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Multiple component networks and signal processing
Basic edge detector:
(Vardi et al., 2013b)
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Suitability of DLGs to brain functionality• Short synaptic delays
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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
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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
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(Vardi et al., 2013b)
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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
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(Vardi et al., 2013b)
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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.