Dynamic neuronal encoding in neuromorphic circuits

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Content Dynamic Neuronal Encoding in Neuromorphic Circuits by Rami A. Alzahrani A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) May 2022 Copyright 2022 Rami A. Alzahrani Dedication For my loving and supportive parents, wife, and future kids. ii Acknowledgements I would like to thank my advisor, Dr. Alice C. Parker, for her valuable guidance and mentorship throughout my journey proceeding a Ph.D at USC. Her endless support and encouragement have always been the reason behind expanding my creativity and intuition levels when facing dicul- ties and frustrations while completing this dissertation. Her unique insight and unique expertise have opened doors of curiosity in me to traverse the academic challenges in the neuromorphic engineering eld and have motivated me to prove the value of our research. I want to thank my dissertation and qualifying committee members, Dr. Carl Kesselman, Dr. Han Wang, Dr. Chongwu Zhou, and Dr. Joshua Yang whose advice and expertise have made this dissertation excel. In addition, I would like to thank my colleagues and faculty mentors in the Ming Hsieh Department of Electrical Engineering, with whom I have had productive and inspirational discussions about academic work and research. Last but not least, I would like to thank my loving and supportive parents and wife, without whom this dissertation is not possible. iii TableofContents Dedication ii Acknowledgements iii ListofTables vi ListofFigures vii Abstract xv Chapter1: Introduction 1 Chapter2: BackgroundandRelatedWork 8 2.1 Neuroscience Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Axon Initial Segment Denition . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 Voltage Gated Ion Channels at The AIS . . . . . . . . . . . . . . . . . . . . 11 2.1.3 Dynamical Neuronal Modulation and Signal Processing at The AIS . . . . 13 2.1.4 Bursting Through Calcium Ion Channels . . . . . . . . . . . . . . . . . . . 15 2.1.5 Astrocytes Roles in Synaptic Strengthening . . . . . . . . . . . . . . . . . 16 2.1.6 Background on Synaptic Strengthening . . . . . . . . . . . . . . . . . . . 18 2.2 Background in Neuromorphic Engineering . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Neuronal Coding Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Mathematical Neuron Models . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3 Hardware-based Neuron Models . . . . . . . . . . . . . . . . . . . . . . . 24 Chapter3: RichBehavioralAISElectronicModel 28 3.1 Neuromorphic Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Various Spiking and Bursting Patterns . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 Converting Dynamic Stimulus to APs . . . . . . . . . . . . . . . . . . . . 34 3.2.1.1 The Generation of Various Spiking Patterns . . . . . . . . . . . 35 3.2.1.2 The Generation of Various Bursting Patterns . . . . . . . . . . . 37 3.2.1.3 The Generation of Other Spiking Patterns . . . . . . . . . . . . 39 3.2.2 The Working Principles of The AIS Modulation . . . . . . . . . . . . . . . 40 3.3 Threshold Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 iv Chapter4: ElectronicAutonomousSpikingEncoding 47 4.1 Popular Encoding Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Neuromorphic Electronic Implementations . . . . . . . . . . . . . . . . . . . . . . 49 4.2.1 Dynamic Electronic Encoding Model . . . . . . . . . . . . . . . . . . . . . 49 4.2.2 Calcium Modulated Electronic Synapse Model . . . . . . . . . . . . . . . . 50 4.2.3 The Dendritic Arbor Electronic Model . . . . . . . . . . . . . . . . . . . . 53 4.3 Dynamic Coding Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.3.1 Rate Coding Behavior at Neuron N5 . . . . . . . . . . . . . . . . . . . . . 57 4.3.2 Coincident Coding Behaviour at Neuron N4 . . . . . . . . . . . . . . . . . 60 Chapter5: NeuromorphicNeurontoNeuronSignalingUsingVariousAPPatterns 65 5.1 Synaptic Strengthening Circuit Implementations . . . . . . . . . . . . . . . . . . . 66 5.1.1 Neuromorphic Synapse Strengthening Using Presynaptic Rate . . . . . . . 70 5.1.2 Neuromorphic Synapse Strengthening using STDP . . . . . . . . . . . . . 74 Chapter 6: Neuromorphic Pattern-Specic Filtering Neurons in Decoding an AP Origin 82 6.1 Neuromorphic Neuronal Pattern Filtering . . . . . . . . . . . . . . . . . . . . . . . 82 6.1.1 All Patterns-Pass Neuron Circuit Model . . . . . . . . . . . . . . . . . . . 84 6.1.2 Bursts-Pass Neuron Circuit Model . . . . . . . . . . . . . . . . . . . . . . 87 6.1.3 Spikes-Pass Neuron Circuit Model . . . . . . . . . . . . . . . . . . . . . . 92 6.1.4 Phase-Pass Neuron Circuit Model . . . . . . . . . . . . . . . . . . . . . . . 95 6.1.5 Burst-Widths-Pass Topology Circuit Model . . . . . . . . . . . . . . . . . 100 6.2 Decoding the Origins of Various AP Patterns . . . . . . . . . . . . . . . . . . . . . 104 Chapter7: Conclusion 112 References 118 v ListofTables 2.1 A comparison between dierent spiking models adopted from [91]. FLOPS is the number of oating point operations. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 vi ListofFigures 2.1 A graphical representation of the voltage-space distribution for a generated action potential in pyramidal neurons (adopted from [12]). SD and IS represent the somatodendritic and the axon initial segment regions, respectively. The dotted line shows the voltage space distribution without theN + a ion channels in the nodal region (t=0.85ms and t=0.95ms) and the somatodendritic region (t=1.35ms). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Structural and biophysical interaction during axon initial segment (AIS) plasticity (adopted from [54]). (A) shows the eect of the AIS elongation in NL neurons. (B) represents the eect on depolarizing the hippocampal dentate granule cells for 3 hours, that shortens the AIS. (C) shows a depolarization eect for two days on the pyramidal neurons that causes the AIS to move distally, yet the axo-axonic synapses remain at the original location, boosting the suppressive eects of distal movement on excitability . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 An illustration of the communication protocols between astrocyte and synaptic terminals for strengthening or weakening the synaptic connection. Modied from [76]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 A simple neuron model circuit as a combination ofK + andNa + transistor channels, adopted from [94] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 A recovery variableu circuit, adopted from [102] . . . . . . . . . . . . . . . . . . 26 2.6 A membrane voltagev circuit, adopted from [102] . . . . . . . . . . . . . . . . . . 26 3.1 The general block diagram of the BioRC dynamic encoding neuronal model. To test the model hypothesis, a simple modulation function is used where the modulation function block is a simple direct path from the Vsoma block to the AIS modulation block, hence the dotted border line is used for the modulation function block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 vii 3.2 The Schematic diagram of the proposed neuron model in whichINV 1 is a single stage CMOS inverter, andCOMP 1,COMP 2,COMP 3 are low power dierential-based comparators. To enhance readability, the dashed and the solid connections are used interchangeably. . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 The schematic diagram of the comparators. . . . . . . . . . . . . . . . . . . . . . . 32 3.4 A sketch illustration of spiking and bursting APs showing the model’s voltage- gated ion channels contribution in shaping APs, (A). (B) shows the model’s conditions associated with the generation of single burst (SB), tonic bursts (TB), regular spikes (RS), integrator spikes (INT), class-1 spikes (CS1), subthreshold oscillation (OSC), phasic spikes (PS), phasic spike with depolarization after potential (PS-DAP), regular spikes with depolarization after potentials (RS-DAP), and mixed mode (MIX). The shape of the stimulus patterns determine spiking patterns when all other parameters are the same. . . . . . . . . . . . . . . . . . . 35 3.5 The relationship between various simulatedVsoma shapes and their corre- sponding action potentials for (A) regular spikes, (B) phasic spikes, (C) tonic bursts, (D) single burst per stimulus, (E) class-1 excitable, (F) subthreshold oscillations, (G) depolarization after potential, (H) integrator, and (I) mixed mode, following the table shown in Fig. 3.4. . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.6 The relationship betweenVsoma (Red) andV CA (Blue) for all plausible patterns; (A) regular spiking; (B) phasic spiking; (C) tonic bursting; (D) single burst per stimulus; (E) class-1 excitable spikes; (F) subthreshold oscillations; (G) depolarization after potential; (H) integrator spiking; (I) mixed mode. The ideal relative refractory period for spikes and bursts isRRP S andRRP B , respectively. T d represents COMP3 propagation delay. . . . . . . . . . . . . . . . . . . . . . . . 41 3.7 The model behaviors for dynamicVsoma shapes. (A) represents dierent AP patterns at whichVsoma > Vsoma_Thre, and (B) shows AP patterns for the sameVsoma variations, however, with a threshold variability represented by the gray shaded region for allVsoma < Vsoma_Thre values. AP1 and AP4 are generated at whichCa + + < CaThre andAdapt > V dd =2. AP2 and AP5 represent the outputs at whichAdapt>V dd =2 andCa++ = [0, 500mV]. AP3 and AP6 exhibit PS spiking pattern whereCa + +<CaThre andAdapt<V dd =2. ZOOM2 and ZOOM5 are enlarged versions of the green shaded areas associated with AP2 and AP5 outputs, respectively. . . . . . . . . . . . . . . . . . . . . . . . 45 4.1 The schematic diagram of the autonomous encoding model with AER, where INV is a single-stage CMOS inverter, and COMP is a low power comparator, adopted from [118]. The dashed and solid connections are used interchangeably to simplify the schematic connections. . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2 The schematic diagram of theCa +2 modulated synapse model. . . . . . . . . . . . 51 viii 4.3 Dierent excitatory postsynaptic potentials (EPSPs) corresponding to dierent presynapticCa +2 ion concentrations for (A) spiking and (B) bursting AP patterns. 52 4.4 Dierent excitatory postsynaptic potentials (EPSPs) corresponding to dierent presynapticCa +2 ion concentrations for (A) spiking and (B) bursting AP patterns. 53 4.5 Prior BioRC dendritic arbor model adopted from [137]. Using the current mirror topology, the design separates the excitatory postsynaptic potentials (EPSP) from the inhibitory postsynaptic potentials (IPSP). Each EPSP input is controlled by a control unit (CU). The CU controls the summation mode as three dierent summation modes are linear, super-linear, and sub-linear. Each of the CU circuits consists of two compactor circuits and other digital logic gates. . . . . . . . . . . 54 4.6 The dendritic arbor schematic model, whereEPSP is the excitatory postsynaptic potential signal,Vsoma is resulting membrane potential, andVb1 is the leakage control biasing voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.7 A simulation of the dendritic arbor circuit for two action potentialsAP 1 and AP 2.EPSP is the induced excitatory postsynaptic potential. . . . . . . . . . . . 56 4.8 An experimental neuronal network. S1 to S5 represent the implementedCa +2 modulated synapse circuits, and N1 to N5 represent the implemented dynamic encoding model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.9 A simulation result for N5 neuron with low synaptic Ca +2 concentration (Ca +2 = 400mV ). T d is the time delay required by neuronN5 to encode its high-rate synaptic inputs into APs. . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.10 A simulation result for N5 neuron with high synaptic Ca +2 concentration (Ca +2 = 700mV ). T d is the time delay required by neuronN5 to encode its high-rate synaptic inputs into APs. . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.11 A simulation result forN4 neuron with randomly generated spiking patterns using neuronsN1 andN2. The results are divided into four groups to test the eect ofCa +2 ion modulation on the network’s performance. EPSP is the output of excitatory synapsesS1,S2, andS3 to the received APs pattern and Ca +2 ion concentration signaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.12 A simulation result forN4 neuron with randomly generated bursting patterns using neuronsN1 andN2. The results are divided into four groups to test the eect ofCa +2 ion modulation on the network’s performance. EPSP is the output of excitatory synapsesS1,S2, andS3 to the received APs pattern and Ca +2 ion concentration signaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 ix 5.1 An earlier BioRC spike time-dependent plasticity (STDP) model, adopted from [103]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 A schematic diagram of the BioRC spike time-dependent plasticity (STDP) model using dopamine signaling, adopted from [142]. . . . . . . . . . . . . . . . . . . . . 68 5.3 The neuronal network that was used during the implementation of spike time- dependent plasticity (STDP) using dopamine signaling, where the process of generating long-term potentiation (LTP) and long-term depression (LTD) requires inputs from other neurons, adopted from [142]. . . . . . . . . . . . . . . 68 5.4 The schematic diagram for the astrocyte to demonstrate synaptic plasticity based on the repeated APs at the presynaptic neuron. Cleft1 represents the sensed NT at the synaptic cleft region, andPreAP1 acts as an enabling signal to acknowledge the astrocyte about activities at the presynaptic terminal. . . . . . . . . . . . . . . 70 5.5 The BioRC neuromorphic conguration between the astrocyte and the synapse circuits using the repeated presynaptic activities protocol. . . . . . . . . . . . . . 71 5.6 An experimental neuronal network to demonstrate synaptic plasticity using astrocyte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.7 Simulation results for the experimental network with the proposed astrocyte model based on repeated presynaptic activities, modeled as a regular spiking patterns. AP1, AP2, and AP3 are the output of presynaptic neurons N1, N2, and N3, respectively. AP4 is the output of the postsynaptic neuron, N4. The EPSPs are the excitatory postsynaptic potentials of synapses S1, S2, and S3. LTP1, LTP2, and LTP3 represent the long-term potentiation of synapses S1, S2, and S3, respectively. LTD1, LTD2, and LTD3 represent the long-term depression of synapses S1, S2, and S3, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.8 The schematic diagram for astrocyte to cause synaptic plasticity based on the synchronized timing between the presynaptic and postsynaptic neurons. . . . . . 75 5.9 The BioRC neuromorphic conguration between the astrocyte and the synapse circuits using the STDP protocol. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.10 Simulation results for the experimental network with the proposed astrocyte model based on repeated presynaptic activities. AP1, AP2, and AP3 are the output of presynaptic neurons N1, N2, and N3, respectively. AP4 is the output of the postsynaptic neuron, N4. The EPSPs are the excitatorty postsynaptic potentials of synapses S1, S2, and S3. . . . . . . . . . . . . . . . . . . . . . . . . . 77 x 5.11 The simulated results of the postsynaptic neuron (N4) to dierent spiking patterns generated by presynaptic neurons (N1,N2, andN3) for strong synaptic connections. Dierent colors indicate variousN4 postsynaptic responses to various presynaptic spiking patterns. SB and RS represent single burst and regular spiking patterns, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.12 The simulated results of the postsynaptic neuron (N4) to dierent spiking patterns generated by presynaptic neurons (N1,N2, andN3) for weak synaptic connections. Dierent colors indicate variousN4 postsynaptic responses to various presynaptic spiking patterns. SB and RS represent single burst and regular spiking patterns, respectively. X represents undetected spikes asN4 recognizes selective information encoded in the shape of AP patterns, such as various burst widths, and information encoded in the timing between spikes, such as the case of synchronized spikes. . . . . . . . . . . . . . . . . . . . . . . . . 80 6.1 A small experimental neuronal network demonstrating the functionality of all-patterns-pass output neuron (N A ). N1 andN2 represent regular spiking input neurons, and N3 represents bursting input neuron. S1, S2, and S3 represent theCa +2 modulated synapse model [150]. . . . . . . . . . . . . . . . . . 85 6.2 The behavioural responses of All-patterns-pass ltering neuron (N A ) using three input neurons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, andS3).EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3 The schematic diagram of a bursts-passing neuron (N B ), whereCOMP 1 and COMP 2 are low power voltage compactors (Fig. 3.3). The red and blue arrows represent the propagation delays fromCOMP 2 to M19 and M15 andCOMP 1 to M20, respectively. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, and Ca+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 800mV (activated) to set the bursting mode forN B . . . . . . . . . . . . . . . . . . . . . . . 90 6.4 A small experimental neuronal network demonstrating the functionality of a burst-pass output neuron (N B ). N1 andN2 represent regular spiking input neurons, andN3 represents the bursting input neuron.S1,S2, andS3 represent theCa +2 modulated synapse model [150]. . . . . . . . . . . . . . . . . . . . . . . 91 6.5 The behavioural responses of bursts-pass neuron lter (N B ) using three input neurons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, and S3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 xi 6.6 The schematic diagram of spikes-passing neuron N S , where COMP 1 and COMP 2 are low power voltage compactors (Fig. 3.3). The red and blue arrows represent the propagation delays fromCOMP 2 to M19 and M15 andCOMP 1 to M20, respectively. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, andCa+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the spiking mode forN S . . . . . . . . . . . . . . . . . . . . . . 94 6.7 A small experimental neuronal network demonstrating the functionality of spikes-pass neuron lter (N S ). N1 andN2 represent regular spiking input neurons, andN3 represents bursting input neuron.S1,S2, andS3 represent the Ca +2 modulated synapse model [150]. . . . . . . . . . . . . . . . . . . . . . . . . 95 6.8 The behavioural responses of spikes-pass neuron lter (N S ) using three input neurons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, and S3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.9 The schematic diagram of spikes-passing neuron N P , where COMP 1 and COMP 2 are low power voltage compactors (Fig. 3.3). The blue and red arrows represent the propagation delays fromCOMP 2 to M15 andCOMP 1 to M20. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, andCa+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the phasic spiking mode forN P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.10 A small experimental neuronal network demonstrating the functionality of phase-pass neuron lter (N P ). N1 and N2 represent regular spiking input neurons, andN3 represents bursting input neuron.S1,S2, andS3 represent the Ca +2 modulated synapse model [150]. . . . . . . . . . . . . . . . . . . . . . . . . 99 6.11 The behavioural responses of phase-pass neuron lter (N P ) using three input neurons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, and S3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.12 A small experimental neuronal network demonstrating the functionality of bursts-width-pass neuronal topology (N W ). N1 and N2 represent regular spiking input neurons, andN3 represents bursting input neuron.S1,S2,S3 and S4 represent theCa +2 modulated synapse model [150]. . . . . . . . . . . . . . . . 102 xii 6.13 The behavioural responses of bursts-width-pass lter (N W ) using three input neurons (N1, N2, andN3), N B is bursts-pass andN P is phase-pass neuron lters, and fourCa +2 modulated synapses (S1,S2,S3 andS4).EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. . . . . . . 103 6.14 A chicken’s avian sound localization circuit, adopted from [159]. (A) represents dierent color-coding sound source locations in the azimuth space. (B) Schematic auditory brainstem representation. Nucleus Laminaris (NL), also known as coincidence detectors, map azimuthal space for the color-coding sound sources locations. The ipsilateral axon terminals (magenta) support inputs to the dorsal dendrites of NL, while the contralateral (green) support systematical delay timing from medial to lateral. Both ipsilateral and contralateral inputs to NL are provided by a single avian cochlear nucleus magnocellularis (NM) axon projecting to both NLs. Various physical properties of NM axons represent dierent resonance frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.15 A general block diagram for a network of neurons with dierent ltering capabilities performing dynamic decoding for the origins of various AP patterns from the outputs of a network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.16 A detailed schematic diagram of the Decoding Bursts Origin and the Decoding Spikes Origin subblocks discussed in Fig. 6.15, where the rst decodes bursts origins usingN Wsum andN W1 neurons, and the second decodes the network spikes origins usingN Ssum andN S1 neurons. N A neurons couple the output fromN Wsum andN W1 , in the case of decoding bursts, or fromN Ssum andN S1 neurons, in the case of decoding spikes, at which if the received APs arrive in a concurrent time, they will produce coincident bursts at the output terminal of N A neurons. Consequently, neuronsN B andN P separate the coincident bursts from other spikes and identify their phase change. . . . . . . . . . . . . . . . . . . 107 6.17 The neuronal responses involved in decoding a burst origin of input neuronN A1 , from the output bursts of a network (N Bsum ). N Wsum andN W1 convert bursts into spiking domain using two consecutive spikes per burst to indicate the start and end times of the bursts fromN Bsum andN A1 , respectively. N A couples the outputs fromN Wsum andN W1 neurons to coincident bursts (indicated as dashed boxes) when input are correlated in time and into regular spikes when they are not correlated. N B neuron is used to pass the generated coincident bursts and block other regular spikes, andN P neuron converts the coincident back to a spiking domain to indicate which ofN A1 bursts contributed to an output burst at the output neuron of the network (N Bsum ). . . . . . . . . . . . . . . . . . . . . 110 xiii 6.18 The neuronal responses involved in decoding a spike origin of input neuronN A1 , from the output spikes of a network (N Ssum ).N S1 passes regular spiking AP and block bursting AP from neuronN A1 . N A couples the outputs fromN Ssum and N S1 neurons to coincident bursts when input are correlated (indicated as dashed boxes) in time and into regular spikes when they are not correlated.N B neuron is used to pass the generated coincident bursts and block other regular spikes, andN P neuron converts the coincident back to a spiking domain to indicate which ofN A1 bursts contributed to an output burst at the output neuron of the network (N Bsum ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 xiv Abstract Biological neurons signal each other in a rich and complex manner to perform complex cogni- tive computing tasks in real-time; such biological capability enables the interdisciplinary eld of neuromorphic engineering (NE) to implement various information processing systems to perform brain-like computations intelligently and autonomously, utilizing distributed memory-processing architecture. Our neuromorphic work focuses on modeling rich neural encoding behaviors. Using electronics as the basis of our neuromorphic approach, we developed circuits that demonstrate dierent neural behaviors depending on various input spiking patterns (neural codes) from the presynaptic neurons. We achieve that by creating dynamic neural encoding circuits that encode various presynaptic spiking inputs into dierent postsynaptic spiking outputs utilizing the Axon Initial Segment’s (AIS) modulation and processing capabilities. The circuits are constructed based on the biophysical mechanisms of various voltage-gated ion channels, such as the activation/deactivation of Calcium (Ca +2 ), Potassium (K + ), and Sodium (Na + ) ion channels by which our intended circuits emulate various neural responses. The gener- ated spiking patterns are consistent with the spiking patterns produced by the Izhikevich math- ematical model describing biological neuronal responses. Such patterns include regular spikes (RS), phasic spikes (PS), tonic bursts (TB), single burst per stimulus (SB), class-1 excitable spikes (CS1), subthreshold oscillations (OSC), depolarization after potential (DAP), integrator (INT), and xv mixed-mode (MIX). Furthermore, we show how our circuits emulate other biological behaviors such as the neural threshold variability. We posit that such dynamic neural encoding is essential in enabling autonomous behavioral electronic systems for the future technology of articially intelligent systems. Through circuit simulations, we show that our proposed neuromorphic circuits can autonomously encode various received presynaptic spikes and their timing of occurrence into dierent postsynaptic spiking patterns using the coincident encoding behavior of Layer 5 Pyramidal Neurons (L5PN) as an example. In other words, our neural circuits can detect synchronized presynaptic inputs through the generation of burst spiking patterns, which suggests that the timing of input spiking is vital in the encoding of neural information. Furthermore, we show how postsynaptic neurons exhibit complex behavioral responses resembling dierent received spiking patterns from presynaptic neurons using our electronic dynamical neural encoding model. Moreover, based on our developed hardware-based theory of AIS modulation, we describe how modeling a dynamic encoding in electronics can be vital in enhancing the processing ca- pability of a given neuromorphic neural network. Such capability includes the implementation of pattern-specic ltering responses. The term ltering refers to the process by which a neu- ron responds selectively to distinct presynaptic patterns by which the classication and other pattern-specic processes in a neural network are accomplished. To examine such processing ca- pability, we built an electronic experimental neuronal network capable of decoding information regarding the origin of an AP from the output of the neuronal network employing ve dierent electronic neuron ltering models, including all-patterns-pass neuron (N A ), bursts-pass neuron (N B ), spikes-pass neuron (N S ), phase-pass neuron (N P ), and bursts-width-pass topology (N W ). xvi Chapter1 Introduction Inspired by biological neuronal behaviors, neuromorphic engineering (NE) enables various infor- mation processing approaches utilizing a distributed memory-processing architecture, and this feature distinguishes neuromorphic systems from conventional Von-Neumann-based computing systems. The ultimate objective of NE is to design systems with a brain-like computation capa- bility. MIT Technology Review listed this interdisciplinary eld among the top 10 technology breakthroughs in 2014 and the top 10 emerging technologies by the World Economic Forum in 2015. NE provides two pathway solutions: rst, developing hardware-based solutions for sci- entists to aid the study and discovery of new neurobiological properties; second, for engineers to harness the known biological properties in developing an articial neuronal network that can autonomously learn and perform complex tasks in real-time, such designs are being used in appli- cations such as prosthetic devices [1, 2], sensory applications [3, 4, 5], and biomimetic approaches used for bio-inspired computing [6, 7]. A biological neuron consists of somatodendritic and axon compartments. The rst is to convert the received graded presynaptic stimulus into subthreshold oscillation, and the second is to process such oscillation and generate AP to postsynaptic targets. One of the fundamental modeling aspects of building neuromorphic systems is knowing how 1 synaptic input properties are transcribed into dierent spiking patterns. In other words, what neuronal code to use. Therefore, how and where a spike is formed is crucial in understanding the neuronal code and its processing capabilities. In the cortical region, spikes are initiated at the Axon Initial Segment (AIS) region [8, 9]. The AIS is the region between the somatodendritic and the axon compartments. In neuroscience literature, the AIS region is identied as the site of spike generation, signal processing, neuronal modulation, and neuronal activity regulation[10, 11, 12, 13, 14, 15]. During the last decade, the BioRC project, led by Dr. Alice Parker [16], has focused on the electronic design of neuromorphic circuits demonstrating some of the brain’s biological cog- nition, learning, and memory capabilities. Building autonomous systems that learn and behave intelligently requires high processing capabilities. There are a few neuron spiking models can demonstrate complex behavioral capabilities in terms of the generation of various spiking patterns, including the mathematical conductance- based model of Hodgkin and Huxley [17], and the Izhikevich simple spiking model [18]. Despite the great learning and pattern recognition tasks of such models, they rely on conventional central processing units (CPUs), or in some cases, graphical processing unit (GPUs) for solving dieren- tial equations describing complex spiking behaviors. For example, the Blue Brain Project utilizes 8,000 CPUs of the IBM Blue Gene supercomputer to emulate 10,000 neurons in the rat neocortical column, with ion channels modeled with Hodgkin and Huxley equations. Another example, the SpiNNaker project, requires 18 ARM networked processors to mimic 18,000 biological neurons using Izhikevich’s model [18, 19]. Therefore, modeling such complex behaviors in electronics is crucial for enabling scalable, intelligent, and on-chip neuromorphic autonomous processes in real-time. 2 Hodgkin and Huxley’s pioneering work has revealed many aspects of how dierent stimu- lation leads to dierent signaling behaviors using the squid giant axon. Their work underlined the baseline of various spiking properties at the axon involved in rich neuronal signaling. They identied how the spiking threshold rises identical to the activation of the Potassium (K + ) con- ductance to which there is a higher degree of inactivation than the case at resting potential where K + conductance is much lower. In addition, Hodgkin and Huxley have shown how the amplitude of stimulus can be encoded in the shape of the produced spiking pattern. For example, stimulat- ing the squid giant axon with a small amplitude current pulse causes some oscillations to appear at the tail of the generated spike due to the change ofK + conductance by which the ability of inactivation is reduced. Moreover, they discover how increasing the temperature aects the squid giant axon signaling by causing it to produce a narrower spike duration compared to the dura- tion associated with a lower temperature, suggesting a higher level of information processing exists within individual neurons. In addition, they concluded that the conduction velocity is a function of the axon physical characteristics (i.e. radius, internal resistance, and the capacitance per unit area of the axon), and how an axon can be described using cable theory. Nevertheless, in the most introductory neuroscience literature, neurons are dened as integrators by which they integrate (sum) their dierent synaptic stimuli. If the sum of the stimuli is larger than a particular threshold value, then a neuron generates an "all or non" spike, and when it is less than the threshold, the neuron is said to be silent. However, such description does not answer how inhibitory neurons spike when they only have inhibitory synapses (IPSP), how neurons produce various AP patterns when receiving the same synaptic inputs and vice versa, or how neurons 3 encode information related to the time of the presynaptic APs. Those are important perspec- tives that need to be addressed when developing meaningful neuronal encoding models, particu- larly hardware-based models that can solve complex engineering tasks in real-time and perform brain-like computations without the need for external processing units. There is much evidence suggesting that describing biological neurons as integrators might be an oversimplied encoding model, including dendritic spike generation [20, 21], location of exciting synapses [22], current spiking activity of a neuron related to its past activity [23, 24], and the role of back-propagating APs [25]. A distributed memory-processing architecture using synaptic weights is what primarily dis- tinguishes neuromorphic systems from other conventional systems. In neuromorphic systems, the neuronal code scheme used determines the level of processing capabilities. However, most current neuromorphic systems use a simple neuronal encoding scheme such as Integrate-and- Fire (I&F) and leaky Integrate-and-Fire (Leaky I&F). Consequently, due to the static encoding framework of I&F, we hypothesize that those systems require a signicant number of neurons to increase the computational capability than systems with complex neuronal encoding schemes. On the other hand, other neuromorphic implementations combine dierent biological neuronal aspects, such as dendritic computations and astrocytic modeling, to improve the processing capa- bilities of neuromorphic systems. For example, dendritic computations depend on the synapses’ locations and include dendritic spiking and other nonlinear responses. Also, the origins of the signals (space distribution of the synapses) can be encoded in the generated spiking shapes [22]. The BioRC project has demonstrated many dendritic models using electronics, including how such locations of synapses and magnitudes of the Post Synaptic Potentials (PSPs) on the dendrite aect the process of dendritic integration [26, 27]. Between the complexity of modeling dendritic 4 computations and the desire of using simple encoding neuronal models, we focused on model- ing the site responsible for the generation of all APs patterns observed in biological neurons, the AIS. To mimic the AIS dynamic encoding behavior in electronics, we introduce the concept of neuronal modulation proposed by our developed hardware-based theory. Accordingly, this dis- sertation demonstrates, using electronics, how neuronal modulation at the AIS region enhances the neuronal code through which various synaptic input properties result in dierent AP patterns. In other words, neurons can be tuned dynamically and not statically, as in the case of simple I&F and leaky I&F encoding models, to recognize various synaptic input properties and promote intel- ligent behavior in neuromorphic systems. Hence, focusing on how a biological neuron perceives and processes information, the dissertation aims at developing an electronic neuronal encoding model, using the role of AIS to increase the processing capabilities, enhance the autonomous and learning abilities of computational neuromorphic systems to execute complex processes such as patterns specic ltering and decoding information regarding the origin of an AP from the output of a neuronal network. In addition, processing information regarding the timing of various AP patterns is one of the main characteristics of biological neurons. In the cortical region, for example, more than 75% of the neurons are pyramidal neurons (PNs) [28]. PNs are well known for their distinct long axons allowing them to reach multiple cortical layers. One of the widely-studied neuronal encoding behaviors in the cortical region is coincidence detection [29, 30], by which the encoding of spikes depends on the synchronized timing of the presynaptic inputs (time correlation between spikes) [29, 31, 32]. Using our electronic dynamical neuronal encoding implementations and calcium (Ca +2 ) modulated synapses models, this dissertation will demonstrate the capability of our electronic model in mimicking the coincident detection behavior of PNs through bursting by 5 which an AP origin can be decoded from the output of the neuronal network. On the other hand, in most neuromorphic systems utilizing a simple neuronal encoding scheme, learning is based on the concept of synaptic plasticity by which the synaptic strength between two neurons solely determines whether a neuron generates an AP. This dissertation demonstrates that rich learning behaviors are not dependent only on the strength of the synaptic connection but also on the timing between the spikes and other various properties of synaptic inputs (i.e. shape, frequency, phase, and intensity), by which neuron to neuron signaling, regarding the pattern and the time of the received AP, can be improved. The chapters in this dissertation are organized as follows. chapter 2 provides an overview of the mechanisms involved in generating dierent AP patterns at the AIS region. We also compare our encoding approach to other state-of-art relevant models in neuromorphic engineering. In chapter 3, we introduce our model’s generated patterns and compare them to those found in bi- ological neurons, including regular spikes (RS), phasic spikes (PS), tonic bursts (TB), single burst per stimulus(SB), class-1 excitable spikes(CS1), subthreshold oscillations (OSC), depolarization after potential (DAP), integrator (INT), and mixed-mode (MIX). We also discussed the dynamic activation and deactivation of dendritic voltage-gatedCa +2 channels by emulating the eect of the calcium-induced T-current observed in biological neurons exerting bursting APs (i.e. pyra- midal and thalamic cortical neurons), as well as a discussion of threshold variability. In chapter 4, we introduce an excitatoryCa 2+ modulated synapse model modied from our earlier BioRC synapse model [33], and a simple dendritic arbor model to be used for building a simple dendritic computation compartmental model to prove how rich and autonomous processing capabilities can be accomplished even with simple dendritic models. As a result, dynamic neuronal encoding schemes, such as coincident detection and rate codes, are discussed. chapter 5 introduces two 6 simple astrocytic compartmental models involved in synaptic plasticity to describe the dynamic learning capabilities associated with various AP patterns. The rst model depicts synaptic plas- ticity induced by repeated activities at the presynaptic terminal, and the second model depicts synaptic plasticity induced by the synchronous timing between the presynaptic and postsynaptic activities. chapter 6, based on our hardware-based theory, presents the implementations of ve distinct neuronal ltering behaviors in electronics. (1) All-patterns-pass (N A ) ltering neuron that is capable of detecting all presynaptic patterns, including coincident spikes. (2) Bursts-pass (N B ) ltering neuron that detects and passes bursting AP patterns and blocks other regular spik- ing patterns. (3) Spikes-pass (N S ) ltering neuron that permits regular spiking patterns and pre- vents bursting AP patterns. (4) Phase-pass (N P ) ltering neuron that recognizes the phase change in presynaptic inputs. (5) Bursts-width-pass (N W ) ltering neuron that signals the start and the end times of each detected presynaptic burst (burst width signaling). We then demonstrate how these neuronal ltering behaviors can be applied in conjunction with the coincident detection to decode information about the origin of an AP from the output of a neuronal network, demon- strating the ability to perform complex processing capabilities such as location-based processes. 7 Chapter2 BackgroundandRelatedWork 2.1 NeuroscienceBackground The human brain is a very sophisticated, complex, and creative information-processing system. It consists of nerve cells — neurons along with other cells. In general, a neuron generates and propagates action potentials (AP) using voltage-gated ion channels [34]. Ionic channels allow ions to ow from the exterior to the cell’s interior or vice versa, such as theK + ion channels andNa + ion channels, respectively. In theK + channel, ions cannot ow inside a polarized cell; in other words, the ow depends on the ions’ electromotive force. On the other hand, theK + channel allows ions to ow into the cell’s interior when the cell is depolarized [34, 35]. Other ion channels examples include Sodium (Na + ), Calcium (Ca + ), Chloride (Cl ), and Proton (H + ) ion channels. Notwithstanding the advances in technology, the detailed mechanism of how ion channels work has not been fully explored. Neurons communicate via small structures called neuronal junctions or with a muscle cell via neuromuscular junctions. Both neuronal and neuromuscular junctions are referred to as synapses. There are two types of synapses, chemical, and electrical synapses. In the case of 8 a chemical synapse, each ending of a presynaptic neuron forms a knoblike structure separated from an adjacent postsynaptic neuron by a microscopic space called the synaptic cleft, typically 0.02-micron wide [36]. When an AP arrives at the presynaptic terminals, it causes the synaptic vesicles’ movement toward the presynaptic membrane to fuse with the membrane and release a chemical substance called a neurotransmitter. A neurotransmitter transmits the AP to the postsynaptic neuron by diusing across the synaptic cleft and binding to receptor molecules on the postsynaptic mem- brane. Depending on the particular reaction between the two neurons, a neurotransmitter may excite or inhibit the postsynaptic neuron. Depending on the type of the postsynaptic receptor type, a neurotransmitter may inhibit or excite activity in the postsynaptic neuron resulting in an inhibitory postsynaptic potential (IPSP) or excitatory postsynaptic potential (EPSP), respectively. On the other hand, electrical synapses are reciprocal pathways for ionic current and small organic molecules [37]. They allow the adjacent neurons to have direct communication between their diused membranes through channels called gap junctions. Electrical synapses allow faster synaptic transmission for APs compared to chemical synapses; they also help to synchronize entire groups of neurons. Electrical synapses are now being intensively examined in mammals. The typical locations of electrical synapses are found between excitatory projection neurons of the inferior olivary nucleus and between inhibitory interneurons of the neocortex, hippocampus, and thalamus [37]. 9 2.1.1 TheAxonInitialSegmentDenition As we discussed earlier, biological neurons are highly polarized cells by which they ensure di- rectional signaling throughout the mammalian central nervous system (CNS). They do that by converting the graded synaptic inputs received at the dendrites and soma (Somatodendritic com- partment) into APs. The generated APs then propagate reliably through the axon hillock com- partment to signal the targeted postsynaptic neuron [38]. Superior to the classical view that describes the axon hillock as a reliable medium for the initiation and propagation of the AP to the postsynaptic targets, the physical and geometrical properties of the axon, and the unique properties of the reported ion channels at the Axon Initial Segment (AIS) determine various complex behaviors, including signal processing and timing of numerous events in the brain. The highly excitable region of the AIS is located at the region between the somatodendritic and the axon compartments (Figure 2.1). On average, the AIS location varies between 20 - 60 m distance relative to the cell body for myelinated axons in which the axon extends from the cell body. This physical separation allows the preservation of the molecular identity of the somatodendritic and axon compartments. Therefore, knowing where the spikes are initiated is crucial to understand how dierent graded synaptic inputs are converted to dierent action potential patterns. In cortical neurons, the initiation (sudden rise) of AP occurs at the AIS because the AP gener- ation threshold is lowest in this region compared to the somatodendritic and axon compartments [8, 9, 13]. Several reasons explain why the threshold required for the AP initiation at the AIS is lowest. First, the AIS diameter is an order of magnitude smaller than the soma, which implies a smaller characteristic capacitance; thus, a less inward current is required to provoke APs [12]. 10 Figure 2.1: A graphical representation of the voltage-space distribution for a generated action po- tential in pyramidal neurons (adopted from [12]). SD and IS represent the somatodendritic and the axon initial segment regions, respectively. The dotted line shows the voltage space distribution without theN + a ion channels in the nodal region (t=0.85ms and t=0.95ms) and the somatoden- dritic region (t=1.35ms). Second, there is a higher density of voltage-gated ion channels per unit area than at the soma, specically, the low threshold voltage-gated ion channels [13]. The voltage-gated ion channels reported at the AIS site include voltage-gated Sodium channels (N av ) and voltage-gated Potas- sium channels (K v ). 2.1.2 VoltageGatedIonChannelsatTheAIS Voltage-gated ion channels are distributed into specic neuron locations to perform specic func- tions; Hence, inaccurate distribution of the voltage-gated ion channels can cause a deciency in 11 the neuronal network. Therefore, investigating each type of voltage-gated ion channel and its role in neuronal signaling is crucial in understanding how neurons encode and transfer information [39]. TheN av channels are the main ion channels responsible for generating the inward current. There are four subtypes of N av channels found throughout the CNS (N av 1:1, N av 1:2, N av 1:3, N av 1:6), however, the mainN av subtype that can be found at the AIS region is theN av 1:6 at a distal location from the soma [40, 41]. On the other hand, theN av 1:1 andN av 1:2 target mainly a cell-type-specic manner and can be clustered at a proximal distance from the soma [42, 43]. TheN av channels found at the AIS are specialized and have dierent properties compared to those found in the somatodendritic compartment in which they control the neuronal ring prop- erties. For example, theN av channels expressed at the AIS region have an activation/deactivation threshold voltage of 10mV lower than those at the somatodendritic compartment [42, 44]. In- terestingly, the N av located at the AIS of the Granule cells (found in the granular layer of the cerebellum) can be activated/deactivated by a factor of two times the speed of those located at the soma [45]. Moreover, in some cases, theN av at the AIS region has reported some capabili- ties of not undergoing a complete deactivation phase, leading to the generation of the persistent N a current. Such current contributes to the generation of higher frequency APs (burst genera- tion); Therefore, theN av channels found at the AIS contribute mainly to lowering the neuronal threshold, and consequently, increase excitability. Another type of ion channel reported at the AIS is theK av ion channel. TheK v channel play a signicant role in shaping APs due to their lower threshold activation and shunting properties (repolarization of APs) [46, 47]. Moreover, theK v channels play a signicant role in modulat- ing the neuronal thresholds, interspike time intervals, and the frequency of the generated APs 12 patterns. The main type ofK v channel is theK v 1. TheK v 1 channels, in particular, have a fast activation time, yet slower deactivation time [47, 48]. Such properties lead to the conclusion that theK v 1 at the AIS is responsible for the AP repolarization independently of the somatic AP waveform and the transmitter release regulation at the synaptic terminals of the axon hillock [47]. 2.1.3 DynamicalNeuronalModulationandSignalProcessingatTheAIS With the advances in the electrical and optical recording methods used in experimental neuro- science, recent discoveries have suggested that the AIS’s role is more complicated than being a trigger site for AP initiation. It also a site of complex neuronal modulation and adaptive neu- ronal signal processing [13, 14, 15]. Such capabilities can be realized through the AIS’sstructural plasticity. The term structural plasticity describes the continuous physical changes of the AIS length and location relative to the soma in an activity-dependent manner. Therefore, the AIS is the site of neuronal structural plasticity, and neuronal activity regulation [10, 11] by which the AIS governs the dynamical neuronal signal processing. Structurally, the AIS length and location relative to the soma vary with neuronal activities [49]. This structural plasticity of the AIS is capable of altering neuronal excitability through slow adaptation processes. With such variations, for example, neurons in the avian nucleus laminaris (NL) pathway can adapt to particular frequencies during sound localization processes because the length and the location of the AIS relative to the soma vary with the tuning frequency, also known as the characteristic frequency (CF) of the neuron. The tuning frequency is the preferred stimulus frequency by which the neuron shows maximum response [50]. In other words, the 13 shorter the AIS and more distal from the soma in a neuron, the higher the tuning frequency of that neuron because at a distal location, the AIS has a smaller shunting conductance of theK v ion channels, and the loading eect of the somatodendritic compartment is reduced at further distances from the soma [51, 52]. In contrast, the neuron’s excitability is reduced when longer AIS is located distally from the soma because of the increase in charge dissipation along the AIS region. Thus, the AP’s depolarization becomes more dicult, especially in the presence of the shunting conductance of theK v ion channels. Therefore, the negative correlation between length and the location of the AIS can maxi- mize excitability. Also, the unique structural property of the AIS allows the nucleus laminaris neurons to interpret and respond accurately to their synaptic inputs at the desired characteristic frequency; hence, ensuring a precise calculation of the interaural time dierence (ITD) between the two ears in the mammalian against a wide range of sound frequencies [53]. For example, in Figure 2.2(A), the AIS’s elongation and the replacement ofKv1 withKv7 cause an increase in the neuron’s excitability. Such structural elongation requires 3-7 days to take place. Another example of the AIS structural plasticity can be shown in Figure 2.2(C), where the further the AIS location is relative to the soma, the less excitable the neuron is. Such a change in location can take place within a two-day period. Moreover, in cortical and hippocampal regions, the AIS is the only targeted site for the Chan- delier cells (a specialized type of GABAergic interneuron known for its remarkable precision in targeting only the AIS of pyramidal neurons) [55]. Interestingly, they have peculiar morpho- logical characteristics by which they form their synaptic connections with the AIS of pyramidal neurons symmetrically; hence, they are referred to as axo-axonic cells. Therefore, the Chandelier cells can directly modulate the AP’s generation of the excitatory neurons through the axo-axenic 14 Figure 2.2: Structural and biophysical interaction during axon initial segment (AIS) plasticity (adopted from [54]). (A) shows the eect of the AIS elongation in NL neurons. (B) represents the eect on depolarizing the hippocampal dentate granule cells for 3 hours, that shortens the AIS. (C) shows a depolarization eect for two days on the pyramidal neurons that causes the AIS to move distally, yet the axo-axonic synapses remain at the original location, boosting the suppressive eects of distal movement on excitability synapses located at the AIS region of the targeted neurons [56, 57], and synchronize neuronal activities [58] (Figure 2.2). 2.1.4 BurstingThroughCalciumIonChannels In addition, the intracellular Ca +2 mechanism plays a signicant role in neuronal signaling, where this mechanism increases the neuronal ring rate (burst generation) [59]. Bursting APs can be generated externally throughout a network of neurons to generate rhythmic motor pat- terns [60], such as the neurons found in the central pattern generator (CPG) [61], or intrinsically using voltage-gated Calcium channels (C av ). In general, C av channels can be categorized into 15 high-voltage (HVA) and low-voltage (LVA) activated channels based on the threshold activation voltage. The activation of HVA channels, such as T-typeCa +2 channels, during small cell de- polarization causes a more substantial cell depolarization at which bothC av andN av channels become activated, which result in the generation of bursting APs [62]. 2.1.5 AstrocytesRolesinSynapticStrengthening Glial cells, such as astrocytes, are critical to neuronal signaling and contribute to various com- plex neuronal responses [63]. Astrocytes have been shown to participate in neuronal activities modulation for a specic neuronal network within a specic region in the brain [64]. Thus, understanding astrocyte’s roles is crucial when simulating a specic region of the brain or sim- ulating the oscillations of the whole-brain rhythms [65]. In recent years, laboratory neuroscien- tists have revealed much evidence suggesting that astrocytes are far more involved in neuronal signal processing, learning, and storing memory. For example, astrocytes support learning and memory formation by which they inuence synaptic plasticity, the process of strengthening or weakening a synaptic connection between two neurons [66, 65]. Besides, astrocytes improve the synchronization of neuronal activity at hippocampal CA1 neurons [67]. Moreover, several pro- posed hypotheses suggest that astrocytes store memory by the organization of their ion channels [68], promote motor skills learning [69], and can modulate other cognitive processes [70]. Long-term synaptic plasticity is a widely accepted concept in neuroscience that correlates cel- lular changes with learning and memory [71]. In general, there are two types of long-term plas- ticity. First, long-term potentiation (LTP), the process by which the synaptic connection between a presynaptic neuron to a postsynaptic neuron is strengthened, results in a larger induced EPSP 16 at the latter’s dendrite. Second, long-term depression (LTD), the process by which the synaptic connection between a presynaptic neuron to a postsynaptic neuron is weakened, resulting in a decreased induced EPSP at the latter’s dendrite [72, 73]. Several protocols are associated with the formation of LTP and LTD, including (1) repeated presynaptic stimulus-based plasticity where individual synapse strengthening depends on the rate of the presynaptic AP from the presynap- tic neuron, and (2) precise spikes timing of presynaptic and postsynaptic-based plasticity, also known as Spike Time-Dependent Plasticity (STDP) [74, 75]. Figure 2.3 shows the process of astrocytic activity in synaptic plasticity. When an intrinsic AP reaches the presynaptic terminal, the voltage-gatedCa +2 channels open to allow the inux ofCa +2 . The inux ofCa +2 causes the synaptic vesicles to fuse with the presynaptic’s mem- brane (exocytosis) to release neurotransmitters (NT) into the synaptic cleft. Consequently, the released NTs diuse to the postsynaptic terminal. On the other hand, the astrocyte senses the released NT at the synaptic cleft using particular NT receptor types, resulting in intrinsic astro- cyticCa +2 oscillations within the astrocyte. The intrinsic astrocyticCa +2 oscillations then cause chemical substances to be released back to the presynaptic terminal, thus, creating a controlled positivefeedback signaling between the presynaptic and postsynaptic neurons. In particular, this communication protocol is governed by the release of Glutamate NT from the astrocyte to the presynaptic terminal, that eventually increases the Ca +2 inux of the presynaptic neuron by which synaptic connection is strengthened. 17 Figure 2.3: An illustration of the communication protocols between astrocyte and synaptic ter- minals for strengthening or weakening the synaptic connection. Modied from [76]. 2.1.6 BackgroundonSynapticStrengthening In biological neurons, the synaptic strength between presynaptic and postsynaptic neurons dic- tates the AP transmission between the two neurons. This process is by which the astrocyte plays a signicant role. It provides neurons with information in a positive feedback manner, by which the astrocyte senses the released neurotransmitters at the synaptic cleft region (the space between presynaptic and postsynaptic terminals), then controls the presynaptic neurotransmit- ters’ release by increasing/decreasing theCa +2 inux at the presynaptic terminal. The astrocyte controls the presynaptic neurotransmitters’ release by the activation of metabotropic glutamate receptors (mGluRs) [77] or through the activation of NMDA receptors [78] which eventually control the inux ofCa +2 into the presynaptic terminal. 18 2.2 BackgroundinNeuromorphicEngineering The understanding of the neuronal code is one of the central challenges in neuroscience. The neu- ronal code is dened as a sequence of APs that the brain may use to encode, decode, and process sensory and/or cognitive information [79]. Typically, scientists use experimental approaches to characterize a neuronal code. In such procedures, stimuli are introduced to an animal to quantify various properties of spiking patterns. Although experimental approaches are non-biological, several coding schemes have been developed and used signicantly in modern neuronal net- works. 2.2.1 NeuronalCodingSchemes Two of the most popular neuronal coding schemes are rate code and temporal code. It is well established that both ’rate code’ and ’temporal code’ carry information about sensory inputs. Rate coding is the rst neuronal code discovered by Adrian in 1926 [80]. In a rate coding scheme, neurons process information based on the average APs at a specic time. For instance, in sensory systems, the intensity of stimuli is proportional to AP’s rate; hence, rate code is well known for its robustness when dealing with such systems. However, it limits the amount of information a neuron can process. In other words, it is very limited in areas where AP’s rate is reduced [81]. Therefore, to resolve such a limitation problem of neuronal rate code, many dierent cod- ing schemes have been characterized using tuning curves to explain why neuronal activities in various cortex areas are much less than those in sensory systems. For example, one approach suggests that reducing APs count in the cortex compared to the sensory system can be related to spike-frequency adaptation mechanisms, where coding strategy and biophysical mechanism 19 play a signicant role in reducing cortical neuronal activities [82]. Another example suggests optimizing the tuning curve using a nite time window instead of the assumption of a innite time window can explain the reduction of neuronal activities between the sensory and cortical regions [83]. Despite the enormous number of research that focuses on explaining the reasons behind the reduction of APs in the cortex compared to the number of APs on the sensory system, the question remained unanswered of how neuronal systems process information. Another group of scientists suggests that neurons use temporal code to process information using the precise timing of APs or interspike intervals. Studies have estimated that neurons have a resolution on a scale of one-millisecond [84], which means that a postsynaptic neuron can detect the dierence between two presynaptic APs within a millisecond distance between them. Such high precision is required when processing information embedded in sounds, for instance, [85]. In contrast to the rate code, the temporal code is a powerful tool for characterizing dierent APs sequences in various cortical regions. However, the vulnerability of temporal code is its ability to individualize fast APs sequences found in sensory systems compared to the rate code where the rate of fast APs sequences determine neuronal behavior and not individual spikes. Therefore, to overcome this problem, researchers suggested using onset latencies, where individual neurons are capable of detecting the rst spike from a sequence of received spikes[86]. A third party of scientists has proposed that neuronal coding is indeed a combination be- tween rate and temporal coding. For example, a conducted experiment has suggested that the hippocampal pyramidal cells use both codes independently to determine the spatial aspects of the environment [87]. In other words, the temporal code takes the phase relationship to the coexisting cycle of the hippocampal theta rhythm, where these codes can represent a dierent variable depending on the phase dierence. 20 2.2.2 MathematicalNeuronModels There is a wide verity of mathematical neuronal models, also known as spiking neuron models, that can be expressed in the form of ordinary dierential equations (ODE), including the Integrate and Fire (I&F) model and its dierent model variations (i.e. the leaky I&F, the adaptive I&F, Etc.), the Hodgkin–Huxley model [88], and the Izhikevich model [18]. The I&F is one of the most widely used neuron spiking models. It is the simplest neuronal spik- ing model by which it describes a neuron as an integrator where a neuron integrates its synaptic inputs and then compares the result with a threshold value. In the I&F model, a neuron generates a spike only when the neuron’s specic threshold value is exceeded. Despite its simplicity, it is not computationally useful as it fails to explain many of the cortical neuronal behaviors, and it does not provide any biophysical meaning. The equation describing the I&F model is shown in 2.1. v 0 =I +abv; ifvv thresh ; thenv c (2.1) Where v thresh represents the neuron’s membrane potential, I represents the input current (stimulus), and a;b;c are the parameters describing the peak and the resting potential of the generated spike. On the other hand, the Hodgkin–Huxley model (H&H) [17], is one of the essential neuronal spiking models. Hodgkin was the rst to experiment with the dynamic bifurcation concept be- fore the actual development of the mathematical bifurcation theory was published. The model consists of many parameters describing the activation and deactivation of ion channels and other 21 biophysical dynamics. Despite the complex representation of the H&H model, it provides bio- physical meaning describing neuronal behaviors. Hence, it is a widely used model in the eld of computational biology. Besides, the H&H model describes the neurons as dynamical systems by which the model classies the neuron behaviors into three classes according to their excitability through studying the frequency to the current relationship (Class1, Class2, and Class3). In Class1 excitability, the neuron’s spiking frequency increases with the increase of the injected current’s amplitude [89]. InClass2 excitability, the neuron generates spikes at a small range of frequencies independent of the injected current amplitude [89]. InClass3 excitability, the neu- ron spikes with a single spike corresponding to a pulse of injected current, and at a very high pulse of current, a neuron may exhibit tonic spiking. The Izhikevich mathematical model consists of two Equations 2.2 and 2.3. Despite the lack of any biophysical meaning compared to H&H model, it is an excellent mathematical model because it is as simple as the I&F model, yet it can produce many of the cortical neuronal behaviors based on four parametersa,b,c, andd [18]. The model is based on the mathematical theory of bifur- cation and the phase portrait. Bifurcation theory states that "In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a systemcausesasudden"qualitative"ortopologicalchangeinitsbehavior. Generally,atabifurcation, the local stability properties of equilibria, periodic orbits, or other invariant sets changes "[90]. v 0 = 0:04v 2 + 5v + 140u +I; ifv 30mV; thenv c (2.2) u 0 =a(bvu); ifv 30mV; thenu u +d (2.3) 22 Wherev represent the neuron’s membrane potential,u is the recovery variable,I represents the input current, and a;b;c are dimensionless parameters describing the time scale of u, the sensitivity ofu, and the after-spike reset value of the membrane potential, respectively. A com- parison between other neuron spiking models is shown in Table 2.1, where the complexity of a model is measured based on the number of oating points (FLOPS) operations [91]. Table 2.1: A comparison between dierent spiking models adopted from [91]. FLOPS is the num- ber of oating point operations. In general, despite the great learning and pattern recognition tasks of such mathematical models, they are not the best solutions when scalability is concerned as they rely on conventional central processing units (CPUs), or in some cases, graphical processing units (GPUs) for solving dierential equations describing the complex neuronal spiking behavior. 23 2.2.3 Hardware-basedNeuronModels Another alternative to spiking neuron modeling discussed in the previous section is the hardware- based model. Such a modeling approach relies on very-large-scale integration (VLSI) of inter- connected electronic devices, that displays voltage variations that resemble of various biological neuronal mechanisms [92]. These models can be fault-tolerant and usually follow a distributed- memory computational architecture using dierent synaptic weights [93]. Also, hardware neu- ronal models have the capability of emulating the electrophysiological behavior of real neurons and conductances [94], and the high energy eciency as such models do not require general- purpose computers, which makes them suitable for real-time large-scale neuronal emulations as they are independent of scale. Hence, hardware neuron modeling is an eective strategy for the development of practical brain-inspired applications and solutions. Using the same neuron modeling methodologies, the BioRC group and many others have shown various electronic im- plementations of neurons, synapses, and other related mechanisms [26, 95, 96, 97, 98]. Previous hardware implementations of neurons are typically limited in their processing ca- pabilities due to the use of static modeling of the integrate and re (I&F) framework. In general, such an approach is convenient and computationally ecient; however, it lacks insight from the biological structure, the timing, and other various biological properties of the postsynaptic ac- tion potentials due to passive modeling of the currents [99]. In an I&F hardware model, circuit implementations are derived from or based on the assumption that a neuron generates a spike only when its membrane potential exceeded a particular threshold value. Thus, it ignores one of the most critical neuronal aspects, called neuronal encoding. neuronal encoding is crucial in understanding and enhancing neuronal processing capabilities. Thus, the generation of various 24 cortical neuronal behaviors exhibiting neuronal encoding is involved in much biological signal processing. Inspired by the pioneering work of Hodgkin and Huxley [17], other hardware models that use ion channels modeling were capable of producing biophysical neuronal behaviors [100, 101, 94]. Farquhar and Hasler [94] showed how it is possible to model ionic channels, includingK + and Na + ion channels, using 6 transistors operated in the subthreshold domain (Figure 2.4). Although their model is considered an elegant neuron model, it lacks modeling various neuronal spiking and bursting patterns autonomously without changing circuit congurations. Figure 2.4: A simple neuron model circuit as a combination ofK + andNa + transistor channels, adopted from [94] 25 In order to create a rich behavioral neuron model, several circuit implementations have been built based on Izechivich’s mathematical spiking neuron model [18, 91] by converting mathe- matical equations into circuit congurations [102], Figure 2.5 and Figure 2.6 show the Cauwen- berghs’s implementation of the Izechivich’s recovery variable equation, u, and the membrane potential equationv, respectively. Despite the emulation of a wide range of neuron behaviors, the model does not carry biophysical meaning, and it requires changing circuit conguration for the emulation of various spiking patterns. Figure 2.5: A recovery variableu circuit, adopted from [102] Figure 2.6: A membrane voltagev circuit, adopted from [102] 26 The Biomimetic Real-time Cortex (BioRC) group have demonstrated various aspects of neu- ronal modeling, including the implementation of spike-timing-dependent plasticity (STDP) to mimic learning mechanisms in biological neurons [103], learning without forgetting by [104], using dopamine signaling as a reward in learning [105], spiking with a particular set of inputs [106], and recently, spiking in response to specic frequencies [107]. With the library of neuro- morphic circuits that we have implemented and as part of our investigation of how the human brain might learn new tasks without forgetting old ones, we have begun to examine neuronal signaling and how dierent patterns may convey dierent information. Therefore, our BioRC neuronal encoding models are based on mimicking various biological ion channels and the re- lation of these ionic channels in generating various spiking and bursting patterns with respect to various synaptic properties in an autonomous way. This property may inuence the future of neuromorphic autonomous systems. 27 Chapter3 RichBehavioralAISElectronicModel Biological neurons signal each other in a rich and complex manner to perform complex cognitive computing tasks in real time. The implementation of such capabilities using electronic circuits is a dicult task. Many neuromorphic circuits mimic dierent aspects of a biological neuron, yet neuronal modulation has received little focus. Modulation is a key aspect of understanding how neurons process and interpret information. We posit that each neuron may have a unique built- in modulation function depending on its role. This chapter introduces a new technique capable of converting continuous stimulus shapes into modulated spiking/bursting patterns to build rich behavioral electronic neurons. We test the hypotheses using the simplest modulation function (direct correlation). The results show plausible excitatory spiking patterns consistent with spiking patterns produced by the Izhikevich mathematical model reecting various biological neuronal behaviors [18]. In general, neuromorphic systems rely on very large-scale integration (VLSI) of intercon- nected electronic devices, which allows these systems to resemble various biological neuronal mechanisms [92]. Such systems are considered to be fault-tolerant and usually follow a dis- tributed memory-computational architecture using dierent synaptic weights as memory [93]. 28 We and many others have shown various electronic implementations of neurons, synapses, and other related mechanisms [26, 95, 96, 97, 98]. Our previous neuromorphic Biomimetic Real-time Cortex group (BioRC) work have demonstrated capabilities such as the implementation of spike- timing-dependent plasticity to mimic learning mechanisms in biological neurons [103, 108, 104], learning without forgetting [104], using dopamine signaling as a reward in learning [105], spiking with a particular set of inputs [106], and recently, spiking in response to specic frequencies [107]. With the library of neuromorphic circuits that we have implemented and as part of our investiga- tion of how the human brain might learn new tasks without forgetting old ones, we have begun to examine neuronal signaling and how dierent patterns may convey dierent information. The most widely accepted neuronal computation scheme views neurons as a centralized unit at which an action potential (AP) takes place if the summation of the synaptic input at the soma exceeds a certain threshold, whether the summation is performed linearly or non-linearly (current or conductance-based, respectively) [109]. Dendritic computation has shown to play a signicant role in neuronal signaling. In 2004, Polsky et al. discussed how the locations of the synapses in pyramidal neurons play a signicant role in the summation of the received presynaptic inputs [110]. The BioRC group has demonstrated various neuromorphic dendritic computations [26]. In 2017, Sardi et al. conducted an experiment concluding that a biological neuron consists of multi- ple independent threshold units [22]. Motivated by the realizations described in [22], we built an electronic neuron consisting of two dendritic branches to encode information about the origin of the stimulus by observing the variability of the repolarization time of a single spike [106]. Our modeling hypothesis suggests that the inuence of stimulus dynamics on the induced APs may follow an unknown type of neuronal modulation. Here, the term neuronal modulation refers to the process by which a neuron translates its synaptic inputs to a distinct AP pattern. 29 Although such modulation has not been well discussed in the literature, a biological basis is pro- posed [111]. The proposed model can be used in building a rich behavioral neuromorphic neuron to perform complex tasks. Fig. 3.1 shows the general block diagram of the proposed model. To investigate the behavioral capabilities, (1) we modeled the output of various dendritic computa- tions using the parameterVsoma, in whichVsoma can be any analog or digital signal, and (2) a direct correlation is used betweenVsoma and the AIS modulation block. A direct correlation means there is no modulation function; hence the modulation function is shown as a dashed box (Fig. 3.1), to show that even with the simplest type of modulation, the neuronal computation can be increased, although other types of modulation function can be used to perform neuronal arith- metic operations (e.g. dierentiation or integration). We demonstrate the circuit using Cadence Virtuoso Simulator Tools. Figure 3.1: The general block diagram of the BioRC dynamic encoding neuronal model. To test the model hypothesis, a simple modulation function is used where the modulation function block is a simple direct path from the Vsoma block to the AIS modulation block, hence the dotted border line is used for the modulation function block. 3.1 NeuromorphicImplementation The BioRC dynamic encoding neuronal model given here is a modied version of the previous BioRC voltage-based axon hillock design [26], to support dynamic activation-deactivation ofC av channels and provide a direct stimulus to AP modulation using a direct path from Vsoma to 30 AIS block. The model’s schematic diagram consists ofSomatodendtritic,Amp,Cav,Nav,Kv, SpikingGenerator, andAISModulation sub-blocks, shown in Fig. 3.2 with dierent colors. In Fig. 3.2, theSomatodendtritic sub-block models the threshold variabilities and provides infor- mation about the dendritic Calcium ion concentration. Amp is a controlled amplication stage to provide variable gain for the subsequent sub-blocks. C av models the eect of the voltage- gated Calcium ion channels through bursting. SpikingGenerator,K v , andN av sub-blocks are adopted from Hsu’s model in whichSpiking Generator uses gated cross-coupled inverters to model the spike initiation mechanisms, K v models voltage-gated Potassium ion channels, and N av models voltage-gated Sodium ion channels. TheAISModulation sub-block models the AIS signal processing by correlating a stimulus dynamic into specic AP patterns. Moreover, there are seven parameters to provide a wide range of variability in modulating and shaping the APs: Figure 3.2: The Schematic diagram of the proposed neuron model in whichINV 1 is a single stage CMOS inverter, andCOMP 1,COMP 2,COMP 3 are low power dierential-based comparators. To enhance readability, the dashed and the solid connections are used interchangeably. • The parameterVsoma models the output of the dendritic computations to be used as an input to the dynamic encoding neuronal model, while parameterVsoma_Thre models the 31 threshold variability to dynamically control neuronal activities. Hence, the sensitivity of detecting smallerVsoma potentials is inversely proportional to the value ofVsoma_Thre. • The parameterCa + + designates the dendriticCa +2 ion concentration, whereas the pa- rameterCaThre models the dynamic threshold activation ofC av channels. • The parameterAdapt controls the current ow through M16 (Threshold Calcium current [112]) when the Ca +2 ion channel is opened (M17 is turned on); hence, regulating the maximum burst width. However, when theCa +2 ion channel is closed (M17 is turned o), Adapt controls the frequency of spikes through M19. Therefore,Adapt regulates current ow and burst width. • The parametersN a + andK+ represent the Sodium ion concentration and the Potassium ion concentration at the AIS, respectively, whereasC A models the AIS characteristic ca- pacitance per unit area determining the AIS width and conduction velocity characteristics. Figure 3.3: The schematic diagram of the comparators. In addition, the model consists of three low power dierential-based comparators (COMP 1, COMP 2, and COMP 3). COMP 1 models threshold variabilities by comparing Vsoma and Vsoma_Thre,COMP 2 monitors dendriticCa +2 concentrations and consequently activates and 32 deactivatesC av channels, andCOMP 3 controls the generation of action potentials based on the voltage acrossC A to allow various stimulus shapes to generate dierent spiking patterns. The comparators’ schematic diagram is shown in Fig. 3.3, in whichin+ andin are the comparators’ positive and negative input terminals, respectively. The output from the dierential pair amplier is followed by two cascaded inverters to digitize the output voltage swing into logic "1" for (in> 0) and logic "0" for (in< 0) where in = (in+) (in). In other words, COMP 1 outputs a logic "1" when the membrane potential exceeds a cer- tain threshold (Vsoma > Vsoma_Thre) and outputs logic "0" whenVsoma < Vsoma_Thre. Similarly, in modelingC av channels,COMP 2 outputs a logic "1" when the dendriticCa +2 con- centration exceeds theC av threshold activation voltage (Ca + +>CaThre), and outputs logic "0" whenCa++<CaThre to deactivateC av channels. As a result, AP patterns can be classied into bursting APs ifCOMP 2 exhibits logic "1" and spiking APs otherwise. Likewise,COMP 3 compares Vsoma and V CA (voltage across capacitor C A where C A represents the biophysical capacitance per unit area of the AIS region). Consequently,COMP 3 outputs a logic "1" when V CA >Vsoma, to inhibit the generation of APs by activating transistor M15, and a logic "0" when V CA <Vsoma to allow APs depolarization. ComparingV CA andVsoma usingCOMP 3 allows a direct AP modulation. In other words, the generated AP depends on the shape ofVsoma. Such dependency leads to continuous generation of various spiking/bursting patterns. 33 3.2 VariousSpikingandBurstingPatterns 3.2.1 ConvertingDynamicStimulustoAPs In this section, we simulate the model’s schematic diagram shown in Fig. 3.2, using Cadence Virtuoso Simulator Tools to show that various spiking patterns can be generated continuously as a function of ion channels (N a +,K+,Ca + + ),Adapt, and dynamicVsoma shapes. However, to simplify the analysis, throughout this chapter, N a + and K+ are set to be 900mV and 0V, respectively. The contribution of the ion channels in shaping APs is summarized in the sketch illustration of both single and burst AP patterns shown in Fig. 3.4(A), in which N a + sets the peak spike/burst amplitude,K+ sets the spike/burst resting potential, and the dierence between Ca + + andCaThre denes the mode of APs (bursting or spiking mode). The current states (conditions) of ion channels,Adapt, andVsoma required for generating a specic pattern, are outlined in Fig. 3.4(B) for regular spikes (RS), phasic spikes (PS), tonic bursts (TB), single burst per stimulus(SB), class-1 spikes (CS1), subthreshold oscillation (OSC), depolarization after potential (DAP), integrator spikes (INT), and mixed mode (MIX) patterns. In Fig. 3.4(B), when two or more patterns have the same setup conditions, such as (RS, INT, CS1, OSC) and (TB, SB) patterns, switching between patterns depends solely on the dynamic shapes of Vsoma. For example, the generation of both SB and TB patterns requires Adapt > V dd =2, Ca + + > CaThre, and K+ = 0, hence, the selection between SB and TB patterns depends on the dynamic shape ofVsoma. Similarly, the generation of RS, INT, CS1, and OSC patterns requiresAdapt>V dd =2,Ca + +<CaThre, andK+ = 0, thus, the selection between RS, INT, CS1, and OSC patterns depends on the shape ofVsoma. 34 Figure 3.4: A sketch illustration of spiking and bursting APs showing the model’s voltage-gated ion channels contribution in shaping APs, (A). (B) shows the model’s conditions associated with the generation of single burst (SB), tonic bursts (TB), regular spikes (RS), integrator spikes (INT), class-1 spikes (CS1), subthreshold oscillation (OSC), phasic spikes (PS), phasic spike with depo- larization after potential (PS-DAP), regular spikes with depolarization after potentials (RS-DAP), and mixed mode (MIX). The shape of the stimulus patterns determine spiking patterns when all other parameters are the same. The simulation results of the model’s schematic diagram for the previously mentioned spik- ing/bursting patterns are shown in Fig. 3.5 using similar stimulus shapes ofVsoma presented in the Izhikevich mathematical model [18]. To discuss how each individual pattern is formed, we group the results into three groups based on the generation conditions required for each pattern. 3.2.1.1 TheGenerationofVariousSpikingPatterns The RS, INT, CS1, and OSC patterns are generated whenCa++<CaThre andAdapt>V dd =2. The rst condition is to inhibit bursting and permit spiking formation, and the second condition is to prevent current ow through transistors M19 and M20, forcing the current of M3 to ow only through M1. Since these patterns have the same conditions of generation, information about the stimuli is needed to identify which pattern the model should produce. 35 Figure 3.5: The relationship between various simulatedVsoma shapes and their corresponding action potentials for (A) regular spikes, (B) phasic spikes, (C) tonic bursts, (D) single burst per stimulus, (E) class-1 excitable, (F) subthreshold oscillations, (G) depolarization after potential, (H) integrator, and (I) mixed mode, following the table shown in Fig. 3.4. 36 • TheRS pattern shown in Fig. 3.5(A) is generated using a constant voltage pulse of stimulus (Vsoma = 300mV). The RS pattern frequency is directly proportional to the amplitude of Vsoma (stimulus intensity). • The INT pattern shown in Fig. 3.5(H) corresponds to a train of short stimulus (Vsoma = 150mV, and width = 4ns per pulse). Due to the accumulation of charges on capacitorC A , the model is capable of detecting consecutive rapid events (T 1 = 6ns). In contrast, when the time between consecutive stimulus increases (T 2 = 26ns), the model becomes less excitable due to the loss of the accumulated charges onC A . • The CS1 pattern shown in Fig. 3.5(E) resembles a ramp-like stimulus shape (Vsoma = 800mV, with rising timet r = 60ns). The result is consistent with the generated RS pattern, at which the frequency of spikes is proportional to the amplitude ofVsoma. • The OSC pattern shown in Fig. 3.5(F) takes place when Vsoma = 100mV at which C A experiences multiple charging and discharging phases due to the small stimulus amplitudes. However, when introducing further stimuli (Vsoma = 200mV and width = 8ns per pulse), the model exhibits spikes. This might be important for detecting small perturbations of stimuli. 3.2.1.2 TheGenerationofVariousBurstingPatterns The TB (Fig. 3.5(C)) and SB (Fig. 3.5(D)) patterns are formed when Ca + + > CaThre and Adapt > V dd =2. When Ca + + > CaThre, the output of COMP 2 sets the gate voltage of M17 toV dd ; Consequently, transistor M17 is switched on, allowing the current to ow from M4 through M16 and M17. Hence, reducing the gate voltage of M6 and M9 to a value nearV th6 (the 37 threshold voltage of M6). The current passing through M16 and M17 resembles T-current (low Threshold-Calcium current discussed in [112]). Therefore, at each rising edge of an individual intra-burst, transistor M6 operates in the subthreshold region while M9 operates in the triode region. In contrast, at each falling edge of an individual intra-burst, M9 and M6 switch their operating regions where M9 operates in the subthreshold region, and M6 operates in the triode region. This continuous switching results in a consecutive generation of the intra-burst spikes. Although the model relies on simulation results for extracting design parameters, the relation of the current as a function of the input gate voltage for M6 can be approximated using the drain- source current model (3.1) for the triode (linear region) and (3.2) for the subthreshold operation regions. Similarly, for M9, by using p ,V SG ,V SD ,jV thp j instead of n ,V GS ,V DS ,V thn , respectively. I DS = n C ox W L [(V GS V th )V DS V 2 DS 2 ] (3.1) I DS =I 0 e V GS nV T (3.2) Where n is the mobility of electrons, p is the mobility of holes,C ox is the oxide capacitance, W is the diusion width, L is the diusion length, V GS is the gate-source voltage, V DS is the drain-source voltage,I 0 is the characteristic leakage current,n is the subthreshold slope factor, andV T is the thermal voltage. • TheTB pattern shown in Fig. 3.5(C) corresponds to a constant input voltage pulse (Vsoma = 300mV). The number of intra-burst spikes is proportional to theVsoma amplitude (stimu- lus intensity). In other words, the burst width increases as theVsoma amplitude increases. 38 Thus, the TB-Adapt term is used to indicate tonic bursts with dierent widths as a func- tion of dynamicVsoma amplitude by which the generated burst width is proportional to the shape ofVsoma. An example of TB-Adapt response can be seen in Fig. 3.7(A), ZOOM2 sub-plot. • TheSB pattern shown in Fig. 3.5(D) corresponds to two single bursts per stimulus. There are two scenarios for the generation of SB pattern; (1) when the width of stimulus is shorter than the time required forCOMP 3 to turn transistor M15 on (Vsoma = 300mV, and width = 2ns). (2) when the amplitude of stimulus is higher than the maximum voltage value across capacitorC A (Vsoma = 700mV, and width = 6ns). 3.2.1.3 TheGenerationofOtherSpikingPatterns Unlike the previously mentioned spiking patterns, DAP, PS, and MIX patterns have dierent setup conditions and parameters. • The DAP pattern requiresCa + + < CaThre andK+ > 0. SinceK+ determines the resting potential voltage, the DAP pattern is directly proportional toK+. To generate the DAP pattern, other spiking patterns are required. Therefore, PS-DAP and RS-DAP are introduced to represent PS pattern and RS pattern with the DAP eect, respectively. Fig. 3.5(G) shows RS pattern without DAP (leftmost three spikes) forK+ = 0, and RS pattern with DAP (Rightmost three spikes), at whichK+= 900mV. • The PS pattern requires transistors M19 and M20 to be turned on so that M3 current can ow through M1, M19, and M20 to further decrease the gate voltage of M4, M2, and M18, see Fig. 3.5(B). Therefore, the PS pattern requiresCa + +<CaThre andAdapt<V dd =2. 39 • TheMIX pattern is generated using the dynamic activation and deactivation ofC av chan- nels. In other words, the model produces bursting patterns whenCa + +>CaThre and spiking patterns whenCa + +<CaThre, see Fig. 3.5(I). In both cases, the generation of mixed pattern requiresAdapt>V dd =2 to allow current ow through M16 and M17. 3.2.2 TheWorkingPrinciplesofTheAISModulation Understanding how the AIS Modulation sub-block converts dynamic stimulus into various spiking/bursting patterns requires a discussion of the relationship betweenVsoma andV CA (the inputs ofCOMP 3) is needed. Fig. 3.6 represents the relationship betweenVsoma (red wave- form) andV CA (blue waveform) for all previously simulated patterns. In Fig. 3.6, the relationship can be described using the relative refractory period (RRP), in other words, the time between two consecutive spikes/bursts. The ideal RRP for spikes and bursts are denoted asRRP S (green shaded region) andRRP B (light blue shaded region) in Fig. 3.6, respectively, in which bothRRP S andRRP B represent the period at which V CA > Vsoma. However, because switching from V CA > Vsoma to V CA < Vsoma usingCOMP 3 is not ideal (spontaneous switching), COMP3 propagation delay (T d ) is added (red shaded region) as shown in Fig. 3.6. Thus, the actual relative refractory period can be extracted graphically from Fig. 3.6 as (RRP S +T d ) for spikes, and (RRP B +T d ) for bursts patterns. During burst formation, capacitorC A withstands multiple fast charging and discharging phases per burst due to the formation of the intra-burst spikes, whereas during spike generation, capacitorC A undergoes a single charging phase and a discharging phase per spike. Accordingly, 40 Figure 3.6: The relationship betweenVsoma (Red) andV CA (Blue) for all plausible patterns; (A) regular spiking; (B) phasic spiking; (C) tonic bursting; (D) single burst per stimulus; (E) class-1 excitable spikes; (F) subthreshold oscillations; (G) depolarization after potential; (H) integrator spiking; (I) mixed mode. The ideal relative refractory period for spikes and bursts isRRP S and RRP B , respectively.T d represents COMP3 propagation delay. 41 RRP B is smaller thanRRP S . However, since the value ofT d depends on the physical properties of the design, it remains the same for both spike and burst patterns. Modeling the role ofRRP at the AIS allows various stimulus shape patterns to result in gen- erating dierent spiking patterns through which V CA , the voltage across the capacitor C A , is compared with the stimulus shapeVsoma usingCOMP 3. Therefore, for the RS pattern (Fig. 3.6(A)), as the amplitude ofVsoma remains constant, theRRP S remains the same for all subse- quent spikes. For the PS pattern (Fig. 3.6(B)), due to the activation of M19 and M20, theRRP S is the largest compared to other patterns. In the TB pattern (Fig. 3.6(C)), theRRP B remains the same for all consecutive bursts due to the constant amplitude ofVsoma. In the SB pattern (Fig. 3.6(D)), the rst stimulus represents the scenario whereRRP B is larger than the width ofVsoma and the second stimulus represents the scenario at which V > 0 where V =VsomaV CA . For the CS1 (Fig. 3.6(E)), theRRP S is inversely proportional to the amplitude ofVsoma; in other words, RRP S1 < RRP S7 . For the OSC pattern (Fig. 3.6(F)), the relationship betweenVsoma andV CA is plotted in the logarithmic scale to show the voltage oscillation ofV CA . For the DAP pattern (Fig. 3.6(G)), whenK+ > 0, the rightmost three spikes compared to the leftmost three spikes, have slightly largerV CA ; hence, largerRRP S . In the INT pattern (Fig. 3.6(H)), theV CA is higher for rapid, occurring stimulus compared to slower stimulus. In the MIX pattern (Fig. 3.6(I)), the value ofV CA is higher in the case of spiking compared to bursting; thus,RRP S >RRP B . Analytically, the relationship betweenVsoma andV CA can be approximated using the RC analysis at the positive terminal ofCOMP 3 in which the total capacitance (C tot ), the equivalent resistance for M11 (R 11 ), and the equivalent resistance for M12 (R 12 ) are shown in (3.3), (3.4), and (3.5), respectively. C tot =C g13 +C A +C in +C d11 +C d12 (3.3) 42 R 11 = 1=( 11 (V dd V thn )) (3.4) R 12 = 1=( 12 (V dd jV thp j)) (3.5) WhereC g is the gate capacitance;C in is the input capacitance ofCOMP 3;C d is the drain ca- pacitance; 12 and 11 are the beta eective of M12 and M11, respectively;V dd is the DC supply voltage. Using the RC time constant method, the value ofV CA , the voltage across capacitorC A , can be determined using the capacitor charging and discharging equations given in (3.6) and (3.7), respectively. Therefore, the discharging time (t dis ) can be approximated using (3.8) because when V CA Vsoma, the compactor circuit at the AIS, namelyCOMP 3, will output a logic "1" causing M15 to turn ON, hence shunting the formation of the spikes at the output terminal of the neuron. On the other hand, the charging time (t ch ) can be approximated using (3.9) because whenV CA < Vsoma,COMP 3 will output a logic "0" causing M15 to turn OFF, allowing the formation of the spikes at the output terminal of the neuron. V CA =Vsoma (1e t R 11 C tot ) (3.6) V CA =Vsomae t R 12 C tot (3.7) t dis =R 11 C tot ln ( V CA (0) Vsoma ); forV CA Vsoma (3.8) 43 t ch =R 12 C tot ln ( Vsoma V CA Vsoma ); forV CA <Vsoma (3.9) 3.3 ThresholdVariability Biological neurons have variable thresholds. This variability is inversely proportional to the out- put spiking rate [113, 114]. As Hsu has shown, the threshold for spiking can be modulated by the slope of Vsoma, with spiking initiated earlier with faster Vsoma rise [26, 115, 116]. Moreover, other factors, such as the mechanisms of ion channels and synaptic properties, can alter neuronal threshold [117]. In the dynamic encoding neuronal model, both constant and variable thresholds can be modeled usingCOMP 1. Fig. 3.7 shows the simulated behaviors of the model’s schematic using Cadence Virtuoso Simulator Tools at a xed and dynamic neuronal threshold forNa+ = 900mV,K+ = 0V, andCaThre =300mV. Fig. 3.7(A) shows the ring behaviors associated with a xed neuronal threshold, where (Vsoma_Thre = 0V). As a result, the model is capable of detecting all dynamic stimulus shapes since Vsoma > Vsoma_Thre. The output waveforms (AP1, AP2, and AP3) are generated at dierent conditions. In other words, the patterns within each of the output waveforms, have the same setup conditions; thus, depending on the dynamic shapes ofVsoma, various patterns are generated; • AP1 is generated usingCa + +<CaThre andAdapt>V dd =2, whereCa + + = 0V and CaThre = 300mV. The ring patterns include RS, OSC, INT, and CS1. • AP2 is generated using variableCa +2 concentrations (Ca + + = [0, 500mV]), andAdapt> V dd =2. WhenCa + + > CaThre the generated patterns include SB, TB, and TB-Adapt 44 Figure 3.7: The model behaviors for dynamicVsoma shapes. (A) represents dierent AP patterns at whichVsoma > Vsoma_Thre, and (B) shows AP patterns for the sameVsoma variations, however, with a threshold variability represented by the gray shaded region for all Vsoma < Vsoma_Thre values. AP1 and AP4 are generated at whichCa + + < CaThre andAdapt > V dd =2. AP2 and AP5 represent the outputs at whichAdapt>V dd =2 andCa++ = [0, 500mV]. AP3 and AP6 exhibit PS spiking pattern whereCa + +<CaThre andAdapt<V dd =2. ZOOM2 and ZOOM5 are enlarged versions of the green shaded areas associated with AP2 and AP5 outputs, respectively. 45 (denote bursts with various widths depending on the amplitude of theVsoma), whereas whenCa + +<CaThre, the resulting patterns of AP2 are the same as AP1. • AP3 shows PS pattern whereCa + +<CaThre andAdapt<V dd =2. Here,Ca + + = 0V, CaThre = 300mV andAdapt = 0V. In contrast, Fig. 3.7(B) shows similarVsoma shapes; however, with a dynamic variation of Vsoma_Thre (gray signal). AtVsoma>Vsoma_Thre, the outputs of AP4, AP5, and AP6 are the same as AP1, AP2, and AP3, respectively, yet, whenVsoma < Vsoma_Thre, there are no permeable spiking/bursting APs. ZOOM2 and ZOOM5 are enlarged versions of the green shaded areas shown in AP2 and AP5, respectively. In summary, in this chapter, a CMOS electronic model is proposed to emulate biological neu- rons’ rich, dynamic behaviors. We have shown through circuit simulations that by converting stimulus dynamics shapes (modeled using Vsoma) into specic AP patterns, the model is capa- ble of producing dierent AP patterns in real-time, including regular spikes, phasic spikes, tonic bursts, single burst per stimulus, class-1 excitable spikes, subthreshold oscillations, depolarization after potential, integrator, and mixed-mode. Moreover, we have shown how the model utilizes a dynamic threshold to mimic biological neurons. The proposed model can be used to build a rich behavioral neuromorphic system capable of performing complex tasks. 46 Chapter4 ElectronicAutonomousSpikingEncoding Understanding how biological neurons encode information through neuronal signaling is crucial in building rich computational electronic-based neuromorphic systems. This chapter presents im- plementing a neuromorphic neuron model capable of processing and performing complex tasks autonomously and in real-time through neuronal modulation and dynamic neuronal encoding. We test the autonomous behavioral capability by mimicking Layer 5 Pyramidal Neurons’ (L5PNs) coincident detection encoding behavior using a small network of neurons. The results show that individual output neurons can autonomously encode dierent received input AP patterns and their times of occurrence into unique output AP patterns. Such a property might inuence future neuromorphic autonomous encoding systems without the need for a large number of neurons. Signaling in biological neurons is complex and not completely understood. Biological neurons encode and process complex information dynamically, autonomously, and in adaptive ways based on their received synaptic input properties and the past received patterns. Such processing capa- bility has inspired a rich behavioral neuromorphic model using neuronal modulation[118] based on Izhikevich’s mathematical model of spiking neuron patterns [18]. In addition, neuromorphic engineering enables various information processing designs, for example utilizing a distributed 47 memory-processing architecture by using various synaptic weights as memory units [92]. Such neuromorphic designs are being used in applications such as prosthetic devices [1, 2, 119, 120], sensory applications [3, 4, 5], and biomimetic approaches used for bio-inspired computing [6, 7, 121]. Lee has explored spike shapes that indicate neuronal signal origins [106], and Yue has shown spiking frequencies can be used to signify meaning [107]. However, the neuronal code, complex signaling between neurons, has not been fully explored. Therefore, in this chapter, we focus on modeling autonomous neuronal behavior using a rich signal processing capability by implementing a dynamic neuromorphic neuron model. The pro- posed neuron model combines three neuromorphic circuit implementations, including a dynamic encoding circuit,Ca +2 modulated synapse circuit, and a dendritic arbor circuit. Section 4.2 de- scribes the neuromorphic implementation of each circuit of the proposed neuron model. Using a small neuronal network, Section 4.3 demonstrates the neuron model’s autonomous behavioral capability by mimicking one of the most widely-observed biological neuronal behaviors in the cortical region, the coincidence detection encoding scheme. Moreover, our design supports one of the most used communication protocols in neuromorphic systems: the Address Event Repre- sentation (AER) presented by Mahowald and Sivilotti [122, 123]. Thus, in our implementation, neurons can produce an AP only when their address is triggered and remain silent otherwise. 4.1 PopularEncodingSchemes Neuronal coding schemes are a highly debated topic in neuroscience [124, 125, 126]. An earlier view of the neuronal coding scheme modeled neuronal behavior as integrate and re (I&F), where neurons encode the average ring rate of the received Action Potentials (AP) [124, 125]. Despite 48 the simplicity of I&F, there is low reliability when describing the irregular ring behavior of cor- tical neurons [127], with little to no information regarding the timing of the received or generated spikes [124]. On the other hand, others proposed that biological neurons by nature are coincidence detec- tors, where neurons use the synchronized timing of the synaptic inputs to encode information (correlation between received spikes) [29, 30, 31, 32]. For instance, in the somatosensory sys- tem, synchronization is essential in the transmission of sensory information between dierent brain regions[128]. Moreover, cortical neurons, such as layer 5 pyramidal neurons (L5PNs), are sensitive to time synchronization between stimuli, where they signal with a bursting AP pattern when synchronized events are detected [129, 59, 130]. Coincidence detection employing dendritic spiking has been demonstrated in neuromorphic circuits by Hsu [26], [131] and others. 4.2 NeuromorphicElectronicImplementations 4.2.1 DynamicElectronicEncodingModel The dynamic encoding model is modied from [118]. In this chapter, the modeling complex- ity is reduced to support future dense integrated neuromorphic systems utilizing Address Event Representation (AER) protocol, a protocol that rst presented by Mahowald and Sivilotti [122, 123]. In addition, the modied model, like the previous model, is capable of generating various AP patterns based on various synaptic input properties autonomously (i.e. a neuron requires no external controls to change its signaling pattern). The schematic diagram of the dynamic encod- ing model is shown in Figure 4.1, whereAER represents the neuron’s address; in other words, 49 AER enables the neuron to evaluate the received synaptic inputs only when its designated ad- dress is triggered, andVsoma represents the nonlinear summation of the induced Post Synaptic Potentials (PSPs). The working principles ofSpikeGenerator,Na,K+, andAISModulation subblocks are discussed in [118]. Figure 4.1: The schematic diagram of the autonomous encoding model with AER, where INV is a single-stage CMOS inverter, and COMP is a low power comparator, adopted from [118]. The dashed and solid connections are used interchangeably to simplify the schematic connections. 4.2.2 CalciumModulatedElectronicSynapseModel Modeling the role of Ca +2 in synaptic signaling is essential in understanding the relationship that a group of neurons shares within a specic brain region. Also, Ca +2 is involved in many aspects of long and short-term synaptic plasticity [132, 133, 134]. The proposed synapse circuit, shown in Figure 4.2, has evolved from an earlier Biomimetic Real-time Cortex (BioRC) synapse model [33, 135]. The circuit emulates the eect ofCa +2 on neuronal activity by modulating the synaptic connection. When an AP arrives at the presynaptic terminal, the voltage potential at the drain terminal of transistor N3 will be pulled up using transistors N4 and P1. Therefore, 50 the voltage representing maximum neurotransmitter (V NTmax ) concentrations can be calculated usingV NTmax = VddVth4, whereVth4 is the threshold voltage of N4. At the repolarization phase of the received AP, the NT concentration will be decreased using N3 and N2. In biological neurons, the NT decaying rate is referred to as the reuptake process. Given that N3 and N2 are identical transistors, the NT decaying rate can be approximated based on the total ON resistance (R tot ) of N3 and N2 using (4.1) and the total capacitance (C tot2 ) at the drain terminal of N2 using (4.2). Thus, the decaying rate is approximated using (4.3) Figure 4.2: The schematic diagram of theCa +2 modulated synapse model. R tot 1 n C ox W L [1=(V GS3 V th3 ) + 1=(V GS2 V th2 )] (4.1) C tot =C gN2 +C dN2 +C sN3 (4.2) 51 V Decaying =V NTmax e t R tot C tot (4.3) Where n is the mobility of electrons,C ox is the oxide capacitance,W andL are the diu- sion width and length, respectively. Using the Ca +2 ion concentration, transistor N5 controls the strength of synaptic connection by regulating the neurotransmitter release to the postsynap- tic terminal. On the other hand, (W=L) P3 =(W=L) P2 determines the receptor concentration by which the current through transistor N6 is mirrored to transistor N7. The lower the channel resistance of P3 with respect to P2, the larger the EPSP, reecting more receptors. The signal Spread controls the decay of the output excitatory postsynaptic potential,EPSP . As shown in Figure 4.3 and Figure 4.4, the generation of variousEPSP waveforms can be accomplished by modulating the synaptic strength using dierentCa +2 ion concentrations for both spiking and bursting responses, respectively. Figure 4.3: Dierent excitatory postsynaptic potentials (EPSPs) corresponding to dierent presy- napticCa +2 ion concentrations for (A) spiking and (B) bursting AP patterns. 52 Figure 4.4: Dierent excitatory postsynaptic potentials (EPSPs) corresponding to dierent presy- napticCa +2 ion concentrations for (A) spiking and (B) bursting AP patterns. 4.2.3 TheDendriticArborElectronicModel In the BioRC project, dierent dendritic arbor circuits are utilized to demonstrate dendritic-like computations using the induced subthreshold PSPs [136, 137, 26]. Most recently, in [137], Pezh- man has demonstrated a nonlinear low power BioRC dendritic arbor model. His model consists of EPSP blocks, Sink to Source current mirror (M1-M2), Source to sink current mirror (M3- M4), and IPSP block. The adder exhibits nonlinear behavior when more than two EPSPs are active simultaneously using a Nonlinear Enable (NLE) signal produced by an external circuit (Figure 4.5). In such implementation, the goal was to (1) address the power consumption by eliminating the non-zero Vgs issue associated with the classical voltage adders when excitatory post synap- tic potentials (EPSP) and inhibitory post synaptic potentials (IPSP) are combined using the same input transistors such as the one discussed in [33], and (2) to capture the nonlinear responses. 53 Figure 4.5: Prior BioRC dendritic arbor model adopted from [137]. Using the current mirror topology, the design separates the excitatory postsynaptic potentials (EPSP) from the inhibitory postsynaptic potentials (IPSP). Each EPSP input is controlled by a control unit (CU). The CU controls the summation mode as three dierent summation modes are linear, super-linear, and sub-linear. Each of the CU circuits consists of two compactor circuits and other digital logic gates. Here, we use a simplied dendritic model based on the current mirror topology to support compact dendritic integration. The proposed model utilizes a single transistor per synapse to 54 perform dendritic summations as well as it facilitates inter-branch currents summation such that they can be summed up without requiring additional adders (Figure 4.6). Using the electrophysi- cal characteristics of CMOS devices, the proposed dendritic adder can autonomously perform the sub-linear, linear, and super-linear summation behaviors without the need for extra controlling units as per the most recent BioRC model [137]. Figure 4.6: The dendritic arbor schematic model, where EPSP is the excitatory postsynaptic potential signal,Vsoma is resulting membrane potential, andVb1 is the leakage control biasing voltage. In the presented dendritic arbor model, the summation of the induced currents at transistors N1 and N2 is mirrored using (W=L) P2 =(W=L) P1 , at which transistor N4 converts the mirrored current into membrane potential (Vsoma) usingVb1, through which the model mimics the bio- logical leakage eect at the dendritic arbor (i.e. the signal decaying time at the dendritic arbor). To test the dendritic arbor circuit model, we generated two excitatory postsynaptic potentials EPSP 1pre andEPSP 2pre, using the dynamic encoding model (Figure 4.1), to generateAP 1 andAP 2. Then theCa +2 modulated synapse model (Figure 4.2) is used to convert the generated 55 AP 1 andAP 2 toEPSP 1 andEPSP 2, respectively. Consequently, the dendrite arbor circuit is used to perform the dendritic summation onEPSP 1 andEPSP 2 as shown in Figure 4.7. Figure 4.7: A simulation of the dendritic arbor circuit for two action potentialsAP 1 andAP 2. EPSP is the induced excitatory postsynaptic potential. 4.3 DynamicCodingBehaviors To illustrate the autonomous behavioral capabilities of the proposed neuron model, a small ex- perimental neuronal network is constructed using the dynamic encoding model and the dendritic arbor model for (N1, N2, N3, N4, N5), and theCa +2 modulated synapse model for (S1, S2, S3, S4, S5) (Figure 4.8). We show that the network can encode information using the total rate of input spikes and coincident detection schemes interchangeably depending on various synaptic input properties. Therefore, by using dierent simulation cases, we test (1) the eect of dendriticCa +2 concentra- tion in modulating the synaptic connections for synapses S1, S2, S3, S4, and S5, and their eect on 56 Figure 4.8: An experimental neuronal network. S1 to S5 represent the implementedCa +2 modu- lated synapse circuits, and N1 to N5 represent the implemented dynamic encoding model. the postsynaptic neurons N4 and N5, and (2) the dynamic autonomous behavior of the network by mimicking the biological coincident detection behavior of layer 5 pyramidal neurons. 4.3.1 RateCodingBehavioratNeuronN5 To test the eect of the dendriticCa +2 concentration on modulating the output of neuronN5, neuronsN1 andN3 generate a random train of spikes. Using lowCa +2 concentration (400mV ) for synapsesS4 andS5, neuronN5 responds only to a higher rate of synaptic inputs at which the time interval betweenAP 1 andAP 3 is short. Also, such a response is associated with a nite delay denoted byT d as shown in Figure 4.9. This delay is inversely proportional to the value of Ca +2 concentration at synapsesS4 andS5. 57 Figure 4.9: A simulation result forN5 neuron with low synapticCa +2 concentration (Ca +2 = 400mV ).T d is the time delay required by neuronN5 to encode its high-rate synaptic inputs into APs. 58 Figure 4.10: A simulation result forN5 neuron with high synapticCa +2 concentration (Ca +2 = 700mV ).T d is the time delay required by neuronN5 to encode its high-rate synaptic inputs into APs. On the other hand, Figure 4.10 shows a stronger response of neuronN5 to the same synap- tic inputs when using higher Ca +2 concentrations (700mV ) by which neuron N5 responded to both slower and higher spiking rates with shorter T d delay compared to the previous case (Ca +2 = 400mV ). Therefore, the excitability of neuron N5 depends on the strengths of its synapticCa +2 concentrations. In biological neurons,Ca +2 is essential for enhancing neuronal excitability, spiking regulation, learning, and memory[138, 139, 140]. 59 4.3.2 CoincidentCodingBehaviouratNeuronN4 We explore the network’s coincident detection behavior by mimicking the behavior of L5PNs (level 5 pyramidal neurons), where synchronous spikes are signaled with a bursting AP pattern. We use neuronN1 to generate synchronous APs by forming a connection with neuronN4 using two synapses, S1 andS2. Furthermore, to test the network’s reliability in distinguishing syn- chronous APs, we added a third synapseS3 by which neuronsN2 andN4 are connected. Then, we divided the coincident detection simulation into two cases based on the received AP pattern. The rst case when neuronsN1 andN2 generate regular spiking patterns (Figure 4.11), and the second case when neuronsN1 andN2 generate bursting patterns (Figure 4.12). In both cases, neuronN4 changes its behavior autonomously based on various stimulus properties, including timing, shape, and frequency of the received stimulus. In Figure 4.11, we divided the generated patterns into four groups corresponding to dierent Ca +2 ion concentration levels. • Group1 shows that a low concentration ofCa +2 ions (Ca +2 = 200mV ) results in a very weak EPSPs whereN4 is not capable of detecting any of the received spikes. • Group2 indicates that when a higherCa +2 concentration is applied (Ca +2 = 400mV ),N4 detects the synchronous spiking events generated by N1 through S1 and S2 only. The coincident detection occurs at a nite time delay from the time of the synchronized events. • Group3 shows improved neuronal excitability by which N4 detects both the single and synchronous spikes atCa +2 = 600mV . The synaptic synchronization is signaled with a bursting pattern similar to L5PNs behavior with a shorter time delay compared toGroup2. 60 Figure 4.11: A simulation result forN4 neuron with randomly generated spiking patterns using neurons N1 and N2. The results are divided into four groups to test the eect of Ca +2 ion modulation on the network’s performance. EPSP is the output of excitatory synapsesS1,S2, andS3 to the received APs pattern andCa +2 ion concentration signaling. 61 • Group4 demonstrates similar neuronal capability withGroup3 by whichN4 detects both the single and synchronous spikes atCa +2 = 800mV . However, the synchronous events are signaled with a higher bursting width. Similarly, the bursting AP case, Fig. 4.12, is divided into four groups corresponding to dierent Ca +2 ion concentrations.N1 andN4 exhibit bursting spikes. • Group1 shows similar response toGroup1 from Figure 4.11 at which the low concentration ofCa +2 ions (Ca +2 = 200mV ) results in a very weak EPSPs whereN5 is not capable of detecting any of the received bursts. • InGroup2,N4 detects the synchronous bursting events by generating a single spike, sim- ilar to Group2 when synchronous regular spiking AP patterns are detected at Ca +2 = 400mV . • Group3 shows a higher width bursting AP pattern to indicate a coincident bursting APs event (i.e. six intra-spike counts) atCa +2 = 600mV . Moreover, the single burst generated byN2 is detected in an adaptive way by whichN4 generates a single burst followed by a single spike to encode the strength of the received burst throughN2. When comparing the result withGroup3 from Figure 4.11, we note thatN4 is capable of changing its behavior based on the received AP pattern in an adaptive way to dierentiate between dierent received AP patterns. • Group4 showed that at Ca +2 = 800mV , N4 detects both the single and synchronous bursts by generating two bursts with dierent widths to dierentiate between the coinci- dent and regular synaptic bursts. 62 Figure 4.12: A simulation result forN4 neuron with randomly generated bursting patterns using neurons N1 and N2. The results are divided into four groups to test the eect of Ca +2 ion modulation on the network’s performance. EPSP is the output of excitatory synapsesS1,S2, andS3 to the received APs pattern andCa +2 ion concentration signaling. 63 In summary, in this chapter, a dynamic CMOS neuron model is proposed to emulate biological neurons’ dynamic signal processing capability. The neuron model includes a dynamic encoding circuit, aCa +2 modulated synapse circuit, and a dendritic arbor circuit. Through circuit simu- lations, we show how the model can encode information autonomously using a small neuronal network. We conclude that the synapticCa +2 modulation and the autonomous capability of the dynamic encoding models are vital for generating complex neuronal behaviors, a property that might inuence future technology. In the following chapters, we demonstrate how such encod- ing capabilities can enhance learning and perform complex neuronal processes such as decoding the location of an AP from the output of a given neuronal network using the concept of neuronal ltering and the coincident detection encoding scheme. 64 Chapter5 NeuromorphicNeurontoNeuronSignalingUsingVarious APPatterns Using electronic circuits, this chapter models how dierent received spiking patterns produce dierent synaptic strengths using our dynamic neuron circuit model. In other words, we exam- ine through circuit simulations how various received AP patterns contribute to various dynamic postsynaptic responses, including synapse strengthening; thus, enhancing learning. Here, the term learning denes the formation of dierent synaptic strengths and signaling between neu- rons using various spiking patterns in the BioRC neuromorphic circuits. Moreover, this chapter shows how dynamic synapse strengths corresponding to various spiking patterns can increase information processing between neuromorphic neurons by showing how a postsynaptic neuron recognizes and convert distinct presynaptic responses from other presynaptic neurons. To model dynamic synaptic strengths, we created neuromorphic astrocytic compartment circuit model to convert dierent AP patterns into dierent presynapticCa +2 signals. Then, the generatedCa +2 signals are used with ourCa +2 modulated synapse circuit model and dynamic encoding neuron circuit model discussed in chapters 4 and 3, respectively. 65 5.1 SynapticStrengtheningCircuitImplementations With the enormous experimental neuroscience studies investigating many astrocytic roles in- volved in neuronal signaling, described in chapter 2, our astrocytic compartmental circuit model focuses on modeling the astrocytic mechanisms involved in synapse strengthening using various spiking patterns to increase neuron-to-neuron information signaling. We and many others have demonstrated various neuronal mechanisms to demonstrate learning using spike timing depen- dent plasticity (STDP) [141], STDP with dopamine signaling [142], learning without forgetting, unsupervised learning, and timing-perceptive learning through nonvolatile memory devices and dedicated network architectures [143], and other learning models such as rewiring using pro- grammable AER architectures [144, 145]. In the BioRC group, the earliest STDP modeling was created by Joshi [103]. In this model (Fig. 5.1), the circuit detects the timing dierences between the backpropagating AP relative to the presynaptic AP, where each synapse requires additional circuits, including receptor activation, magnesium block removal, NMDA deactivation, and cal- cium channel circuits. However, there are some limitations associated with this STDP model, including integration complexity per individual synapse and utilization of many control signals, causing it to be an unsuitable candidate for autonomous neuromorphic modeling where control signals should be minimized. Other limitations include a single AP pattern processing (i.e. phasic AP pattern), making it incompatible with our dynamic rich behavioral neuron model. Moreover, Yue has demonstrated the most recent BioRC STDP model by using noisy neuron and dopamine signaling to show how short-term and long-term STDP learning can be accom- plished (Fig. 5.2), [142]. In this model, learning is performed using a neuronal network (Fig. 5.3) instead of a single neuron. The network includes a dopaminergic neuron to control dopamine 66 Figure 5.1: An earlier BioRC spike time-dependent plasticity (STDP) model, adopted from [103]. reward signaling and anoisyneuron to initiate learning mechanisms. Notwithstanding the capa- bility of modeling learning using a regular spiking AP pattern, the circuit cannot process other spiking patterns. Besides, long-term learning can only be performed using a network of neu- rons rather than a single neuron since a dopaminergic neuron is required to create a long-term potentiation of synaptic strengths. Kun’s STDP circuit only looks at the relationship between postsynaptic and presynaptic spikes and not the timing between them. 67 Figure 5.2: A schematic diagram of the BioRC spike time-dependent plasticity (STDP) model using dopamine signaling, adopted from [142]. Figure 5.3: The neuronal network that was used during the implementation of spike time-de- pendent plasticity (STDP) using dopamine signaling, where the process of generating long-term potentiation (LTP) and long-term depression (LTD) requires inputs from other neurons, adopted from [142]. Besides STDP modeling, we and others in the BioRC group have modeled dierent astrocytic roles. For example, Irizarry-Valle has modeled the emulation of the neuro-astrocyte interactions and the astrocytic role in neuronal phase synchrony [146, 97], respectively. Other astrocyte mod- eling includes the modulation of AP transmission frequency [147]. Moreover, using circuit im- plementations, Lee has shown how information regarding the geolocation of the synapses can be encoded in the tails of single spikes and how astrocytic roles can be used in repairing damaged 68 neuronal connections using left and right eyes neuronal signaling as an example [106]. Notwith- standing the emulation capabilities that the previously mentioned STDP and astrocytic models have, such models, lack processing capabilities of various AP patterns that our dynamic neuron model generates. With such limitations, these models require large amount of hardware and other control signals, when considering autonomous, large, integrated neuromorphic systems. Therefore, we focus on modeling compartmental neuro-astrocyte signaling, including dynamic synapse strengthening using various presynaptic AP patterns. In the subsequent sections, at rst, we discuss our two proposed neuromorphic astrocytic compartmental models. First, we show an astrocyte compartment model demonstrating synaptic plasticity based on repeated presynaptic activities. Second, we show an astrocytic compartment model demonstrating STDP [148]. 69 5.1.1 NeuromorphicSynapseStrengtheningUsingPresynapticRate Our astrocytic compartmental circuit model demonstrating synaptic plasticity based on repeated presynaptic activities, is shown in Fig. 5.4. The model demonstrates long-term potentiation (LTP), based on the rate of presynaptic neuron activities, and long-term depression (LTD), through other retrograde messengers represented using some leakage properties. In other words, strengthening the synaptic connection is proportional to the frequency and the pattern of the presynaptic spikes. Figure 5.4: The schematic diagram for the astrocyte to demonstrate synaptic plasticity based on the repeated APs at the presynaptic neuron. Cleft1 represents the sensed NT at the synaptic cleft region, andPreAP1 acts as an enabling signal to acknowledge the astrocyte about activities at the presynaptic terminal. Using the 45nm CMOS Technology node, P1 and P3 transistors represent the LTP charging path, while transistor N1 models LTD using some leakage properties. Cleft1 represents the re- leased NT concentration by the presynaptic terminal of synapse S1, and PreAP1 works as an 70 enabling control signal to acknowledge to the astrocyte about any ongoing activity at the presy- naptic terminal of S1. A capacitor is used to convert the accumulated charges into LTP1/LTD1 potential to strengthen/weaken the synaptic connection depending on the rate and the pattern of the received presynaptic spikes. The model uses 3 transistors per synapse to model synapse strengthening through repeated presynaptic activities. Thus, the overall neuromorphic astrocyte to synapse modeling is shown in Fig. 5.5 Figure 5.5: The BioRC neuromorphic conguration between the astrocyte and the synapse circuits using the repeated presynaptic activities protocol. We use the experimental neuronal network shown in Fig. 5.6, to illustrate synapse strength- ening through repeated presynaptic activity. The network consists of our implemented dynamic encoding model for neuronsN1,N2, andN3, ourCa +2 modulated synapse model for synapses 71 Figure 5.6: An experimental neuronal network to demonstrate synaptic plasticity using astrocyte. S1,S2, andS3, our dendritic arbor model to sumEPSP 1,EPSP 2, andEPSP 3 intoVsoma4, and our proposed astrocyte compartment model shown in (Fig. 5.4). Simulation results of our circuits are discussed in detail using Virtuoso simulator tools. In our experimental network, neu- ronsN1,N2, andN3 generate dierent spiking rates at the presynaptic terminals of synapses S1,S2, andS3, respectively. Consequently, the generated spikes induce an LTP based on the rate of activity (frequency of spikes) at the presynaptic terminals (Fig. 5.7). An LTD follows the gen- erated LTP expressed as a decaying potential based on theleakage biasing voltage. For example, in (Fig. 5.7), the postsynaptic neuronN4 was able to detect the activity caused by neuronN1, due to the higher rate of spikes, much faster than other presynaptic neurons,N2 andN3. This is because the strength of the synapseS1 is higher than those of other synapses att = 0:23us. 72 Figure 5.7: Simulation results for the experimental network with the proposed astrocyte model based on repeated presynaptic activities, modeled as a regular spiking patterns. AP1, AP2, and AP3 are the output of presynaptic neurons N1, N2, and N3, respectively. AP4 is the output of the postsynaptic neuron, N4. The EPSPs are the excitatory postsynaptic potentials of synapses S1, S2, and S3. LTP1, LTP2, and LTP3 represent the long-term potentiation of synapses S1, S2, and S3, respectively. LTD1, LTD2, and LTD3 represent the long-term depression of synapses S1, S2, and S3, respectively. 73 5.1.2 NeuromorphicSynapseStrengtheningusingSTDP STDP, in biological neurons, begins when a postsynaptic AP takes place at the postsynaptic neuron, causing a Ca +2 inux in the postsynaptic neuron. The Ca +2 inux, in turn, triggers the astrocyte to sense the activity at the postsynaptic neuron through the endocannabinoids 2- arachidonyl glycerol (2-AG), causing the astrocyte to release glutamate, triggering the NMDARs receptor at the presynaptic neurons. The trigger of the presynaptic neuron’s NMDAR receptor provokes long-term potentiation (LTP) [149]. Consequently, our astrocytic compartmental cir- cuit model, demonstrating STDP, is simplied by which it includes sensing the postsynaptic and presynaptic activities to strengthen or weaken the synaptic connection between the two neurons without the detailed modeling of other astrocytic processes. Thus, by using the same network (Fig. 5.6), a demonstration of STDP learning protocol using the astrocytic compartment circuit model (Fig. 5.8) can be achieved through the relative synchronous timing between presynaptic and postsynaptic spikes to encode the strengths of synapsesS1,S2, andS3. This astrocyte compartment circuit model generates LTP and LTD based on the analog syn- chronization timing between the presynaptic AP arrival time and the postsynaptic AP produce time. In other words, when a postsynaptic neuron generates AP, all its synapses that participated in the generation of that AP are strengthened (LTP), each based on its relative timing to the gen- erated AP timing. On the other hand, all synapses that did not participate in the AP generation are weakened (LTD). Here, the presynaptic neurons areN1,N2, andN3, and the postsynaptic neuron isN4. In the astrocyte compartment model (Fig. 5.8), presynaptic and postsynaptic activ- ities are described byPreAP andPostAP signals, respectively. The model uses three transistors 74 Figure 5.8: The schematic diagram for astrocyte to cause synaptic plasticity based on the syn- chronized timing between the presynaptic and postsynaptic neurons. per synapse; besides, a single CMOS inverter per postsynaptic neuron to connect multiple presy- naptic neurons to one postsynaptic neuron. Thus, the overall neuromorphic astrocyte to synapse modeling is shown in Fig. 5.9 Using the experimental network (Fig. 5.6), ifS1 participates in generating a postsynaptic AP, then the activation of transistors P1 and P3 will overdrive transistor N3, hence generating an analog LTP at the capacitor with an intensity relative to the degree of synchronization timing betweenN1 andN4 neurons. However, If synapseS1 did not cause a postsynaptic AP at the output of neuronN4,PreAP will turn transistor P1 o, resulting in an LTD through transistor N1. Consequently, the output signalCa modulates the strength of the designated synaptic con- nection. The verication of the results is performed using Cadence Virtuoso Simulator Tools by which the neuronal network generates dierent AP frequencies using the presynaptic neurons 75 Figure 5.9: The BioRC neuromorphic conguration between the astrocyte and the synapse circuits using the STDP protocol. N1, N2, andN3 to the postsynaptic neuron, N4 using synapsesS1, S2, andS3, respectively (Fig. 5.10). To discuss the simulation results, we have highlighted four regions, including Region 1, Re- gion 2, Region 3, and Region 4 (Fig. 5.10). In Region 1, as AP1, AP2, and AP3 arrived at the same time, neuron N4 re with a coincident behavior at which it produces two high-frequency spikes, hence it strengthens synapsesS1,S2, andS3 due to their participation in generating a postsynaptic AP4. In Region 2, since AP4, the activity at the neuronN4, is independent of the presynaptic neuron,N3, both synapsesS1 andS2 are strengthened (LTP) while synapseS3 is weakened (LTD). In Region 3, the postsynaptic neuronN4, does not generate an AP due to the 76 Figure 5.10: Simulation results for the experimental network with the proposed astrocyte model based on repeated presynaptic activities. AP1, AP2, and AP3 are the output of presynaptic neu- rons N1, N2, and N3, respectively. AP4 is the output of the postsynaptic neuron, N4. The EPSPs are the excitatorty postsynaptic potentials of synapses S1, S2, and S3. 77 weak induced stimulation from neuronN3. In Region 4, another highlighted coincident detec- tion event due to a strong stimulus from the presynaptic neuronsN1 andN2. In this case, both S1 andS2 are potentiated, whileS3 is depressed. The astrocytic compartmental circuit model is simplied to accommodate dense autonomous neuronal networks and governs neuron to neuron signaling using the dynamic encoding neuron model. More specically, it allows various spik- ing patterns from presynaptic neurons to cause distinctive behavioral responses at the output of a postsynaptic neuron. An example of how a postsynaptic neuron can recognize presynaptic patterns distinctively is shown in (Fig. 5.11) and (Fig. 5.12), at whichN1,N2, andN3 provide dif- ferent presynaptic spiking patterns, including regular spiking and various burst widths patterns. NeuronN4, on the other hand, represents the postsynaptic neuron that will be utilized to detect dierent AP patterns generated byN1,N2, andN3. We test the response of the postsynaptic neuron (N4) using the STDP model for the case of strong synaptic connections (Fig. 5.11), and weak synaptic connections (Fig. 5.12). In the case of a strong synaptic connection (Fig. 5.11), neuronN4 is capable of detecting and passing various presynaptic spiking patterns, including dierent bursts widths. On the contrary, weak synaptic connections (Fig. 5.12), cause neuronN4 to selectively rec- ognize information encoded in the shape of AP pattern (i.e. detection of various burst widths), and information encoded in the timing between spikes (i.e. detection of synchronized regular spikes). In detecting various burst widths,N4 responses with multiple spikes corresponding to the width of the presynaptic bursts at which wider presynaptic bursts causes higher number of postsynaptic regular spikes than narrower presynaptic bursts. We use color-coding regions to indicate dierent encoding capabilities in both (Fig. 5.11) and (Fig. 5.12). Green regions repre- sent theN4 response to wide presynaptic bursts, red regions indicateN4 response to narrower 78 Figure 5.11: The simulated results of the postsynaptic neuron (N4) to dierent spiking patterns generated by presynaptic neurons (N1,N2, andN3) for strong synaptic connections. Dierent colors indicate variousN4 postsynaptic responses to various presynaptic spiking patterns. SB and RS represent single burst and regular spiking patterns, respectively. presynaptic bursts, blue region determinesN4 detection of synchronized presynaptic spikes, and yellow region represents the detection of regular spiking patterns. 79 Figure 5.12: The simulated results of the postsynaptic neuron (N4) to dierent spiking patterns generated by presynaptic neurons (N1,N2, andN3) for weak synaptic connections. Dierent colors indicate variousN4 postsynaptic responses to various presynaptic spiking patterns. SB and RS represent single burst and regular spiking patterns, respectively. X represents undetected spikes asN4 recognizes selective information encoded in the shape of AP patterns, such as var- ious burst widths, and information encoded in the timing between spikes, such as the case of synchronized spikes. In summary, two types of synaptic strengthening protocols using the astrocytic compartmen- tal circuit model are discussed. The protocols include presynaptic activity rates and STDP. Unlike other astrocyte and STDP circuit models, the presented models are simplied to aid the build of a dense neuromorphic neuronal network as well as enabling an extra dimension in enhancing 80 neuron to neuron signaling at which a postsynaptic neuron can detect various presynaptic AP patterns depending on the current state of their synaptic strength. For example, in the case of a strong synaptic connection, the postsynaptic neuron can detect all presynaptic AP patterns, unlike other synaptic strengthening models where only a regular spiking pattern is detected for strong synaptic connection, and no spike is detected for weak synaptic connection. However, in the case of a weak synaptic connection, the postsynaptic neuron can selectively recognize spe- cic and vital information, such as detecting various burst widths and synchronized (arriving at the same time) spikes, indicating a coincident event. In the next chapter, we will be using the case of strong synaptic connection to decoding information regarding the origin of the spike as an application of the rich capability of our dynamic neuronal encoding model. 81 Chapter6 NeuromorphicPattern-SpecicFilteringNeuronsin DecodinganAPOrigin 6.1 NeuromorphicNeuronalPatternFiltering Biological neurons process information by dynamically encoding dierent presynaptic proper- ties into various postsynaptic AP patterns. Earlier in this thesis, a biomimetic electronic neuron model demonstrated such processing capability had been implemented using dynamic encod- ing theory expressed as neuronal modulation at the AIS region to produce complex AP patterns based on various presynaptic EPSP characteristics. In this chapter, using the same developed electronic dynamic encoding theory, we demonstrate how modeling a dynamic encoding in elec- tronics can be vital in enhancing the processing capability of a given neuromorphic neuronal network. There are many applications to show the importance of modeling neuronal dynamic encoding behaviors. One of such is AP pattern ltering. The term ltering is the process by which our neuromorphic neuron responds selectively to particular received presynaptic spiking patterns. In other words, a neuron is capable of passing specic presynaptic AP patterns and 82 blocking others. The AP pattern ltering functionality enables the lteration and classication of pattern-specic processes in a neuronal network. For example, such classication abilities can be applied todecode information regarding the origin of an AP (i.e. extracting which of a neuronal network output patterns correspond to which of the input neurons was active and when). Using our theoretical dynamic encoding approach at the AIS region, ve dierent electronic neuronal pattern ltering implementations can be constructed. The rst type is theAll-patterns- pass neuron (N A ). This type of lter passes all received AP patterns and operates as an APs combiner where it combines multiple received AP inputs, from the somatodendritic compart- ment, into a single AP output, at the axon hillock terminals. The second type is theBursts-pass neuron (N B ). Such neuron selectively passes burst AP patterns and blocks other regular spik- ing patterns. The third type is the Spikes-pass neuron (N S ). The-spikes-pass neuron permits the propagation of regular spiking patterns and blocks other bursting patterns. The fourth type of neuron lters is the Phase-pass neuron (N P ), at which a neuron res a spike each time the phase changes. For example, when a neuron receives a presynaptic spike, it generates a single spike indicating a positive phase change (the rising edge of the spike). When the neuron detects a presynaptic burst at its somatodendritic compartment, it produces two spikes, one signaling the positive phase change (the rising edge of the burst) and the other signaling a negative phase change (the falling edge of the burst). The distance between the two spikes designates the width of the received burst. The fth type of neuronal ltering utilizing the AIS encoding is Bursts- width-pass topology (N W ). In this topology, two types of neuron lters are utilized in series to convert the received bursts into two spikes indicating starting and ending times of the burst (burst width signaling). This type of ltering is necessary since it transforms bursts into regu- lar spikes and combines them with other regular spikes. The implementations of these neuronal 83 lters increase the information processing by allowing a neuronal network to send and detect information regarding the shape, phase, widths, and timing of the received AP patterns. Each of these patterns and experiments illustrating them are shown below. Each dierent ltering circuit utilizes the same circuit principles discussed in chapters 3 and 4; however, the dierence between ltering circuits discussed in this chapter and the dynamic encoding circuits discussed in earlier chapters is the AIS circuit conguration. In this chapter, the AIS of each ltering circuit is set to recognize and detect specic spiking patterns, while the AIS region discussed in earlier chapters is used to produce and identify a wide range of spiking and bursting patterns. Therefore, the circuit explanation for each ltering neuron is focused on explaining the AIS conguration. 6.1.1 AllPatterns-PassNeuronCircuitModel The All-patterns-pass neuron (N A ) depicts a neuron’s ability to reproduce various presynaptic AP patterns seen at its somatodendritic compartment to signal consequent postsynaptic neurons. This type of neuron lter can be utilized as a patterns combiner in a neuronal network, where it combines various AP patterns from multiple presynaptic neurons into a single output, containing all received presynaptic AP patterns at its axon hillock terminals. The circuit schematic diagram of theN A neuronal lter is shown in Fig. 4.1. The functions ofAER,Vsoma,SpikeGenerator, Na,K+, andAISModulation are discussed in [118, 150], whereVsoma represents the nonlin- ear summation of the induced Post Synaptic Potentials (PSPs), reecting theCa +2 ion concentra- tion at the somatodendritic compartments using theCa +2 modulated synapse model (Fig. 4.2). WhenCa +2 ion concentration increases higher thanVth 17 , the threshold voltage of transistor M17, theCa +2 ion channel will become activated; hence a current will ow through transistors 84 M16 and M17, resembling the T-current (low Threshold-Calcium current discussed in [112]). The higher the current ow is, the higher the burst width. To examine the functionality of theN A neuron lter, an experimental neuronal network is composed using three input neurons and three synapses (Fig. 6.1). The input neuron (N3) is set to produce a bursting AP pattern, and the other two input neurons (N1 andN2) are set to create a regular spiking AP pattern. The synapsesS1,S2, andS3, areCa +2 modulated synapses (Fig. 4.2). The output neuron is an all-pass neuron (N A ). Figure 6.1: A small experimental neuronal network demonstrating the functionality of all- patterns-pass output neuron (N A ). N1 and N2 represent regular spiking input neurons, and N3 represents bursting input neuron. S1, S2, and S3 represent the Ca +2 modulated synapse model [150]. With the assumption that all received spiking patterns are not arriving at the same time, the AP pattern of neuronN A is shown in Fig. 6.2 at whichN A res a single spike when a presynaptic spike is detected and a burst when a presynaptic burst is recognized. Moreover, the produced bursts at the axon hillock output of neuronN A support the exact width of the received initial bursts. Accordingly, neuronN A can be used as a combiner where it combines various neuronal activities seen at its dendritic tree into its axon hillock terminal. 85 If two or more spikes are projected simultaneously from dierent input neurons to neuronN A , the resulting AP pattern at the output of neuronN A will exhibit a burst designating a coincident detection, as discussed earlier in chapter 4 (Fig. 4.11). Such coincident detection property is very benecial when decoding information regarding the origin of an AP pattern from the output neurons. 86 Figure 6.2: The behavioural responses of All-patterns-pass ltering neuron (N A ) using three input neurons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, andS3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. 6.1.2 Bursts-PassNeuronCircuitModel Thalamic relay neurons react to numerous presynaptic inputs selectively in two distinct modes; bursting mode or regular spiking mode [151]. Bursts are induced by the slow inward calcium 87 T-current resulting from the activation of theCa +2 ion channels. In general, bursts are thought to carry critical information compared to regular spikes, for instance, making unreliable synapses reliable [152], and increasing signal-to-noise ratio by reducing noise [153, 154]. Therefore, it is essential to incorporate important biological behaviors when building a neuromorphic neuronal network capable of performing complex tasks such as decoding the origin of an AP from the network output. The Bursts-pass ltering neuron (N B ) depicts a neuron’s ability to pass presynaptic bursting AP inputs seen at its somatodendritic compartment selectively and blocks other presynaptic spik- ing inputs when signaling consequent postsynaptic neurons. This neuron lter can isolate the bursts from other regular spike inputs, ensuring the bursts’ propagation. The circuit schematic diagram of theN B neuronal lter is shown in Fig. 6.3, whereCOMP 1 andCOMP 2 are low- power compactor circuits (Fig. 3.3). TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potas- sium, and calcium ion channels are represented by Na+, K+, and Ca+, respectively, where Na+ = 900mV ,K+ = 0V , andCa+ = 800mV (activated) to set the bursting mode forN B . Therefore, theBursting AIS block is xed to permit bursts and block regular spike propaga- tion. The Bursting AIS associates the received excitatory postsynaptic potentials (Vsoma) with a xed biasing voltage (Vb), whereVb denes the dierence in amplitude between spike and burst patterns. WhenVsoma is higher thanVb, indicating the detection of bursts,COMP 2 outputs a logic "0" becauseVsoma is assigned to the negative terminal ofCOMP 2, which leads to permitting burst propagation. Therefore, when COMP 2 outputs a logic "0", the shunting transistors (M15 and M19) will be switched OFF, permitting the propagation of the bursts at the output ofN B . On the other hand, whenCOMP 2 outputs a logic "1" (i.e. Vsoma is lower than 88 Vb), the shunting transistors (M15 and M19) will be switched ON to prevent the propagation of spikes at the output ofN B . The value of having another shunting transistor (M19), compared to the earlier implementation of the dynamic neuronal model (Fig. 4.1), where there was only one shunting transistor (M15), is to block spikes formation for all the values ofVsoma_ThreVb. Accordingly, M19 should be sized to have a strong pulldown capability compared toCOMP 1. In addition, the propagation delay fromCOMP 2 to M19 and M15 (t pd2 ), noted as a red arrow (Fig. 6.3), should be smaller than the propagation delay from COMP 1 to M20 (t pd1 ), the transistor responsible for triggering the neuron responses, noted as a blue arrow (Fig. 6.3). In other words, COMP 2 should be faster thanCOMP 1 to shunt any detected spikes through transistors M15 and M19 regardless of the output ofCOMP 1. Therefore, whenCOMP 2 detects a spike at its input terminals, it will output a logic "1" to turn ON transistors M15 and M19, causing transistor M20 to turn OFF to prevent the detected spike from passing to the output terminal of the neu- ron. The assumption used in this scheme is that transistor M19 is strong enough to overwrite the output ofCOMP 1 when it turns ON. By using the RC time constant analysis, the propagation delay forCOMP 2 andCOMP 1 (t pd2 andt pd1 ), can be approximated using equations 6.5 and 6.6, sequentially. V LH2 =V dd (1e t R p4;2 (C g15 +C g19 ) ) (6.1) V LH1 =V dd (1e t R p4;1 (C g20 +C d19 ) ) (6.2) V HL2 =V dd e t R n4;2 (C g15 +C g19 ) (6.3) V HL1 =V dd e t R n4;1 (C g20 +C d19 ) (6.4) 89 Figure 6.3: The schematic diagram of a bursts-passing neuron (N B ), where COMP 1 and COMP 2 are low power voltage compactors (Fig. 3.3). The red and blue arrows represent the propagation delays fromCOMP 2 to M19 and M15 andCOMP 1 to M20, respectively. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, andCa+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 800mV (activated) to set the bursting mode forN B . t pd2 = t pLH2 +t pHL2 2 (6.5) t pd1 = t pLH1 +t pHL1 2 (6.6) WhereC g is the gate capacitance;C d is the drain capacitance;V dd is the DC supply voltage; V HL2 andV HL1 describing the transient voltage when the output of the compactor circuit changes from logic "1" to logic "0" forCOMP 2 andCOMP 1, respectively. On the other hand,V LH2 and V LH1 dene the transient voltage when the output of the compactor circuit changes from logic "0" to logic "1" forCOMP 2 andCOMP 1, sequentially. To examine the functionality of theN B neuron lter, an experimental neuronal network is composed using three input neurons and three synapses (Fig. 6.4). The input neuron (N3) is set to produce a bursting AP pattern, and the other two input neurons (N1 andN2) are set to create 90 Figure 6.4: A small experimental neuronal network demonstrating the functionality of a burst- pass output neuron (N B ).N1 andN2 represent regular spiking input neurons, andN3 represents the bursting input neuron.S1,S2, andS3 represent theCa +2 modulated synapse model [150]. a regular spiking AP pattern. The synapsesS1,S2, andS3, areCa +2 modulated synapses (Fig. 4.2). The output neuron is a burst-pass neuron (N B ). The AP pattern of neuronN B is shown in Fig. 6.5 at whichN B passes all bursts from input neuronN 3 while blocking regular spikes from the two other input neurons,N 1 andN 2 . Moreover, the produced bursts at the axon hillock output of neuron N B support the exact width of the received initial bursts. 91 Figure 6.5: The behavioural responses of bursts-pass neuron lter (N B ) using three input neu- rons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, andS3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. 6.1.3 Spikes-PassNeuronCircuitModel The Spikes-pass ltering neuron (N S ) depicts a neuron’s ability to pass presynaptic spiking inputs seen at its somatodendritic compartment selectively and blocks other presynaptic bursting inputs when signaling consequent postsynaptic neurons. Unlike the bursts-pass neuron lter discussed 92 earlier, spikes-pass neuron lter isolates spikes from other bursting inputs, allowing the propaga- tion of spiking AP patterns. The circuit schematic diagram ofN S neuronal lter is shown in Fig. 6.6, whereCOMP 1 andCOMP 2 are low power voltage compactors (Fig. 3.3). TheAER repre- sents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+, K+, andCa+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the spiking mode forN S . Therefore, theSpikingAIS block is xed to permit regular spiking APs and block bursting APs propagation. Similar to aBursting AIS, theSpiking AIS asso- ciates the received excitatory postsynaptic potentials (Vsoma) with a xed biasing voltage (Vb), whereVb denes the dierence in amplitude between spiking and bursting patterns. However, whenVsoma is higher thanVb, indicating the detection of bursts,COMP 2 outputs a logic "1" becauseVsoma is assigned to the positive terminal ofCOMP 2, which leads to blocking bursts propagation. Therefore, whenCOMP 2 outputs a logic "1", the shunting transistors (M15 and M19) will be switched ON, preventing the propagation of the bursts at the output of N S . On the other hand, whenCOMP 2 outputs a logic "0" (i.e. Vsoma is lower thanVb), the shunting transistors (M15 and M19) will be switched OFF to allow the propagation of spikes at the output ofN S . Similar to the bursts-passing neuron lter, the value of having another shunting transistor (M19) beside M15 is to block bursts formation for all the values ofVsoma_ThreVb. Accord- ingly, M19 should be sized to have a strong pulldown capability compared toCOMP 1. Also, the propagation delay fromCOMP 2 to M19 and M15 (t pd2 ), noted as a red arrow (Fig. 6.6), should be smaller than the propagation delay fromCOMP 1 to M20 (t pd1 ), the transistor responsible for triggering the neuron responses, noted as a blue arrow (Fig. 6.6). Therefore, the RC time con- stant analysis is the same for the case of burst-pass neuron lter, where the propagation delay 93 for COMP 2 and COMP 1 (t pd2 and (t pd1 )), can be approximated using equations 6.5 and 6.6, respectively. Figure 6.6: The schematic diagram of spikes-passing neuronN S , whereCOMP 1 andCOMP 2 are low power voltage compactors (Fig. 3.3). The red and blue arrows represent the propagation delays fromCOMP 2 to M19 and M15 andCOMP 1 to M20, respectively. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+, K+, andCa+, respectively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the spiking mode forN S . To check the functionality of theN S neuron lter, an experimental neuronal network is com- posed using three input neurons and three synapses (Fig. 6.7). The input neuron (N3) is set to produce a bursting AP pattern, and the other two input neurons (N1 andN2) are set to create a regular spiking AP pattern. The synapsesS1,S2, andS3, areCa +2 modulated synapses (Fig. 4.2). The output neuron is a spikes-pass neuron (N S ). Thus, the AP pattern of neuron N S is shown in Fig. 6.8 at whichN S passes all spikes from input neuronsN 1 andN 2 while blocking bursting APs from neuronN 3 . 94 Figure 6.7: A small experimental neuronal network demonstrating the functionality of spikes- pass neuron lter (N S ).N1 andN2 represent regular spiking input neurons, andN3 represents bursting input neuron.S1,S2, andS3 represent theCa +2 modulated synapse model [150]. 6.1.4 Phase-PassNeuronCircuitModel The phase-pass ltering neuron (N P ) depicts a neuron’s ability to re a spike each time it de- tects a phase change, whether it was a positive or negative phase change, at its somatodendritic compartment. In other words, when a phase-pass ltering neuron receives a presynaptic spike, it forms a single spike indicating the detection of a positive phase change (rising edge of AP). When it receives a single burst, it produces two spikes; one indicates a positive phase change (rising edge of burst), and the other indicates a negative phase change (falling edge of the burst). Therefore, each received input spike is represented by a single spike, and each received input burst is represented by two spikes, informing the burst’s starting and ending times at the output of a phase-pass ltering neuron. Hence, in the case of bursts detecting, the refractory period (the silence time between two consecutive spikes) between the starting and ending spikes, represent- ing a burst, depends on how wide or narrow the received burst is, indicating the ability to encode information regarding the width of the input burst in the silence time between the two spikes and in the form of spikes. 95 Figure 6.8: The behavioural responses of spikes-pass neuron lter (N S ) using three input neu- rons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, andS3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. The circuit schematic diagram ofN P neuronal lter is shown in Fig. 6.9, whereCOMP 1 and COMP 2 are low power voltage compactors (Fig. 3.3). TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, andCa+, respec- tively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the spiking mode 96 forN P . Therefore, thePhaseSensitiveAIS block is xed to detect any phase change. Like aSpiking AIS, thePhaseSensitiveAIS associates the received excitatory postsynaptic po- tentials (Vsoma) with a xed biasing voltage (Vb), whereVb denes the dierence in amplitude between spiking and bursting patterns. However, whenVsoma is higher thanVb, indicating the detection of bursts,COMP 2 outputs a logic "1" becauseVsoma is assigned to the positive termi- nal ofCOMP 2, which leads to blocking bursts propagation. Therefore, whenCOMP 2 outputs a logic "1", the shunting transistor (M15) will be switched ON, preventing the propagation of the bursts at the output ofN P . On the other hand, whenCOMP 2 outputs a logic "0" (i.e. Vsoma is lower thanVb), the shunting transistor (M15) will be switched OFF to allow the propagation of spikes at the output ofN P . However, the phase-pass ltering neuron sustains a single shunt- ing transistor (M15) to identify the rst edge of a received burst input by allowingCOMP 1 to trigger its initiation beforeCOMP 2 block it at the output terminal. Thus, the propagation delay fromCOMP 2 to M15 (t pdp2 ), noted as a blue arrow (Fig. 6.9), should be higher than the prop- agation delay fromCOMP 1 to M20 (t pdp1 ), the transistor responsible for triggering the neuron responses, noted as a red arrow (Fig. 6.9). Therefore, using the RC time constant analysis for a phase-pass neuron lter, the propagation delays for COMP 2 and COMP 1 (t pdp2 and (t pdp1 )), can be approximated using equations 6.11 and 6.12, respectively. V LHp2 =V dd (1e t R p4;2 (C g15 ) ) (6.7) V LHp1 =V dd (1e t R p4;1 (C g20 ) ) (6.8) V HLp2 =V dd e t R n4;2 (C g15 ) (6.9) 97 Figure 6.9: The schematic diagram of spikes-passing neuronN P , whereCOMP 1 andCOMP 2 are low power voltage compactors (Fig. 3.3). The blue and red arrows represent the propagation delays fromCOMP 2 to M15 andCOMP 1 to M20. TheAER represents the neuron address by which it allows a neuron to evaluate its synaptic inputs only when its address is triggered. The sodium, potassium, and calcium ion channels are represented byNa+,K+, andCa+, respec- tively, whereNa+ = 900mV ,K+ = 0V , andCa+ = 0V (deactivated) to set the phasic spiking mode forN P . V HLp1 =V dd e t R n4;1 (C g20 ) (6.10) t pdp2 = t pLH2 +t pHL2 2 (6.11) t pdp1 = t pLH1 +t pHL1 2 (6.12) WhereV HLp2 andV HLp1 describe the transient voltage for phasic-pass ltering neuron im- plementation when the output of the compactor circuit changes from logic "1" to logic "0" for COMP 2 andCOMP 1, respectively. On the other hand,V LHp2 andV LHp1 dene the transient voltage for the phasic-pass ltering neuron, when the output of the compactor circuit changes from logic "0" to logic "1" forCOMP 2 andCOMP 1, sequentially. 98 To test the functionality of theN P neuron lter, an experimental neuronal network is com- posed using three input neurons and three synapses (Fig. 6.10). The input neuron (N3) is set to produce a bursting AP pattern, and the other two input neurons (N1 andN2) are set to create a regular spiking AP pattern. The synapsesS1,S2, andS3, areCa +2 modulated synapses (Fig. 4.2). The output neuron is a burst-pass neuron (N P ). Figure 6.10: A small experimental neuronal network demonstrating the functionality of phase- pass neuron lter (N P ).N1 andN2 represent regular spiking input neurons, andN3 represents bursting input neuron.S1,S2, andS3 represent theCa +2 modulated synapse model [150]. The AP pattern of neuronN P is shown in Fig. 6.11 at whichN P passes all spikes from input neuronsN 1 andN 2 , and signaling the start and the end times of other bursting APs from neuron N 3 . This allows signaling information related to the received input burst’s widths using the silence time between the two spikes representing a burst. 99 Figure 6.11: The behavioural responses of phase-pass neuron lter (N P ) using three input neu- rons (N1,N2, andN3), and threeCa +2 modulated synapses (S1,S2, andS3). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. 6.1.5 Burst-Widths-PassTopologyCircuitModel The bursts-width-pass topology (N W ), as the name indicates, depicts a neuron’s ability to pass presynaptic bursting inputs seen at its somatodendritic compartment selectively in the form of spikes. The bursts-width-pass topology consists of a bursts-pass ltering neuron (N B ) followed 100 by a phase-pass ltering neuron (N P ) in series. The rst one lters out unwanted input spikes while passing other input bursts, and the second one converts each burst into two spikes. bursts- width-pass topology ltering is important when processing information in the spiking domain. A spiking domain refers to the process by which various input patterns are encoded in the form of regular spikes because processing burst-related information is much simpler in the spiking domain than in the bursting domain. For example, when an input spike arrives within the same time window of another input burst, it becomes complex to lter the single spike from the high- frequency input burst. Hence, by converting the burst into two spikes, overlapping the burst and the spike will be minimized. The circuit schematic diagram of N W neuronal lter utilizes a bursts-pass ltering neuron (Fig. 6.3) as an input neuron to a phase-pass ltering neuron (Fig. 6.9) at which the state of the voltage-gated ion channels are Na+ = 900mV , K+ = 0V , and Ca+ = 800mV (to activate the bursting mode), for the bursts-pass ltering neuron, andNa+ = 900mV ,K+ = 0V , and Ca+ = 0V (to activate the phasic spiking mode). Other propagation time conditions and circuit implementations remain the same as discussed earlier for each of the neuron lters. To test the functionality of theN W neuron lter, an experimental neuronal network is composed using three input neurons (N 1 ,N 2 , andN 3 ) and four synapses (Fig. 6.12). The input neuron (N3) is set to produce a bursting AP pattern, and the other two input neurons (N1 andN2) are set to create a regular spiking AP pattern. The synapsesS1,S2,S3 andS4, areCa +2 modulated synapses (Fig. 4.2). The combination ofN B andN P creates bursts-width-passing neuronal behaviour. The network responses are shown in Fig. 6.13 at which neuronN B passes input bursts from neuronN 3 and blocks all other regular spiking inputs from neuronsN 1 andN 2 . consequently, 101 Figure 6.12: A small experimental neuronal network demonstrating the functionality of bursts- width-pass neuronal topology (N W ). N1 andN2 represent regular spiking input neurons, and N3 represents bursting input neuron.S1,S2,S3 andS4 represent theCa +2 modulated synapse model [150]. neuronN P decode each permitted burst fromN B through synapseS4 into two spikes represent- ing the start and end times of the received burst. As explained in the next section, the results are important when discussing how an AP origin can be decoded from an output of a neuronal network using the coincident detection protocol and the implemented neuron lters. 102 Figure 6.13: The behavioural responses of bursts-width-pass lter (N W ) using three input neu- rons (N1,N2, andN3),N B is bursts-pass andN P is phase-pass neuron lters, and fourCa +2 modulated synapses (S1,S2,S3 andS4). EPSPs are the excitatory postsynaptic potentials at the output of each synapse model. 103 6.2 DecodingtheOriginsofVariousAPPatterns It has been widely accepted that the auditory brainstems of birds and mammals use interaural time dierences (ITD) to localize sounds, where individual neuron recives inputs from the right and left ears and compare the dierences between their arrival times with an accuracy considered the highest in any other known temporal process [155, 156]. In birds, for example, the Nucleus Laminaris (NL) neurons, known as coincidence detector neurons [157], receive excitatroy lateral (from both ears) inputs through precise arranged axons, known as delay lines [156, 158]. The schematic arrangment of delay lines creates azimuthal space map indicating the location of the received sound sources 6.14. Figure 6.14: A chicken’s avian sound localization circuit, adopted from [159]. (A) represents dier- ent color-coding sound source locations in the azimuth space. (B) Schematic auditory brainstem representation. Nucleus Laminaris (NL), also known as coincidence detectors, map azimuthal space for the color-coding sound sources locations. The ipsilateral axon terminals (magenta) support inputs to the dorsal dendrites of NL, while the contralateral (green) support systematical delay timing from medial to lateral. Both ipsilateral and contralateral inputs to NL are provided by a single avian cochlear nucleus magnocellularis (NM) axon projecting to both NLs. Various physical properties of NM axons represent dierent resonance frequencies. 104 Inspired by the general scheme of birds’ auditory systems when encoding the azimuthal lo- cation of a sound source, dynamic electronic decoding neuronal modes can decode information regarding an AP origin from the output of a given neuronal network. In particular, the coin- cident encoding protocol and previously discussed ltering neurons, including all-patterns-pass (N A ), bursts-pass (N B ), spikes-pass (N S ), phase-pass (N P ), and bursts-width-pass (N W ) ltering neurons circuit models. To demonstrate the decoding process in electronics, (1) various input AP patterns from input neurons are assumed to arrive at dierent times, and (2) to examine the worst-case scenario, all synaptic connections are assumed to be strong. The worst-case scenario is classied when all spiking and bursting inputs are successfully conveyed in the output of a neuronal network, where all input AP patterns are to be derived (decoded) from the output pat- terns without losses in the network. In an actual neuronal network implementation, however, dierent synapses have dierent synaptic strengths, governed by the role of astrocyte and STDP protocol, as discussed in chapter 5. Therefore, with these two assumptions, the block diagram for the constructed decoding protocol is shown in Fig. 6.15. Figure 6.15: A general block diagram for a network of neurons with dierent ltering capabili- ties performing dynamic decoding for the origins of various AP patterns from the outputs of a network. 105 In Fig. 6.15, the input neurons consist of all-pass ltering neurons to dynamically encode excitatory postsynaptic potentials, modeled as Vsoma, into dierent AP patterns. Then, the encoded outputs of input neurons are fed to a neuronal network consisting of bursts-pass and spikes-pass ltering interneurons. There are two output neurons for the interneurons network; the rst permits higher frequency APs as bursts, and the second permits lower frequency APs as regular spikes. Both outputs are then correlated, using a coincident detection scheme, with the initial inputs from input neurons using the Decoding Bursts Origin subblock for bursting AP patterns and Decoding Spikes Origin subblock for regular spiking AP patterns. Like the biologi- cal chicken’s avian system, delays are required to ensure equal propagation delays for successful coincident detection. However, unlike biological coincident detector neurons, where delays are accomplished by changing the length of the axons, a series of all-patterns-pass ltering neurons are used to meet the delay specication in our decoding structure. Thus, the number of delay neu- rons required in our implementation should equal the number of neuronal network layers. Fig. 6.16 exhibits a detailed schematic representation of the bursts and spikes decoding process. The bursts decoding process consists of ve ltering neurons; including bursts-width-pass (N Wsum andN W1 ), all-patterns-pass (N A ), bursts-pass (N B ), and phase-pass (N P ). TheN Wsum andN W1 neurons detect burst patterns from the output of the network and an input neuron, respectively, then convert them to the spiking domain, where each burst is represented by two spikes indicat- ing the starting and ending times of its width. After that,N A couples the output fromN Wsum and N W1 neurons by which correlated APs form coincident bursts, and uncorrelated ones propagate as regular spikes. Next,N B neuron allows all coincident bursts (correlated inputs), seen at the output ofN A , to pass and block other uncorrelated ones, revealing information regarding burst 106 origins and times. Subsequently, the ltered coincident bursts will be converted back to the spik- ing domain using a positive phase pass neuron lter, by which the output reects information regarding the decoded burst’s origin and width. The same process can be applied for the case of decoding regular spiking patterns; however, two spikes-pass ltering neurons (N Ssum andN S1 ) are utilized to pass regular spikes instead ofN Wsum andN W1 , which were used to pass bursts widths. Figure 6.16: A detailed schematic diagram of the Decoding Bursts Origin and the Decoding Spikes Origin subblocks discussed in Fig. 6.15, where the rst decodes bursts origins usingN Wsum and N W1 neurons, and the second decodes the network spikes origins usingN Ssum andN S1 neurons. N A neurons couple the output from N Wsum and N W1 , in the case of decoding bursts, or from N Ssum andN S1 neurons, in the case of decoding spikes, at which if the received APs arrive in a concurrent time, they will produce coincident bursts at the output terminal of N A neurons. Consequently, neuronsN B andN P separate the coincident bursts from other spikes and identify their phase change. To test the decoding process, two input neurons are utilized (N A1 andN A2 ) to represent two dierent azimuthal space locations with various AP patterns. Next, the outputs fromN A1 and 107 N A2 are supplied to an interneurons network consisting of two types of ltering neurons,N S and N B , at which the ltering process divides the inputs fromN A1 andN A2 , representing dierent azimuthal space locations, into high and low frequencies in the form of bursting and spiking APs. Although the role of astrocyte and STDP protocol are what govern the strengthen and weakening of synaptic connections (discussed in chapter 5), all synaptic connections are assumed to be strong to test the worst-case scenario of the decoding process where all APs patterns fromN A1 andN A2 are exhibited at the outputs of the network in the form of bursting and spiking AP patterns. Fig. 6.17 shows the process of decoding the bursts of the input neuronN A1 from the output bursts of a network, represented by (N Bsum ). TheN Wsum converts allN Bsum bursts into spiking domain using two consecutive spikes per burst to indicate the start and end times of the burst, and N W1 converts all N A1 bursts into spiking domain using two consecutive spikes per burst indicating the start and end times. Then, N A ltering neuron couple the outputs fromN Wsum andN W1 neurons, at which the correlated spikes generate coincident bursts, and the uncorrelated spikes propagate as a regular spiking pattern. Thus, N B neuron is used to pass the generated coincident bursts and block other spikes. The output fromN B neuron, indicating the coincident bursts, is then converted back to spiking domain using positive phase detection (N P ) neuron, indicating the start and end time of N A1 bursts that contributed to the generation of N Bsum bursts. The same methodology can be applied to decode the regular spikes ofN A1 neuron from the output spikes of a network, represented by (N Ssum ) (Fig. 6.18); however, instead of using N W1 , which is used to convert N A1 bursts into regular spikes, indicating their widths, N S1 is used to pass the regular spikes and block the bursts fromN A1 neuron. If the synaptic connections were not assumed to be strong, then theN A1 various AP patterns may or may not contribute to the generation of any activity at the network outputs (N Bsum and 108 N Ssum ), similar to biological neuronal behaviors, by which decoding information regarding the origin of an AP becomes more vital in neuronal information signaling. Although the decoding scheme is motivated by the birds’ biological sound localization process, it can be used in neu- romorphic systems to perform location-based recognition processes, such as steering a robot to nd a human speaker or in a rescue situation where visual contact is obscured [160]. 109 Figure 6.17: The neuronal responses involved in decoding a burst origin of input neuronN A1 , from the output bursts of a network (N Bsum ). N Wsum andN W1 convert bursts into spiking do- main using two consecutive spikes per burst to indicate the start and end times of the bursts from N Bsum andN A1 , respectively. N A couples the outputs fromN Wsum andN W1 neurons to coinci- dent bursts (indicated as dashed boxes) when input are correlated in time and into regular spikes when they are not correlated. N B neuron is used to pass the generated coincident bursts and block other regular spikes, andN P neuron converts the coincident back to a spiking domain to indicate which ofN A1 bursts contributed to an output burst at the output neuron of the network (N Bsum ). 110 Figure 6.18: The neuronal responses involved in decoding a spike origin of input neuronN A1 , from the output spikes of a network (N Ssum ).N S1 passes regular spiking AP and block bursting AP from neuronN A1 .N A couples the outputs fromN Ssum andN S1 neurons to coincident bursts when input are correlated (indicated as dashed boxes) in time and into regular spikes when they are not correlated. N B neuron is used to pass the generated coincident bursts and block other regular spikes, andN P neuron converts the coincident back to a spiking domain to indicate which ofN A1 bursts contributed to an output burst at the output neuron of the network (N Bsum ). 111 Chapter7 Conclusion This dissertation focused on the hardware modeling of dynamic biological neural processing to investigate how biological neurons could encode information about our 3D world into various action potential patterns using dierent synaptic input properties. The primary goal of the re- search was to incorporate biological aspects in each neuron model to (1) increase its computation and processing capabilities and (2) maintain the autonomous conguration exibility for future neuromorphic systems. We believed that increasing the processing capability of individual neu- rons allows autonomous processing and may reduce the need for a larger number of neurons in a given neuromorphic system, reducing extensive connectivity and power consumption prob- lems. Also, the dissertation has discussed how modeling the complexity of various neural spiking behaviors using mathematical models is great for emulating rich biological neuron behaviors. However, these models lack real-time executions because they rely on external central process- ing units (CPUs), or in some cases, graphical processing units (GPUs) for solving dierential equations describing the neural spiking behavior. For example, the Blue Brain Project utilizes 8,000 CPUs of the IBM Blue Gene supercomputer to emulate 10,000 neurons in the rat neocor- tical column. Another example, the SpiNNaker project, requires 18 ARM networked processors 112 to mimic 18,000 biological neurons using Izhikevich’s simple mathematical model of a spiking neuron [18, 19]. Therefore, we follow hardware-based neuromorphic modeling to describe rich neural spiking behaviors that overcome external computing requirements. Our proposed BioRC dynamical neural modeling, compared to other well known neuromorphic electronic models, fo- cused on modeling the encoding mechanisms involved in the neurological signal processing at the site of AIS. The AIS is the site responsible for AP initiation, AP modulation, tuning of the ring frequency, and neural signal processing by which biological neurons are not integrators by nature but dynamical systems. In other words, neurons can convey information in spikes’ tim- ing and the rate of spikes simultaneously. We built our dynamic neuronal encoding model using distributed threshold unit modeling, including a threshold unit to enable the system’s dynamics (modeled as external threshold variability) and a second threshold unit at the AIS for modeling signal processing and neural modulation. Throughout circuit simulations, we showed that the dynamical BioRC model mimics the neurological ring complexity by generating various spiking and bursting patterns in real-time corresponding to dierent synaptic properties. In chapter 3, we have examined our model’s generated patterns. The generated patterns are then compared to those found in biological neurons. Such patterns include regular spikes (RS), phasic spikes (PS), tonic bursts (TB), single burst per stimulus(SB), class-1 excitable spikes(CS1), subthreshold oscillations (OSC), depolarization after potentials (DAP), integrators (INT), and mixed-mode (MIX). Moreover, we have discussed how our dynamical concept involves not only the AIS but the modeling of the dynamic activation and deactivation of dendritic voltage-gated Ca +2 channels at which the model emulates the eect of the Calcium-induced T-current found in biological neurons that exert bursting APs (i.e. pyramidal and thalamic cortical neurons). Thus, the model can control (1) the minimum rebound range of bursts and (2) the minimum synaptic 113 input amplitude required for generating bursts by specifying the amount of the Calcium-induced T-current. On the other hand, the absence of the T-current results in low spiking frequency; hence the model switches to the phasic spiking pattern. Besides the adaptation mechanisms, in chapter 3, other processes related to the real-time variations of the synaptic inputs are discussed. First, when the model exerts spiking patterns, the synaptic inputs’ intensity (amplitude) is directly correlated to the frequency of the spiking APs. In other words, the frequency scales up with the amplitude of the stimulus (similar to the spiking behavior of Hodgkin and Huxley model [17]). Second, when the model exerts bursting patterns, the synaptic stimulus’s amplitude is directly correlated with the generated bursts’ width (the Intra-Spike count). As a result, we have shown that the model can also generate adaptive bursting (TB-Adapt pattern) and variable spiking frequencies. Also, we explained, through circuit implementations, how a biological neuron’s threshold can be altered by the mechanisms of voltage-gated ion channels, synaptic properties, and neuron activities. In neuromorphic circuits, the neural variability is a crucial aspect as it governs the translation of the synaptic inputs into APs [161]. In dense neuromorphic systems, the use of a xed threshold value may result in high or low spiking activities in which the former is more sensitive to the simultaneous spike collisions problem at the output of the AER stage [162], and the latter suers from detecting low stimulus activities. Therefore, we have demonstrated xed and variable threshold behaviors using a low-power dierential-based comparator to provide external digital/analog control of the neural threshold needed for neural modulation and other processing capabilities. Then, in chapter 4, we proposed other remaining aspects of neural signaling that are required to reach our research goal. Up to this point, all membrane potentials used in the experiments 114 were provided as an external voltage signal usingVsoma to investigate all plausible spiking and bursting behaviors. Therefore, in chapter 4, we discussed the implementations of a modied excitatory synapse model from our earlier BioRC synapse model [33], with (1) aCa 2+ modula- tion capability to control the release of neurotransmitters from the presynaptic to postsynaptic neurons, and (2) a self-biasing neurotransmitter concentration circuit. The synapse model is con- structed based on the current mirror topology to avoid loading the subsequent stages, such as the dendritic arbor. Also, in chapter 4, we have demonstrated a dendritic arbor model to convert the received EPSPs into a membrane potential using a current-based addition circuit by which a sin- gle transistor per synapse is required to perform addition. The dendritic arbor implementation uses current mirror interfaces with other synapses to support large and dense neural network integration. Using the proposed dynamic neuron model, excitatory synapse model, and dendritic arbor model, we have shown the importance of our dynamic neuromorphic modeling by which we create an experimental neural network to explore the dynamics of our models. The neural network has demonstrated two types of neural encoding autonomously. The rst is the neural rate encoding behavior. The second is the coincident detection behavior through bursting, sim- ilar to pyramidal neuron behavior by which, in neuroscience, coincident detection is considered one of the most ecient coding schemes that distinguish cortical neurons from sensory neurons’ behaviors. Chapter 5 involved modeling compartmental astrocytic roles in creating dynamic synapse strengths corresponding to dierent presynaptic spiking patterns. The models are based on the presynaptic activity rates and the STDP. Unlike other astrocyte and STDP circuit models, the presented models are simplied for dense neuromorphic electronic-based neuronal networks 115 and enhance neuron-to-neuron signaling. Therefore, a postsynaptic neuron can identify vari- ous presynaptic AP patterns depending on the current state of its synaptic strength. Then, we examined two cases of synaptic strengths and their eect on postsynaptic responses. In the case of a strong synaptic connection, the postsynaptic neuron exhibited strong recognition capability for all presynaptic AP patterns, unlike other synaptic strengthening models where only a regu- lar spiking pattern is detected for strong synaptic connection, and no spike is detected for weak synaptic connection. In the case of a weak synaptic connection, using our model, the postsy- naptic neuron is switched to selectively identify specic and vital information, such as detecting various burst widths and synchronized (arriving at the same time) spikes, indicating information time-encoding. Using our theoretical dynamic encoding approach at the AIS region, in chapter 6, we demon- strated ve dierent electronic neural pattern ltering implementations, including all-patterns- pass neuron (N A ), bursts-pass neuron (N B ), spikes-pass neuron (N S ), phase-pass neuron (N P ), and bursts-width-pass topology (N W ). TheN A neuron passes all received AP patterns. TheN B neuron selectively passes burst AP patterns and blocks other regular spiking patterns. TheN S neuron permits the propagation of regular spiking patterns and blocks other bursting patterns. The N P res a spike each time the phase changes. As a result, when a N P neuron receives a presynaptic spike, it generates a single spike indicating a positive phase change (the rising edge of the spike). When theN P neuron detects a presynaptic burst at its somatodendritic compart- ment, it produces two spikes, one signaling the positive phase change (the rising edge of the burst) and the other signaling a negative phase change (the falling edge of the burst). The dis- tance between the two spikes designates the width of the received burst. In theN W topology, however, two types of ltering neurons are utilized in series to convert the received bursts into 116 two spikes indicating starting and ending times of the burst (burst width signaling). Such type of ltering is necessary since it transforms bursts into regular spikes and combines them with other regular spikes. Also, in chapter 6, we showed how the implementations of these neural lters in- crease the information processing by allowing a neural network to send and detect information regarding the shape, phase, widths, and timing of the received AP patterns. Then, we explained how such processing capabilities could be used, in electronics neuronal network, to decode in- formation regarding an AP origin from the output response of the neuronal network to prove how complex processes, such as location-based processes, can be utilized on-chip, in real-time, without the need for external processing units. 117 References [1] Ranu Jung. System and method for neuromorphic controlled adaptive pacing of respiratory muscles and nerves. US Patent 9,872,989. Jan. 2018. [2] Ranu Jung, Shah Vikram Jung, and Brundavani Srimattirumalaparle. Neuromorphic controlled powered orthotic and prosthetic system. US Patent 8,790,282. July 2014. [3] Elisabetta Chicca, Fabio Stefanini, Chiara Bartolozzi, and Giacomo Indiveri. “Neuromorphic electronic circuits for building autonomous cognitive systems”. In: Proceedings of the IEEE 102.9 (2014), pp. 1367–1388. [4] Yulia Sandamirskaya. “Dynamic neural elds as a step toward cognitive neuromorphic architectures”. In: Frontiers in Neuroscience 7 (2014), p. 276. [5] Giacomo Indiveri, Elisabetta Chicca, and Rodney J Douglas. “Articial cognitive systems: From VLSI networks of spiking neurons to neuromorphic cognition”. In: Cognitive Computation 1.2 (2009), pp. 119–127. [6] Yeongjun Lee and Tae-Woo Lee. “Organic synapses for neuromorphic electronics: From brain-inspired computing to sensorimotor nervetronics”. In: Accounts of chemical research 52.4 (2019), pp. 964–974. [7] Mohammad Sarim, Thomas Schultz, Rashmi Jha, and Manish Kumar. “Ultra-low energy neuromorphic device based navigation approach for biomimetic robots”. In: 2016 IEEE National Aerospace and Electronics Conference (NAECON) and Ohio Innovation Summit (OIS). IEEE. 2016, pp. 241–247. [8] Zachary F Mainen, Jasdan Joerges, John R Huguenard, and Terrence J Sejnowski. “A model of spike initiation in neocortical pyramidal neurons”. In: Neuron 15.6 (1995), 1427 bibrangedash /1439.doi: 10.1016/0896-6273(95)90020-9. [9] Lucy M Palmer and Greg J Stuart. “Site of action potential initiation in layer 5 pyramidal neurons”. In: Journal of Neuroscience 26.6 (2006), 1854 bibrangedash /1863.doi: 10.1523/JNEUROSCI.4812-05.2006. 118 [10] Hiroshi Kuba, Rei Yamada, Go Ishiguro, and Ryota Adachi. “Redistribution of Kv1 and Kv7 enhances neuronal excitability during structural axon initial segment plasticity”. In: Nature communications 6.1 (2015), pp. 1–12. [11] Matthew S Grubb, Yousheng Shu, Hiroshi Kuba, Matthew N Rasband, Verena C Wimmer, and Kevin J Bender. “Short-and long-term plasticity at the axon initial segment”. In: Journal of Neuroscience 31.45 (2011), pp. 16049–16055. [12] Maarten HP Kole and Greg J Stuart. “Signal processing in the axon initial segment”. In: Neuron 73.2 (2012), 235 bibrangedash /247.doi: 10.1016/j.neuron.2012.01.007. [13] Dominique Debanne, Emilie Campanac, Andrzej Bialowas, Edmond Carlier, and Gisèle Alcaraz. “Axon physiology”. In: Physiological reviews (2011). [14] Kae-Jiun Chang and Matthew N Rasband. “Excitable domains of myelinated nerves: axon initial segments and nodes of Ranvier”. In: Current topics in membranes. Vol. 72. Elsevier, 2013, 159 bibrangedash /192. [15] Christophe Leterrier and Bénédicte Dargent. “No Pasaran! Role of the axon initial segment in the regulation of protein transport and the maintenance of axonal identity”. In: Seminars in cell & developmental biology. Vol. 27. Elsevier. 2014, 44 bibrangedash /51. [16] Bio-mimetic real-time cortex project. http://ceng.usc.edu/~parker/BioRC_research.html. [17] Alan L Hodgkin and Andrew F Huxley. “A quantitative description of membrane current and its application to conduction and excitation in nerve”. In: The Journal of physiology 117.4 (1952), p. 500. [18] Eugene M Izhikevich. “Simple model of spiking neurons”. In:IEEETransactionsonneural networks 14.6 (2003), pp. 1569–1572. [19] Steve B Furber, Francesco Galluppi, Steve Temple, and Luis A Plana. “The spinnaker project”. In: Proceedings of the IEEE 102.5 (2014), pp. 652–665. [20] Knut Holtho, Yury Kovalchuk, and Arthur Konnerth. “Dendritic spikes and activity-dependent synaptic plasticity”. In: Cell and tissue research 326.2 (2006), 369 bibrangedash /377. [21] Jackie Schiller and Yitzhak Schiller. “NMDA receptor-mediated dendritic spikes and coincident signal amplication”. In: Current opinion in neurobiology 11.3 (2001), 343 bibrangedash /348. 119 [22] Shira Sardi, Roni Vardi, Anton Sheinin, Amir Goldental, and Ido Kanter. “New types of experiments reveal that a neuron functions as multiple independent threshold units”. In: Scientic reports 7.1 (2017), pp. 1–17. [23] Bertil Hille et al. Ion channels of excitable membranes (Sinauer, Sunderland, MA). 2001. [24] Justin Keat, Pamela Reinagel, R Clay Reid, and Markus Meister. “Predicting every spike: a model for the responses of visual neurons”. In: Neuron 30.3 (2001), 803 bibrangedash /817. [25] Michele Migliore, Dax A Homan, Jerey C Magee, and Daniel Johnston. “Role of an A-type K+ conductance in the back-propagation of action potentials in the dendrites of hippocampal pyramidal neurons”. In: Journal of computational neuroscience 7.1 (1999), 5 bibrangedash /15. [26] Chih-Chieh Hsu. “Dendritic Computation and Plasticity in Neuromorphic Circuits”. Copyright - Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Analyte descriptor - N.A; Last updated - 2019-10-19. PhD thesis. Los Angeles, CA, USA: University of Southern California, 2014. [27] Michael London and Michael Häusser. “Dendritic computation”. In: Annu. Rev. Neurosci. 28 (2005), pp. 503–532. [28] JG Parnavelas. “The origin of cortical neurons”. In: Brazilian journal of medical and biological research 35.12 (2002), pp. 1423–1429. [29] William R Softky and Christof Koch. “The highly irregular ring of cortical cells is inconsistent with temporal integration of random EPSPs”. In: Journal of Neuroscience 13.1 (1993), pp. 334–350. [30] Jose-Manuel Alonso, W Martin Usrey, and R Clay Reid. “Precisely correlated ring in cells of the lateral geniculate nucleus”. In: Nature 383.6603 (1996), pp. 815–819. [31] Charles F Stevens and Anthony M Zador. “Input synchrony and the irregular ring of cortical neurons”. In: Nature neuroscience 1.3 (1998), pp. 210–217. [32] Emilio Salinas and Terrence J Sejnowski. “Impact of correlated synaptic input on output ring rate and variability in simple neuronal models”. In: Journal of neuroscience 20.16 (2000), pp. 6193–6209. [33] Alice C Parker, Jonathan Joshi, Chih-Chieh Hsu, and Nav Aman Deep Singh. “A carbon nanotube implementation of temporal and spatial dendritic computations”. In: 2008 51st Midwest Symposium on Circuits and Systems. IEEE. 2008, pp. 818–821. [34] Zara Sands, Alessandro Grottesi, and Mark SP Sansom. “Voltage-gated ion channels”. In: Current Biology 15.2 (2005), R44–R47. 120 [35] Martin Heine, Anna Ciuraszkiewicz, Andreas Voigt, Jennifer Heck, and Arthur Bikbaev. “Surface dynamics of voltage-gated ion channels”. In: Channels 10.4 (2016), pp. 267–281. [36] Adish Dani, Bo Huang, Joseph Bergan, Catherine Dulac, and Xiaowei Zhuang. “Superresolution imaging of chemical synapses in the brain”. In: Neuron 68.5 (2010), pp. 843–856. [37] Barry W Connors and Michael A Long. “Electrical synapses in the mammalian brain”. In: Annu. Rev. Neurosci. 27 (2004), pp. 393–418. [38] Yousheng Shu, Alvaro Duque, Yuguo Yu, Bilal Haider, and David A McCormick. “Properties of action-potential initiation in neocortical pyramidal cells: evidence from whole cell axon recordings”. In: Journal of neurophysiology 97.1 (2007), 746 bibrangedash /760.doi: 10.1152/jn.00922.2006. [39] Helen C Lai and Lily Y Jan. “The distribution and targeting of neuronal voltage-gated ion channels”. In: Nature Reviews Neuroscience 7.7 (2006), pp. 548–562. [40] Audra Van Wart, James S Trimmer, and Gary Matthews. “Polarized distribution of ion channels within microdomains of the axon initial segment”. In: Journal of Comparative Neurology 500.2 (2007), pp. 339–352. [41] Tatiana Boiko, Audra Van Wart, John H Caldwell, S Rock Levinson, James S Trimmer, and Gary Matthews. “Functional specialization of the axon initial segment by isoform-specic sodium channel targeting”. In: Journal of Neuroscience 23.6 (2003), pp. 2306–2313. [42] Wenqin Hu, Cuiping Tian, Tun Li, Mingpo Yang, Han Hou, and Yousheng Shu. “Distinct contributions of Na v 1.6 and Na v 1.2 in action potential initiation and backpropagation”. In: Nature neuroscience 12.8 (2009), pp. 996–1002. [43] Andrea Lorincz and Zoltan Nusser. “Cell-type-dependent molecular composition of the axon initial segment”. In: Journal of Neuroscience 28.53 (2008), pp. 14329–14340. [44] Anthony M Rush, Sulayman D Dib-Hajj, and Stephen G Waxman. “Electrophysiological properties of two axonal sodium channels, Nav1. 2 and Nav1. 6, expressed in mouse spinal sensory neurones”. In: The Journal of physiology 564.3 (2005), pp. 803–815. [45] Christoph Schmidt-Hieber and Josef Bischofberger. “Fast sodium channel gating supports localized and ecient axonal action potential initiation”. In: Journal of Neuroscience 30.30 (2010), pp. 10233–10242. [46] Jamie Johnston, Ian D Forsythe, and Conny Kopp-Scheinpug. “SYMPOSIUM REVIEW: Going native: voltage-gated potassium channels controlling neuronal excitability”. In: The Journal of physiology 588.17 (Aug. 2010), 3187 bibrangedash /3200.doi: 10.1113/jphysiol.2010.191973. 121 [47] Maarten HP Kole, Johannes J Letzkus, and Greg J Stuart. “Axon initial segment Kv1 channels control axonal action potential waveform and synaptic ecacy”. In: Neuron 55.4 (2007), 633 bibrangedash /647.doi: 10.1016/j.neuron.2007.07.031. [48] Yousheng Shu, Yuguo Yu, Jing Yang, and David A McCormick. “Selective control of cortical axonal spikes by a slowly inactivating K+ current”. In: Proceedings of the National Academy of Sciences 104.27 (2007), pp. 11453–11458. [49] Matthew S Grubb and Juan Burrone. “Activity-dependent relocation of the axon initial segment ne-tunes neuronal excitability”. In: Nature 465.7301 (2010), pp. 1070–1074. [50] Hua-an Tseng, Diana Martinez, and Farzan Nadim. “The frequency preference of neurons and synapses in a recurrent oscillatory network”. In: Journal of Neuroscience 34.38 (2014), pp. 12933–12945. [51] Hiroshi Kuba, Takahiro M Ishii, and Harunori Ohmori. “Axonal site of spike initiation enhances auditory coincidence detection”. In: Nature 444.7122 (2006), pp. 1069–1072. [52] Allan T Gulledge and Jaime J Bravo. “Neuron morphology inuences axon initial segment plasticity”. In: Eneuro 3.1 (2016). [53] Hiroshi Kuba, Ryota Adachi, and Harunori Ohmori. “Activity-dependent and activity-independent development of the axon initial segment”. In: Journal of Neuroscience 34.9 (2014), pp. 3443–3453. [54] Rei Yamada and Hiroshi Kuba. “Structural and functional plasticity at the axon initial segment”. In: Frontiers in cellular neuroscience 10 (2016), p. 250. [55] Brian D Clark, Ethan M Goldberg, and Bernardo Rudy. “Electrogenic tuning of the axon initial segment”. In: The Neuroscientist 15.6 (2009), pp. 651–668. [56] Allyson Howard, Gabor Tamas, and Ivan Soltesz. “Lighting the chandelier: new vistas for axo-axonic cells”. In: Trends in neurosciences 28.6 (2005), pp. 310–316. [57] Alan R Woodru, Laura M McGarry, Tim P Vogels, Melis Inan, Stewart A Anderson, and Rafael Yuste. “State-dependent function of neocortical chandelier cells”. In: Journal of Neuroscience 31.49 (2011), pp. 17872–17886. [58] SR Cobb, EH Buhl, K Halasy, O Paulsen, and P Somogyi. “Synchronization of neuronal activity in hippocampus by individual GABAergic interneurons”. In: Nature 378.6552 (1995), pp. 75–78. [59] Adam S Shai, Costas A Anastassiou, Matthew E Larkum, and Christof Koch. “Physiology of layer 5 pyramidal neurons in mouse primary visual cortex: coincidence detection through bursting”. In: PLoS Comput Biol 11.3 (2015), e1004090. 122 [60] Irene Elices and Pablo Varona. “Asymmetry factors shaping regular and irregular bursting rhythms in central pattern generators”. In: Frontiers in computational neuroscience 11 (2017), p. 9.doi: 10.3389/fncom.2017.00009. [61] Eve Marder and Dirk Bucher. “Central pattern generators and the control of rhythmic movements”. In: Current biology 11.23 (2001), R986–R996.doi: 10.1016/S0960-9822(01)00581-4. [62] Donald C Cooper. “The signicance of action potential bursting in the brain reward circuit”. In: Neurochemistry international 41.5 (2002), pp. 333–340.doi: 10.1016/S0197-0186(02)00068-2. [63] Michael M Halassa and Philip G Haydon. “Integrated brain circuits: astrocytic networks modulate neuronal activity and behavior”. In: Annual review of physiology 72 (2010), pp. 335–355. [64] Gertrudis Perea, Mriganka Sur, and Alfonso Araque. “Neuron-glia networks: integral gear of brain function”. In: Frontiers in cellular neuroscience 8 (2014), p. 378. [65] Mirko Santello, Nicolas Toni, and Andrea Volterra. “Astrocyte function from information processing to cognition and cognitive impairment”. In: Nature neuroscience 22.2 (2019), 154 bibrangedash /166. [66] Maurizio De Pittà, Nicolas Brunel, and Andrea Volterra. “Astrocytes: Orchestrating synaptic plasticity?” In: Neuroscience 323 (2016), pp. 43–61. [67] Tommaso Fellin, Olivier Pascual, Sara Gobbo, Tullio Pozzan, Philip G Haydon, and Giorgio Carmignoto. “Neuronal synchrony mediated by astrocytic glutamate through activation of extrasynaptic NMDA receptors”. In: Neuron 43.5 (2004), pp. 729–743. [68] Robert M Caudle. “Memory in astrocytes: a hypothesis”. In: Theoretical Biology and Medical Modelling 3.1 (2006), pp. 1–10. [69] Ragunathan Padmashri, Anand Suresh, Michael D Boska, and Anna Dunaevsky. “Motor-skill learning is dependent on astrocytic activity”. In: Neural plasticity 2015 (2015). [70] Michael M Halassa, Cedrick Florian, Tommaso Fellin, James R Munoz, So-Young Lee, Ted Abel, Philip G Haydon, and Marcos G Frank. “Astrocytic modulation of sleep homeostasis and cognitive consequences of sleep loss”. In: Neuron 61.2 (2009), pp. 213–219. [71] Tim VP Bliss and Terje Lømo. “Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path”. In: The Journal of physiology 232.2 (1973), pp. 331–356. 123 [72] Christian Lüscher and Robert C Malenka. “NMDA receptor-dependent long-term potentiation and long-term depression (LTP/LTD)”. In: Cold Spring Harbor perspectives in biology 4.6 (2012), a005710. [73] Christian Henneberger, Thomas Papouin, Stéphane HR Oliet, and Dmitri A Rusakov. “Long-term potentiation depends on release of D-serine from astrocytes”. In: Nature 463.7278 (2010), pp. 232–236. [74] Henry Markram, Joachim Lübke, Michael Frotscher, and Bert Sakmann. “Regulation of synaptic ecacy by coincidence of postsynaptic APs and EPSPs”. In: Science 275.5297 (1997), pp. 213–215. [75] Gina G Turrigiano and Sacha B Nelson. “Homeostatic plasticity in the developing nervous system”. In: Nature reviews neuroscience 5.2 (2004), pp. 97–107. [76] Alfonso Araque, Vladimir Parpura, Rita P Sanzgiri, and Philip G Haydon. “Tripartite synapses: glia, the unacknowledged partner”. In: Trends in neurosciences 22.5 (1999), pp. 208–215. [77] Gertrudis Perea and Alfonso Araque. “Astrocytes potentiate transmitter release at single hippocampal synapses”. In: Science 317.5841 (2007), 1083 bibrangedash /1086. [78] Pascal Jourdain, Linda H Bergersen, Khaleel Bhaukaurally, Paola Bezzi, Mirko Santello, Maria Domercq, Carlos Matute, Fiorella Tonello, Vidar Gundersen, and Andrea Volterra. “Glutamate exocytosis from astrocytes controls synaptic strength”. In: Nature neuroscience 10.3 (2007), pp. 331–339. [79] Arvind Kumar, Stefan Rotter, and Ad Aertsen. “Spiking activity propagation in neuronal networks: reconciling dierent perspectives on neural coding”. In: Nature reviews neuroscience 11.9 (2010), pp. 615–627. [80] Edgar D Adrian. “The impulses produced by sensory nerve endings: Part I”. In: The Journal of physiology 61.1 (1926), p. 49. [81] Run Van Rullen and Simon J Thorpe. “Rate coding versus temporal order coding: what the retinal ganglion cells tell the visual cortex”. In: Neural computation 13.6 (2001), pp. 1255–1283. [82] Steven A Prescott and Terrence J Sejnowski. “Spike-rate coding and spike-time coding are aected oppositely by dierent adaptation mechanisms”. In: Journal of Neuroscience 28.50 (2008), pp. 13649–13661. [83] Alexander P Nikitin, Nigel G Stocks, Robert P Morse, and Mark D McDonnell. “Neural population coding is optimized by discrete tuning curves”. In: Physical review letters 103.13 (2009), p. 138101. 124 [84] Daniel A Butts, Chong Weng, Jianzhong Jin, Chun-I Yeh, Nicholas A Lesica, Jose-Manuel Alonso, and Garrett B Stanley. “Temporal precision in the neural code and the timescales of natural vision”. In: Nature 449.7158 (2007), pp. 92–95. [85] Xiaoqin Wang, Thomas Lu, Daniel Bendor, and Edward Bartlett. “Neural coding of temporal information in auditory thalamus and cortex”. In: Neuroscience 154.1 (2008), pp. 294–303. [86] Roozbeh Kiani, Hossein Esteky, and Keiji Tanaka. “Dierences in onset latency of macaque inferotemporal neural responses to primate and non-primate faces”. In:Journal of neurophysiology 94.2 (2005), pp. 1587–1596. [87] John Huxter, Neil Burgess, and John O’Keefe. “Independent rate and temporal coding in hippocampal pyramidal cells”. In: Nature 425.6960 (2003), pp. 828–832. [88] Alan L Hodgkin, Andrew F Huxley, and Bernard Katz. “Measurement of current-voltage relations in the membrane of the giant axon of Loligo”. In: The Journal of physiology 116.4 (1952), p. 424. [89] Alan L Hodgkin. “The local electric changes associated with repetitive action in a non-medullated axon”. In: The Journal of physiology 107.2 (1948), p. 165. [90] Grégory Faye. “An introduction to bifurcation theory”. In: NeuroMathComp Laboratory, INRIA, Sophia Antipolis, CNRS, ENS Paris, France (2011). [91] Eugene M Izhikevich. “Which model to use for cortical spiking neurons?” In: IEEE transactions on neural networks 15.5 (2004), pp. 1063–1070. [92] Giacomo Indiveri, Bernabé Linares-Barranco, Tara Julia Hamilton, André van Schaik, Ralph Etienne-Cummings, Tobi Delbruck, Shih-Chii Liu, Piotr Dudek, Philipp Häiger, Sylvie Renaud, Johannes Schemmel, Gert Cauwenberghs, John Arthur, Kai Hynna, Fopefolu Folowosele, Sylvain Saighi, Teresa Serrano-Gotarredona, Jayawan Wijekoon, Yingxue Wang, and Kwabena Boahen. “Neuromorphic silicon neuron circuits”. In: Frontiers in neuroscience 5 (May 2011), p. 73.issn: 1662-453X.doi: 10.3389/fnins.2011.00073. [93] Giacomo Indiveri and Shih-Chii Liu. “Memory and information processing in neuromorphic systems”. In: Proceedings of the IEEE 103.8 (June 2015), pp. 1379–1397. issn: 1558-2256.doi: 10.1109/JPROC.2015.2444094. [94] Ethan Farquhar and Paul Hasler. “A bio-physically inspired silicon neuron”. In: IEEE Transactions on Circuits and Systems I: Regular Papers 52.3 (2005), 477 bibrangedash /488. 125 [95] Mohammad Mahvash and Alice C Parker. “Synaptic variability in a cortical neuromorphic circuit”. In: IEEE transactions on neural networks and learning systems 24.3 (Jan. 2013), pp. 397–409.issn: 2162-2388.doi: 10.1109/TNNLS.2012.2231879. [96] Giacomo Indiveri, Fabio Stefanini, and Elisabetta Chicca. “Spike-based learning with a generalized integrate and re silicon neuron”. In: Proceedings of 2010 IEEE International Symposium on Circuits and Systems. Paris, France: IEEE, 2010, pp. 1951–1954.doi: 10.1109/ISCAS.2010.5536980. [97] Yilda Irizarry-Valle and Alice Cline Parker. “An astrocyte neuromorphic circuit that inuences neuronal phase synchrony”. In: IEEE transactions on biomedical circuits and systems 9.2 (2015), pp. 175–187.issn: 1940-9990.doi: 10.1109/TBCAS.2015.2417580. [98] Theodore Yu, Terrence J Sejnowski, and Gert Cauwenberghs. “Biophysical neural spiking, bursting, and excitability dynamics in recongurable analog VLSI”. In: IEEE transactions on biomedical circuits and systems 5.5 (2011), pp. 420–429.doi: 10.1109/TBCAS.2011.2169794. [99] Theodore Yu and Gert Cauwenberghs. “Analog VLSI neuromorphic network with programmable membrane channel kinetics”. In: 2009 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE. 2009, 349 bibrangedash /352. [100] Mario F Simoni, Gennady S Cymbalyuk, Michael Elliott Sorensen, Ronald L Calabrese, and Stephen P DeWeerth. “A multiconductance silicon neuron with biologically matched dynamics”. In: IEEE Transactions on Biomedical Engineering 51.2 (2004), 342 bibrangedash /354. [101] Sylvain Saïghi, Yannick Bornat, Jean Tomas, and Sylvie Renaud. “Neuromimetic ICs and system for parameters extraction in biological neuron models”. In: 2006 IEEE International Symposium on Circuits and Systems. IEEE. 2006, 5 bibrangedash /pp. [102] Venkat Rangan, Abhishek Ghosh, Vladimir Aparin, and Gert Cauwenberghs. “A subthreshold aVLSI implementation of the Izhikevich simple neuron model”. In: 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology. IEEE. 2010, 4164 bibrangedash /4167. [103] Jonathan Joshi, Alice C Parker, and Chih-Chieh Hsu. “A carbon nanotube cortical neuron with spike-timing-dependent plasticity”. In: 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Minneapolis, MN, USA: IEEE, 2009, pp. 1651–1654.doi: 10.1109/IEMBS.2009.5333251. 126 [104] Kun Yue, Yizhou Liu, Roger K Lake, and Alice C Parker. “A brain-plausible neuromorphic on-the-y learning system implemented with magnetic domain wall analog memristors”. In: Science advances 5.4 (2019), eaau8170.doi: 10.1126/sciadv.aau8170. [105] Saeid Barzegarjalali and Alice C Parker. “An analog neural network that learns Sudoku-like puzzle rules”. In: 2016 Future Technologies Conference (FTC). San Francisco, CA, USA: IEEE, 2016, pp. 838–847.doi: 10.1109/FTC.2016.7821701. [106] Rebecca K Lee and Alice C Parker. “An Electronic Neuron with Input-Specic Spiking”. In: 2019 International Joint Conference on Neural Networks (IJCNN). Budapest, Hungary, Hungary: IEEE, 2019, pp. 1–8.doi: 10.1109/IJCNN.2019.8852276. [107] Kun Yue, Xiaoyu Wang, Jay Jadav, Akshay Vartak, and Alice C. Parker. “Analog Neurons That Signal with Spiking Frequencies”. In: Proceedings of the International Conference on Neuromorphic Systems. ICONS ’19. Knoxville, TN, USA: Association for Computing Machinery, 2019.isbn: 9781450376808.doi: 10.1145/3354265.3354273. [108] Jonathan Joshi. Plasticity in CMOS neuromorphic circuits. University of Southern California, 2013. [109] Anthony N Burkitt. “A review of the integrate-and-re neuron model: I. Homogeneous synaptic input”. In: Biological cybernetics 95.1 (2006), pp. 1–19.doi: 10.1007/s00422-006-0068-6. [110] Alon Polsky, Bartlett W Mel, and Jackie Schiller. “Computational subunits in thin dendrites of pyramidal cells”. In: Nature neuroscience 7.6 (2004), pp. 621–627. [111] Gonzalo G de Polavieja, Annette Harsch, Ingo Kleppe, Hugh PC Robinson, and Mikko Juusola. “Stimulus history reliably shapes action potential waveforms of cortical neurons”. In: Journal of Neuroscience 25.23 (2005), pp. 5657–5665.doi: 10.1523/JNEUROSCI.0242-05.2005. [112] JR Huguenard. “Low-threshold calcium currents in central nervous system neurons”. In: Annual review of physiology 58.1 (1996), pp. 329–348.doi: 10.1146/annurev.ph.58.030196.001553. [113] Rony Azouz and Charles M Gray. “Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo”. In: Proceedings of the National Academy of Sciences 97.14 (2000), pp. 8110–8115.doi: 10.1073/pnas.130200797. [114] DA Henze and G Buzsáki. “Action potential threshold of hippocampal pyramidal cells in vivo is increased by recent spiking activity”. In: Neuroscience 105.1 (2001), pp. 121–130. doi: 10.1016/S0306-4522(01)00167-1. 127 [115] Rony Azouz and Charles M Gray. “Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical”. In: (). [116] Michael A Farries, Hitoshi Kita, and Charles J Wilson. “Dynamic spike threshold and zero membrane slope conductance shape the response of subthalamic neurons to cortical input”. In: Journal of Neuroscience 30.39 (2010), pp. 13180–13191. [117] Jonathan Platkiewicz and Romain Brette. “A Threshold Equation for Action Potential Initiation”. In: PLOS Computational Biology 6.7 (2010), pp. 1–16.doi: 10.1371/journal.pcbi.1000850. [118] Rami A. Alzahrani and Alice C. Parker. “Neuromorphic Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling”. In: International ConferenceonNeuromorphicSystems2020. ICONS 2020. Oak Ridge, TN, USA: Association for Computing Machinery, 2020.isbn: 9781450388511.doi: 10.1145/3407197.3407204. [119] Stefano Buccelli, Yannick Bornat, Ilaria Colombi, Matthieu Ambroise, Laura Martines, Valentina Pasquale, Marta Bisio, Jacopo Tessadori, Przemysław Nowak, Filippo Grassia, et al. “A neuromorphic prosthesis to restore communication in neuronal networks”. In: IScience 19 (2019), 402 bibrangedash /414. [120] Hanna Keren, Johannes Partzsch, Shimon Marom, and Christian G Mayr. “A biohybrid setup for coupling biological and neuromorphic neural networks”. In: Frontiers in neuroscience 13 (2019), p. 432. [121] Timothee Levi, Takuya Nanami, Atsuya Tange, Kazuyuki Aihara, and Takashi Kohno. “Development and applications of biomimetic neuronal networks toward brainmorphic articial intelligence”. In: IEEE Transactions on Circuits and Systems II: Express Briefs 65.5 (2018), 577 bibrangedash /581. [122] Massimo Antonio Sivilotti.WiringconsiderationsinanalogVLSIsystems,withapplication to eld-programmable networks. 1991. [123] Misha Mahowald. “VLSI analogs of neuronal visual processing: a synthesis of form and function”. PhD thesis. California Institute of Technology Pasadena, 1992. [124] Michael N Shadlen and William T Newsome. “Noise, neural codes and cortical organization”. In: Current opinion in neurobiology 4.4 (1994), pp. 569–579. [125] Peter König, Andreas K Engel, and Wolf Singer. “Integrator or coincidence detector? The role of the cortical neuron revisited”. In: Trends in neurosciences 19.4 (1996), pp. 130–137. 128 [126] Michael N Shadlen and William T Newsome. “The variable discharge of cortical neurons: implications for connectivity, computation, and information coding”. In: Journal of neuroscience 18.10 (1998), pp. 3870–3896. [127] R Christopher Decharms and Anthony Zador. “Neural representation and the cortical code”. In: Annual review of neuroscience 23.1 (2000), 613 bibrangedash /647. [128] Stephane A Roy and Kevin D Alloway. “Coincidence detection or temporal integration? What the neurons in somatosensory cortex are doing”. In: Journal of Neuroscience 21.7 (2001), pp. 2462–2473. [129] Greg J Stuart and Michael Häusser. “Dendritic coincidence detection of EPSPs and action potentials”. In: Nature neuroscience 4.1 (2001), pp. 63–71. [130] Matthew E Larkum, Walter Senn, and Hans-R Lüscher. “Top-down dendritic input increases the gain of layer 5 pyramidal neurons”. In: Cerebral cortex 14.10 (2004), pp. 1059–1070. [131] C-C Hsu and A. C. Parker. “Dynamic Spike Threshold and Nonlinear Dendritic Computation for Coincidence Detection in Neuromorphic Circuits”. In: 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC’14). IEEE. 2014. [132] Robert S Zucker. “Calcium-and activity-dependent synaptic plasticity”. In: Current opinion in neurobiology 9.3 (1999), pp. 305–313. [133] Gordon M Shepherd. The synaptic organization of the brain. Oxford university press, 2004. [134] Wade G Regehr and David W Tank. “Calcium concentration dynamics produced by synaptic activation of CA1 hippocampal pyramidal cells”. In: Journal of Neuroscience 12.11 (1992), pp. 4202–4223. [135] Jonathan Joshi, Chih-Chieh Hsu, Alice C Parker, and Pankaj Deshmukh. “A carbon nanotube cortical neuron with excitatory and inhibitory dendritic computations”. In: 2009 IEEE/NIH Life Science Systems and Applications Workshop. IEEE. 2009, pp. 133–136. [136] H Chaoui. “CMOS analogue adder”. In: Electronics Letters 31.3 (1995), pp. 180–181. [137] Pezhman Mamdouh and Alice C Parker. “A switched-capacitor dendritic arbor for low-power neuromorphic applications”. In: 2017 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE. 2017, 1 bibrangedash /4. 129 [138] Céline Roussel, Thomas Erneux, SN Schimann, and David Gall. “Modulation of neuronal excitability by intracellular calcium buering: from spiking to bursting”. In: Cell Calcium 39.5 (2006), pp. 455–466. [139] Mary B Kennedy. “Regulation of neuronal function by calcium”. In: Trends in neurosciences 12.11 (1989), pp. 417–420. [140] Michael J Berridge, Martin D Bootman, and Peter Lipp. “Calcium-a life and death signal”. In: Nature 395.6703 (1998), pp. 645–648. [141] Idongesit E Ebong and Pinaki Mazumder. “CMOS and memristor-based neural network design for position detection”. In: Proceedings of the IEEE 100.6 (2011), pp. 2050–2060. [142] Kun Yue and Alice C Parker. “Analog Neurons with Dopamine-Modulated STDP”. In: 2019 IEEE Biomedical Circuits and Systems Conference (BioCAS). IEEE. 2019, pp. 1–4. [143] Kun Yue, Yizhou Liu, Roger K Lake, and Alice C Parker. “A brain-plausible neuromorphic on-the-y learning system implemented with magnetic domain wall analog memristors”. In: Science advances 5.4 (2019), eaau8170. [144] Simeon A Bamford. “Synaptic rewiring in neuromorphic VLSI for topographic map formation”. PhD thesis. The University of Edinburgh, 2009. [145] Simeon A Bamford, Alan F Murray, and David J Willshaw. “Large developing receptive elds using a distributed and locally reprogrammable address–event receiver”. In: IEEE transactions on neural networks 21.2 (2010), pp. 286–304. [146] Yilda Irizarry-Valle, Alice C Parker, and Jonathan Joshi. “A CMOS neuromorphic approach to emulate neuro-astrocyte interactions”. In: The 2013 International Joint Conference on Neural Networks (IJCNN). IEEE. 2013, pp. 1–7. [147] Mahnaz Ranjbar and Mahmood Amiri. “An analog astrocyte–neuron interaction circuit for neuromorphic applications”. In: Journal of Computational Electronics 14.3 (2015), pp. 694–706. [148] Todd A Fiacco and Ken D McCarthy. “Intracellular astrocyte calcium waves in situ increase the frequency of spontaneous AMPA receptor currents in CA1 pyramidal neurons”. In: Journal of Neuroscience 24.3 (2004), pp. 722–732. [149] Rogier Min, Mirko Santello, and Thomas Nevian. “The computational power of astrocyte mediated synaptic plasticity”. In: Frontiers in computational neuroscience 6 (2012), p. 93. [150] Rami A. Alzahrani and Alice C. Parker. “Neuromorphic Autonomous Spiking Encoding”. In: 2021 IEEE International Symposium on Circuits and Systems (ISCAS). 2021, pp. 1–5. doi: 10.1109/ISCAS51556.2021.9401769. 130 [151] S Murray Sherman. “Tonic and burst ring: dual modes of thalamocortical relay”. In: Trends in neurosciences 24.2 (2001), pp. 122–126. [152] John E Lisman. “Bursts as a unit of neural information: making unreliable synapses reliable”. In: Trends in neurosciences 20.1 (1997), pp. 38–43. [153] Jos J Eggermont and Geo M Smith. “Burst-ring sharpens frequency-tuning in primary auditory cortex.” In: Neuroreport 7.3 (1996), pp. 753–757. [154] Rüdiger Krahe and Fabrizio Gabbiani. “Burst ring in sensory systems”. In: Nature Reviews Neuroscience 5.1 (2004), pp. 13–23. [155] Lloyd A Jeress. “A place theory of sound localization.” In: Journal of comparative and physiological psychology 41.1 (1948), p. 35. [156] Benedikt Grothe, Michael Pecka, and David McAlpine. “Mechanisms of sound localization in mammals”. In: Physiological reviews 90.3 (2010), pp. 983–1012. [157] Hagai Agmon-Snir, Catherine E Carr, and John Rinzel. “The role of dendrites in auditory coincidence detection”. In: Nature 393.6682 (1998), pp. 268–272. [158] Catherine E Carr and Masakazu Konishi. “Axonal delay lines for time measurement in the owl’s brainstem”. In: Proceedings of the National Academy of Sciences 85.21 (1988), pp. 8311–8315. [159] Brian J Fischer and Armin H Seidl. “Resolution of interaural time dierences in the avian sound localization circuit—a modeling study”. In: Frontiers in computational neuroscience 8 (2014), p. 99. [160] Caleb Rascon and Ivan Meza. “Localization of sound sources in robotics: A review”. In: Robotics and Autonomous Systems 96 (2017), pp. 184–210. [161] Chao Huang, Andrey Resnik, Tansu Celikel, and Bernhard Englitz. “Adaptive spike threshold enables robust and temporally precise neuronal encoding”. In: PLoS computational biology 12.6 (2016), e1004984. [162] N Qiao, H Mostafa, F Corradi, M Osswald, F Stefanini, D Sumislawska, and G Indiveri. A recongurable on-line learning spiking neuromorphic processor comprising 256 neurons and 128 K synapses Front. 2015. 131

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Creator Alzahrani, Rami A. (author)

Core Title Dynamic neuronal encoding in neuromorphic circuits

Contributor Electronically uploaded by the author (provenance)

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Degree Conferral Date 2022-05

Publication Date 07/28/2023

Defense Date 01/21/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag decoding a spike origin,electronics rich behavioral neurons,neuromorphic circuits,neuromorphic engineering,neuronal code,neuronal networks,OAI-PMH Harvest

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Language English

Advisor Parker, Alice C. (committee chair), Kesselman, Carl (committee member), Wang, Han (committee member), Yang, Joshua (committee member), Zhou, Chongwu (committee member)

Creator Email eng.ramizahrany@gmail.com,ralzahra@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC110575735

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Rights Alzahrani, Rami A.

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Abstract (if available)

Abstract Biological neurons signal each other in a rich and complex manner to perform complex cognitive computing tasks in real-time; such biological capability enables the interdisciplinary field of neuromorphic engineering (NE) to implement various information processing systems to perform brain-like computations intelligently and autonomously, utilizing distributed memory-processing architecture. Our neuromorphic work focuses on modeling rich neural encoding behaviors. Using electronics as the basis of our neuromorphic approach, we developed circuits that demonstrate different neural behaviors depending on various input spiking patterns (neural codes) from the presynaptic neurons. We achieve that by creating dynamic neural encoding circuits that encode various presynaptic spiking inputs into different postsynaptic spiking outputs utilizing the Axon Initial Segment’s (AIS) modulation and processing capabilities. ❧ The circuits are constructed based on the biophysical mechanisms of various voltage-gated ion channels, such as the activation/deactivation of Calcium (Ca+2), Potassium (K+), and Sodium (Na+) ion channels by which our intended circuits emulate various neural responses. The generated spiking patterns are consistent with the spiking patterns produced by the Izhikevich mathematical model describing biological neuronal responses. Such patterns include regular spikes (RS), phasic spikes (PS), tonic bursts (TB), single burst per stimulus (SB), class-1 excitable spikes (CS1), subthreshold oscillations (OSC), depolarization after potential (DAP), integrator (INT), and mixed-mode (MIX). Furthermore, we show how our circuits emulate other biological behaviors such as the neural threshold variability. ❧ We posit that such dynamic neural encoding is essential in enabling autonomous behavioral electronic systems for the future technology of artificially intelligent systems. Through circuit simulations, we show that our proposed neuromorphic circuits can autonomously encode various received presynaptic spikes and their timing of occurrence into different postsynaptic spiking patterns using the coincident encoding behavior of Layer 5 Pyramidal Neurons (L5PN) as an example. In other words, our neural circuits can detect synchronized presynaptic inputs through the generation of burst spiking patterns, which suggests that the timing of input spiking is vital in the encoding of neural information. Furthermore, we show how postsynaptic neurons exhibit complex behavioral responses resembling different received spiking patterns from presynaptic neurons using our electronic dynamical neural encoding model.❧ Moreover, based on our developed hardware-based theory of AIS modulation, we describe how modeling a dynamic encoding in electronics can be vital in enhancing the processing capability of a given neuromorphic neural network. Such capability includes the implementation of pattern-specific filtering responses. The term filtering refers to the process by which a neuron responds selectively to distinct presynaptic patterns by which the classification and other pattern-specific processes in a neural network are accomplished. To examine such processing capability, we built an electronic experimental neuronal network capable of decoding information regarding the origin of an AP from the output of the neuronal network employing five different electronic neuron filtering models, including all-patterns-pass neuron (NA), bursts-pass neuron (NB ), spikes-pass neuron (NS ), phase-pass neuron (NP ), and bursts-width-pass topology (NW ).