Role of Noise in Spontaneous Activity of Networks of Neurons on Patterned Silicon Emulated by Noise–activated CMOS Neural Nanoelectronic Circuits

Background noise in biological cortical microcircuits constitutes a powerful resource to assess their computational tasks, including, for instance, the synchronization of spiking activity, the enhancement of the speed of information transmission, and the minimization of the corruption of signals. We explore the correlation of spontaneous firing activity of ≈ 100 biological neurons adhering to engineered scaffolds by governing the number of functionalized patterned connection pathways among groups of neurons. We then emulate the biological system by a series of noise-activated silicon neural network simulations. We show that by suitably tuning both the amplitude of noise and the number of synapses between the silicon neurons, the same controlled correlation of the biological population is achieved. Our results extend to a realistic silicon nanoelectronics neuron design using noise injection to be exploited in artificial spiking neural networks such as liquid state machines and recurrent neural networks for stochastic computation.

In this regard, networks of stochastic spiking neurons have been used for solving constraint satisfaction problems where noise is believed to play a key role in the problem-solving ability of the human brain [42][43][44][45]. For instance, neurons' activity is correlated in the isolated regions of the auditory cortex to which the neuron

Methods
In this section, we introduce our methods for studying noise propagation in distinct neuronal regions. First, we discuss the experimental set-up for a group of biological neurons. In the second section, we design a quasiequivalent setting for the artificial model of the experimental part to perform predictions on the dynamics of the real network.

Experimental setup for investigating noise propagation in biological neural circuits
Biological neurons, which are obtained from animal brains [63] or stem cell differentiation [64], can be cultivated in-vitro under a defined physicochemical condition. Neurons are adherent cells, and hence an appropriate scaffold is essential for their growth. A number of microfabrication methods, including semiconductor lithography or soft lithography, have been utilized to engineer the scaffold to control the growth area at single-cell or multi-cellular scales [56,[65][66][67][68].
After approximately a week in culture, neuronal networks begin to form synaptic connections and spontaneously generate bursting activity that is highly synchronized within the network [29,56]. We previously showed using micropatterned rat cortical neurons that neuronal correlation in the spontaneous bursting activity decreases with the size of the network [56]. This section uses a similar culture to show that correlation between a group of living neurons can be regulated by altering the number of neurite guidance pathways that bridge neuron islands. The experimental results and their analyses herein are obtained from independent datasets from those presented in a previous publication [69].
The materials and methods used in fabricating micropatterned substrates, culturing primary neurons, and recording spontaneous neural activity have been described previously [56,68]. Briefly, poly − D − lysine and 2 − [methoxy (polyethleneoxy)propyl]trimethoxysilane were used as cell-permissive and non-permissive layers, respectively, and were patterned on a glass coverslip using electron-beam lithography. The micropatterns used in the current experiment consisted of four square islands of 200 × 200 μm 2 and 5 μm-wide lines that interconnect the island. Three geometries with a different number of interconnecting lines were compared, i.e., no-bond and triple-bond structures, which have zero and three lines between a pair of islands.
Primary neurons were obtained from embryonic rat cortices, plated on the micropatterned coverslips, and cultured for ten days. Then, the cells were loaded with the fluorescence calcium indicator Fluo-4 AM (Molecular Probes), and their spontaneous activity was measured by calcium imaging. Images were obtained every 200ms for 6 or 9 min using an inverted microscope (Nikon Eclipse TE300) equipped with a 20 × objective lens (numerical aperture, 0.75) and a cooled-CCD camera (Hamamatsu Orca-ER). The image sequences were later analyzed offline using the ImageJ (NIH) and custom-written Perl programs [56].
Representative phase-contrast micrographs of living neuronal networks grown on the micropatterned substrate are shown in figures 1(B) and 1(C). Neurons adhered and grew neurites only on the permissive domains. Very little non-specific adhesion or neurite growth was observed in the non-permissive area. The number of cells in each network was counted from the images. It was evaluated to be 148, 143, and 154 cells for the no-bond, single-bond, and triple-bond structures.
Next, spontaneous neural activity was measured by fluorescence calcium imaging, and the effect of changing the number of interconnections between neuronal islands was analyzed by evaluating the Pearson correlation coefficient. The correlation coefficient of neuron pairs is calculated using the Pearson correlation coefficient equation described in appendix B. We discuss our observations thoroughly in the Results section. 2.2. CMOS artificial neural networks setting for quantifying the rate of correlated-activity in distinct neuronal islands To emulate the noise activation of biological neurons, we first define a biologically plausible silicon neuron model so that response to electronic noise injection is realistic. The neuron is designed based on a simplified Hodgkin-Huxley (HH) spiking neuron model [71], which is designed and simulated in a 0.35 μm CMOS technology [72]. A sodium-potassium conductance-based model of spiking neurons biased in the sub-threshold regime is implemented. Neurons are designed with a lower time-constant to spike three orders of magnitude faster than real neurons (more details on the implementation are provided in appendix A). Such speed-mode implementation allows faster data processing, requires smaller capacitor values, and as a result, reduces the physical size of the circuit. To model a background noise, we designed a voltage to current converter capable of delivering a zero-mean white and pink current noise to the neurons (see appendix A). Typically, noise is naturally present in CMOS devices, ranging from white and pink (1/f ) noise [73], to telegraph noise [74][75][76], to 1/f 1/2 noise [77,78], rooted in the atomistic scale. The most straightforward strategy consists of amplifying such natural noise and exploiting it in the circuit by injection in the selected nodes.
Synapses are junctions where neurons communicate with each other. Chemical synapses can be either excitatory or inhibitory. We adopted a synapse circuit model, called CMOS differential-pair integrator (DPI) [79], to wire neurons.
To emulate and reverse-engineer the experimental system topology constructed from four neuronal islands of biological neurons adhering stick to the patterned region, we designed and simulated a network of spiking neurons comprising 64 silicon neurons and 1024 DPI synapses in the presence of white background noise. Individual islands comprising 16 silicon neurons and 256 synapses are designed and are exposed to white noise. Next, the correlation of spiking activity of the four neuronal islands is controlled by tuning the number of the equivalent of interneurons connecting distinct neuronal islands and the number of synapses excited by the same output interneuron. The observations are quantitatively accounted for by employing a correlation coefficient matrix of stochastic events (Appendix B for methods). Figure 3(A) represents a network of 16 silicon neurons and 256 reconfigurable synapses. To be consistent with networks of typical hybrid systems of real neurons on artificial solid-state structures, we adopted a ratio between inhibitory and excitatory synapses in the range 5% to 10%. In our case, such a ratio is set to 8%. The output of each neuron is connected to 16 synapses presented in a row in order to be able to connect to the other 15 neurons and themselves. The output of a neuron is connected directly to the input of each synapse. The synapse output is connected to the input nodes of the next neurons through an nMOS switch. By choosing whether the switch is closed or open, one can connect arbitrarily any neuron to the others. White noise is applied through the V-I converter to each neuron. A single source of noise (noise of an on-chip resistor) distributes the noise to all neurons of an island to emulate potential local fluctuations affecting all the neurons similarly within the same neuronal island. A distinct noise generator solicits each island to emulate distinct regions with no common local potential fluctuations.
A random network topology (figure 3(C)) is configured on the 16-neuron network. The random structure is selected in each island by the random permutation function in MATLAB. Where n random synapse IDs are selected out of 256 synapses in each neuronal island. We define four islands of such 16-neuron SNN as shown in figure 3(B). Each island of neurons consists of different network topologies. In each island, 92% of the synapses are excitatory and 8% inhibitory, which emulates a reasonable average ratio typical of realistic biological networks of spiking neurons.
In figure 3(B), circles and hexagons represent neurons and synapses, respectively. The green synapses are those activated. For instance, in row number 4 (R4) of island 1 (top left), the 10th synapse is green, indicating that neuron N4 stimulates neuron N10 through that synapse. In the first island (top left), we implement a lowdensity connection in a random topology By 25 connections; on the contrary, in the second island (top right), we implement a higher density of 50 connections in order to demonstrate the influence of the variation of the number of connections of each island on the correlation of the spiking activities. Such difference is reflected in figure 5(A), where the correlation of island 1 is lighter than that for island 2.
We adopt the same random network topology on the third (bottom left) and fourth (bottom right) islands to observe the variation of spiking activity of neurons when we inject uncorrelated sources of noise to the same network topology. As described, all neurons in each island are connected to a single source of the noise.

Correlation-rate of spontaneous activity of groups of neurons
The correlation coefficient matrix is calculated for three different experiments and graphically represented in figure 2. In the no-bond structure, the correlation of the synchronized bursting activity was high only for neurons belonging to the same island and were otherwise nearly zero. By connecting the islands of biological neurons by an individual connection, the correlation among different islands is switched. Finally, in the triplebond structure, the correlation is high across nearly all neuron pairs.
These results confirm the findings reported in [69] and were used as reference datasets for the numerical and circuit modeling (see sections 3.2 and 3.3).
The observations indicate that the neural correlation can be controlled using micropatterned substrates by changing the number of interconnections. This is in agreement with a previous work which showed that the likelihood of an activity being transferred between two neuronal populations increased with the number of interconnecting micro tunnels in a microfluidic device [80].
The spontaneous activity in biological neuronal networks is triggered by the spontaneous release of either synaptic vesicles or ion channel stochasticity, which temporally induce fluctuation of the neuronal membrane potential. It is interesting from an engineering point of view that up to 80% of the metabolic energy consumed in the brain seems to be used in maintaining the spontaneous activity [81]. Their possible role in neural computation has been suggested to include learning [23], event directionality [24], stochastic resonance [25], management of binocular rivalry [27], and coherence [29], just to mention some examples. In the next section, we design an artificial version of this experiment to evaluate and predict some attributes of the system. Notwithstanding, a full understanding of the functional role of such an energy-consuming background activity awaits further research.

Simulation of Islands of Silicon Neurons with Internal Low-Density Connectivity
We aim to characterize the influence of spike trains generated by distinct regions and observe how the correlation among spiking activity is created thanks to the propagation of the signaling on the receiving neuron's surrounding network. The correlation propagates thanks to interneurons' equivalent, and synchronization of spiking activity is rapidly achieved when few inter-connective synapses are employed.
To investigate the variation of correlation between the spiking activities in different islands, we perform simulations by using the network represented in figure 3(B).
In the first configuration, the islands of neurons are not mutually connected. By applying uncorrelated current-mode white noise with a power of 200 pA Hz to the islands for a simulation time of 240 μs, we obtain the spiking activity of the neurons represented in figure 3(D). As a result, we observe highly correlated firing activity only from neurons of the same island.
In the second simulated configuration, four islands of neurons are connected in a ring topology through interconnected synapses, such that island one is connected to island two by means of 8 one-to-one interneurons via unidirectional synapses, in the same way, the island two is connected to island 4, the 4 to the 3, and the 3 to the island 1. In such ring topology, we achieved the spiking activity of the neurons represented in figure 3(E), which shows correlation.
In order to assess the correlation quantitatively, we explore the correlation coefficient matrix. Figure 4 illustrates the correlation coefficient matrices of spiking activity of islands of silicon neurons in the mentioned simulations. In matrices, the correlation spectrum color-bar represents uncorrelated regions with blue and highly correlated regions with dark red.
When the islands are not connected (figure 4(A)), as a result of applying the same noise to all the neurons of an island, mutually connected by synapses, the self-spiking activity of the islands is highly correlated while, like in the case of biological neurons, neuron activity across different islands is not correlated.
When islands are connected (figure 4(B)) using synapses, each island's activity spreads to neighboring islands, a high correlation involves all the neurons of the network. Qualitatively, to observe a similar correlation to the biological case with only one pathway, eight one-to-one connections are needed, suggesting that either  figure 1(C). The color-bar shows the amount of correlation coefficient from uncorrelated regions (blue) to highly correlated areas (dark red). In case A, the islands are not connected and the correlation is significant only for neurons within the same island. In cases B and C, the correlation progressively increases by adding 1 and 3 pathway connections respectively among the islands in a ring topology. several neurites connect the biological neuron islands or several synapses per neuron are involved. The condition of multiple synapses associated with the same neuron is developed in the next section.

Simulation of islands of neurons with multiple synapses
To achieve a high correlation between the island by employing only a few neuron connections, the microconnectome of the artificial interneurons here consists of adding multiple synapses to the interneurons. Figures 5(A) to (D) represents the correlation matrix of the activity of the neurons in cases of isolated islands, which refer to the connections represented in 5(E) to (H) respectively. Cases A-E provide the background of the correlation when there is no connection among neurons of distinct islands. Cases B-F represent a limiting case when one neuron excited by three synapses solicits 15 over the 16 neurons of the neighboring island (3 × 15). It is worth noting that even if almost all the neurons of the next island are solicited, the correlation does not saturate among distinct islands. At a microscopic level, we may interpret this due to the difficulty of affecting by an individual spiking signal the activity within the island, whose neurons are synchronously solicited by the local noise. The case C-G with three connections of kind (3 × 8) shows a much stronger correlation even if the number of synapses to input neurons on the next islands are cut off a half, thanks to the triple excitation connection. Such a condition provides a result that is closer to the 3N pathway connection of biological islands. The difference from the previous case can be interpreted by the combined action of more distinct input signals interfering with the synchronous activity within the island, therefore partially breaking its correlated spiking activity and therefore leaving room for the action of the other input signals. Finally, the case D-H of three (9 × 15) connected neurons represents again a limiting case where almost all the neurons of the next islands are fed, which exhibits even higher (but not saturated despite the connection to all the neurons of the next island) correlation. The lack of saturation is a consequence of having imposed distinct noise fluctuations on all the neurons of each island, a simplified biological system model. The biological system and the artificial CMOS system ignited by noise, as discussed above, behave very similarly. The findings suggest that in the biological islands, the spontaneous connections along the pathways by neurites of neurons in distinct islands, despite the difficulties of the process adopted from Sect. 2, are very likely and very efficient. In the spirit of indicating future refinements of the noise injection in artificial neuron system, we also observe that the assumption that a single local noise affects the sub-populations of neurons may be relaxed by reducing the influence radius of each source of noise to only first neighbors.

Conclusions
To conclude, we prepared and experimentally characterized a biological system comprising four populations of about 25 neurons each, attached to engineered scaffolds, and mutually connected in a ring topology by pathways where neurites can grow. Neurons adhered and grew neurites only on the permissive domains defined by the scaffolds and the pathways. The number of neurites is tuned by varying the number of available pathways to control the degree of correlation of the spiking activity among the neurons of distinct populations. Three connections per pair of populations are sufficient to spread an almost complete correlation of the whole network. Next, we designed and simulated the artificial version of such a system by an artificial network of CMOS silicon neurons operating in speed mode. The silicon system includes both excitatory and inhibitory synapses, and it is equipped with interneurons to enable communication between distinct islands, which induce spontaneous firing into higher correlation. We proposed a robust implementation of artificial silicon neurons by designing compact electronic CMOS microcircuits equipped with white and pink noise generators. We employed noise to activate the spontaneous firing activity of the neurons, and we characterized the statistics of the response of individual neurons to noise. Finally, the simulations of a ring of four noise-activated silicon islands are assessed by varying the number of interneurons and synapses. The correlation between distinct islands is more effectively increased by adding synapses to interneurons than additional independent interneurons. The results observed on the artificial neuron system suggest that the biological network is effective in the formation of synapses during its growth after the adhesion process on the micropatterned substrate.  [72]. Capacitor C m stands for the membrane capacitance. When a positive input current stimulates the capacitance, it starts to be charged, and consequently, the membrane potential, V m , increases. When V m reaches V Na th , transistor M1 turns on and sinks current I M1 . The current I M1 is mirrored by the transistor M4 and creates the sodium activation current, I Na which builds up the up-swing of the action potential. Simultaneously, I M1 is also mirrored by the transistor M5 to charge the capacitor C N , thus increasing exponentially the current I K of the transistor M6. Therefore, V m quickly drops to its resting potential. The threshold of activation of the sodium conductance is set by V Na th . It controls the threshold of the firing of the neuron. Pulse width of the spike is controlled by I Na max through V Na max . The neuron's refractory period is set by the voltage V R controlling the current I R of the transistor M7. The neuron is designed such that it fires three orders of magnitude faster than the biological neurons. This has been obtained using small value capacitors (C m = C N = 500fF) with a beneficial effect on the area occupation. The size of a single CMOS neuron is 35 × 35 μm 2 , six times smaller than previous implementations [82,83].

A.2. Excitatory CMOS Silicon Synapse
Biological synapses are modeled by an exponentially decaying time-course, having different time constants for different types of synapses [85]. In order to implement a silicon synapse, we have used a current-mode low-pass filter described by a first-order differential equation of the type: in where I stands for the output current, τ is the constant time of the synapse and I in represents the input stimulus to the synapse, [85]. The time constant is three orders of magnitude faster than that of biological synpses to be compatible with the silicon neuron. The differential-pair integrator (DPI) circuit [79] shown in figure 6(b) is designed as an excitatory synapse. Voltage-spikes from the presynaptic neurons arrive at the input-transistor, QMN in , and are converted into current-inputs. By applying trans-linear principle in which, the sum of transistor voltages can be replaced by the multiplication of their currents [86], and by writing the current-voltage relationship of the capacitor C s , the dynamics of the circuit can be presented as: in which C s represents the synapse capacitor, k is the sub-threshold slope factor and U T stands for the thermal voltage. Note that by adjusting the value of the synapse capacitor, C s , and I t one can control the time constant of the synapse.

A.3. Inhibitory CMOS Silicon Synapse
The inhibitory synapse consists of a complementary version of the excitatory synapse shown in figure 6(b). Figure 6(c) represents the inhibitory synapse circuit. The working principle of such a circuit is similar to that of an excitatory synapse. All nMOS transistors are replaced with pMOSs and vice versa. At the input of the inhibitory synapse, a CMOS inverter circuit consisting of the transistors indicated as QP0 and QN0 are used to invert the upcoming voltage-spikes from the presynaptic neuron. Eventually, an inhibiting current pulse I out is generated at the circuit's output once the synapse gets stimulated from a presynaptic neuron. Figure 6. Schematic of the network elements. (a) CMOS implementation of a fast-mode sodium-potassium neuron. The neuron circuit comprises a voltage-gated sodium conductance channel (red), a voltage-gated potassium channel (light blue), a coupling element between the sodium and potassium channels (green) and a refractory period tuner (yellow). The voltage, V m , on capacitor C m is the membrane potential. Biasing voltages V Na th , V Na max and V R set the threshold for firing, pulse width and refractory period of the action potential, respectively. The value of capacitors together with input current I in determines the frequency of firing of the neuron. (b) CMOS implementation of an excitatory synapse using a current-mode log-domain CMOS differential-pair integrator (DPI) [79]. (c) Complementary DPI synapse circuit designed and utilized as inhibitory synapse. (d)A CMOS voltage to current (V-I) converter with a very low output dc current designed for converting the thermal noise of a resistor into a zero-mean white noise current. The V-I converter circuit consists of a modified Howland current source structure (red) [84] together with an integrator(blue). The current noise is applied as input to each neuron in order to induce stochastic behavior of spiking neurons.

A.4. Current Noise Generator
Many methods to implement integrated noise generators are reported in the literature based on the direct amplification of the thermal noise of a resistor [87], oscillator-sampling architectures [88], and deterministic chaos [89]. The output of such noise generators is a voltage with the desired power spectral density. To inject a current noise compatible with the silicon neuron, the two-stage voltage-to-current converter shown in figure 6(d) is designed. The output current should be in the range of hundreds of nA, at zero-mean, independent of the neuron's input voltage and with a bandwidth up to a few MHz to allow the operation of the neurons in speed-mode. To satisfy all these requirements, we have designed the bi-directional current source structure shown in the red box of figure 6(d). A Howland architecture [84] is used and specifically modified to have a very high output impedance (in the range of tens of GΩ), maintaining compatibility with standard CMOS technology. The large resistors required by the standard Howland circuit are substituted with the small value capacitors (100fF) C2-C5. To provide DC feedback to the operational amplifier UAmp2, we add the transistors QM1 and QM2 in parallel to C4 and C5, respectively. They are used as pseudo-resistors [90] to have a high resistance (hundreds of GΩ) occupying a small silicon area. In addition to a high output impedance, the pseudoresistors implement an effective AC coupling that reduces the mean value of the injected noise to less than 1pA for a noise current as large as a few μA. rms The modified Howland circuit converts the input voltage into a current with a conversion factor given by the admittance of capacitor C2. Thus the output current would increase with the frequency given a white noise as input. To recover a flat frequency response from the noise source to the output current, the voltage noise source is first amplified with the integrator stage shown in blue in figure 6(d) and then converted into a current with the modified Howland circuit. An additional pseudo-resistor implemented with QI avoids the saturation of the operational amplifier UAmp1 in the integrator stage, assuring a DC feedback path. The power spectral density of the output current results V n /R1 2 · (C2/C1) 2 , where V n is the input voltage noise.
Such circuit is able to convert a voltage noise with a non-zero mean in a zero-mean white or pink current noise compatible with the silicon neurons above. The physical source of the noise is a resistor followed by a voltage amplifier as in [87]. White noise is obtained by amplifying the thermal noise of a non-biased resistor. By forcing a current through the resistor, a pink noise (1/f noise) proportional to the current's square is generated [91], amplified and used as input of the voltage-to-current converter. The gain of the voltage amplifier is tuned to change the power of the current noise injected in the neuron. Tuning of the power has been obtained with an ideal voltage amplifier that assures a frequency response independent of the power noise to simplify the comparison of the simulation results with different noise amplitudes.

Appendix B. Correlation coefficient matrix calculation
We aim to mathematically characterize the influence of spike trains generated by the neurons of each island and observe how the correlation among spiking activity is created. For this purpose we use Pearson correlation coefficient of two random variables which is a linear measure of their dependence [92]. If each of the variables has N samples, the Pearson correlation coefficient is defined as: where μ A and σ A are the mean and standard deviation of A, respectively, and μ B and σ B are the mean and standard deviation of B. Correlation coefficient can be written in terms of covariance of A and B: The correlation coefficient matrix of two random variables for all pairs of variables as the following: A and B are directly correlated to themselves thus the diagonal entries of the matrix are 1. The matrix is symmetric such that ρ(A, B) = ρ(B, A) Since spiking activities of the neurons inside the 64 neuron network are random variables, we can simply build their correlation coefficient matrix (64 × 64) in order to find their dependence quantitatively. For calculating the correlation coefficient matrix of the spiking activity of neurons, we utilize MATLAB function corrcoef(X). It returns the matrix of correlation coefficients for X, where the columns of X represent random variables and the rows represent the samples.

Appendix C. Quantification of the noise-response of a single CMOS neuron
In this section, we investigate the white and pink noise-response of a single Hodgkin-Huxley (HH) spiking neurons [71] which is designed and simulated in a 350 nm CMOS technology [57,72]. A sodium-potassium conductance-based model of spiking neurons biased in the sub-threshold regime is implemented. Neurons are designed with a lower time-constant to spike three orders of magnitude faster than real neurons (more details on the implementation are provided in appendix A). Such speed-mode implementation allows faster data processing and carries as a by-product a decrease of the capacitor values used in the circuit, resulting in a reduction of its size. To model the background noise, we designed a voltage to current converter capable of delivering a zero-mean white and pink current noise to the neurons (see appendix A). In general, noise is naturally present in CMOS devices, from white and pink (1/f ) noise [73], to telegraph noise [74], to 1/f 1/2 noise [77]. The most straightforward strategy consists of amplifying such natural noise and exploiting it in the circuit by injection in the selected nodes. We now turn to the response of a single silicon neuron to the input noise to address the stochastic nature of the spiking activity, the inter-spike interval (ISI) distribution of the spiking activity, and the relationship between input current noise amplitude and the spiking rate of the neuron, respectively. Two transient 50 ms simulations of the silicon neuron are performed in Cadence and Spectre simulator, where white and pink-noise are injected into the neuron. The RMS amplitude of the current noise in both cases is equally set to 1.5 μA. Such noise value causes the neuron to generate an adequate spike rate to perform ISI and inter-train intervals (ITI) analysis. As a result, one can explore the features of the neuron's responses to different noise spectrum signals and compare how the inter-spike intervals ISI and ITI are affected. Figure 7(A) shows the power spectrum of the current noise employed for the simulations. The noise spectrum covers the operating frequency of the silicon neuron (1MHz) and starts from a frequency much lower than the typical spiking activity, shown in figure 7(C) for white and pink noise.
ISI distribution of the spiking activity of a neuron helps quantify the neuron's electrical properties such as its refractory period, mean-firing rate, and randomness of the spiking pattern, and therefore of the network [93]. Figure 7(D) describes how the number of spike events varies upon increasing the amplitude of the input noise. Normally, the silicon neuron spikes with an amplitude of 2.5V when a deterministic current stimulates it. For detecting a spike, a threshold voltage above which the counter identifies a spike is determined as follows. Figure 7(D) includes the trend of the number of detected spikes versus injected input noise for different spike detection thresholds. Counting stabilizes for the detection threshold voltage of 1 V. For a threshold of less than 1 V, random fluctuations would be considered spike events, therefore, affecting relevant information. Figure 7(E) shows the ISI histogram for the 50 ms transient simulation of the silicon neuron by injecting a zero-mean white noise to its input. The simulation is repeated for four different amplitudes of the injected input white noise ranging from 350 to 600 pA/ √ Hz. By increasing the amplitude of the noise, the histogram is denser and shifted to shorter time intervals. The vertical line shows the natural period of spike activity of the neuron in case of a constant input current, with amplitude equivalent to the noise RMS values injected in the simulations. A high number of spike events lay on the left side of their corresponding no-noise simulation results. Notice that the cross point of each histogram with its corresponding no-noise condition happens approximately at the same spike rate. ISI and ITI of the spiking activities of the silicon neuron between the case of white and pink noise stimuli are compared in figures 7(E) and (F). The pink noise makes a longer tail on the histogram than the white noise in agreement with other reports [94]. Furthermore, the histogram in the case of white noise is much denser than the one in pink noise. This implies that the white noise stimulus increases the excitability of a neuron within its natural refractory period at a higher rate than the pink noise stimulus. In addition to analysis on the ISI distributions, we also plot the ITI histograms to see how different noise sources affect the propagation of a train of spike events. For both white and pink noise stimuli, the distribution of spiking activity is approximately concurrent. For the simulation of the correlation among the islands discussed in section 2.2, we adopt white noise, which proves more effective to induce the neurons' excitation from the ISI point of view.