## 2 Materials and Methods
### Analysis Metrics  
The framework adapts and incorporates an extensive array of tools [9; 10] (as listed in Table 2 below) in order to analyze the results from the GPU simulations. The outcomes derived from the analysis are systematically stored in a database using the Python library \"sqlite3\"([[https://www.sqlite.org/index.html](https://www.sqlite.org/index.html)]([https://www.sqlite.org/index.html](https://www.sqlite.org/index.html)), accessed on 1 November 2023), where they are formatted and organized using Structured Query Language (SQL).  
The phase locking index (PLI) is a statistical measure frequently employed in the fields of neuroscience and signal processing. Its primary purpose is to evaluate the level of phase synchronization or phase consistency observed between the different nodes of the time-series, notably in the context of electroencephalography (EEG) and magnetoencephalography (MEG) data analysis [9; 30; 31]. The PLI serves as a quantification tool for assessing the degree to which the phase angles of two signals exhibit synchronization tendencies over a period of time.  
The terms \"up\" and \"down\" states are utilized to denote distinct patterns of neuronal activity within the brain. These patterns are of particular significance in the realms of neural oscillations and sleep research. They are closely linked to the sleep-wake cycle and serve as vital components for comprehending the dynamics of brain function throughout periods of sleep and wakefulness.  
The acronym \"PSD\" refers to \"Power Spectral Density\" in the field of signal processing. This fundamental concept serves as a means to articulate the manner in which power or energy is distributed within a signal concerning its frequency components. PSD plays a  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Metric** & **Description** \\ \hline mean\_FC & Average FC from Pearson corr. of time-series firing rate \\ \hline mean\_PLI & Average PLI between brain regions. \\ \hline mean\_UD\_duration & Mean duration of UP and DOWN states \\ \hline psd\_fmax\_ampmax & PSD frequency peaks and amplitude \\ \hline fit\_psd\_slope & Fits \(log(PSD)=log(\beta/f^{\alpha})\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The incorporated analysis metrics showing the function name and description.  
pivotal role by furnishing essential insights into the spectral characteristics and frequency content of the signal under examination.  
The PSD is approximated by the following function:  
\[log(PSD)=log(\beta/f^{\alpha})\]  
in which \(f\) is the frequency; \(\alpha\) and \(\beta\) are the parameters that affect the shape and the amplitude of the function, respectively. The goal of fitting the PSD to this particular function is to find the values of the parameters \(\alpha\) and \(\beta\) that best describe the observed data. By applying a logarithm to both sides of the equation, a linear relationship is obtained, which is easier to work with mathematically. By fitting the PSD data to this function and determining the values of \(\alpha\) and \(\beta\), we can gain a better understanding of how the power in the signal is distributed across different frequencies and the characteristics of the spectral density.