# Estimation of Synaptic Activity during Neuronal Oscillations
## 3 Results  
In order to test the estimation procedure, we apply Algorithm 1 (see Section 2.2) to membrane potential traces, often referred to as _actual_ membrane potential traces, obtained computationally from the pyramidal cell model (see Section 2.1.1). This model will be considered either with additive noise (3), or without it (1). Moreover, in our simulations we consider the model with different synapticdrives to simulate spiking regimes without (Section 3.1) and with (Section 3.2) short subthreshold regimes interspersed (see Section 2.1.2 for more details in the synaptic drive). For the different synaptic drives, we perform the estimation of conductances using different base models in Algorithm 1, step 3b. First, as we know that, by construction, the actual membrane potential follows the pyramidal neuron model, we consider this model as the base model, so we can test how powerful the estimation procedure is if we know the exact neural model. In this case, we deepen our results by exploring the cases where the data have been obtained with different amounts of noise and where the \(T-g_{syn}\) curve has been constituted using different discretizations. However, in most of the cases, the specific model that describes the neural data we have in consideration is not always known; therefore, an approximation of it is required. For this reason, second, we use the exponential integrate-and-fire (EIF) model with constant adaptation as a base model and try to approximate the activity of the pyramidal cells to it (as in [30]; see also Section 2.1). Finally, we explore the situation of having a small sample of \((g_{syn},T(g_{syn}))\) pairs which are obtained with some additive noise rather than having a reference model to obtain a more precise \(T-g_{syn}\) curve. This specific case could be given when trying to obtain the \(T-g_{syn}\) curve experimentally, where data are obtained with measurement noise and variability across trials. In this case, we first generate a small sample of \((g_{syn},T(g_{syn}))\) pairs where we add a small bias in order to simulate possible errors in the recordings. Then, we use a proper fitting to obtain the \(G_{syn}(T)\) curve to be able to proceed with the estimation procedure (see Section 3.1.4 for more details on how). We will refer to this curve as the \(T-g_{syn}\)_experimental curve. In Table 1, we provide a summary of the results found in the different subsections. \begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
\begin{tabular}{} \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Outline of the different cases studied in Section 3 (_Results_). \begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline \(g_{syn}\) & \begin{tabular}{} \end{tabular}  & \begin{tabular}{} \end{tabular}  & \begin{tabular}{} \end{tabular}  & \ \begin{tabular}{} \end{tabular}  & \begin{tabular}{} \end{tabular}  \\ \hline \(10^{-5}\) & \(1.69\times 10^{-3}\) & \(2.435\times 10^{-9}\) & \(1.501\times 10^{-7}\) \\ \(10^{-4}\) & \(1.730\times 10^{-3}\) & \(2.978\times 10^{-9}\) & \(1.501\times 10^{-7}\) \\ \(10^{-3}\) & \(9.907\times 10^{-3}\) & \(8