# Estimation of Synaptic Activity during Neuronal Oscillations
## 3 Results
### Estimation in the Spiking Regime with Interspersed Short Subthreshold Periods  
In this section, we aim to explore whether the estimation procedure can be also used when short periods of subthreshold activity interrupt the spiking regime. Note that, if those silent periods are sufficiently large (for instance, greater than 100 ms), one could use a combination of the spiking estimation procedure developed in Section 2.2 and a subthreshold estimation procedure (for instance, the so-called _QIF method_ presented in [23], which takes into account the spike initialization and possible subthreshold activity). However, for shorter subthreshold regimes, this combination could be not possible (as some methods require a certain amount of data to be used) or could cause a lot of misestimations induced by recent spike activity. For these reasons, we consider a synaptic conductance trace (see Section 2.1.2), depicted in Figure 8(a) (black trace), which causes spiking regimes interleaved with subthreshold regimes (of 50 ms of duration, approximately) when this is used into the pyramidal cell model (see Figure 8(b) (black trace)).  
Results presented in Figure 8(a) show that the estimation procedure provided in Algorithm 1 is able to reproduce the synaptic drive, either if we use as a base model to generate the \(T-g_{syn}\) table the pyramidal cell model (blue trace) or the EIF model (green curve). In both cases, the reconstruction of the membrane potential using the estimated conductances maintains the spike frequency, thus keeping unchanged the firing rate (Figure 8(b), \(c\), respectively). On the other hand, when the simulated experimental curve is used, conductances around \([0.02,0.04]\) are not well estimated, as it happened when considering just the spiking regime, see Section 3.1.4. These misestimates alter the spike frequency in the membrane potential reconstructed using the estimated conductances as synaptic  
Figure 7: **Results of the estimation procedure applied to a membrane potential generated through the pyramidal cell model with additive noise and using a simulated \(T-g_{syn}\) curve in the estimation procedure.** Panel (**a**) shows the actual \(T-g_{syn}\) curve (blue curve), the \(T-g_{syn}\) curve obtained with the EIF method (black curve), a simulation of an experimental \(T-g_{syn}\) curve (red dots), and an exponential fitting of the experimental curve (red curve). Panel (**b**) shows the scatter plot of the prescribed conductances versus the estimated ones; the red line represents the identity line. Panel (**c**) shows the prescribed conductances (black curve) and the estimated conductances (red curve). In panel (**a**), the experimental curve (red dots) has been computed using 10 different trials where noise has been added to the period (a random normal distributed value with 0 mean and 0.5 standard deviation and dots has been interpolated using the exponential fitting).  
inputs (see Figure 8b), by adding extra spikes in the silent regime and displacing the spiking time-onset in the spiking regime.  
Errors of the estimation in the different cases are presented in Table 5, where we can see also that both the pyramidal cell model and its EIF approximation lead to similar errors, while the experimental curve leads to higher errors.