Nevertheless, the correlation grid enabled the analysts to find the correct connection architecture for each of these three data sets.
Moreover, the correlation grid was developed to help solve the following reverse problem: identification of the connection architecture between spike train generating units, which may produce a spike train dataset similar to the one under analysis.
This technique, called the correlation grid, enables investigators to identify groups of spike trains, where each pair of spike trains has a high probability of generating spikes approximately simultaneously or within a constant time shift.
Because an explicit discrete technique is used to solve the governing equations, and there is no correlation between grid calculations in a single time step, the parallel dam-break model can be easily realized by adding OpenMP instructions to the loop structure of the grid calculations.
(Noise correlation between grid cells was investigated in Mathis et al. (2013); Dunn et al. (2015)—they found positive correlation between aligned grids of similar periods and some evidence for weak negative correlation for grids differing in phase).
The literature search was performed by using MEDLINE and PubMed electronic databases with the following key words: "intensive care", "critical care," "glucose," "sugar," "glycemic," "insulin," "Bland Altman," "agreement," "validation," "reliability," "accuracy," "correlation," "Clarke grid," and "bias".
Since the presence or absence of noise correlations is not a main point of our paper, we have simply indicated (Discussion, fourth paragraph) that Mathis et al. and Dunn et al. investigated noise correlations between grid cells and found positive correlations for aligned grids (i.e. similar phase) of the same scale and weak correlations otherwise.
Concerning the roles of correlations between grid cells, as Reviewer 1 points out, there is now work by the Herz group (Mathis et al., 2013) and by the Roudi group (Dunn et al., 2015) that suggests that there are only weak noise correlations between grid cells that are not aligned and of the same period (we now cite this work in the fourth paragraph of the Discussion).
Analysis of spatial correlations in grid firing, of manipulations to grid circuits, and recording of grid cell membrane potential in behaving animals, collectively point towards continuous two-dimensional network attractor states as explanations for grid firing (Bonnevie et al., 2013; Domnisoru et al., 2013; Schmidt-Hieber and Häusser, 2013; Yoon et al., 2013).
This is apparently also the message that they derive from their Figure 9. Meanwhile Dunn, Morreaunet and Roudi (2015) also report positive noise correlations for grids with similar phases, and vanishing or sometimes negative correlations for grids with very different phases.
An inviscid vortex convection benchmark case is used to quantify the correlation between the grid quality metric and the solution accuracy, for three common geometric features found in grids: abrupt changes in the grid metrics, skewness, and grid stretching.
