Figure 4: Correlation triangles reconstruct all possible dependencies between neurons. On the left, a graph composed of four neurons A, B, C and D (polygon ABCD). Each edge is associated with a correlation peak and corresponding correlation delay τAB , τBC , τCD, and τDA. True connections are indicated by solid lines. The delay τDA corresponds to an indirect connection which the algorithm must identify and discard. This is indicated by a dotted line. On the right, the polygon ABCD is decomposed in four triangles ABC, ACD, ABD, and BCD (each color represents a different triplet). The participating correlation triangles reconstruct all possible dependencies among all neurons in the polygon ABCD. Each correlation link is associated with a correlation peak whose amplitude and width depends on the length of the indirect correlation path connecting the two correlated neurons (see Figure 3). In triangles ACD and ABD, the delay τDA results from a signal that has propagated through three links AB, BC and CD. Thus, τDA will be detected and discarded because having lower amplitude and wider peak than the other peaks.
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