Figure 3
RCC5 analyses. (A) Two regions with soft boundaries, e.g. two firing fields \(\upsilon _i\) and \(\upsilon _j\), can overlap, \(\textsf {PO}(\upsilon _i,\upsilon _j)\), be proper parts of each other, \(\textsf {PP}(\upsilon _i, \upsilon _j)\) or \(\textsf {PPi}(\upsilon _i,\upsilon _j)\), be disconnected \(\textsf {DR}(\upsilon _i,\upsilon _j)\) or coincide \(\textsf {EQ}(\upsilon _i,\upsilon _j)\). (B) Number \(N_x(t)\) of inconsistent triples of RCC5 relationships appearing in the \({\mathcal {R}}_5(t)\) relational framework constructed for the same neuronal ensemble as illustrated in Fig. 2. The barcode diagram for the corresponding integrating coactivity complex (Fig. 2B) is shown in the background, to illustrate the correspondence between the RCC5 and the homological dynamics. \(T_{{{\,\mathrm{{\textsf {RCC5}}}\,}}}\) (dotted line) marks the time when inconsistencies in the \({\mathcal {R}}_5(t)\) schema disappear. Results averaged over 10 repetitions, error margins shown by the dashed lines. (C) The net number of changes of RCC5-relationships between two subsequent moments of time, \(N_c(t)\), shown by the blue line, and the number \(N_d(t)\) of changes that violate the RCC5 continuity order (top right panel), shown by the orange line. For better illustration, \(N_d(t)\) is scaled up by a factor of 10. Initially, discontinuous events are frequent but shortly before \(T_{{{\,\mathrm{{\textsf {RCC5}}}\,}}}\) they disappear entirely, leaving the stage to qualitatively continuous sequences. The same barcodes are added in the background, error margins shown by dashed lines.
