Figure 4 shows object groupings yielded by the co-variation network in Figure 2B.
Figure 4.
Co-variation network is partitioned into minimully coupled object groups. Coupling is determined by the ratio of the summed internal and external link weghts in the groups. Link weghts are incremented each time an episode of co-variation is observed on the corresponding objects. In this way, the history of observation is recorded continuously as object linking and link weght variation, followed by network partitioning each time such linking and/or variation takes place. (Groupings can contain distant objects. For clarity, they are shown as proximal custers).
Figure 5 explains the process in greater detail.
Figure 5.
Accumulation of observations progresses from connected fragments to a connected network, with the links weighted based on the relative frequency of co-variation episodes among the corresponding variables. The network is dynamically partitioned into maximally cohesive and minimally coupled non-overlapping subnets. LA is a network plasticity index and sL is a cluster stability index (both determined by the changes in weight ratios).
Interlocking representational hierarchy forms as the subnets stabilize in the bottom layer. A network starts to form in the layer above such that each node represents a stable structure in the layer below.
Figure 6.
Representation of observation history in the VAN Interlocking Hierarchical Structure. In the VAN Hierarchy, units in all the levels (i.e., Entities (bottom level), Entitiy groupings (second level), etc.) remain interconnected so that all the vertical structures are laterally interlocked. As a result, as the observation progresses, group compositions at each level can undergo changes involving unit transfers between the groups. Entities in the bottom level are considered "discovered" after a sufficiently long period of vertical and lateral stabilization.
Finally, Figure 7 illustrates the key feature of the VAN model determining its dynamics. Energy barriers bound unit groupings such that the height of the barrier is a function of the ratio of the sums of the internal and external weights in the group. Energy barriers at the boundaries ascribe energy landscape to each level in the representational hierarchy. The landscapes in the different levels maintain global interdependence, punctuated by the barriers. Landscapes ensure global coherence in the structure and preserve it as a functional whole composed of dynamic Entities separated by the barriers.
Figure 7.
A, B, C, D, and E are distinct entities bounded by the energy barriers. Because of the barriers, changes in any Entity propagate through the entry structure affecting other Entities to the extent determined by the barriers at their bounds. As the behavior of the observed objects changes, the Entities can merge, shrink, expand and dissolve.
Further discussion of Figure 7 in the context of emergent or occluded behavior is warranted. The first instance of emergent behavior must initially be ignored as noise or dismissed by incorporation into an existing structure. Subsequent observations begin to cohere into the more weakly associated entities D and E. At this point, the temporal behavior of the energy landscape becomes important. One asks whether the associated cluster gains or loses strength over time. Clearly, a gain in strength represents truly emergent behavior. What, however, if one of the entities D or E remain weakly associated, neither gaining nor losing strength? This represents occluded behavior. Occlusion may be nothing more than under-reporting with respect to that entity, but it may also represent systematic suppression of other observables or outright (deliberate) misrepresentation of other observables so that they become associated with other entities. A persistent weak entity cluster is the hint that triggers the best investigators in all fields. It represents the suspicion that more lies beneath the visible iceberg.
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