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Commutative diagram of morphism mappings from a big system SY S to a small system SY S . In red are indicated the matrix representations to be discussed for network representation.

Commutative diagram of morphism mappings from a big system SY S to a small system SY S . In red are indicated the matrix representations to be discussed for network representation.

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Figure 1: Modeling of the brain regions and model lumping for...
FIG. 1. The sigmoidal shape of the function f and its effects on...
Figure 3: Commutative diagram of morphism mappings from a big system SY...
Figure 4 shows a base network, a lumped network and the morphism between.
+6 Figure 6: Matrix representation of a connectivity permutation: Each...
Morphisms for Lumping Finite-Size Linear System Realizations of Componentized Neural Networks
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  • Aug 2020
We present here a system morphism methodology to give insight into the lumping process of networks of linear systems. Mean field assumptions are summarized as an example of two particular/significant assumptions for lumping: Homogeneity and fixed-point preservation in the lumped network model. Behavioral homogeneity (all linear systems having the s...
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Context 1
... 5. A system morphism or generalized homomorphism 10 , between a detailed system SY S (or base system) and another abstract system SY S (or lumped system), is a pair (g, h) such that (cf. Figure 3): ...
Context 2
... 1. From a matrix representation point of view, let H : Q → onto Q be a linear mapping, then H is a homomorphism from a big network of linear systems to a small network of linear systems, if the following conditions hold (cf. Figure 3): ...

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