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Each of the levels or modules can have different histories and separate evolutionary trajectories (see examples in Serb and Oakley 2005) and therefore may exhibit either convergent or parallel patterns.

In practice, the discrete gradient modules can have relatively small local maximums on the object edges and then the stopping function can be relatively far from zero on the edges, and the curve may pass through the boundary.

This indicates that very distantly related modules can have the same specificity.

Conversely, neurons occurring in different modules can have small distance between each other in terms of lineage.

Similar(56)

We have demonstrated that multiple heterogeneous factors in a module can have combinatorial effects on GE.

It has been demonstrated that the linker type, length, and flexibility, as well as fusion of the bioactive peptide or protein to the C or N terminus of the half-life-extension module, can have profound effects on the activity of the fusion proteins.

These are signaling modules and can have component complexes (or their important nodes) that interact both genetically and physically.

In Definition 2.3, we can easily see that (1) for each f in (E^{ast}), (vert f(x) vert leq Vert f Vert ^{ast}cdot Vert x Vert,forall xin E);   (2) since ((E^{ast}, Vert cdot Vert ^{ast})) is also an RN module, we can have its random conjugate space (((E^{ast})^{ast},( Vert cdot Vert ^{ast})^{ast})) (briefly, ((E^{astast}, Vert cdot Vert ^{astast}))).

In particular, when J is surjective, we call ((E, Vert cdot Vert )) to be random reflexive [21].  . for each f in (E^{ast}), (vert f(x) vert leq Vert f Vert ^{ast}cdot Vert x Vert,forall xin E); since ((E^{ast}, Vert cdot Vert ^{ast})) is also an RN module, we can have its random conjugate space (((E^{ast})^{ast},( Vert cdot Vert ^{ast})^{ast})) (briefly, ((E^{astast}, Vert cdot Vert ^{astast}))).

Additional File 4 shows that black and blue module genes can have very different enrichment results that tend to be very different from those of a standard analysis.

As described in the main text, the module assignments of paralogs can have four possible fates right after duplication: conserved, neo-functionalized, symmetrically diverged and asymmetrically diverged.

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