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Register subclass as a “virtual subclass” of this ABC. For example:

Changed in version 3.3: Returns the registered subclass, to allow usage as a class decorator.

Changed in version 3.4: To detect calls to , you can use the function.

You can also override this method in an abstract base class:

(Must be defined as a class method.)

Check whether subclass is considered a subclass of this ABC. This means that you can customize the behavior of ``` issubclass ``` further without the need to call ``` register() ``` on every class you want to consider a subclass of the ABC. (This class method is called from the ``` __subclasscheck__() ``` method of the ABC.)

This method should return ``` True ``` , ``` False ``` or ``` NotImplemented ``` . If it returns ``` True ``` , the subclass is considered a subclass of this ABC. If it returns ``` False ``` , the subclass is not considered a subclass of this ABC, even if it would normally be one. If it returns ``` NotImplemented ``` , the subclass check is continued with the usual mechanism.

For a demonstration of these concepts, look at this example ABC definition:

The ABC ``` MyIterable ``` defines the standard iterable method, Womens 28124 TBar Sandals Grey Silver 9 UK Marco Tozzi nBCwyp
, as an abstract method. The implementation given here can still be called from subclasses. The ``` get_iterator() ``` method is also part of the ``` MyIterable ``` abstract base class, but it does not have to be overridden in non-abstract derived classes.

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class method defined here says that any class that has an ``` __iter__() ``` method in its ``` __dict__ ``` (or in that of one of its base classes, accessed via the Marchesa Notte Woman Ruffled Beadembellished Crepe Dress Bright Pink Size 12 Marchesa Iwsx3kUZ
list) is considered a ``` MyIterable ``` too.

Finally, the last line makes ``` Foo ``` a virtual subclass of ``` MyIterable ``` , even though it does not define an ``` __iter__() ``` method (it uses the old-style iterable protocol, defined in terms of Espadrille Bamba by 520031 Taupe Victoria U8vitF1PkF
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). Note that this will not make ``` get_iterator ``` available as a method of ``` Foo ``` , so it is provided separately.

The scheme in ( 21 ) is the basis for the computation of the shear rate and all cellular contributions to it. In the following, we will separately discuss shear in the absence of topological transitions (i.e., between the states I 1 and I 2 ) and the shear by topological transitions.

The overall tissue shear rate ${\stackrel{\sim }{v}}_{ij}$ between the states I 1 and I 2 is computed as the average triangle shear rate:

(22)

In this equation, the average corresponds to an area-weighted average over all triangles, where the area weights are taken from state I 1 . More generally, for any triangle-based quantity q m , we define such an average by

(23)

Here, the sum runs over all triangles m of the network, ${A}_{X}^{m}$ denotes the area of triangle m in state X ∈ { O n , I 1 , I 2 , I 3 , O n + 1 }, and A X is the total area of the triangulation in state X : ${A}_{X}=\underset{m}{\sum }{A}_{X}^{m}$ . The index X is necessary, because the triangle areas generally change between two states. The average quantity q m may be evaluated for a network state Y different from X if both contain the same set of triangles. Interestingly, the large-scale shear rate ${\stackrel{\sim }{v}}_{ij}$ can equally be computed from margin displacements alone ( Merkel, 2014 ; Merkel et al., in preparation). Furthermore, since there is no shear occurring during topological transitions, the average shear rate ${\stackrel{\sim }{v}}_{ij}$ between the intermediate states I 1 and I 2 also corresponds to the average shear rate between the observed states O n and O n + 1 .