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It has found its application in various fields including military, diplomatic, personal and intellectual property applications. The technique has been used in various forms for 2500 years or long. Steganography literally means secret writing. As an example, we derive the form of the lattice for a linear chain of identical cells with feedback.

#Jmp hide graph builder overlay how to#

In particular, we describe how to determine whether the lattice contains more than the equality relation. We discuss the structure of this lattice and computational issues associated with it. However, the intersection of two balanced equivalence relations need not be balanced, as we show by a simple example, so this lattice is not a sublattice of the lattice of all equivalence relations with its usual operations of meet and join. As partial compensation, the lattice of balanced equivalence relations can then be proved complete. This context requires some modifications to the standard framework. Some aspects of the theory make use of infinite networks, so we work in the category of networks of ‘finite type’, a class that includes all locally finite networks.

The partial order is defined by refinement. We prove that the set of all balanced equivalence relations on a network forms a lattice, in the sense of a partially ordered set in which any two elements have a meet and a join. In their approach the network is assumed to be finite. concept of a ‘balanced equivalence relation’, which depends solely on the network architecture.

Golubitsky, Stewart, Pivato and Török have presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of the. The associated coupled cell network is a labelled directed graph that indicates how the cells are coupled, and which cells are equivalent. A coupled cell system is a collection of dynamical systems, or ‘cells’, that are coupled together.