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The physical network topology can be directly represented in a network diagram, as it is simply the physical graph represented by the diagrams, with network nodes as vertices and connections as undirected or direct edges (depending on the type of connection). [3]
Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates , or signal types may differ between two different networks, yet their logical ...
A monoidal category where every object has a left and right adjoint is called a rigid category. String diagrams for rigid categories can be defined as non-progressive plane graphs, i.e. the edges can bend backward. In the context of categorical quantum mechanics, this is known as the snake equation.
The monoidal product of two diagrams is represented by placing one diagram above the other. Indeed, all ZX-diagrams are built freely from a set of generators via composition and monoidal product, modulo the equalities induced by the compact structure and the rules of the ZX-calculus given below.
In topology, a branch of mathematics, a topological monoid is a monoid object in the category of topological spaces. In other words, it is a monoid with a topology with respect to which the monoid's binary operation is continuous. Every topological group is a topological monoid.
The second is a two dimension torus, in the shape of a 'doughnut'. The animation illustrates how a two dimension torus is generated from a rectangle by connecting its two pairs of opposite edges. At one dimension, a torus topology is equivalent to a ring interconnect network, in the shape of a circle. At two dimensions, it becomes equivalent to ...
This is one of the diagrams used in the definition of a monoidal cateogory. It takes care of the case for when there is an instance of an identity between two objects. commutes. A strict monoidal category is one for which the natural isomorphisms α, λ and ρ are identities. Every monoidal category is monoidally equivalent to a strict monoidal ...
The ratio of switching nodes to processor nodes is greater than one in a butterfly network. Such topology, where the ratio of switching nodes to processor nodes is greater than one, is called an indirect topology. [1] The network derives its name from connections between nodes in two adjacent ranks (as shown in figure 1), which resembles a ...