Topological node

Neural network models are distinguished by network topology, node characteristics, and training or learning rules. They are important because they can match current shop status and the desired performance measures to near-optimal scheduling strategies and they can learn (Yih and lones 1992). 

In a daisy chain, each topology node is connected to the next in linear fashion. The traffic from node A to node C (and vice versa) has to pass through node B. This topology is used by certain camera interfaces to connect two cameras to a central node, which reduces cable use and cost (Fig. 8). 

There is one node within each switching power supply that has the highest ac voltage compared to the others. This node is the ac node found at the drain (or collector) of the power switch. In nonisolated dc/dc converters, this node is also connected to the inductor and catch (or output) rectifier. In transformer-isolated topologies, there are as many ac nodes as there are windings on the transformer. Electrically, they still represent a common node, only reflected through the transformer. Special attention must be paid to each ac node separately. 

Switching losses occur at two equivalent nodes within every switching power supply the drain (or collector) of the power switch(es), and the anode of the output rectifier(s). These are the only ac nodes within each type of PWM switching power supply. Within the nontransformer isolated topologies, these nodes are physically one node where the collector (or drain) of the power switch is directly connected to the anode of the output rectifier. Within transformer-isolated topologies, these two nodes are separated by the transformer and the two nodes are treated slightly differently. 

An arbitrary endpoint can also be marked as "root". A tree with a root will be called a planted tree the vertices different from the root are nodes. If no root is marked, the tree is called an unrooted or free tree. From a topological point of view, two trees with the same structure are identical the exact definition of this and some similar, less familiar notions, will be discussed in Sections 34-35. In the sequel, we use the following notations ... 

T number of topologically different planted trees with n nodes. 

The series (2) of Sec. 3, too, is a generating function the collection of figures comprises the planted trees which are topologically different. The nodes of the rooted trees play the role of the balls in the figure there is only one category of balls, and thus the series depends only on one variable. Figure 1 indicates how the figures (planted trees) of the same content (number of nodes) are combined in the coefficients. 

Pursuing this correspondence between a C-H graph and the corresponding C-graph we find a new interpretation of the numbers p and R p is the number of topologically different free C-trecs with n vertices, R is the number of planted C-trees with n nodes. In other words ... 

If the principal node K is an endpoint, the planted tree consists of a , the root and the stem, which connects these two points. There are no vertices of degree 4, there are no principal branches. There are no two noncongruent planted trees of this type, whether we deal with topological, spatial, or planar congruence. Hence... 

Now we turn to arbitrary planted trees with a total of n nodes denotes the number of topologically different trees, the... 

The number of topologically different planted C-trees with n nodes is 1), as we have noted in Sec. 37. It is easy to see that... 

A relationship between the numbers A and corresponds to the similarity of the two equations (2.36) and ( ) [of (2.37) and (1 )]. Choose a topological planted tree counted by with n nodes of the same species. Then label these n nodes individually. The resulting... 

Recall the elegant Euler s theorem that states that for a 2-d structure the number of nodes minus the number of edges (struts) plus the number of faces = 1, or — S +F = 1. This topology theorem is easy to prove. An examination of Table 3 shows some examples of this theorem and indicates how to prove it. 

In the transformed graph, the only nodes are pipes and supersources and an edge leads from one node to another iff there is a path connecting the corresponding nodes in the topological graph, and no other pipe or source lies on this path. 

T-shaped tridentate nodes, the diiodobenzenes as linear bidentate modules that space the nodes and ribbons compounded of consecutive rectangles are formed [155] (Fig. 11). A similar topology is present in the co-crystal CBr4/Ph4P+Br where bromide anions and carbon tetrabromide both work as tridentate notes that alternate in the ribbon [121]. 

The mathematical abstraction of the topology of a pipeline network is called a graph which consists of a set of vertices (sometimes also referred to as nodes, junctions, or points)... 

Small networks that contain just one node can manage simple tasks (we shall see an example shortly). As the name implies, most networks contain several nodes between half a dozen and fifty nodes is typical, but even much larger networks are tiny compared with the brain. As we shall see in this chapter and the next, the topology adopted by a network of nodes has a profound influence on the use to which the network can be put. 

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