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where (12) is defined as oper3 in Table 1, and the message from a factor node to a variable node can be taken as the prediction phase for location tracking.
In addition, consider a prediction phase with two incoming Gaussian messages illustrated as the right part of Figure 2. According to (9) and (11), a message from a factor node to a variable node is the integration of the product of two incoming messages enforced on the factor node.
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A message from a factor node to variable nodes is the sum of factor contributions and is illustrated in the middle and left parts of Figure 13. Figure 13 Illustration of the evaluation of the message sent by a factor node to an adjacent variable node and the evaluation of the message sent by a variable node to an adjacent factor node.
More specifically, let μ M i → p k p k denote the message to be passed from a factor node v(M i ) to a variable node v(p k ), and let μ p k → M i p k denote the message to be passed from the variable node v(p k ) to the factor node v(M i ). Figure 4 shows the two kinds of messages passing on in a fragment of a factor graph.
where (10) is defined as oper1 in Table 1, i.e., a message from a variable node to a factor node is the product of incoming messages.
Namely, the message from a variable node to a factor node can be taken as the correction phase for location tracking.
A message from a variable node to a factor node is the product of incoming messages and is illustrated in the middle and right parts of Figure 13.
For instance, the message from a variable node v to a factor node u in BP is analogous to assigning function or abundance of complexes (factor nodes in the complex-protein bipartite network), and the following process of message passing from u to v corresponds to assignment to proteins with previously unknown functions or abundance.
It is important to note that a factor node can send a message to a variable node after the factor node has received incoming messages from all other neighboring variable nodes.
In addition, a variable node can send a message to a factor node after it has received incoming messages from all other neighboring factor nodes.
Overall, implementing a multi-node send is as simple as sending from the source node to an intermediary node.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com