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In the former, all agents are distinguishable because each one is identified by a unique integer, and the state of the system is given by the values of S a) for each a∈ A. In a Petri net, the agents (tokens) are distinguished only by their species attributes, and the state of the net is given by the markings of the place nodes, i.e., the number of agents in each species.
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We map the elements of the steady state probability vector π (i,j) from state to index by assigning a unique integer index to identify each state.
Field PMID (PubMed ID) is a unique integer number assigned by NLM to each article.
Each segment is then labeled with a unique integer value, and these initial segments are expanded by iterated minimum and maximum filtering.
For any nonzero rational number, there exists a unique integer such that, where and are integers not divisible by.
Given primes, with, by considering their product, then for any set of given integers there exists a unique integer that solves the system of simultaneous congruences, and it can be obtained by.
We realized this by defining a function that maps each possible N-neuron sub-matrix to a unique integer value.
For every integer there exists a unique integer such that.
This representation guarantees a unique integer for each possible path.
Each node is labeled with a unique integer for identification purposes.
For any nonzero rational number a, there exists a unique integer r such that a = p r m / n, where m and n are integers not divisible by p. Then | a | p : = p − r defines a non-Archimedean norm on Q.
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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