Palindrom
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First encounter with the term, I'd like some help understanding it. I know there are several approaches, but this one is important to me because I'm trying to understand an article that uses it throughout its text.
Definition: Let G=(V,E) be a finite (connected) graph and let S be a finite set. A random element X taking values in S^V is said to be a Markov random field if for each W\subset V, the conditional distribution of X(W) given X(V\W) depends on X(V\W) only through its values on \partial W.
It goes on to write this mathematically, which I will write down here if you ask me to. My problem is with the phrase "A random element X taking values in...".
I just want to know from where to where X is. Obviously X takes values in S^V, so this is the range of X. What is its domain?
Definition: Let G=(V,E) be a finite (connected) graph and let S be a finite set. A random element X taking values in S^V is said to be a Markov random field if for each W\subset V, the conditional distribution of X(W) given X(V\W) depends on X(V\W) only through its values on \partial W.
It goes on to write this mathematically, which I will write down here if you ask me to. My problem is with the phrase "A random element X taking values in...".
I just want to know from where to where X is. Obviously X takes values in S^V, so this is the range of X. What is its domain?