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Let I be the indicator matrix whose elements indicate whether the distance between a pair of nodes is equal to or less than 3.
Towards that end, let (Delta _{t}' in {0,1}^{Ntimes N}) be the difference indicator matrix that only indicates the packets that are received at current time t, i.e., Delta_{t}'= Delta_{t} - S^{downarrow}Delta_{t-1}. (20).
Let (Delta _{t}in mathbb {R}^{Ntimes N}) be an indicator matrix with binary elements {0,1} indicating the complete buffer contents of (bar {f}'_{t}) at time t.
Clearly, from the all zero difference indicator matrix, it is possible to get to any other difference indicator matrix in a finite number of steps.
(2008) to the indicator matrix solution obtained by spectral clustering and the application of K-means (plus a constant matrix).
With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities.
Similar(18)
Thus, the number of distinct difference indicator matrices reduces to L=M+1.
The sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
In the following, we will show that the number of distinct difference indicator matrices is finite for bounded N, and that the sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
The number L of distinct difference indicator matrices is upper bounded by: L leq (N+1 bigg(1+frac{1}{2}N(N+1)bigg)^{N-1} (21).
Thus, it is possible to jump between any two difference indicator matrices in a finite number of steps.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com