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The notation $$\mathbf{V}_{[i-n_c+1,i]}$$ represents a subsequence, or 'window', of vectors selected from a larger sequence denoted by $$\mathbf{V}$$. This specific window consists of $$n_c$$ consecutive vectors, starting at index $$i-n_c+1$$ and ending at index $$i$$.

Vector Sequence Window Notation ($$\mathbf{V}_{[i-n_c+1,i]}$$)

A sequence of vectors is given by $\mathbf{V} = (\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5, \mathbf{v}_6, \mathbf{v}_7, \mathbf{v}_8)$. A specific subsequence, or 'window', is selected from this sequence: $(\mathbf{v}_4, \mathbf{v}_5, \mathbf{v}_6, \mathbf{v}_7)$. If this window is represented by the notation $\mathbf{V}_{[i-n_c+1, i]}$, what are the integer values of the final index $i$ and the window size $n_c$?

Determining Window Parameters from a Subsequence

Consider a sequence of vectors $\mathbf{V}$ and a subsequence defined by the notation $\mathbf{V}_{[i-n_c+1,i]}$. If the final index $i$ is incremented by one, and the window size $n_c$ is held constant, the starting index of the subsequence will also be incremented by one.

Consider a sequence of vectors $\mathbf{X} = (\mathbf{x}_1, \mathbf{x}_2, \mathbf{x}_3, \mathbf{x}_4, \mathbf{x}_5, \mathbf{x}_6)$. Which subsequence is represented by the notation $\mathbf{X}_{[i-n_c+1, i]}$ when the final index $i=5$ and the window size $n_c=4$?

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