Some doubts on TM algorithm

Science Numenta Theory
1

I’m reading the BAMI book. While reading the chapter of TM, there come some doubts.

  1. If there are 4 cells in each column, why 4^100 ways of representation?
    For 4 cells, there will be 2^4=16 ways of representation. And for 100 columns and 4 cells in each, there will be 16^100 ways of representation. Why it says only 4^100 ways?
  2. There is a sentence in this chapter, "This determination is done on a column-by-column basis so a predictive match or mismatch is never an “all-or-nothing” event. " what does it mean?
    for I’m not a native English speaker, it’s hard for me to comprehensive this sentence.
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Each unique context for a particular input is assumed to be encoded as one active cell per minicolumn. So a single minicolumn with 4 cells has 4 different ways to represent a single cell being active, which represent 4 unique contexts. When more than one cell are active, that represents multiple contexts (for example when there is ambiguity and the system is not certain about the context, then there will be multiple cells active).

This means that when one of the minicolumns burst, it doesn’t automatically mean that all of the other minicolumns will also burst. The logic which determines whether the minicolumn should burst is run for each minicolumn separately. So some of them might burst, and others might not.

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