Numerical series density - page 22

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NO.P./P.NumberDelta++--Delta++Delta--
1 10
2 13 3 3
3 15 2 2
4 21 6
5 31 10 10 18
6 40 9
7 42 2 2 27
8 46 4
9 51 5
10 56 5
11 65 9 9 34
12 71 6 6 29
13 78 7 7 13
14 81 3 3 10
15 190 109 109 112
16 223 33
17 232 9 9 151
18 250 18 18 60
19 260 10 10 28
20 545 285 285 295
Total: 441 32 532 245

Is it like this or not?

What should I do next?

 
-Aleks-:

The numbers are not random, but just the ones you highlighted ++ - maximum when rising , and -- minimum when falling. So I have not yet understood - what to change - most of your colour markings matched V2, the rest, I can admit, are errors - which you reported. Please clarify.

they can't go two in a row. It's like fractals, only 3 at a time (those are like crayfish, 5 at a time but big)

a local maximum is a delta that is not smaller than the previous one and larger than the one following it. We color it purple.

a local minimum - on the contrary. we mark it with green

from purple to green - the distance between the dots decreases (i.e. the density increases), from purple to green - the distance increases (and the density decreases)

and then we will count the distances between purples. We obtain a zigzag by group discharges.

and the distances between the greens and zigzag by them, we obtain a zigzag by group densities.
 
-Aleks-:
NO.P./P.NumberDelta++--Delta++Delta--
1 10
2 13 3 3
3 15 2 2
4 21 6
5 31 10 10 18
6 40 9
7 42 2 2 27
8 46 4
9 51 5
10 56 5
11 65 9 9 34
12 71 6 6 29
13 78 7 7 13
14 81 3 3 10
15 190 109 109 112
16 223 33
17 232 9 9 151
18 250 18 18 60
19 260 10 10 28
20 545 285 285 295
Total: 441 32 532 245

Is it like this or not?

What should I do next?

seems to be correct...
the minima of Delta-- (the maxima of Delta++) should show the desired
 
Maxim Kuznetsov:
they can't go two in a row. It's like fractals, only 3 at a time (those are like crayfish, 5 at a time but big)

What "means two in a row"? How by 3?

I don't know what I'm doing wrong... maybe write out the deltas themselves in two rows - there aren't many, but it would be clearer... maybe...

 
Maxim Kuznetsov:
seem to be correct...
minima delta-- (maxima delta++) should show what you're looking for

Oh, I'm wondering what's wrong.

Found 78 and 81 - as if yes - the densest, but the second densest are 31 to 42?

What about the numbers from 10 to 21?


 
-Aleks-:

Oh, I'm wondering what's wrong with it.

Found 78 and 81 - like yes - the densest, but the second densest is 31 to 42?

What about the numbers from 10 to 21?


found - yes, they are...

We can't be sure about the numbers from 10 to 21 - we don't know what came before them.
 
Maxim Kuznetsov:
the one we found, yes, it is...

With numbers from 10 to 21 we can't say anything for sure - we don't know what was there before them.

All in all, an interesting option!

However, it is not clear how to find the next density region - suppose we think that two numbers in the region are too small?

 
just a note: in general, we have several "kinds" of densities (starting from groups and gaps, and they are non-mirrored) :-)

and recursive-fractal algorithm (groups-collapse-supercollapse-clusters....) and at each step the number of variants of "densities" doubles and it is not always possible to compare their sum correctly.
 
-Aleks-:

All in all an interesting option!

However, it is not clear how to find the next density region - suppose we think that two numbers in the region are too few?

now back to the very beginning of the thread :-)

"what is the density of a point equal to" ?
 
-Aleks-:

All in all an interesting option!

However, it is not clear how to find the next density region - suppose we think that two numbers in the region are too few?

the problem was to find dense clusters of points. To do this we took the density and actually deferentialised, i.e. got the derivative. Based on the derivative we can say "here is the maximum", "here is the minimum", here the density increases, here slowly decreases.

But we cannot compare absolute values - to do this we need to calculate the original function (in this case, just take and count the number of points in some vicinity of extrema)
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