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Interpreting a formula


Interpretor

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Hello!

I'm trying to understand the following formula, and pretty much need help with all parts of it:

 

post-99797-0-05352100-1377011642_thumb.png

 

If anyone out there could help me I'd be extremely happy smile.png!

 

 

 

Best regards,

The Interpretator

Edited by Interpretor
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Looks to me like the description of some form of mapping x(p) - the 1st, 2nd, 3rd, pth value of x is equal to the any of the subsequant values of x from p+1, p+2, plus a factor k which runs from zero to m-1, this runs to a ceiling where it tops out because the k value is equal to the end value. But makes no sense to me either. maybe someone else - my maths is pretty basic

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Looks to me like some instruction in some programming language for generating a recursive loop.

 

If this is true then the equals sign is not meant to be read as equality but

 

x(p) is replaced by x(p+k) where k is already defined previously in the program and the loop runs through for stated values of p,

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It may help if we know the context of this expression. Where did it come from?

 

Different branches of mathematics can have their own set of notations. Thus, it is quite possible that this is quite a simple idea, but we just don't recognise it.

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  • 3 weeks later...

Hello! Thank you for the answers and sorry for my delayed reply (made this thread just before going on vacation). The formula presented above is used to determine the onset of a muscle reaction, with data gathered per millisecond in a time series.

 

Here follows the remaining information I have, hopefully, I'm not breaching any copywright laws by presenting it here:

 

1.

 

The scalar time seriers {x1,x2,...,xi,...,xn} is embedded in a delayed m-dimensional space, where vectors are constructed as (the formula above).

 

The probability Bm® that two sequences match for m points is computed by counting the average number of vector pairs, for which the distance is lower than the tolerance r. Similarly, Am®

 

is defined for an embedding dimension of m + 1. It is then calculated as:

 

Answer(x,m,r)=-ln(Am®/Bm®)

 

 

I hope this information is enough to solve the meaning of this formula.

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  • 2 weeks later...

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