This is a spinoff from the previous post. In that post, we remarked that whenever one receives a new piece of information , the prior odds between an alternative hypothesis and a null hypothesis is updated to a posterior odds , which can be computed via Bayes’ theorem by the formula wh...
where is the extension of by zero to all of . Thus for instance (which technically makes a seminorm rather than a norm), and one can calculate where , and we use the averaging notation . The significance of the Gowers norms is that they control other multilinear forms that show up...
Rather than delving in to the maths and risking discovering that I needed more components I didn’t have, I started playing with the values I actually did have. Here’s a plot of the before-and-after empirical results. The green curve is the modified version. The level at 50Hz is now ...
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Simple maths remind us that multiplying a positive number with a negative number has a negative result. In other words, the accurate mathematical result is negative, the truncated result is also negative, but the sign flag still isn't set. I'm not sure what else should be considered in ...
Mainframe copybook filter - now displays a red bar at column 72 - any data beyond here gets truncated in line with mainframe commenting standards. COM function addSimpleFilter() now exports the isUnicode option. Much more complex pattern matches now allowed - increased limit of capturing patte...
Your large prime numbers are not the keys themselves, but rather are used to generate the keys with a bit of maths. For completeness, here’s how it actually works: Take two large primes, p and q. Call their product n. Compute the Carmichael totient function of n, L(n). Choose a ...
So to summarise – assuming correctly implemented floating-point maths in the DAW and all it’s plugins, I agree – dither is probably optional apart from the final fixed-point file. But since we KNOW this isn’t the case with legacy Pro Tools, which is incredibly widespread, and it MAY...
Simple maths remind us that multiplying a positive number with a negative number has a negative result. In other words, the accurate mathematical result is negative, the truncated result is also negative, but the sign flag still isn't set. I'm not sure what else should be considered in ...