On the scientific side, we have discovered some new techniques and constructions to show that a given equational theory does not imply another one, and have also discovered some exotic algebraic structures, such as the “Asterix” and “Obelix” pair, that have interesting features, and which ...
More subtle are the anti-implications, in which we have to show that a law does not imply a law . In principle, one just has to exhibit a magma that obeys but not . In a large fraction of cases, one can simply search through small finite magmas – such as magmas on two, three, ...
In literal terms, what is the standard error of the mean? What does it mean to say that a result is "statistically significant"? Explain how to find the percentage of measurements in the data set that fall within an interval. How does sample size affect the width of the intervals? Explai...
1) If you were asked to mathematically determine how many standard deviations a value is from the mean, would you use: (a) a Survey (b) a Central Limit Theorem (c) a Transformation (d) a Z score. 2) A z score is c...
What you learn from this is that between September and November, afterthe original OPERA result(what I call OPERA-1) was released publicly and the media frenzy began, OPERA personnel did what they should do: they made many studies of their work to see if they could find mist...
The basic concept behind PINN training is that it can be thought of as an unsupervised strategy that does not require labelled data, such as results from prior simulations or experiments. The PINN algorithm is essentially a mesh-free technique that finds PDE solutions by converting the problem ...
I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, “But how can it be like that?” because you will get “...
, but rather “How many extra nines of safety does it add?”. As one final comparison between nines of safety and other standard risk measures, we give the following proposition regarding large deviations from the mean. Proposition 12 Let be a normally distributed random variable of standard...
On the scientific side, we have discovered some new techniques and constructions to show that a given equational theory does not imply another one, and have also discovered some exotic algebraic structures, such as the “Asterix” and “Obelix” pair, that have interesting features, and which ...