Archive for the ‘Random Numbers’ Category

Non-Uniform Random Variate Generation

Wednesday, January 7th, 2015

Non-Uniform Random Variate Generation by Luc Devroye.

From the introduction:

Random number generatlon has Intrigued sclentlsts for a few decades, and a lot of effort has been spent on the creatlon of randomness on a determlnlstlc (non-random) machlne, that Is, on the deslgn of computer algorlthms that are able to produce “random” sequences of lntegers. Thls Is a dlfflcult task. Such algorlthms are called generators, and all generators have flaws because all of them construct the n -th number In the sequence In functlon of the n -1 numbers precedlng It, lnltlallzed wlth a nonrandom seed. Numerous quantltles have been lnvented over the years that measure Just how “random” a sequence Is, and most well-known generators have been subJected to rlgorous statlstlcal testlng. How-ever, for every generator, It ls always posslble to And a statlstlcal test of a (possl- bly odd) property to make the generator flunk. The mathernatlcal tools that are needed to deslgn and analyze these generators are largely number theoretlc and comblnatorlal. These tools differ drastically from those needed when we want to generate sequences of lntegers wlth certain non-unlform dlstrlbutlons, glven that a perfect unlform random number generator 1s avallable. The reader should be aware that we provlde hlm wlth only half the story (the second half). The assGmptlon that a perfect unlform random number generator 1s avallable 1s now qulte unreallstlc, but, wlth tlme, It should become less so. Havlng made the assumptlon, we can bulld qulte a powerful theory of non-unlform random varlate generatlon.

You will need random numbers for some purposes in information retrieval but that isn’t why I mention this eight hundred (800) + page tome.

The author has been good enough to put the entire work up on the Internet and you are free to use it for any purpose, even reselling it.

I mention it because in a recent podcast about Solr 5, the greatest emphasis was on building and managing Solr clusters. Which is a very important use case if you are indexing and searching “big data.”

But in the rush to index and search “big data,” to what extent are we ignoring the need to index and search Small But Important Data (SBID)?

This book would qualify as SBID and even better, it already has an index against which to judge your Solr indexing.

And there are other smallish collections of texts. The Michael Brown grand jury transcripts, which are < 5,000 pages, the CIA Torture Report at 6,000 pages, and many others. Texts that don’t qualify as “big data” but still require highly robust indexing capabilities.

Take Non-Uniform Random Variate Generation as a SBID and practice target for Solr.

I first saw this in a tweet by Computer Science.

‘Sounds of Silence’ Proving a Hit: World’s Fastest Random Number Generator

Sunday, July 15th, 2012

‘Sounds of Silence’ Proving a Hit: World’s Fastest Random Number Generator

From the post:

Researchers at The Australian National University have developed the fastest random number generator in the world by listening to the ‘sounds of silence’.

The researchers — Professor Ping Koy Lam, Dr Thomas Symul and Dr Syed Assad from the ANU ARC Centre of Excellence for Quantum Computation and Communication Technology — have tuned their very sensitive light detectors to listen to vacuum — a region of space that is empty.

Professor Lam said vacuum was once thought to be completely empty, dark, and silent until the discovery of the modern quantum theory. Since then scientists have discovered that vacuum is an extent of space that has virtual sub-atomic particles spontaneously appearing and disappearing.

It is the presence of these virtual particles that give rise to random noise. This ‘vacuum noise’ is omnipresent and may affect and ultimately pose a limit to the performances of fibre optic communication, radio broadcasts and computer operation.

“While it has always been thought to be an annoyance that engineers and scientists would like to circumvent, we instead exploited this vacuum noise and used it to generate random numbers,” Professor Lam said.

“Random number generation has many uses in information technology. Global climate prediction, air traffic control, electronic gaming, encryption, and various types of computer modelling all rely on the availability of unbiased, truly random numbers.

All the talk about security and trust reminded me of this post.

Just in case your topic map software needs random numbers for encryption or other purposes.

See: Quantum Random Number Generator for papers and a live random number feed.

Assuming you “trust” some alphabet soup agency has not spoofed the IP address and has its own feed of pseudo-random numbers in place of the real one.

If not, you need to build your own quantum detector, assuming you “trust” the parts have not been altered to produces their “random” numbers.

If not, you could build your own parts, but only if you remember to wear your tin hat at all times to prevent/interfere with mind control efforts.

Trust is a difficult issue.