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“Nowadays, age ain’t nothing but a number. It is how people embrace technology, from social networks to smartphones to intelligent appliances, that contributes to the digital lifestyle that is now synonymous with Gen-C.” — Meet Generation C: The Connected Customer - Brian Solis (via ibmsocialbiz)

(Source: fredericw, via ibmsocialbiz)

The Internet’s Turning Us Into Cyborgs — But Is That a Bad Thing?We are giving away two copies of

I Love Charts: The Bookand offering a sneak peek at the chapter on the Internet over here. Check it out!

The Internet’s Turning Us Into Cyborgs — But Is That a Bad Thing?We are giving away two copies of

I Love Charts: The Bookand offering a sneak peek at the chapter on the Internet over here. Check it out!

Using last.fm Data to Map Geographic Flow of MusicBy tapping into the last.fm API, these Irish researchers modeled the geographic flow of musical influence. They were able to identify where certain tastes frequently originated, and draw a hierarchy of influential cities (like the chart shown above for North America).

Surprisingly, the size of a city doesn’t associate very strongly with how influential it is. That means that despite its enormous size, NYC isn’t that much more influential than Portland or Austin. There are prevailing theories that large cities are the drivers of cultural invention, but this seems to show (for music, at least) that a connected online world is leveling that playing field.

Also, they have a graph displaying “

Normalized Radiohead vs. Normalized Coldplay”, which has to go down as one of the best figures in a research paper, ever.

(via arXiv)

Very cool paper.

geographic flow of music

Thomae’s function, named after Carl Johannes Thomae, also known as thepopcorn function, theraindrop function, thecountable cloud function, themodified Dirichlet function, theruler function,^{[1]}theRiemann functionor theStars over Babylon(by John Horton Conway) is a modification of the Dirichlet function. This real-valued functionf(x) is defined as follows:If

x= 0 we takeq= 1. It is assumed here that gcd(p,q) = 1 andq> 0 so that the function is well-defined and non-negative.

DiscontinuitiesThe popcorn function is perhaps the simplest example of a function with a complicated set of discontinuities:

fis continuous at all irrational numbers and discontinuous at all rational numbers.

Informal ProofClearly,

fis discontinuous at all rational numbers: since the irrationals are dense in the reals, for any rationalx, no matter whatεwe select, there is an irrationalaeven nearer to ourxwheref(a) = 0 (whilef(x) is positive). In other words,fcan never get “close” and “stay close” to any positive number because its domain is dense with zeroes.To show continuity at the irrationals, assume without loss of generality that our

εis rational (for any irrationalε, we can choose a smaller rationalεand the proof is transitive). Since ε is rational, it can be expressed in lowest terms asa/b. We want to show thatf(x) is continuous whenxis irrational.Note that

ftakes a maximum value of 1 at each whole integer, so we may limit our examination to the space between and . Sinceεhas a finite denominator ofb, the only values for whichfmay return a value greater thanεare those with a reduced denominatorno larger than b. There exist only a finite number of values between two integers with denominator no larger thanb, so these can be exhaustively listed. Settingδto be smaller than the nearest distance fromxto one of these values guarantees every value withinδofxhasf(x) <ε.

Facebook's Telescope on Human Behavior - Technology Review -

One research group inside Facebook, known as the Data Team, is tasked with the challenge of mathematically sifting through that data to look for patterns that explain the how and why of human social interactions. The people who do that, mostly PhDs with research experience in computer and social sciences, look for insights that will help Facebook tune its products, but have also begun to publish their findings in the scientific community.

Data team. Wow