# Sylvia

## Apr 26

[video]

“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 Book and 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 Book and offering a sneak peek at the chapter on the Internet over here. Check it out!

Using last.fm Data to Map Geographic Flow of Music

By 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 the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function,[1] the Riemann function or the Stars over Babylon (by John Horton Conway) is a modification of the Dirichlet function. This real-valued function f(x) is defined as follows:

$f(x)=\begin{cases} \frac{1}{q}\mbox{ if }x=\frac{p}{q}\mbox{ is a rational number}\\ 0\mbox{ if }x\mbox{ is irrational}. \end{cases}$

If x = 0 we take q = 1. It is assumed here that gcd(pq) = 1 and q > 0 so that the function is well-defined and non-negative.

## Discontinuities

The popcorn function is perhaps the simplest example of a function with a complicated set of discontinuitiesf is continuous at all irrational numbers and discontinuous at all rational numbers.

Informal Proof

Clearly, f is discontinuous at all rational numbers: since the irrationals are dense in the reals, for any rational x, no matter what ε we select, there is an irrational a even nearer to our x where f(a) = 0 (while f(x) is positive). In other words, f can 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 ε is rational (for any irrational ε, we can choose a smaller rational ε and the proof is transitive). Since ε is rational, it can be expressed in lowest terms as a/b. We want to show that f(x) is continuous when x is irrational.

Note that f takes a maximum value of 1 at each whole integer, so we may limit our examination to the space between $\lfloor x \rfloor$ and $\lceil x \rceil$. Since ε has a finite denominator of b, the only values for which f may return a value greater than ε are those with a reduced denominator no larger than b. There exist only a finite number of values between two integers with denominator no larger than b, so these can be exhaustively listed. Setting δ to be smaller than the nearest distance from x to one of these values guarantees every value within δ of x has f(x) < ε.

(via )

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