Hi Hoon,
That is good research question. Before, my point is: get a common
ruler and put over most 'power laws' you see. It is not an easy
exercise. Many cases you find a cut-off point and clear tail. Other
cases you find 2 power-laws regimes and so on.
See:
Power laws, Pareto distributions and Zipf's law -
MEJ Newman - Contemporary Physics, 2005 - Taylor & Francis
However, many cases you do not find anything... there is no section in
the curve that is clearly straight, and any chosen 'cut-off' point
generates a different exponent, sometimes very different... are they
power-laws?
About your question, the power law behaviour is more clearly observed
in the tail, 'top values'. Therefore, it is not the small chunks of
space that will change it, but the generalisation process that creates
the large objects (long lines in this case). If different
generalisation processes generate different or closely related
power-laws regimes it is a question to be addressed.
In my opinion, the results can be a lot affected by the artificial
boundary choosen in the map, the quality of the data and the
generalisation process.
Best Regards,
Lucas Figueiredo
On 01/06/07, Hoon Park <[log in to unmask]> wrote:
> Lucas
>
> A question: If we include, following 'TeleAtlas' for instance, to map such
> countless bits of space as 'The ramp to the car park at 1-19 Torrington
> Plc' or 'The entrance to the emergency services at UCH' into a street
> network, could it change its degree distribution from a 'log-normal' to
> a 'power-law'? If so, can we really claim that the degree distribution of
> street networks does not follow a power law but a log-normal?
>
> Regards,
> Hoon
>
>
> >On Thu, 31 May 2007 19:24:49 +0100, Lucas Figueiredo
> ><[log in to unmask]> wrote:
> >
> >>On 31/05/07, Rui Carvalho <[log in to unmask]> wrote:
> >>> Pitty no one knows what a street is...
> >>
> >>Certainly it is not a segment (or route) between two junctions.
> >>Otherwise we would have things like "Oxford Street sector A, B, C" and
> >>so on...
> >
> >The ramp to the car park at 1-19 Torrington Plc. This comes in GPS car
> >navigation systems as a decision point? is it a street?
> >
> >The entrance to the emergency services at UCH (that's UCL Hospital for
> non
> >Londoners). Is it a street?
> >
> >This question appears when you process data from services like TeleAtlas -
> >the most accurate data available on street networks...
> >
> >Looks like Alan should organize that 'mass observation' on what a street
> >is after all...
> >
> >Comments welcome!
> >
> >Rui
> >
> >
> >>
> >>Regards,
> >>
> >>Lucas Figueiredo
> >>http://www.flickr.com/photos/lucasfigueiredo/
> >>
> >>Mindwalk
> >>http://www.mindwalk.com.br
> >========================================================================
>
--
Lucas Figueiredo
http://www.flickr.com/photos/lucasfigueiredo/
Mindwalk
http://www.mindwalk.com.br
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