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Archive for February 5th, 2008

Here’s a terse little paper and experiment showing some clean (easy to understand and rework) results.

DISCUSSION

Past research on the benefits of network structure on the flow of information has often focused on the positive properties of small-world networks [2, 3]. The results of our research cast this view in the wider perspective of fit between network structure and problem space, highlighting the importance of exploration vs. imitation. For the network structures we studied, the lattice promotes the most exploration, followed by the small-world, and the random networks, with the fully connected network producing the least exploration. The needle payout function requires the most exploration to find the global maximum, followed by the multimodal, and then the unimodal. Since there is a tradeoff between the exploration of a problem space and the exploitation of good solutions [4, 5] this tradeoff seems to be highly relevant to the ability of a group to succeed at our task.

Winter A. Mason, Andy Jones, Robert L. Goldstone

That’s pretty academic talk and I’m going to add to it.  Check this essay out.  Combining the two essays and we have something interesting.  The Lattice network set up is best at solving a problem requiring exploration AND we are unable to construct an algorithm that can optimize the traversing of the lattice.  The best path emerges simply by trying to solve the problem AND it’s better than other networks like Small World.

Here’s some quick definitions: (from this nice little doc)

Lattice Network

Rural areas resemble societies long ago and is characterized as “structured lattice.”  That is, people in rural areas are more likely to be friends with each other, while having less bridging friendship ties with the outside world.

Small World

Urban areas resemble random connection societies.  That is, from telecommunication advances that are readily available in urban areas, more friendship bridging ties are available.

Okay, now a fun exercise is defining the structure of MySpace, Facebook, LinkedIn, Open Source Community and sussing out why each one may be so good at what it does.    This is purely me just toying with an idea (what do you think?).

MySpace – Full.  You can and do connect to anyone and everyone.  It’s a race for connectivity and theirs no real “neighbor” paradigm.  MySpace definitely has the imitation feel to it.

Facebook – Lattice, small world.  Your neighbors typically are your college mates and work mates.  Apps, links and “problems” propogate and are reworked quickly, far more quickly  in my experience, than on MySpace.

LinkedIn – Lattice.  hard to assess linkedin’s ability to solve problems or propogate thinking.  It’s mostly a lead gen network.

Master Software Developer Competition – Lattice.  but hard to say.  There seemed to be a few key nodes and generally some “neighborhoods”.  On slashdot it was full, but once the Google group took over the network structure changed a lot.  Hmmm… need to think on that.

Open Source – Lattice, sometimes small world.  Open source projects generally are not completely wide open (there’s a skill level required/credibility) and their aren’t random.  Ideas, code propogate 1 or 2 degrees from the original node.  Very rarely isn’t it full, like the internet.  Everyone connected.  Ideas and problems are very efficiently solved in open source but it’s damn near impossible to predict who, what, when.

 The implication that network structure alone can have that big an impact is very interesting, and a powerful concept to understand if you are in the business of solving problems or socializing ideas/policies or marketing a product.

Methinks the network structure is a proxy for the schedules of reinforcement at play. Different structures reinforce behavior in different ways.

~Russ

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