Possible projects (Spatial Networks)
These early ones are conceptual; later there will be more explicit math questions.
- (8/30)
Look at articles in journal Networks and spatial economics
to see if some model/problem there can be adapted to our setting in an interesting way.
- (8/30) Create/edit Wikipedia articles on the basic topics related to this course, starting with the
(currently very poor) article on
spatial Poisson processes
and the (rather incomplete?) article on
spatial networks.
- (9/4) Draw figures of all listed networks on a realization of random points.
- (9/4) Are there interesting general methods that, given n points in general position, output some
connected network with junctions?
- (9/11) Can you devise some interesting math model/question in the ``road-dual network" context?
- (9/13) Find good data, and/or a systematic classification of the
different topologies in the ``leaf-labeled" planar model of road networks.
- (9/16) Study the "Route-length in tree-networks" conjecture.
- (9/23) re "Networks based on powers of edge-lengths':
Literature on this model? Simulations, as done for the beta-skeleton family.
- (9/23)
For (say) Gabriel or DT, can one give sharp conditions for configurations
to have the property that length-per-unit area is O(1) ?
- (9/23)
Is it true for RNG and Gabriel that worst-case r_{ave} is same order as worst-case r^*?
- (9/30): Can the Penrose - Yukich (2001) CLT technique be applied to
our kind of ``optimal networks"?
- (9/30): (literature survey): compare the technical assumptions on "locality" used,
in our spatial setting, for proving CLTs and for proving LDs and within the LWC methodology.