14,658 research outputs found
Ghetto of Venice: Access to the Target Node and the Random Target Access Time
Random walks defined on undirected graphs assign the absolute scores to all
nodes based on the quality of path they provide for random walkers. In city
space syntax, the notion of segregation acquires a statistical interpretation
with respect to random walks. We analyze the spatial network of Venetian canals
and detect its most segregated part which can be identified with canals
adjacent to the Ghetto of Venice.Comment: 14 pages, 3 figure
Transport Networks Revisited: Why Dual Graphs?
Deterministic equilibrium flows in transport networks can be investigated by
means of Markov's processes defined on the dual graph representations of the
network. Sustained movement patterns are generated by a subset of automorphisms
of the graph spanning the spatial network of a city naturally interpreted as
random walks. Random walks assign absolute scores to all nodes of a graph and
embed space syntax into Euclidean space.Comment: 12 page
Random Walks Estimate Land Value
Expected urban population doubling calls for a compelling theory of the city.
Random walks and diffusions defined on spatial city graphs spot hidden areas of
geographical isolation in the urban landscape going downhill. First--passage
time to a place correlates with assessed value of land in that. The method
accounting the average number of random turns at junctions on the way to reach
any particular place in the city from various starting points could be used to
identify isolated neighborhoods in big cities with a complex web of roads,
walkways and public transport systems
Intelligibility and First Passage Times In Complex Urban Networks
Topology of urban environments can be represented by means of graphs. We
explore the graph representations of several compact urban patterns by random
walks. The expected time of recurrence and the expected first passage time to a
node scales apparently linearly in all urban patterns we have studied In space
syntax theory, a positive relation between the local property of a node
(qualified by connectivity or by the recurrence time) and the global property
of the node (estimated in our approach by the first passage time to it) is
known as intelligibility. Our approach based on random walks allows to extend
the notion of intelligibility onto the entire domain of complex networks and
graph theory.Comment: 19 pages, 4 figures, English UK, the Harvard style reference
Performance Comparisons of Greedy Algorithms in Compressed Sensing
Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recovery the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large scale empirical investigation into the behavior of three of the state of the art greedy algorithms: NIHT, HTP, and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recovery the sparsest solution is accurately determined, and throughout this region additional performance characteristics are presented. Contrasting the recovery regions and average computational time for each algorithm we present algorithm selection maps which indicate, for each problem size, which algorithm is able to reliably recovery the sparsest vector in the least amount of time. Though no one algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise and for a variety of problem classes. The algorithm selection maps presented here are the first of their kind for compressed sensing
- …