Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table

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

Census Tract License Areas: Disincentive for Sharing the 3.5GHz band?

Flexible licensing model is a necessary enabler of the technical and procedural complexities of Spectrum Access System (SAS)-based sharing framework. The purpose of this study is to explore the effectiveness of 3.5GHz Licensing Framework - based on census tracts as area units, areas whose main characteristic is population. As such, the boundary of census tract does not follow the edge of wireless network coverage. We demonstrate why census tracts are not suitable for small cell networks licensing, by (1) gathering and analysing the official census data, (2) exploring the boundaries of census tracts which are in the shape of nonconvex polygons and (3) giving a measure of effectiveness of the licensing scheme through metrics of area loss and the number of people per census tract with access to spectrum. Results show that census tracts severely impact the effectiveness of the licensing framework since almost entire strategically important cities in the U.S. will not avail from spectrum use in 3.5GHz band. Our paper does not seek to challenge the core notion of geographic licensing concept, but seeks a corrective that addresses the way the license is issued for a certain area of operation. The effects that inappropriate size of the license has on spectrum assignments lead to spectrum being simply wasted in geography, time and frequency or not being assigned in a fair manner. The corrective is necessary since the main goal of promoting innovative sharing in 3.5 GHz band is to put spectrum to more efficient use.Comment: 7 pages, 5 figures, conferenc