Common scaling laws for city highway systems and the mammalian neocortex

Abstract

A variety of scaling laws are known for the mammalian neocortex relating gray matter volume, total number of synapses [1,2], white matter volume [3][4][5][6][7][8][9], number of neurons [6,[10][11][12], surface area [4,5,[13][14][15][16], axon caliber [1,17], and number of cortical areas or compartments [18]. These neocortical scaling laws appear to be a consequence of selection pressure for a sheet-like structure (namely, gray matter) to economically maintain a high level of interconnectedness [1,2,19,20]. We might therefore expect to find similar scaling laws for any sheetlike structure under similar selection pressures, in which case the neocortex would be just an instance of a more general kind of structure.Here, we investigate city highway systems as a potential kind of network which may be driven by similar principles as the neocortex. In contrast to neurons, which are conduits for information-related signals on which brain computations rely, highways are conduits for physical materials and people. But from the perspective of the city as a whole, the materials and people that highways transport are crucial to the large-scale function carried out by the city, and are, in a sense, signals-that one signal is electric and the other physical may not matter in regards to the fundamental principles governing them. In addition to the prima facie analogy between city highway networks and the brain's neural connections, there are several other reasons we chose to examine city highway networks. First, the organization of city highway networks tends to be driven by political and economic forces over decades, rather than being planned in advanced following known principles of highway engineering [21]-i.e., city highways systems are a result of an evolution-like mechanism. Second, cities are under selection pressure to efficiently interconnect via highways and roads. Third, because cities lie on the land they are approximately a surface, or a sheet. Fourth, highway network data are readily available (and our data set consists of 60 U.S. cities varying in population from 10 4 to nearly 10 7 , see Table 2 for raw data). Finally, the organization of city highway systems is interesting in and of itself: nearly half of Earth's 6.6 billion people now live in cities, and cities are becoming ever larger and densely populated. The proper functioning of a city requires that people and materials be quickly moved throughout it. This is a very difficult design problem, one that is magnified by the fact that city population tends to grow much faster than city surface area, and cities tend to increase in population over time, so that the efficient highway network must constantly evolve from the pre-existing one. Identification of scaling laws governing how highway organization scales with city size could potentially lead to better highway systems, and more efficiently running cities.

Non-linear Amplification of Variability Through Interaction Across Scales Supports Greater Accuracy in Manual Aiming: Evidence From a Multifractal Analysis With Comparisons to Linear Surrogates in the Fitts Task

“…Indeed, broad interdependence of disparate physiological tissues is a central theme of the multifractal tensegrity hypothesis and a main motivation for using multifractal geometry to make explicitly estimable the non-linear interactions governing a cohesive system across many scales (Ingber, 2006; Van Orden et al, 2012; Turvey and Fonseca, 2014). Indeed, the dawning picture we have of the nervous system suggests a causal relationship run by non-linear interactions across scale (Morgane et al, 2005; Changizi and DeStefano, 2009; Deco et al, 2011). To the point, beyond muddying our ability to identify clear parts with reliably stable and distinct responsibilities, these non-linear interactions appear to be the very physiological support that allows the nervous system to operate as impressively as it does.…”

Superlinear and sublinear urban scaling in geographical networks modeling cities

“…In particular, it has been elucidated that urban indicators quantifying city activities on average scale with the population size in a power-law manner. These include many creative productivities and infrastructure volumes [14][15][16][17] such as the gross domestic product (GDP), the number of patents, human online activities [18], prosocial behaviors [19], quantities related to highway systems [20], the number of crimes [21], the number of supply stations [22], and emissions of CO 2 [23] and NO 2 [24]. There exist several models explaining such allometric scaling behavior [25][26][27][28] and fluctuations around average power-law relations [29][30][31].…”

Smart City 4.0 from the Perspective of Open Innovation

“…Changizi [24] found that the brain and the city both connect much more intensively to function more optimally as they grow bigger, and they both follow similar experiential principles (Scaling laws). Wedeen [25] has suggested a new view of the structure of a brain starts that sees it as a simple, elementary structure with MRI analysis, and it is similar to New York City's street grids that are directed to a particular object.…”