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people working in these fields, especially in the bigger cities. A recent attempt to
provide a quantitative evaluation of the relationships between city size and urban
organization showed that many of the characteristics of cities in national urban sys-
tems could be summarized as a power relation that varied with size (Bettencourt
et al. 2007 ). Such relations have been found in many organisms, for growth often
displays a − 1/4 power function, so that devolops it has slower growth and gets big-
ger in a predictable way. The infrastructure aspects of cities, such as road surfaces,
power cables, gas stations, displayed a similar − 1/4 power relation. However, when
variables linked to inventions, patents, R&D activity etc, were measured in vari-
ous urban systems, the power relations of these variables clustered around a + 1/4
scaling relationship, meaning that growth in these variables accelerated as the cities
became bigger. Bettencourt and his co-workers speculated that these relationships
stemmed from the fact that infrastructure growth involved economies of scale as
the city got bigger, effectively slowing down the rate of growth in these variables,
whereas variables of innovations and wealth creation accelerated with size. It is
worth noting that similar rates of growth also occurred with crime and the spread of
infectious diseases, showing that growth may have some disadvantages, as studies
of urban diseconomies have shown, although most were attributed to poor urban
management in resolving problems (Richardson 1973 ).
This finding of a general relationship between the concentration of knowledge
activities and larger urban places has been shown by many empirical studies. For
example, an early report on the Knowledge Economy locations in the European
Community (Drewett et al 1988 ) showed that in the 240 major city regions in Eu-
rope with over 250,00 people, only 15 contained more than 10 headquarters of the
largest 1000 industrial firms and 469 of these biggest companies had head offices in
only five locations (London and South-East England (216), Paris and Ile-de-France
(131), Dusseldorf and Rhine-Ruhr (51), Randstad (39), Frankfurt-Darmstadt (32)),
with a clear emphasis upon the first two. Other studies in Europe have shown simi-
lar patterns (Capello 2013 ), while a more detailed survey of companies employed in
four new technologies (biotechnology, aeronautics and space, artificial intelligence,
and textiles and clothing) revealed that 80 % of all innovative R&D projects were
located in ten major regions of innovation and that over three-quarters of public
research funding was also concentrated in these areas, namely, the previous five
centres, plus Munich, Lyon-Grenoble, Turin and Milan (Hilpert 1992 ). Similar con-
centrations have been found in the United States. Audretsch and Feldman ( 1996 ),
using innovation citations from over a hundred scientific and trade journals, showed
that California (41.7 %) and Massachusetts (12 %) accounted for over half of the
innovations in the computer industry by 1982, a result of the well-known concen-
tration of these activities in Silicon Valley (O'Mara 2005 ) and Route 128 around
Boston (Rosegart and Lampe 1992 ; Mackun 2013 ). This pattern of concentration
of the research side of the industry in a few locations, which are usually called
research clusters, has been duplicated in many other counties (Cooke 2001 ; Cooke
and Swartz 2007 ).
A more general attempt to measure the location of initial research activity , rather
than numbers of research companies, spending, or employment, has been made by
Matthieson and his colleagues at the University of Copenhagen. Their analysis of
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