Urban scaling analysis has introduced a new scientific paradigm to the study of cities. With it, the notions of size, heterogeneity and structure have taken a leading role. These notions are assumed to be behind the causes for why cities differ from one another, sometimes wildly. However, the mechanisms by which size, heterogeneity and structure shape the general statistical patterns that describe urban economic output are still unclear. Given the rapid rate of urbanization around the globe, we need precise and formal mathematical understandings of these matters. In this context, I perform in this dissertation probabilistic, distributional and computational explorations of (i) how the broadness, or narrowness, of the distribution of individual productivities within cities determines what and how we measure urban systemic output, (ii) how urban scaling may be expressed as a statistical statement when urban metrics display strong stochasticity, (iii) how the processes of aggregation constrain the variability of total urban output, and (iv) how the structure of urban skills diversification within cities induces a multiplicative process in the production of urban output.

Regional differences of inventive activity and economic growth are important in economic geography. These differences are generally explained by the theory of localized knowledge spillovers, which argues that geographical proximity among economic actors fosters invention and innovation. However, knowledge production involves an increasing number of actors connecting to non-local partners. The space of knowledge flows is not tightly bounded in a given territory, but functions as a network-based system where knowledge flows circulate around alignments of actors in different and distant places. The purpose of this dissertation is to understand the dynamics of network aspects of knowledge flows in American biotechnology. The first research task assesses both spatial and network-based dependencies of biotechnology co-invention across 150 large U.S. metropolitan areas over four decades (1979, 1989, 1999, and 2009). An integrated methodology including both spatial and social network analyses are explicitly applied and compared. Results show that the network-based proximity better defines the U.S. biotechnology co-invention urban system in recent years. Co-patenting relationships of major biotechnology centers has demonstrated national and regional association since the 1990s. Associations retain features of spatial proximity especially in some Midwestern and Northeastern cities, but these are no longer the strongest features affecting co-inventive links. The second research task examines how biotechnology knowledge flows circulate over space by focusing on the structural properties of intermetropolitan co-invention networks. All analyses in this task are conducted using social network analysis. Evidence shows that the architecture of the U.S. co-invention networks reveals a trend toward more organized structures and less fragmentation over the four years of analysis. Metropolitan areas are increasingly interconnected into a large web of networked environment. Knowledge flows are less likely to be controlled by a small number of intermediaries. San Francisco, New York, Boston, and San Diego monopolize the central positions of the intermetropolitan co-invention network as major American biotechnology concentrations. The overall network-based system comes close to a relational core/periphery structure where core metropolitan areas are strongly connected to one another and to some peripheral areas. Peripheral metropolitan areas are loosely connected or even disconnected with each other. This dissertation provides empirical evidence to support the argument that technological collaboration reveals a network-based system associated with different or even distant geographical places, which is somewhat different from the conventional theory of localized knowledge spillovers that once dominated understanding of the role of geography in technological advance.