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The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
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The coherence of US cities.

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Cities aim for economic diversification, but it requires expanding capabilities. This study reveals that urban economic coherence remains stable over time, with diversification constrained by city size.

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Area of Science:

  • Urban Economics
  • Economic Geography
  • Complexity Science

Background:

  • Diversified economies are crucial for urban growth and development.
  • Economic diversification often necessitates expanding a city's capability base, presenting a trade-off between growth and cost.
  • Understanding how cities manage this trade-off is key to sustainable urban development.

Purpose of the Study:

  • To analyze how cities manage the trade-off between economic diversification and its associated costs.
  • To measure the coherence of economic activities within cities as an indicator of diversification management.
  • To investigate the long-term development of the US urban system from 1850 to the present.

Main Methods:

  • Defining and measuring economic coherence as the technological distance between productive units in a city.
  • Utilizing historical census data (over 600M records) for economic activities from 1850-1940.
  • Analyzing patent records and detailed occupational/industrial profiles for recent decades.

Main Results:

  • Despite significant shifts in US economic geography over 170 years, average urban economic coherence has remained constant.
  • Economic coherence consistently decreases with city size across different time periods and datasets.
  • This inverse relationship between coherence and city size suggests universal constraints on diversification.

Conclusions:

  • Urban economic systems exhibit a stable level of coherence over long periods, indicating consistent patterns in diversification.
  • City size acts as a universal constraint on economic diversification, irrespective of the specific era or economic structure.
  • Future urban development strategies should consider these size-dependent constraints on diversification.