Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 153 tok/s
Gemini 2.5 Pro 50 tok/s Pro
GPT-5 Medium 20 tok/s Pro
GPT-5 High 28 tok/s Pro
GPT-4o 79 tok/s Pro
Kimi K2 198 tok/s Pro
GPT OSS 120B 428 tok/s Pro
Claude Sonnet 4.5 38 tok/s Pro
2000 character limit reached

Valeriepieris Circles Reveal City and Regional Boundaries in England and Wales (2502.07451v1)

Published 11 Feb 2025 in stat.AP and physics.soc-ph

Abstract: We propose a new method of determining regional and city boundaries based on the Valeriepieris circle, the smallest circle containing a given fraction of the data. By varying the fraction in the circle we can map complex spatial data to a simple model of concentric rings which we then fit to determine natural density cutoffs. We apply this method to population, occupation, economic and transport data from England and Wales, finding that the regions determined by this method affirm well known social facts such as the disproportionate wealth of London or the relative isolation of the North East and South West of England. We then show how different data sets give us different views of the same cities, providing insight into their development and dynamics.

Summary

  • The paper introduces a concentric ring model using Valeriepieris circles to derive data-driven urban and regional boundaries from diverse spatial datasets in England and Wales.
  • Analysis of population, economic, and occupational data reveals distinct zones for London, the South East, and other regions, highlighting socio-economic and transport disparities.
  • Findings suggest that using multiple dataset-driven boundaries is necessary for urban analysis, offering a data-driven alternative to fixed administrative lines.

A Concentric Ring Model for Defining City and Regional Boundaries: Insights from Valeriepieris Circles

This paper introduces a novel methodology for determining city and regional boundaries by leveraging the concept of Valeriepieris circles—a computational tool originally suggested for capturing population density by defining the smallest circle containing a given fraction of the global population. The authors extend this concept to map complex spatial data into a more manageable model of concentric rings, which can then be analyzed to identify natural density cutoffs. The investigation is centered on England and Wales, utilizing various datasets including population, occupation, economic activity, and transport data.

The approach taken in this paper aims to derive boundaries from the data itself rather than relying on predefined political or administrative lines, which may be subject to historical or political bias. The researchers applied the Valeriepieris circle methodology to the national and city scale data of England and Wales, uncovering significant patterns in the spatial distribution of resources and the socio-economic landscape.

Key Results

  1. England and Wales as a Case Study: The analysis of population data affirmed three distinct zones: London, the South East, and a broader region encompassing other major parts of England and Wales. Notably, certain peripheral regions such as the North East and South West were found outside the broader boundary, reflecting known socio-cultural and economic divides.
  2. Economic and Occupational Concentration: The GVA and high-prestige jobs (L1 occupations) showed a pronounced concentration in central London, with the economic activity notably more centralized compared to population distribution. Conversely, lower supervisory roles (L10 occupations) were more dispersed, extending beyond London, indicating a socio-economic stratification aligned with geographic distribution.
  3. Transport Network Analysis: The bus stop dataset, representative of road transport density, diverged significantly from other datasets. The boundary for bus stops, interestingly, showed a pronounced north-west focus rather than a concentration in the south-east, highlighting disparities in transport network densities that could impact accessibility equity.
  4. City Boundary Analysis: At the city level, boundaries defined through population data align closely with official administrative boundaries in locations such as London. However, when using economic or transport data, boundaries differ, offering insights into administrative regions versus functional urban regions.

Implications

The findings underscore the inadequacy of single, fixed city definitions when assessing urban and regional dynamics. Each type of dataset—demographic, economic, occupational, transport—provides a distinct perspective of what constitutes a city or region. Consequently, this paper suggests that multiple definitions should be used, depending on the question or policy concern at hand.

From a methodological standpoint, the concentric ring model and the Valeriepieris circle approach provide a versatile and data-driven alternative to traditional geographical delineation techniques. This has significant implications for urban planning and the paper of socio-economic regionalism, offering a means to reconcile observed spatial phenomena with their underlying social and economic continua.

Speculations on Future Developments

The integration of this method into defining urban and regional spaces presents opportunities for refining urban scaling laws, with potential applications extending to global cities. The detailed transformation of spatial data into one-dimensional radial profiles opens new avenues for analysis in urban studies, potentially informing models that predict urban form and function.

Further research could focus on applying this methodology globally and assessing how robust it is across diverse geographies. Moreover, the relationship between the ring model parameters and established urban theories, such as allometric scaling, would be an intriguing area of exploration, potentially bridging disparate theoretical frameworks in urban science.

Dice Question Streamline Icon: https://streamlinehq.com
Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets

This paper has been mentioned in 1 tweet and received 8 likes.

Upgrade to Pro to view all of the tweets about this paper: