The intra-urban space is essentially an organized structure of complexity that consists of centers at different hierarchical levels or scales. This kind of complexity can be measured from the perspective of living structure inspired by Christopher Alexander's organic view of space. Previous studies have revealed that the living structure can be used to characterize the structural complexity of photos, satellite images and urban systems. However, its potential to measure intra-urban complexity using massive point-based datasets remains underexplored. This study introduces a recursive method to analyze intra-urban complexity using massive point-of-interest (POI) data. By recursively decomposing urban substructures, we quantified structural complexity based on the livingness of substructures using a unified criterion. Our findings indicate that cities or intra-urban areas with higher livingness exhibit greater structural complexity. The resulting substructures exhibit power-law distributions and align closely with human activity patterns across multiple spatial scales in four large cities in China. Remarkably, intra-urban structures can be effectively understood with no more than four levels of recursive decomposition. Furthermore, we found that the urban centers or core areas can be effectively located using the proposed method. These insights underscore the potential of living structure as a framework for understanding and measuring the organized complexity of intra-urban spaces.

Urban structure can be better comprehended through analyzing its cores. Geospatial big data facilitate the identification of urban centers in terms of high accuracy and accessibility. However, previous studies seldom leverage multi-source geospatial big data to identify urban centers from a topological perspective. This study attempts to identify urban centers through the spatial integration of multi-source geospatial big data, including nighttime light imagery (NTL), building footprints (BFP) and street nodes of OpenStreetMap (OSM). We use a novel topological approach to construct complex networks from intra-urban hotspots based on the theory of centers by Christopher Alexander. We compute the degree of wholeness value for each hotspot as the centric index. The overlapped hotspots with the highest centric indices are regarded as urban centers. The identified urban centers in New York, Los Angeles, and Houston are consistent with their downtown areas, with overall accuracy of 90.23%. In Chicago, a new urban center is identified considering a larger spatial extent. The proposed approach can effectively and objectively prevent counting those hotspots with high intensity values but few neighbors into the result. This study proposes a topological approach for urban center identification and a bottom-up perspective for sustainable urban design.

The hierarchical structure of geographic or urban space can be well-characterized by the concept of living structure, a term coined by Christopher Alexander. All spaces, regardless of their size, possess certain degrees of livingness that can be mathematically quantified. While previous studies have successfully quantified the livingness of small spaces such as images or artworks, the livingness of geographic space has not yet been characterized in a recursive manner. Zipf’s law has been observed in urban systems and intra-urban structures. However, whether Zipf’s law is applicable to the hierarchical substructures of geographic space has rarely been investigated. In this study, we recursively extract the substructures of geographic space using global nighttime light imagery. We quantify the livingness of global cities considering the number of substructures (S) and their inherent hierarchy (H). We further investigate the scaling properties of the extracted substructures across scales and the relationships between livingness and population for global cities. The results demonstrate that all substructures of global cities form a living structure that conforms to Zipf’s law. The degree of livingness better captures population distribution than nighttime light intensity values for the global cities. This study contributes in three aspects: First, it considers global cities as a whole to quantify spatial livingness. Second, it applies the concept of livingness to cities to better capture the spatial structure of the population using nighttime light data. Third, it introduces a novel method to recursively extract substructures from nighttime images, offering a valuable tool to investigate urban structures across multiple spatial scales.

Knowing the multi-level influences of determinants on medical-service resumptions is of great benefits to the policymaking for medical-service recovery at different levels of study units during the post-COVID-19 pandemic era. This article evaluated the hospital- and city-level resumptions of medical services in mainland China based on the data of location-based service (LBS) requests of mobile devices during the two time periods (December 2019 and from February 21 to March 18, 2020). We selected medical-service capacity, human movement, epidemic severity, and socioeconomic factors as the potential determinants on medical-service resumptions and then explicitly assessed their multi-level explanatory powers and the interactive effects of paired determinants using the geographical detector method. The results indicate that various determinants had different individual explanatory powers and interactive relationships/effects at different levels of medical-service resumptions. The current study provides a novel multi-level insight for assessing work resumption and individual/interactive influences of determinants, and considerable implications for regionalized recovery strategies of medical services.

According to Gestalt theory, any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The figure consists of numerous autogenerated substructures with an inherent hierarchy of far more smalls than larges. Through these substructures, the structural beauty of an image (L), or equivalently the livingness of space, can be computed by the multiplication of the number of substructures (S) and their inherent hierarchy (H). This definition implies that the more substructures something has, the more living or more structurally beautiful it is, and the higher the hierarchy of the substructures, the more living or more structurally beautiful. This is the nonrecursive approach to the structural beauty of images or the livingness of space. In this article we develop a recursive approach, which derives all substructures of an image (instead of its figure) and continues the deriving process for those decomposable substructures until none of them are decomposable. All of the substructures derived at different iterations (or recursive levels) together constitute a living structure; hence the notion of living images. We have applied the recursive approach to a set of images that have been previously studied in the literature and found that (1) the number of substructures of an image is far lower (3 percent on average) than the number of pixels and the centroids of the substructures can effectively capture the skeleton or saliency of the image; (2) all the images have a recursive level more than four, indicating that they are indeed living images; (3) no more than 3 percent of the substructures are decomposable, implying that a vast amount of the substructures are not decomposable; (4) structural beauty can be well measured by the recursively defined substructures, as well as their decomposable subsets. Despite a slightly higher computational cost, the recursive approach is proven to be more robust than the nonrecursive approach. The recursive approach and the nonrecursive approach both provide a powerful means to study the livingness or vitality of space in cities and communities.

The disputed endorsement of inherited visceral and universal aesthetic preferences justifies the scientific validity of Alexander’s living structure. Apart from implying a resource-efficient way to promote well-being through urban design, the premise favors a collective approach to human self-perception and social justice. To better understand the contributions of Alexander, this article explores current knowledge about visceral and universal aesthetic preferences for living structure and if and how the new kind of city science, a mathematical model describing living structure, can be used for further testing. It also elaborates on the social impact of living structure, including its premise, and the potential of the new kind of city science to support social sustainability. A literature synthesis on living structure, the new kind of city science, and the premise showed a positive link between well-being and exposure to living structure. Limitations in research design nevertheless precluded conclusions about the associated visceral and universal aesthetic preferences. The new kind of city science was found appropriate for further research by holistically representing living structure. Moreover, like the hypothesized biological origin, social learning and sociocultural transmission were found to theoretically support the premise of universality and a collective approach to human identity and social justice, with further societal implications. For the concept of living structure to support social sustainability, it must be coupled with the promotion of empowerment and community mobilization. Hence, the operationalization of the new kind of city science should align with Alexander’s call for bottom-up approaches.

COVID-19 vaccination coverage was studied by race/ethnicity, up-to-date doses, and by how it was affected by social vulnerability and spatial accessibility at the census-tract level in Milwaukee County, WI, USA. Social vulnerability was quantified at the census-tract level by an aggregate index and its sub-components calculated using the principal components analysis method. The spatial accessibility was assessed by clinic-to-population ratio and travel impedance. Ordinary least squares (OLS) and spatial regression models were employed to examine how social vulnerability and spatial accessibility relate to the vaccination rates of different doses. We found great disparities in vaccination rates by race and between areas of low and high social vulnerability. Comparing to non-Hispanic Blacks, the vaccination rate of non-Hispanic Whites in the county is 23% higher (60% vs. 37%) in overall rate (one or more doses), and 20% higher (29% vs. 9%) in booster rate (three or more doses). We also found that the overall social-vulnerability index does not show a statistically significant relationship with the overall vaccination rate when it is defined as the rate of people who have received one or more doses of vaccines. However, after the vaccination rate is stratified by up-to-date doses, social vulnerability has positive effects on one-dose and two-dose rates, but negative effects on booster rate, and the effects of social vulnerability become increasingly stronger and turn to negative for multi-dose vaccination rates, indicating the increasing challenges of high social vulnerability areas to multi-dose vaccination. The large negative effects of socio-economic status on the booster rate suggests the importance of improving general socio-economic conditions to promote multi-dose vaccination rates.

The third or organismic view of space states that space is neither lifeless nor neutral, but a living structure capable of being more living or less living, thus different fundamentally from the first two mechanistic views of space: Newtonian absolute space and Leibnizian relational space. The living structure is defined as a physical and mathematical structure or simply characterized by the recurring notion (or inherent hierarchy) of far more small substructures than large ones. This paper seeks to lay out a new geography as a science of the Earth's surface founded on the third view of space. The new geography aims not only to better understand geographic forms and processes but also - maybe more importantly - to make geographic space or the Earth?s surface to be living or more living. After introducing two fundamental laws of geography: Tobler's law on spatial dependence (or homogeneity) and scaling law on spatial heterogeneity, we argue that these two laws are fundamental laws of living structure that favour statistics over exactitude, because the former (or statistics) tends to make a structure more living than the latter  (or exactitude). We present the concept of living structure through some working examples and make it clear how a living structure differs from a non-living structure, under the organismic worldview that was first conceived by the British philosopher Alfred Whitehead (1861-1947). In order to make a structure or space living or more living, we illustrate two design principles - differentiation and adaptation - using two paintings and two city plans. The new geography is a science of living structure, dealing with a wide range of scales, from the smallest scale of ornaments on walls to the scale of the entire Earth's surface.

As Christopher Alexander discovered, all space or matter – either organic or inorganic – has some degree of order in it according to its structure and arrangement. The order refers to a kind of structural character, called living structure, which is defined as a mathematical structure that consists of numerous substructures with an inherent hierarchy. Across the hierarchy, there are far more small substructures than large ones, while on each level of the hierarchy the substructures are more or less similar in size. In this paper we develop a new approach to representing geographic space as a hierarchy of recursively defined subspaces for computing the degree of order. A geographic space is first represented as a hierarchy of recursively defined subspaces, and all the subspaces are then topologically represented as a network for computing the degree of order of the geographic space, as well as that of its subspaces. Unlike conventional geographic representations, which are mechanical in nature, this new geographic representation is organic, conceived, and developed under the third view of space; that is, space is neither lifeless nor neutral, but a living structure capable of being more living or less living. Thus, the order can also be referred to as life, beauty, coherence, or harmony. We applied the new representation to three urban environments, 253 patterns, and 35 black-white strips to verify it and to demonstrate advantages of the new approach and the new kind of order. We further discuss the implications of the approach and the order on geographic information science and sustainable urban planning.

The large concentration of the world’s population in cities, along with rapid urbanization, have brought numerous environmental and socioeconomic challenges to sustainable urban systems (SUS). However, current SUS studies focus heavily on ecological aspects, rely on SUS indicators that are not supported by available data, lack comprehensive analytical frameworks, and neglect SUS regional differences. This paper develops a novel approach to assessing urban sustainability from regional perspectives using commonly enumerated socioeconomic statistics. It integrates land use and land cover change data and ecosystem service values, applies data mining analytics to derive SUS indicators, and evaluates SUS states as trade-offs among relevant SUS indicators. This synthetic approach is called the integrated socioeconomic and land-use data mining–based multi-objective assessment (ISL-DM-MOA). The paper presents a case study of urban sustainability development in cities and counties in Inner Mongolia, China, which face many environmental and sustainable development problems. The case study identifies two SUS types: (1) several large cities that boast well-developed economies, diversified industrial sectors, vital transportation locations, good living conditions, and cleaner environments; and (2) a few small counties that have a small population, small urban construction areas, extensive natural grasslands, and primary grazing economies. The ISL-DM-MOA framework innovatively synthesizes currently available socioeconomic statistics and environmental data as a unified dataset to assess urban sustainability as a total socio-environmental system. ISL-DM-MOA deviates from the current indicator approach and advocates the notion of a data-mining-driven approach to derive urban sustainability dimensions. Furthermore, ISL-DM-MOA diverges from the concept of a composite score for determining urban sustainability. Instead, it promotes the concept of Pareto Front as a choice set of sustainability candidates, because sustainability varies among nations, regions, and locations and differs between political, economic, environmental, and cultural systems.