Multifractal scaling analyses of urban street network structure: the cases of twelve megacities in China

Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory.Comment: 32 pages, 9 figures, 5 table

Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland

Revealing spatiotemporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities and date, this paper is aimed at exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square calculation is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceeds the Euclidean dimension of embedding space when moment order q<<0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows. First, self-similar patterns developed in the process of Covid-19 pandemic, which seem be dominated by multi-scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.Comment: 22 pages,6 figures, 4 table

: FRACTALOPOLIS MODEL - ACCESSIBILITY, EVALUATION & MORPHOLOGICAL RULES

page number: 74A sustainable and sustaining planning strategy is globally important for metropolitan areas. Sustainable planning addresses the development of strategies to reduce the use of resources, increase economic efficiency and improve integration of social aspects. In contrast, splinter development (e.g. urban sprawl) involves damage to nature and generation of an increasing volume of traffic (these are the main criticisms following a study by Newman and Kenworthy (1989) on the relationship between settlement density and energy consumption). Interestingly, the overly compact city also has this effect as it may generate traffic flows for accessing green and leisure areas, or changes of residence due to a favouring of sites that lie farther away from the centre than the inhabitants' current places of residence. Households not only consume urban amenities integrated into densely populated areas, but also aspire to have access to green and leisure areas. Schwanen et al. (2004) showed that households usually optimize their residential choice with respect to accessibility to various types of amenities, which is inherently linked to the frequentation rate of these amenities (daily, weekly, monthly, and occasional) (c.f. spatial practice of people). Moreover, on an urban scale, over-compactness causes ecological problems such as a lack of green wedges for supplying the city with fresh air (urban microclimate). Thus, we aim to find a solution for managing dispersed development which marries the twin elements of green and built-up space in a highly efficient manner. This solution also needs to incorporate dynamic aspects of a city as well as minimizing traffic costs and emissions. Based on the observation that urban space is founded on the principle of fractal geometry, it seems interesting to explore to what extent fractal geometry may be drawn upon for solving the spatial antagonism of compactness and urban sprawl.Une stratégie d'aménagement durable représente un enjeu important pour le développement des agglomérations contemporaines. L'aménagement durable implique le développement de stratégies visant à réduire l'utilisation des ressources, accroître l'efficacité économique et améliorer l'intégration des aspects sociaux (ex. environnements conviviaux pour les piétons, équilibre entre modes de transport public/privé, réseaux routiers performants, viabilisation des terres agricoles, économie du mouvement ; accès à l'emploi pour tous, commerces, services ; santé, culture et loisirs). A l'inverse, le développement fractal (ex. étalement urbain) n'est pas sans répercussions néfastes sur la nature et tend à augmenter le volume du trafic (principales critiques émises dans une étude de Newman & Kenworthy, 1989, portant sur les relations entre densité d'implantation et consommation d'énergie). Fait intéressant, une ville trop compacte induit un effet semblable car elle peut être à l'origine de flux de trafic pour accéder aux espaces verts et récréatifs ou des déménagements vers des endroits plus éloignés du centre que les lieux de résidence actuels des citadins. Les ménages ne se contentent pas d'utiliser les aménagements urbains intégrés dans les zones à forte densité de population, ils aspirent également à un accès aux espaces verts et récréatifs. Schwanen et al. (2004) ont mis en évidence le fait que les ménages tendaient à optimiser leur choix de résidence en fonction de l'accessibilité de divers types de commodités, un phénomène foncièrement lié au taux de fréquentation (quotidienne, hebdomadaire, mensuelle et occasionnelle) de ces dernières (cf. pratiques spatiales de la population). A l'échelle urbaine, une compacité excessive entraîne par ailleurs des problèmes écologiques, tels que le manque d'espaces verts pour approvisionner la ville en air frais (microclimat urbain). Nous recherchons ainsi une solution afin de gérer le développement fractal de manière à pouvoir concilier efficacement le couple antinomique espaces verts/espaces urbanisés. Cette solution doit également intégrer les aspects dynamiques d'une ville et minimiser les émissions et les coûts du trafic et prévenir la désagrégation des terres agricoles. Sur la base de l'observation selon laquelle l'espace urbain repose sur le principe de la géométrie fractale, il paraît intéressant d'explorer dans quelle mesure la géométrie fractale peut être mise à contribution en vue de résoudre l'antagonisme spatial compacité/étalement urbain

Aplicación de redes complejas a la descripción de la dinámica de contaminantes atmosféricos

Air pollution has been a major concern among environmental scientists due to its importance to public health. Among the different pollutants that can be found in the air, one can point out tropospheric ozone as one of the most studied ones in the recent years, due to the risk derived for living beings. As a result of the many factors involved in the creation and destruction of this gas, the analysis of its dynamics is quite complicated. Traditionally, conventional statistical methods have been employed, while in the last decades multifractal approaches have gained importance. This is due to their suitability describing systems with a great degree of variability. This thesis focuses on the evaluation and implementation of complex networks for the analysis of tropospheric O3 dynamics. The studies carried out are based on the Visibility Graph (VG) technique, which transforms time series into complex networks that inherit the properties of the first ones. In the first part, a combination of the VG and the multifractal Sand-Box (SB) algorithms is performed. By doing this, authors analyze the generalized fractal dimensions and the singularity spectra. Then, a comparison was made between these multifractal parameters and the quantities obtainable from the degree distribution of the resulting graphs. Regarding the second part of this thesis, the VG methodology was used on O3 time series from rural and urban stations, in order to retrieve the centrality parameters from the obtained networks. This way, degree, shortest path and betweenness are studied to support the use of this technique and find new information. Results show that this methodology can indeed differentiate between ozone measurements in urban and countryside environments, providing new insights about the dynamics. In the third and last part of this document, authors propose an alternative approach to the VG, called Sliding Visibility Graph (SVG). This new technique takes advantage of the fact that visibility adjacency matrices are mostly empty, since the bast majority of the nodes are not connected to each other. Thanks to this, it is possible to apply effectively a sliding window approach to lessen considerably the computation time, reducing one order the time efficiency (from O(N2) to O(N). This is especially convenient when dealing with very large time series. As the resulting network approximates the original VG, it has been evaluated how it converges to the VG case for different types of series, as there lies the actual interest of this tool. As expected, the SVG results converge quite rapidly to the exact values, especially for random and O3 concentration series.La contaminación atmosférica es uno de los principales problemas estudiados dentro de la ciencia ambiental, debido a su gran impacto en la salud pública. Entre los diferentes contaminantes que podemos encontrar en el aire, merece la pena destacar el ozono troposférico (O3) como uno de los más estudiados en los últimos años, debido al alto riesgo para los seres vivos. Como resultado de los numerosos factores implicados en la creación y destrucción de este gas, el análisis de sus dinámicas es bastante complejo. Tradicionalmente, se han usado métodos estadísticos convencionales, mientras que en las últimas décadas han ganado importancia las técnicas multifractales. Esto se debe a su adecuación para describir sistemas con un grado elevado de variabilidad. Esta tesis se centra en la evaluación e implementación de las redes complejas para el análisis de la dinámica del O3. Los estudios llevados a cabo se basan en el uso de la técnica del Grafo de Visibilidad (GV), que transforma series temporales en redes complejas que heredan propiedades de las primeras. En la primera parte, se utiliza una combinación del GV y del algoritmo multifractal Sand-Box (SB). Gracias a esto, es posible obtener las dimensiones fractales generalizadas y el espectro de singularidades. Por último, se ha realizado una comparación entre los parámetros multifractales y las cantidades obtenibles directamente a partir de la distribución del grado de los grafos resultantes. En cuanto a la segunda parte de esta tesis, el método del GV es usado en series temporales de O3 de estaciones rurales y urbanas, con la finalidad de obtener los parámetros de centralidad de las redes conseguidas. De este modo, el grado, el camino mínimo y la intermediación se estudian para refutar la aplicabilidad del GV y buscar nueva información. Los resultados muestran que en efecto esta metodología puede permitir diferenciar entre medidas de ozono en medios rurales y urbanos. En la tercera y última parte de este documento, los autores proponen un método alternativo al GV, llamado Grafo de Visibilidad Deslizante (GVD). Esta nueva técnica se aprovecha del hecho de que las matrices de adyacencia de los GV son prácticamente vacías, puesto que la mayoría de los vértices no están conectados entre sí. Gracias a ello, es posible aplicar de forma efectiva un algoritmo de ventana deslizante para reducir considerablemente el tiempo de cálculo, bajando en uno el orden de magnitud de la eficiencia (de O (N2) a O (N)). Esto es especialmente provechoso cuando se trata con series temporales muy grandes. Debido a que la red resultante aproxima al GV original, se ha evaluado cómo converge al segundo para diferentes tipos de series temporales, que es donde reside en interés real de esta herramienta. Como era de esperar, los resultados del GVD convergen rápidamente a los valores exactos, especialmente para series aleatorias y concentración de O3

Study On Land Use Aggregation Pattern Of Luohe City Based On Spatial Heterogeneity

The spatial layout of land use can reflect the health of urban development and inform the construction of green infrastructure. Many layout measurements have been proposed for lands in homogeneous spaces. Researchers and planners have used them to describe the urban structure and identify current problems in pursuit of problem-oriented optimizations. Now, with the urban expansion and accessibility development, the urban space has gradually changed from homogeneous to heterogeneous. However, the study of land use layout based on heterogeneous space is insufficient. Different land use types are expected to be allocated more scientifically, so providing more objective evidence on the urban land layout is necessary. Among them, the Aggregation-Diffusion status of each type of land is the most basic and vital information. In this paper, the spectral, index, and inversion data of Landsat 8 and Sentinel2 were collected, combined with NPP/VIIRS, and the Weka-EM clustering method was used to determine the boundary of build-up area in Luohe City (China) to obtain our study area. Then, we improve the traditional RAD by measuring roads \u27Efficiency value\u27 using Space Syntax: the homogeneous space is weighted to describe the effect of spatial heterogeneity for each land type. Therefore, by comparing the differences in the aggregation-diffusion land layout of these two spaces, the results are as follows: first of all, RAD shows that there is a dense core in Luohe City, in which priority development of ecological land can achieve a multiplier effect with half the effort. Secondly, in AAD, the basic unit based on efficiency value shows apparent spatial heterogeneity in Luohe urban space, represented by the contour line. The benefits of the greenway will be more fully realized where the contours are dense. Thirdly, comparing the description of the Aggregation-Diffusion situation of each land type by RAD and AAD, it can be found that: each land type has a different sensitivity to spatial heterogeneity, and AAD is a more accurate way of spatial description; Both AAD and RAD indicate a significant radial differentiation of land use in Luohe, which means that the significance of greenway construction in this religion is further enhanced. In addition to the greenway’s fundamental ecological implications, it also plays a vital role in facilitating the material-energy flow as well as promoting integration and equitable urban development

Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models

Traffic microsimulation models use the movement of individual driver-vehicle-units (DVUs) and their interactions, which allows a detailed estimation of the traffic noise using Common Noise Assessment Methods (CNOSSOS). The Dynamic Traffic Noise Assessment (DTNA) methodology is applied to real traffic situations, then compared to on-field noise levels from measurement campaigns. This makes it possible to determine the influence of certain local traffic factors on the evaluation of noise. The pattern of distribution of vehicles along the avenue is related to the logic of traffic light control. The analysis of the inter-cycles noise variability during the simulation and measurement time shows no influence from local factors on the prediction of the dynamic traffic noise assessment tool based on CNOSSOS. A multifractal approach of acoustic waves propagation and the source behaviors in the traffic area are implemented. The novelty of the approach also comes from the multifractal model's freedom which allows the simulation, through the fractality degree, of various behaviors of the acoustic waves. The mathematical backbone of the model is developed on Cayley-Klein-type absolute geometries, implying harmonic mappings between the usual space and the Lobacevsky plane in a Poincare metric. The isomorphism of two groups of SL(2R) type showcases joint invariant functions that allow associations of pulsations-velocities manifolds typ

Fractal Gaussian Networks: A Sparse Random Graph Model Based on Gaussian Multiplicative Chaos

The accepted article, arXiv:2008.03038v2 [stat.ML] (for this version) is available at: https://doi.org/10.48550/arXiv.2008.03038. An earlier version of this paper was presented in part at the 37th International Conference on Machine Learning (ICML) 2020.10.13039/501100001459-Ministry of Education, Singapore (MOE) (Grant Number: R-146-000-250-133 and R-146-000-312-114); UC Davis’s Center for Data Science and Artificial Intelligence Research (CeDAR) Innovative Data Science Seed Funding Program 10.13039/100000001-NSF (Grant Number: DMS-2053918); 10.13039/501100001866-Fonds Nationalde la Recherche, Luxembourg (FNR) (Grant Number: MISSILe (R-AGR-3410-12-Z)); Luxembourg and Singapore Universities.https://arxiv.org/abs/2008.0303

Morfogénesis y fractalidad: análisis de la ciclorruta de Bogotá, Colombia

The cities exhibit a principle of fractal ordering –fractal and self-affinity or independent self-similar patterns of scale– which was demonstrated as a morphological characteristic of urban complexity for several decades.&nbsp;This study explores and develops a complex approach to the cycle path of the city of Bogotá D.C (Colombia) through fractal estimates and densities of its different spaces. Complementary methodologies such as geographic information systems (GIS) for the processing of data were used.&nbsp;As a result, the sites of greater and lesser density in the structure of the Bogota´s bikeway are shown as an indicator of evolution and planning. It was concluded that the set of sizes of the fractal dimensions has a power law distribution -represented by a dashed line- which reaffirms its fractal nature.&nbsp;As an innovative aspect, this work proposes to establish a possible connection between the social sciences and the complexity sciences, among which are the fractal geometry, from a transdisciplinary exploration that contributes to the recent studies on urban complexity from Latin America.Las ciudades exhiben un principio de ordenamiento fractal –patrones fractales y auto-afines o auto-similares independientes de escala–, el cual fue demostrado como característica morfológica de la complejidad urbana desde hace algunas décadas (Batty y Longley, 1994). Este estudio explora y desarrolla un abordaje complejo de la ciclorruta de la ciudad de Bogotá D.C (Colombia), a través de estimaciones fractales y densidades de sus diferentes espacios. Se utilizaron metodologías complementarias como los sistemas de información geográfica (SIG) para el procesamiento de los datos. Como resultado se evidencia los sitios de mayor y menor densidad en la estructura de la ciclorruta bogotana, como indicador de evolución y planeación. Se concluyó que el conjunto de los tamaños de las dimensiones fractales presenta una distribución tipo ley de potencia –representada por una línea en picada–, lo cual reafirma su naturaleza fractal. Como aspecto innovador este trabajo propone establecer una conexión posible entre las ciencias sociales y las ciencias de la complejidad, entre las que se encuentran la Geometría fractal, a partir de una exploración transdisciplinar que contribuya a los estudios recientes sobre complejidad urbana desde Latinoamérica

Measuring urban form : overcoming terminological inconsistencies for a quantitative and comprehensive morphologic analysis of cities

Unprecedented urbanisation processes characterise the Great Acceleration, urging urban researchers to make sense of data analysis in support of evidence-based and large-scale deci- sion-making. Urban morphologists are no exception since the impact of urban form on funda- mental natural and social patterns (equity, prosperity and resource consumption’s efficiency) is now fully acknowledged. However, urban morphology is still far from offering a comprehensive and reliable framework for quantitative analysis. Despite remarkable progress since its emergence in the late 1950s, the discipline still exhibits significant terminological inconsistencies with regards to the definition of the fundamental components of urban form, which prevents the establishment of objective models for measuring it. In this article, we present a study of existing methods for measuring urban form, with a focus on terminological inconsistencies, and propose a systematic and comprehensive framework to classify urban form characters, where ‘urban form character’ stands for a characteristic (or feature) of one kind of urban form that distinguishes it from another kind. In particular, we introduce the Index of Elements that allows for a univocal and non-interpretive description of urban form characters. Based on such Index of Elements, we develop a systematic classification of urban form according to six categories (dimension, shape, spatial distribution, intensity, connectivity and diversity) and three conceptual scales (small, medium, large) based on two definitions of scale (extent and grain). This framework is then applied to identify and organise the urban form characters adopted in available literature to date. The resulting classification of urban form characters reveals clear gaps in existing research, in particular, in relation to the spatial distribution and diversity characters. The proposed framework reduces the current inconsistencies of urban morphology research, paving the way to enhanced methods of urban form systematic and quantitative analysis at a global scale