A Fractal Approach to Urban Boundary Delineation Based on Raster Land Use Maps: A Case of Shanghai, China

Given the diverse socioecological consequences of rapid urban sprawl worldwide, the delineation and monitoring of urban boundaries have been widely used by local governments as a planning instrument for promoting sustainable development. This study demonstrates a fractal method to delineate urban boundaries based on raster land use maps. The basic logic is that the number of built-up land clusters and their size at each dilation step follows a power-law function. It is assumed that two spatial subsets with distinct fractal characteristics would be obtained when the deviation between the dilation curve and a straight line reaches the top point. The top point is regarded to be the optimum threshold for classifying the built-up land patches, because the fractality of built-up land would no longer exist beyond the threshold. After that, all the built-up land patches are buffered with the optimum threshold and the rank-size distribution of new clusters can be re-plotted. Instead of artificial judgement, hierarchical agglomerative clustering is utilized to automatically classify the urban and rural clusters. The approach was applied to the case of Shanghai, the most rapidly urbanizing megacity in China, and the dynamic changes of the urban boundaries from 1994 to 2016 were analyzed. On this basis, urban–rural differences were further explored through several fractal or nonfractal indices. The results show that the proposed fractal approach can accurately distinguish the urban boundary without subjective choice of thresholds. Extraordinarily different fractal dimensions, aggregation and density and similar average compactness were further identified between built-up land in urban and rural areas. The dynamic changes in the urban boundary indicated rapid urban sprawl within Shanghai during the study period. In view of the popularization and global availability of raster land use maps, this paper adds fuels to the cutting-edge topic of distinguishing the morphological criteria to universally describe urban boundaries.

Spatial and Temporal Spread of the COVID-19 Pandemic Using Self Organizing Neural Networks and a Fuzzy Fractal Approach

In this article, the evolution in both space and time of the COVID-19 pandemic is studied by utilizing a neural network with a self-organizing nature for the spatial analysis of data, and a fuzzy fractal method for capturing the temporal trends of the time series of the countries considered in this study. Self-organizing neural networks possess the capability to cluster countries in the space domain based on their similar characteristics, with respect to their COVID-19 cases. This form enables the finding of countries that have a similar behavior, and thus can benefit from utilizing the same methods in fighting the virus propagation. In order to validate the approach, publicly available datasets of COVID-19 cases worldwide have been used. In addition, a fuzzy fractal approach is utilized for the temporal analysis of the time series of the countries considered in this study. Then, a hybrid combination, using fuzzy rules, of both the self-organizing maps and the fuzzy fractal approach is proposed for efficient coronavirus disease 2019 (COVID-19) forecasting of the countries. Relevant conclusions have emerged from this study that may be of great help in putting forward the best possible strategies in fighting the virus pandemic. Many of the existing works concerned with COVID-19 look at the problem mostly from a temporal viewpoint, which is of course relevant, but we strongly believe that the combination of both aspects of the problem is relevant for improving the forecasting ability. The main idea of this article is combining neural networks with a self-organizing nature for clustering countries with a high similarity and the fuzzy fractal approach for being able to forecast the times series. Simulation results of COVID-19 data from countries around the world show the ability of the proposed approach to first spatially cluster the countries and then to accurately predict in time the COVID-19 data for different countries with a fuzzy fractal approach.

Unknown pages of the state of sheba history in the context of modern and biblical archaeology

In the Sheba state, 2 thousand years before the emergence of Islam, there was a monotheistic doctrine unknown to science, whose supporters were called the first Arabian prophets (hanifas) and actually equated with Muslims. This conclusion was obtained using the modern methodology of cognition — fractal approach, hermeneutics methods, logic-semantic analysis, abdication, etc. The results of the study showed, that at the end of the 15th century ВС the Egyptian religion of the Sun ('Monism) was perceived in the Sheba state, where King Yataamar ruled, and became the spiritual basis of this 157 civilization. After the conflict with the state of Israel (loth century ВС), the Queen of Sheba was forced to recognize the power of King Solomon and his religion. During the revival of this state in the VIII century ВС, Atonism was again declared the official religion until the V century ВС. This religious doctrine, which arose during the reign of Pharaoh Akhenaten (1436—1402 ВС), did not disappear shortly after his death (according to modern Egyptologists), and today is represented in the beliefs of the Mandei community (southern Iraq) and their scripture by Jinze.

FRACTAL APPROACH TO MECHANICAL AND ELECTRICAL PROPERTIES OF GRAPHENE/SIC COMPOSITES

Graphene and carbon nanotubes have a Steiner minimum tree structure, which endows them with extremely good mechanical and electronic properties. A modified Hall-Petch effect is proposed to reveal the enhanced mechanical strength of the SiC/graphene composites, and a fractal approach to its mechanical analysis is given. Fractal laws for the electrical conductivity of graphene, carbon nanotubes and graphene/SiC composites are suggested using the two-scale fractal theory. The Steiner structure is considered as a cascade of a fractal pattern. The theoretical results show that the two-scale fractal dimensions and the graphene concentration play an important role in enhancing the mechanical and electrical properties of graphene/SiC composites. This paper sheds a bright light on a new era of the graphene-based materials.

New Semi Quantitative Approach for Interpreting Vertical Electrical Sounding (VES) Measurements by Using Fractal Modeling Technique, Case Study from Khanasser Valley, Northern Syria

Fractal modeling technique, with adapting the concentration-number (C-N) model and the threshold break points concept is newly proposed to interpret vertical electrical sounding (VES) measurements distributed along a given profile. New semi quantitative approach is consequently proposed to rapidly differentiate between different apparent resistivity populations, where 2D semi quantitative interpretation and a primary geological analysis could be constructed. The new technique is practiced and tested on a case study taken from Khanasser Valley, Northern Syria, where different selected profiles (LP1, LP2, LP3, and TP5) are interpreted. The availability and the feasibility of the proposed approached are confirmed and approved through the different comparisons between the multi fractal established cross sections and the traditional 1D VES interpretation models. It is recommended to routinely use this new proposed fractal approach in the geoelectrical researches for interpreting VES measurements distributed along a given profile.