It is well known that determining the exact values of crossing number for circulant graphs is very difficult. Even so, some important results in this field are still proved. D.J. Ma was proved that the crossing number of C(2m + 2, m) is m + 1[8]. Then such problem for C(n, 3) was further solved [7]. Pak Tung Ho and X. Lin obtained accurate values for the crossover numbers of C (3m, m) and C (3m + 1, m)[4][5]. In this paper, as a complement, we show that the edges from the principal cycle of C(9, 3) do not cross each other in an optimal drawing.

PPGIS platforms have been widely used to map social actors since the emergence of open access webGIS platforms. This identification of citizen initiatives is based on the physical location, but is rarely combined with social networking. This research seeks to close that gap by using the platIC web-based mapping tool for citizen initiatives, together with their interrelationships. Therefore, a methodical procedure has been defined to construct a geolocalised graph by identifying and categorising linked nodes. Method steps have been tested in three case studies in the Malaga region: Malaga city, Benalmadena, and Valle del Genal. They were selected for a comparative analysis in three different urban and socio-economic scenarios, namely: a tourist destination with a high density of Spanish population and floating city users; a sun-and-beach destination with a significant presence of resident foreign population; and a rural area suffering from depopulation, respectively. Mapping reveals a higher density of citizen initiatives in central urban areas and with social conflicts. Social graphs show a wider interconnection of nodes in rural areas, but isolated nodes are spread more widely there. Monitoring active citizen initiatives could serve as a basis for local administration to involve the citizenry in the management of current issues in the urban and rural context. Future research may promote new plugins to improve participatory process through webGIS platforms.

This paper presents an effective method for performing audio steganography, which would help in improving the security of information transmission. Audio steganography is one of the techniques for hiding secret messages within an audio file to maintain communication secrecy from unwanted listeners. Most of these conventional methods have several drawbacks related to distortion, detectability, and inefficiency. To mitigate these issues, a new scheme is presented which combines the techniques of image interpolation with LSB encoding. It selects non-seed pixels to allow reversibility and diminish distortion in medical images. Our technique also embeds a fragile watermarking scheme to identify any breach during transmission to recover data securely and reliably. A magic rectangle has also been used for encryption to enhance data security. This paper proposes a robust, low-distortion audio steganography technique that provides high data integrity with undetectability and will have wide applications in sectors like e-healthcare, corporate data security, and forensic applications. In the future, this approach will be refined for broader audio formats and overall system robustness.

More and more urban studies researchers and students are using images. This choice often stems from the need to illustrate, analyse and understand territories and urban phenomena. This contribution seeks to demonstrate, on the basis of examples drawn from scientific productions in Greater Lomé, how the photographic approach makes it possible to apprehend the urban phenomenon. Three forms of image use can be identified in the documents consulted. On the one hand, images are a source of data to support information received through observation. On the other hand, photography is a technique for collecting metadata which, when triangulated with several sources, enables a query to be answered. Finally, the diachronic and chronological analysis of images of a social reality enables us to detect the visible and the invisible in order to take a critical look at the social world and the dynamics of social relationships.

Census 2022 of Saudi Arabia was released recently, with 12 years of intercensal interval. Although it appeared provisional having no reports similar to the 2010 census, efforts to analyze, interpret, disseminate, and discuss were essential for building structures and systems at par with demographic trends and patterns. An analysis was carried out with this census data compared to 2004 and 2010 to track population change—demographic pace, trends, and patterns—over the two decades. Data from all three censuses were analyzed with conventional demographic techniques. A reduction in growth was observed with a declining percentage of the childhood population but with an expanding percentage of the adults (working age) indicating a demographic dividend resulted, mostly, from fertility decline. An aging trend established by the previous censuses was lost, recently: the constriction of the pyramid of 2010 was changed to a different shape. Not only the percentage distribution trends were uneven but also the age-based indices. Thus, these trends revealed a demographic difference to an extent, that demands standardized reports, uniform procedures for the data collection and compilation, and geographic distribution equations. The increasing concentration in urban centers of major administrative areas—Al-Riyadh, Makkah Al-Mokarramah, and the Eastern Region demand redistribution policies. Self-contained townships appear as a strategic option in population redistribution, guaranteeing quality standards and lifestyle.