Using Fractal Analysis in Modeling Trends in the National Economy

Box-Counting Fractal Analysis: A Primer for the Clinician

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Fractal algorithms and RGB image processing in scribal and ink identification on an 1819 secret initiation manuscript to the "Philike Hetaereia"

Historical texts incorporate important characteristics that need to be assessed including genre, text structure and content. Often overlooked are characteristics of handwritten manuscripts commonly divided into legibility, readability and aesthetics. To determine the scientific feasibility of classification of handwritten texts an objective approach is developed to describe twenty handwritten pages of an 1819 Greek manuscript, that refers to the initiation to the Greek secret "friendly society" (Philike Hetaereia) organization, established as part of the Greek independence against the Ottoman Turks. It is investigated through a fractal and RGB image analysis approach. Fractal Minkowski Dimension was applied on the handwritten text and the RGB color analysis on the ink and paper and both were used as a non-invasive manner and revealed interesting results. The novel RGB image analysis and the fractal analysis of the manuscript identified respectively, five iron gall inks and four scribes from the ink content and handwritten styles, of the compact five lines text and whole text pages. The novel approach was verified with another old manuscript of known ink pigments, as well as with thirteen known handwritten texts of that period and four prints representing modern and similar period texts substantiating the findings of the novel methods.

Structural Fractal Analysis of the Active Site of Acetylcholinesterase in Complexes with Huperzine A, Galantamine, and Donepezil

The fractal dimension (D) of the active site of hAChE in the unliganded state and as part of complexes with hyperzine A, galantamine, and donepezil is calculated using molecular interatomic-distance histograms. Fractal matrices of structural changes (FMSCs) are formed by pairwise comparison of the values of D and by revealing the significance of their differences. FMSCs are found to be used to quantitatively estimate the changes in the structures of the molecules in various states. When analyzing FMSCs, we found that the most significant structural changes are related to the Glu202 amino acid residue. No structural perturbations are revealed in the case of Trp86, Gly122, Ala204, Phe338, Tyr341, Gly448, and Ile451.

The Use of Sholl and Kolmogorov Complexity Analysis in Researching on the Sustainable Development of Creative Economies in the Development Region of Bucharest‒Ilfov, Romania

Nowadays, creative economies stand as a relevant indicator of the sustainable development of local and regional ones. The study aims to highlight the spatial behaviour of creative economies in the Bucharest‒Ilfov Development Region, the most dynamic and complex regional economy in Romania. In order to assess the spatial dynamics of creative economies in the region, an economic database was created, at the level of the territorial administrative unit, for the two economic indicators considered important for the study, number of employees and turnover, under the auspices of the Classification of National Economy Activities (NACE). The establishment of creative economies was made following the Government Decision no. 859 of 2014, with 66 codes for this sector. Annual cartographic models were developed for each indicator in QGIS (a free and open–source cross–platform desktop geographic information system application that supports viewing, editing, and analysis of geospatial data), for the period 2000–2016. For a relevant analysis of spatial behaviour, we used Sholl and Kolmogorov complexity, which highlighted specific patterns of spatial dynamics that help us to understand the role of creative economies in the sustainable development of regional economies. The results highlighted the role of accessibility corridors in the development of the regional economy.