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Entropies and entropy-like quantities play an increasing role in modern non-linear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropy-based coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.

fault diagnosis --- empirical mode decomposition --- auditory attention --- Dempster-Shafer evidence theory --- simulation --- uncertainty of basic probability assignment --- center of pressure displacement --- particle size distribution --- multivariate analysis --- symbolic analysis --- permutation entropy --- short time records --- co-evolution --- plausibility transformation --- experiment of design --- cross-entropy method --- weighted Hartley entropy --- firefly algorithm --- embedded dimension --- entropy measure --- effective transfer entropy --- treadmill walking --- ordinal patterns --- complex fuzzy set --- entropy visualization --- belief entropy --- signal classification --- machine learning evaluation --- novelty detection --- selfsimilar measure --- Permutation entropy --- automatic learning --- cross wavelet transform --- cross-visibility graphs --- Kolmogorov-Sinai entropy --- distance --- Shannon-type relations --- Tsallis entropy --- market crash --- support vector machine (SVM) --- conditional entropy of ordinal patterns --- sample entropy --- learning --- electroencephalography (EEG) --- meta-heuristic --- entropy --- data transformation --- information entropy --- signal analysis --- synchronization analysis --- similarity indices --- data analysis --- geodesic distance --- auditory attention classifier --- entropy measures --- distance induced vague entropy --- analog circuit --- vague entropy --- complex vague soft set --- entropy balance equation --- parametric t-distributed stochastic neighbor embedding --- global optimization --- learning systems --- image entropy --- algorithmic complexity --- support vector machine --- system coupling --- relevance analysis --- Chinese stock sectors --- Shannon entropy --- linear discriminant analysis (LDA) --- information --- information transfer --- dual-tasking --- non-probabilistic entropy

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Much of the urban research focuses on the large metropolitan areas in South Africa. This book assesses spatial planning in the second-tier cities of the country. Secondary cities are vital as they perform essential regional, and in some cases, global economic roles and help to distribute the population of a country more evenly across its surface. Apartheid planning left South African cities fragmented segregated and with low densities. Post-apartheid policies aim to reverse these realities by emphasising integration, higher densities and upgrading. Achieving these aims has been challenging and often the historical patterns continue. The evidence shows that two opposing patterns prevail, namely increased densities and continued urban sprawl. This book presents ten case studies of spatial planning and spatial transformation in secondary cities of South Africa. The book frames these case studies against complexity theory and suggests that the post-apartheid response to apartheid planning represents a linear deviation from history. The ten case studies then reveal how difficult it is for local decision-makers to find appropriate responses and how current responses often result in contradictory results. Often these cities are highly vulnerable and they find it difficult to plan in the context of uncertainty. The book also highlights how these cities find it difficult to stand on their own against the influence of interest groups (property developers, mining companies, traditional authorities, other spheres of government). The main reasons include weak municipal finance statements, the dependence on national and provincial government for capital expenditure, limited investment in infrastructure maintenance, the lack of planning capacity, the inability to implement plans and the unintended and sometimes contrary outcomes of post-apartheid planning policies.

City & town planning - architectural aspects --- Secondary cities --- spatial transformation --- Secondary cities and research and policy in South Africa --- spatial planning --- Post-apartheid spatial policy --- complex spaces --- Complex adaptive systems --- Socioecological systems --- Implications for planning in complex systems --- Adaptive co-evolution --- Collaborative and adaptive planning and leadership --- Urban sprawl --- Gated estates --- Drakenstein Municipality’s spatial problems --- sprawl --- Policy for spatial containment --- Spatial planning for the Limpopo energy hub --- Mining booms and busts --- Settlement planning and housing policy for mining towns --- Infrastructure --- Spatial change --- Spatial transformation and complexity --- Complexity of planning in Mahikeng --- Planning in a difficult space --- Policy and planning frameworks --- Demographics --- Planning for spatial transformation --- Matjhabeng: planning in the face of the Free State Goldfields decline --- Context and changes in Matjhabeng --- Welkom’s economy and global market forces --- Spatial changes in Matjhabeng --- 1990–2013 --- Spatial planning in Matjhabeng: 1994–2018 --- The 2005/2006 spatial development framework --- The 2013 spatial development framework --- The 2015 Matjhabeng by-laws --- Precinct plans --- realistic plans in a situation of economic stagnation --- Mbombela: a growing provincial capital and tourism destination --- Spatial and population change --- Municipal infrastructure --- Main spatial challenges --- Spatial priorities and plans --- N4 Maputo corridor --- Participatory planning --- Balancing urban and rural land development --- Integrated development --- Msunduzi: spatially integrating Kwazulu-Natal’s diverse capital --- the contribution of the spatial development framework to spatial transformation --- Factors affecting spatial change in Polokwane Local Municipality --- Settlement hierarchy --- Corridors and transportation --- Water and sanitation infrastructure --- Spatial planning problems in Rustenburg --- Internal dynamics that hinder spatial transformation --- External dynamics that hinder spatial transformation --- Quality of the spatial development framework and planning process --- Spatial planning and complexity lessons --- Complexity as a lens to assess spatial planning instruments --- Interconnected nodes and car-free transport --- Optimal land use --- Resource custodianship --- Promotion of agriculture and food production --- and preservation of heritage --- Complexity in spatial planning for Stellenbosch Municipality --- complexity theory and spatial change