Böcker av Fivos Papadimitriou

Geo-Topology is an exploration of the depth and breadth of the relationships between Geography and Topology, with applications ranging from Landscape Geography to Social Geography and from Spatial Analysis to Geospatial Technologies. It shows how topics of geographical research (landscapes, borders, spatial social relationships etc) can be examined by using mathematical concepts and methods of Topology, exposing the realm of geo-topological modelling and visualization through Point-Set Topology, Knot Theory, Reeb graphs, Topological Surfaces (i.e. Möbius bands and Klein bottles), Differential Topology, Network Analysis, Combinatorial Topology, Braid Theory and Ultrametric Topology. Besides geographers, this book is a trove of new ideas for landscape ecologists, mathematicians, data scientists, sociologists, psychologists, anthropologists and educators. Geo-Topology is a systematic introduction to topological thinking in Geography, also by highlighting the significance of Topology for Geographical Education, as well as for the Philosophy and Epistemology of Geography.

This book offers a comprehensive exposition of the mathematical methods that can be used to model landscape dynamics. It is systematically shown how mathematical models of progressively higher complexity can be derived from ordinary landscape maps and related data in ways that enable researchers to predict future landscape transformations and to assess landscape stability, sustainability and resilience.These models are deterministic (i.e. linear or non-linear systems of differential equations), stochastic (i.e. Markovian), or combined deterministic-and-stochastic (using stochastic differential equations), whereas topics and challenging problems related to complexity (spatial randomness, chaotic behaviors, riddled systems etc) are also examined in the book.

This is the first book on spatial entropy in the scientific literature. It links spatial entropy with landscape analysis, landscape diversity and geo-information. It gives all the essential tools that a researcher needs in order to study the spatial entropy of physical as well as artificial landscapes (created with artificial life, swarm intelligence etc). This book explores the fascinating world of the interplay between spatial entropy, spatial information, self-organization and emergence and gives geographers and landscape scientists several alternative mathematical methods to study them, i.e. Shannon's formula, measures from non-extensive thermodynamics, from directional statistics and network theory. An essential book for researchers in landscape analysis and geo-informatics.     

This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems.