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This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.

Mathematics. --- Computers. --- Computer graphics. --- Visualization. --- Manifolds (Mathematics). --- Complex manifolds. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Computing Methodologies. --- Computer Graphics. --- Topology. --- Mathematical analysis. --- Information visualization. --- Data visualization --- Visualization of information --- 517.1 Mathematical analysis --- Mathematical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Information science --- Visual analytics --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Cell aggregation --- Artificial intelligence. --- Artificial Intelligence. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Digital techniques --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Math --- Science

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This book provides a short, hands-on introduction to the science of complexity using simple computational models of natural complex systems-with models and exercises drawn from physics, chemistry, geology, and biology. By working through the models and engaging in additional computational explorations suggested at the end of each chapter, readers very quickly develop an understanding of how complex structures and behaviors can emerge in natural phenomena as diverse as avalanches, forest fires, earthquakes, chemical reactions, animal flocks, and epidemic diseases.Natural Complexity provides the necessary topical background, complete source codes in Python, and detailed explanations for all computational models. Ideal for undergraduates, beginning graduate students, and researchers in the physical and natural sciences, this unique handbook requires no advanced mathematical knowledge or programming skills and is suitable for self-learners with a working knowledge of precalculus and high-school physics.Self-contained and accessible, Natural Complexity enables readers to identify and quantify common underlying structural and dynamical patterns shared by the various systems and phenomena it examines, so that they can form their own answers to the questions of what natural complexity is and how it arises.

Complexity (Philosophy) --- Physics --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Philosophy --- Emergence (Philosophy) --- Methodology. --- Burridge-Knopoff stick-slip model. --- Gutenberg-Richter law. --- Johannes Kepler. --- Olami-Feder-Christensen model. --- Python code. --- accretion. --- active flockers. --- agents. --- automobile traffic. --- avalanches. --- cells. --- cellular automata. --- chaos. --- clusters. --- complex behavior. --- complex structure. --- complex system. --- complexity. --- computational model. --- computer program. --- contagious diseases. --- criticality. --- diffusion-limited aggregation. --- earthquake forecasting. --- earthquakes. --- emergence. --- emergent behavior. --- emergent structure. --- epidemic spread. --- epidemic surges. --- excitable system. --- flocking. --- forest fires. --- fractal clusters. --- fractal geometry. --- growth. --- hodgepodge machine. --- infection rate. --- iterated growth. --- lattice. --- lichens. --- natural complex system. --- natural complexity. --- natural order. --- natural phenomena. --- nature. --- open dissipative system. --- panic. --- passive flockers. --- pattern formation. --- percolation threshold. --- percolation. --- phase transition. --- planetary motion. --- power-law. --- random walk. --- randomness. --- repulsion. --- rule-based growth. --- sandpile. --- scale invariance. --- segregation. --- self-organization. --- self-organized criticality. --- self-propulsion. --- self-similarity. --- simple rules. --- small-world network. --- solar flares. --- spaghetti. --- spatiotemporal pattern. --- spiral. --- tagging algorithm. --- traffic jams. --- waves. --- wildfire management.