Boundaries of a Complex World

1. Front Matter

   Pages i-xviii

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2. Arts and Nonlinear Systems: ‘Nonlineart’

   1. Front Matter

      Pages 1-2

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   2. Introduction

      • Andrei Ludu

      Pages 3-7

   3. Boundary in Visual Perception and Arts

      • Andrei Ludu

      Pages 9-76

   4. Boundary in Social Systems

      • Andrei Ludu

      Pages 77-105

3. Mathematical Language

   1. Front Matter

      Pages 107-110

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   2. Boundary in Continuous Mathematics

      • Andrei Ludu

      Pages 111-161

   3. Boundary in Discrete Mathematics

      • Andrei Ludu

      Pages 163-206

4. Applications

   1. Front Matter

      Pages 207-209

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   2. The Boundary in the Philosophy of Science

      • Andrei Ludu

      Pages 211-216

   3. Networks and Their Boundaries

      • Andrei Ludu

      Pages 217-233

   4. Big Data Systems

      • Andrei Ludu

      Pages 235-249

   5. Liquid Boundaries

      • Andrei Ludu

      Pages 251-339

   6. Conclusions

      • Andrei Ludu

      Pages 341-345

5. Back Matter

   Pages 347-363

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The 2nd edition of this book provides novel topics and studyies in boundaries of networks and Big Data Systems.The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics.

In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility.

This graduate-level text addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.

 

• Dynamical Free Boundaries
• Mathematical Modeling of Complex Systems
• Robustness and Resilience of Complex Systems
• Boundaries in complex Systems
• Art and Complexity
• Boundaries and Frames in Science

• Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, USA

  Andrei Ludu

Dr. A. Ludu graduated in 1980 the MS Program in Theoretical Physics and Mathematics from University of Bucharest and he had received his Ph. D. in Physics in 1989 from the “H. Hulubei National Institute of Physics” in Bucharest-Magurele, Romania with a thesis on group transformations approach on hot and dense plasma. He worked as a senior researcher in this Institute until 1985, and he joined the Dept. Theoretical Physics at University of Bucharest University as Associate Professor until 1996. Between 1986 and 2001 he was postdoctoral researcher at Louisiana State University in Baton Rouge, and he joined Northwestern State University as Professor of Physics until 2011. At present he is Professor of Mathematics and Director of the Wave Lab in the Dept. of Mathematics at Embry-Riddle Aeronautical University in Daytona Beach. He published more than 80 peer reviewed paper in scientific journals and 4 books on the topics of solitons and nonlinear systems, applied differential geometry in physics, quantum groups, fluid dynamics, nuclear theory, biophysics, ultra-high energy density systems and wavelets. He was invited to work and give talks at prestigious centers of research including Los Alamos Natl. Lab, ICTP Trieste, Antwerp University, Universite Libre de Bruxelles,  US Navy Research Labs, Plymouth University, Trinity College, Niels Bohr Institute, Abo Akademi, Dalian University of Technology, etc. He was guest professor for more than ten years at J. Liebig University in Giessen and Goethe University in Frankfurt/Main, Germany. He was awarded the Mildred Hart Bailey Research Award and he is honorary member of several professional associations and science groups. In 1992 he predicted the existence of shape solitons orbiting on the surface of spheres (rotons). These predictions were continuously confirmed experimentally in systems like heavy nuclei collisions, flat electron drops, liquid drops and Leidenfrost drops and tori between 2007 and present.  Dr. Luduis married since 1980 to Maria, who is also Professor of Mathematics, and they have a daughter Delia working in graphic design. He is VFR private pilot and practiced AMA enduro motorcycling.   

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