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This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.

Mathematics. --- Computer mathematics. --- Geometry. --- Number theory. --- Topology. --- Combinatorics. --- Computational Mathematics and Numerical Analysis. --- Number Theory. --- Combinatorics --- Algebra --- Mathematical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Number study --- Numbers, Theory of --- Mathematics --- Euclid's Elements --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Topological spaces --- Spaces, Topological --- Computer science

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This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles, written by leading experts, on low-dimensional topology and its applications. The content addresses a wide range of historical and contemporary invariants of knots and links, as well as related topics including: three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology, hyperbolic knots and geometric structures of three-dimensional manifolds, the mechanism of topological surgery in physical processes, knots in nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The chapters are based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Algebra. --- Geometry. --- Topology. --- Discrete mathematics. --- Biomathematics. --- Statistical physics. --- Algebra. --- Geometry. --- Topology. --- Discrete Mathematics. --- Mathematical and Computational Biology. --- Statistical Physics and Dynamical Systems. --- Physics --- Mathematical statistics --- Physics --- Biology --- Biology --- Mathematics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematics --- Euclid's Elements --- Mathematics --- Mathematical analysis --- Statistical methods --- Mathematics

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This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles, written by leading experts, on low-dimensional topology and its applications. The content addresses a wide range of historical and contemporary invariants of knots and links, as well as related topics including: three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology, hyperbolic knots and geometric structures of three-dimensional manifolds, the mechanism of topological surgery in physical processes, knots in nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The chapters are based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Algebra. --- Geometry. --- Topology. --- Discrete mathematics. --- Biomathematics. --- Statistical physics. --- Discrete Mathematics. --- Mathematical and Computational Biology. --- Statistical Physics and Dynamical Systems.

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• Reference Manager
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This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles, written by leading experts, on low-dimensional topology and its applications. The content addresses a wide range of historical and contemporary invariants of knots and links, as well as related topics including: three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology, hyperbolic knots and geometric structures of three-dimensional manifolds, the mechanism of topological surgery in physical processes, knots in nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The chapters are based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.

Algebra. --- Geometry. --- Topology. --- Discrete mathematics. --- Biomathematics. --- Statistical physics. --- Discrete Mathematics. --- Mathematical and Computational Biology. --- Statistical Physics and Dynamical Systems.

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Mathematics