Algebraic Modeling of Topological and Computational Structures and Applications: THALES, Athens, Greece, July 1-3, 2015

Description

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. Front Matter ....Pages i-xv Front Matter ....Pages 1-1 Link Invariants from the Yokonuma–Hecke Algebras (Konstantinos Karvounis, Sofia Lambropoulou)....Pages 3-35 A Survey on Temperley–Lieb-type Quotients from the Yokonuma–Hecke Algebras (Dimos Goundaroulis)....Pages 37-55 Representation Theory of Framisations of Knot Algebras (Maria Chlouveraki)....Pages 57-75 Invariants for Links from Classical and Affine Yokonuma–Hecke Algebras (Loic Poulain d’Andecy)....Pages 77-95 On the Framization of the Hecke Algebra of Type \({\texttt {B}}\) (Marcelo Flores)....Pages 97-115 Link Diagrams in Seifert Manifolds and Applications to Skein Modules (Boštjan Gabrovšek, Maciej Mroczkowski)....Pages 117-141 The Braid Approach to the HOMFLYPT Skein Module of the Lens Spaces L(p, 1) (Ioannis Diamantis, Sofia Lambropoulou)....Pages 143-176 Some Hecke-Type Algebras Derived from the Braid Group with Two Fixed Strands (Dimitrios Kodokostas, Sofia Lambropoulou)....Pages 177-187 Braid Groups in Handlebodies and Corresponding Hecke Algebras (Valeriy G. Bardakov)....Pages 189-203 Infinite Loop Spaces, Dyer–Lashof Algebra, Cohomology of the Infinite Symmetric Group and Modular Invariants (Nondas E. Kechagias)....Pages 205-234 Front Matter ....Pages 235-235 Linking in Systems with One-Dimensional Periodic Boundaries (Kenneth C. Millett, Eleni Panagiotou)....Pages 237-257 On the Height of Knotoids (Neslihan Gügümcü, Louis H. Kauffman)....Pages 259-281 Fourier Braids (Stephan Klaus)....Pages 283-296 Molecular Simulation of Ionic Liquids: Complex Dynamics and Structure (Niki Vergadou)....Pages 297-312 Topological Surgery in Nature (Stathis Antoniou, Sofia Lambropoulou)....Pages 313-336 Front Matter ....Pages 337-337 Automorphisms of Curves (Jannis A. Antoniadis, Aristides Kontogeorgis)....Pages 339-361 Building and Integrating Semantic Theories over Institutions (Nicola Angius, Maria Dimarogkona, Petros Stefaneas)....Pages 363-374 Generic Constructions and Generic Limits (Sergey V. Sudoplatov, Yiannis Kiouvrekis, Petros Stefaneas)....Pages 375-398 On Combining Algebraic Specifications with First-Order Logic via Athena (Katerina Ksystra, Nikos Triantafyllou, Petros Stefaneas)....Pages 399-422 A Rule-Based Approach for Air Traffic Control in the Vicinity of the Airport (Theodoros Mitsikas, Petros Stefaneas, Iakovos Ouranos)....Pages 423-438 Sequential Machines and Affine Musical Contours (Marianthi Bozapalidou)....Pages 439-445 A Formal Representation of Video Content with the Picture Hyperoperation (Antonios Kalampakas, Nikolaos Triantafyllou, Katerina Ksystra, Petros Stefaneas)....Pages 447-451 Novel Approaches to Medical Information Processing and Analysis (Evi Karali)....Pages 453-482