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Algebraic Modeling of Topological and Computational Structures and Applications

THALES, Athens, Greece, July 1-3, 2015

  • Sofia Lambropoulou
  • Doros Theodorou
  • Petros Stefaneas
  • Louis H. Kauffman
Conference proceedings AlModTopCom 2015

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 219)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Algebraic Modeling of Topological Structures

  3. Algebraic Modeling of Applications

    1. Front Matter
      Pages 235-235
    2. Kenneth C. Millett, Eleni Panagiotou
      Pages 237-257
    3. Neslihan Gügümcü, Louis H. Kauffman
      Pages 259-281
    4. Stephan Klaus
      Pages 283-296
    5. Stathis Antoniou, Sofia Lambropoulou
      Pages 313-336
  4. Algebraic Modeling of Computational Structures

    1. Front Matter
      Pages 337-337
    2. Jannis A. Antoniadis, Aristides Kontogeorgis
      Pages 339-361
    3. Nicola Angius, Maria Dimarogkona, Petros Stefaneas
      Pages 363-374
    4. Sergey V. Sudoplatov, Yiannis Kiouvrekis, Petros Stefaneas
      Pages 375-398
    5. Katerina Ksystra, Nikos Triantafyllou, Petros Stefaneas
      Pages 399-422
    6. Theodoros Mitsikas, Petros Stefaneas, Iakovos Ouranos
      Pages 423-438
    7. Marianthi Bozapalidou
      Pages 439-445
    8. Antonios Kalampakas, Nikolaos Triantafyllou, Katerina Ksystra, Petros Stefaneas
      Pages 447-451

About these proceedings

Introduction

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.

Keywords

topology algebraic modeling knot theory braids Jones polynomial knot algebras low dimensional topology algebra and computer science number theory polymer entanglements applications to natural sciences

Editors and affiliations

  • Sofia Lambropoulou
    • 1
  • Doros Theodorou
    • 2
  • Petros Stefaneas
    • 3
  • Louis H. Kauffman
    • 4
  1. 1.Department of Applied MathematicsNational Technical University of AthensAthensGreece
  2. 2.School of Chemical EngineeringNational Technical University of AthensAthensGreece
  3. 3.Department of Applied MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-68103-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-68102-3
  • Online ISBN 978-3-319-68103-0
  • Series Print ISSN 2194-1009
  • Series Online ISSN 2194-1017
  • Buy this book on publisher's site