Algebraic modeling of topological and computational structures and applications : THALES, Athens, Greece, July 1-3, 2015

著者

• Lambropoulou, Sofia
• Theodorou, Doros N.
• Stefaneas, Petros
• Kauffman, Louis H.

書誌事項

Algebraic modeling of topological and computational structures and applications : THALES, Athens, Greece, July 1-3, 2015

Sofia Lambropoulou ... [et al.], editors

（Springer proceedings in mathematics & statistics, v. 219）

Springer, c2017

注記

Other editors: Doros Theodorou, Petros Stefaneas, Louis H. Kauffman

"Extras online"- Cover

"Additional material to this book can be downloaded from http://extras.springer.com"

Includes bibliographical references

内容説明・目次

内容説明

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.

目次

Chapter 1: Algebraic Modeling of Topological Structures - Knot invariants - framization of knot algebras - Knots and braids in 3-manifolds - Poly-free groups, Lie algebras, braid groups and homotopy groups of spheres Chapter 2: Algebraic Modeling of Applications - Topological study of polymer entanglements - Molecular simulation of ionic liquids - Dynamical systems and topological surgery Chapter 3: Algebraic Modeling of Computational Structures - Modeling based on algebraic specifications - Algebraic techniques for the modeling of video - Cryptography and coding theory - Applications in medical imaging Contributed talks in the Thales Workshop, 1-3 July 2015 1: Algebraic Modeling of Topological Structures Elements of Khovanov Homology University of Illinois at Chicago Word problem for virtual braid groups Luis Paris Univ. Bourgogne Franche-Comte, F-21000 Dijon, France A new skein invariant for classical links from the Yokonuma-Hecke algebras Sofiaa Lambropoulou National Technical University of Athens Classification of Markov traces on Yokonuma-Hecke algebras L. Poulain d'Andecy Universite de Reims Framization of the Temperley-Lieb algebra Dimos Goundaroulis National Technical University of Athens Quotient algebras of mixed braid groups with two fixed strands Dimitrios Kodokostas National Technical University of Athens Representation theory of framisations of knot algebras M. Chlouveraki Univers ite de Versailles The HOMFLYPT skein module of the lens spaces L(p ,1) Maciej Mroczkowski (joint work with Bostjan Gabrovsek) Institute of Mathematics, University of Gdansk The isomorphism function from S3(L(p,1)) to the free module Bostjan Gabrovsek (joint work with Maciej Mroczkowski) FME, University of Ljubljana The Homflypt skein module of L(p,1) via braids Ioannis Diamantis and Sofiaa Lambropoulou National Technical University of Athens Infinite loop spaces, Steenrod, Dyer-Lashof and Dickson algebras Nondas Kechagias Department of Mathematics, University of Ioannina 2: Algebraic Modeling of Applications Entanglements in Molecular Simulations of Polymers Christos Tzoumanekas, Stefanos D. Anogiannakis, Georgios G. Vogiatzis, and Doros N. Theodorou School of Chemical Engineering, National Technic al University of Athens Models of Knotting and Linking in P olymeric S ystems /p>K enneth C. Millett University of California, Santa Barbara A study of the entanglement in systems of curves with Periodic Boundary Conditions E Panagiotou University of California, Santa Barbara Threading of ring poly(ethylene oxide) molecules by linear chains or other rings in the melt: molecular dynamics simulations followed by a geometric analysis Dimitrios Tsalikis, Vlasis Mavrantzas University of Patras Chain Size and Shape Dependence of the Tendency for Entanglement in Linear Polymer Melts Christos Tzoumanekas, Stefanos D. Anogiannakis and Doros N. Theodorou School of Chemical Engineering, National Technical University of Athens Extending Topological Surgery to Natural Processes Sofia Lambropoulou and Stathis Antoniou National Technical University of Gr eece Molecular Simulation of Ion ic Liquids: S tructure, Dynamic s and Permeabi lity Properties Niki Vergadou1 and Eleni Androulaki1 and Ioannis G. Economou1,2 1National Center for Scientific Research Demokritos, Institute of Nanoscience and Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory and 2Texas A&M University at Qatar, Chemical Engineering Program, Education City, PO Box 23874, Doha, Qatar On (p-)almost direct products and residual properties of pure braid groups of surfaces P. Bellingeri Laboratoire Nicolas Oresme ESPE de Basse Normandie Universit de Caen 3: Algebraic Modeling of Computational Structures On Algebraic Modeling of Computational Structures Petros Stefaneas National Technical University of Athens Chemlambda, universality and self-multipli cation Louis H. K auffman Univer sity of Illinois at Chic ago Towards the integration of Athena with CafeOBJ using tool support Konstantine Arkoudas1, Katerina Ksystra2, Nikos Triantafyllou2, and Petros Stefaneas2 1Bloomberg R & D, U.S.A., 2National Technical University of Athens, Greece Cafe2JML: Integrating Behavioral Algebraic Speci_cations with Design by Contract Nikolaos Triantafyllou and Petros Stefaneas National Technical University of Athens Towards Formal Open Standards: the Case of RSS Konstantinos Barlas1 and Eleni Berki2 Petros Stefaneas1 and George Koletsos1 1National Technical University of Athens and 2University of Tampere Fixed Point Logics as Institutions Kiouvrekis Yiannis, Stefaneas P etros National T echnical University of Athens p> Syntax, Se mantics and the Formalisation of Scientific Theories Nicola Angius1, Maria Dimarogona2 and Petros Stefaneas2 1University of Sassari, Italy 2National Technical University of Athens Composition of Specification Modules: recent developments Razvan Diaconescu Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania On Operators at Classes of Structures S. V. Sudoplatov Sobolev Institute of Mathematics. An algebraic approach to pictures S. Bozapalides Aristotle University of Thessaloniki Thoughts on IT Investment Analysis A. Alencar The Tercio Pacitti Institute Federal University of Rio de Janeiro The way to universal logic J. Bezi au Co nstructing Class Invariants Arist ides Kontogeorgis Department of Mathematics, University of Athens Poster Session A Categorical Model for the Virtual Braid Group L. H. Kauffman1, S. Lambropoulou2 1University of Illinois at Chicago, 2National Technical University of Athens Knotoids N. Gugumcu1, L. H. Kauffman2, S. Lambropoulou1 1National Technical University of Athens, 2University of Illinois at Chicago p-adic framed braids J. Juyumaya1, S. Lambropoulou2 1Universidad de Valparaiso, 2National Technical University of Athens The Juyumaya-Lambropoulou classical link invariants from the Yokonuma-Hecke algebras M. Chlouveraki1 , J. Juyumaya2, K. Karvounis 3, S. Lambropoulou4 1Universite de Versai lles Saint-Quentin-en-Yvelines, 2Universidad de Valparaiso, 3Universitat Zurich, 4National Technical University of Athens Markov trace on the bt-algebra and tied links F. Aicardi1, J. Juyumaya2 1International School for Advanced Studies, 2Universidad de Valparaiso Framization of the Temperley-Lieb algebra D. Goundaroulis National Technical University of Athens Braid equivalences in 3-manifolds with rational surgery description I. Diamantis, S. Lambropoulou National Technical University of Athens A new basis for the Homypt skein module of the solid torus I. Diamantis, S. Lambropoulou National Technical University of Athens The Isomorphism Conjecture for Subgrou ps of Aut(Fn) - Equivariant and Stratified Rigidity of Quasitoric Manifolds V. Metaftsis, E. Prassidis University of the Aegean Loop spaces, Steenrod, Dyer-Lashof, Dickson algebras N. Kechagias University of Ioannina Constructing Class Invariants A. Kontogeorgis University of Athens The linking number in systems with Periodic Boundary Conditions E. Panagiotou1, S. Lambropoulou2, C. Tzoumanekas2, D. N. Theodorou2 1University of California, Santa Barbara, 2National Technical University of Athens Extending Topological Surgery to Natural Processes S. Lambropoulou, S. Antoniou National Technical University of Athens An Algebraic Framework for the Verification of Context-aware Adaptive Systems K. Ksystr a, P. Stefaneas, P. Frangos National Techn ical University of Athens Towards Formal Open Standards: the Case of RSS v2.0 K. Barlas1, E. Berki2, P. Stefaneas1, G. Koletsos1 1National Technical University of Athens, 2University of Tampere Towards formal representation and comparison of video content using algebraic semiotics N. Triantafyllou1, K. Ksystra1, P. Stefaneas1, A. Kalampakas2 1National Technical University of Athens, 2American University of the Middle East Applications to medical imaging E. Karali National Technical University of Athens

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詳細情報

• NII書誌ID(NCID): BB25246351
• ISBN:
  • 9783319681023
• LCCN: 2017953823
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cham
• ページ数/冊数: xv, 482 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BB10167422