Algebraic Modeling of Topological and Computational Structures and Applications

THALES, Athens, Greece, July 1-3, 2015
Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-3-319-88549-0
Verlag: Springer International Publishing

Buch, Englisch, Band 219, 482 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 750 g

Reihe: Springer Proceedings in Mathematics & Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lambropoulou, Sofia

Kauffman, Louis H.

Theodorou, Doros

Stefaneas, Petros

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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 S(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 Systems/p>

K

enneth C. MillettUniversity 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: Structure, Dynamics and Permeability Properties Niki Vergadou and Eleni Androulaki and Ioannis G. Economou

National Center for Scientific Research Demokritos, Institute of Nanoscience and Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory and Texas 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 Chicago

Towards the integration of Athena with CafeOBJ using tool support

Konstantine Arkoudas, Katerina Ksystra, Nikos Triantafyllou, and Petros Stefaneas

Bloomberg R & D, U.S.A., National 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 Barlas and Eleni Berki Petros Stefaneas and George Koletsos

National Technical University of Athens and University of Tampere

Fixed Point Logics as Institutions

Kiouvrekis Yiannis, Stefaneas P

etros

National T

echnical University of Athensp>

Syntax, Se

mantics and the Formalisation of Scientific Theories

Nicola Angius, Maria Dimarogona and Petros Stefaneas

University of Sassari, Italy

National 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 Tércio 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 AthensPoster Session

A Categorical Model for the Virtual Braid Group

L. H. Kauffman, S. Lambropoulou

University of Illinois at Chicago, National Technical University of Athens

Knotoids

N. Gugumcu, L. H. Kauffman, S. Lambropoulou

National Technical University of Athens, University of Illinois at Chicago

p-adic framed braids

J. Juyumaya, S. Lambropoulou

The Juyumaya-Lambropoulou classical link invariants from the Yokonuma-Hecke algebras

M. Chlouveraki

, J. Juyumaya, K. Karvounis3, S. Lambropoulou

Universite de Versai

lles Saint-Quentin-en-Yvelines, Universidad de Valparaiso, Universitat Zurich, National Technical University of Athens

Markov trace on the bt-algebra and tied links

F. Aicardi, J. Juyumaya

International School for Advanced Studies, Universidad 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. Panagiotou, S. Lambropoulou, C. Tzoumanekas, D. N. Theodorou

University of California, Santa Barbara, National 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. Barlas

National Technical University of Athens, University of Tampere

Towards formal representation and comparison of video content using algebraic semiotics

N. Triantafyllou, K. Ksystra

National Technical University of Athens, American University of the Middle East

Applications to medical imaging

E. Karali

National Technical University of Athens