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

ISBN-13: 9783319681023 / Angielski / Twarda / 2017 / 482 str.

Sofia Lambropoulou; Doros Theodorou; Petros Stefaneas

Opis

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).

Spis treści

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. Economou^1,2

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 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 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. Barlas^{1, 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. Ksystra^{1, 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

Blurb

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.