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Longrigg, Jonathan James. „Aspects of Braid group cryptography“. Thesis, University of Newcastle Upon Tyne, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.492947.
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Franko, Jennifer M. „Braid group representations via the Yang Baxter equation“. [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3278226.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 5995. Advisers: Zhenghan Wang; Kent Orr. Title from dissertation home page (viewed May 9, 2008).
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Weinberger, Oskar. „The braid group, representations and non-abelian anyons“. Thesis, KTH, Matematik (Inst.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-167993.
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This bachelor’s thesis concerns unitary linear representations of the braid group, motivated by their connection to two dimensional particle statistics and certain quasi-particles called non-abelian anyons. Particle statistics in two dimensions is related to the braid group via the fundamental group of the configuration space of indistinguishable particles in two dimensions, and non-abelian anyons correspond to non-commutative unitary representations of the braid group. In the aim of understanding these connections and studying the mathematical possibilities for non-abelian anyons, algebraic and topological definitions as well as results about braids and their representations are presented and investigated. The focus is on representations of low dimension, and a characterisation of low-dimensional irreducible complex representations is analysed. The unitarisability of such representations and the consequences for non-abelian anyons are then considered.Detta kandidatexamensarbete berör unitära linjära representationer av flätgruppen, med motivering av deras koppling till två dimensionell partikelstatistik och de kvasipartiklar som kallas icke-abelska anyoner. Partikelstatistik i två dimensioner är relaterat till flätgruppen via fundamental gruppen av konfigurationsrummet av icke-särskiljbara partiklar i två dimensioner, och icke-abelska anyoner svarar mot icke-kommutativa unitära representationerav flätgruppen. I syfte att förstå dessa kopplingar och studera de matematiska möjligheterna för icke-abelska anyoner presenteras och undersöks algebraiska och topologiska definitioner såväl som resultat för flätor och deras representationer. Fokus är på representationer med låg dimension, och en karaktärisering av lågdimensionella irreducibla komplexa representationer analyseras. Vidarebetraktas unitariserbarheten av sådana representationer och konsekvenserna för icke-abelska anyoner.
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Cornwell, Christopher R. „On the Combinatorics of Certain Garside Semigroups“. Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.
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Puente, Philip C. „Crystallographic Complex Reflection Groups and the Braid Conjecture“. Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011877/.
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Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the space with reflecting hyperplanes removed has a presentation mimicking that of the Coxeter presentation; one need only remove relations giving generators finite order. N.V Dung used a semi-cell construction to prove the Braid theorem for affine Weyl groups. Malle conjectured that the Braid theorem holds for all crystallographic complex reflection groups after constructing Coxeter-like reflection presentations. We show how to extend Dung's ideas to crystallographic complex reflection groups and then extend the Braid theorem to some groups in the infinite family [G(r,p,n)]. The proof requires a new classification of crystallographic groups in the infinite family that fail the Steinberg theorem.
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Henderson, Roger William. „Cryptanalysis of braid group cryptosystem and related combinatorial structures“. Thesis, Royal Holloway, University of London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440519.
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Sweeney, Andrew. „A Study of Topological Invariants in the Braid Group B2“. Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3407.
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The Jones polynomial is a special topological invariant in the field of Knot Theory. Created by Vaughn Jones, in the year 1984, it is used to study when links in space are topologically different and when they are topologically equivalent. This thesis discusses the Jones polynomial in depth as well as determines a general form for the closure of any braid in the braid group B2 where the closure is a knot. This derivation is facilitated by the help of the Temperley-Lieb algebra as well as with tools from the field of Abstract Algebra. In general, the Artin braid group Bn is the set of braids on n strands along with the binary operation of concatenation. This thesis also shows results of the relationship between the closure of a product of braids in B2 and the connected sum of the closure of braids in B2. Results on the topological invariant of tricolorability of closed braids in B2 and (2,n) torus links along with their obverses are presented as well.
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Penrod, Keith G. „Infinite Product Group“. BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/976.
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The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.
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East, James Phillip Hinton. „On Monoids Related to Braid Groups and Transformation Semigroups“. School of Mathematics and Statistics, 2006. http://hdl.handle.net/2123/2438.
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East, James Phillip Hinton. „On Monoids Related to Braid Groups and Transformation Semigroups“. Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/2438.
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Mund, Jens. „Quantum field theory of particles with braid group statistics in 2+1 dimensions“. [S.l. : s.n.], 1998. http://www.diss.fu-berlin.de/1999/7/index.html.
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Meiners, Justin. „Computing the Rank of Braids“. BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8947.
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We describe a method for computing rank (and determining quasipositivity) in the free group using dynamic programming. The algorithm is adapted to computing upper bounds on the rank for braids. We test our method on a table of knots by identifying quasipositive knots and calculating the ribbon genus. We consider the possibility that rank is not theoretically computable and prove some partial results that would classify its computational complexity. We then present a method for effectively brute force searching band presentations of small rank and conjugate length.
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Sönnerlind, Erik, und Gustav Brage. „Braid group statistics and exchange matrices of non-abelian anyons : with representations in Clifford algebra“. Thesis, KTH, Skolan för teknikvetenskap (SCI), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-231567.
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When leaving classical physics and entering the realm of quantum physics, there are many new concepts being introduced. One of the most fundamental ideas in quantum mechanics is that particles no longer have exact known positions, but instead expected values and prob- abilities. This leads to the phenomena of truly identical particles, since they no longer can be distinguished simply by their positions. An important property differentiating different kinds of particles is how a system behaves when two such identical particles are exchanged. Historically, this divided particles into bosons and fermions, corresponding to symmetry and antisymmetry under an exchange. However, in two dimensions a new type of particle appears. These particles are called anyons, and behave differently when particles are exchanged. Anyons can be further divided into abelian and non-abelian anyons, of which this thesis will focus on the latter. The ex- changes can then be represented by the fundamental group of the configuration space of the particles, and in two dimensions this fundamental group is the braid group. Using rotors from a Clifford algebra and studying excitations of Majorana fermions, this thesis will show a way to calculate the exchange matrices of non-abelian anyons, and their corresponding eigenvalues. Furthermore, suggestions on a generalization of this framework along with areas where it can be applied are given.När man lämnar klassisk fysik och övergår till den kvantfysikaliska världen introduceras många nya koncept. En av de mest grundläggande idéerna inom kvantmekaniken är att partiklar inte längre har exakta positioner, eftersom dessa ersatts av väntevärden och sannolikheter. Detta leder till fenomenet att partiklar kan vara verkligt identiska, eftersom de inte längre kan särskiljas med hjälp av sina positioner. En viktig egenskap som särskiljer olika typer av partiklar är hur ett system beter sig vid ett utbyte av två sådana identiska partiklar. Historiskt sett delade denna egenskap upp partiklar i bosoner och fermioner, som uppvisar symmetri respektive antisymmetri vid ett partikelutbyte. I två dimensioner uppstår dock en ny typ av partiklar. Dessa partiklar kallas anyoner och beter sig annorlunda vid ett partikelutbyte. Vidare kan de delas upp i abelska och icke-abelska anyoner, varav denna rapport kommer fokusera på de senare. Utbytena kan representeras av den fundamentala gruppen av partiklarnas konfigurationsrum, och i två dimensioner blir denna fundamentala grupp flätgruppen. Genom att använda rotorer från en Cliffordalgebra och studera excitationer av Majoranafermioner, så visar denna rapport ett sätt att beräkna utbytesmatriserna för icke-abelska anyoner och deras tillhörande egenvärden. Vidare ges förslag på en generalisering av detta ramverk, tillsammans med områden där det kan tillämpas.
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Ison, Molly Elizabeth. „Two Aspects of Topology in Graph Configuration Spaces“. Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/29214.
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A graph configuration space is generated by the movement of a finite number of robots on a graph. These configuration spaces of points in a graph are topologically interesting objects. By using local, combinatorial properties, we define a new classification of graphs whose configuration spaces are pseudomanifolds with boundary. In algebraic topology, graph configuration spaces are closely related to classical braid groups, which can be described as fundamental groups of configuration spaces of points in the plane. We examine this relationship by finding a presentation for the fundamental group of one graph configuration space.Master of Science
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Hartsell, Jack. „A Normal Form for Words in the Temperley-Lieb Algebra and the Artin Braid Group on Three Strands“. Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3504.
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The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
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Calligaris, Pierpaolo. „Finite orbits of the action of the pure braid group on the character variety of the Riemann sphere with five boundary components“. Thesis, Loughborough University, 2017. https://dspace.lboro.ac.uk/2134/25536.
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In this thesis, we classify finite orbits of the action of the pure braid group over a certain large open subset of the SL(2,C) character variety of the Riemann sphere with five boundary components, i.e. Σ5. This problem arises in the context of classifying algebraic solutions of the Garnier system G2, that is the two variable analogue of the famous sixth Painleve equation PVI. The structure of the analytic continuation of these solutions is described in terms of the action of the pure braid group on the fundamental group of Σ5. To deal with this problem, we introduce a system of co-adjoint coordinates on a big open subset of the SL(2,C) character variety of Σ5. Our classifica- tion method is based on the definition of four restrictions of the action of the pure braid group such that they act on some of the co-adjoint coordi- nates of Σ5 as the pure braid group acts on the co-adjoint coordinates of the character variety of the Riemann sphere with four boundary components, i.e. Σ4, for which the classification of all finite orbits is known. In order to avoid redundant elements in our final list, a group of symmetries G of the large open subset is introduced and the final classification is achieved modulo the action of G. We present a final list of 54 finite orbits.
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Brien, Renaud. „Normal Forms in Artin Groups for Cryptographic Purposes“. Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23145.
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With the advent of quantum computers, the security of number-theoretic cryptography has been compromised. Consequently, new cryptosystems have been suggested in the field of non-commutative group theory. In this thesis, we provide all the necessary background to understand and work with the Artin groups. We then show that Artin groups of finite type and Artin groups of large type possess an easily-computable normal form by explicitly writing the algorithms. This solution to the word problem makes these groups candidates to be cryptographic platforms. Finally, we present some combinatorial problems that can be used in group-based cryptography and we conjecture, through empirical evidence, that the conjugacy problem in Artin groups of large type is not a hard problem.
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Pizarro, Pavel Jesus Henriquez. „Representações do grupo de tranças por automorfismos de grupos“. Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-16042012-102241/.
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A partir de um grupo H e um elemento h em H, nós definimos uma representação : \'B IND. n\' Aut(\'H POT. n\' ), onde \'B IND. n\' denota o grupo de trança de n cordas, e \'H POT. n\' denota o produto livre de n cópias de H. Chamamos a a representação de tipo Artin associada ao par (H, h). Nós também estudamos varios aspectos de tal representação. Primeiramente, associamos a cada trança um grupo \' IND. (H,h)\' () e provamos que o operador \' IND. (H,h)\' determina um grupo invariante de enlaçamentos orientados. Então damos uma construção topológica da representação de tipo Artin e do invariante de enlaçamentos \' IND.(H,h)\' , e provamos que a representação é fiel se, e somente se, h é não trivialFrom a group H and a element h H, we define a representation : \' B IND. n\' Aut(\'H POT. n\'), where \'B IND. n\' denotes the braid group on n strands, and \'H POT. n\' denotes the free product of n copies of H. We call the Artin type representation associated to the pair (H, h). Here we study various aspects of such representations. Firstly, we associate to each braid a group \' IND. (H,h)\' () and prove that the operator \' IND. (H,h)\' determines a group invariant of oriented links. We then give a topological construction of the Artin type representations and of the link invariant \' iND. (H,h)\' , and we prove that the Artin type representations are faithful if and only if h is nontrivial
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Chettih, Safia. „Dancing in the stars| Topology of non-k-equal configuration spaces of graphs“. Thesis, University of Oregon, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10193648.
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We prove that the non-k-equal configuration space of a graph has a discretized model, analogous to the discretized model for configurations on graphs. We apply discrete Morse theory to the latter to give an explicit combinatorial formula for the ranks of homology and cohomology of configurations of two points on a tree. We give explicit presentations for homology and cohomology classes as well as pairings for ordered and unordered configurations of two and three points on a few simple trees, and show that the first homology group of ordered and unordered configurations of two points in any tree is generated by the first homology groups of configurations of two points in three particular graphs, K1,3, K1,4, and the trivalent tree with 6 vertices and 2 vertices of degree 3, via graph embeddings.
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Akueson, Anani. „Eléments de géométrie tressée“. Valenciennes, 1998. https://ged.uphf.fr/nuxeo/site/esupversions/2b3a587c-d83e-4d2a-96f1-a05576bb88fb.
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Notre thèse est consacrée à la géométrie tressée, en particulier celle qui traite des objets munis d'un opérateur de Yang-Baxter (YB) (autrement dit, une solution de l'équation de Yang-Baxter quantique (EYBQ). Dans la première partie, sont étudiées certaines structures géométriques sur l'hyperboloïde quantique (une déformation de l'hyperboloïde classique). Les critères de raison d'être de tous les objets introduits sont de deux types : invariance par rapport à l'action du groupe quantique correspondant et platitude de la déformation (cela signifie simplement que la quantité d'éléments reste inchangé lors de la déformation). Nous introduisons le module tangent sur hyperboloïde quantique et montrons qu'il est projectif et muni d’une ancre quantique (i. E. Une action de ce module sur l'espace des fonctions sur l'hyperboloïde quantique). Une métrique et une connexion tressées ont été définies et leurs existences sont montrées. Une version d'un complexe de de Rham sans règle de Leibniz est construite et sa cohomologie est calculée sur l'hyperboloïde quantique. L'objectif principal de la deuxième partie est de décrire l'analogue du groupe quantique de Drinfel'd-Jimbo lié aux solutions non quasiclassiques (i. E. Celles qui ne sont pas des déformations de la volte habituelle) de l'EYBQ. Cela se fait par le biais de l'algèbre des fonctions quantiques correspondantes pour laquelle, il est montre qu'il existe un couplage (canonique), coordonné avec les structures d'algèbres et de coalgèbres. On a montré que, pour les solutions de l'équation de YB liées aux algèbres de type Temperly-Lieb, ce couplage est non dégénéré sur son espace générateur. Cela renforce l'hypothèse selon laquelle les groupes quantiques lies a ces algèbres coïncident avec leurs duaux.
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Guichard, Christelle. „Les nombres de Catalan et le groupe modulaire PSL2(Z)“. Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAM057/document.
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Dans ce mémoire de thèse, on étudie le morphisme de monoïde $mu$du monoïde libre sur l'alphabet des entiers $nb$,`a valeurs dans le groupe modulaire $PSL_2(zb)$,considéré comme monoïde, défini pour tout entier $a$ par $mu(a)=begin{pmatrix} 0 & -1 1 & a+1 end{pmatrix}.$Les nombres de Catalan apparaissent naturellement dans l'étudede sous-ensembles du noyau de $mu$.Dans un premier temps, on met en évidence deux systèmes de réécriture, l'un sur l'alphabet fini ${0,1}$, l'autresur l'alphabet infini des entiers $nb$ et on montreque ces deux systèmes de réécriture définissent des présentations de monoïde de $PSL_2(zb)$ par générateurs et relations.Par ailleurs, on introduit le morphisme d'indice associé `a l'abélianisé du rev^etement universel de $PSL_2(zb)$,le groupe $B_3$ des tresses `a trois brins. Interprété dans deux contextes différents,le morphisme d'indice est associé au nombre de "demi-tours".Ensuite, dans les quatrième et cinquième parties, on dénombre des sous-ensembles du noyau de $mu_{|{0,1}}$ etdu noyau de $mu$, bigradués par la longueur et l'indice. La suite des nombres de Catalan et d'autres diagonales du triangle de Catalan interviennentsimplement dans les résultats.Enfin, on présente l'origine géométrique de cette étude : on explicite le lien entre l'objectif premier de la thèse qui était l'étudedes polygones convexes entiers d'aire minimale et notre intéret pour le monoïde engendré par ces matrices particulières de $PSL_2(zb)$In this thesis, we study a morphism of mono"id $mu$ between the free mono"id on the alphabet of integers $nb$and the modular group $PSL_2(zb)$ considered as a mono"id, defined for all integer $a$by $mu(a)=begin{pmatrix} 0 & -1 1 & a+1 end{pmatrix}.$ The Catalan Numbers arised naturally in the study ofsubsets of the kernel of the morphism $mu$.Firstly, we introduce two rewriting systems, one on the finite alphabet ${0,1}$, and the other on the infinite alphabet of integers $nb$. We proove that bothof these rewriting systems defines a mono"id presentation of $PSL_2(zb)$ by generators and relations.On another note, we introduce the morphism of loop associated to the abelianised of the universal covering group of $PSL_2(zb)$, the group $B_3$ ofbraid group on $3$ strands. In two different contexts, the morphism of loop is associated to the number of "half-turns".Then, in the fourth and the fifth parts, we numerate subsets of the kernel of $mu_{|{0,1}}$ and of the kernel of $mu$,bi-graduated by the morphism of lengthand the morphism of loop. The sequences of Catalan numbers and other diagonals of the Catalan triangle come into the results.Lastly, we present the geometrical origin of this research : we detail the connection between our first aim,which was the study of convex integer polygones ofminimal area, and our interest for the mono"id generated by these particular matrices of $PSL_2(zb)$
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Gonzalez, Pagotto Pablo. „Sur les monoïdes des classes de groupes de tresses“. Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM049.
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Hurwitz a montre qu’un revêtement ramifié f:M→N de surfaces avec lieu de ramification P⊂N détermine et est déterminé, à un automorphisme intérieur près du groupe symétrique S_m , par un homomorphisme π_1(NP, ∗) → S_m . Ce résultat réduit les questions d’existence et d’unicité à un problème combinatoire. Pour un ensemble de générateurs convenable de π_1(NP, ∗), une représentation π_1(NP, ∗) → S_m détermine et est déterminée par une suite (a_1 , b_1 , . . . , a_g , b_g , z_1, . . . , z_k ) d’éléments de S_m satisfaisant [a_1 , b_1 ] · · · [a_g , b_g ]z_1 · · · z_k = 1. La suite (a_1, b_1 , . . . , a_g , b_g , z_1 , . . . , z_k) de permutations est appelé un système de Hurwitz pour f. Par conséquent, pour comprendre les classes de revêtements ramifiés, on doit étudier les orbites des systèmes de Hurwitz par des actions sur S_m. Une de ces actions est la conjugaison simultanée qui conduit à l’étude de l’ensemble des classes doubles des groupes symétriques. Dans le premier chapitre, nous présentons les travaux récents de Neretin sur la structure multiplicative sur l’ensemble S_∞S^n_∞ /S_∞ . Dans le deuxième chapitre, nous visons étendre les résultats de Neretin au groupe B_∞ des tresses à support fini avec un nombre infini de brins. Nous montrons que B_∞ B^n_∞/B_∞ admet une telle structure multiplicative et expliquons comment cette structure est liée à des constructions similaires dans Aut(F_∞) et GL(∞). Nous définissons également une généralisation à un paramètre de la structure habituelle de monoïde sur l'ensemble des classes doubles de GL(∞) et montrons que la représentation de Burau fournit un foncteur entre les catégories des classes doubles de B_∞ et de GL(∞). Le dernier chapitre est consacré à l'étude des homomorphismes π_1(NP, ∗) → G, où G est un groupe discret. Nous exposons la classification stable de tels homomorphismes selon Samperton et de nouveaux résultats concernant le nombre de stabilisations nécessaires pour les rendre équivalents par rapport aux mouvements de Hurwitz. Nous explorons ensuite une généralisation de la classification des revêtements ramifiés finis en introduisant la monodromie des tresses associée à des surfaces plongées en codimension 2. Suivant des idées de Kamada, nous définissons la monodromie des tresses associée à des surfaces tressées correspondant à G = B_∞ et nous étudions les fonctions sphériques associées aux représentations des groupes des tressesHurwitz showed that a branched cover f:M→N of surfaces with branch locus P⊂N determines and is determined, up to inner automorphism of the symmetric group S_m, by a homomorphism π_1(NP, ∗) → S_m . This result reduces the questions of existence and uniqueness of branched covers to combinatorial problems. For a suitable set of generators for π_1(NP, ∗), a representation π_1(NP, ∗) → S_m determines and is determined by a sequence (a_1 , b_1 , . . . , a_g , b_g , z_1, . . . , z_k ) of elements of S_m satisfying [a_1, b_1 ] · · · [a_g , b_g ]z_1 · · · z_k = 1. Thesequence (a_1 , b_1 , . . . , a_g , b_g , z_1 , . . . , z_k ) of permutations is called a Hurwitz system for f .Therefore, to understand the classes of branched covers one need to study the orbits of Hurwitz systems by suitable actions on S^n_m, n = 2g+k. One of such actions is the simultaneous conjugation that leads to the study of the set of double cosets of symmetric groups.In Chapter 1 we bring an exposition of the recent work of Neretin on the multiplicative structure on the set S_∞S^n_∞/S_∞ .In Chapter 2 we aim at extending Neretin’s results to the group B_∞ of finitely supported braids on infinitely many strands. We prove that B_∞B^n_∞/B_∞ admits such a multiplicative structure and explain how this structure is related to similar constructions in Aut(F_∞ ) and GL(∞). We also define a one-parameter generalization of the usual monoid structure on the set of double cosets of GL(∞) and show that the Burau representation provides a functor between the categories of double cosets of B_∞ and GL(∞).The last chapter is dedicated to the study of homomorphisms π_1(NP, ∗) → G, G a discrete group. We give an exposition of the stable classification of such homomorphisms following the work of Samperton and some new results concerning the number of stabilizations necessary to make them equivalent with respect to Hurwitz moves. We also explore a generalization of the classification of finite branched covers by introducing the braid monodromy for surfaces embedded in codimension 2. Following ideas of Kamada we defined a braid monodromy associated to braided surfaces, which correspond to G = B_∞ and study the spherical functions associated to braid group representations
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Cumplido, Cabello María. „Sous-groupes paraboliques et généricité dans les groupes d'Artin-Tits de type sphérique“. Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1S022/document.
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Dans la première partie de cette thèse on étudiera la conjecture de généricité: dans le graphe de Cayley du groupe modulaire d'une surface fermée on regarde une boule centrée à l'identité et on s'intéresse à la proportion de sommets pseudo-Anosov dans cette boule. La conjecture de généricité affirme que cette proportion doit tendre vers 1 quand le rayon de la boule tend vers l'infini. On montre qu'elle est bornée inférieurement par un nombre strictement positif et on montre des résultats similaires pour une grande classe de sous-groupes du groupe modulaire. On présente aussi des résultats analogues pour des groupes d'Artin-Tits de type sphérique, en sachant que dans ce cas, être pseudo-Anosov est analogue à agir loxodromiquement sur un complexe delta-hyperbolique convenable. Dans la deuxième partie on donne des résultats sur les sous-groupes paraboliques des groupes d'Artin-Tits de type sphérique: le standardisateur minimal d'une courbe dans le disque troué est la tresse minimale positive qui la fait devenir ronde. On construit un algorithme pour le calculer d'une façon géométrique. Ensuite, on généralise le problème pour les groupes d'Artin-Tits de type sphérique. On montre aussi que l'intersection de deux sous-groupes paraboliques est un sous-groupe parabolique et que l'ensemble de sous-groupes paraboliques est un treillis par rapport à l'inclusion. Finalement, on définit le complexe simplicial des sous-groupes paraboliques irréductibles, et on le propose comme l'analogue du complexe de courbesIn the first part of this thesis we study the genericity conjecture: In the Cayley graph of the mapping class group of a closed surface we look at a ball of large radius centered on the identity vertex, and at the proportion of pseudo-Anosov vertices among the vertices in this ball. The genericity conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero and prove similar results for a large class of subgroups of the mapping class group. We also present analogous results for Artin--Tits groups of spherical type, knowing that in this case being pseudo-Anosov is analogous to being a loxodromically acting element. In the second part we provide results about parabolic subgroups of Artin-Tits groups of spherical type: The minimal standardizer of a curve on a punctured disk is the minimal positive braid that transforms it into a round curve. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin--Tits groups of spherical type. We also show that the intersection of two parabolic subgroups is a parabolic subgroup and that the set of parabolic subgroups forms a lattice with respect to inclusion. Finally, we define the simplicial complex of irreducible parabolic subgroups, and we propose it as the analogue of the curve complex for mapping class groups
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Kell, Christian [Verfasser], Martin [Akademischer Betreuer] Kreuzer und Vladimir [Akademischer Betreuer] Shpilrain. „A Structure-based Attack on the Linearized Braid Group-based Diffie-Hellman Conjugacy Problem in Combination with an Attack using Polynomial Interpolation and the Chinese Remainder Theorem / Christian Kell ; Martin Kreuzer, Vladimir Shpilrain“. Passau : Universität Passau, 2019. http://d-nb.info/1190352699/34.
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Stylianakis, Charalampos. „Braid groups, mapping class groups, and Torelli groups“. Thesis, University of Glasgow, 2016. http://theses.gla.ac.uk/7466/.
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This thesis discusses subgroups of mapping class groups of particular surfaces. First, we study the Torelli group, that is, the subgroup of the mapping class group that acts trivially on the first homology. We investigate generators of the Torelli group, and we give an algorithm that factorizes elements of the Torelli group into products of particular generators. Furthermore, we investigate normal closures of powers of standard generators of the mapping class group of a punctured sphere. By using the Jones representation, we prove that in most cases these normal closures have infinite index in the mapping class group. We prove a similar result for the hyperelliptic mapping class group, that is, the group that consists of mapping classes that commute with a fixed hyperelliptic involution. As a corollary, we recover an older theorem of Coxeter (with 2 exceptional cases), which states that the normal closure of the m-th power of standard generators of the braid group has infinite index in the braid group. Finally, we study finite index subgroups of braid groups, namely, congruence subgroups of braid groups. We discuss presentations of these groups and we provide a topological interpretation of their generating sets.
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Kalka, Arkadius G. „Linear representations of braid groups and braid-based cryptography“. [S.l.] : [s.n.], 2007. http://www.gbv.de/dms/weimar/toc/58986095X_toc.pdf.
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Kim, Djun Maximilian. „Braid groups, orderings, and algorithms“. Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0028/NQ38913.pdf.
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Lawrence, Ruth Jayne. „Homology representations of braid groups“. Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236125.
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McLeay, Alan. „Subgroups of mapping class groups and braid groups“. Thesis, University of Glasgow, 2018. http://theses.gla.ac.uk/9075/.
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This thesis studies the subgroup structure of mapping class groups. We use techniques that fall into two categories: analysing the group action on a family of simplicial complexes, and investigating regular, finite-sheeted covering spaces. We use the first approach to prove that a wide class of normal subgroups of mapping class groups of punctured surfaces are geometric, that is, they have the extended mapping class group as their group of automorphisms, expanding on work of BrendleMargalit. For example, we determine that every member of the Johnson filtration is geometric. By considering punctured spheres, we also establish the automorphism groups of many normal subgroups of the braid group. The second approach is to relate subgroups of each of the mapping class groups associated to a covering space, namely, the liftable and symmetric mapping class groups. Given that the two surfaces have boundary, we consider covers in which either every mapping class lifts or every mapping class is fibre-preserving. We classify all covers that fall into one of these cases. In Chapter 1 we recall some preliminaries before stating the main results of the thesis. We then extend Brendle-Margalit's definition of complexes of regions to surfaces with punctures. Chapter 2 proves that the automorphism group of a complex of regions is the extended mapping class group, resolving in part a metaconjecture of N. V. Ivanov. In Chapter 3 we construct a complex of regions associated to a general normal subgroup of a mapping class group of a surface with punctures. We then apply the main result of the previous chapter to establish that such a normal subgroup is geometric. Finally, Chapter 4 presents joint work with Tyrone Ghaswala. We give a proof of the Birman-Hilden Theorem for surfaces with boundary and then prove the classifications of regular, finite-sheeted covering spaces of surfaces with boundary discussed above. We conclude by investigating an infinite family of branched covers of the disc. This family induces embeddings of the braid group into mapping class groups. We prove that each of these embeddings maps a standard generator of the braid group to a product of Dehn twists about curves forming a chain, providing an answer to a question of Wajnryb.
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Bangert, Patrick David. „Algorthmic problems in the braid groups“. Thesis, University College London (University of London), 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417929.
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Recio-Mitter, David. „Topological complexity of surface braid groups“. Thesis, University of Aberdeen, 2018. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=237921.
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The topological complexity was introduced by Michael Farber in 2003 motivated by applications of algebraic topology to robotics. It is a numerical homotopy invariant of a space which measures the instability of motion planning. In this thesis we determine this invariant for unordered configuration spaces of surfaces in many cases and reduce it to a few possible values in other cases. We also determine the topological complexity of mixed configuration spaces and related spaces. In contrast to the ordered configuration spaces, these computations remained elusive because the standard methods do not work here, as we argue in the Appendix. Apart from the interest from the motion planning perspective to decide whether unordered or ordered configurations have a higher topological complexity, there is another motivation. Namely, it is an open problem to give an algebraic description of the topological complexity of an aspherical space in terms of the fundamental group. The spaces under consideration are aspherical and so the topological complexity (being a homotopy invariant) becomes an invariant of their fundamental groups, the surface braid groups. The computation of the topological complexity of surface braid groups and their finite index subgroups thus provides further examples which might help tackle this open problem. Furthermore, the results could be used to gain information about the subgroup structure of surface braid groups. Often the topological complexity is calculated indirectly without actually finding an optimal motion planner which realizes it. Nonetheless, in some cases we will construct explicit motion planners and then prove that they are optimal. All those motion planners are collected in the last chapter.
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Rodrigues, Lucas, und Daniel Karlsson. „Why Do We Hate Brands? : A qualitative study of how the dark side of branding is influenced by group identification“. Thesis, Umeå universitet, Företagsekonomi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-111206.
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Abstract The purpose of this thesis was to gain a better understanding of the relatively new concept of Brand Hate. More specifically, how Brand Hate can occur in people with no to little experience with certain brands, so called non-customers. We want to believe that humans are a rational being that takes decisions based on all the available information and does not jump to conclusions before all options have been exhausted. But upon closer examination theoretical concepts such as brand love can be found. A concept that argues that users of a brand utilize the brand itself in order to internally identify values he or she holds, as well as showcasing those values and personality traits externally to others. With this theory as a basis the relatively new concept of Brand Hate was born. The new concept, posits that there has to be another side of the brand love, where people actually hate or dislike the brand. Up to this point very little research has been done within the area, and that is where the authors of this thesis saw an opportunity to fill a research gap. There has been no previous research attempting to understand WHY these negative feelings comes to present themselves within people. But as soon as the work on the thesis had started another opportunity presented itself, it seemed as though people hate or dislike brands that they themselves does not even use. As a result non-customers became the focal point of investigation of this thesis. The research itself included three different focus groups, with in total nineteen respondents that discussed a wide variety of topics. During the sessions the discussions touched upon what brands they disliked, why they disliked them and how the respondents identified with other groups of people. This gave the authors the ability to gain a deeper understanding of the psychological reasoning behind why certain brands the respondents did not use were severely hated or disliked. The findings from the research seem to point in one very specific direction, group identification is an integral reason why non-customers started to hate or dislike brands. No matter how good companies are creating an appealing brand, that same brand will always risk to become distorted, as a result of the different targeted user groups. This research shows that people let their emotions and prejudices come between what they perceive a brand to be, and what companies want them to be. The result is people prematurely judging brands based upon the customers of that brand. If the respondents did not like the user group of a certain brand, that same brand would be inscribed with all the negative connotations with the user groups, thereby distorting the public brand image far from what the companies might intend them to be.
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Kwon, Oh Kang. „Irreducible representations of braid groups via quantized enveloping algebras“. Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/32624.
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Gandolfi, Guillaume. „Résultats sur les extensions singulières des groupes d'Artin et de tresses virtuelles“. Thesis, Normandie, 2020. http://www.theses.fr/2020NORMC215.
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Cette thèse se propose d’étudier deux objets liés aux monoïdes de tresses singulières, le morphisme de désingularisation et la famille des invariants de Vassiliev, transposés dans les cadres respectifs des monoïdes d’Artin singuliers et des monoïdes de tresses virtuelles singulières. Dans le premier chapitre, on rappelle les définitions de ces deux objets dans leur contexte d'origine, celui des monoïdes de tresses singulières qui sont des extensions des groupes de tresses, puis celles des principales problématiques s'y rapportant, qui sont la déterminations de l'injectivité du morphisme de désingularisation et de la séparabilité des tresses (classiques ou singulières) par les invariants de Vassiliev, ainsi que les résultats qui répondent à ces problématiques. Dans le second chapitre, on redonne les fondamentaux de la théorie des groupes d'Artin et les définitions des principales familles de groupes d'Artin avant de rappeler la définition d'extension singulière associée à un groupe d'Artin. On démontre alors l'analogue singulier du résultat de Van der Lek sur les sous-groupes paraboliques d'un groupe d'Artin pour les monoïdes singuliers d'Artin de type FC et de type affine. On rappelle qu'il est également possible dans ce nouveau contexte de définir un morphisme de désingularisation, des invariants de Vassiliev ainsi que de reformuler les mêmes problématiques que dans le cades des tresses, et après avoir redonné les résultats connus sur ces problématiques pour les groupes d'Artin angle droit et les groupes d'Artin de type I, on démontre l'injectivité du morphisme de désingularisation pour les groupes d'Artin de type A affine ainsi que la séparabilité des éléments des groupes de type A affine et de type B par leurs invariants de Vassiliev respectifs. Dans les troisième et quatrièmes chapitres, on rappelle les définitions des groupes de tresses virtuelles, qui sont d'autres extensions des groupes de tresses, et des monoïdes de tresses virtuelles singulières qui leur sont associés. On démontre que les monoïdes de tresses virtuelles singulières sont bien des extensions communes aux groupes de tresses virtuelles et aux monoïdes de tresses singulières. On étend ensuite aux tresses virtuelles singulières les interprétations combinatoires (en termes de diagrammes de Gauss) et topologiques (en termes de classes stables de tresses abstraites) déjà connues pour les tresses virtuelles. Enfin, après avoir redéfini le morphisme de désingularisation et les invariants de Vassiliev pour les tresses virtuelles, on montre que la résolution des problématiques qui y sont liées est équivalente à la résolution de ces mêmes problématiques pour une famille de groupes d'Artin particuliers qui sont des sous-groupes des groupes de tresses virtuelles. On conclut la thèse par une étude sur le problème de la plongeabilité d'un monoïde dans sa monoïde dans son groupe enveloppant sur laquelle on s'appuie pour démontrer certains résultats de la thèseThis thesis offers to study two objects related to singular braid monoids, the desingularization map and the family of Vassiliev invariants, in the respective framework of the singular Artin monoids and the singular virtual braid monoids. In the first chapter, we recall the definitions of these two objects in their original setting, namely the setting of the singular braid monoids which are extensions of the braid groups, before stating the problems which are related to these objects, i.e. deciding whether the desingularization map is one-to-one and whether the Vassilev invariants separate the (classical or singular) braids, as well as the results that answer them. In the second chapter, we give the basics of the theory of Artin groups and the definition of the main families of Artin groups before recalling the definition of the singular extension of an Artin group. We prove a singular version of Van der Lek's theorem on parabolic subgroups of an Artin group for singular Artin monoids of FC type and of affine type. We recall that it is still possible to define in this new framework a desingularization map, Vassiliev invariants and to state the same problems as in the framework of braids, and after giving the results already known about these problems for right angle Artin groups and Artin groups of type I, we prove that the desingularization maps for Artin groups of type A affine are one-to-one and that the Vassiliev invariants respectively of Artin groups of type A affine and of type B separate the elements of these groups. In the third and furth chapter, we recall the definitions of the virtual braid groups, which are other extensions of braid groups, and the singular virtual braid monoids related to them. We show that the singular virtual braid monoids are indeed common extensions of the virtual braid groups and of the singular braid monoids. We then extend to singular virtual braids the combinatorial and topological interpretation (respectively in terms of Gauss diagrams and in terms of stable classes of abstract braids) which was already known for virtual braids. Finally, after defining the desingularization map and the Vassilev invariants for virtual braids, we show that the resolution of the problems related to these objects is equivalent to the resolution of the same problems for a family of Artin groups which appears to be subgroups of the virtual braid groups. We end the thesis with a study on the embeddability of a monoid in its enveloping group, on which several results of the thesis are based on
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Tosello, Francesco. „Una presentazione dei gruppi delle trecce“. Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21278/.
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The braid groups can be thought of as a generalisation of the symmetric group, in which not only the permutation but also the direction of exchange of points is considered; the consequence of this is that transpositions no longer have order two, indeed in the braid groups there are no elements of finite order. In this paper we follow the idea
of Fox R. and Neuwirth L. to discuss a proof of the presentation of the braid groups. First of all we recall some prerequisites: mainly results on groups, CW complexes,
foundamental groups and covering spaces. Then we give the proof of this presentation, obtained by considering the braid groups as foundamental groups of certain configuration
spaces. Finally, we have also derived a presentation of the symmetric group, exploiting a short exact sequence involving pure braids, braids and permutations. We belive that
the main contribution of this dissertation could be the wealth of examples, proofs and references which, in our opinion, were scarce in the original paper, to the point of making necessary the modification of some otherwise imprecise constructions.
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Valeriani, D. „Improving group decision making with collaborative brain-computer interfaces“. Thesis, University of Essex, 2017. http://repository.essex.ac.uk/19981/.
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Groups are generally superior to individuals in making decisions. However, time constraints and authoritarian leaders could nullify the potential advantages provided by groups. This thesis proposes a hybrid collaborative Brain-Computer Interface (cBCI) for improving performance in group decision-making. Neural signals recorded via electroencephalography are integrated with other physiological and behavioural measures to predict the likelihood of the user being correct in a decision, i.e., decision confidence. Behavioural responses from multiple users are then weighed according to these confidence estimates to obtain group decisions. The proposed cBCI has been tested with a variety of decision-making tasks, including visual matching, visual search with traditional and realistic stimuli, face recognition from multiple viewpoints, and speech perception. Groups assisted by the cBCI were significantly superior in making decisions than both individuals and traditional equally-sized groups making decisions using the majority method. This thesis also investigates the impact that a constrained form of communication has on individual and group performance in a visual-search experiment. When decision makers are able to exchange information during the experiment, their performance dramatically decreases. However, the cBCI yields superior group decisions even in this context. The confidence estimated by the cBCI is also a more reliable predictor of correctness than the confidence reported by participants after making a decision. When group members were allowed to communicate during visual search, their reported confidence was totally unrelated to the decision correctness, while in a speech perception task reported confidences were very good predictors of correctness. On the contrary, the cBCI?s confidence estimates correlated with correctness in all experiments. When critical decisions involving substantial risks have to be made (e.g., in defence), the proposed cBCI could be a useful tool to reduce the number of erroneous group decisions, thereby saving money and lives.
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Combe, Noémie. „On a new cell decomposition of a complement of the discriminant variety : application to the cohomology of braid groups“. Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0140.
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Cette thèse concerne principalement deux objets classiques étroitement liés: d'une part la variété des polynômes complexes unitaires de degré $d>1$ à une variable, et à racines simples (donc de discriminant différent de zéro), et d'autre part, les groupes de tresses d'Artin avec d brins. Le travail présenté dans cette thèse propose une nouvelle approche permettant des calculs cohomologiques explicites à coefficients dans n'importe quel faisceau. En vue de calculs cohomologiques explicites, il est souhaitable d'avoir à sa disposition un bon recouvrement au sens de Čech. L'un des principaux objectifs de cette thèse est de construire un tel recouvrement basé sur des graphes (appelés signatures) qui rappellent les `dessins d'enfant' et qui sont associées aux polynômes complexes classifiés par l'espace de polynômes. Cette décomposition de l'espace de polynômes fournit une stratification semi-algébrique. Le nombre de composantes connexes de chaque strate est calculé dans le dernier chapitre ce cette thèse. Néanmoins, cette partition ne fournit pas immédiatement un recouvrement adapté au calcul de la cohomologie de Čech (avec n'importe quels coefficients) pour deux raisons liées et évidentes: d'une part les sous-ensembles du recouvrement ne sont pas ouverts, et de plus ils sont disjoints puisqu'ils correspondent à différentes signatures. Ainsi, l'objectif principal du chapitre 6 est de ``corriger'' le recouvrement de départ afin de le transformer en un bon recouvrement ouvert, adapté au calcul de la cohomologie Čech. Cette construction permet ensuite un calcul explicite des groupes de cohomologie de Čech à valeurs dans un faisceau localement constantThis thesis mainly concerns two closely related classical objects: on the one hand, the variety of unitary complex polynomials of degree $ d> 1 $ with a variable, and with simple roots (hence with a non-zero discriminant), and on the other hand, the $d$ strand Artin braid groups. The work presented in this thesis proposes a new approach allowing explicit cohomological calculations with coefficients in any sheaf. In order to obtain explicit cohomological calculations, it is necessary to have a good cover in the sense of Čech. One of the main objectives of this thesis is to construct such a good covering, based on graphs that are reminiscent of the ''dessins d'enfants'' and which are associated to the complex polynomials. This decomposition of the space of polynomials provides a semi-algebraic stratification. The number of connected components in each stratum is counted in the last chapter of this thesis. Nevertheless, this partition does not immediately provide a ''good'' cover adapted to the computation of the cohomology of Čech (with any coefficients) for two related and obvious reasons: on the one hand the subsets of the cover are not open, and moreover they are disjoint since they correspond to different signatures. Therefore, the main purpose of Chapter 6 is to ''correct'' the cover in order to transform it into a good open cover, suitable for the calculation of the Čech cohomology. It is explicitly verified that there is an open cover such that all the multiple intersections are contractible. This allows an explicit calculation of cohomology groups of Čech with values in a locally constant sheaf
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Ma, Zheng. „Probabilistic Boolean network modeling for fMRI study in Parkinson's disease“. Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/4172.
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Recent research has suggested disrupted interactions between brain regions may contribute
to some of the symptoms of motor disorders such as Parkinson’s Disease (PD). It is therefore
important to develop models for inferring brain functional connectivity from data obtained
through non-invasive imaging technologies, such as functional magnetic resonance imaging
(fMRI). The complexity of brain activities as well as the dynamic nature of motor disorders
require such models to be able to perform complex, large-scale, and dynamic system computation. Traditional models proposed in the literature such as structural equation modeling
(SEM), multivariate autoregressive models (MAR), dynamic causal modeling (DCM), and
dynamic Bayesian networks (DBNs) have all been suggested as suitable for fMRI data analysis. However, they suffer from their own disadvantages such as high computational cost (e.g.
DBNs), inability to deal with non-linear case (e.g. MAR), large sample size requirement
(e.g. SEM), et., al. In this research, we propose applying Probabilistic Boolean Network
(PBN) for modeling brain connectivity due to its solid stochastic properties, computational
simplicity, robustness to uncertainty, and capability to deal with small-size data, typical for
fIVIRI data sets. Applying the proposed PBN framework to real fMRI data recorded from
PD subjects enables us to identify statistically significant abnormality in PD connectivity by
comparing it with normal subjects. The PBN results also suggest a mechanism of evaluating
the effectiveness of L-dopa, the principal treatment for PD. In addition to PBNs’ promising application in inferring brain connectivity, PBN modeling for brain ROTs also enables
researchers to study dynamic activities of the system under stochastic conditions, gaining
essential information regarding asymptotic behaviors of ROTs for potential therapeutic intervention in PD. The results indicate significant difference in feature states between PD
patients and normal subjects. Hypothesizing the observed feature states for normal subject
as the desired functional states, we further explore possible methods to manipulate the dynamic network behavior of PD patients in the favor of the desired states from the view of
random perturbation as well as intervention. Results identified a target ROT with the best
intervention performance, and that ROl is a potential candidate for therapeutic exercise.
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Evens, Samuel R. (Samuel Robert). „Transfer for compact lie groups, induced representations, and braid relations“. Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/80453.
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Damiani, Céleste. „The topology of loop braid groups : applications and remarkable quotients“. Caen, 2016. http://www.theses.fr/2016CAEN2021.
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Dans cette thèse nous étudions les groupes de tresses de cercles, nous explorons leurs applications topologiques et certains quotients remarquables. La thèse se compose de quatre parties : - Unification des formalismes pour les groupes de tresses de cercles. Plusieurs formulations ont été utilisées pour les groupes de tresses de cercles en différents domaines ; nous présentons ces interprétations et prouvons leur équivalence. - Une version topologique du théorème de Markov pour les entrelacs de tores ruban. Avec l’interprétation des tresses de cercles comme objets noués dans l’espace de dimension 4, nous présentons une version du Théorème de Markov pour les groupes de tresses de cercles avec clôture dans l’analogue du tore solide dans l’espace de dimension 4. - Invariants d’Alexander pour enchevêtrements ruban et algèbres de circuit. Nous définissons un invariant d’Alexander pour enchevêtrements ruban. De cela nous extrayons une généralisation fonctorielle du polynôme d’Alexander. Cet invariant a une signification topologique profonde, mais n’est pas simplement calculable. Nous établissons une correspondance avec le polynôme d’Alexander en plusieurs variables pour enchevêtrements introduit par Archibald pour résoudre ce problème. - Quotients des groupes de tresses virtuelles. Nous étudions les groupes de tresses de cercles symétriques, et nous en décrivons la structure. Comme conséquence nous montrons que tout entrelacs «fused » admets un représentant comme clôture d’une tresse de cercles symétrique pureIn this these we study loop braid groups, we explore some of their topological applications and some remarquable quotients. The thesis is composed by four parts:- Unifying the different approaches to loop braid groups. Several formulations are being used by researchers working with loop braid groups in different fields; we present these interpretations and prove their equivalence. - A topological version of Markov’s theorem for ribbon torus-links. Using the understanding of the interpretation of loop braids as knotted objects in the 4-dimensional space, we give a topological proof of a version of Markov theorem for loop braids with closure in a solid torus in the 4-dimensional space. - Alexander invariants for ribbon tangles. We define an Alexander invariant on ribbon tangles. From this invariant we extract a functorial generalization of the Alexander polynomial. This invariant has a deep topological meaning, but lacks a simple way of computation. To overcome this problem we establish a correspondence with Archibal’s multivariable Alexander polynomial for tangles. - Quotients of the virtual braid group. We study the groups of unrestricted virtual braids, a family of quotients of the loop braid groups, and describe their structure. As a consequence we show that any fused link admits as a representative the closure of a pure unrestricted virtual braid
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Coles, Ben. „Conjugacy in braid groups and the LKB representation, and Bessis-Garside groups of rank 3“. Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/90207/.
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In the first part of this thesis, we give a survey of the conjugacy problem in the braid group, describing the solution provided by Garside theory, and outlining the progress that has been made towards a polynomial time solution in recent years using refinements of Garside's solution, and the Thurston-Nielsen classification of braids, which reduces the problem to the case of pseudo-Anosov braids. Using the faithful Lawrence-Krammer-Bigelow representation of the braid groups, we consider how the eigenspaces of pseudo-Anosov braids can under certain conditions yield invariants of their conjugacy class and thus lead us towards a polynomial time solution of the conjugacy problem. In the second part we introduce Bessis-Garside groups, a generalisation of the methods used by Bessis in his papers on dual braid monoids. We consider the groups given by taking the quotient of the free group by the orbits of its generators under the action of some subgroup of the braid group, and find that in many cases this construction can give us a group with a Garside structure. By means of introduction we review the simple rank 2 case, and summarise examples of such groups already known to admit Garside structures, in particular due to the work of Digne. We then go on to give all those of such groups which can be found as quotients of affine and spherical Artin groups of rank 3. We show that all such groups may be given a cycle presentation, or equivalently may be given as labelled-oriented-graph presented groups, and give conditions on such presentations that are equivalent to the group admitting a `dual' Garside structure. Restricting by the cycle lengths occurring in such presentations we give all Bessis-Garside groups of rank 3 which have all cycles length at most 4, and discuss the case of Bessis-Garside groups with uniform cycle length.
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Yurasovskaya, Ekaterina. „Homotopy string links over surfaces“. Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2747.
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In his 1947 work "Theory of Braids" Emil Artin asked whether the braid
group remained unchanged when one considered classes of braids under linkhomotopy,
allowing each strand of a braid to pass through itself but not
through other strands. We generalize Artin's question to string links over
orientable surface M and show that under link-homotopy surface string links
form a group PBn(M), which is isomorphic to a quotient of the surface pure
braid group PBn(M). Surface braid groups and their properties are an area
of active research by González-Meneses, Paris and Rolfsen, Goçalves and
Guaschi, and our work explores the geometric and visual beauty of this
subject. We compute a presentation of PBn(M) in terms of the generators
and relations and discuss the orderability of the group in the case when the
surface in question is a unit disk D.
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Repo, Jesper. „Brand Culture : Between consumers and brands“. Thesis, Linnéuniversitetet, Ekonomihögskolan, ELNU, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-15220.
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The empirical data that lies behind this survey comes from field work between 1992 and 1995. This field work represents work I made myself as a sales-man for the company, Malmberg Original Water. The task was to implement the Malmberg mineral water brand on the restaurant market of the South-Swedish area. Our aim was to reach the upper-scale, premium market of restaurants. The mission was successfully completed, and at 1996 we had completed the position as the most exclusively positioned mineral water brand in Skåne (Southernmost Sweden). How could we fulfill this mission so fast, and with a very limited marketing budget (=0)?The secret key was that we managed to work and be in line with the values of our targeted customer group. We lived close to the customers and developed what was in line with their needs. This follows the research of Porter (1980) and Philipson (2011), serving the customer groups´ needs. Despite lack of money and budget from PR and promotion we made a large effort of serving and doing service towards our targeted customers.The thesis also focuses the target group´s importance for the construction of the brand identity. Strategic brand management-literature normally considers the target group taken-for-granted. Consumer research-literature, on the other hand, considers it as something vague and undefined. By applying a perspective of cultural values between the company, the brand and the target group it is possible to qualify the target group more than just refer to it as consumers or customers. The thesis also point to the conclusion not to consider brand identity as an independent entity, but dependent on the customers and the consumers. The consumers give birth to the brand. Finally since the target group is a group that is constantly set in motion, the brand also should reflect and represent change.
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Jordan, David Andrew. „Quantized multiplicative quiver varieties and actions of higher genus braid groups“. Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67790.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 109-112).
In this thesis, a new class of algebras called quantized multiplicative quiver varieties A (Q), is constructed, depending upon a quiver Q, its dimension vector d, and a certain "moment map" parameter . The algebras Ad(Q) are obtained via quantum Hamiltonian reduction of another algebra D,(Matd(Q)) relative to a quantum moment map pq, both of which are also constructed herein. The algebras Dq(Matd(Q)) and A (Q) bear relations to many constructions in representation theory, some of which are spelled out herein, and many more whose precise formulation remains conjectural. When Q consists of a single vertex of dimension N with a single loop, the algebra Dq(MatA(Q)) is isomorphic to the algebra of quantum differential operators on G = GLN. In this case, for any n E Z>o, we construct a functor from the category of Dq-modules to representations of the type A double affine Hecke algebra of rank n. This functor is an instance of a more general construction which may be applied to any quasi-triangular Hopf algebra H, and yields representations of the elliptic braid group of rank n.
by David Andrew Jordan.
Ph.D.
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Self, Megan. „Identifying the Physical Activity Needs of Outpatients with a Traumatic Brain Injury“. Thesis, University of North Texas, 2011. https://digital.library.unt.edu/ark:/67531/metadc84274/.
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Traumatic brain injury (TBI) is a significant public health issue due to the incidence, complexity, and cost associated with treatment – emphasizing the need for effective rehabilitation programs. One mode of rehabilitation that has been demonstrated to improve health and reduce healthcare costs is health promotion programs (HPPs) that incorporate physical activity (PA). However, PA is not currently incorporated into the standard of care post-TBI. The purpose of this study was to conduct group interviews among individuals with a TBI undergoing outpatient rehabilitation to determine PA knowledge, attitudes, intentions, and barriers. Results will be used to develop a HPP that focuses on facilitating PA participation as part of the rehabilitation process. Seventeen participants completed a series of group interviews (2-3 people/group) regarding their PA needs. A qualitative research design was adopted and trustworthiness was established through triangulation of data (i.e., theoretical underpinning; multiple researchers and data-coders). A cross-case analysis was completed to identify themes and conceptual patterns. The main themes identified were (1) an inability to differentiate between PA and physical therapy, (2) a limited knowledge of PA health benefits and the relationship to rehabilitation, and (3) an interest in participating in a PA HPP as part of their rehabilitation. HPPs for outpatients with a TBI should educate individuals about PA, the associated health benefits, and the role PA plays in the rehabilitation process. A well designed HPP may increase the likelihood that individuals adopt and maintain PA as part of the rehabilitation process, thus reducing the risk of morbidity and mortality.
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Beschin, Nicoletta. „Imagining half the world : investigation of representational neglect with group studies and single cases“. Thesis, University of Aberdeen, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275060.
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Based on ten experiments, this thesis examines representational neglect in brain damaged patients and in matched controls. The patients sometimes show a specific deficit in visual imaging: neglected one half of their mental representations. Although several studies addressed the issue of visuo-perceptual neglect, the representational defect is underinvestigated. Only a few standardized tests are available for its detention and assessment, and therefore rarely it is diagnosed in clinical practise or investigated in experimental work. In this thesis some new tests to investigate representational neglect are proposed. Moreover, representational neglect is evaluated in different sensory modalities (visual, tactile as well as within the personal domain) to address the issue of supramodality or plurimodality of this deficit.
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Pool, Jonathan. „Brief group music therapy for acquired brain injury : cognition and emotional needs“. Thesis, Anglia Ruskin University, 2013. http://arro.anglia.ac.uk/312324/.
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Injuries to the brain are the leading cause of permanent disability and death. Survivors of acquired brain injury (ABI) experience cognitive impairments and emotional problems. These often persist into community rehabilitation and are among the most significant needs for those in chronic stages of rehabilitation. There is a dearth of research providing evidence of music therapy addressing cognitive deficits and emotional needs in a holistic approach. This research answers the question how can brief group music therapy address cognitive functional gains and emotional needs of people with acquired brain injury. A mixed methods design was used to investigate the effect of 16 sessions of weekly group music therapy on attention and memory impairments, and emotional needs of ten ABI survivors in community rehabilitation. Quantitative data were collected to determine the effect of treatment on attention and memory functioning, mood state, and the satisfaction of emotional needs. Qualitative data were collected to reveal survivors’ experiences of brain injury and brief group music therapy. Analysis of the data showed that the intervention improved sustained attention (p<.05, r=.80) and immediate memory recall (p>.05, r=.46), and that the effect of treatment increased with dosage. Overall, the intervention was more effective than standard care, and cognitive functional gains continued after treatment for some ABI survivors. The intervention addressed emotional needs of feeling confident (p<.05, d=.88), feeling part of a group (p<.05, d=.74), feeling productive/useful (p<.05, d=.90), feeling supportive (p<.05, d=.75), feeling valued (p<.05, d=.74), and enjoyment (p<.05, d=.34). Improvements in these domains were observed in the immediate term and over the course of therapy. Music therapy enabled emotional adjustment through the development of selfawareness and insight. This study offers a music therapy method to deliver a holistic approach in rehabilitation. It demonstrates that music therapy can provide a cost effective, holistic treatment for ABI survivors.
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Melocro, Letícia. „Uma ordenação para o grupo de tranças puras“. Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-11012017-142019/.
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Neste trabalho apresentamos uma descrição geométrica do grupo de tranças no disco Bpnq e sua apresentação em termos de geradores e relatores no famoso teorema da apresentação de Artin. Mostraremos também que o grupo de tranças puras PBpnq, grupo que possui a permutação trivial das cordas, é bi-ordenável, ou seja, exibiremos uma ordenação para PBpnq que será invariante pela multiplicação em ambos os lados. Esse processo é dado a partir da combinação da técnica de pentear Artin e a expansão Magnus para grupos livres.In this work, we present a geometric description of the braids groups of the disk Bpnq and its presentation in terms of generators and relations in the famous theorem of Artin\'s presentation. We also show that groups of pure braids, denoted by PBpnq, groups that have the trivial permutation of the strings, are bi-orderable, that is, we will present the explicit construction of a strict total ordering of pure braids PBpnq which is invariant under multiplying on both sides. This process is given from the combination of the techniques of combing Artin and Magnus expansion to free groups.
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Moldrich, Randal Xavier Joseph 1975. „Functional roles of group II metabotropic glutamate receptors in injury and epilepsy“. Monash University, Dept. of Pharmacology, 2002. http://arrow.monash.edu.au/hdl/1959.1/7710.
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Thomas, Veronica L. „SECRET CONSUMPTION: RESPONSES TO SOCIAL GROUP INFLUENCE UNDER CONDITIONS OF CONFLICTING BRAND PREFERENCES“. Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1301945806.
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