Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Characterization of entanglement transformation via group representation theory

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group SL(2, C) circle times SL(2, C), composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo-orthonormalized. The two-to-one homomorphism is then established for the group SL(2, C) circle times SL(2, C) onto the SO(4, C). It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

The representation of highly pathogenic avian influenza in the Chinese media

In the early 2000s the threat of Highly Pathogenic Avian Influenza captured the attention of the world's media. While China is often considered the epicentre of the panzootic, few studies have explored coverage of this variant of avian flu in China. To address this issue, the authors examined the portrayal of Highly Pathogenic Avian Influenza across four Chinese newspapers at the local and national level. A textual analysis was performed on 160 articles across an eight-year period from 2001–2008. The study approach drew from Critical Discourse Analysis and Social Representation Theory. The headline analysis showed the extent that risk of the disease was subverted by the depiction of a strong and efficient ‘China’ that was a global leader in the fight against the disease. Ideological referents were called upon to stress teamwork in confronting the crisis. The diachronic analysis illustrated how the relationship between commercial interests, science and public health risks played out within the Chinese media.

A gauge theory for continuous spin particles

In this dissertation we explore the features of a Gauge Field Theory formulation for continuous spin particles (CSP). To make our discussion as self-contained as possible, we begin by introducing all the basics of Group Theory - and representation theory - which are necessary to understand where the CSP come from. We then apply what we learn from Group Theory to the study of the Lorentz and Poincaré groups, to the point where we are able to construct the CSP representation. Finally, after a brief review of the Higher-Spin formalism, through the Schwinger-Fronsdal actions, we enter the realm of CSP Field Theory. We study and explore all the local symmetries of the CSP action, as well as all of the nuances associated with the introduction of an enlarged spacetime, which is used to formulate the CSP action. We end our discussion by showing that the physical contents of the CSP action are precisely what we expected them to be, in comparison to our Group Theoretical approach.

Theorizing the use of multiple conceptual models in combination

Conceptual modelling continues to be an important means for graphically capturing the requirements of an information system. Observations of modelling practice suggest that modellers often use multiple conceptual models in combination, because they articulate different aspects of real-world domains. Yet, the available empirical as well as theoretical research in this area has largely studied the use of single models, or single modelling grammars. We develop a Theory of Combined Ontological Coverage by extending an existing theory of ontological expressiveness of conceptual modelling grammars. Our new theory posits that multiple conceptual models are used to increase the maximum coverage of the real-world domain being modelled, whilst trying to minimize the ontological overlap between the models. We illustrate how the theory can be applied to analyse sets of conceptual models. We develop three propositions of the theory about evaluations of model combinations in terms of users’ selection, understandability and usefulness of conceptual models.

Defining the density debate in Brisbane: how urban consolidation is represented in the media

Rapid population growth, changing demographic profiles and increased focus on sustainable urban form has led to significant changes in settlement patterns in Australian cities. Growth management strategies are increasingly employed to help cities manage strain on infrastructure, housing and ecosystems. Urban consolidation is one such strategy and has been adopted by all Australian capital cities. Despite strong governmental support, urban consolidation has triggered much academic debate and has often been accompanied by staunch community opposition and complaints from the development industry about barriers to the provision of higher density housing. Greater understanding of stakeholder representations of higher density housing is important for planning, given the strong policy focus on urban consolidation nationally. This paper contributes to existing urban consolidation literature by empirically demonstrating how urban consolidation is represented in Brisbane’s newspaper media through the use of metaphors. Its conceptual departure point is Social Representations Theory, drawing on the theory’s notion of objectification to illustrate how the media translates the abstract notion of urban consolidation into a tangible and understandable object. The objectification of urban consolidation is identified and discussed relative to four themes: land use conflict; growth; neighbourhood change and apartment living. This paper argues that understanding stakeholder representations is important for planners seeking to promote and negotiate delivery of higher density development. It concludes that stakeholder representations can highlight key areas of contention to be addressed by planners, provide indications on the likelihood of public acceptance of increased housing densities and delineate the boundaries of urban consolidation debates.

A Success Story or a Failure? : Representing the European Integration in the Curricula and Textbooks of Five Countries

The economic, political and social face of Europe has been changing rapidly in the past decades. These changes are unique in the history of Europe, but not without challenges for the nation states. The support for the European integration varies among the countries. In order to understand why certain developments or changes are perceived as threatening or as desired by different member countries, we must consider the social representations of the European integration on the national level: how the EU is represented to its citizens in media and in educational systems, particularly in the curricula and textbooks. The current study is concerned with the social representations of the European integration in the curricula and school textbooks in five European countries: France, Britain, Germany, Finland and Sweden. Besides that, the first volume of the common Franco-German history textbook was analyzed, since it has been seen as a model for a common European history textbook. As the collective representations, values and identities are dominantly mediated and imposed through media and educational systems, the national curricula and textbooks make an interesting starting point for the study of the European integration and of national and European identities. The social representations theory provides a comprehensive framework for the study of the European integration. By analyzing the curricula and history and civics textbooks of major educational publishers, the study aimed to demonstrate what is written on the European integration and how it is portrayed how the European integration is understood, made familiar and concretized in the educational context in the five European countries. To grasp the phenomenon of the European integration in the textbooks in its entirety, it was investigated from various perspectives. The two analysis methods of content analysis, the automatic analysis with ALCESTE and a more qualitative theory-driven content analysis, were carried out to give a more vivid and multifaceted picture of the object of the research. The analysis of the text was complemented with the analysis of visual material. Drawing on quantitative and qualitative methods, the contents, processes, visual images, transformations and structures of the social representations of European integration, as well as the communicative styles of the textbooks were examined. This study showed the divergent social representations of the European integration, anchored in the nation states, in the five member countries of the European Union. The social representations were constructed around different central core elements: French Europe in the French textbooks, Ambivalent Europe in the British textbooks, Influential and Unifying EU in the German textbooks, Enabling and Threatening EU in the Finnish textbooks, Sceptical EU in the Swedish textbooks and EU as a World Model in the Franco-German textbook. Some elements of the representations were shared by all countries such as peace and economic aspects of the European cooperation, whereas other elements of representations were found more frequently in some countries than in others, such as ideological, threatening or social components of the phenomenon European integration. The study also demonstrated the linkage between social representations of the EU and national and European identities. The findings of this study are applicable to the study of the European integration, to the study of education, as well as to the social representation theory.

Directed Nonabelian Sandpile Models on Trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

As representações sociais de profissionais de saúde acerca do paciente psiquiátrico: aspectos descritivos e de zona muda

A presença de pacientes crônicos em instituições psiquiátricas tem se constituído como um desafio humano, político e programático para esta área assistencial. Frente a isto, definiu-se como objetivo geral deste estudo analisar a reconstrução sócio-cognitiva do profissional de saúde mental acerca do paciente psiquiátrico crônico, contextualizando com a sua permanência institucional e o processo assistencial. Como objetivos específicos, descrever os conteúdos e a estrutura das representações sociais do paciente psiquiátrico crônico para os profissionais; identificar a existência de conteúdos implícitos nas formações discursivas dos profissionais de saúde referentes ao paciente crônico institucionalizado; e analisar a perspectiva assistencial implementada na atenção a esses indivíduos no contexto institucional a partir das representações sociais do paciente crônico. Trata-se de uma pesquisa qualitativa, desenvolvida com o aporte teórico-metodológico da Teoria das Representações Sociais em sua abordagem estrutural, em dois hospitais colônias localizados na cidade do Rio de Janeiro. Os dados foram coletados através de evocações livres em dois momentos. No primeiro, com 159 profissionais e no segundo utilizou-se a técnica de substituição com 151 profissionais. Os dados gerados foram analisados pelo software EVOC 2003 e organizados pelo quadro de quatro casas. Utilizou-se, ainda, a análise de similitude. Quanto à representação do paciente psiquiátrico, a mesma foi organizada ao redor das dimensões assistencial-institucional (cuidado), imagética (louco) e afetividade positiva (atenção), que se desdobram nos demais quadrantes, com destaque para a primeira e a segunda. A análise de similitude revelou que o léxico cuidado, obteve o maior número de ligações. Quanto à representação do paciente crônico em contexto normativo, a dimensão assistencial-institucional mostrou-se fortemente presente (cuidado, paciência e dependente), seguida da imagética (abandonado) e da de necessidade (carência). No entanto, na análise de similitude, a afetividade positiva (amor) mostra-se central com maior número de ligações de léxicos. Em contextos contra-normativos, a representação revelou-se negativa (louco, não e medo). A análise de similitude demonstrou uma representação estruturada através de uma imagem e de uma afetividade negativas. Conclui-se que os avanços na área de saúde mental, nos últimos 30 anos, não foram capazes de realizar mudanças representacionais sob fenômenos que ancoram em imagens produzidas desde os primórdios da humanidade. Ressalta-se a possível existência de uma zona muda acerca do paciente psiquiátrico crônico.

Práticas e representações sociais do trabalho em equipe na Marinha do Brasil

A presente dissertação teve como objetivo investigar as representações sociais do trabalho em equipe na Marinha do Brasil. A fundamentação teórica do trabalho foi proporcionada pela perspectiva psicossocial das representações sociais de S. Moscovici, com ênfase sobre a abordagem estrutural complementar devida a J-C. Abric. Quanto à parte empírica, aplicou-se numa etapa exploratória a técnica do grupo focal. Numa etapa seguinte, aplicou-se conjuntamente um questionário com perguntas abertas e fechadas e uma técnica de evocação livre a cento e trinta e nove militares, pertencentes aos círculos de Suboficiais e Sargentos, de Oficiais Intermediários e Subalternos e de Oficiais Superiores, oriundos da Força de Superfície e da Força de Submarinos. Os resultados revelaram a presença de diferentes representações sociais do trabalho em equipe entre Oficiais e Praças, e também entre as Forças Operativas pesquisadas. Foi evidenciado que, pelo fato da liderança ser o conteúdo central das representações sociais de equipe na MB, existe uma resistência por parte de todos os grupos pesquisados em formar equipes mais autônomas, apesar de as condutas de lideranças estarem voltadas para o incentivo de opiniões e valorização das participações dos integrantes da equipe.

Salve a Luz e Salve a Força: dimensões psicossociais na Doutrina do Santo Daime

A presente tese tem como objetivo analisar as mirações do Santo Daime dentro de um enfoque psicossocial. Tendo como base teórica a teoria das representações sociais e a psicologia social, será feita uma análise do estado alterado de consciência conhecido como miração, resultante do uso ritual do chá do Santo Daime. Utilizamos uma metodologia de pesquisa qualitativa, que envolveu extensa pesquisa bibliográfica, bem como entrevistas semi-estruturadas com membros do grupo daimista conhecido como Cefluris, ou linha do Padrinho Sebastião. A partir deste material, foi feita uma análise onde se procurou compreender a miração articulada às práticas sociais e ao discurso dos membros da doutrina. O Daime é uma religião relativamente pequena, com poucos seguidores, mas desperta interesse de diversas áreas de pesquisa por ter como ponto central a experiência do chá com propriedades psicoativas e a uma série de práticas e discursos ecumênicos, populares e ecológicos. Outro ponto debatido é sua relação com outras religiões e saberes que ao longo da História articulam o ser humano com as chamadas Plantas Mestras, ou enteógenas. A psicologia social e o estudo das religiões sem dúvida podem contribuir muito para aprofundar a compreensão nesta área de grande importância para o mundo contemporâneo.

Representação social da confiança

Esta tese focaliza como tema principal a representação social da confiança. Qual a importância da confiança para a sociedade contemporânea, para as organizações de produção e para as relações interpessoais. A fundamentação teórica é a Teoria das Representações Sociais tomada em sua equação: representação = figura/significado. A metodologia da pesquisa consistiu na realização de grupos focais e na expressão imagética e verbal da confiança. A análise dos textos visuais conjuntamente com os verbais possibilitou uma percepção bastante acurada desta representação social.