On Borel equivalence relations in generalized Baire space

"Vegeu el resum a l'inici del document del fitxer adjunt."

On [summation of 1 raised to the power 1] equivalence relations over the natural numbers

"Vegeu el resum a l'inici del document del fitxer adjunt"

Fuzzy tolerance/equivalence relations from intersection, union and complement operators and their application to a clustering method

This master thesis work introduces the fuzzy tolerance/equivalence relation and its application in cluster analysis. The work presents about the construction of fuzzy equivalence relations using increasing generators. Here, we investigate and research on the role of increasing generators for the creation of intersection, union and complement operators. The objective is to develop different varieties of fuzzy tolerance/equivalence relations using different varieties of increasing generators. At last, we perform a comparative study with these developed varieties of fuzzy tolerance/equivalence relations in their application to a clustering method.

EMERGENT CONDITIONAL RELATIONS IN A GO/NO-GO PROCEDURE: FIGURE-GROUND AND STIMULUS-POSITION COMPOUND RELATIONS

Past research has demonstrated emergent conditional relations using a go/no-go procedure with pairs of figures displayed side-by-side on a computer screen. The present Study sought to extend applications Of this procedure. In Experiment, 1, we evaluated whether emergent conditional relations Could be demonstrated when two-component stimuli were displayed in figure-ground relationships-abstract figures displayed on backgrounds of different colors. Five normal)), capable adults participated. During training, each two-component stimulus Was presented successively. Responses emitted in the presence of some Stimulus pairs (A1B1, A2B2, A3B3, B1C1, B2C2 and B3C3) were reinforced, whereas responses emitted in the presence of other pairs (A1B2, A1B3, A2B1, A2B3, A3B1, A3B2, B1C2, B1C3, B2C1, B2C3, B3C1 and B3C2) were not. During tests, new configurations (AC and CA) were presented, thus emulating structurally the matching-to-sample tests employed in typical equivalence Studies. All participants showed emergent relations consistent with stimulus equivalence during testing. In Experiment 2, we systematically replicated the procedures with Stimulus compounds consisting Of four figures (A1, A2, C1 and C2) and two locations (left - B1 and right - 132). A,11 6 normally capable adults exhibited emergent stimulus-stimulus relations. Together, these experiments show that the go/no-go procedure is a potentially useful alternative for Studying emergent. conditional relations when matching-to-sample is procedurally cumbersome or impossible to use.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Relational learning in children with deafness and cochlear implants

This four-experiment series sought to evaluate the potential of children with neurosensory deafness and cochlear implants to exhibit auditory-visual and visual-visual stimulus equivalence relations within a matching-to-sample format. Twelve children who became deaf prior to acquiring language (prelingual) and four who became deaf afterwards (postlingual) were studied. All children learned auditory-visual conditional discriminations and nearly all showed emergent equivalence relations. Naming tests, conducted with a subset of the: children, showed no consistent relationship to the equivalence-test outcomes.. This study makes several contributions: to the literature on stimulus equivalence. First; it demonstrates that both pre- and postlingually deaf children-can: acquire auditory-visual equivalence-relations after cochlear implantation, thus demonstrating symbolic functioning. Second, it directs attention to a population that may be especially interesting for researchers seeking to analyze the relationship. between speaker and listener repertoires. Third, it demonstrates the feasibility of conducting experimental studies of stimulus control processes within the limitations of a hospital, which these children must visit routinely for the maintenance of their cochlear implants.

A behavioral analysis tool for models of software systems

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia Informática

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Median Independent Inequality Orderings

To date, inequality orderings for ordered response data are only suitable for comparing distributions that share a common median state. In this paper we propose a methodology for comparing distributions irrespective of their medians. We set out to do so by introducing a general pre-ordering and equivalence relation defined over distributions with different median responses, leading us naturally to derive a partial ordering over equivalence classes. We then discuss the implications of our results for the axiomatic derivation of inequality indices for ordered response data.

Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Clones sous-maximaux inf-réductibles

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Criação de um Microtesauro na área da Dança

Este trabalho de Investigação teve como objetivo a construção de um microtesauro na área da Dança. Face à inexistência de um Tesauro especializado na área da Dança, quer a nível nacional, quer internacional, e para dar resposta às necessidades de uma recuperação mais eficaz de informação nas Unidades Documentaisi Especializadas em Dança. Neste caso, em particular, no Centro de Informação e Documentação (CDI) da Escola Superior de Dança (ESD). Percebeu-se que a construção deste microtesauro, tendo em conta as normas nacionais e internacionais para o efeito. No âmbito das funções desempenhadas no CDI foi identificada a necessidade de existir um instrumento de Linguagem Documental adequado, que permitisse nas Pesquisas bibliográficas, recuperar por Assunto os documentos existentes na Base de Dados. A Pesquisa Bibliográfica, apenas disponível por Título e por Autor, veio a revelar-se insuficiente, e a impossibilidade de pesquiasr os documentos por Assunto traduzia-se numa carência crescente dos utilizadores e do próprio Serviço. A Metodologia seguida para a construção deste Microtesauro, teve como base uma lista de Termos de Indexação construída a partir da análise de uma amostra de 125 monografias e a consulta de várias fontes de informção (monografias e obras de referência, linguagens documentais, e entrevistas informais a docentes da ESD). A análise, quantificação e qualificação dos termos que constituem este microtesauro teve o acompanhamento, avaliação e adequação contínua por parte de alguns docentes da ESD, investigadores e especialistas em Dança. A Dança, enquanto objeto de exploração teórica, revela-se uma disciplina transversal a várias áreas do conhecimento que, agrupadas em classes, correspondem a 8 áreas do saber, relacionadas com a Dança, tendo em consideração as temáticas do espólio documental do CDI e as matérias lecionadas nas Unidades Curriculares dos cursos de Licenciatura e Mestrados da ESD. O microtesauro na área da Dança, que resulta do nosso trabalho de investigação, é constituído por Descritores, Não-Descritores, e suas relações de equivalência hierárquicas e associativas, apresentando-se no final deste trabalho, em apêndice, devido à sua dimensão. O mesmo resulta de um processos de construção individual, inicialmente elaborado de forma manual e posteriormente transposto para um Software Documental CDS/ISIS para Windows, que veio agilizar a estruturação do microtesauro. Este microtesauro na área da Dança, em Língua Portuguesa, constitui um importante contributo para as Bibliotecas e Centros de Documentação que detêm documentação nesta área específica, dado colmatar uma lacuna existente neste domínio do conhecimento.

Quantified Interference: Information Theory and Information Flow

The paper investigates which of Shannon’s measures (entropy, conditional entropy, mutual information) is the right one for the task of quantifying information flow in a programming language. We examine earlier relevant contributions from Denning, McLean and Gray and we propose and motivate a specific quantitative definition of information flow. We prove results relating equivalence relations, interference of program variables, independence of random variables and the flow of confidential information. Finally, we show how, in our setting, Shannon’s Perfect Secrecy theorem provides a sufficient condition to determine whether a program leaks confidential information.