Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-16T12:52:36Z No. of bitstreams: 2 Dissertação EnioPerez.pdf: 2190954 bytes, checksum: 8abd6c2cd31279e28971c632f6ed378b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-16T14:10:30Z (GMT) No. of bitstreams: 2 Dissertação EnioPerez.pdf: 2190954 bytes, checksum: 8abd6c2cd31279e28971c632f6ed378b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-16T14:10:30Z (GMT). No. of bitstreams: 2 Dissertação EnioPerez.pdf: 2190954 bytes, checksum: 8abd6c2cd31279e28971c632f6ed378b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2011-08-26 / Intuitively, the basic idea of Design Theory consists of a way to select subsets, also called blocks, of a finite set, so that some properties are satisfied. The more general case are the blocks designs. A PBD is an ordered pair (S;B), where S is a finite set of symbols, and B is a collection of subsets of S called blocks, such that each pair of distinct elements of S occur together in exactly one block of B. A Steiner Triple System is a particular case of a PBD, where every block has size only 3, being called triples. The main focus is in building technology systems. By resolvability is discussed as a Steiner Triple Systems is resolvable, and when it is not resolvable. This theory has several applications, eg, embeddings and even problems related to computational complexity. / Intuitivamente, a idéia básica de um Planejamento Combinatório consiste em uma maneira de selecionar subconjuntos, também chamados de blocos, de um conjunto finito, de modo que algumas propriedades especificadas sejam satisfeitas. O caso mais geral são os planejamentos balanceados. Um PBD é um par ordenado (S;B), onde S é um conjunto finito de símbolos, e B é uma coleção de subconjuntos de S chamados blocos, tais que cada par de elementos distintos de S ocorrem juntos em exatamente um bloco de B. Um Sistema Triplo de Steiner é um caso particular de um PBD, em que todos os blocos tem tamanho único 3, sendo chamados de triplas. O foco principal está nas técnicas de construção dos sistemas. Por meio da resolubilidade se discute quando um Sistema Triplo de Steiner é resolvível e quando não é resolvível. Esta teoria possui várias aplicações, por exemplo: imersões e até mesmo problemas relacionados à complexidade computacional.

A presente pesquisa discute as contribuições do pensamento filosófico-estético e pedagógico de Rudolf Steiner (1861-1925) e da Rítmica de Émile Jaques-Dalcroze (1865-1950) para os processos de ensino-aprendizagem em Música no contexto escolar, especialmente no período compreendido entre 7 e 14 anos de idade. A partir da pesquisa bibliográfica dos textos de ambos os autores, abarcando conferências, publicações e artigos, o trabalho consistiu, primeiramente, em sintetizar alguns conceitos fundamentais para a Antroposofia, ciência do espírito que Rudolf Steiner elaborou no início do século XX, como ampliação do campo de conhecimento das ciências naturais. Steiner adota a cosmovisão de Goethe e Schiller, bem como seu método cognitivo contemplativo, como alternativa ao materialismo mecanicista do pensamento cartesiano. O estudo revela a correspondência entre os pensamentos de Rudolf Steiner e Émile Jaques-Dalcroze em muitos aspectos, comprovando a hipótese da possibilidade de um fecundo diálogo e mútua complementação entre os dois contemporâneos. Dalcroze, em sentido inverso ao de Steiner, parte da observação e da intuição sobre sua experiência prática como docente de Música, compositor e intérprete, para a elaboração de uma filosofia estético-pedagógica. Dalcroze criou a Rítmica como um método ou um caminho para o desenvolvimento de uma escuta criativa, com o corpo inteiro, encontrando a musicalidade na expressão gestual e no movimento corporal. Ambos os autores apresentam uma concepção expandida de ritmo como princípio que urde toda a vida e toda arte, essencial a todo o processo educativo. Eles ainda trazem múltiplas contribuições importantes para a reflexão sobre a prática pedagógica em Música na atualidade, especialmente no tangente à arte de educar pelo ritmo, em que a improvisação e o aspecto lúdico potencializam a expressão criativa em aula. A dialética entre liberdade e estrutura, integrando escuta e corpo pela respiração e o movimento, e a concepção integrada das artes, como processos estésicos e poiéticos complexos, estendem a sua importância à apreciação dos repertórios modernos e pós-modernos na Educação Musical contemporânea. / This research discusses the contributions of Austrian philosopher Rudolf Steiner\'s (1861-1925) philosophical, aesthetic and pedagogical thought and of Austrian-Swiss musician, composer and music educator Émile Jaques-Dalcroze\'s (1865-1950) Eurythmics to the Music teaching-learning process in elementary and secondary school, especially concerning children between 7 and 14 years of age. Based on bibliographical research comprehending original texts - papers and books - and conferences, this work aims at, first of all, providing a synthesis of some concepts that are fundamental to Anthroposophy - a spiritual science founded by Rudolf Steiner at the beginning of the XXth. century and intended to be an expansion of natural science\'s scope of knowledge. Steiner adopts Goethe\'s and Schiller\'s artistic cosmovision and their cognition method, founded on contemplative observation of nature, as an alternative for the mechanical philosophy of Cartesian materialism. The study shows the many matching aspects of Steiner\'s and Dalcroze\'s thoughts, showing that it is possible to establish a prolific and mutual complementary dialogue between these two contemporaries, given that the latter followed the inverse path of the former toward his aesthetic and pedagogical philosophy, taking as starting point an intuitive approach of his own practical experience as Music teacher, composer and performer. Dalcroze created the Eurhytmics as a method or way to develop creative listening with the whole body, finding musicality in gestural expression and body movement. Both authors present an expanded conception of rhythm as the essence of life, that which unites all the arts and should be a component of every educational process. They also bring great contributions to the consciousness about pedagogical practices in Music at present, specially concerning the art of education through rhythm, taking improvisation and its playful nature as resources to enhance the creative expression in class. The dialectics between freedom and structure, integrating listening to the body as a whole through breathing and movement, as well as their integrated conception of Arts as a complex aesthetic and poetic process expand its importance toward the appreciation of modern and postmodern repertoires in the contemporary Musical Education.

Rudolf Steiner (1861-1925) foi um filósofo, jornalista e educador. Atualmente seu nome está associado ao movimento Camphill de educação curativa, sua arquitetura, vários estudos sobre religião, à agricultura biodinâmica, à medicina antroposófica e à pedagogia Waldorf. O objetivo principal desta pesquisa é investigar a contribuição e validade das concepções sobre o querer, o sentir e o pensar de Rudolf Steiner para os estudos literários. Espera-se contribuir para a ressignificação do papel da literatura como força impulsora na mediação entre o sentimento e a razão para o desenvolvimento e constituição do pensar conceitual e formação do ser harmônico e integral. Esta tese contém uma introdução e seis capítulos. O capítulo 1 dá uma ideia geral do contexto de Rudolf Steiner e trata de sua formação, carreira, interesses profissionais, bem como sobre algumas possíveis influências sobre seu pensamento. O capítulo 2 apresenta as concepções do homem, do querer, do sentir e do pensar que aparecem na obra Filosofia da Liberdade e suas relações com outros estudos do autor. Discute também a importância da arte e das narrativas para a formação do ser humano integral, harmônico e espiritualmente livre. O capítulo 3 compara as ideias de Steiner acerca do pensar, da criança, das narrativas com as concepções de Edgar Morin e Walter Benjamin. Também apresenta indicações de narrativas propostas por seguidores de Steiner. O capítulo 4 apresenta a metodologia e as obras utilizadas na experiência estética de recepção de leitura desenvolvida com ex-alunos formados pela pedagogia Waldorf e ex-alunos formados por outras pedagogias. O capítulo 5 discute os resultados da pesquisa. O capítulo 6 apresenta algumas considerações finais sobre o assunto. / Rudolf Steiner (1861-1925) was a philosopher, journalist and educator. Nowadays his name is usually associated with the Camphill moviment of curative education, architecture, biodynamical agriculture, the anthroposophical medicine, several studies on religion and the Waldorf education. The aim of this research is to examine the contribution and validity of Rudolf Steiners concepts of willing, feeling and thinking that may be seen in literary studies. This work is expected to render some contrtibution to resignifying the role of literature as a thrust in mediating feelings and reason in order to develop and constitute conceptual thinking as well as in forming a harmonious and wholesome being. This thesis contains an introduction and six chapters. Chapter 1 provides a general overlook of Steiners context and deals with his background, career, professional interests as well as some of the possible influences he received. Chapter 2 studies Steiners concepts of man, willing, feeling and thinking presented in his work The Philosophy of Freedom as well as in other works by Steiner. It also discusses the importance of Art and the importance of narrative to form a wholesome and harmonious being who is also spiritually free. Chapter 3 compares Steiner\'s ideas about thinking, about the child and about the narratives that follow conceptions by Edgar Morin and Walter Benjamin. It also presents indications of narrative proposed by Steiners followers. Chapter 4 presents the methodology and the works used in the aesthetic experience of reading reception, which was developed with alumni graduated in Waldorf and alumni graduated in other pedagogies. Chapter 5 discusses the results of the research. Chapter 6 presents some final thoughts on the subject.

The Steiner Tree problem has appeared in the Karp's list of the first 21 NP-hard problems and is well known as one of the most fundamental problems in Network Design area. We study the Node-Weighted version of the Prize Collecting Steiner Tree problem. In this problem, we are given a simple graph with a cost and penalty value associated with each node. Our goal is to find a subtree T of the graph minimizing the cost of the nodes in T plus penalty of the nodes not in T. By a reduction from set cover problem it can be easily shown that the problem cannot be approximated in polynomial time within factor of (1-o(1))ln n unless NP has quasi-polynomial time algorithms, where n is the number of vertices of the graph. Moss and Rabani claimed an O(log n)-approximation algorithm for the problem using a Primal-Dual approach in their STOC'01 paper \cite{moss2001}. We show that their algorithm is incorrect by providing a counter example in which there is an O(n) gap between the dual solution constructed by their algorithm and the optimal solution. Further, evidence is given that their algorithm probably does not have a simple fix. We propose a new algorithm which is more involved and introduces novel ideas in primal dual approach for network design problems. Also, our algorithm is a Lagrangian Multiplier Preserving algorithm and we show how this property can be utilized to design an O(log n)-approximation algorithm for the Node-Weighted Quota Steiner Tree problem using the Lagrangian Relaxation method. We also show an application of the Node Weighted Quota Steiner Tree problem in designing algorithm with better approximation factor for Technology Diffusion problem, a problem proposed by Goldberg and Liu in \cite{goldberg2012} (SODA 2013). In Technology Diffusion, we are given a graph G and a threshold θ(v) associated with each vertex v and we are seeking a set of initial nodes called the seed set. Technology Diffusion is a dynamic process defined over time in which each vertex is either active or inactive. The vertices in the seed set are initially activated and each other vertex v gets activated whenever there are at least θ(v) active nodes connected to v through other active nodes. The Technology Diffusion problem asks to find the minimum seed set activating all nodes. Goldberg and Liu gave an O(rllog n)-approximation algorithm for the problem where r and l are the diameter of G and the number of distinct threshold values, respectively. We improve the approximation factor to O(min{r,l}log n) by establishing a close connection between the problem and the Node Weighted Quota Steiner Tree problem.

The aim of this essay is, firstly, to – through a text analysis – compare the curriculum of Waldorf education in Sweden (in the essay referred to as “WL”) to the Swedish national curriculum “Lpo 94”, to uncover possible differences and similarities between these documents, and, secondly, to present the roots and educational philosophies that these two curricula, respectively, are based upon. The purpose hereby is to be able to trace, describe and explain the differences between the pedagogical practices of Waldorf education and that of conventional Swedish schools. In the essay, a historical investigation of the main traditions of ideas behind the Swedish national curriculum is briefly carried out, where I swiftly present the educational philosophies of John Dewey (1859-1952) and Lev S. Vygotsky (1896-1934). Next, an investigation of the worldview and philosophy of Rudolf Steiner (1861-1925) is effectuated, where I attempt to bring to light Steiner’s anthroposophical and holistic worldview – a worldview that throughout the 20th century has developed into an international and wide-ranging anthroposophical movement – as well as his concepts of knowledge, science and educational philosophy. It is made clear that Steiner’s texts and lectures are continuously centred on a holistic outlook on mankind and nature, as well as the spiritual development of humankind and deeper development of the mind. Even though the text analysis of the two curricula shows several similarities between the curriculum of Waldorf education and the national one – in particular regarding in what way the text is structured, as well as in what way the basic (democratic) values are expressed – the analysis also displays a wide range of differences. The curriculum of the Waldorf education displays a closer relation to Steiner’s holistic worldview and educational ideas than does Lpo 94 to the educational ideas of Dewey and Vygotsky, and it focuses more on the importance of the child’s playing activities, creativity and art compared to conventional schools, even though these perspectives do exist here as well. It is argued that, above all, it is the outlook on mankind behind the curriculum that shapes the educational system and the practices within it. The outlook on mankind of Steiner and the Waldorf curriculum focuses on the importance of the pupil’s spiritual development, something that is seldom – if ever – considered in the conventional school. This seems to have an impact on the Waldorf schools in the sense that the pupil is less likely to share materialistic values, and, instead, to have a better understanding of civic and democratic values as a whole. Thus, the curriculum of Waldorf education can – in a much higher degree than the national one, Lpo 94 – be viewed as a “curriculum for the soul”, i.e. to be a curriculum that focuses on the pupil’s spiritual development. Curriculum, Waldorf education, Lpo 94, Rudolf Steiner, educationalphilosophy, anthroposophy, John Dewey, Lev S. Vygotsky

A linear space is a set of points and lines such that any pair of points lie on exactly one line together. This is equivalent to a pairwise balanced design PBD(v, K), where there are v points, lines are regarded as blocks, and K ⊆ Z≥2 denotes the set of allowed block sizes. The dimension of a linear space is the maximum integer d such that any set of d points is contained in a proper subspace. Specifically for K = {3, 4, 5}, we determine which values of v admit PBD(v,K) of dimension at least three for all but a short list of possible exceptions under 50. We also observe that dimension can be reduced via a substitution argument. / Graduate / 0405 / jniezen@uvic.ca

The Steiner Tree problem has appeared in the Karp's list of the first 21 NP-hard problems and is well known as one of the most fundamental problems in Network Design area. We study the Node-Weighted version of the Prize Collecting Steiner Tree problem. In this problem, we are given a simple graph with a cost and penalty value associated with each node. Our goal is to find a subtree T of the graph minimizing the cost of the nodes in T plus penalty of the nodes not in T. By a reduction from set cover problem it can be easily shown that the problem cannot be approximated in polynomial time within factor of (1-o(1))ln n unless NP has quasi-polynomial time algorithms, where n is the number of vertices of the graph. Moss and Rabani claimed an O(log n)-approximation algorithm for the problem using a Primal-Dual approach in their STOC'01 paper \cite{moss2001}. We show that their algorithm is incorrect by providing a counter example in which there is an O(n) gap between the dual solution constructed by their algorithm and the optimal solution. Further, evidence is given that their algorithm probably does not have a simple fix. We propose a new algorithm which is more involved and introduces novel ideas in primal dual approach for network design problems. Also, our algorithm is a Lagrangian Multiplier Preserving algorithm and we show how this property can be utilized to design an O(log n)-approximation algorithm for the Node-Weighted Quota Steiner Tree problem using the Lagrangian Relaxation method. We also show an application of the Node Weighted Quota Steiner Tree problem in designing algorithm with better approximation factor for Technology Diffusion problem, a problem proposed by Goldberg and Liu in \cite{goldberg2012} (SODA 2013). In Technology Diffusion, we are given a graph G and a threshold θ(v) associated with each vertex v and we are seeking a set of initial nodes called the seed set. Technology Diffusion is a dynamic process defined over time in which each vertex is either active or inactive. The vertices in the seed set are initially activated and each other vertex v gets activated whenever there are at least θ(v) active nodes connected to v through other active nodes. The Technology Diffusion problem asks to find the minimum seed set activating all nodes. Goldberg and Liu gave an O(rllog n)-approximation algorithm for the problem where r and l are the diameter of G and the number of distinct threshold values, respectively. We improve the approximation factor to O(min{r,l}log n) by establishing a close connection between the problem and the Node Weighted Quota Steiner Tree problem.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.

A critical set in a Latin square of order n is a set of entries in an n×n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of critical sets grows super-exponentially as the order of the Latin square increases. It is difficult to find patterns in Latin squares of small order (order 5 or less) which can be generalised in the process of creating new theorems. Thus, I have written many algorithms to find critical sets with various properties in Latin squares of order greater than 5, and to deal with other related structures. Some algorithms used in the body of the thesis are presented in Chapter 3; results which arise from the computational studies and observations of the patterns and subsequent results are presented in Chapters 4, 5, 6, 7 and 8. The cardinality of the largest critical set in any Latin square of order n is denoted by lcs(n). In 1978 Curran and van Rees proved that lcs(n)<=n²-n. In Chapter 4, it is shown that lcs(n)<=n²-3n+3. Chapter 5 provides new bounds on the maximum number of intercalates in Latin squares of orders m×2^α (m odd, α>=2) and m×2^α+1 (m odd, α>=2 and α≠3), and a new lower bound on lcs(4m). It also discusses critical sets in intercalate-rich Latin squares of orders 11 and 14. In Chapter 6 a construction is given which verifies the existence of a critical set of size n²÷ 4 + 1 when n is even and n>=6. The construction is based on the discovery of a critical set of size 17 for a Latin square of order 8. In Chapter 7 the representation of Steiner trades of volume less than or equal to nine is examined. Computational results are used to identify those trades for which the associated partial Latin square can be decomposed into six disjoint Latin interchanges. Chapter 8 focusses on critical sets in Latin squares of order at most six and extensive computational routines are used to identify all the critical sets of different sizes in these Latin squares.