In this thesis, we investigate the integrability properties of some evolutionary type nonlinear equations in (1+1)-dimensions both with commutative and non-commutative variables. We construct the recursion operators, based on the Lax representation, for such equations. Finally, we question the notion of integrability for a certain one-component non-commutative equation. [We stress that calculations in this thesis are not original.]

This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences.

This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences.

This M.A. thesis is an autoethnographic study of my personal experiences teaching Grade Two after ten years of teaching middle school. It takes place over a five year span from 2007 to 2012. It is presented as a series of fictional, performative, and narrative pieces, where the reader is invited along on my journey to discover who I am (becoming) as Teacher, and the (re)invention of myself as Teacher. The study takes a creative, arts- based approach, presented as a curriculum lab book that is formatted differently than a traditional thesis. On the right side of each page is a novelette comprised of narratives, stories, dialogue, and poems; on the left side of the page are literature links and implications, definitions, reflections, and recursive segments. Areas that are highlighted in this thesis include living in the hybridity of culture, dwelling in the spaces of planned and lived curriculum, and the pedagogy of reinvention. The focus of this research story is reflection and practice, ways to approach change in our pedagogy, and to demonstrate autoethnography as a methodology for the exploration of Teacher identity. / Graduate

O presente trabalho visa analisar a relevância da propriedade recursiva na definição da maneira como a faculdade da linguagem se apresenta na cognição da espécie humana. Para tanto, faz-se necessário o levantamento das teorias correntes que buscam tal definição, como os trabalhos de Hauser, Chomsky e Fitch (2002), Jackendoff e Pinker (2005), e suas respectivas considerações sobre questões como a exclusividade da propriedade recursiva à espécie humana e ao domínio da linguagem e sua importância na distinção entre a linguagem humana e os sistemas de comunicação de outras espécies. Também é considerado o trabalho de Karlsson (2010) para auxiliar na delimitação do conceito de recursividade e na reflexão sobre sua possível potencialidade de aplicação infinita. Ao final, conclui-se que a recursividade é um princípio da Gramática Universal e uma das características da linguagem humana de papel fundamental e distintivo na caracterização dessa faculdade mental de nossa espécie, estando presente em todas as línguas, ainda que com restrições de aplicação sujeitas aos parâmetros particulares de cada sistema linguístico. / This study aims to analyze the relevance of recursion in the definition of how the language faculty is established in the human species’ cognition. Therefore, it is necessary to survey the current theories that seek this definition, such as the work of Hauser, Chomsky and Fitch (2002), Jackendoff and Pinker (2005), and their considerations on issues like the uniqueness of the recursive property in our species, its uniqueness in the language field and its importance in the distinction between human language and the communication systems of other species. It is also taken into account the work of Karlsson (2010), in helping to define the concept of recursion and to consider the recursion’s potentially infinite application. Finally, we reach the conclusion that recursion is a principle of Universal Grammar and a very important aspect of human language, playing a distinctive role in the characterization of this cognitive faculty of our species. It is found in all languages, despite the application restrictions subject to the particular parameters of each linguistic system.

O presente trabalho visa analisar a relevância da propriedade recursiva na definição da maneira como a faculdade da linguagem se apresenta na cognição da espécie humana. Para tanto, faz-se necessário o levantamento das teorias correntes que buscam tal definição, como os trabalhos de Hauser, Chomsky e Fitch (2002), Jackendoff e Pinker (2005), e suas respectivas considerações sobre questões como a exclusividade da propriedade recursiva à espécie humana e ao domínio da linguagem e sua importância na distinção entre a linguagem humana e os sistemas de comunicação de outras espécies. Também é considerado o trabalho de Karlsson (2010) para auxiliar na delimitação do conceito de recursividade e na reflexão sobre sua possível potencialidade de aplicação infinita. Ao final, conclui-se que a recursividade é um princípio da Gramática Universal e uma das características da linguagem humana de papel fundamental e distintivo na caracterização dessa faculdade mental de nossa espécie, estando presente em todas as línguas, ainda que com restrições de aplicação sujeitas aos parâmetros particulares de cada sistema linguístico. / This study aims to analyze the relevance of recursion in the definition of how the language faculty is established in the human species’ cognition. Therefore, it is necessary to survey the current theories that seek this definition, such as the work of Hauser, Chomsky and Fitch (2002), Jackendoff and Pinker (2005), and their considerations on issues like the uniqueness of the recursive property in our species, its uniqueness in the language field and its importance in the distinction between human language and the communication systems of other species. It is also taken into account the work of Karlsson (2010), in helping to define the concept of recursion and to consider the recursion’s potentially infinite application. Finally, we reach the conclusion that recursion is a principle of Universal Grammar and a very important aspect of human language, playing a distinctive role in the characterization of this cognitive faculty of our species. It is found in all languages, despite the application restrictions subject to the particular parameters of each linguistic system.

O presente trabalho visa analisar a relevância da propriedade recursiva na definição da maneira como a faculdade da linguagem se apresenta na cognição da espécie humana. Para tanto, faz-se necessário o levantamento das teorias correntes que buscam tal definição, como os trabalhos de Hauser, Chomsky e Fitch (2002), Jackendoff e Pinker (2005), e suas respectivas considerações sobre questões como a exclusividade da propriedade recursiva à espécie humana e ao domínio da linguagem e sua importância na distinção entre a linguagem humana e os sistemas de comunicação de outras espécies. Também é considerado o trabalho de Karlsson (2010) para auxiliar na delimitação do conceito de recursividade e na reflexão sobre sua possível potencialidade de aplicação infinita. Ao final, conclui-se que a recursividade é um princípio da Gramática Universal e uma das características da linguagem humana de papel fundamental e distintivo na caracterização dessa faculdade mental de nossa espécie, estando presente em todas as línguas, ainda que com restrições de aplicação sujeitas aos parâmetros particulares de cada sistema linguístico. / This study aims to analyze the relevance of recursion in the definition of how the language faculty is established in the human species’ cognition. Therefore, it is necessary to survey the current theories that seek this definition, such as the work of Hauser, Chomsky and Fitch (2002), Jackendoff and Pinker (2005), and their considerations on issues like the uniqueness of the recursive property in our species, its uniqueness in the language field and its importance in the distinction between human language and the communication systems of other species. It is also taken into account the work of Karlsson (2010), in helping to define the concept of recursion and to consider the recursion’s potentially infinite application. Finally, we reach the conclusion that recursion is a principle of Universal Grammar and a very important aspect of human language, playing a distinctive role in the characterization of this cognitive faculty of our species. It is found in all languages, despite the application restrictions subject to the particular parameters of each linguistic system.

Orientadores: Jônatas Manzolli, Fernando Augusto de Almeida Hashimoto / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Artes / Made available in DSpace on 2018-08-21T15:36:18Z (GMT). No. of bitstreams: 1 Campos_CleberdaSilveira_D.pdf: 5383709 bytes, checksum: 9fbbd1f6fb089fb64097a7c772db5d62 (MD5) Previous issue date: 2012 / Resumo: Dentro da linha de pesquisa de processos criativos voltados à composição e à improvisação por meios acústicos e tecnológicos, a Tese apresenta um estudo focado na aplicação de processos graduais e recursivos para gerar estruturas musicais no contexto da percussão mediada por suporte tecnológico. Do repertório para percussão vinculada à noção de Processo Gradual, conceito criado por Reich (1968), extraíram-se Modelos para Processos Criativos em Percussão (MPCP). O estudo pormenorizado desses modelos permitiu a articulação de nuances, detalhes e diferenças existentes nos processos graduais aplicados à percussão, aqui representada pelo instrumento africano Djembê. O processamento computacional permitiu identificar, organizar, controlar e expandir as diferenças presentes nas estruturas sonoras através da criação de uma Taxonomia de Gestos Musicais Interpretativos (TGMI). Analisou-se o espectrograma para medir as frequências características e as durações das ressonâncias do Djembê. Tais medições, relacionadas às características físicas e geométricas do instrumento e com a parametrização da TGMI, nortearam o desenvolvimento de processos de interação musical. Adotaram-se, ainda, outros dois componentes na metodologia de pesquisa: 1) Modelagem sonora pré-composicional em que amostras sonoras do Djembê foram gravadas, analisadas e relacionadas às possibilidades de controle por computador - procedimento realizado em tempo diferido. O processo de análise foi conduzido à aplicação sistemática dos MPCP em Estudos Recursivos para Improvisação em Tempo Real; 2) Oficinas de criação em que foram relacionados ciclos musicais aplicados ao Djembê e manipulados pela improvisação via programação em Pure Data (PD), em tempo real. Ao final, concluiu-se que o conceito de Processo Gradual de Reich, relacionado aos instrumentos de percussão, foi ampliado com a TGMI desenvolvida durante a pesquisa. O processamento computacional vinculado a recursividade permitiram a manipulação de nuances sonoras encontradas nas oficinas, que produziram novos modelos timbrístico texturais no contexto da performance musical mediada por processos tecnológicos / Abstract: This Thesis presents a research on creative processes focusing composition and improvisation with percussion instruments and technology. It is a study on an application of Music Gradual Processes and recursive structures to musical improvisation. More specifically, it studies works composed for percussion based on the notion of Gradual Process, a concept created by Reich (1968), and extract from them Models for Creative Processes in Percussion (MPCP). The detailed study of these models brought up the possibility of articulating the nuances, details, variations on gradual processes applied to percussion. Further, we apply these models in compositional studies for the African percussion instrument - Djembe. The recursive models enabled to organize, control and expand the variation sound structures through the development of a methodology for a Taxonomy of Interpretive Musical Gestures (TGMI) of the Djembe. We analyzed the spectrogram to measure characteristic frequencies and durations of resonances produced by the Djembe. Such quantitative measures, which are related to the physical and geometrical characteristics of this instrument, enabled musical interaction in real time. In addition to this quantitative analysis, research methodology was based on two other components: 1) Workshops where the Djembe sound samples were recorded, analyzed and related to control via digital technology - procedure performed off-line; 2) Workshops in which they were created music cycles applied to African percussion instruments and manipulated through improvisation, used to generate melodic textural profiles programmatically in Pure Data (PD), a procedure performed in real time. Then the analysis was conducted to a systematic development of recursive MPCP Studies for Improvisation in real time. The Thesis conclusion point out to: Reich's Gradual Process concept, related exclusively with percussion instruments, has been expanded with the TGMI and computer processing enabled creation of new models for timbre and textural improvisation and for studying musical performance mediated by digital technology / Doutorado / Processos Criativos / Doutor em Música

Don’t eat the yellow snow—Urine in art: events of interpretationUrine seams to evoke feelings. Through four different lenses, this bachelor’s thesisexamines urine in four different works of art. The works of art are Three Grazes bySally Mann, Manneken Pis by Hieronymus Duquesnoy the younger, Fideicommissumby Ann-Sofie Sidén and Bad Bad Boy by Tommi Toija, all of which in some waycontains urine as part of their motif. The four perspectives are The body as abject, Thebody as observed, The body as communication and The body as phenomenon. Thethesis reaches the conclusion that urine must be regarded as part of a syntagm and thissyntagm is interpreted in the light of a culturally conditioned resonance, part of amake-believe culture that can and, as it were, also interpret water as urine. To interpretwater as urine depends on where the water is pouring from in an overall body syntagm.Furthermore, depending on what gender the body is interpreted as (male or female) theurine will carry different value connotations. Interpreting art is thus reverberating aMake-Believe regime as a recursive process. A Make-believe regime in itself containsa phenomenological intention.

Numbers are an important part of the cultural knowledge in the modern world. Its use is fundamental in the conception and development of modern science. There are different sets of numbers called numerical systems. The most frequently used numerical system is the set of natural numbers that is composed of positive integers. Natural numbers have several forms to express the cardinality; the most frequently used is the base-10 number system, it represents the number using base quantities and powers of ten. For example, the current calendar year could be expressed as 2018 ; it’s notation describes the additive and multiplicative composition of base quantities and powers of ten (i.e., 2*103 + 0*102 + 1*101 + 8*100). Also, we can use the notation 11111100010 (i.e., 1*210 + 1*29 + 1*28 + 1*27 + 1*26 + 1*25 + 0*24 + 0*23 + 0*22 + 1*21 + 0*20) to express the same calendar year in base-2. Base number systems express cardinal values using addition and multiplication (two operations defined in natural numbers). However, even if the base-10 system looks close to the human experience; it is an abstract form that requires an external representation to communicate cardinal values. An example of these external representations are cardinal numbers, for example, the number 2018 is represented in English using the words two thousand eighteen, but in Spanish, the cardinal number dos mil dieciocho is used. Cardinal numbers are a particular case in childhood development because it is the first exposure that children have to the natural numbers. Then the properties of the cardinal numbers could be an essential part of children's number comprehension. But one question arises in this frame: What are the children's capacities that permit the children to understand cardinal numbers? One possibility that is proposed in the field of number cognition is that children’s comprehension of recursion in language triggers the acquisition of natural numbers. For some authors, recursion is an operation that is shared between natural numbers (specifically, cardinal numbers) and language (Barner, 2017; Cheung et al., 2017; Yang, 2016). In this study, we explore the relationship between recursion in language and cardinal numbers. To do so, we study the comprehension of recursive genitives and the production of cardinal numbers in English- speaking and Mandarin-speaking children. The results suggest an association in Mandarin-speaking children, but not in English-speaking children. While these empirical results are inconclusive, I provide a theoretical analysis that gives some insights into how the structure of cardinal numbers could be defined using the concept of recursion.