Triangle-roundedness in matroids

A matroid $N$ is said to be triangle-rounded in a class of matroids $\mathcal{M}$ if each $3$-connected matroid $M\in \mathcal{M}$ with a triangle $T$ and an $N$-minor has an $N$-minor with $T$ as triangle. Reid gave a result useful to identify such matroids as stated next: suppose that $M$ is a binary $3$-connected matroid with a $3$-connected minor $N$, $T$ is a triangle of $M$ and $e\in T\cap E(N)$; then $M$ has a $3$-connected minor $M'$ with an $N$-minor such that $T$ is a triangle of $M'$ and $|E(M')|\le |E(N)|+2$. We strengthen this result by dropping the condition that such element $e$ exists and proving that there is a $3$-connected minor $M'$ of $M$ with an $N$-minor $N'$ such that $T$ is a triangle of $M'$ and $E(M')-E(N')\subseteq T$. This result is extended to the non-binary case and, as an application, we prove that $M(K_5)$ is triangle-rounded in the class of the regular matroids

Biomechanical Modelling of Musical Performance: A Case Study of the Guitar

Merged with duplicate record 10026.1/2517 on 07.20.2017 by CS (TIS)Computer-generated musical performances are often criticised for being unable to match the expressivity found in performances by humans. Much research has been conducted in the past two decades in order to create computer technology able to perform a given piece music as expressively as humans, largely without success. Two approaches have been often adopted to research into modelling expressive music performance on computers. The first focuses on sound; that is, on modelling patterns of deviations between a recorded human performance and the music score. The second focuses on modelling the cognitive processes involved in a musical performance. Both approaches are valid and can complement each other. In this thesis we propose a third complementary approach, focusing on the guitar, which concerns the physical manipulation of the instrument by the performer: a biomechanical approach. The essence of this thesis is a study on capturing, analyzing and modelling information about motor and biomechanical processes of guitar performance. The focus is on speed, precision, and force of a guitarist's left-hand. The overarching questions behind our study are: 1) Do unintentional actions originating from motor and biomechanical functions during musical performance contribute a material "human feel" to the performance? 2) Would it be possible determine and quantify such unintentional actions? 3) Would it be possible to model and embed such information in a computer system? The contributionst o knowledgep ursued in this thesis include: a) An unprecedented study of guitar mechanics, ergonomics, and playability; b) A detailed study of how the human body performs actions when playing the guitar; c) A methodologyt o formally record quantifiable data about such actionsin performance; d) An approach to model such information, and e) A demonstration of how the above knowledge can be embeddedin a system for music performance

Ubiquitous Computing meets Ubiquitous Music

Ubiquitous Computing meets Ubiquitous Musi

Formulação Com Dupla Reciprocidade Hipersingular do Método dos Elementos de Contorno Aplicada aos Probblemas Difusivos-advectivos

Apresentam-se neste trabalho duas diferentes formulações do Método dos Elementos de Contorno, geradas para o modelamento de problemas bidimensionais de transferência de calor com escoamento, nos quais os fenômenos de difusão e convecção forçada estão associados. A primeira delas é fundamentada no procedimento conhecido como Dupla Reciprocidade Singular (FDRS), criado originalmente para solução de problemas de autovalor. Esta técnica foi aprimorada por diversos autores para muitas outras categorias de problemas, entre os quais o caso abordado no presente trabalho, usando uma interpolação com funções de base radial para o tratamento das derivadas espaciais dos termos convectivos. A segunda formulação é a Dupla Reciprocidade Hipersingular (FDRH), que apresenta uma estrutura similar à Dupla Reciprocidade Singular, mas é obtida a partir da equação integral inversa diferenciada com relação à direção normal ao contorno, de modo que a ordem das derivadas dos núcleos se altera. Assim os núcleos das integrais passam a ter ingularidades de ordem superior (1/r e 1/r²) em relação às existentes na FDRS (ln r e 1/r). Realizam-se, então, simulações com exemplos que possuem solução analítica, onde é analisada a influência de importantes parâmetros, tais como o refinamento da malha e a velocidade do escoamento. Restrições físicas, limitações numéricas, precisão e outras características importantes relacionadas a cada formulação são discutidas com detalhe