The thesis for the Master of Music degree in Composition consists of live performances of original works composed during graduate study. The student is expected to have written and performed approximately forty-five minutes of music for various media. My compositions were performed on January 27 (Autumn Fantasia) and February 20 (Five Elements) of 2006, and March 12 (Bounce!), 30 (The Little Fairy), April 3 (String Quartet No.1), August 15 (Ballads of Four Seasons) and November 19 (Three Pieces for Solo Violin) of 2007. Briefly, each work was written in different compositional approach such as the timbres, specific colors, textures, themes and rhythmic practices. Autumn Fantasia and The Little Fairy explore the transformations and developments of thematic material. Bounce! is a piece in the procedure of tempo modulations and polyrhythmic practices. The textural experiment is the "source" for String Quartet No. 1. In both Ballads of Four Seasons and Five Elements, I employed the oriental tone color (pentatonic scales) in one particular line combining with western-based (chromaticism) sonority and sounding in other parts. Finally, to accumulate every compositional skills and techniques, Three Pieces for Solo Violin is a work binding each practices altogether.

The thesis for the Master of Music degree in Composition consists of live performances of original works composed during graduate study. The student is expected to have written and performed approximately forty-five minutes of music for various media. My compositions were performed on January 27 (Autumn Fantasia) and February 20 (Five Elements) of 2006, and March 12 (Bounce!), 30 (The Little Fairy), April 3 (String Quartet No.1), August 15 (Ballads of Four Seasons) and November 19 (Three Pieces for Solo Violin) of 2007. Briefly, each work was written in different compositional approach such as the timbres, specific colors, textures, themes and rhythmic practices. Autumn Fantasia and The Little Fairy explore the transformations and developments of thematic material. Bounce! is a piece in the procedure of tempo modulations and polyrhythmic practices. The textural experiment is the "source" for String Quartet No. 1. In both Ballads of Four Seasons and Five Elements, I employed the oriental tone color (pentatonic scales) in one particular line combining with western-based (chromaticism) sonority and sounding in other parts. Finally, to accumulate every compositional skills and techniques, Three Pieces for Solo Violin is a work binding each practices altogether.

The thesis for the Master of Music degree in Composition consists of live performances of original works composed during graduate study. The student is expected to have written and performed approximately forty-five minutes of music for various media. My compositions were performed on January 27 (Autumn Fantasia) and February 20 (Five Elements) of 2006, and March 12 (Bounce!), 30 (The Little Fairy), April 3 (String Quartet No.1), August 15 (Ballads of Four Seasons) and November 19 (Three Pieces for Solo Violin) of 2007. Briefly, each work was written in different compositional approach such as the timbres, specific colors, textures, themes and rhythmic practices. Autumn Fantasia and The Little Fairy explore the transformations and developments of thematic material. Bounce! is a piece in the procedure of tempo modulations and polyrhythmic practices. The textural experiment is the "source" for String Quartet No. 1. In both Ballads of Four Seasons and Five Elements, I employed the oriental tone color (pentatonic scales) in one particular line combining with western-based (chromaticism) sonority and sounding in other parts. Finally, to accumulate every compositional skills and techniques, Three Pieces for Solo Violin is a work binding each practices altogether. / Arts, Faculty of / Music, School of / Graduate

This dissertation creates practical methods for Poincaré return mappings of individual and networked neuron models. Elliptic bursting models are found in numerous biological systems, including the external Globus Pallidus (GPe) section of the brain; the focus for studies of epileptic seizures and Parkinson's disease. However, the bifurcation structure for changes in dynamics remains incomplete. This dissertation develops computer-assisted Poincaré ́maps for mathematical and biologically relevant elliptic bursting neuron models and central pattern generators (CPGs). The first method, used for individual neurons, offers the advantage of an entire family of computationally smooth and complete mappings, which can explain all of the systems dynamical transitions. A complete bifurcation analysis was performed detailing the mechanisms for the transitions from tonic spiking to quiescence in elliptic bursters. A previously unknown, unstable torus bifurcation was found to give rise to small amplitude oscillations. The focus of the dissertation shifts from individual neuron models to small networks of neuron models, particularly 3-cell CPGs. A CPG is a small network which is able to produce specific phasic relationships between the cells. The output rhythms represent a number of biologically observable actions, i.e. walking or running gates. A 2-dimensional map is derived from the CPGs phase-lags. The cells are endogenously bursting neuron models mutually coupled with reciprocal inhibitory connections using the fast threshold synaptic paradigm. The mappings generate clear explanations for rhythmic outcomes, as well as basins of attraction for specific rhythms and possible mechanisms for switching between rhythms.

The dissertation consists of two parts: (1) the essay and (2) the composition. The essay elucidates the composer's creative process of the orchestral works, The Heidegger Collection. The Heidegger Collection has five movements. The titles of each movement are derived from the key philosophical concepts from Heidegger's most significant writing, Being and Time: (1) State-of-Mind, (2) Idle-Talk, (3) Moment-of-Vision, (4) Dread, and (5) Being-towards-the-End. The essay discusses the meanings of the five concepts, and explains how I express my reaction to Heidegger's thinking through music composition. The essay also discusses the essential musical language of The Heidegger Collection, such as interval cycles, polyrhythmic patterns, algorithmic elements, portamento effects, chaos theory, and oriental influence.