"Double Rainbow," "Appalachiana," and "'The Invisible Mass': Exploring Compositional Technique in Alfred Schnittke's Second Symphony"

This dissertation consists of three distinct components: (1) “Double Rainbow,” a notated composition for an acoustic ensemble of 10 instruments, ca. 36 minutes. (2) “Appalachiana”, a fixed-media composition for electro-acoustic music and video, ca. 30 minutes, and (3) “'The Invisible Mass': Exploring Compositional Technique in Alfred Schnittke’s Second Symphony”, an analytical article.

(1) Double Rainbow is a ca. 36 minute composition in four movements scored for 10 instruments: flute, Bb clarinet (doubling on bass clarinet), tenor saxophone (doubling on alto saxophone), french horn, percussion (glockenspiel, vibraphone, wood block, 3 toms, snare drum, bass drum, suspended cymbal), piano, violin, viola, cello, and double bass. Each of the four movements of the piece explore their own distinct character and set of compositional goals. The piece is presented as a musical score and as a recording, which was extensively treated in post-production.

(2) Appalachiana, is a ca. 30 minute fixed-media composition for music and video. The musical component was created as a vehicle to showcase several approaches to electro-acoustic music composition –fft re-synthesis for time manipulation effects, the use of a custom-built software instrument which implements generative approaches to creating rhythm and pitch patterns, using a recording of rain to create rhythmic triggers for software instruments, and recording additional components with acoustic instruments. The video component transforms footage of natural landscapes filmed at several locations in North Carolina, Virginia, and West Virginia into a surreal narrative using a variety of color, lighting, distortion, and time-manipulation video effects.

(3) “‘The Invisible Mass:’ Exploring Compositional Technique in Alfred Schnittke’s Second Symphony” is an analytical article that focuses on Alfred Schnittke’s compositional technique as evidenced in the construction of his Second Symphony and discussed by the composer in a number of previously untranslated articles and interviews. Though this symphony is pivotal in the composer’s oeuvre, there are currently no scholarly articles that offer in-depth analyses of the piece. The article combines analyses of the harmony, form, and orchestration in the Second Symphony with relevant quotations from the composer, some from published and translated sources and others newly translated by the author from research at the Russian State Library in St. Petersburg. These offer a perspective on how Schnittke’s compositional technique combines systematic geometric design with keen musical intuition.

Algorithms for Geometric Matching, Clustering, and Covering

With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from many different sources such as vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which together contain useful high-level information about people's movement patterns.

The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing a matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters.

The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. More specifically, a subset of vertices in the road network are selected to place charging stations so that every shortest path contains enough charging stations and can be traveled by an EV without draining the battery. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this

shortest-path cover problem.