Mathematical Programming Models for Influence Maximization on Social Networks

In this dissertation, we apply mathematical programming techniques (i.e., integer programming and polyhedral combinatorics) to develop exact approaches for influence maximization on social networks. We study four combinatorial optimization problems that deal with maximizing influence at minimum cost over a social network. To our knowl- edge, all previous work to date involving influence maximization problems has focused on heuristics and approximation. We start with the following viral marketing problem that has attracted a significant amount of interest from the computer science literature. Given a social network, find a target set of customers to seed with a product. Then, a cascade will be caused by these initial adopters and other people start to adopt this product due to the influence they re- ceive from earlier adopters. The idea is to find the minimum cost that results in the entire network adopting the product. We first study a problem called the Weighted Target Set Selection (WTSS) Prob- lem. In the WTSS problem, the diffusion can take place over as many time periods as needed and a free product is given out to the individuals in the target set. Restricting the number of time periods that the diffusion takes place over to be one, we obtain a problem called the Positive Influence Dominating Set (PIDS) problem. Next, incorporating partial incentives, we consider a problem called the Least Cost Influence Problem (LCIP). The fourth problem studied is the One Time Period Least Cost Influence Problem (1TPLCIP) which is identical to the LCIP except that we restrict the number of time periods that the diffusion takes place over to be one. We apply a common research paradigm to each of these four problems. First, we work on special graphs: trees and cycles. Based on the insights we obtain from special graphs, we develop efficient methods for general graphs. On trees, first, we propose a polynomial time algorithm. More importantly, we present a tight and compact extended formulation. We also project the extended formulation onto the space of the natural vari- ables that gives the polytope on trees. Next, building upon the result for trees---we derive the polytope on cycles for the WTSS problem; as well as a polynomial time algorithm on cycles. This leads to our contribution on general graphs. For the WTSS problem and the LCIP, using the observation that the influence propagation network must be a directed acyclic graph (DAG), the strong formulation for trees can be embedded into a formulation on general graphs. We use this to design and implement a branch-and-cut approach for the WTSS problem and the LCIP. In our computational study, we are able to obtain high quality solutions for random graph instances with up to 10,000 nodes and 20,000 edges (40,000 arcs) within a reasonable amount of time.

Investigation into the Influence of Build Parameters on Failure of 3D Printed Parts

Additive manufacturing, including fused deposition modeling (FDM), is transforming the built world and engineering education. Deep understanding of parts created through FDM technology has lagged behind its adoption in home, work, and academic environments. Properties of parts created from bulk materials through traditional manufacturing are understood well enough to accurately predict their behavior through analytical models. Unfortunately, Additive Manufacturing (AM) process parameters create anisotropy on a scale that fundamentally affects the part properties. Understanding AM process parameters (implemented by program algorithms called slicers) is necessary to predict part behavior. Investigating algorithms controlling print parameters (slicers) revealed stark differences between the generation of part layers. In this work, tensile testing experiments, including a full factorial design, determined that three key factors, width, thickness, infill density, and their interactions, significantly affect the tensile properties of 3D printed test samples.

THE PERFORMER’S INFLUENCE ON FRANCO-BELGIAN COMPOSITIONS FROM 1870 TO 1930

The turn of the 20th century marked an ascendancy of the Franco-Belgian school of composers. French composers were inspired by the great German composers of the Romantic era, and they created their own defined national style that emerged toward the end of the 19th century. The Franco-Belgian composers’ special emphasis on tone, timbre and color encouraged a more individual, personally interpretative approach. These devices underscore the importance and influence a performer can have on the outcome of a piece. I researched the relationship between composers and violinists at a time when the Franco-Belgian style developed and flourished. The Franco-Belgian school of violin playing emerged from the Paris and Brussels conservatories as well as the symbiotic relationship between the performers and composers. Three recitals in collaboration with pianist David Ballena, which comprise this dissertation project, were performed at the University of Maryland. Each recital featured music for violin and piano from 1870 through 1930. The repertoire was chosen to reflect a performer’s influence on a composer. I examined specific composer/performer relationships that helped shape the birth of a newly defined “French” style of playing. My research focused on the stylistic interactions composers, such as César Franck, his disciple Guillaume Lekeu had with the leading prominent Belgian violinist Eugène Ysaye and between Maurice Ravel and the Hungarian violinist Jelly d’Aranyi. I also looked into the personal relationship between friends who inspired each other: Gabriel Fauré and Paul Viardot, Edouard Lalo and Pablo de Sarasate, Claude Debussy and Arthur Hartmann, and the young Lili Boulanger and Yvonne Astruc. Furthermore, I looked into the unfulfilled love between Maurice Ravel and Hélène Jourdan-Morhange, as well as the marriage of Olivier Messiaen with Claire Delbos, both relationships resulting in masterpieces for violin that have remained a part of the standard violin repertoire. My research led me to understand what type of violin playing each composer had in mind while composing, all of which led me to understand the importance a performer has in preserving national styles. The recitals were recorded on compact discs and archived within the Digital Repository at the University of Maryland (DRUM).

IMPROMPTU: FROM PUBLISHER'S IMPULSE TO AN ESTABLISHED SMALL­ SCALE GENRE IN PIANO LITERATURE

The word 'impromptu' began to appear in music literature in the early 19th century, specifically as title for a relatively short composition written for solo piano. The first impromptus appear to have been named so by the publishers. However, the composers themselves soon embraced the title to indicate, for the most part, fairly short character pieces. Impromptus do not follow any specific structural pattern, although many are cast in ternary form. The formal design ranges from strict compound ternary in the early impromptus to through-composed and variation forms. The peak of impromptu's popularity undoubtedly came during the middle and late19th century. However, they are still being composed today, albeit much less frequently. Although there have been many variants of impromptus in relation to formal design and harmonic language over the years, the essence of impromptu remains the same: it is still a short character piece with a general feeling of spontaneity. Overall, impromptus may be categorized into several different groups: some appear as part of a larger cycle, such as Dvorak's G minor Impromptu from his Piano Pieces, B. 110; many others use an element of an additional genre that enhances the character ofthe impromptu, such as Liszt's Valse-Impromptu and Antonio Bibalo's Tango Impromptu; yet another group consists of works based on opera themes, such as Liszt's Impromptu Brillant sur des themes de Rossini et Spontini and Czerny's Impromptus et variations sur Oberon, Op. 134. My recording project includes well-known impromptus, such as Schubert's Op. 142 and the four by Chopin, as well as lesser known works that have not been performed or recorded often. There are four impromptus that have been recorded here for the first time, including those written by Leopold Godowsky, Antonio Bibalo, Altin Volaj, and Nikolay Mazhara. I personally requested the two last named composers to contribute impromptus to this project. My selection represents works by twenty composers and reflects the different types of impromptus that have been encountered through almost three hundred years of the genre's existence, from approximately 1817 (VoriSek) to 2008 (Volaj and Mazhara).

Post-1945 Danish Piano Trio Literature: A Recording Dissertation

This recording dissertation surveys post-1945 literature written for piano trio (violin, violoncello and piano) by ten Danish composers. The literature was first considered for inclusion by searching a database provided by the Danish Music Information Center (www.mic.dk). Scores were rented from the publisher Edition Wilhelm Hansen AS, or purchased from the publisher Samfundet til Udgivelse af Dansk Musik. An additional score published by Viking Musikforlag was used as well. The music was then studied and evaluated for selection. During the selection process, the following criteria were considered: 1) quality of the compositions; 2) recognition of the composers at the national or international level; 3) whether the compositions had been previously recorded; and 4) variety of compositional styles. The selected works are written by Niels Viggo Bentzon, Vagn Holmboe, Anders Koppel, Herman D. Koppel, Bent Lorentzen, Anders Nordentoft, Per Norgard, Michael Nyvang, Karl Aage Rasmussen, and Poul Rovsing Olsen. The selected compositions were practiced, rehearsed, and performed under direct supervision of the composers and other expert musicians. In order to better understand the compositional style of each composer, relevant books, articles, and recordings were researched and studied. This recording dissertation is supported by a written document. A subjective preference for program balance was exercised to determine the order of recorded works. The written document is divided into chapters defined by composer, following the order of the recorded document, which include the composers' biographies and notes referring to the recorded compositions. The recording took place at the Manzius Gaarden, Birkerod, Denmark during three sessions: July 31-August 2, 2002, March 2 and 3, 2003, and June 2-4, 2003. The music for this dissertation was recorded by the members of the Jalina Trio; Line Fredens, violin, Janne Fredens, cello and Natsuki Fukasawa, piano. Aksel Trige, a well-respected recording engineer, was engaged for the recording and editing. Additionally, a Hamburg Steinway concert grand piano was rented and a Joseph Guarnerius filius Andreas Cremona violin (1706) was provided by the Augustinus Fonden, Denmark. The cellist used her own instrument, Vuillaume of Paris (c. 1850). The expense of this recording was partially paid by generous grants from the Augustinus Fonden, the Solist Foreningen af 1921, and the Dansk Musikerforbunds Kollective Rettighedsmidler. The compositions selected for this recording dissertation are assumed to be previously unrecorded, with the exception of Poul Rovsing Olsen's Trio II.