Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

Into the Bends of Time and Musical Forces in Jazz: Group Interaction and Double-time in “My Foolish Heart” as performed by the Bill Evans Trio with Scott LaFaro and Paul Motian.

Into the Bends of Time is a 40-minute work in seven movements for a large chamber orchestra with electronics, utilizing real-time computer-assisted processing of music performed by live musicians. The piece explores various combinations of interactive relationships between players and electronics, ranging from relatively basic processing effects to musical gestures achieved through stages of computer analysis, in which resulting sounds are crafted according to parameters of the incoming musical material. Additionally, some elements of interaction are multi-dimensional, in that they rely on the participation of two or more performers fulfilling distinct roles in the interactive process with the computer in order to generate musical material. Through processes of controlled randomness, several electronic effects induce elements of chance into their realization so that no two performances of this work are exactly alike. The piece gets its name from the notion that real-time computer-assisted processing, in which sound pressure waves are transduced into electrical energy, converted to digital data, artfully modified, converted back into electrical energy and transduced into sound waves, represents a “bending” of time.

The Bill Evans Trio featuring bassist Scott LaFaro and drummer Paul Motian is widely regarded as one of the most important and influential piano trios in the history of jazz, lauded for its unparalleled level of group interaction. Most analyses of Bill Evans’ recordings, however, focus on his playing alone and fail to take group interaction into account. This paper examines one performance in particular, of Victor Young’s “My Foolish Heart” as recorded in a live performance by the Bill Evans Trio in 1961. In Part One, I discuss Steve Larson’s theory of musical forces (expanded by Robert S. Hatten) and its applicability to jazz performance. I examine other recordings of ballads by this same trio in order to draw observations about normative ballad performance practice. I discuss meter and phrase structure and show how the relationship between the two is fixed in a formal structure of repeated choruses. I then develop a model of perpetual motion based on the musical forces inherent in this structure. In Part Two, I offer a full transcription and close analysis of “My Foolish Heart,” showing how elements of group interaction work with and against the musical forces inherent in the model of perpetual motion to achieve an unconventional, dynamic use of double-time. I explore the concept of a unified agential persona and discuss its role in imparting the song’s inherent rhetorical tension to the instrumental musical discourse.

British Double Agents and Operation Fortitude: A New Perspective

On June 6th, 1944, Allied forces stormed the beaches of Normandy as a part of Operation Overlord, the Allied invasion of France. While they experienced pockets of stiff resistance, Allied troops sustained far fewer casualties than they had expected. The reason for this was due to Operation Fortitude, a deception mission that intended to fool Hitler about the time and location of the Allied invasion mission. The use of double agents by British Intelligence services was essential for the effective execution of Fortitude. The story of the double agents goes beyond their success during Fortitude. Double agents were initially recruited as German agents, but key agents immediately turned themselves in to British authorities upon reaching the nation. These agents decided to become involved with British Intelligence due to broader circumstances that were happening in Europe. The emergence of Fascist regimes disrupted the political landscape of Europe and led to widespread condemnation from political and social spheres. Their development as double agents became crucial to their effectiveness during Operation Fortitude. Their successful infiltration of German Intelligence allowed them to convince Hitler and German High Command that the main Allied invasion force would come at the Pas de Calais instead of Normandy. The result was that the Allies met an unprepared German defense force on D-Day and were able to advance past the beaches. The work of the double agents during Fortitude saved thousands of Allied lives and was vital to the success of Operation Overlord.

Genetic Analysis of Mitotic Recombination in Saccharomyces cerevisiae

Mitotic genome instability can occur during the repair of double-strand breaks (DSBs) in DNA, which arise from endogenous and exogenous sources. Studying the mechanisms of DNA repair in the budding yeast, Saccharomyces cerevisiae has shown that Homologous Recombination (HR) is a vital repair mechanism for DSBs. HR can result in a crossover event, in which the broken molecule reciprocally exchanges information with a homologous repair template. The current model of double-strand break repair (DSBR) also allows for a tract of information to non-reciprocally transfer from the template molecule to the broken molecule. These “gene conversion” events can vary in size and can occur in conjunction with a crossover event or in isolation. The frequency and size of gene conversions in isolation and gene conversions associated with crossing over has been a source of debate due to the variation in systems used to detect gene conversions and the context in which the gene conversions are measured.

In Chapter 2, I use an unbiased system that measures the frequency and size of gene conversion events, as well as the association of gene conversion events with crossing over between homologs in diploid yeast. We show mitotic gene conversions occur at a rate of 1.3x10-6 per cell division, are either large (median 54.0kb) or small (median 6.4kb), and are associated with crossing over 43% of the time.

DSBs can arise from endogenous cellular processes such as replication and transcription. Two important RNA/DNA hybrids are involved in replication and transcription: R-loops, which form when an RNA transcript base pairs with the DNA template and displaces the non-template DNA strand, and ribonucleotides embedded into DNA (rNMPs), which arise when replicative polymerase errors insert ribonucleotide instead of deoxyribonucleotide triphosphates. RNaseH1 (encoded by RNH1) and RNaseH2 (whose catalytic subunit is encoded by RNH201) both recognize and degrade the RNA in within R-loops while RNaseH2 alone recognizes, nicks, and initiates removal of rNMPs embedded into DNA. Due to their redundant abilities to act on RNA:DNA hybrids, aberrant removal of rNMPs from DNA has been thought to lead to genome instability in an rnh201Δ background.

In Chapter 3, I characterize (1) non-selective genome-wide homologous recombination events and (2) crossing over on chromosome IV in mutants defective in RNaseH1, RNaseH2, or RNaseH1 and RNaseH2. Using a mutant DNA polymerase that incorporates 4-fold fewer rNMPs than wild type, I demonstrate that the primary recombinogenic lesion in the RNaseH2-defective genome is not rNMPs, but rather R-loops. This work suggests different in-vivo roles for RNaseH1 and RNaseH2 in resolving R-loops in yeast and is consistent with R-loops, not rNMPs, being the the likely source of pathology in Aicardi-Goutières Syndrome patients defective in RNaseH2.