Principles of Pitch Organization in Béla Bartók's 'Duke Bluebeard's Castle'

The topic of my doctoral thesis is to demonstrate the usefulness of incorporating tonal and modal elements into a pitch-web square analysis of Béla Bartók's (1881-1945) opera, 'A kékszakállú herceg vára' ('Duke Bluebeard's Castle'). My specific goal is to demonstrate that different musical materials, which exist as foreground melodies or long-term key progressions, are unified by the unordered pitch set {0,1,4}, which becomes prominent in different sections of Bartók's opera. In Bluebeard's Castle, the set {0,1,4} is also found as a subset of several tetrachords: {0,1,4,7}, {0,1,4,8}, and {0,3,4,7}. My claim is that {0,1,4} serves to link music materials between themes, between sections, and also between scenes. This study develops an analytical method, drawn from various theoretical perspectives, for conceiving superposed diatonic spaces within a hybrid pitch-space comprised of diatonic and chromatic features. The integrity of diatonic melodic lines is retained, which allows for a non-reductive understanding of diatonic superposition, without appealing to pitch centers or specifying complete diatonic collections. Through combining various theoretical insights of the Hungarian scholar Ernő Lendvai, and the American theorists Elliott Antokoletz, Paul Wilson and Allen Forte, as well as the composer himself, this study gives a detailed analysis of the opera's pitch material in a way that combines, complements, and expands upon the studies of those scholars. The analyzed pitch sets are represented on Aarre Joutsenvirta's note-web square, which adds a new aspect to the field of Bartók analysis. Keywords: Bartók, Duke Bluebeard's Castle (Op. 11), Ernő Lendvai, axis system, Elliott Antokoletz, intervallic cycles, intervallic cells, Allen Forte, set theory, interval classes, interval vectors, Aarre Joutsenvirta, pitch-web square, pitch-web analysis.

Maximum Loss Calculation using Scenario Analysis, Heavy Tails and Implied Volatility Patterns

The objective of this paper is to improve option risk monitoring by examining the information content of implied volatility and by introducing the calculation of a single-sum expected risk exposure similar to the Value-at-Risk. The figure is calculated in two steps. First, there is a need to estimate the value of a portfolio of options for a number of different market scenarios, while the second step is to summarize the information content of the estimated scenarios into a single-sum risk measure. This involves the use of probability theory and return distributions, which confronts the user with the problems of non-normality in the return distribution of the underlying asset. Here the hyperbolic distribution is used to describe one alternative for dealing with heavy tails. Results indicate that the information content of implied volatility is useful when predicting future large returns in the underlying asset. Further, the hyperbolic distribution provides a good fit to historical returns enabling a more accurate definition of statistical intervals and extreme events.

On the principles of Japanese forest policy since 1950.

XVIII IUFRO World Congress, Ljubljana 1986.

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.