Sergei Rachmaninoff's Étude Tableau op. 39, no. 7; arranged for full band

Thesis (M.M.)--Boston University, 196

Valuing Financial Flexibility

Two facts that corporations, underwriters and investors have been forced to confront are increased capital market volatility and increased complexity in the design of securities. However, these two facts, increased volatility and increased complexity, are not unrelated. Virtually all of the complexity in securities can be viewed as the inclusion of different options in a straight debt contract. Given the fact that the value of options is driven most significantly by volatility, the advantage of including options, i.e. financial flexibility, in securities has increased with increased market volatility. This would appear to explain why corporate issuers and institutional investors have shown substantial interest in securities which improve their flexibility in volatile markets. Therefore, techniques which can consistently reflect the role of volatility in the value of options or flexibility, should be of interest to issuers, underwriters, and investors.This paper summarizes the results of some research by Jones, Masonand Rosenfeld (MR), (1984), and presents some new results, which test the ability of a CCA model based on Black and Scholes' option pricingprinciples to predict the market price of callable corporate debt, andtherefore, the price of such common debt covenants as call provisions andcall protection, In addition, some numerical CCA results are reportedwhich demonstrate the impact of changing interest rate volatility on the value of call provisions and call protection.

Improving the quality of consent to randomised controlled trials by using continuous consent and clinician training in the consent process

Objectives: To assess whether continuous consent, a process whereby information is given to research participants at different stages in a trial, plus clinician training in that process was effective when used by clinicians gaining consent to the TOBY trial. The TOBY trial is a randomised controlled trial investigating the use of whole body cooling for neonates with evidence of perinatal asphyxia. Obtaining valid informed consent for TOBY is difficult; as such, it is a good test of the effectiveness of continuous consent. Methods: Semi-structured interviews were conducted with 30 sets of parents who gave consent to TOBY and with 10 clinicians who sought it using the continuous consent process. Analysis focused on the validity of parental consent based upon the consent components of competence, information, understanding and voluntariness. Results: 19/27 (70%) couples had no significant problems with consent validity at the point of signature. Problems lay mainly with the parents’ competence and understanding. Mothers particularly had competence problems in the early stages of consent. The understanding problems were primarily to do with side effects. Problems in both areas (competence and understanding) reduced markedly, particularly for mothers, in the post signature phase when further discussion took place. Randomisation was generally understood but unpopular. Clinicians did not always give information in stages during the short period of time available before parents gave consent. However, most clinicians were able to give follow up information. Discussion: The consent validity compares favourably with similar trials examined in a comparable study (the Euricon study). Conclusion: Researchers should consider adopting elements of the continuous consent process and clinician training in RCTs, particularly where they have concerns about the quality of consent they are likely to obtain using a conventional process.</p

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and for any pair of simple Heisenberg modules. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties for the Heisenberg and lattice vertex operator algebras and a continuous orbifolding of the rank two fermion vertex operator super algebra. We compute the genus two Heisenberg vector $n$-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity for these theories.Comment: 57 Pages, 5 figures. This is an extended version of roughly one half of arXiv:0712.062

Should desperate volunteers be included in randomised controlled trials?

Randomised controlled trials (RCTs) sometimes recruit participants who are desperate to receive the experimental treatment. Some claim this practice is unethical for at least three reasons. The first is that the notion of equipoise, which is often used as a justification for running a RCT, is subjective and value-based. Desperate volunteers are clearly not in equipoise and it is their values that should take precedence. The second is that clinicians who enter patients onto trials are disavowing their therapeutic obligation to deliver the best treatment to patients; they are following trial protocols rather than delivering individualised care. Research is not treatment; its ethical justification is different. Consent is crucial. This leads to the third reason: desperate volunteers do not give a proper consent; they are, in effect, coerced. We begin our reply by advocating a notion of equipoise based on, first, expert knowledge and, second, widely shared values. Where such collective, expert equipoise exists there is a prima facie case for a RCT. Next we argue that trial entry does not involve clinicians’ disavowing their therapeutic obligation; individualised care based on whims and fancies is not in patients’ best interest. Finally, we argue that where equipoise exists it is acceptable to limit access to experimental agents. In the cases desperate volunteers are not coerced because their desperation does not translate into a right to receive what they desire. </p

Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas for the genus two partition function for free bosonic theories and lattice vertex operator algebras $V_L$. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. We also compute the genus two Heisenberg vector $n$-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity. We compare our results with those obtained in the companion paper, when a pair of tori are sewn together, and show that the partition functions are not compatible in the neighborhood of a two-tori degeneration point. The \emph{normalized} partition functions of a lattice theory $V_L$ \emph{are} compatible, each being identified with the genus two theta function of $L$.Comment: 51 pages, 3 figure

Vertex Operators and Modular Forms

The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite group and its irreducible characters; the algebraic structure determines a set of numerical invariants, and arithmetic properties of the invariants provides feedback in the form of restrictions on the algebraic structure. One of the main points of these Notes is to explain how this works, and to give some reasonably interesting examples.Comment: 118 pages. These are notes based on a series of lectures at the Graduate Workshop " A Window into Zeta and Modular Physics " at MSRI, Berkeley, June 2008 http://www.msri.org/calendar/sgw/WorkshopInfo/449/show_sgw. Submitted to Mathematical Sciences Research Institute Publication

Slow‐Wave Structures Utilizing Superconducting Thin‐Film Transmission Lines

Slow‐wave propagation of electromagnetic waves in transmission lines formed of thin‐film superconductors has been studied theoretically and experimentally. Previous theoretical analyses have been extended to include nonlocal theories. Strong dependence of phase velocity is found on film thickness and interfilm spacing when these become less than a few penetration depths. Velocity is also modified by coherence length, mean free path, nature of reflection of electrons at the film surfaces, and by temperature and magnetic field. Experimental measurements were made to verify the dependence on thickness, spacing, and temperature by means of a resonance technique. Agreement with theory was excellent in the case of temperature. Data taken for varying thickness and spacing verified the general trend of theoretical predictions. They indicate a nonlocal behavior with some specular reflection, but scatter of the data taken for different films prevents precise comparison of theory and experiment. Estimates of bulk penetration depths were made for indium, λ_In = 648±130 Å. For tantalum a rough estimate could be made of λTa = 580 Å. Data were consistent with the estimate of coherence length for indium of ξ_0 ≈ 3000 Å. Velocity was found to be independent of frequency in the range 50–500 MHz, while losses increased as the square. Pulse measurements indicated that delays of several microseconds and storage of several thousand pulses on a single line are feasible

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction