Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Generalized stochastic Schroedinger equations for state vector collapse

A number of authors have proposed stochastic versions of the Schr\"odinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two directions for generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations, there is an infinity of possible stochastic Schr\"odinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schr\"odinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to $\delta^3(\vec 0)$, arising from the local double commutator in the drift term.Comment: 24 pages Plain TeX. Minor changes, some new references. To appear in Journal of Physics

A Markovian Model for the Valuation of Human Assets Acquired by an Organizational Purchase

A corporation acquires the assets and liabilities of a securities brokerage firm for a price in excess of net book value. A Markov analysis is used in conjunction with human resource accounting to value a pool of account executives employed by the brokerage firm. The tax implications of imputing a portion of the purchase price premium to the pool of human assets (as opposed to goodwill) are discussed

Affective evolutionary music composition with MetaCompose

This paper describes the MetaCompose music generator, a compositional, extensible framework for affective music composition. In this context ‘affective’ refers to the music generator’s ability to express emotional information. The main purpose of MetaCompose is to create music in real-time that can express different mood-states, which we achieve through a unique combination of a graph traversal-based chord sequence generator, a search-based melody generator, a pattern-based accompaniment generator, and a theory for mood expression. Melody generation uses a novel evolutionary technique combining FI-2POP with multi-objective optimization. This allows us to explore a Pareto front of diverse solutions that are creatively equivalent under the terms of a multi-criteria objective function. Two quantitative user studies were performed to evaluate the system: one focusing on the music generation technique, and the other that explores valence expression, via the introduction of dissonances. The results of these studies demonstrate (i) that each part of the generation system improves the perceived quality of the music produced, and (ii) how valence expression via dissonance produces the perceived affective state. This system, which can reliably generate affect-expressive music, can subsequently be integrated in any kind of interactive application (e.g., games) to create an adaptive and dynamic soundtrack

Does case misclassification threaten the validity of studies investigating the relationship between neck manipulation and vertebral artery dissection stroke? No

Background: The purported relationship between cervical manipulative therapy (CMT) and stroke related to vertebral artery dissection (VAD) has been debated for several decades. A large number of publications, from case reports to case–control studies, have investigated this relationship. A recent article suggested that case misclassification in the case–control studies on this topic resulted in biased odds ratios in those studies. Discussion: Given its rarity, the best epidemiologic research design for investigating the relationship between CMT and VAD is the case–control study. The addition of a case-crossover aspect further strengthens the scientific rigor of such studies by reducing bias. The most recent studies investigating the relationship between CMT and VAD indicate that the relationship is not causal. In fact, a comparable relationship between vertebral artery-related stroke and visits to a primary care physician has been observed. The statistical association between visits to chiropractors and VAD can best be explained as resulting from a patient with early manifestation of VAD (neck pain with or without headache) seeking the services of a chiropractor for relief of this pain. Sometime after the visit the patient experiences VAD-related stroke that would have occurred regardless of the care received. This explanation has been challenged by a recent article putting forth the argument that case misclassification is likely to have biased the odds ratios of the case–control studies that have investigated the association between CMT and vertebral artery related stroke. The challenge particularly focused on one of the case–control studies, which had concluded that the association between CMT and vertebral artery related stroke was not causal. It was suggested by the authors of the recent article that misclassification led to an underestimation of risk. We argue that the information presented in that article does not support the authors’ claim for a variety of reasons, including the fact that the assumptions upon which their analysis is based lack substantiation and the fact that any possible misclassification would not have changed the conclusion of the study in question. Conclusion: Current evidence does not support the notion that misclassification threatens the validity of recent case–control studies investigating the relationship between CMT and VAD. Hence, the recent re-analysis cannot refute the conclusion from previous studies that CMT is not a cause of VAD.https://doi.org/10.1186/s12998-016-0124-

The importance of selecting the correct site to apply spinal manipulation when treating spinal pain:Myth or reality? A systematic review

The concept that spinal manipulation therapy (SMT) outcomes are optimized when the treatment is aimed at a clinically relevant joint is commonly assumed and central to teaching and clinical use (candidate sites). This systematic review investigated whether clinical effects are superior when this is the case compared to SMT applied elsewhere (non-candidate sites). Eligible study designs were randomized controlled trials that investigated the effect of spinal manipulation applied to candidate versus non-candidate sites for spinal pain. We obtained data from four different databases. Risk of bias was assessed using an adjusted Cochrane risk of bias tool, adding four items for study quality. We extracted between-group differences for any reported outcome or, when not reported, calculated effect sizes from the within-group changes. We compared outcomes for SMT applied at a ‘relevant’ site to SMT applied elsewhere. We prioritized methodologically robust studies when interpreting results. Ten studies, all of acceptable quality, were included that reported 33 between-group differences—five compared treatments within the same spinal region and five at different spinal regions. None of the nine studies with low or moderate risk of bias reported statistically significant between-group differences for any outcome. The tenth study reported a small effect on pain (1.2/10, 95%CI − 1.9 to − 0.5) but had a high risk of bias. None of the nine articles of low or moderate risk of bias and acceptable quality reported that “clinically-relevant” SMT has a superior outcome on any outcome compared to “not clinically-relevant” SMT. This finding contrasts with ideas held in educational programs and clinical practice that emphasize the importance of joint-specific application of SMT.</p