From Schritte and Wechsel to Coxeter Groups

The PLR-moves of neo-Riemannian theory, when considered as reflections on the edges of an equilateral triangle, define the Coxeter group $\widetilde S_3$. The elements are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. The left action of $\widetilde S_3$ on the Tonnetz gives rise to interesting chord sequences. We compare the system of transformations in $\widetilde S_3$ with the system of Schritte and Wechsel introduced by Hugo Riemann in 1880. Finally, we consider the point reflection group as it captures well the transition from Riemann's infinite Tonnetz to the finite Tonnetz of neo-Riemannian theory.Comment: 14 pages for the Mathematics and Computation in Music Conference in June 2019 in Madrid, the revised version extends the music theoretic discussio

Acoustical transducer calibrating system and apparatus

An acoustical transducer calibrating system includes a differential pressure actuating device having an inner chamber for applying differential pressures to the transducer, and an outer chamber for vacuum sealing. Mounted within the inner chamber is an electrostatic actuator for exciting the transducer at selected frequencies so that its sensitivity can be determined for different operating ambient pressures

Motion segmentation by consensus

We present a method for merging multiple partitions into a single partition, by minimising the ratio of pairwise agreements and contradictions between the equivalence relations corresponding to the partitions. The number of equivalence classes is determined automatically. This method is advantageous when merging segmentations obtained independently. We propose using this consensus approach to merge segmentations of features tracked on video. Each segmentation is obtained by clustering on the basis of mean velocity during a particular time interva

Stably free modules over virtually free groups

Let $F_m$ be the free group on $m$ generators and let $G$ be a finite nilpotent group of non square-free order; we show that for each $m\ge 2$ the integral group ring ${\bf Z}[G\times F_m]$ has infinitely many stably free modules of rank 1.Comment: 9 pages. The final publication is available at http://www.springerlink.com doi:10.1007/s00013-012-0432-

Standing on the Shoulders of Giants: The Cleft Palate-Craniofacial Journal (1964-1989)Electronic Archive

Current research and clinical practice in cleft palate and craniofacial disorders “stands on the shoulders of giants” who came before us. To enable thirty years of seminal research articles to become digitally available to a worldwide community of students, scholars, and clinicians, a collaboration was forged in 2004 between University of Pittsburgh’s Digital Research Library (DRL) and ACPA, (with the agreement of Allen Press), to create an electronic archive of the first thirty years of the Cleft Palate Craniofacial Journal . The work was performed pro bono, by all parties

On the Red-Green-Blue Model

We experimentally study the red-green-blue model, which is a sytem of loops obtained by superimposing three dimer coverings on offset hexagonal lattices. We find that when the boundary conditions are ``flat'', the red-green-blue loops are closely related to SLE_4 and double-dimer loops, which are the loops formed by superimposing two dimer coverings of the cartesian lattice. But we also find that the red-green-blue loops are more tightly nested than the double-dimer loops. We also investigate the 2D minimum spanning tree, and find that it is not conformally invariant.Comment: 4 pages, 7 figure

The Impact of Securities Laws on Developing Companies: Would the Wright Brothers Have Gotten Off the Ground?

Suppose the Wright brothers, to pursue their dreams of manned flight, needed outside financing. Confronted with the intimidating regulatory requirements of today \u27s state and federal securities laws, would they ever have gotten off the ground? With historical illustrations, this Essay presents an entertaining look at the serious problems that would be encountered today by entrepreneurs who have ideas but need capital to develop them. It analyzes the regulatory maze and prohibitions of state and federal securities laws and concludes that, in today\u27s marketplace, the Wright brothers probably would have violated several laws to obtain essential financing for their venture