Pairwise Well-Formed Modes and Transformations

One of the most significant attitudinal shifts in the history of music occurred in the Renaissance, when an emerging triadic consciousness moved musicians towards a new scalar formation that placed major thirds on a par with perfect fifths. In this paper we revisit the confrontation between the two idealized scalar and modal conceptions, that of the ancient and medieval world and that of the early modern world, associated especially with Zarlino. We do this at an abstract level, in the language of algebraic combinatorics on words. In scale theory the juxtaposition is between well-formed and pairwise well-formed scales and modes, expressed in terms of Christoffel words or standard words and their conjugates, and the special Sturmian morphisms that generate them. Pairwise well-formed scales are encoded by words over a three-letter alphabet, and in our generalization we introduce special positive automorphisms of $F3$, the free group over three letters.Comment: 12 pages, 3 figures, paper presented at the MCM2017 at UNAM in Mexico City on June 27, 2017, keywords: pairwise well-formed scales and modes, well-formed scales and modes, well-formed words, Christoffel words, standard words, central words, algebraic combinatorics on words, special Sturmian morphism

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

The Kinematics of HH 34 from HST Images with a Nine-year Time Baseline

We study archival HST [S II] 6716+30 and Hα images of the HH 34 outflow, taken in 1998.71 and in 2007.83. The ~9 yr time baseline and the high angular resolution of these observations allow us to carry out a detailed proper-motion study. We determine the proper motions of the substructure of the HH 34S bow shock (from the [S II] and Hα frames) and of the aligned knots within ~30'' from the outflow source (only from the [S II] frames). We find that the present-day motions of the knots along the HH 34 jet are approximately ballistic, and that these motions directly imply the formation of a major mass concentration in ~900 yr, at a position similar to the one of the present-day HH 34S bow shock. In other words, we find that the knots along the HH 34 jet will merge to form a more massive structure, possibly resembling HH 34S

Malignancy within a tail gut cyst:a case of retrorectal carcinoid tumour

Purpose. Tailgut cysts with malignant transformation are rare entities. We discuss the diagnostic strategy and treatment of a malignancy within a tailgut cyst. Methods. In this study we report on the case of a 61-year-old man with a malignant neuroendocrine tumour arising within a tailgut cyst and an overview of the literature emphasising the histopathological characteristics and differential diagnosis. Results. Our patient presented with lower back pain, rectal pain, and increased urgency of defecation. MRI scan and CT-guided biopsy on histological analysis revealed a diagnosis of carcinoid tumour of the presacral space. The patient subsequently underwent an abdominoperineal excision of the rectum. Conclusions. This case highlights the importance of tailgut cysts as a differential diagnosis of presacral masses. It is a rare congenital lesion developing from remnants of the embryonic postanal gut and is predominantly benign in nature. Approximately half of cases remain asymptomatic; therefore, diagnosis is often delayed. Magnetic resonance imaging is the investigation of choice and an awareness of the possibility of malignant potential is critical to avoiding missed diagnosis and subsequent morbidity. Complete surgical excision allows accurate diagnosis, confirmation of oncological clearance, and prevention of mortality

Fast simulation of a quantum phase transition in an ion-trap realisable unitary map

We demonstrate a method of exploring the quantum critical point of the Ising universality class using unitary maps that have recently been demonstrated in ion trap quantum gates. We reverse the idea with which Feynman conceived quantum computing, and ask whether a realisable simulation corresponds to a physical system. We proceed to show that a specific simulation (a unitary map) is physically equivalent to a Hamiltonian that belongs to the same universality class as the transverse Ising Hamiltonian. We present experimental signatures, and numerical simulation for these in the six-qubit case.Comment: 12 pages, 6 figure

Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference

We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2

Survey of Terrestrial Invertebrate Species from Byers Cave; Dade County, Georgia

Byers Cave is one of Georgia’s largest cave systems and is inhabited by a wide variety of unique invertebrate organisms that have not been documented or studied. From March 2008 through April 2010, baited ramp pit-fall traps and visual surveys were used to sample and document invertebrate species that live in this cave system. After three trapping periods and four visual surveys, we collected over 4,400 individuals comprising 13 orders, 29 families and 34 species. The majority of these species were troglophiles and trogloxenes; however, there were also numerous troglobitic species present