The Topology of Tile Invariants

In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a set of regions tileable by $T$ is isomorphic to a quotient of the second homology group of a 2-complex built from $T$. In this topological setting we derive some well-known tile invariants, one of which we apply to the solution of a tiling question involving modified rectangles.Comment: 25 pages, 24 figure

Lack of Transparency in the Premarket Approval Process for Aquadvantage Salmon

After a lengthy premarket approval process, the Food and Drug Administration (FDA) has just deemed AquAdvantage Salmon, a fast-growing, genetically engineered salmon, safe for human consumption. AquAdvantage Salmon is the first genetically engineered animal designed for human consumption to go to market in the United States. Because there have been no significant changes to the statutory or regulatory framework governing agricultural biotechnology since it was established in the 1980s, the FDA reviews applications of genetically engineered animals under the New Animal Drug Application (NADA) provisions of the Federal Food, Drug, and Cosmetic Act (FDCA). The FDA’s treatment of genetically engineered food as a new animal drug has been criticized due to potential environmental and human health risks, and because of a lack of transparency throughout the regulatory process. After providing an overview of the premarket approval process, this Issue Brief argues that even under the NADA provisions, the FDA’s premarket approval risk assessment should be more transparent. In particular, the justification for trade secret status of relevant biotechnology is undermined, if not extinguished, by the need for public consideration of the biotechnology’s safety and effectiveness after a certain time in the approval process. Furthermore, the comment period prior to advisory committee meetings should be lengthened to allow for greater scientific input on safety and effectiveness, and an independent body should be created to communicate with the public about food safety

Generalised Moonshine and Abelian Orbifold Constructions

We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the basic concepts in MCFT and Abelian orbifold constructions of MCFTs and summarise some of the relevant physics lore surrounding such constructions including aspects of the modular group, the fusion algebra and the notion of a self-dual MCFT. The FLM Moonshine Module, $V^\natural$, is historically the first example of such a construction being a $Z_2$ orbifolding of the Leech lattice MCFT, $V^\Lambda$. We review the usefulness of these ideas in understanding Monstrous Moonshine, the genus zero property for Thompson series which we have shown is equivalent to the property that the only meromorphic $Z_n$ orbifoldings of $V^\natural$ are $V^\Lambda$ and $V^\natural$ itself (assuming that $V^\natural$ is uniquely determined by its characteristic function $J(\tau)$. We show that these constraints on the possible $Z_n$ orbifoldings of $V^\natural$ are also sufficient to demonstrate the genus zero property for Generalised Moonshine functions in the simplest non-trivial prime cases by considering $Z_p\times Z_p$ orbifoldings of $V^\natural$. Thus Monstrous Moonshine implies Generalised Moonshine in these cases.Comment: Talk presented at the AMS meeting on Moonshine, the Monster and related topics, Mt. Holyoke, June 1994, 16 pp, Plain TeX with AMS Font

Controlled Surface Collection at the Spinach Patch Site, Franklin County, Arkansas

This paper discusses the technique of controlled surface collection as an interpretative aid at the Spinach Patch site, 3FR1, a prehistoric village site in Ozark Reservoir. The research involved was made possible through a cooperative agreement with the National Park Service, Southeast Region

Reciprocating linear motor

A reciprocating linear motor is formed with a pair of ring-shaped permanent magnets having opposite radial polarizations, held axially apart by a nonmagnetic yoke, which serves as an axially displaceable armature assembly. A pair of annularly wound coils having axial lengths which differ from the axial lengths of the permanent magnets are serially coupled together in mutual opposition and positioned with an outer cylindrical core in axial symmetry about the armature assembly. One embodiment includes a second pair of annularly wound coils serially coupled together in mutual opposition and an inner cylindrical core positioned in axial symmetry inside the armature radially opposite to the first pair of coils. Application of a potential difference across a serial connection of the two pairs of coils creates a current flow perpendicular to the magnetic field created by the armature magnets, thereby causing limited linear displacement of the magnets relative to the coils