Diagonal Peg Solitaire

We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the "central game", which begins and ends at the center. In some cases we can prove analytically that our solutions are the shortest possible, in other cases we apply A* or bidirectional search heuristics.Comment: 20 pages, 11 figure

Solving Triangular Peg Solitaire

We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).Comment: 23 pages, 14 figures; published version including comments by John Beasle

Fringe field simulations of a non-scaling FFAG accelerator

Fixed-field Alternating Gradient (FFAG) accelerators offer the potential of high-quality, moderate energy ion beams at low cost. Modeling of these structures is challenging with conventional beam tracking codes because of the large radial excursions of the beam and the significance of fringe field effects. Numerous tune resonances are crossed during the acceleration, which would lead to beam instability and loss in a storage ring. In a non-scaling FFAG, the hope is that these resonances can be crossed sufficiently rapidly to prevent beam loss. Simulations are required to see if this is indeed the case. Here we simulate a non-scaling FFAG which accelerates protons from 31 to 250 MeV. We assume only that the bending magnets have mid-plane symmetry, with specified vertical bending field in the mid-plane (y=0). The magnetic field can be obtained everywhere using a power series expansion, and we develop mathematical tools for calculating this expansion to arbitrary order when the longitudinal field profile is given by an Enge function. We compare the use of a conventional hard-edge fringe with a more accurate, soft-edge fringe field model. The tune 1/3 resonance is the strongest, and crossing it in the hard-edge fringe model results in a 21% loss of the beam. Using the soft-edge fringe model the beam loss is less than 6%.Comment: 12 pages; 12 figure

J.S. Bell's Concept of Local Causality

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure

Fc receptor modulation in mononuclear phagocytes maintained on immobilized immune complexes occurs by diffusion of the receptor molecule

We describe a method for synchronously assembling antigen-antibody complexes underneath macrophages adherent to an antigen-coated surface. We have used this method to study the mechanism of Fc receptor (FcR) disappearance that occurs when resident and thioglycollate-elicited mouse macrophages are cultured on immune complex-coated surfaces. Erythrocytes opsonized with IgG (E(IgG) and a monoclonal antibody (2.4G2 IgG) directed against the trypsin-resistant FcR (FcRII) were used as indicators of the presence and distribution of FcRII molecules on the macrophage plasma membrane. Inhibitors of aerobic (NaCN) and anerobic (2-deoxyglucose, NaF) glycolysis and pinocytosis, of protein biosynthesis (cycloheximide), and of cytoskeletal function (cytochalasin B and D, colchicine, podophyllotoxin, taxol) did not reduce the rate or extent of FcRII modulation. Moreover, treatment of the macrophages with 0.1-0.5% formaldehyde did not reduce the extent of FcRII modulation as measured by the disappearance of E(IgG) binding sites. FcRII modulation was markedly slowed when the temperature was decreased to 2-4 degrees C. These results prove that FcRII modulation is governed by diffusion of the receptor in the plasma membrane. From the speed of FcRII disappearance from the macrophage's upper surface we calculate that the receptor has a diffusion coefficient at 37 degrees C of 2.5 X 10(-9) cm2/s. This finding indicates that FcRII, in its unligated form, is not linked to the macrophage's cytoskeleton, and that the receptor is capable of accommodating spatially to any distribution of ligands on a particle's surface