Mass Anomalous Dimension at Large N

In this work we attempt to determine the mass anomalous dimension of the SU(N) gauge theory with two Dirac fermions in the adjoint representation, in the limit of large N. The method uses the mode number of the Dirac operator, as done in arXiv:1204.4432 for the SU(2) theory in a large volume. Taking advantage of large-N volume reduction we do this on a 2^4 lattice, but we should still get infinite-volume physics in the large-N limit. We find promising initial results, both volume reduction and the mode number method seem to work, but the effective volume of our lattices is probably still too small to reliably determine the mass anomalous dimension at the IRFP, and so results at larger N are required.Comment: 7 pages, 7 figures, Proceedings of The 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australi

Transient spatiotemporal chaos collapses into periodic and steady states in an electrically-coupled neural ring network

Chaotic behavior in a spatially extended system is often referred to as spatiotemporal chaos. The trajectories of a system as it evolves through state space are described by irregular spatial and temporal patterns. In mathematical biology, spatiotemporal chaos has been demonstrated in chemotaxis models (Painter & Hillen, 2011) predator-prey models (Sherratt, J. & Fowler, A., 1995) and the Hogdkin-Huxley neural model (Wang, Lu, & Chen, 2006). Transient chaos is a special case of chaotic dynamics in which the system dynamics collapses without external perturbation. Rather, collapse is an intrinsic property of the system. Here, we diff usively couple many spiking neurons into a ring network and fi nd that the network dynamics can collapse on to two diff erent species of attractor: the limit cycle and the steady-state solution

Head and pelvic movement asymmetry during lungeing in horses with symmetrical movement on the straight

REASONS FOR PERFORMING STUDY: Lungeing is commonly used as part of standard lameness examinations in horses. Knowledge of how lungeing influences motion symmetry in sound horses is needed. OBJECTIVES: The aim of this study was to objectively evaluate the symmetry of vertical head and pelvic motion during lungeing in a large number of horses with symmetric motion during straight line evaluation. STUDY DESIGN: Cross‐sectional prospective study. METHODS: A pool of 201 riding horses, all functioning well and considered sound by their owners, were evaluated in trot on a straight line and during lungeing to the left and right. From this pool, horses with symmetric vertical head and pelvic movement during the straight line trot (n = 94) were retained for analysis. Vertical head and pelvic movements were measured with body mounted uniaxial accelerometers. Differences between vertical maximum and minimum head (HDmax, HDmin) and pelvic (PDmax, PDmin) heights between left and right forelimb and hindlimb stances were compared between straight line trot and lungeing in either direction. RESULTS: Vertical head and pelvic movements during lungeing were more asymmetric than during trot on a straight line. Common asymmetric patterns seen in the head were more upward movement during push‐off of the outside forelimb and less downward movement during impact of the inside limb. Common asymmetric patterns seen in the pelvis were less upward movement during push‐off of the outside hindlimb and less downward movement of the pelvis during impact of the inside hindlimb. Asymmetric patterns in one lunge direction were frequently not the same as in the opposite direction. CONCLUSIONS: Lungeing induces systematic asymmetries in vertical head and pelvic motion patterns in horses that may not be the same in both directions. These asymmetries may mask or mimic fore‐ or hindlimb lameness