The Organization and Role During Locomotion of the Proximal Musculature of the Cricket Foreleg. II. Electromyographic Activity During Stepping Patterns

A description is made of the patterns of electrical activity in the proximal muscles of the cricket foreleg during restrained locomotion and seeking movements, while the animal is held by the mesonotum, allowing the legs complete freedom of movement. 1. The initiation of the swing phase corresponds to the onset of the abductor muscle activity (Fig. 1). Its duration is matched by that of abduction-promotion and does not depend on the step frequency. Leg position is more variable at the end of the stance than at the end of the swing. 2. The promotor and abductor muscle activities are linked (Fig. 2). At least three units can be distinguished in each and the duration of their bursts is independent of the period (Fig. 3). 3. In the double depressors of the trochanter, muscles 77-lb,c (Fig. 4), one unit per muscle was identified, bursting during the swing phase. The duration of the burst is independent of the period. Some isolated potentials occasionally occur during the stance phase. 4. The overall activity in the lateral and medial remotors is coupled to the period; three main patterns can be described, depending upon the muscle bundle and the velocity of movement (Fig. 5). 5. In the coxal depressors two patterns of activity are described which depend on velocity of stepping (Fig. 6): (i) during regular and fast stepping (at frequencies greater than 2–5 Hz), the activity is coupled to that of the double depressors; (ii) during slow or irregular stepping, the activity is biphasic: an initial burst is followed after a latency correlated to the period by a second one in the second half of the stance phase. Conversely, the latency between the end of the second burst and the onset of the following abductor burst does not depend on the period. In most cases, a fast neurone (large amplitude, short phasic activation) is recruited when a slow one reaches high rates of discharge

Vassiliev knot invariants and Chern-Simons perturbation theory to all orders

At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover these are finite type invariants whose order coincides with the order in the perturbative expansion. Together they combine to give a universal Vassiliev invariant.Comment: Revised version, includes a detailed proof of formula (5.26) for $\log Z$, and several minor changes. 31 pages, 19 figures, epsf.sty, Late

The Organization and Role During Locomotion of the Proximal Musculature of the Cricket Foreleg : I. Anatomy and Innervation

The structure of the proximal segments of the cricket (Gryllus bimaculatus) foreleg, together with the associated musculature and its innervation are described. The morphology of 50 motor neurones involved in the control of this musculature has been revealed using backfilling techniques with cobalt, horseradish peroxidase and Lucifer Yellow. The ‘ball and socket’ pleurocoxal joint is moved by three sets of anatomical antagonists (promotor-remotor, abductor-adductor, anterior-posterior rotator muscles) inserted on each side of the three axes of rotation. The axial coxotrochanteral joint is moved by the intrinsic levator and the depressor muscles; these depressors are composed of an intrinsic (coxotrochanteral) and a ‘double’ (pleurotrochanteral) subgroup. The double depressors, and all the muscles inserting on the trochantin (promotors) or the anterior coxal rim (adductor, abductors, anterior rotators) are supplied by at least eighteen neurones, whose axons run in nerve 3. The muscles that insert on the posterior coxal rim (remotors, posterior rotators) are innervated by at least twelve similar neurones whose axons run in nerve 4. The intrinsic coxal muscles are supplied by branches of nerve 5 (ten motor neurones to the levators, two to the depressors). Three presumably common inhibitors, and one Dorsal Unpaired Median (DUM) neurone have also been found

From stochastic quantization to bulk quantization: Schwinger-Dyson equations and S-matrix

In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. This is advantageous, in particular for gauge theories, because it allows a different type of gauge fixing that avoids the Gribov problem. Traditionally, in this approach, the fictitious 5th time is the analog of computer time in a Monte Carlo simulation of 4-dimensional Euclidean fields. A Euclidean probability distribution which depends on the 5th time relaxes to an equilibrium distribution. However a broader framework, which we call ``bulk quantization", is required for extension to fermions, and for the increased power afforded by the higher symmetry of the 5-dimensional action that is topological when expressed in terms of auxiliary fields. Within the broader framework, we give a direct proof by means of Schwinger-Dyson equations that a time-slice of the 5-dimensional theory is equivalent to the usual 4-dimensional theory. The proof does not rely on the conjecture that the relevant stochastic process relaxes to an equilibrium distribution. Rather, it depends on the higher symmetry of the 5-dimensional action which includes a BRST-type topological invariance, and invariance under translation and inversion in the 5-th time. We express the physical S-matrix directly in terms of the truncated 5-dimensional correlation functions, for which ``going off the mass-shell'' means going from the 3 physical degrees of freedom to 5 independent variables. We derive the Landau-Cutokosky rules of the 5-dimensional theory which include the physical unitarity relation.Comment: 26 pages, Tex, 1 figure includes 2 graph

Diablo Canyon power plant site ecological study Quarterly Report no. 17: July 1 - September 30, 1977

During the quarter a total of 38 random 30-m2 and 152 random 1/4-m2 subtidal stations were surveyed. Red abalone, Haliotis rufescens, densities remained very low. There was a continued decline in densities of giant red sea urchins, Strongylocentrotus franciscanus, in Diablo Cove as well as the North Control area. The annual shore census of bull kelp, Nereocystis luetkeana, revealed the lowest number of plants in the surface canopy in Diablo Cove since 1973. The subtidal station data supported this observation. Sea otter, Enhydra lutris, observations were continued. A small group of otters continued to raft in the Cove east of Lion Rock. Some of these otters probably forage as far south as South Cove. The survey of 11 random intertidal stations completed our Upwelling sampling effort. (16pp.