Properties of the Optokinetic Motor Fibres in the Rock Lobster: Build-Up, Flipback, Afterdischarge and Memory, Shown by Their Firing Patterns

The properties of sets of motor fibres responding to both clockwise and anticlockwise rotation have been studied in the oculomotor nerve of the rock lobster. There are probably three, but perhaps four, units in each set. None of these fibres has statocyst input, but there is weak input onto the tonic fibres from the antennal joints such that the eye turns in the direction toward which the antenna points. Many preparations show bilateral visual input onto all fibres but the degree of coupling between the eyes is very variable, and at times can be nearly totally absent. Depending on the speed of rotation the fibres show a gradual build-up in frequency, during rotation in the preferred direction, interrupted by flipbacks. During the fast stage of the resulting nystagmic movements all agonistic fibres can be completely inhibited and all antagonistic ones can be activated, usually for a period of about 0.5 sec. Fibre activity is demonstrated which appears to underlie an ‘optokinetic memory’ of contrasting target position in the visual field. It consists of (a) very prolonged after-discharges for a stationary striped pattern (b) resumption of discharges at an appropriate frequency after dark periods up to 2 min, and (c) adjustment of such frequencies to changes in stripe position during the dark period. The fibres show habituation to repeated stripe movement but the response can be dishabituated by passive rotation of the animal. The largest visual responses were obtained to intermediate speeds of stripe rotation (about 2°/sec)

Input Sources and Properties of Position-Sensitive Oculomotor Fibres in the Rock Lobster, Panulirus Interruptus (Randall)

Sets of head-up, head-down, eye-up and eye-down motor fibres were studied in the oculomotor nerve of the rock lobster. An eye-withdrawal fibre was also investigated. Apart from the statocyst input, light distribution on the eyes has the strongest influence on the position-sensitive fibres. Weaker optokinetic input from moving targets is also present. Strongly habituating input is obtained from the antennal joints. This input causes orientation of the eye toward the direction in which the antenna points. The same antennule movement in the vertical plane can result in either excitation or inhibition of the head-down fibre, suggesting the presence of two opposing inputs, presumably from the statocysts and basal joint receptors of the antennule. The inputs on to the position-sensitive fibres which indicate body position are such as to stabilize the eye position in space during body movement. The optokinetic and antennal joint inputs are probably involved in tracking and antennal pointing reactions. The eye-withdrawal fibre is stimulated by touch of the head and around the eye, but is inhibited by the excited state

Conformal ``thin sandwich'' data for the initial-value problem of general relativity

The initial-value problem is posed by giving a conformal three-metric on each of two nearby spacelike hypersurfaces, their proper-time separation up to a multiplier to be determined, and the mean (extrinsic) curvature of one slice. The resulting equations have the {\it same} elliptic form as does the one-hypersurface formulation. The metrical roots of this form are revealed by a conformal ``thin sandwich'' viewpoint coupled with the transformation properties of the lapse function.Comment: 7 pages, RevTe

Extrinsic Curvature and the Einstein Constraints

The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors which involves a weight function. In stationary spacetimes, there is a natural choice of the weight function such that the transverse traceless part of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex

Freire re-viewed

The work of Paulo Freire is associated with themes of oppression and liberation, and his critical pedagogy is visionary in its attempts to bring about social transformation. Freire has created a theory of education that embeds these issues within social relations that center around both ideological and material domination. In this review essay, Sue Jackson explores three books: Freire’s final work Pedagogy of Indignation; Cesar Augusto Rossatto’s Engaging Paulo Freire’s Pedagogy of Possibility, which attempts to engage Freire’s pedagogy of possibility; and C.A. Bowers and Frederique Apffel-Marglin’s edited collection Re-thinking Freire, which asks readers to reconsider Freire’s work in light of globalization and environmental crises. Jackson questions the extent to which Freire’s pedagogical approaches are useful to educators as well as to “the oppressed,” and whether challenges to re-think Freire can lead to new kinds of critical pedagogies

Waveless Approximation Theories of Gravity

The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability -- are associated with the presence of gravitational waves. We have developed a number of ``waveless approximation theories'' (WAT) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory

Robust evolution system for Numerical Relativity

The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust 3D calculations. The potential of the resulting numerical code is demonstrated by using the Schwarzschild black hole as a test-bed. Its evolution can be followed up to times greater than one hundred black hole masses.Comment: 11 pages, 4 figures; figure correcte

No-go theorem for bimetric gravity with positive and negative mass

We argue that the most conservative geometric extension of Einstein gravity describing both positive and negative mass sources and observers is bimetric gravity and contains two copies of standard model matter which interact only gravitationally. Matter fields related to one of the metrics then appear dark from the point of view of an observer defined by the other metric, and so may provide a potential explanation for the dark universe. In this framework we consider the most general form of linearized field equations compatible with physically and mathematically well-motivated assumptions. Using gauge-invariant linear perturbation theory, we prove a no-go theorem ruling out all bimetric gravity theories that, in the Newtonian limit, lead to precisely opposite forces on positive and negative test masses.Comment: 19 pages, no figures, journal versio

Excision boundary conditions for black hole initial data

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference, minor content changes including additional post-Newtonian comparison. Version accepted by PR