36 research outputs found
Measuring miniature eye movements by means of a SQUID magnetometer
A new technique to measure small eye movements is reported. The precise recording of human eye movements is necessary for research on visual fatigue induced by visual display units.1 So far all methods used have disadvantages: especially those which are sensitive or are rather painful.2,3 Our method is based on a transformation of mechanical vibrations into magnetic flux variations. In order to do this a small magnet is embedded in a close-fitting soft contact lens. The magnetic flux variations caused by eyeball movements during fixation are measured by means of a SQUID magnetometer. The recordings show the typical fixation pattern of a human eye. This pattern is composed of three kinds of movements: saccades, drift and microtremor. The last-mentioned type of movements are displacements in the order of 2 μm. It is possible to distinguish between movements which are perpendicular to each other
Twistor geometry of a pair of second order ODEs
We discuss the twistor correspondence between path geometries in three
dimensions with vanishing Wilczynski invariants and anti-self-dual conformal
structures of signature . We show how to reconstruct a system of ODEs
with vanishing invariants for a given conformal structure, highlighting the
Ricci-flat case in particular. Using this framework, we give a new derivation
of the Wilczynski invariants for a system of ODEs whose solution space is
endowed with a conformal structure. We explain how to reconstruct the conformal
structure directly from the integral curves, and present new examples of
systems of ODEs with point symmetry algebra of dimension four and greater which
give rise to anti--self--dual structures with conformal symmetry algebra of the
same dimension. Some of these examples are analogues of plane wave
space--times in General Relativity. Finally we discuss a variational principle
for twistor curves arising from the Finsler structures with scalar flag
curvature.Comment: Final version to appear in the Communications in Mathematical
Physics. The procedure of recovering a system of torsion-fee ODEs from the
heavenly equation has been clarified. The proof of Prop 7.1 has been
expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda
Sources of pain related responses to posterior tibial nerve stimulation
Brain responses to posterior tibial nerve stimulation were examined in patients who suffered from a proven neuropathic (traumatic) pain. The aim of this study was to learn if these responses could be used for the assessment of persistent pain and its relief in chronic pain patients. Experiments were carried out in five patients, where usual strategies had failed and spinal cord stimulation was applied. It was found that the measured evoked responses, when these patients were in pain, showed additional waves at latencies at around 110 ms and 150 ms after stimulation of the posterior tibial nerve. The magnetic field and electrical potential distributions at these latencies were dipolar and the responses at 110 ms and 150 ms could be ascribed to two equivalent current dipoles situated in two distinct areas in the brain. In patients, who underwent spinal cord stimulation, the additional wave disappeared once the patient was in a pain free condition. For this group of patients the additional waves appear to be related to the perception of pain and this may offer an objective method to assess this kind of pain and study the effects of spinal cord stimulation. Although not mentioned here, similar results were found for median nerve stimulation
A Comparison of the LVDP and {\Lambda}CDM Cosmological Models
We compare the cosmological kinematics obtained via our law of linearly
varying deceleration parameter (LVDP) with the kinematics obtained in the
{\Lambda}CDM model. We show that the LVDP model is almost indistinguishable
from the {\Lambda}CDM model up to the near future of our universe as far as the
current observations are concerned, though their predictions differ
tremendously into the far future.Comment: 6 pages, 5 figures, 1 table, matches the version to be published in
International Journal of Theoretical Physic
Topography and source analysis of brain activity associated with selective spatial atten¬tion and memory search
Topography and source analysis of brain activity associated with selective spatial atten¬tion and memory search
The Kinematic Algebra From the Self-Dual Sector
We identify a diffeomorphism Lie algebra in the self-dual sector of
Yang-Mills theory, and show that it determines the kinematic numerators of
tree-level MHV amplitudes in the full theory. These amplitudes can be computed
off-shell from Feynman diagrams with only cubic vertices, which are dressed
with the structure constants of both the Yang-Mills colour algebra and the
diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour
algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We
further study perturbative gravity, both in the self-dual and in the MHV
sectors, finding that the kinematic numerators of the theory are the BCJ
squares of the Yang-Mills numerators.Comment: 29 pages, 5 figures. v2: references added, published versio
Spinor classification of the Weyl tensor in five dimensions
We investigate the spinor classification of the Weyl tensor in five
dimensions due to De Smet. We show that a previously overlooked reality
condition reduces the number of possible types in the classification. We
classify all vacuum solutions belonging to the most special algebraic type. The
connection between this spinor and the tensor classification due to Coley,
Milson, Pravda and Pravdov\'a is investigated and the relation between most of
the types in each of the classifications is given. We show that the black ring
is algebraically general in the spinor classification.Comment: 40 page
Report on workshop A1: Exact solutions and their interpretation
I report on the communications and posters presented on exact solutions and
their interpretation at the GRG18 Conference, Sydney.Comment: 9 pages, no figures. Many typos corrected. Report submitted to the
Proceedings of GR18. To appear in CQ
The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
We obtain the necessary and sufficient conditions for a two-component
(2+1)-dimensional system of hydrodynamic type to possess infinitely many
hydrodynamic reductions. These conditions are in involution, implying that the
systems in question are locally parametrized by 15 arbitrary constants. It is
proved that all such systems possess three conservation laws of hydrodynamic
type and, therefore, are symmetrizable in Godunov's sense. Moreover, all such
systems are proved to possess a scalar pseudopotential which plays the role of
the `dispersionless Lax pair'. We demonstrate that the class of two-component
systems possessing a scalar pseudopotential is in fact identical with the class
of systems possessing infinitely many hydrodynamic reductions, thus
establishing the equivalence of the two possible definitions of the
integrability. Explicit linearly degenerate examples are constructed.Comment: 15 page