230 research outputs found
Pure-radiation gravitational fields with a simple twist and a Killing vector
Pure-radiation solutions are found, exploiting the analogy with the Euler-
Darboux equation for aligned colliding plane waves and the Euler-Tricomi
equation in hydrodynamics of two-dimensional flow. They do not depend on one of
the spacelike coordinates and comprise the Hauser solution as a special
subcase.Comment: revtex, 9 page
Conformal Ricci collineations of static spherically symmetric spacetimes
Conformal Ricci collineations of static spherically symmetric spacetimes are
studied. The general form of the vector fields generating conformal Ricci
collineations is found when the Ricci tensor is non-degenerate, in which case
the number of independent conformal Ricci collineations is \emph{fifteen}; the
maximum number for 4-dimensional manifolds. In the degenerate case it is found
that the static spherically symmetric spacetimes always have an infinite number
of conformal Ricci collineations. Some examples are provided which admit
non-trivial conformal Ricci collineations, and perfect fluid source of the
matter
Expanding, axisymmetric pure-radiation gravitational fields with a simple twist
New expanding, axisymmetric pure-radiation solutions are found, exploiting
the analogy with the Euler-Darboux equation for aligned colliding plane waves.Comment: revtex, 5 page
A computational study of stimulus driven epileptic seizure abatement
This is the final version of the article. Available from Public Library of Science via the DOI in this record.Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.This work was supported by the EPSRC (EP/K026992/1), the BBSRC, the DTC for Systems Biology (University of Manchester), and the Nanyang Technological University Singapore. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
PB15. Neurophysiological biomarker for the clinical development of tuberous sclerosis [Abstract]
Aim
To investigate the neuronal networks in children with tuberous sclerosis complex (TS) undergoing treatment with Everolimus.
Methods
Sleep and wake electroencephalography (EEG) before and one year after the start of the treatment with Everolimus were investigated in 13 patients with TS. To investigate functional and effective connectivity within the network generating the delta and theta activity in the background sleep and wake EEG, the methods of dynamic imaging of coherent sources (DICS) and renormalized partial directed coherence (RPDC) were applied.
Results
Sources before the treatment. Independent of location of the tubera and severity of epilepsy, delta activity in the background EEG pattern in patients with TS was associated with the sources in the medial prefrontal cortex, the supplementary motor area and the putamen during sleep. Theta waves during sleep were associated with sources in the prefrontal cortex, sensory cortex, hippocampus and the thalamus. The sources of delta frequency during wakefulness were identified at the posterior parietal cortex, the parahippocampal gyrus and the Broca area. Sources at theta frequency were found at the sensorymotor cortex, the prefrontal cortex, the primary visual cortex and the thalamus at awake state.
Sources after the treatment. The sources one year after the start of the therapy, for both delta and delta frequencies were located in the same areas as before, however with a significantly weaker strength of coherence.
The RPDC analysis at baseline showed strong bidirectional connections between described sources. The RPDC analyses after the one year of treatment showed significantly weaker unidirectional connections within the described network.
At the follow up patients were grouped in two groups; group 1: five patients with >50% reduction of seizures and spike wave index, group 2: eight patients with <50% reduction of seizures and spike wave index. Interestingly, at follow up patients from the group 1 had decreased values in absolute power of the sources, coherence values and strength of connections. Whereas, patients from the group 2 had increased values in all above mentioned parameters.
Conclusion
The current study described the neuronal network in children with severe epilepsies due to TS. Regardless of the locations of the tubera the DICS analyses showed a complex network of cortical and subcortical sources with strong bidirectional connections. The described network was significantly weaker after one year under the treatment with Everolimus and appears to be characteristic for the children with TS and severe epilepsy
Does the Isotropy of the CMB Imply a Homogeneous Universe? Some Generalised EGS Theorems
We demonstrate that the high isotropy of the Cosmic Microwave Background
(CMB), combined with the Copernican principle, is not sufficient to prove
homogeneity of the universe -- in contrast to previous results on this subject.
The crucial additional factor not included in earlier work is the acceleration
of the fundamental observers. We find the complete class of irrotational
perfect fluid spacetimes admitting an exactly isotropic radiation field for
every fundamental observer and show that are FLRW if and only if the
acceleration is zero. While inhomogeneous in general, these spacetimes all
possess three-dimensional symmetry groups, from which it follows that they also
admit a thermodynamic interpretation. In addition to perfect fluids models we
also consider multi-component fluids containing non-interacting radiation, dust
and a quintessential scalar field or cosmological constant in which the
radiation is isotropic for the geodesic (dust) observers. It is shown that the
non-acceleration of the fundamental observers forces these spacetimes to be
FLRW. While it is plausible that fundamental observers (galaxies) in the real
universe follow geodesics, it is strictly necessary to determine this from
local observations for the cosmological principle to be more than an
assumption. We discuss how observations may be used to test this.Comment: replaced with final version. Added discusion and ref
Slowly Rotating Homogeneous Stars and the Heun Equation
The scheme developed by Hartle for describing slowly rotating bodies in 1967
was applied to the simple model of constant density by Chandrasekhar and Miller
in 1974. The pivotal equation one has to solve turns out to be one of Heun's
equations. After a brief discussion of this equation and the chances of finding
a closed form solution, a quickly converging series solution of it is
presented. A comparison with numerical solutions of the full Einstein equations
allows one to truncate the series at an order appropriate to the slow rotation
approximation. The truncated solution is then used to provide explicit
expressions for the metric.Comment: 16 pages, uses document class iopart, v2: minor correction
A simple theorem to generate exact black hole solutions
Under certain conditions imposed on the energy-momentum tensor, a theorem
that characterizes a two-parameter family of static and spherically symmetric
solutions to Einstein's field equations (black holes), is proved. A discussion
on the asymptotics, regularity, and the energy conditions is provided. Examples
that include the best known exact solutions within these symmetries are
considered. A trivial extension of the theorem includes the cosmological
constant {\it ab-initio}, providing then a three-parameter family of solutions.Comment: 14 pages; RevTex; no figures; typos corrected; references adde
A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle
The validity of the Weak Equivalence Principle relative to a local inertial
frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e
type interpretation. Given the previously established first Post-Newtonian
concordance of dynamics with General Relativity, the principle is to this order
compatible with GRT. The gravitationally modified Lorentz transformations, on
which the observations in physical coordinates depend, are shown to provide a
physical interpretation of \emph{parallel transport}. A development of
``geodesic'' deviation in terms of the present model is given as well.Comment: v1: 9 pages, 2 figures, v2: version to appear in International
Journal of Theoretical Physic
Bondi-Sachs metrics and Photon Rockets
We study the Bondi-Sachs rockets with nonzero cosmological constant. We
observe that the acceleration of the systems arises naturally in the asymptotic
symmetries of (anti-) de Sitter spacetimes. Assuming the validity of the
concepts of energy and mass previously introduced in asymptotically flat
spacetimes, we find that the emission of pure radiation energy balances the
loss of the Bondi mass in certain special families of the Bondi-Sachs rockets,
so in these there is no gravitational radiation.Comment: 12 pages, to appear in General Relativity and Gravitatio
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