40 research outputs found
Short term synaptic depression model—Analytical solution and analysis
In this article we present analytical solutions of the single and pair pulse time evolution of a plastic neocortical synapse described by the TM-model. We show that this model is equivalent to the receptor-desensitization model with three kinetic states. For the TM-model we derive the analytical form of a measure of paired pulse depression. We analyze the sensitivity of the synaptic depression phenomenon on model parameters and derive the relative importance of each of the parameters. The closed form of the measure of synaptic depression allows fitting the model to experimental data. The fitted parameters are used to make predictions about the asymptotic properties of the postsynaptic currents. We show that for synapses with the ratio of inactivation and recovery rates of the same order, the synaptic depression does not preclude the rate-coding of information: e.g. in the pyramid–pyramid connections of adult rat neocortex, rate-coding is possible for higher frequencies
The need for dark matter in galaxies
Cooperstock and Tieu have proposed a model to account for galactic rotation
curves without invoking dark matter. I argue that no model of this type can
work
Coarse-graining of inhomogeneous dust flow in General Relativity via isometric embeddings
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional Euclidean space and deriving the time evolution equations for them. In contrast to the popular Buchert's scheme it allows to coarse-grain tensorial quantities in a coordinate-independent way. The framework can be used to estimate backreaction in inhomogeneous cosmological models
Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric
A new definition of quasi--local angular momentum of non--axisymmetric
marginally outer trapped surfaces is proposed. It is based on conformal
decomposition of the two--dimensional metric and the action of the group of
conformal symmetries. The definition is completely general and agrees with the
standard one in axi--symmetric surfaces.Comment: Final version to appear in Classical and Quantum Gravity. One
reference adde
Fundamental properties and applications of quasi-local black hole horizons
The traditional description of black holes in terms of event horizons is
inadequate for many physical applications, especially when studying black holes
in non-stationary spacetimes. In these cases, it is often more useful to use
the quasi-local notions of trapped and marginally trapped surfaces, which lead
naturally to the framework of trapping, isolated, and dynamical horizons. This
framework allows us to analyze diverse facets of black holes in a unified
manner and to significantly generalize several results in black hole physics.
It also leads to a number of applications in mathematical general relativity,
numerical relativity, astrophysics, and quantum gravity. In this review, I will
discuss the basic ideas and recent developments in this framework, and
summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th
International Conference on General Relativity and Gravitation, 8-13 July
2007, Sydney, Australi
Conformal Einstein equations and Cartan conformal connection
Necessary and sufficient conditions for a space-time to be conformal to an
Einstein space-time are interpreted in terms of curvature restrictions for the
corresponding Cartan conformal connection
Accelerating the Universe with Gravitational Waves
Inflation generically produces primordial gravitational waves with a red
spectral tilt. In this paper we calculate the backreaction produced by these
gravitational waves on the expansion of the universe. We find that in radiation
domination the backreaction acts as a relativistic fluid, while in matter
domination a small dark energy emerges with an equation of state w=-8/9.Comment: 18 pages, 4 figures. Replaced with version published by JCAP - some
discussion and references added concerning second-order gravitational waves,
typeset in JHEP styl
Polyakov soldering and second order frames : the role of the Cartan connection
The so-called "soldering" procedure performed by A.M. Polyakov in [1] for a
SL(2,R)-gauge theory is geometrically explained in terms of a Cartan connection
on second order frames of the projective space RP^1. The relationship between a
Cartan connection and the usual (Ehresmann) connection on a principal bundle
allows to gain an appropriate insight into the derivation of the genuine "
diffeomorphisms out of gauge transformations" given by Polyakov himself.Comment: Accept\'e pour publication dans Lett. Math. Phy
Light propagation in statistically homogeneous and isotropic universes with general matter content
We derive the relationship of the redshift and the angular diameter distance
to the average expansion rate for universes which are statistically homogeneous
and isotropic and where the distribution evolves slowly, but which have
otherwise arbitrary geometry and matter content. The relevant average expansion
rate is selected by the observable redshift and the assumed symmetry properties
of the spacetime. We show why light deflection and shear remain small. We write
down the evolution equations for the average expansion rate and discuss the
validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular
diameter distance and two typos. No change in result