2,222 research outputs found
Controlling Steering Angle for Cooperative Self-driving Vehicles utilizing CNN and LSTM-based Deep Networks
A fundamental challenge in autonomous vehicles is adjusting the steering
angle at different road conditions. Recent state-of-the-art solutions
addressing this challenge include deep learning techniques as they provide
end-to-end solution to predict steering angles directly from the raw input
images with higher accuracy. Most of these works ignore the temporal
dependencies between the image frames. In this paper, we tackle the problem of
utilizing multiple sets of images shared between two autonomous vehicles to
improve the accuracy of controlling the steering angle by considering the
temporal dependencies between the image frames. This problem has not been
studied in the literature widely. We present and study a new deep architecture
to predict the steering angle automatically by using Long-Short-Term-Memory
(LSTM) in our deep architecture. Our deep architecture is an end-to-end network
that utilizes CNN, LSTM and fully connected (FC) layers and it uses both
present and futures images (shared by a vehicle ahead via Vehicle-to-Vehicle
(V2V) communication) as input to control the steering angle. Our model
demonstrates the lowest error when compared to the other existing approaches in
the literature.Comment: Accepted in IV 2019, 6 pages, 9 figure
Asymptotic simplicity and static data
The present article considers time symmetric initial data sets for the vacuum
Einstein field equations which in a neighbourhood of infinity have the same
massless part as that of some static initial data set. It is shown that the
solutions to the regular finite initial value problem at spatial infinity for
this class of initial data sets extend smoothly through the critical sets where
null infinity touches spatial infinity if and only if the initial data sets
coincide with static data in a neighbourhood of infinity. This result
highlights the special role played by static data among the class of initial
data sets for the Einstein field equations whose development gives rise to a
spacetime with a smooth conformal compactification at null infinity.Comment: 25 page
A rigidity property of asymptotically simple spacetimes arising from conformally flat data
Given a time symmetric initial data set for the vacuum Einstein field
equations which is conformally flat near infinity, it is shown that the
solutions to the regular finite initial value problem at spatial infinity
extend smoothly through the critical sets where null infinity touches spatial
infinity if and only if the initial data coincides with Schwarzschild data near
infinity.Comment: 37 page
Can one detect a non-smooth null infinity?
It is shown that the precession of a gyroscope can be used to elucidate the
nature of the smoothness of the null infinity of an asymptotically flat
spacetime (describing an isolated body). A model for which the effects of
precession in the non-smooth null infinity case are of order is
proposed. By contrast, in the smooth version the effects are of order .
This difference should provide an effective criterion to decide on the nature
of the smoothness of null infinity.Comment: 6 pages, to appear in Class. Quantum Gra
On the existence and convergence of polyhomogeneous expansions of zero-rest-mass fields
The convergence of polyhomogeneous expansions of zero-rest-mass fields in
asymptotically flat spacetimes is discussed. An existence proof for the
asymptotic characteristic initial value problem for a zero-rest-mass field with
polyhomogeneous initial data is given. It is shown how this non-regular problem
can be properly recast as a set of regular initial value problems for some
auxiliary fields. The standard techniques of symmetric hyperbolic systems can
be applied to these new auxiliary problems, thus yielding a positive answer to
the question of existence in the original problem.Comment: 10 pages, 1 eps figur
Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
The Conformal Einstein equations and the representation of spatial infinity
as a cylinder introduced by Friedrich are used to analyse the behaviour of the
gravitational field near null and spatial infinity for the development of data
which are asymptotically Euclidean, conformally flat and time asymmetric. Our
analysis allows for initial data whose second fundamental form is more general
than the one given by the standard Bowen-York Ansatz. The Conformal Einstein
equations imply upon evaluation on the cylinder at spatial infinity a hierarchy
of transport equations which can be used to calculate in a recursive way
asymptotic expansions for the gravitational field. It is found that the the
solutions to these transport equations develop logarithmic divergences at
certain critical sets where null infinity meets spatial infinity. Associated to
these, there is a series of quantities expressible in terms of the initial data
(obstructions), which if zero, preclude the appearance of some of the
logarithmic divergences. The obstructions are, in general, time asymmetric.
That is, the obstructions at the intersection of future null infinity with
spatial infinity are different, and do not generically imply those obtained at
the intersection of past null infinity with spatial infinity. The latter allows
for the possibility of having spacetimes where future and past null infinity
have different degrees of smoothness. Finally, it is shown that if both sets of
obstructions vanish up to a certain order, then the initial data has to be
asymptotically Schwarzschildean to some degree.Comment: 32 pages. First part of a series of 2 papers. Typos correcte
Improved existence for the characteristic initial value problem with the conformal Einstein field equations
We adapt Luk's analysis of the characteristic initial value problem in
General Relativity to the asymptotic characteristic problem for the conformal
Einstein field equations to demonstrate the local existence of solutions in a
neighbourhood of the set on which the data are given. In particular, we obtain
existence of solutions along a narrow rectangle along null infinity which, in
turn, corresponds to an infinite domain in the asymptotic region of the
physical spacetime. This result generalises work by K\'ann\'ar on the local
existence of solutions to the characteristic initial value problem by means of
Rendall's reduction strategy. In analysing the conformal Einstein equations we
make use of the Newman-Penrose formalism and a gauge due to J. Stewart.Comment: 44 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1911.0004
On smoothness-asymmetric null infinities
We discuss the existence of asymptotically Euclidean initial data sets to the
vacuum Einstein field equations which would give rise (modulo an existence
result for the evolution equations near spatial infinity) to developments with
a past and a future null infinity of different smoothness. For simplicity, the
analysis is restricted to the class of conformally flat, axially symmetric
initial data sets. It is shown how the free parameters in the second
fundamental form of the data can be used to satisfy certain obstructions to the
smoothness of null infinity. The resulting initial data sets could be
interpreted as those of some sort of (non-linearly) distorted Schwarzschild
black hole. Its developments would be so that they admit a peeling future null
infinity, but at the same time have a polyhomogeneous (non-peeling) past null
infinity.Comment: 13 pages, 1 figur
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