380 research outputs found
Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes
We examine the gravitational wave recoil waves and the associated net kick
velocities in non-axisymmetric Robinson-Trautman spacetimes. We use
characteristic initial data for the dynamics corresponding to non-head-on
collisions of black holes. We make a parameter study of the kick distributions,
corresponding to an extended range of the incidence angle in the
initial data. For the range of examined () the kick distributions as a function of the symmetric mass
parameter satisfy a law obtained from an empirical modification of the
Fitchett law, with a parameter that accounts for the non-zero net
gravitational momentum wave fluxes for the equal mass case. The law fits
accurately the kick distributions for the range of examined, with a
rms normalized error of the order of . For the equal mass case the
nonzero net gravitational wave momentum flux increases as increases,
up to beyond which it decreases. The maximum net
kick velocity is about for for the boost parameter considered.
For the distribution is a monotonous function of
. The angular patterns of the gravitational waves emitted are examined.
Our analysis includes the two polarization modes present in wave zone
curvature.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.122
Desenvolvimento gonadal de Deuterodon langei Travassos (Teleostei: Characidae)
Desenvolvimento gonadal de Deuterodon langei Travassos (Teleostei: Characidae) Gonadal development of Deuterodon langei Travassos (Teleostei: Characidae
The Efficiency of Gravitational Bremsstrahlung Production in the Collision of Two Schwarzschild Black Holes
We examine the efficiency of gravitational bremsstrahlung production in the
process of head-on collision of two boosted Schwarzschild black holes. We
constructed initial data for the characteristic initial value problem in
Robinson-Trautman spacetimes, that represent two instantaneously stationary
Schwarzschild black holes in motion towards each other with the same velocity.
The Robinson-Trautman equation was integrated for these initial data using a
numerical code based on the Galerkin method. The final resulting configuration
is a boosted black hole with Bondi mass greater than the sum of the individual
mass of each initial black hole. Two relevant aspects of the process are
presented. The first relates the efficiency of the energy extraction
by gravitational wave emission to the mass of the final black hole. This
relation is fitted by a distribution function of non-extensive thermostatistics
with entropic parameter ; the result extends and validates
analysis based on the linearized theory of gravitational wave emission. The
second is a typical bremsstrahlung angular pattern in the early period of
emission at the wave zone, a consequence of the deceleration of the black holes
as they coalesce; this pattern evolves to a quadrupole form for later times.Comment: 16 pages, 4 figures, to appear in Int. J. Modern Phys. D (2008
Faster Homomorphic Encryption over GPGPUs via hierarchical DGT
Privacy guarantees are still insufficient for outsourced data processing in the cloud. While employing encryption is feasible for data at rest or in transit, it is not for computation without remarkable performance slowdown. Thus, handling data in plaintext during processing is still required, which creates vulnerabilities that can be exploited by malicious entities. Homomorphic encryption (HE) schemes are natural candidates for computation in the cloud since they enable processing of ciphertexts without any knowledge about the related plaintexts or the decryption key. This work focuses on the challenge of developing an efficient implementation of the BFV HE scheme on CUDA. This is done by combining and adapting different approaches from the literature, namely the double-CRT representation and the Discrete Galois Transform. Moreover, we propose and implement an improved formulation of the DGT inspired by classical algorithms, which computes the transform up to times faster than the state-of-the-art. By using these approaches, we obtain up to times faster homomorphic multiplication
Performance of Hierarchical Transforms in Homomorphic Encryption: A case study on Logistic Regression inference
Recent works challenged the Number-Theoretic Transform (NTT) as the most efficient method for
polynomial multiplication in GPU implementations of Fully Homomorphic Encryption schemes such
as CKKS and BFV. In particular, these works argue that the Discrete Galois Transform (DGT) is a
better candidate for this particular case. However, these claims were never rigorously validated, and
only intuition was used to argue in favor of each transform. This work brings some light on the dis-
cussion by developing similar CUDA implementations of the CKKS cryptosystem, differing only in
the underlying transform and related data structure. We ran several experiments and collected perfor-
mance metrics in different contexts, ranging from the basic direct comparison between the transforms
to measuring the impact of each one on the inference phase of the logistic regression algorithm. Our
observations suggest that, despite some specific polynomial ring configurations, the DGT in a stan-
dalone implementation does not offer the same performance as the NTT. However, when we consider
the entire cryptosystem, we noticed that the effects of the higher arithmetic density of the DGT on
other parts of the implementation is substantial, implying a considerable performance improvement
of up to 15% on the homomorphic multiplication. Furthermore, this speedup is consistent when we
consider a more complex application, indicating that the DGT suits better the target architecture
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