173,705 research outputs found
Fault-tolerant quantum computation
Recently, it was realized that use of the properties of quantum mechanics
might speed up certain computations dramatically. Interest in quantum
computation has since been growing. One of the main difficulties of realizing
quantum computation is that decoherence tends to destroy the information in a
superposition of states in a quantum computer, thus making long computations
impossible. A futher difficulty is that inaccuracies in quantum state
transformations throughout the computation accumulate, rendering the output of
long computations unreliable. It was previously known that a quantum circuit
with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per
gate. We show, for any quantum computation with t gates, how to build a
polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of
inaccuracy and decoherence per gate, for some constant c. We do this by showing
how to compute using quantum error correcting codes. These codes were
previously known to provide resistance to errors while storing and transmitting
quantum data.Comment: Latex, 11 pages, no figures, in 37th Symposium on Foundations of
Computing, IEEE Computer Society Press, 1996, pp. 56-6
Forecasting trends with asset prices
In this paper, we consider a stochastic asset price model where the trend is
an unobservable Ornstein Uhlenbeck process. We first review some classical
results from Kalman filtering. Expectedly, the choice of the parameters is
crucial to put it into practice. For this purpose, we obtain the likelihood in
closed form, and provide two on-line computations of this function. Then, we
investigate the asymptotic behaviour of statistical estimators. Finally, we
quantify the effect of a bad calibration with the continuous time mis-specified
Kalman filter. Numerical examples illustrate the difficulty of trend
forecasting in financial time series.Comment: 26 pages, 11 figure
Simple Recurrent Units for Highly Parallelizable Recurrence
Common recurrent neural architectures scale poorly due to the intrinsic
difficulty in parallelizing their state computations. In this work, we propose
the Simple Recurrent Unit (SRU), a light recurrent unit that balances model
capacity and scalability. SRU is designed to provide expressive recurrence,
enable highly parallelized implementation, and comes with careful
initialization to facilitate training of deep models. We demonstrate the
effectiveness of SRU on multiple NLP tasks. SRU achieves 5--9x speed-up over
cuDNN-optimized LSTM on classification and question answering datasets, and
delivers stronger results than LSTM and convolutional models. We also obtain an
average of 0.7 BLEU improvement over the Transformer model on translation by
incorporating SRU into the architecture.Comment: EMNL
A Verifiable Fully Homomorphic Encryption Scheme for Cloud Computing Security
Performing smart computations in a context of cloud computing and big data is
highly appreciated today. Fully homomorphic encryption (FHE) is a smart
category of encryption schemes that allows working with the data in its
encrypted form. It permits us to preserve confidentiality of our sensible data
and to benefit from cloud computing powers. Currently, it has been demonstrated
by many existing schemes that the theory is feasible but the efficiency needs
to be dramatically improved in order to make it usable for real applications.
One subtle difficulty is how to efficiently handle the noise. This paper aims
to introduce an efficient and verifiable FHE based on a new mathematic
structure that is noise free
Standardization of computational experiments in unsteady turbulent boundary-layer flow
Numerical experiments are proposed as standard cases to be computed by all who plan to analyze unsteady turbulent boundary layer behavior. In this way, differences between the results obtained by various methods can be compared in a completely defined environment. The test cases range in difficulty from time relaxation study of the steady flow on a flat plate to the analysis of unsteady reversed flow. Initial and boundary conditions are fully defined for each case and representative outputs are presented. It is recommended that tabulated samples of computations of these test cases be published in a compendium of results
An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole
The description of the inspiral of a stellar-mass compact object into a
massive black hole sitting at a galactic centre is a problem of major relevance
for the future space-based gravitational-wave observatory LISA (Laser
Interferometer Space Antenna), as the signals from these systems will be buried
in the data stream and accurate gravitational-wave templates will be needed to
extract them. The main difficulty in describing these systems lies in the
estimation of the gravitational effects of the stellar-mass compact object on
his own trajectory around the massive black hole, which can be modeled as the
action of a local force, the self-force. In this paper, we present a new
time-domain numerical method for the computation of the self-force in a
simplified model consisting of a charged scalar particle orbiting a nonrotating
black hole. We use a multi-domain framework in such a way that the particle is
located at the interface between two domains so that the presence of the
particle and its physical effects appear only through appropriate boundary
conditions. In this way we eliminate completely the presence of a small length
scale associated with the need of resolving the particle. This technique also
avoids the problems associated with the impact of a low differentiability of
the solution in the accuracy of the numerical computations. The spatial
discretization of the field equations is done by using the pseudospectral
collocation method and the time evolution, based on the method of lines, uses a
Runge-Kutta solver. We show how this special framework can provide very
efficient and accurate computations in the time domain, which makes the
technique amenable for the intensive computations required in the
astrophysically-relevant scenarios for LISA.Comment: 15 pages, 9 figures, Revtex 4. Minor changes to match published
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