754,028 research outputs found
Faster Geometric Algorithms via Dynamic Determinant Computation
The computation of determinants or their signs is the core procedure in many
important geometric algorithms, such as convex hull, volume and point location.
As the dimension of the computation space grows, a higher percentage of the
total computation time is consumed by these computations. In this paper we
study the sequences of determinants that appear in geometric algorithms. The
computation of a single determinant is accelerated by using the information
from the previous computations in that sequence.
We propose two dynamic determinant algorithms with quadratic arithmetic
complexity when employed in convex hull and volume computations, and with
linear arithmetic complexity when used in point location problems. We implement
the proposed algorithms and perform an extensive experimental analysis. On one
hand, our analysis serves as a performance study of state-of-the-art
determinant algorithms and implementations. On the other hand, we demonstrate
the supremacy of our methods over state-of-the-art implementations of
determinant and geometric algorithms. Our experimental results include a 20 and
78 times speed-up in volume and point location computations in dimension 6 and
11 respectively.Comment: 29 pages, 8 figures, 3 table
Efficient implementation of finite volume methods in Numerical Relativity
Centered finite volume methods are considered in the context of Numerical
Relativity. A specific formulation is presented, in which third-order space
accuracy is reached by using a piecewise-linear reconstruction. This
formulation can be interpreted as an 'adaptive viscosity' modification of
centered finite difference algorithms. These points are fully confirmed by 1D
black-hole simulations. In the 3D case, evidence is found that the use of a
conformal decomposition is a key ingredient for the robustness of black hole
numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.
NASA MSFC hardware in the loop simulations of automatic rendezvous and capture systems
Two complementary hardware-in-the-loop simulation facilities for automatic rendezvous and capture systems at MSFC are described. One, the Flight Robotics Laboratory, uses an 8 DOF overhead manipulator with a work volume of 160 by 40 by 23 feet to evaluate automatic rendezvous algorithms and range/rate sensing systems. The other, the Space Station/Station Operations Mechanism Test Bed, uses a 6 DOF hydraulic table to perform docking and berthing dynamics simulations
Modeling sparse connectivity between underlying brain sources for EEG/MEG
We propose a novel technique to assess functional brain connectivity in
EEG/MEG signals. Our method, called Sparsely-Connected Sources Analysis (SCSA),
can overcome the problem of volume conduction by modeling neural data
innovatively with the following ingredients: (a) the EEG is assumed to be a
linear mixture of correlated sources following a multivariate autoregressive
(MVAR) model, (b) the demixing is estimated jointly with the source MVAR
parameters, (c) overfitting is avoided by using the Group Lasso penalty. This
approach allows to extract the appropriate level cross-talk between the
extracted sources and in this manner we obtain a sparse data-driven model of
functional connectivity. We demonstrate the usefulness of SCSA with simulated
data, and compare to a number of existing algorithms with excellent results.Comment: 9 pages, 6 figure
A Theory of Solving TAP Equations for Ising Models with General Invariant Random Matrices
We consider the problem of solving TAP mean field equations by iteration for
Ising model with coupling matrices that are drawn at random from general
invariant ensembles. We develop an analysis of iterative algorithms using a
dynamical functional approach that in the thermodynamic limit yields an
effective dynamics of a single variable trajectory. Our main novel contribution
is the expression for the implicit memory term of the dynamics for general
invariant ensembles. By subtracting these terms, that depend on magnetizations
at previous time steps, the implicit memory terms cancel making the iteration
dependent on a Gaussian distributed field only. The TAP magnetizations are
stable fixed points if an AT stability criterion is fulfilled. We illustrate
our method explicitly for coupling matrices drawn from the random orthogonal
ensemble.Comment: 27 pages, 6 Figures Published in Journal of Physics A: Mathematical
and Theoretical, Volume 49, Number 11, 201
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