428,888 research outputs found
Stationary viscoelastic wave fields generated by scalar wave functions
The usual Helmholtz decomposition gives a decomposition of any vector valued
function into a sum of gradient of a scalar function and rotation of a vector
valued function under some mild condition. In this paper we show that the
vector valued function of the second term i.e. the divergence free part of this
decomposition can be further decomposed into a sum of a vector valued function
polarized in one component and the rotation of a vector valued function also
polarized in the same component. Hence the divergence free part only depends on
two scalar functions. Further we show the so called completeness of
representation associated to this decomposition for the stationary wave field
of a homogeneous, isotropic viscoelastic medium. That is by applying this
decomposition to this wave field, we can show that each of these three scalar
functions satisfies a Helmholtz equation. Our completeness of representation is
useful for solving boundary value problem in a cylindrical domain for several
partial differential equations of systems in mathematical physics such as
stationary isotropic homogeneous elastic/viscoelastic equations of system and
stationary isotropic homogeneous Maxwell equations of system. As an example, by
using this completeness of representation, we give the solution formula for
torsional deformation of a pendulum of cylindrical shaped homogeneous isotropic
viscoelastic medium
Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training
We consider the convex quadratic linearly constrained problem
with bounded variables and with huge and dense Hessian matrix that arises
in many applications such as the training problem of bias support vector machines.
We propose a decomposition algorithmic scheme suitable to parallel implementations
and we prove global convergence under suitable conditions. Focusing
on support vector machines training, we outline how these assumptions
can be satisfied in practice and we suggest various specific implementations.
Extensions of the theoretical results to general linearly constrained problem
are provided. We included numerical results on support vector machines with
the aim of showing the viability and the effectiveness of the proposed scheme
Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks
Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re¬stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen¬troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-M&N schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust
Parallel growing and training of neural networks using output parallelism
In order to find an appropriate architecture for a large-scale real-world application automatically and efficiently, a natural method is to divide the original problem into a set of sub-problems. In this paper, we propose a simple neural network task decomposition method based on output parallelism. By using this method, a problem can be divided flexibly into several sub-problems as chosen, each of which is composed of the whole input vector and a fraction of the output vector. Each module (for one sub-problem) is responsible for producing a fraction of the output vector of the original problem. The hidden structure for the original problem’s output units are decoupled. These modules can be grown and trained in parallel on parallel processing elements. Incorporated with a constructive learning algorithm, our method does not require excessive computation and any prior knowledge concerning decomposition. The feasibility of output parallelism is analyzed and proved. Some benchmarks are implemented to test the validity of this method. Their results show that this method can reduce computational time, increase learning speed and improve generalization accuracy for both classification and regression problems
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