45,131 research outputs found
Sparsity-Based Kalman Filters for Data Assimilation
Several variations of the Kalman filter algorithm, such as the extended
Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in
science and engineering applications. In this paper, we introduce two
algorithms of sparsity-based Kalman filters, namely the sparse UKF and the
progressive EKF. The filters are designed specifically for problems with very
high dimensions. Different from various types of ensemble Kalman filters
(EnKFs) in which the error covariance is approximated using a set of dense
ensemble vectors, the algorithms developed in this paper are based on sparse
matrix approximations of error covariance. The new algorithms enjoy several
advantages. The error covariance has full rank without being limited by a set
of ensembles. In addition to the estimated states, the algorithms provide
updated error covariance for the next assimilation cycle. The sparsity of error
covariance significantly reduces the required memory size for the numerical
computation. In addition, the granularity of the sparse error covariance can be
adjusted to optimize the parallelization of the algorithms
Field Induced Jet Micro-EDM
Electrical discharge machining (EDM) is of the potential of
micro/nano meter scale machining capability. However,
electrode wear in micro-EDM significantly deteriorates the
machining accuracy, thus, it needs to be compensated in
process. To solve this problem, a novel micromachining
method, namely field induced jet micro-EDM, is proposed in
this paper, in which the electrical field induced jet is used as
the micro tool electrode. A series of experiments were carried
out to investigate the feasibility of proposed method. Due to
the electrolyte can be supplied automatically by the capillary
effect and the electrostatic field, it is not necessary to use
pump or valves. The problem of electrode wear does not exist
at all in the machining process because of the field induced jet
will be generated periodically. It is also found that the workpiece
material can be effectively removed with a crater size of
about 2 micrometer in diameter. The preliminary experimental results
verified that the field induced jet micro-EDM is an effective
micromachining method
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
Let be the coarse moduli space of CY manifolds arising
from a crepant resolution of double covers of branched along
hyperplanes in general position. We show that the monodromy group of a
good family for is Zariski dense in the corresponding
symplectic or orthogonal group if . In particular, the period map does
not give a uniformization of any partial compactification of the coarse moduli
space as a Shimura variety whenever . This disproves a conjecture of
Dolgachev. As a consequence, the fundamental group of the coarse moduli space
of ordered points in is shown to be large once it is not a
point. Similar Zariski-density result is obtained for moduli spaces of CY
manifolds arising from cyclic covers of branched along
hyperplanes in general position. A classification towards the geometric
realization problem of B. Gross for type bounded symmetric domains is
given.Comment: 48 page
Micromechanical model of crack growth in fiber reinforced ceramics
A model based on the micromechanical mechanism of crack growth resistance in fiber reinforced ceramics is presented. The formulation of the model is based on a small scale geometry of a macrocrack with a bridging zone, the process zone, which governs the resistance mechanism. The effect of high toughness of the fibers in retardation of the crack advance, and the significance of the fiber pullout mechanism on the crack growth resistance, are reflected in this model. The model allows one to address issues such as influence of fiber spacing, fiber flexibility, and fiber matrix friction. Two approaches were used. One represents the fracture initiation and concentrated on the development of the first microcracks between fibers. An exact closed form solution was obtained for this case. The second case deals with the development of an array of microcracks between fibers forming the bridging zone. An implicit exact solution is formed for this case. In both cases, a discrete fiber distribution is incorporated into the solution
Partial Observability and its Consistency for PDEs
In this paper, a quantitative measure of partial observability is defined for
PDEs. The quantity is proved to be consistent if the PDE is approximated using
well-posed approximation schemes. A first order approximation of an
unobservability index using an empirical Gramian is introduced. Several
examples are presented to illustrate the concept of partial observability,
including Burgers' equation and a one-dimensional nonlinear shallow water
equation.Comment: 5 figures, 25 pages. arXiv admin note: substantial text overlap with
arXiv:1111.584
Self-weighted Multiple Kernel Learning for Graph-based Clustering and Semi-supervised Classification
Multiple kernel learning (MKL) method is generally believed to perform better
than single kernel method. However, some empirical studies show that this is
not always true: the combination of multiple kernels may even yield an even
worse performance than using a single kernel. There are two possible reasons
for the failure: (i) most existing MKL methods assume that the optimal kernel
is a linear combination of base kernels, which may not hold true; and (ii) some
kernel weights are inappropriately assigned due to noises and carelessly
designed algorithms. In this paper, we propose a novel MKL framework by
following two intuitive assumptions: (i) each kernel is a perturbation of the
consensus kernel; and (ii) the kernel that is close to the consensus kernel
should be assigned a large weight. Impressively, the proposed method can
automatically assign an appropriate weight to each kernel without introducing
additional parameters, as existing methods do. The proposed framework is
integrated into a unified framework for graph-based clustering and
semi-supervised classification. We have conducted experiments on multiple
benchmark datasets and our empirical results verify the superiority of the
proposed framework.Comment: Accepted by IJCAI 2018, Code is availabl
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