5,754 research outputs found
A remark on the Restricted Isometry Property in Orthogonal Matching Pursuit
This paper demonstrates that if the restricted isometry constant
of the measurement matrix satisfies then a greedy algorithm called Orthogonal Matching
Pursuit (OMP) can recover every --sparse signal in
iterations from A\x. By contrast, a matrix is also constructed with the
restricted isometry constant such that
OMP can not recover some -sparse signal in iterations. This
result positively verifies the conjecture given by Dai and Milenkovic in 2009
Structural damage identification using mathematical optimization techniques
An identification procedure is proposed to identify damage characteristics (location and size of the damage) from dynamic measurements. This procedure was based on minimization of the mean-square measure of difference between measurement data (natural frequencies and mode shapes) and the corresponding predictions obtained from the computational model. The procedure is tested for simulated damage in the form of stiffness changes in a simple fixed free spring mass system and symmetric cracks in a simply supported Bernoulli Euler beam. It is shown that when all the mode information is used in the identification procedure it is possible to uniquely determine the damage properties. Without knowing the complete set of modal information, a restricted region in the initial data space has been found for realistic and convergent solution from the identification process
Sparse integrative clustering of multiple omics data sets
High resolution microarrays and second-generation sequencing platforms are
powerful tools to investigate genome-wide alterations in DNA copy number,
methylation and gene expression associated with a disease. An integrated
genomic profiling approach measures multiple omics data types simultaneously in
the same set of biological samples. Such approach renders an integrated data
resolution that would not be available with any single data type. In this
study, we use penalized latent variable regression methods for joint modeling
of multiple omics data types to identify common latent variables that can be
used to cluster patient samples into biologically and clinically relevant
disease subtypes. We consider lasso [J. Roy. Statist. Soc. Ser. B 58 (1996)
267-288], elastic net [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005)
301-320] and fused lasso [J. R. Stat. Soc. Ser. B Stat. Methodol. 67 (2005)
91-108] methods to induce sparsity in the coefficient vectors, revealing
important genomic features that have significant contributions to the latent
variables. An iterative ridge regression is used to compute the sparse
coefficient vectors. In model selection, a uniform design [Monographs on
Statistics and Applied Probability (1994) Chapman & Hall] is used to seek
"experimental" points that scattered uniformly across the search domain for
efficient sampling of tuning parameter combinations. We compared our method to
sparse singular value decomposition (SVD) and penalized Gaussian mixture model
(GMM) using both real and simulated data sets. The proposed method is applied
to integrate genomic, epigenomic and transcriptomic data for subtype analysis
in breast and lung cancer data sets.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS578 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the flag curvature of Finsler metrics of scalar curvature
The flag curvature of a Finsler metric is called a Riemannian quantity
because it is an extension of sectional curvature in Riemannian geometry. In
Finsler geometry, there are several non-Riemannian quantities such as the
(mean) Cartan torsion, the (mean) Landsberg curvature and the S-curvature,
which all vanish for Riemannian metrics. It is important to understand the
geometric meanings of these quantities. In this paper, we study Finsler metrics
of scalar curvature (i.e., the flag curvature is a scalar function on the slit
tangent bundle) and partially determine the flag curvature when certain
non-Riemannian quantities are isotropic. Using the obtained formula for the
flag curvature, we classify locally projectively flat Randers metrics with
isotropic S-curvature.Comment: 23 page
Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster
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