Antenna lobe (AL) in the Drosophila brain is composed of ~50 glomeruli. Each of the glomeruli has a stereotyped shape, position, and neuronal composition. However, manually identification of the glomeruli usually is very time consuming and demands high familiarity with the structure. In this project, we applied Principle Component Analysis method via Singular Value Decomposition to identify a s...

We describe the singular value decomposition (SVD) of yeast genome-scale mRNA lengths distribution data measured by DNA microarrays. SVD uncovers in the mRNA abundance levels data matrix of genes x arrays, i.e., electrophoretic gel migration lengths or mRNA lengths, mathematically unique decorrelated and decoupled "eigengenes." The eigengenes are the eigenvectors of the arrays x arrays correlat...

The impact of the latest combined CHAMP/GRACE/terrestrial measurements Earth gravity model EIGEN-CG03C on the measurement of the Lense-Thirring effect with some linear combinations of the nodes of some of the existing Earth’s artificial satellites is presented. The 1-sigma upper bound of the systematic error in the nodenode LAGEOS-LAGEOS II combination is 3.9% (4% with EIGENGRACE02S, ∼ 6% with ...

∥M − PY (M)∥2 ≤ ∥Σ2∥2 + ∥Σ2Ψ2Ψ † 1∥2 where PY (M) projects column vectors in M in the subspace spanned by the column vectors in Y and † denotes the pseudoinverse. Theorem 2. (Derived From Theorem 2.2 of (Tropp, 2011)) Let X be a finite set of PSD matrices with dimension k (means the size of the square matrix is k× k). λmax(·) and λmin(·) calculate the maximum and minimum eigen value respectively.

mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper the author derives a lower bound for the largest eigen-value and an upper bound for the smallest eigenvalue of Hermitian matrices , based on Weyl's inequalities. Some related results, consequences, applications, and examples...