Vibrio parahaemolyticus possesses two alternate flagellar systems adapted for movement under different circumstances. A single polar flagellum propels the bacterium in liquid (swimming), while multiple lateral flagella move the bacterium over surfaces (swarming). Energy to rotate the polar flagellum is derived from the sodium membrane potential, whereas lateral flagella are powered by the proto...

www.sciencemag.org SCIENCE VOL 339 18 JANUARY 2013 247 COVER Map of highest surface temperature in the north polar region of Mercury superimposed on topography measured by the MESSENGER spacecraft. Red areas surrounding the pole (center) reach temperatures above 450 K. Blue and purple areas inside polar impact craters never exceed 100 K and are suffi ciently cold to harbor water ice and frozen ...

We derive iterative methods for computing the Fréchet derivative of the map which 4 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 5 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 6 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 7 identity that relates the ...

mulas §1.5. Multiplicity-free representations — definition §2. Multiplicity-free theorem — general framework §2.1. Holomorphic bundles and anti-holomorphic maps §2.2. Multiplicity-free theorem — line bundle case §2.3. Geometry on the base space D §2.4. Multiplicity-free theorem — vector bundle case §3. Visible actions on complex manifolds §3.1. Previsible and visible actions on complex manifold...

We derive iterative methods for computing the Fréchet derivative of the map which 6 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 7 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 8 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 9 identity that relates the ...

We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices as well as rectangular matrices having more rows than columns. Our derivation relies on a novel identity that relates the Fréchet ...

We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices as well as rectangular matrices having more rows than columns. Our derivation relies on a novel identity that relates the Fréchet ...

We propose a method of unsupervised learning from stationary, vector-valued processes. A low-dimensional subspace is selected on the basis of a criterion which rewards data-variance (like PSA) and penalizes the variance of the velocity vector, thus exploiting the shorttime dependencies of the process. We prove error bounds in terms of the -mixing coe¢ cients and consistency for absolutely regul...

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...