The present paper considers the operator pencil A ( λ ) = 0 + 1 , where ≠ are bounded linear mappings between complex Hilbert spaces and is neither one-to-one nor onto. Assuming that an isolated singularity of image closed, certain operators defined recursively starting from they shown to provide a characterization null space in principal part resolvent logarithmic residues at 0. relations with...

www.aafp.org/afp AMERICAN FAMILY PHYSICIAN 2211 Dive-Related Barotrauma During descent and ascent in the water, the diver is constantly exposed to alterations of ambient pressure. Barotrauma refers to tissue damage that occurs when a gas-filled body space (e.g., lungs, middle ear) fails to equalize its internal pressure to accommodate changes in ambient pressure. The behavior of gasses at depth...

Arboreal animals with prehensile hands must balance the complex demands of bone strength, grasping and manipulation. An informative example of this problem is that of the aye-aye (Daubentonia madagascariensis), a rare lemuriform primate that is unusual in having exceptionally long, gracile fingers specialized for foraging. In addition, they are among the largest primates to engage in head-first...

Optical quantum circuits can be optimized using gradient descent methods, as the gates in a circuit parametrized by continuous parameters. However, parameter space seen cost function is not Euclidean, which means that Euclidean does generally point direction of steepest ascent. In order to retrieve ascent direction, this work we implement Natural Gradient optical setting, takes local metric ten...

It is classically thought that increases in hemoglobin mass (Hbmass) take several weeks to develop upon ascent to high altitude and are lost gradually following descent. However, the early time course of these erythropoietic adaptations has not been thoroughly investigated and data are lacking at elevations greater than 5000 m, where the hypoxic stimulus is dramatically increased. As part of th...

Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz vectors are derived for various steepest descent/ascent gradient iterations. The analysis shows that poores...

Let R be a local Cohen-Macaulay ring with canonical module ωR. We investigate the following question of Huneke: If the sequence of Betti numbers {β i (ωR)} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide ...

We address the issue of using mini-batches in stochastic optimization of SVMs. We show that the same quantity, the spectral norm of the data, controls the parallelization speedup obtained for both primal stochastic subgradient descent (SGD) and stochastic dual coordinate ascent (SCDA) methods and use it to derive novel variants of mini-batched SDCA. Our guarantees for both methods are expressed...