Adaptive Eigenvalue Computation - Complexity Estimates

This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable sequences, the problem becomes sufficiently well conditioned so that a gradient type iteration can be shown to reduce the error by some fixed factor per step. It then remains to realize these (ideal) iterations within suitable dynamically updated error tolerances. It is shown under which circumstances the adaptive scheme exhibits in some sense asymptotically optimal complexity.Comment: submitted to Math. Com

One-site density matrix renormalization group and alternating minimum energy algorithm

Given in the title are two algorithms to compute the extreme eigenstate of a high-dimensional Hermitian matrix using the tensor train (TT) / matrix product states (MPS) representation. Both methods empower the traditional alternating direction scheme with the auxiliary (e.g. gradient) information, which substantially improves the convergence in many difficult cases. Being conceptually close, these methods have different derivation, implementation, theoretical and practical properties. We emphasize the differences, and reproduce the numerical example to compare the performance of two algorithms.Comment: Submitted to the proceedings of ENUMATH 201

Measuring the elements of the optical density matrix

Most methods for experimentally reconstructing the quantum state of light involve determining a quasiprobability distribution such as the Wigner function. In this paper we present a scheme for measuring individual density matrix elements in the photon number state representation. Remarkably, the scheme is simple, involving two beam splitters and a reference field in a coherent state.Comment: 6 pages and 1 figur

Extracellular MRP8/14 is a regulator of beta 2 integrin-dependent neutrophil slow rolling and adhesion

Myeloid-related proteins (MRPs) 8 and 14 are cytosolic proteins secreted from myeloid cells as proinflammatory mediators. Currently, the functional role of circulating extracellular MRP8/14 is unclear. Our present study identifies extracellular MRP8/14 as an autocrine player in the leukocyte adhesion cascade. We show that E-selectin-PSGL-1 interaction during neutrophil rolling triggers Mrp8/14 secretion. Released MRP8/14 in turn activates a TLR4-mediated, Rap1-GTPase-dependent pathway of rapid beta 2 integrin activation in neutrophils. This extracellular activation loop reduces leukocyte rolling velocity and stimulates adhesion. Thus, we identify Mrp8/14 and TLR4 as important modulators of the leukocyte recruitment cascade during inflammation in vivo

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

Atom Interferometers

Interference with atomic and molecular matter waves is a rich branch of atomic physics and quantum optics. It started with atom diffraction from crystal surfaces and the separated oscillatory fields technique used in atomic clocks. Atom interferometry is now reaching maturity as a powerful art with many applications in modern science. In this review we first describe the basic tools for coherent atom optics including diffraction by nanostructures and laser light, three-grating interferometers, and double wells on AtomChips. Then we review scientific advances in a broad range of fields that have resulted from the application of atom interferometers. These are grouped in three categories: (1) fundamental quantum science, (2) precision metrology and (3) atomic and molecular physics. Although some experiments with Bose Einstein condensates are included, the focus of the review is on linear matter wave optics, i.e. phenomena where each single atom interferes with itself.Comment: submitted to Reviews of Modern Physic

Src family kinase-mediated vesicle trafficking is critical for neutrophil basement membrane penetration

Leukocyte recruitment into inflamed tissue is highly dependent on the activation and binding of integrins to their respective ligands, followed by the induction of various signaling events within the cell referred to as outside-in signaling. Src family kinases (SFK) are the central players in the outside-in signaling process, assigning them a critical role for proper immune cell function. Our study investigated the role of SFK on neutrophil recruitment in vivo using Hck-/- Fgr-/- Lyn-/- mice, which lack SFK expressed in neutrophils. We show that loss of SFK strongly reduces neutrophil adhesion and post-arrest modifications in a shear force dependent manner. Additionally, we found that in the absence of SFK, neutrophils display impaired Rab27adependent surface mobilization of neutrophil elastase, VLA3 and VLA6 containing vesicles. This results in a defect in neutrophil vascular basement membrane penetration and thus strongly impaired extravasation. Taken together, we demonstrate that SFK play a role in neutrophil post-arrest modifications and extravasation during acute inflammation. These findings may support the current efforts to use SFK-inhibitors in inflammatory diseases with unwanted neutrophil recruitment. ©2020 Ferrata Storti Foundatio

Fatty acid metabolism in marine fish: Low activity of fatty acyl Δ5 desaturation in gilthead sea bream ( Sparus aurata ) cells

Marine fish are known to have an absolute dietary requirement for C20 and C22 highly unsaturated fatty acids. Previous studies using cultured cell lines indicated that underlying this requirement in marine fish was either a deficiency in fatty acyl Δ5 desaturase or C18-20 elongase activity. Recently, Ghioni et al. (Biochim. Biophys. Acta, 1437, 170-181, 1999) presented evidence that in turbot cells there was low activity of C18-20 elongase whereas Δ5 desaturase had high activity. In the present study, the fatty acid desaturase/elongase pathway was investigated in a cell line (SAF-1) from another carnivorous marine fish, sea bream. The metabolic conversions of a range of radiolabelled polyunsaturated fatty acids that comprised the direct substrates for Δ6 desaturase ([1-14C]18:2n-6 and [1-14C]18:3n-3), C18-20 elongase ([U-14C]18:4n-3), Δ5 desaturase ([1-14C]20:3n-6 and [U-14C]20:4n-3) and C20-22 elongase ([1-14C]20:4n-6 and [1-14C]20:5n-3) were utilized. The results showed that fatty acyl Δ6 desaturase in SAF-1 cells was highly active and there was substantial C18-20 elongase and C20-22 elongase activities. A deficiency in the desaturation/elongation pathway was clearly identified at the level of the fatty acyl Δ5 desaturase which was very low, particularly with 20:4n-3 as substrate. In comparison, the apparent activities of Δ6 desaturase, C18-20 elongase and C20-22 elongase were approximately 94-fold, 27-fold and 16-fold greater than that for Δ5 desaturase towards their respective n-3 polyunsaturated fatty acid substrates. The evidence obtained in the SAF-1 cell line is consistent with the dietary requirement for C20 and C22 highly unsaturated fatty acids in the marine fish, the sea bream, being primarily due to a deficiency in fatty acid Δ5 desaturase activity