Interpolation problems in function spaces

Let D be a domain in the complex plane, let {zn} be a sequence of distinct points in D, and let {wn} be an arbitrary sequence of complex numbers. Given a space E of functions on D, the problem arises to characterize the pairs of sequences {zn} and {wn} for which there is a function [function of (italic small f)]; [epsilon] E with [function of (italic small f)];(zn) = wn, n = 1, 2,.... In the present paper, we solve a general interpolation problem of this type. We then apply the result to obtain criteria for interpolation by Hp functions, 1 [les] p [les] [infinity], by harmonic functions of class hp, and by functions belonging to certain Hilbert spaces. The main tool is a general theorem, closely related to the Hahn-Banach theorem, on the extension of functionals over normed linear spaces.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34190/1/0000479.pd

Magnetic phases and reorientation transitions in antiferromagnetically coupled multilayers

In antiferromagnetically coupled superlattices grown on (001) faces of cubic substrates, e.g. based on materials combinations as Co/Cu, Fe/Si, Co/Cr, or Fe/Cr, the magnetic states evolve under competing influence of bilinear and biquadratic exchange interactions, surface-enhanced four-fold in-plane anisotropy, and specific finite-size effects. Using phenomenological (micromagnetic) theory, a comprehensive survey of the magnetic states and reorientation transitions has been carried out for multilayer systems with even number of ferromagnetic sub-layers and magnetizations in the plane. In two-layer systems (N=2) the phase diagrams in dependence on components of the applied field in the plane include ``swallow-tail'' type regions of (metastable) multistate co-existence and a number of continuous and discontinuous reorientation transitions induced by radial and transversal components of the applied field. In multilayers (N \ge 4) noncollinear states are spatially inhomogeneous with magnetization varying across the multilayer stack. For weak four-fold anisotropy the magnetic states under influence of an applied field evolve by a complex continuous reorientation into the saturated state. At higher anisotropy they transform into various inhomogeneous and asymmetric structures. The discontinuous transitions between the magnetic states in these two-layers and multilayers are characterized by broad ranges of multi-phase coexistence of the (metastable) states and give rise to specific transitional domain structures.Comment: Manuscript 34 pages, 14 figures; submitted for publicatio

Effector-triggered defence against apoplastic fungal pathogens

Copyright 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license CC BY 3.0 (http://creativecommons.org/licenses/by/3.0/). hR gene-mediated host resistance against apoplastic fungal pathogens is not adequately explained by the terms pathogen-associated molecular pattern (PAMP)-triggered immunity (PTI) or effector-triggered immunity (ETI). Therefore, it is proposed that this type of resistance is termed ‘effector-triggered defence’ (ETD). Unlike PTI and ETI, ETD is mediated by R genes encoding cell surface-localised receptor-like proteins (RLPs) that engage the receptor-like kinase SOBIR1. In contrast to this extracellular recognition, ETI is initiated by intracellular detection of pathogen effectors. ETI is usually associated with fast, hypersensitive host cell death, whereas ETD often triggers host cell death only after an elapsed period of endophytic pathogen growth. In this opinion, we focus on ETD responses against foliar fungal pathogens of cropsPeer reviewe

Human Galectins Induce Conversion of Dermal Fibroblasts into Myofibroblasts and Production of Extracellular Matrix: Potential Application in Tissue Engineering and Wound Repair

Members of the galectin family of endogenous lectins are potent adhesion/growth-regulatory effectors. Their multi-functionality opens possibilities for their use in bioapplications. We studied whether human galectins induce the conversion of human dermal fibroblasts into myofibroblasts (MFBs) and the production of a bioactive extracellular matrix scaffold is suitable for cell culture. Testing a panel of galectins of all three subgroups, including natural and engineered variants, we detected activity for the proto-type galectin-1 and galectin-7, the chimera-type galectin-3 and the tandem-repeat-type galectin-4. The activity of galectin-1 required the integrity of the carbohydrate recognition domain. It was independent of the presence of TGF-beta 1, but it yielded an additive effect. The resulting MFBs, relevant, for example, for tumor progression, generated a matrix scaffold rich in fibronectin and galectin-1 that supported keratinocyte culture without feeder cells. Of note, keratinocytes cultured on this substratum presented a stem-like cell phenotype with small size and keratin-19 expression. In vivo in rats, galectin-1 had a positive effect on skin wound closure 21 days after surgery. In conclusion, we describe the differential potential of certain human galectins to induce the conversion of dermal fibroblasts into MFBs and the generation of a bioactive cell culture substratum. Copyright (C) 2011 S. Karger AG, Base

Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD

Synaptic processes and immune-related pathways implicated in Tourette syndrome.

Tourette syndrome (TS) is a neuropsychiatric disorder of complex genetic architecture involving multiple interacting genes. Here, we sought to elucidate the pathways that underlie the neurobiology of the disorder through genome-wide analysis. We analyzed genome-wide genotypic data of 3581 individuals with TS and 7682 ancestry-matched controls and investigated associations of TS with sets of genes that are expressed in particular cell types and operate in specific neuronal and glial functions. We employed a self-contained, set-based association method (SBA) as well as a competitive gene set method (MAGMA) using individual-level genotype data to perform a comprehensive investigation of the biological background of TS. Our SBA analysis identified three significant gene sets after Bonferroni correction, implicating ligand-gated ion channel signaling, lymphocytic, and cell adhesion and transsynaptic signaling processes. MAGMA analysis further supported the involvement of the cell adhesion and trans-synaptic signaling gene set. The lymphocytic gene set was driven by variants in FLT3, raising an intriguing hypothesis for the involvement of a neuroinflammatory element in TS pathogenesis. The indications of involvement of ligand-gated ion channel signaling reinforce the role of GABA in TS, while the association of cell adhesion and trans-synaptic signaling gene set provides additional support for the role of adhesion molecules in neuropsychiatric disorders. This study reinforces previous findings but also provides new insights into the neurobiology of TS

Gaia Early Data Release 3: Gaia photometric science alerts

Context. Since July 2014, the Gaia mission has been engaged in a high-spatial-resolution, time-resolved, precise, accurate astrometric, and photometric survey of the entire sky. Aims. We present the Gaia Science Alerts project, which has been in operation since 1 June 2016. We describe the system which has been developed to enable the discovery and publication of transient photometric events as seen by Gaia. Methods. We outline the data handling, timings, and performances, and we describe the transient detection algorithms and filtering procedures needed to manage the high false alarm rate. We identify two classes of events: (1) sources which are new to Gaia and (2) Gaia sources which have undergone a significant brightening or fading. Validation of the Gaia transit astrometry and photometry was performed, followed by testing of the source environment to minimise contamination from Solar System objects, bright stars, and fainter near-neighbours. Results. We show that the Gaia Science Alerts project suffers from very low contamination, that is there are very few false-positives. We find that the external completeness for supernovae, CE = 0.46, is dominated by the Gaia scanning law and the requirement of detections from both fields-of-view. Where we have two or more scans the internal completeness is CI = 0.79 at 3 arcsec or larger from the centres of galaxies, but it drops closer in, especially within 1 arcsec. Conclusions. The per-Transit photometry for Gaia transients is precise to 1% at G = 13, and 3% at G = 19. The per-Transit astrometry is accurate to 55 mas when compared to Gaia DR2. The Gaia Science Alerts project is one of the most homogeneous and productive transient surveys in operation, and it is the only survey which covers the whole sky at high spatial resolution (subarcsecond), including the Galactic plane and bulge. © S. T. Hodgkin et al. 2021

Search for electroweak production of single top quarks in ppˉp\bar{p} collisions.

We present a search for electroweak production of single top quarks in the electron+jets and muon+jets decay channels. The measurements use ~90 pb^-1 of data from Run 1 of the Fermilab Tevatron collider, collected at 1.8 TeV with the DZero detector between 1992 and 1995. We use events that include a tagging muon, implying the presence of a b jet, to set an upper limit at the 95% confidence level on the cross section for the s-channel process ppbar->tb+X of 39 pb. The upper limit for the t-channel process ppbar->tqb+X is 58 pb. (arXiv

Search for first-generation scalar and vector leptoquarks

We describe a search for the pair production of first-generation scalar and vector leptoquarks in the eejj and enujj channels by the D0 Collaboration. The data are from the 1992--1996 ppbar run at sqrt{s} = 1.8 TeV at the Fermilab Tevatron collider. We find no evidence for leptoquark production; in addition, no kinematically interesting events are observed using relaxed selection criteria. The results from the eejj and enujj channels are combined with those from a previous D0 analysis of the nunujj channel to obtain 95% confidence level (C.L.) upper limits on the leptoquark pair-production cross section as a function of mass and of beta, the branching fraction to a charged lepton. These limits are compared to next-to-leading-order theory to set 95% C.L. lower limits on the mass of a first-generation scalar leptoquark of 225, 204, and 79 GeV/c^2 for beta=1, 1/2, and 0, respectively. For vector leptoquarks with gauge (Yang-Mills) couplings, 95% C.L. lower limits of 345, 337, and 206 GeV/c^2 are set on the mass for beta=1, 1/2, and 0, respectively. Mass limits for vector leptoquarks are also set for anomalous vector couplings