The Weisfeiler-Leman Dimension of Planar Graphs is at most 3

We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables. The previously best known upper bounds for the dimension and number of variables were 14 and 15, respectively. First we show that, for dimension 3 and higher, the WL-algorithm correctly tests isomorphism of graphs in a minor-closed class whenever it determines the orbits of the automorphism group of any arc-colored 3-connected graph belonging to this class. Then we prove that, apart from several exceptional graphs (which have WL-dimension at most 2), the individualization of two correctly chosen vertices of a colored 3-connected planar graph followed by the 1-dimensional WL-algorithm produces the discrete vertex partition. This implies that the 3-dimensional WL-algorithm determines the orbits of a colored 3-connected planar graph. As a byproduct of the proof, we get a classification of the 3-connected planar graphs with fixing number 3.Comment: 34 pages, 3 figures, extended version of LICS 2017 pape

On Iterative Pre‐Compensation of 3D Laser‐Printed Micro‐Optical Components Using Confocal‐Optical Microscopy

State-of-the-art 3D two-photon laser printing systems already use pre-compensation algorithms to reduce systematic deviations between the printed and the targeted structures. Nevertheless, the remaining deviations are often still larger than the uncontrollable or “statistical” deviations. In principle, it is straightforward to correct for systematic deviations by measuring the difference between printed structure and target and by subtracting the difference from the first target to obtain the next-iteration target. However, in reality, one faces several issues such as noise and systematic errors of the characterization measurement itself, as well as unwanted translations and rotations between the coordinate systems of the characterization setup and the printer, respectively. Two examples of printed structures requiring sub-micrometer accuracy are considered, a large 1D micro-lens array and a specific diffractive optical element. For both, the device performance before the pre-compensation workflow described herein is insufficient for the targeted application and has become sufficient after this workflow. The workflow involving optimizations using cross-correlations with confocal-optical-microscopy data is documented by an open-access program (available via GitLab). This program includes an easy-to-use graphical user interface so that other researchers can immediately profit from it

Rapid Assembly of Small Materials Building Blocks (Voxels) into Large Functional 3D Metamaterials

Herein, various 3D additive manufacturing approaches are reviewed in terms of two important figures of merit: maximum voxel printing rate and minimum voxel size. Voxel sizes from several 100 µm down to the 100 nm scale are covered. Original results on multifocus two‐photon printing at around voxel printing rates of 107 voxels s−1 are presented in this context, which significantly surpass previous best values. These advances are illustrated by and applied to the making of microstructured 3D (chiral) mechanical metamaterials that are composed of more than one‐hundred‐thousand unit cells in three dimensions. Previous best values for unit cells of similar complexity are smaller by two orders of magnitude

Large characteristic lengths in 3D chiral elastic metamaterials

Three-dimensional (3D) chiral mechanical metamaterials enable behaviors not accessible in ordinary materials. In particular, a coupling between displacements and rotations can occur, which is symmetry-forbidden without chirality. In this work, we solve three open challenges of chiral metamaterials. First, we provide a simple analytical model, which we use to rationalize the design of the chiral characteristic length. Second, using rapid multi-photon multi-focus 3D laser microprinting, we manufacture samples with more than 105 micrometer-sized 3D chiral unit cells. This number surpasses previous work by more than two orders of magnitude. Third, using analytical and numerical modeling, we realize chiral characteristic lengths of the order of ten unit cells, changing the sample-size dependence qualitatively and quantitatively. In the small-sample limit, the twist per axial strain is initially proportional to the sample side length, reaching a maximum at the characteristic length. In the thermodynamic limit, the twist per axial strain is proportional to the square of the characteristic length. We show that chiral micropolar continuum elasticity can reproduce this behavior

QMEAN server for protein model quality estimation

Model quality estimation is an essential component of protein structure prediction, since ultimately the accuracy of a model determines its usefulness for specific applications. Usually, in the course of protein structure prediction a set of alternative models is produced, from which subsequently the most accurate model has to be selected. The QMEAN server provides access to two scoring functions successfully tested at the eighth round of the community-wide blind test experiment CASP. The user can choose between the composite scoring function QMEAN, which derives a quality estimate on the basis of the geometrical analysis of single models, and the clustering-based scoring function QMEANclust which calculates a global and local quality estimate based on a weighted all-against-all comparison of the models from the ensemble provided by the user. The web server performs a ranking of the input models and highlights potentially problematic regions for each model. The QMEAN server is available at http://swissmodel.expasy.org/qmean

Planetary system architectures with low-mass inner planets: Direct imaging exploration of mature systems beyond 1 au

The discovery of planets orbiting at less than 1 au from their host star and less massive than Saturn in various exoplanetary systems revolutionized our theories of planetary formation. The fundamental question is whether these close-in low-mass planets could have formed in the inner disk interior to 1 au, or whether they formed further out in the planet-forming disk and migrated inward. Exploring the role of additional giant planets in these systems may help us to pinpoint their global formation and evolution. We searched for additional substellar companions by using direct imaging in systems known to host close-in small planets. The use of direct imaging complemented by radial velocity and astrometric detection limits enabled us to explore the giant planet and brown dwarf demographics around these hosts to investigate the potential connection between both populations. We carried out a direct imaging survey with VLT/SPHERE to look for outer giant planets and brown dwarf companions in 27 systems hosting close-in low-mass planets discovered by radial velocity. Our sample is composed of very nearby (<20pc) planetary systems, orbiting G-, K-, and M-type mature (0.5-10Gyr) stellar hosts. We performed homogeneous direct imaging data reduction and analysis to search for and characterize point sources, and derived robust statistical detection limits. Of 337 point-source detections, we do not find any new bound companions. We recovered the emblematic very cool T-type brown dwarf GJ229B. Our typical sensitivities in direct imaging range from 5 to 30 MJup beyond 2 au. The non-detection of massive companions is consistent with predictions based on models of planet formation by core accretion. Our pilot study opens the way to a multi-technique approach for the exploration of very nearby exoplanetary systems with future ground-based and space observatories.Comment: 49 pages including 31 pages of appendices and references, 31 figures, A&A, accepte

Incommensurate atomic and magnetic modulations in the spin-frustrated β−NaMnO2β-NaMnO_2 triangular lattice

The layered $β-NaMnO_2$, a promising Na-ion energy-storage material, has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q = (0.077(1), 0, 0) structure. Here $Mn^{3+}$ Jahn-Teller distorted $MnO_6$ octahedra form corrugated layer stacking sequences of the $β-NaMnO_2$ type, which are interrupted by flat sheets of the α-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector $k = (_{1/2,1/2,1/2})$, appears below $T_{N1} = 200 K$. Moreover, a second transition into a spatially modulated properscrew magnetic state (k ± q) is established at $T_{N2} = 95 K$, with an antiferromagnetic order parameter resembling that of a two-dimensional (2D) system. The evolution of $^{23}Na$ NMR spin-lattice relaxation identifies a magnetically inhomogeneous state in the intermediate $T$ region $(T_{N2} <T <T_{N1})$, while its strong suppression below $T_{N2}$ indicates that a spin gap opens in the excitation spectrum. High-resolution neutron inelastic scattering confirms that the magnetic dynamics are indeed gapped (Δ∼5 meV) in the low-temperature magnetic phase, while simulations on the basis of the single-mode approximation suggest that Mn spins residing on adjacent antiferromagnetic chains, establish sizable 2D correlations. Our analysis points out that novel structural degrees of freedom promote cooperative magnetism and emerging dielectric properties in this nonperovskite type of manganite

The Osteopontin Level in Liver, Adipose Tissue and Serum Is Correlated with Fibrosis in Patients with Alcoholic Liver Disease

<div><h3>Background</h3><p>Osteopontin (OPN) plays an important role in the progression of chronic liver diseases. We aimed to quantify the liver, adipose tissue and serum levels of OPN in heavy alcohol drinkers and to compare them with the histological severity of hepatic inflammation and fibrosis.</p> <h3>Methodology/Principal Findings</h3><p>OPN was evaluated in the serum of a retrospective and prospective group of 109 and 95 heavy alcohol drinkers, respectively, in the liver of 34 patients from the retrospective group, and in the liver and adipose tissue from an additional group of 38 heavy alcohol drinkers. Serum levels of OPN increased slightly with hepatic inflammation and progressively with the severity of hepatic fibrosis. Hepatic OPN expression correlated with hepatic inflammation, fibrosis, TGFβ expression, neutrophils accumulation and with the serum OPN level. Interestingly, adipose tissue OPN expression also correlated with hepatic fibrosis even after 7 days of alcohol abstinence. The elevated serum OPN level was an independent risk factor in estimating significant (F≥2) fibrosis in a model combining alkaline phosphatase, albumin, hemoglobin, OPN and FibroMeter® levels. OPN had an area under the receiving operator curve that estimated significant fibrosis of 0.89 and 0.88 in the retrospective and prospective groups, respectively. OPN, Hyaluronate (AUROC: 0.88), total Cytokeratin 18 (AUROC: 0.83) and FibroMeter® (AUROC: 0.90) estimated significance to the same extent in the retrospective group. Finally, the serum OPN levels also correlated with hepatic fibrosis and estimated significant (F≥2) fibrosis in 86 patients with chronic hepatitis C, which suggested that its elevated level could be a general response to chronic liver injury.</p> <h3>Conclusion/Significance</h3><p>OPN increased in the liver, adipose tissue and serum with liver fibrosis in alcoholic patients. Further, OPN is a new relevant biomarker for significant liver fibrosis. OPN could thus be an important actor in the pathogenesis of this chronic liver disease.</p> </div

Insights into the Mechanism of Bovine CD38/NAD+Glycohydrolase from the X-Ray Structures of Its Michaelis Complex and Covalently-Trapped Intermediates

Bovine CD38/NAD+glycohydrolase (bCD38) catalyses the hydrolysis of NAD+ into nicotinamide and ADP-ribose and the formation of cyclic ADP-ribose (cADPR). We solved the crystal structures of the mono N-glycosylated forms of the ecto-domain of bCD38 or the catalytic residue mutant Glu218Gln in their apo state or bound to aFNAD or rFNAD, two 2′-fluorinated analogs of NAD+. Both compounds behave as mechanism-based inhibitors, allowing the trapping of a reaction intermediate covalently linked to Glu218. Compared to the non-covalent (Michaelis) complex, the ligands adopt a more folded conformation in the covalent complexes. Altogether these crystallographic snapshots along the reaction pathway reveal the drastic conformational rearrangements undergone by the ligand during catalysis with the repositioning of its adenine ring from a solvent-exposed position stacked against Trp168 to a more buried position stacked against Trp181. This adenine flipping between conserved tryptophans is a prerequisite for the proper positioning of the N1 of the adenine ring to perform the nucleophilic attack on the C1′ of the ribofuranoside ring ultimately yielding cADPR. In all structures, however, the adenine ring adopts the most thermodynamically favorable anti conformation, explaining why cyclization, which requires a syn conformation, remains a rare alternate event in the reactions catalyzed by bCD38 (cADPR represents only 1% of the reaction products). In the Michaelis complex, the substrate is bound in a constrained conformation; the enzyme uses this ground-state destabilization, in addition to a hydrophobic environment and desolvation of the nicotinamide-ribosyl bond, to destabilize the scissile bond leading to the formation of a ribooxocarbenium ion intermediate. The Glu218 side chain stabilizes this reaction intermediate and plays another important role during catalysis by polarizing the 2′-OH of the substrate NAD+. Based on our structural analysis and data on active site mutants, we propose a detailed analysis of the catalytic mechanism

Two warm Neptunes transiting HIP 9618 revealed by TESS and Cheops

peer reviewedHIP 9618 (HD 12572, TOI-1471, TIC 306263608) is a bright (G = 9.0 mag) solar analogue. TESS photometry revealed the star to have two candidate planets with radii of 3.9 ± 0.044 R (HIP 9618 b) and 3.343 ± 0.039 R (HIP 9618 c). While the 20.77291 d period of HIP 9618 b was measured unambiguously, HIP 9618 c showed only two transits separated by a 680-d gap in the time series, leaving many possibilities for the period. To solve this issue, CHEOPS performed targeted photometry of period aliases to attempt to recover the true period of planet c, and successfully determined the true period to be 52.56349 d. High-resolution spectroscopy with HARPS-N, SOPHIE, and CAFE revealed a mass of 10.0 ± 3.1M for HIP 9618 b, which, according to our interior structure models, corresponds to a 6.8 ± 1.4 per cent gas fraction. HIP 9618 c appears to have a lower mass than HIP 9618 b, with a 3-sigma upper limit of 50 d, opening the door for the atmospheric characterization of warm (Teq < 750 K) sub-Neptunes