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Many image processing problems require the enhancement of crossing elongated structures. These problems cannot easily be solved by commonly used coherence-enhancing diffusion methods. Therefore, we propose a method for coherence-enhancing diffusion on the invertible orientation score of a 2D image. In an orientation score, the local orientation is represented by an additional third dimension, ensuring that crossing elongated structures are separated from each other. We consider orientation scores as functions on the Euclidean motion group, and use the group structure to apply left-invariant diffusion equations on orientation scores. We describe how we can calculate regularized left-invariant derivatives, and use the Hessian to estimate three descriptive local features: curvature, deviation from horizontality, and orientation confidence. These local features are used to adapt a nonlinear coherence-enhancing, crossing-preserving, diffusion equation on the orientation score. We propose two explicit finite-difference schemes to apply the nonlinear diffusion in the orientation score and provide a stability analysis. Experiments on both artificial and medical images show that preservation of crossings is the main advantage compared to standard coherence-enhancing diffusion. The use of curvature leads to improved enhancement of curves with high curvature. Furthermore, the use of deviation from horizontality makes it feasible to reduce the number of sampled orientations while still preserving crossings.

Additive manufacturing (AM) of metals, also known as metal 3D printing, typically leads to the formation of columnar grain structures along the build direction in most as-built metals and alloys. These long columnar grains can cause property anisotropy, which is usually detrimental to component qualification or targeted applications. Here, without changing alloy chemistry, we demonstrate an AM solidification-control solution to printing metallic alloys with an equiaxed grain structure and improved mechanical properties. Using the titanium alloy Ti-6Al-4V as a model alloy, we employ high-intensity ultrasound to achieve full transition from columnar grains to fine (~100 µm) equiaxed grains in AM Ti-6Al-4V samples by laser powder deposition. This results in a 12% improvement in both the yield stress and tensile strength compared with the conventional AM columnar Ti-6Al-4V. We further demonstrate the generality of our technique by achieving similar grain structure control results in the nickel-based superalloy Inconel 625, and expect that this method may be applicable to other metallic materials that exhibit columnar grain structures during AM. 3D printing of metals produces elongated columnar grains which are usually detrimental to component performance. Here, the authors combine ultrasound and 3D printing to promote equiaxed and refined microstructures in a titanium alloy and a nickel-based superalloy resulting in improved mechanical properties.

Leaf photosynthesis, coral mineralization, and trabecular bone growth depend on triply periodic minimal surfaces (TPMSs) with hyperboloidal structure on every surface point with varying Gaussian curvatures. However, translation of this structure into tissueengineered bone grafts is challenging. This article reports the design and fabrication of high-resolution three-dimensional TPMS scaffolds embodying biomimicking hyperboloidal topography with different Gaussian curvatures, composed of body inherent β-tricalcium phosphate, by stereolithography-based three-dimensional printing and sintering. The TPMS bone scaffolds show high porosity and interconnectivity. Notably, compared with conventional scaffolds, they can reduce stress concentration, leading to increased mechanical strength. They are also found to support the attachment, proliferation, osteogenic differentiation, and angiogenic paracrine function of human mesenchymal stem cells (hMSCs). Through transcriptomic analysis, we theorize that the hyperboloid structure induces cytoskeleton reorganization of hMSCs, expressing elongated morphology on the convex direction and strengthening the cytoskeletal contraction. The clinical therapeutic efficacy of the TPMS scaffolds assessed by rabbit femur defect and mouse subcutaneous implantation models demonstrate that the TPMS scaffolds augment new bone formation and neovascularization. In comparison with conventional scaffolds, our TPMS scaffolds successfully guide the cell fate toward osteogenesis through cell-level directional curvatures and demonstrate drastic yet quantifiable improvements in bone regeneration.

Various types of structures self-organised by animals exist in nature, such as bird flocks and insect swarms, which stem from the local communications of vast numbers of limited individuals. Through the designing of algorithms and wireless communication, robotic systems can emulate some complex swarm structures in nature. However, creating a swarming robotic system at the microscale that embodies functional collective behaviours remains a challenge. Herein, we report a strategy to reconfigure paramagnetic nanoparticles into ribbon-like swarms using oscillating magnetic fields, and the mechanisms are analysed. By tuning the input fields, the microswarm can perform a reversible elongation with an extremely high aspect ratio, as well as splitting and merging. Moreover, we investigate the behaviours of the microswarm when it encounters solid boundaries, and demonstrate that under navigation, the colloidal microswarm passes through confined channel networks towards multiple targets with high access rates and high swarming pattern stability. Manipulation of paramagnetic microparticles can be exploited for drug delivery. Here the authors manipulate a swarm of such particles and control its shape with a magnetic field so that it can elongate reversibly, split into smaller swarms and thus be guided through a maze with multiple parallel channels.

The enzyme protochlorophyllide oxidoreductase (POR) catalyses a light-dependent step in chlorophyll biosynthesis that is essential to photosynthesis and, ultimately, all life on Earth 1 – 3 . POR, which is one of three known light-dependent enzymes 4 , 5 , catalyses reduction of the photosensitizer and substrate protochlorophyllide to form the pigment chlorophyllide. Despite its biological importance, the structural basis for POR photocatalysis has remained unknown. Here we report crystal structures of cyanobacterial PORs from Thermosynechococcus elongatus and Synechocystis sp. in their free forms, and in complex with the nicotinamide coenzyme. Our structural models and simulations of the ternary protochlorophyllide–NADPH–POR complex identify multiple interactions in the POR active site that are important for protochlorophyllide binding, photosensitization and photochemical conversion to chlorophyllide. We demonstrate the importance of active-site architecture and protochlorophyllide structure in driving POR photochemistry in experiments using POR variants and protochlorophyllide analogues. These studies reveal how the POR active site facilitates light-driven reduction of protochlorophyllide by localized hydride transfer from NADPH and long-range proton transfer along structurally defined proton-transfer pathways. Crystal structures of cyanobacterial protochlorophyllide oxidoreductases reveal the basis of the photocatalytic activities of this enzyme, through the role of its active site in enabling the light-driven reduction of protochlorophyllide.

Hybrid organic–inorganic perovskites have attractive optoelectronic properties including exceptional solar cell performance. The improved properties of perovskites have been attributed to polaronic effects involving stabilization of localized charge character by structural deformations and polarizations. Here we examine the Pb–I structural dynamics leading to polaron formation in methylammonium lead iodide perovskite by transient absorption, time-domain Raman spectroscopy, and density functional theory. Methylammonium lead iodide perovskite exhibits excited-state coherent nuclear wave packets oscillating at ~20, ~43, and ~75 cm −1 which involve skeletal bending, in-plane bending, and c -axis stretching of the I–Pb–I bonds, respectively. The amplitudes of these wave packet motions report on the magnitude of the excited-state structural changes, in particular, the formation of a bent and elongated octahedral PbI 6 4− geometry. We have predicted the excited-state geometry and structural changes between the neutral and polaron states using a normal-mode projection method, which supports and rationalizes the experimental results. This study reveals the polaron formation via nuclear dynamics that may be important for efficient charge separation. Elucidating electron-phonon coupling in hybrid organic-inorganic perovskites may help us to understand the high photovoltaic efficiency. Here, the authors observe low-frequency Raman modes and related nuclear displacements of the Pb–I framework, indicating how these vibrational motions lead to polaron formation in perovskites.

An archetypical layered topological insulator Bi2Se3 becomes superconductive upon doping with Sr, Nb or Cu. Superconducting properties of these materials in the presence of in-plane magnetic field demonstrate spontaneous symmetry breaking: 180◦-rotation symmetry of superconductivity versus 120◦-rotation symmetry of the crystal. Such behavior brilliantly confirms nematic topological superconductivity. To what extent this nematicity is due to superconducting pairing in these materials, rather than due to crystal structure distortions? This question remains unanswered, because so far no visible deviations from the 3-fold crystal symmetry were resolved in these materials. To address this question we grow high quality single crystals of SrxBi2Se3, perform detailed x-ray diffraction and magnetotransport studies and reveal that the observed superconducting nematicity direction correlates with the direction of small structural distortions in these samples (∼0.02% elongation in one crystallographic direction). Additional anisotropy comes from orientation of the crystallite axes. 2-fold symmetry of magnetoresistance observed in the most uniform crystals well above the critical temperature demonstrates that these structural distortions are nevertheless strong enough. Our data in combination with strong sample-to-sample variation of the superconductive anisotropy parameter are indicative for significance of the structural factor in the apparent nematic superconductivity in SrxBi2Se3.

Although the principles of noncovalent bonding are well understood and form the basis for the syntheses of many intricate supramolecular structures, supramolecular noncovalent synthesis cannot yet achieve the levels of precision and complexity that are attainable in organic and/or macromolecular covalent synthesis. Here we show the stepwise synthesis of block supramolecular polymers from metal–porphyrin derivatives (in which the metal centre is Zn, Cu or Ni) functionalized with fluorinated alkyl chains. These monomers first undergo a one-dimensional supramolecular polymerization and cyclization process to form a toroidal structure. Subsequently, successive secondary nucleation, elongation and cyclization steps result in two-dimensional assemblies with concentric toroidal morphologies. The site selectivity endowed by the fluorinated chains, reminiscent of regioselectivity in covalent synthesis, enables the precise control of the compositions and sequences of the supramolecular structures, as demonstrated by the synthesis of several triblock supramolecular terpolymers.Supramolecular structures are typically formed by the one-step self-assembly of building blocks. Now, a greater level of control has been achieved using stepwise non-covalent reactions under kinetic control. Two-dimensional block supramolecular polymers with tailored compositions and sequences were synthesized, and a site selectivity that is reminiscent of regioselectivity in covalent synthesis was observed.

Metazoan gene regulation often involves the pausing of RNA polymerase II (Pol II) in the promoter-proximal region. Paused Pol II is stabilized by the protein complexes DRB sensitivity-inducing factor (DSIF) and negative elongation factor (NELF). Here we report the cryo-electron microscopy structure of a paused transcription elongation complex containing Sus scrofa Pol II and Homo sapiens DSIF and NELF at 3.2 Å resolution. The structure reveals a tilted DNA–RNA hybrid that impairs binding of the nucleoside triphosphate substrate. NELF binds the polymerase funnel, bridges two mobile polymerase modules, and contacts the trigger loop, thereby restraining Pol II mobility that is required for pause release. NELF prevents binding of the anti-pausing transcription elongation factor IIS (TFIIS). Additionally, NELF possesses two flexible ‘tentacles’ that can contact DSIF and exiting RNA. These results define the paused state of Pol II and provide the molecular basis for understanding the function of NELF during promoter-proximal gene regulation. The cryo-electron microscopy structure of a paused transcription elongation complex of RNA polymerase II bound to DRB sensitivity-inducing factor and negative elongation factor is reported at 3.2 Å resolution.

We study the structure of high-speed zero-pressure-gradient turbulent boundary layers up to friction Reynolds number $Re_{\\tau } \\approx 2000$ using direct numerical simulation of the Navier–Stokes equations. Both supersonic and hypersonic conditions with nominal free-stream Mach numbers $M_{\\infty }=2$, $M_{\\infty }=5.86$ and heat transfer at the wall are considered. The present simulations extend the database currently available for wall-bounded flows, enabling us to explore high-Reynolds-number effects even in the hypersonic regime. We first analyse the instantaneous fields to characterize the structure of both velocity and temperature fluctuations. In all cases elongated strips of uniform velocity and temperature (superstructures) are observed in the outer portion of the boundary layer, characterized by a clear association between low-/high-speed momentum and high/low temperature streaks. The results highlight important deviations from the typical organization observed in the inner region of adiabatic boundary layers, revealing that the near-wall temperature streaks disappear in strongly non-adiabatic flow cases. We also focus on the structural properties of regions of uniform streamwise momentum (De Silva, Hutchins & Marusic, J. Fluid Mech., vol. 786, 2016, pp. 309–331) observed in turbulent boundary layers, confirming the presence of such zones in the high-speed regime at high Reynolds number and revealing the existence of similar regions for the temperature field. The accuracy of different compressibility transformations and temperature–velocity relations is assessed extending their range of validation to moderate/high Reynolds numbers. Spanwise spectral densities of the velocity and temperature fluctuations at various wall distances have been calculated revealing the energy content and the size of the turbulent eddies across the boundary layer. Finally, we propose a revised scaling for the characteristic length scales, that is based on the local mean shear computed according to the recent theory by Griffin, Fu & Moin [Proc. Natl Acad. Sci. USA, vol. 118 (34)].