A molecular strand can be knotted and unknotted into three different topologies, depending on the complexing metal ion used (copper or lanthanide or none). The properties of knots are exploited in a range of applications, from shoelaces to the knots used for climbing, fishing and sailing(1). Although knots are found in DNA and proteins(2), and form randomly in other long polymer chains(3,4), methods for tying(5)different sorts of knots in a synthetic nanoscale strand are lacking. Molecular knots of high symmetry have previously been synthesized by using non-covalent interactions to assemble and entangle molecular chains(6-15), but in such instances the template and/or strand structure intrinsically determines topology, which means that only one type of knot is usually possible. Here we show that interspersing coordination sites for different metal ions within an artificial molecular strand enables it to be tied into multiple knots. Three topoisomers-an unknot (0(1)) macrocycle, a trefoil (3(1)) knot(6-15), and a three-twist (5(2)) knot-were each selectively prepared from the same molecular strand by using transition-metal and lanthanide ions to guide chain folding in a manner reminiscent of the action of protein chaperones(16). We find that the metal-ion-induced folding can proceed with stereoinduction: in the case of one knot, a lanthanide(iii)-coordinated crossing pattern formed only with a copper(i)-coordinated crossing of particular handedness. In an unanticipated finding, metal-ion coordination was also found to translocate an entanglement from one region of a knotted molecular structure to another, resulting in an increase in writhe (topological strain) in the new knotted conformation. The knot topology affects the chemical properties of the strand: whereas the tighter 5(2)knot can bind two different metal ions simultaneously, the looser 3(1)isomer can bind only either one copper(i) ion or one lutetium(iii) ion. The ability to tie nanoscale chains into different knots offers opportunities to explore the modification of the structure and properties of synthetic oligomers, polymers and supramolecules.

Fast radio bursts (FRBs) are millisecond-duration radio transients(1,2) of unknown origin. Two possible mechanisms that could generate extremely coherent emission from FRBs invoke neutron star magnetospheres(3-5) or relativistic shocks far from the central energy source(6-8). Detailed polarization observations may help us to understand the emission mechanism. However, the available FRB polarization data have been perplexing, because they show a host of polarimetric properties, including either a constant polarization angle during each burst for some repeaters(9,10) or variable polarization angles in some other apparently one-off events(11,12). Here we report observations of 15 bursts from FRB 180301 and find various polarization angle swings in seven of them. The diversity of the polarization angle features of these bursts is consistent with a magnetospheric origin of the radio emission, and disfavours the radiation models invoking relativistic shocks.

One of the key challenges for nuclear physics today is to understand from first principles the effective interaction between hadrons with different quark content. First successes have been achieved using techniques that solve the dynamics of quarks and gluons on discrete space-time lattices(1,2). Experimentally, the dynamics of the strong interaction have been studied by scattering hadrons off each other. Such scattering experiments are difficult or impossible for unstable hadrons(3-6) and so high-quality measurements exist only for hadrons containing up and down quarks(7). Here we demonstrate that measuring correlations in the momentum space between hadron pairs(8-12) produced in ultrarelativistic proton-proton collisions at the CERN Large Hadron Collider (LHC) provides a precise method with which to obtain the missing information on the interaction dynamics between any pair of unstable hadrons. Specifically, we discuss the case of the interaction of baryons containing strange quarks (hyperons). We demonstrate how, using precision measurements of proton-omega baryon correlations, the effect of the strong interaction for this hadron-hadron pair can be studied with precision similar to, and compared with, predictions from lattice calculations(13,14). The large number of hyperons identified in proton-proton collisions at the LHC, together with accurate modelling(15) of the small (approximately one femtometre) inter-particle distance and exact predictions for the correlation functions, enables a detailed determination of the short-range part of the nucleon-hyperon interaction.

Tissue sculpting during development has been attributed mainly to cellular events through processes such as convergent extension or apical constriction(1,2.) However, recent work has revealed roles for basement membrane remodelling in global tissue morphogenesis(3-5). Upon implantation, the epiblast and extraembryonic ectoderm of the mouse embryo become enveloped by a basement membrane. Signalling between the basement membrane and these tissues is critical for cell polarization and the ensuing morphogenesis(6,7). However, the mechanical role of the basement membrane in post-implantation embryogenesis remains unknown. Here we demonstrate the importance of spatiotemporally regulated basement membrane remodelling during early embryonic development. Specifically, we show that Nodal signalling directs the generation and dynamic distribution of perforations in the basement membrane by regulating the expression of matrix metalloproteinases. This basement membrane remodelling facilitates embryo growth before gastrulation. The establishment of the anterior-posterior axis(8,9) further regulates basement membrane remodelling by localizing Nodal signalling-and therefore the activity of matrix metalloproteinases and basement membrane perforations-to the posterior side of the embryo. Perforations on the posterior side are essential for primitive-streak extension during gastrulation by rendering the basement membrane of the prospective primitive streak more prone to breaching. Thus spatiotemporally regulated basement membrane remodelling contributes to the coordination of embryo growth, morphogenesis and gastrulation.

Decrease in processing speed due to increased resistance and capacitance delay is a major obstacle for the down-scaling of electronics(1-3). Minimizing the dimensions of interconnects (metal wires that connect different electronic components on a chip) is crucial for the miniaturization of devices. Interconnects are isolated from each other by non-conducting (dielectric) layers. So far, research has mostly focused on decreasing the resistance of scaled interconnects because integration of dielectrics using low-temperature deposition processes compatible with complementary metal-oxide-semiconductors is technically challenging. Interconnect isolation materials must have low relative dielectric constants (kappa values), serve as diffusion barriers against the migration of metal into semiconductors, and be thermally, chemically and mechanically stable. Specifically, the International Roadmap for Devices and Systems recommends(4) the development of dielectrics with kappa values of less than 2 by 2028. Existing low-kappa materials (such as silicon oxide derivatives, organic compounds and aerogels) have kappa values greater than 2 and poor thermo-mechanical properties(5). Here we report three-nanometre-thick amorphous boron nitride films with ultralow kappa values of 1.78 and 1.16 (close to that of air, kappa = 1) at operation frequencies of 100 kilohertz and 1 megahertz, respectively. The films are mechanically and electrically robust, with a breakdown strength of 7.3 megavolts per centimetre, which exceeds requirements. Cross-sectional imaging reveals that amorphous boron nitride prevents the diffusion of cobalt atoms into silicon under very harsh conditions, in contrast to reference barriers. Our results demonstrate that amorphous boron nitride has excellent low-kappa dielectric characteristics for high-performance electronics.

The fine-structure constant is determined with an accuracy of 81 parts per trillion using matter-wave interferometry to measure the rubidium atom recoil velocity. The standard model of particle physics is remarkably successful because it is consistent with (almost) all experimental results. However, it fails to explain dark matter, dark energy and the imbalance between matter and antimatter in the Universe. Because discrepancies between standard-model predictions and experimental observations may provide evidence of new physics, an accurate evaluation of these predictions requires highly precise values of the fundamental physical constants. Among them, the fine-structure constant alpha is of particular importance because it sets the strength of the electromagnetic interaction between light and charged elementary particles, such as the electron and the muon. Here we use matter-wave interferometry to measure the recoil velocity of a rubidium atom that absorbs a photon, and determine the fine-structure constant alpha(-1) = 137.035999206(11) with a relative accuracy of 81 parts per trillion. The accuracy of eleven digits in alpha leads to an electron g factor(1,2)-the most precise prediction of the standard model-that has a greatly reduced uncertainty. Our value of the fine-structure constant differs by more than 5 standard deviations from the best available result from caesium recoil measurements(3). Our result modifies the constraints on possible candidate dark-matter particles proposed to explain the anomalous decays of excited states of Be-8 nuclei(4) and paves the way for testing the discrepancy observed in the magnetic moment anomaly of the muon(5) in the electron sector(6).