Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Four-electron deoxygenative reductive coupling of carbon monoxide at a single metal site

Carbon dioxide is the ultimate source of the fossil fuels that are both central to modern life and problematic: their use increases atmospheric levels of greenhouse gases, and their availability is geopolitically constrained. Using carbon dioxide as a feedstock to produce synthetic fuels might, in principle, alleviate these concerns. Although many homogeneous and heterogeneous catalysts convert carbon dioxide to carbon monoxide, further deoxygenative coupling of carbon monoxide to generate useful multicarbon products is challenging. Molybdenum and vanadium nitrogenases are capable of converting carbon monoxide into hydrocarbons under mild conditions, using discrete electron and proton sources. Electrocatalytic reduction of carbon monoxide on copper catalysts also uses a combination of electrons and protons, while the industrial Fischer–Tropsch process uses dihydrogen as a combined source of electrons and electrophiles for carbon monoxide coupling at high temperatures and pressures6. However, these enzymatic and heterogeneous systems are difficult to probe mechanistically. Molecular catalysts have been studied extensively to investigate the elementary steps by which carbon monoxide is deoxygenated and coupled, but a single metal site that can efficiently induce the required scission of carbon–oxygen bonds and generate carbon–carbon bonds has not yet been documented. Here we describe a molybdenum compound, supported by a terphenyl–diphosphine ligand, that activates and cleaves the strong carbon–oxygen bond of carbon monoxide, enacts carbon–carbon coupling, and spontaneously dissociates the resulting fragment. This complex four-electron transformation is enabled by the terphenyl–diphosphine ligand, which acts as an electron reservoir and exhibits the coordinative flexibility needed to stabilize the different intermediates involved in the overall reaction sequence. We anticipate that these design elements might help in the development of efficient catalysts for converting carbon monoxide to chemical fuels, and should prove useful in the broader context of performing complex multi-electron transformations at a single metal site

On the Enigma of Glutathione-Dependent Styrene Degradation in Gordonia rubripertincta CWB2

Heine T, Zimmerling J, Ballmann A, et al. On the Enigma of Glutathione-Dependent Styrene Degradation in Gordonia rubripertincta CWB2. APPLIED AND ENVIRONMENTAL MICROBIOLOGY. 2018;84(9): 16.Among bacteria, only a single styrene-specific degradation pathway has been reported so far. It comprises the activity of styrene monooxygenase, styrene oxide isomerase, and phenylacetaldehyde dehydrogenase, yielding phenylacetic acid as the central metabolite. The alternative route comprises ring-hydroxylating enzymes and yields vinyl catechol as central metabolite, which undergoes meta-cleavage. This was reported to be unspecific and also allows the degradation of benzene derivatives. However, some bacteria had been described to degrade styrene but do not employ one of those routes or only parts of them. Here, we describe a novel "hybrid" degradation pathway for styrene located on a plasmid of foreign origin. As putatively also unspecific, it allows metabolizing chemically analogous compounds (e.g., halogenated and/or alkylated styrene derivatives). Gordonia rubripertincta CWB2 was isolated with styrene as the sole source of carbon and energy. It employs an assembled route of the styrene side-chain degradation and isoprene degradation pathways that also funnels into phenylacetic acid as the central metabolite. Metabolites, enzyme activity, genome, transcriptome, and proteome data reinforce this observation and allow us to understand this biotechnologically relevant pathway, which can be used for the production of ibuprofen. IMPORTANCE The degradation of xenobiotics by bacteria is not only important for bioremediation but also because the involved enzymes are potential catalysts in biotechnological applications. This study reveals a novel degradation pathway for the hazardous organic compound styrene in Gordonia rubripertincta CWB2. This study provides an impressive illustration of horizontal gene transfer, which enables novel metabolic capabilities. This study presents glutathione-dependent styrene metabolization in an (actino-) bacterium. Further, the genomic background of the ability of strain CWB2 to produce ibuprofen is demonstrated

Path integration over closed loops and Gutzwiller's trace formula

In 1967 M.C. Gutzwiller succeeded to derive the semiclassical expression of the quantum energy density of systems exhibiting a chaotic Hamiltonian dynamics in the classical limit. The result is known as the Gutzwiller trace formula. The scope of this review is to present in a self-contained way recent developments in functional determinant theory allowing to revisit the Gutzwiller trace formula in the spirit of field theory. The field theoretic setup permits to work explicitly at every step of the derivation of the trace formula with invariant quantities of classical periodic orbits. R. Forman's theory of functional determinants of linear, non singular elliptic operators yields the expression of quantum quadratic fluctuations around classical periodic orbits directly in terms of the monodromy matrix of the periodic orbits. The phase factor associated to quadratic fluctuations, the Maslov phase, is shown to be specified by the Morse index for closed extremals, also known as Conley and Zehnder index.Comment: Preprint, revised version 132 pages in pdf format. Comments welcom

Miocene waterfowl and other birds from central Otago, New Zealand

Copyright © The Natural History Museum 2007Abundant fossil bird bones from the lower Bannockburn Formation, Manuherikia Group, an Early-Middle Miocene lacustrine deposit, 16–19 Ma, from Otago in New Zealand, reveal the “St Bathans Fauna” (new name), a first Tertiary avifauna of land and freshwater birds from New Zealand. At least 23 species of birds are represented by bones, and probable moa, Aves: Dinornithiformes, by eggshell. Anatids dominate the fauna with four genera and five species described as new: a sixth and largest anatid species is represented by just one bone. This is the most diverse Early-Middle Miocene duck fauna known worldwide. Among ducks, two species of dendrochenines are most numerous in the fauna, but a tadornine is common as well. A diving petrel (Pelecanoididae: Pelecanoides) is described, so extending the geological range of this genus worldwide from the Pliocene to the Middle Miocene, at least. The remaining 16 taxa are left undescribed but include: a large species of gull (Laridae); two small waders (Charadriiformes, genus indet.), the size of Charadrius bicinctus and Calidris ruficollis, respectively; a gruiform represented by one specimen similar to Aptornis; abundant rail (Rallidae) bones, including a common flightless rail and a rarer slightly larger taxon, about the size of Gallirallus philippensis; an ?eagle (Accipitridae); a pigeon (Columbidae); three parrots (Psittacidae); an owlet nightjar (Aegothelidae: Aegotheles sp.); a swiftlet (Apodidae: Collocalia sp.); and three passerine taxa, of which the largest is a member of the Cracticidae. The absence of some waterbirds, such as anserines (including swans), grebes (Podicipedidae) and shags (Phalacrocoracidae), among the abundant bones, indicates their probable absence from New Zealand in the Early-Middle Miocene.T. H. Worthy, A. J. D. Tennyson, C. Jones, J. A. McNamara and B. J. Dougla

Mass Mortality Caused by Highly Pathogenic Influenza A(H5N1) Virus in Sandwich Terns, the Netherlands, 2022

We collected data on mass mortality in Sandwich terns (Thalasseus sandvicensis) during the 2022 breeding season in the Netherlands. Mortality was associated with at least 2 variants of highly pathogenic avian influenza A(H5N1) virus clade 2.3.4.4b. We report on carcass removal efforts relative to survival in colonies. Mitigation strategies urgently require structured research

Small Molecule Activation by Uranium Tris(aryloxides): Experimental and Computational Studies of Binding of N-2, Coupling of CO, and Deoxygenation Insertion of CO2 under Ambient Conditions

Previously unanticipated dinitrogen activation is exhibited by the well-known uranium tris(aryloxide) U(ODtbp)(3), U(OC6H3-Bu-2(t)-2,6)(3), and the tri-tert-butyl analogue U(OTtbp)(3), U(OC6H2-Bu-3(t)-2,4,6)(3), in the form of bridging, side-on dinitrogen complexes [U(OAr)(3)](2)(mu-eta(2):eta(2)-N-2), for which the tri-tert-butyl N-2 complex is the most robust U-2(N-2) complex isolated to date. Attempted reduction of the tris(aryloxide) complex under N-2 gave only the potassium salt of the uranium(III) tetra(aryloxide) anion, K[U(OAr)(4)], as a result of ligand redistribution. The solid-state structure is a polymeric chain formed by each potassium cation bridging two arenes of adjacent anions in an eta(6) fashion. The same uranium tris(aryloxides) were also found to couple carbon monoxide under ambient conditions to give exclusively the ynediolate [OCCO](2-) dianion in [U(OAr)(3)](2)(mu-eta(1):eta(1)-C2O2), in direct analogy with the reductive coupling recently shown to afford [U{N(SiMe3)(2)}(3)](2)(mu-eta(1):eta(1)-C2O2). The related U-III complexes U{N(SiPhMe2)(2)}(3) and U{CH(SiMe3)(2)}(3) however do not show CO coupling chemistry in our hands. Of the aryloxide complexes, only the U(OC6H2-Bu-3(t)-2,4,6)(3) reacts with CO2 to give an insertion product containing bridging oxo and aryl carbonate moieties, U-2(OTtbp)(4)(mu-O)(mu-eta(1):eta(1)-O2COC6H2-Bu-3(t)-2,4,6)(2), which has been structurally characterized. The presence of coordinated N-2 in [U(OTtbp)(3)](2)(N-2) prevents the occurrence of any reaction with CO2, underscoring the remarkable stability of the N-2 complex. The di-tert-butyl aryloxide does not insert CO2, and only U(ODtbp)(4) was isolated. The silylamide also reacts with carbon dioxide to afford U(OSiMe3)(4) as the only uranium-containing material. GGA and hybrid DFT calculations, in conjunction with topological analysis of the electron density, suggest that the U-N-2 bond is strongly polar, and that the only covalent U -> N-2 interaction is pi backbonding, leading to a formal (U-IV)(2)(N-2)(2-) description of the electronic structure. The N-N stretching wavenumber is preferred as a metric of N-2 reduction to the N-N bond length, as there is excellent agreement between theory and experiment for the former but poorer agreement for the latter due to X-ray crystallographic underestimation of r(N-N). Possible intermediates on the CO coupling pathway to [U(OAr)(3)](2)(mu-C2O2) are identified, and potential energy surface scans indicate that the ynediolate fragment is more weakly bound than the ancillary ligands, which may have implications in the development of low-temperature and pressure catalytic CO chemistry