Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Vacuum spacetimes with constant Weyl eigenvalues

Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant A) with constant non-zero Weyl eigenvalues are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2A/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant.

Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

FtsZ Protofilament Curvature is the Opposite of Tubulin Rings

Bacterial tubulin homolog FtsZ assembles straight protofilaments (pfs) that form the scaffold of the cytokinetic Z ring. These pfs can adopt a curved conformation forming a miniring or spiral tube 24 nm in diameter. Tubulin pfs also have a curved conformation, forming 42 nm tubulin rings. We have previously provided evidence that FtsZ generates a constriction force by switching from straight pfs to the curved conformation, generating a bending force on the membrane. In the simplest model the membrane tether, which exits from the C terminus of the globular FtsZ, would have to be on the outside of the curved pf. However, it is well established that tubulin rings have the C terminus on the inside of the ring. Could FtsZ and tubulin rings have the opposite curvature? In the present study we explored the direction of curvature of FtsZ rings by fusing large protein tags to the N or C terminus of the FtsZ globular domain. FtsZ with a protein tag on the N terminus did not assemble tubes. This was expected if the N terminus is on the inside, because the protein tags are too big to fit in the interior of the tube. FtsZ with C-terminal tags assembled normal tubes, consistent with the C terminus on the outside. The FN extension was not visible in negative stain, but thin section EM gave definitive evidence that the C-terminal tag was on the outside of the tubes. This has interesting implications for the evolution of tubulin. It seems likely that tubulin began with the curvature of FtsZ, which would have resulted in pfs curving toward the interior of a disassembling MT. Evolution not only eliminated this undesirable curvature, but managed to reverse direction to produce the outward curving rings, which is useful for pulling chromosomes.

How curvature-generating proteins build scaffolds on membrane nanotubes

Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex sub-cellular structures, and many other cellular phenomena. They form three-dimensional assemblies, which act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we employ various experimental, theoretical and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube’s length. Our work implies that the nature of local protein-membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30–40% of a tube’s surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes. 

Cornered Asymptotically Hyperbolic Metrics

Thesis (Ph.D.)--University of Washington, 2016-08

Lymphoepithelioma-like gastric carcinoma presenting as giant ulcer of the lesser curvature. Case report

Lymphoepithelioma-like gastric carcinoma (LELGC) has special clinicopathologic features that differentiate it from the common gastric adenocarcinoma. LELGC is a rare neoplasm of the stomach with an incidence of 1-4% of all gastric cancers and is characterized by desmoplastic stroma uniformaly infiltrated by abundant lymphocytes and plasma cells. LELGC is closely associated with the Epstein-Barr virus (EBV), with 80-100% of LELGC being EBV-positive. LELGC has a male predominance, occurs in elderly people and is usually located in the upper and middle portion of the stomach. We report a rare case of lymphoepithelioma-like gastric carcinoma located in the lesser curvature at the border of the gastric body to the pyloric antrum.

The BEH Mechanism and its Scalar Boson

SCOPUS: re.j

Scalar field dark matter and the Higgs field

We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range 10^-6 - 10^-4 eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall–Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

All one-loop scalar vertices in the effective potential approach

Using the one-loop Coleman-Weinberg effective potential, we derive a general analytic expression for all the derivatives of the effective potential with respect to any number of classical scalar fields. The result is valid for a renormalisable theory in four dimensions with any number of scalars, fermions or gauge bosons. This result corresponds to the zero-external momentum contribution to a general one-loop diagram with N scalar external legs. We illustrate the use of the general result in two simple scalar singlet extensions of the Standard Model, to obtain the dominant contributions to the triple couplings of light scalar particles under the zero external momentum approximation.