About the mass of certain second order elliptic operators

Let $(M,g)$ be a closed Riemannian manifold of dimension $n \geq 3$ and let $f\in C^{\infty}(M)$, such that the operator $P_f:= \Delta_g+f$ is positive. If $g$ is flat near some point $p$ and $f$ vanishes around $p$, we can define the mass of $P_f$ as the constant term in the expansion of the Green function of $P_f$ at $p$. In this paper, we establish many results on the mass of such operators. In particular, if f:= \frac{n-2}{4(n-1)} \scal_g, i.e. if $P_f$ is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold $M$ such that the mass is non-negative for every metric $g$ as above on $M$, then the mass is non-negative for every such metric on every closed manifold of the same dimension as $M$.Comment: 39 page

Mass endomorphism, surgery and perturbations

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments

AFM imaging of functionalized double-walled carbon nanotubes

We present a comparative study of several non-covalent approaches to disperse, debundle and noncovalently functionalize double-walled carbon nanotubes (DWNTs). We investigated the ability of bovine serum albumin (BSA), phospholipids grafted onto amine-terminated polyethylene glycol (PLPEG2000-NH2), as well as a combination thereof, to coat purified DWNTs. Topographical imaging with the atomic force microscope (AFM) was used to assess the coating of individual DWNTs and the degree of debundling and dispersion. Topographical images showed that functionalized DWNTs are better separated and less aggregated than pristine DWNTs and that the different coating methods differ in their abilities to successfully debundle and disperse DWNTs. Height profiles indicated an increase in the diameter of DWNTs depending on the functionalization method and revealed adsorption of single molecules onto the nanotubes. Biofunctionalization of the DWNT surface was achieved by coating DWNTs with biotinylated BSA, providing for biospecific binding of streptavidin in a simple incubation step. Finally, biotin-BSA-functionalized DWNTs were immobilized on an avidin layer via the specific avidin–biotin interaction

B_{s,d} -> l+ l- in the Standard Model with Reduced Theoretical Uncertainty

We combine our new results for the O(alpha_em) and O(alpha_s^2) corrections to B_{s,d} -> l^+ l^-, and present updated branching ratio predictions for these decays in the standard model. Inclusion of the new corrections removes major theoretical uncertainties of perturbative origin that have just begun to dominate over the parametric ones. For the recently observed muonic decay of the B_s meson, our calculation gives BR(B_s -> mu^+ mu^-) = (3.65 +_ 0.23) * 10^(-9).Comment: 4 pages, 1 figure; v3: matches the published version in Phys. Rev. Lett. 112, 101801 (2014); title and ordering of references modified; results unchange

The self-assembly and evolution of homomeric protein complexes

We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of such complexes naturally takes the system into a region of interaction space where (i) the evolutionarily newer interactions are weaker, (ii) subcomplexes involving the stronger interactions are observed to be thermodynamically stable on destabilization of the protein-protein interactions and (iii) the self-assembly dynamics are hierarchical with these same subcomplexes acting as kinetic intermediates.Comment: 4 pages, 4 figure

AFM imaging of functionalized carbon nanotubes on biological membranes

Multifunctional carbon nanotubes are promising for biomedical applications as their nano-size, together with their physical stability, gives access into the cell and various cellular compartments including the nucleus. However, the direct and label-free detection of carbon nanotube uptake into cells is a challenging task. The atomic force microscope (AFM) is capable of resolving details of cellular surfaces at the nanometer scale and thus allows following of the docking of carbon nanotubes to biological membranes. Here we present topographical AFM images of non-covalently functionalized single walled (SWNT) and double walled carbon nanotubes (DWNT) immobilized on different biological membranes, such as plasma membranes and nuclear envelopes, as well as on a monolayer of avidin molecules. We were able to visualize DWNT on the nuclear membrane while at the same time resolving individual nuclear pore complexes. Furthermore, we succeeded in localizing individual SWNT at the border of incubated cells and in identifying bundles of DWNT on cell surfaces by AFM imaging

The Marine-Derived Kinase Inhibitor Fascaplysin Exerts Anti-Thrombotic Activity

Background: The marine-derived kinase inhibitor fascaplysin down-regulates the PI3K pathway in cancer cells. Since this pathway also plays an essential role in platelet signaling, we herein investigated the effect of fascaplysin on thrombosis. Methods: Fascaplysin effects on platelet activation, platelet aggregation and platelet-leukocyte aggregates (PLA) formation were analyzed by flow cytometry. Mouse dorsal skinfold chambers were used to determine in vivo the effect of fascaplysin on photochemically induced thrombus formation and tail-vein bleeding time. Results: Pre-treatment of platelets with fascaplysin reduced the activation of glycoprotein (GP)IIb/IIIa after protease-activated receptor-1-activating peptide (PAR-1-AP), adenosine diphosphate (ADP) and phorbol-12-myristate-13-acetate (PMA) stimulation, but did not markedly affect the expression of P-selectin. This was associated with a decreased platelet aggregation. Fascaplysin also decreased PLA formation after PMA but not PAR-1-AP and ADP stimulation. This may be explained by an increased expression of CD11b on leukocytes in PAR-1-AP- and ADP-treated whole blood. In the dorsal skinfold chamber model of photochemically induced thrombus formation, fascaplysin-treated mice revealed a significantly extended complete vessel occlusion time when compared to controls. Furthermore, fascaplysin increased the tail-vein bleeding time. Conclusion: Fascaplysin exerts anti-thrombotic activity, which represents a novel mode of action in the pleiotropic activity spectrum of this compound