Exceptional del Pezzo hypersurfaces

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$.Comment: 149 pages, one reference adde

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Energy properness and Sasakian-Einstein metrics

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Backbone rigidity and static presentation of guanidinium groups increases cellular uptake of arginine-rich cell-penetrating peptides

In addition to endocytosis-mediated cellular uptake, hydrophilic cell-penetrating peptides are able to traverse biological membranes in a non-endocytic mode termed transduction, resulting in immediate bioavailability. Here we analysed structural requirements for the non-endocytic uptake mode of arginine-rich cell-penetrating peptides, by a combination of live-cell microscopy, molecular dynamics simulations and analytical ultracentrifugation. We demonstrate that the transduction efficiency of arginine-rich peptides increases with higher peptide structural rigidity. Consequently, cyclic arginine-rich cell-penetrating peptides showed enhanced cellular uptake kinetics relative to their linear and more flexible counterpart. We propose that guanidinium groups are forced into maximally distant positions by cyclization. This orientation increases membrane contacts leading to enhanced cell penetration

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

Sequence-selective DNA recognition and enhanced cellular up-take by peptide–steroid conjugates

Several GCN4 bZIP TF models have previously been designed and synthesized. However, the synthetic routes towards these constructs are typically tedious and difficult. We here describe the substitution of the Leucine zipper domain of the protein by a deoxycholic acid derivative appending the two GCN4 binding region peptides through an optimized double azide–alkyne cycloaddition click reaction. In addition to achieving sequence specific dsDNA binding, we have investigated the potential of these compounds to enter cells. Confocal microscopy and flow cytometry show the beneficial influence of the steroid on cell uptake. This unique synthetic model of the bZIP TF thus combines sequence specific dsDNA binding properties with enhanced cell-uptake. Given the unique properties of deoxycholic acid and the convergent nature of the synthesis, we believe this work represents a key achievement in the field of TF mimicry

Dynamic Measurements of Membrane Insertion Potential of Synthetic Cell Penetrating Peptides

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Langmuir, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://doi.org/10.1021/la403370p.Cell penetrating peptides (CPPs) have been established as excellent candidates for mediating drug delivery into cells. When designing synthetic CPPs for drug delivery applications, it is important to understand their ability to penetrate the cell membrane. In this paper, anionic or zwitterionic phospholipid monolayers at the air-water interface are used as model cell membranes to monitor the membrane insertion potential of synthetic CPPs. The insertion potential of CPPs having different cationic and hydrophobic amino acids were recorded using a Langmuir monolayer approach that records peptide adsorption to model membranes. Fluorescence microscopy was used to visualize alterations in phospholipid packing due to peptide insertion. All CPPs had the highest penetration potential in the presence of anionic phospholipids. In addition, two of three amphiphilic CPPs inserted into zwitterionic phospholipids, but none of the hydrophilic CPPs did. All the CPPs studied induced disruptions in phospholipid packing and domain morphology, which were most pronounced for amphiphilic CPPs. Overall, small changes to amino acids and peptide sequences resulted in dramatically different insertion potentials and membrane reorganization. Designers of synthetic CPPs for efficient intracellular drug delivery should consider small nuances in CPP electrostatic and hydrophobic properties

Existence of Kähler–Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces

We apply Nadel’s method of multiplier ideal sheaves to show that every complex del Pezzo surface of degree at most six whose automorphism group acts without fixed points has a Kähler–Einstein metric. In particular, all del Pezzo surfaces of degree 4, 5, or 6 and certain special del Pezzo surfaces of lower degree are shown to have a Kähler–Einstein metric. These existence statements are not new, but the proofs given in the present paper are less involved than earlier ones by Siu, Tian and Tian–Yau