Kahler-Ricci flow on stable Fano manifolds

We study the Kahler-Ricci flow on Fano manifolds. We show that if the curvature is bounded along the flow and if the manifold is K-polystable and asymptotically Chow semistable, then the flow converges exponentially fast to a Kahler-Einstein metric.Comment: 19 page

Determining atmospheric electric fields using MGMR3D

Cosmic-ray particles impinging on the atmosphere induce high-energy particle cascades in air, an Extensive Air Shower (EAS), emitting coherent radio emission. This emission is affected by the presence of strong electric fields during thunderstorm conditions. To reconstruct the atmospheric electric field from the measured radio footprint of the EAS we use an analytic model for the calculation of the radio emission, MGMR3D. In this work we make an extensive comparison between the results of a microscopic model for radio emission, CoREAS, to obtain an improved parametrization for MGMR3D in the presence of atmospheric electric fields, as well as confidence intervals. The approach to extract the electric field structure is applied successfully to an event with a complicated radio footprint measured by LOFAR during thunderstorm conditions. This shows that, with the improved parametrization, MGMR3D can be used to extract the structure of the atmospheric electric field.Comment: The paper is accepted for publication in Physical Review

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

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

The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. While we do not solve the, expectedly, rich representation theory completely, we present a, to the best of our knowledge new, non -- trivial solution to the representation problem. This solution exists 1. for any target space dimension, 2. for Minkowski signature of the target space, 3. without tachyons, 4. manifestly ghost -- free (no negative norm states), 5. without fixing a worldsheet or target space gauge, 6. without (Virasoro) anomalies (zero central charge), 7. while preserving manifest target space Poincar\'e invariance and 8. without picking up UV divergences. The existence of this stable solution is exciting because it raises the hope that among all the solutions to the representation problem (including fermionic degrees of freedom) we find stable, phenomenologically acceptable ones in lower dimensional target spaces, possibly without supersymmetry, that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string. Moreover, these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem. The solution presented in this paper exploits the flatness of the target space in several important ways. In a companion paper we treat the more complicated case of curved target spaces.Comment: 46 p., LaTex2e, no figure

First detection of a Vssc allele V1016G conferring a high level of insecticide resistance in Aedes albopictus collected from Europe (Italy) and Asia (Vietnam), 2016. A new emerging threat to controlling arboviral diseases

Introduction Aedes albopictus (Skuse) is an important vector of arboviral diseases, including dengue, chikungunya and Zika virus disease. Monitoring insecticide resistance and mechanisms by which the mosquito develops resistance is crucial to minimise disease transmission. Aim To determine insecticide resistance status and mechanisms in Ae. albopictus from different geographical regions. Methods We sampled 33 populations of Ae. albopictus from Asia, Europe and South America, and tested these for susceptibility to permethrin, a pyrethroid insecticide. In resistant populations, the target site for pyrethroids, a voltage-sensitive sodium channel (Vssc) was genotyped. Three resistant sub-strains, each harbouring a resistance allele homozygously, were established and susceptibilities to three different pyrethroids (with and without a cytochrome P450 inhibitor) were assayed. Results Most populations of Ae. albopictus tested were highly susceptible to permethrin but a few from Italy and Vietnam (4/33), exhibited high-level resistance. Genotyping studies detected a knockdown resistance (kdr) allele V1016G in Vssc for the first time in Ae. albopictus. Two previously reported kdr alleles, F1534C and F1534S, were also detected. The bioassays indicated that the strain homozygous for the V1016G allele showed much greater levels of pyrethroid resistance than other strains harbouring F1534C or F1534S. Conclusion The V1016G allele was detected in bothAsian and Italian Ae. albopictus populations, thus a spread of this allele beyond Italy in Europe cannot be ruled out. This study emphasises the necessity to frequently and regularly monitor the V1016G allele in Ae. albopictus, particularly where this mosquito species is the main vector of arboviruses

Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly solved supersymmetric rational Calogero model, including shape invariance, equivalence to a system of free superoscillators and non-uniqueness in the construction of the Hamiltonian, are presented in some detail. This review also includes a formulation of pseudo-hermitian supersymmetric quantum systems with a special emphasis on rational Calogero model. There are quite a few number of many-particle quantum systems with inverse-square interactions which are not exactly solved for a complete set of states in spite of the construction of infinitely many exact eigen functions and eigenvalues. The Calogero-Marchioro model with dynamical SU(1,1|2) supersymmetry and a quantum system related to short-range Dyson model belong to this class and certain aspects of these models are reviewed. Several other related and important developments are briefly summarized.Comment: LateX, 65 pages, Added Acknowledgment, Discussions and References, Version to appear in Jouranl of Physics A: Mathematical and Theoretical (Commissioned Topical Review Article

Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure

Solving Uncalibrated Photometric Stereo using Total Variation

International audienceEstimating the shape and appearance of an object, given one or several images, is still an open and challenging research problem called 3D-reconstruction. Among the different techniques available, photometric stereo (PS) produces highly accurate results when the lighting conditions have been identified. When these conditions are unknown, the problem becomes the so-called uncalibrated PS problem, which is ill-posed. In this paper, we will show how total variation can be used to reduce the ambiguities of uncalibrated PS, and we will study two methods for estimating the parameters of the generalized bas-relief ambiguity. These methods will be evaluated through the 3D-reconstruction of real-world objects