Generalized Bergman kernels on symplectic manifolds of bounded geometry

We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtain the relation between the generalized Bergman kernel on a Galois covering of a compact symplectic manifold and the generalized Bergman kernel on the base. Then we state the full off-diagonal asymptotic expansion of the generalized Bergman kernel, improving the remainder estimate known in the compact case to an exponential decay. Finally, we establish the theory of Berezin-Toeplitz quantization on symplectic orbifolds associated with the renormalized Bochner-Laplacian.Comment: 33 pages, v.2 is a final update to agree with the published pape

The MAPPER2 Database: a multi-genome catalog of putative transcription factor binding sites

The mapper2 Database (http://genome.ufl.edu/mapperdb) is a component of mapper2, a web-based system for the analysis of transcription factor binding sites in multiple genomes. The database contains predicted binding sites identified in the promoters of all human, mouse and Drosophila genes using 1017 probabilistic models representing over 600 different transcription factors. In this article we outline the current contents of the database and we describe its web-based user interface in detail. We then discuss ongoing work to extend the database contents to experimental data and to add analysis capabilities. Finally, we provide information about recent improvements to the hardware and software platform that mapper2 is based on

Retarded long-range potentials for the alkali-metal atoms and a perfectly conducting wall

The retarded long-range potentials for hydrogen and alkali-metal atoms in their ground states and a perfectly conducting wall are calculated. The potentials are given over a wide range of atom-wall distances and the validity of the approximations used is established.Comment: RevTeX, epsf, 11 pages, 2 fig

Prenatal diagnosis of trisomy 6q25.3-qter and monosomy 10q26.12-qter by array CGH in a fetus with an apparently normal karyotype.

We present the prenatal case of a 12.5-Mb duplication involving 6q25-qter and a 12.2-Mb deletion encompassing 10q26-qter diagnosed by aCGH, while conventional karyotype showed normal results. The genotype-phenotype correlation between individual microarray and clinical findings adds to the emerging atlas of chromosomal abnormalities associated with specific prenatal ultrasound abnormalities

Thermoelectric Flux in Superconducting Rings

Definitive measurements by Van Harlingen et al. in 1980 show that the flux induced by a temperature difference across the two junctions of a Pb-In ring exceeds theoretical expectation by a factor, ϳ105. The theory fails owing to ͑mis͒use of a Boltzmann transport equation to describe the thermal diffusion of quasi-particle excitations, a treatment which violates electron conservation. An electron-conserving transport theory is developed and explains the data

A Multi-Agent Neural Network for Dynamic Frequency Reuse in LTE Networks

Fractional Frequency Reuse techniques can be employed to address interference in mobile networks, improving throughput for edge users. There is a tradeoff between the coverage and overall throughput achievable, as interference avoidance techniques lead to a loss in a cell's overall throughput, with spectrum efficiency decreasing with the fencing off of orthogonal resources. In this paper we propose MANN, a dynamic multiagent frequency reuse scheme, where individual agents in charge of cells control their configurations based on input from neural networks. The agents' decisions are partially influenced by a coordinator agent, which attempts to maximise a global metric of the network (e.g., cell-edge performance). Each agent uses a neural network to estimate the best action (i.e., cell configuration) for its current environment setup, and attempts to maximise in turn a local metric, subject to the constraint imposed by the coordinator agent. Results show that our solution provides improved performance for edge users, increasing the throughput of the bottom 5% of users by 22%, while retaining 95% of a network's overall throughput from the full frequency reuse case. Furthermore, we show how our method improves on static fractional frequency reuse schemes

The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the asymptotic expansion using the method of our paper "Generalized Bergman kernels on symplectic manifolds" (math.DG/0411559).Comment: 21 pages, to appear in Internat. J. Math. Precisions added in the abstrac

Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high tensor powers of the line bundle. This gives after integration weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities which we apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a multiplicative constant 1/2 ; v.2 is a final updat