Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography

We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a function on the quasi-Fuchsian deformation space, is an antiderivative of a 1-form given by the difference of Fuchsian and quasi-Fuchsian projective connections. This result can be considered as global quasi-Fuchsian reciprocity which implies McMullen's quasi-Fuchsian reciprocity. We prove that the classical action is a Kahler potential of the Weil-Petersson metric. We also prove that Liouville action functional satisfies holography principle, i.e., it is a regularized limit of the hyperbolic volume of a 3-manifold associated with a quasi-Fuchsian group. We generalize these results to a large class of Kleinian groups including finitely generated, purely loxodromic Schottky and quasi-Fuchsian groups and their free combinations.Comment: 60 pages, proof of the Lemma 5.1 corrected, references and section 5.3 adde

Pointing a ground antenna at a spinning spacecraft using Conscan-simulation results

The results are presented for an investigation of ground antenna pointing errors which are caused by fluctuations of the receiver AGC signal due to thermal noise and a spinning spacecraft. Transient responses and steady-state errors and losses are estimated using models of the digital Conscan (conical scan) loop, the FFT, and antenna characteristics. Simulation results are given for the on-going Voyager mission and for the upcoming Galileo mission, which includes a spinning spacecraft. The simulation predicts a 1 sigma pointing error of 0.5 to 2.0 mdeg for Voyager, assuming an AGC loop SNR of 35 to 30 dB with a scan period varying from 128 to 32 sec, respectively. This prediction is in agreement with the DSS 14 antenna Conscan performance of 1.7 mdeg for 32 sec scans as reported in earlier studies. The simulation of Galileo predicts 1 mdeg error with a 128 sec scan and 4 mdeg with a 32 sec scan under similar AGC conditions

Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find $1-\epsilon$ approximate solutions to the maximum concurrent flow problem and the maximum weighted multicommodity flow problem in time \tilde{O}(m^{4/3}\poly(k,\epsilon^{-1}))

Deep Multitask Learning for Semantic Dependency Parsing

We present a deep neural architecture that parses sentences into three semantic dependency graph formalisms. By using efficient, nearly arc-factored inference and a bidirectional-LSTM composed with a multi-layer perceptron, our base system is able to significantly improve the state of the art for semantic dependency parsing, without using hand-engineered features or syntax. We then explore two multitask learning approaches---one that shares parameters across formalisms, and one that uses higher-order structures to predict the graphs jointly. We find that both approaches improve performance across formalisms on average, achieving a new state of the art. Our code is open-source and available at https://github.com/Noahs-ARK/NeurboParser.Comment: Proceedings of ACL 201

Weyl Semimetal in a Topological Insulator Multilayer

We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator with a quantized Hall conductivity, equal to $e^2/h$ per TI layer. We find that the Weyl semimetal has a nonzero DC conductivity at zero temperature and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically-protected edge states.Comment: 4 pages, 3 figures, published versio

Erratum : Squeezing and entanglement delay using slow light

An inconsistency was found in the equations used to calculate the variance of the quadrature fluctuations of a field propagating through a medium demonstrating electromagnetically induced transparency (EIT). The decoherence term used in our original paper introduces inconsistency under weak probe approximation. In this erratum we give the Bloch equations with the correct dephasing terms. The conclusions of the original paper remain the same. Both entanglement and squeezing can be delayed and preserved using EIT without adding noise when the decoherence rate is small.Comment: 1 page, no figur