Manin-Olshansky triples for Lie superalgebras

Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg, \fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for several series of Lie superalgebras \fa which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward superization of suitable Etingof--Kazhdan's results guarantee then the uniqueness of $q$-quantization of our Lie bialgebras. Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions. To find explicit solutions is a separate (open) problem. It is also an open problem to list (\`a la Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra \fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix

Screw instability of the magnetic field connecting a rotating black hole with its surrounding disk

Screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disk is discussed based on the model of the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process (CEBZMC). A criterion for the screw instability with the state of CEBZMC is derived based on the calculations of the poloidal and toroidal components of the magnetic field on the disk. It is shown by the criterion that the screw instability will occur, if the BH spin and the power-law index for the variation of the magnetic field on the disk are greater than some critical values. It turns out that the instability occurs outside some critical radii on the disk. It is argued that the state of CEBZMC always accompanies the screw instability. In addtition, we show that the screw instability contributes only a small fraction of magnetic extraction of energy from a rotating BH.Comment: 18 pages, 13 figures; Accepted by Ap

Zero-Shot Deep Domain Adaptation

Domain adaptation is an important tool to transfer knowledge about a task (e.g. classification) learned in a source domain to a second, or target domain. Current approaches assume that task-relevant target-domain data is available during training. We demonstrate how to perform domain adaptation when no such task-relevant target-domain data is available. To tackle this issue, we propose zero-shot deep domain adaptation (ZDDA), which uses privileged information from task-irrelevant dual-domain pairs. ZDDA learns a source-domain representation which is not only tailored for the task of interest but also close to the target-domain representation. Therefore, the source-domain task of interest solution (e.g. a classifier for classification tasks) which is jointly trained with the source-domain representation can be applicable to both the source and target representations. Using the MNIST, Fashion-MNIST, NIST, EMNIST, and SUN RGB-D datasets, we show that ZDDA can perform domain adaptation in classification tasks without access to task-relevant target-domain training data. We also extend ZDDA to perform sensor fusion in the SUN RGB-D scene classification task by simulating task-relevant target-domain representations with task-relevant source-domain data. To the best of our knowledge, ZDDA is the first domain adaptation and sensor fusion method which requires no task-relevant target-domain data. The underlying principle is not particular to computer vision data, but should be extensible to other domains.Comment: This paper is accepted to the European Conference on Computer Vision (ECCV), 201

BZ-MC-BP Model for Jet Production from Black Hole Accretion Disc

Three energy mechanisms invoking large-scale magnetic fields are incorporated in a model to interpret jet production in black hole (BH) systems, i.e., the Blandford-Znajek (BZ), the magnetic coupling (MC) and Blandford-Payne (BP) processes. These energy mechanisms can coexist in BH accretion disc based on the magnetic field configurations constrained by the screw instability, provided that the BH spin and the power-law index indicating the variation of the magnetic field at an accretion disc are greater than some critical values. In this model the jets are driven by the BZ process in the Poynting flux regime and by the BP process in the hydromagnetic regime, being consistent with the spine/sheath jet structure observed in BH sources of stellar and supermassive size.Comment: 9 pages, 6 figures, accepted by MNRA

Kosterlitz-Thouless transition of quantum XY model in two dimensions

The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.Comment: 8 pages, 2 tables, 6 figure

Marginal Release Under Local Differential Privacy

Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding correlations in the data to fitting sophisticated prediction models. In this paper, we provide a set of algorithms for materializing marginal statistics under the strong model of local differential privacy. We prove the first tight theoretical bounds on the accuracy of marginals compiled under each approach, perform empirical evaluation to confirm these bounds, and evaluate them for tasks such as modeling and correlation testing. Our results show that releasing information based on (local) Fourier transformations of the input is preferable to alternatives based directly on (local) marginals

Event-triggered distributed H∞ state estimation with packet dropouts through sensor networks

This study is concerned with the event-triggered distributed H∞ state estimation problem for a class of discrete-time stochastic non-linear systems with packet dropouts in a sensor network. An event-triggered communication mechanism is adopted over the sensor network with hope to reduce the communication burden and the energy consumption, where the measurements on each sensor are transmitted only when a certain triggering condition is violated. Furthermore, a novel distributed state estimator is designed where the available innovations are not only from the individual sensor, but also from its neighbouring ones according to the given topology. The purpose of the problem under consideration is to design a set of distributed state estimators such that the dynamics of estimation errors is exponentially mean-square stable and also the prespecified H∞ disturbance rejection attenuation level is guaranteed. By utilising the property of the Kronecker product and the stochastic analysis approaches, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimisation one that can be easily solved via available software packages. Finally, a simulation example is utilised to illustrate the usefulness of the proposed design scheme of event-triggered distributed state estimators.This work was supported in part by Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61203139, 61473076, 61374127 and 61422301, the Shanghai Rising-Star Program of China under Grant 13QA1400100, the ShuGuang project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation under Grant 13SG34, the Fundamental Research Funds for the Central Universities, DHU Distinguished Young Professor Program, and the Alexander von Humboldt Foundation of Germany