Strong deflection gravitational lensing by a modified Hayward black hole

A modified Hayward black hole is a nonsingular black hole. It is proposed to form when the pressure generated by quantum gravity can stop matter's collapse as the matter reaches Planck density. Strong deflection gravitational lensing happening nearby its event horizon might provide some clues of these quantum effects in its central core. We investigate observables of the strong deflection lensing, including angular separations, brightness differences and time delays between its relativistic images, and estimate their values for the supermassive black hole in the Galactic center. We find that it is possible to distinguish the modified Hayward black hole from a Schwarzschild one, but it demands very high resolution beyond current stage.Comment: 10 pages, 1 figur

Towards Structured Deep Neural Network for Automatic Speech Recognition

In this paper we propose the Structured Deep Neural Network (Structured DNN) as a structured and deep learning algorithm, learning to find the best structured object (such as a label sequence) given a structured input (such as a vector sequence) by globally considering the mapping relationships between the structure rather than item by item. When automatic speech recognition is viewed as a special case of such a structured learning problem, where we have the acoustic vector sequence as the input and the phoneme label sequence as the output, it becomes possible to comprehensively learned utterance by utterance as a whole, rather than frame by frame. Structured Support Vector Machine (structured SVM) was proposed to perform ASR with structured learning previously, but limited by the linear nature of SVM. Here we propose structured DNN to use nonlinear transformations in multi-layers as a structured and deep learning algorithm. It was shown to beat structured SVM in preliminary experiments on TIMIT

Improving information centrality of a node in complex networks by adding edges

The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$ nodes and $m$ edges, by creating $k$ new edges incident to $v$. Since $I_v$ is the reciprocal of the sum of resistance distance $\mathcal{R}_v$ between $v$ and all nodes, we alternatively consider the problem of minimizing $\mathcal{R}_v$ by adding $k$ new edges linked to $v$. We show that the objective function is monotone and supermodular. We provide a simple greedy algorithm with an approximation factor $\left(1-\frac{1}{e}\right)$ and $O(n^3)$ running time. To speed up the computation, we also present an algorithm to compute $\left(1-\frac{1}{e}-\epsilon\right)$-approximate resistance distance $\mathcal{R}_v$ after iteratively adding $k$ edges, the running time of which is $\widetilde{O} (mk\epsilon^{-2})$ for any $\epsilon>0$, where the $\widetilde{O} (\cdot)$ notation suppresses the ${\rm poly} (\log n)$ factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201