Distributed Estimation of Graph Spectrum

In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special cases. In the first stage, the algorithm uses a discrete-time linear iteration and the Cayley-Hamilton theorem to convert the problem into one of solving a set of linear equations, where each equation is known to a node. In the second stage, if the nodes happen to know that $W$ is cyclic, the algorithm uses a Lyapunov approach to asymptotically solve the equations with an exponential rate of convergence. If they do not know whether $W$ is cyclic, the algorithm uses a random perturbation approach and a structural controllability result to approximately solve the equations with an error that can be made small. Finally, we provide simulation results that illustrate the algorithm.Comment: 15 pages, 2 figure

Holographic DC Conductivity for a Power-law Maxwell Field

We consider a neutral and static black brane background with a probe power-law Maxwell field. Via the membrane paradigm, an expression for the holographic DC conductivity of the dual conserved current is obtained. We also discuss the dependence of the DC conductivity on the temperature, charge density and spatial components of the external field strength in the boundary theory. Our results show that there might be more than one phase in the boundary theory. Phase transitions could occur where the DC conductivity or its derivatives are not continuous. Specifically, we find that one phase possesses a charge-conjugation symmetric contribution, negative magneto-resistance and Mott-like behavior.Comment: 19 pages, 11 figures. arXiv admin note: text overlap with arXiv:1711.0329

Thermodynamics and Luminosities of Rainbow Black Holes

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As a result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is \textquotedblleft Gravity's rainbow", where the spacetime background felt by a test particle would depend on its energy. Focusing on the \textquotedblleft Amelino-Camelia dispersion relation" which is $E^{2}=m^{2}+p^{2}\left[ 1-\eta\left( E/m_{p}\right) ^{n}\right]$ with $n>0$, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of $\eta$ and $n$ in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with $\eta<0$ and $n\geq2$. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of $\eta$ and $n$.Comment: 32 pages, 12 figure

Spoken Language Intent Detection using Confusion2Vec

Decoding speaker's intent is a crucial part of spoken language understanding (SLU). The presence of noise or errors in the text transcriptions, in real life scenarios make the task more challenging. In this paper, we address the spoken language intent detection under noisy conditions imposed by automatic speech recognition (ASR) systems. We propose to employ confusion2vec word feature representation to compensate for the errors made by ASR and to increase the robustness of the SLU system. The confusion2vec, motivated from human speech production and perception, models acoustic relationships between words in addition to the semantic and syntactic relations of words in human language. We hypothesize that ASR often makes errors relating to acoustically similar words, and the confusion2vec with inherent model of acoustic relationships between words is able to compensate for the errors. We demonstrate through experiments on the ATIS benchmark dataset, the robustness of the proposed model to achieve state-of-the-art results under noisy ASR conditions. Our system reduces classification error rate (CER) by 20.84% and improves robustness by 37.48% (lower CER degradation) relative to the previous state-of-the-art going from clean to noisy transcripts. Improvements are also demonstrated when training the intent detection models on noisy transcripts