16,196 research outputs found
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
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 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 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
Minimal Length Effects on Tunnelling from Spherically Symmetric Black Holes
In this paper, we investigate effects of the minimal length on quantum
tunnelling from spherically symmetric black holes using the Hamilton-Jacobi
method incorporating the minimal length. We first derive the deformed
Hamilton-Jacobi equations for scalars and fermions, both of which have the same
expressions. The minimal length correction to the Hawking temperature is found
to depend on the black hole's mass and the mass and angular momentum of emitted
particles. Finally, we calculate a Schwarzschild black hole's luminosity and
find the black hole evaporates to zero mass in infinite time.Comment: 18 page
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
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