Discrete Approximations of Metric Measure Spaces of Controlled Geometry

We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.Comment: 23 Page

A novel steganography approach for audio files

We present a novel robust and secure steganography technique to hide images into audio files aiming at increasing the carrier medium capacity. The audio files are in the standard WAV format, which is based on the LSB algorithm while images are compressed by the GMPR technique which is based on the Discrete Cosine Transform (DCT) and high frequency minimization encoding algorithm. The method involves compression-encryption of an image file by the GMPR technique followed by hiding it into audio data by appropriate bit substitution. The maximum number of bits without significant effect on audio signal for LSB audio steganography is 6 LSBs. The encrypted image bits are hidden into variable and multiple LSB layers in the proposed method. Experimental results from observed listening tests show that there is no significant difference between the stego audio reconstructed from the novel technique and the original signal. A performance evaluation has been carried out according to quality measurement criteria of Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR)

Analyticity of the Free Energy of a Closed 3-Manifold

The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus $g$ part of the free energy is convergent in a neighborhood of zero, independent of the genus. Our results follow from an estimate of the LMO invariant, in a particular gauge, and from recent results of Bender-Gao-Richmond on the asymptotics of the number of rooted maps for arbitrary genus. We illustrate our results with an explicit formula for the free energy of a Lens space. In addition, using the Painlev\'e differential equation, we obtain an asymptotic expansion for the number of cubic graphs to all orders, stengthening the results of Bender-Gao-Richmond.Comment: This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Heralded qubit amplifiers for practical device-independent quantum key distribution

Device-independent quantum key distribution does not need a precise quantum mechanical model of employed devices to guarantee security. Despite of its beauty, it is still a very challenging experimental task. We compare a recent proposal by Gisin et al. [Phys. Rev. Lett. 105, 070501 (2010)] to close the detection loophole problem with that of a simpler quantum relay based on entanglement swapping with linear optics. Our full-mode analysis for both schemes confirms that, in contrast to recent beliefs, the second scheme can indeed provide a positive key rate which is even considerably higher than that of the first alternative. The resulting key rates and required detection efficiencies of approx. 95% for both schemes, however, strongly depend on the underlying security proof.Comment: 5 pages, 3 figure