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Li, Yang

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Li, Yang
Author's Publications: search.filters.isAuthorOfPublication.8458b5a8-ef6f-4bcf-b782-70d7c1e71ffe

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    Fast parameter estimation in loss tomography for networks of general topology
    (Institute of Mathematical Statistics, 2016) Deng, Ke; Li, Yang; Zhu, Weiping; Liu, Jun
    As a technique to investigate link-level loss rates of a computer network with low operational cost, loss tomography has received considerable attentions in recent years. A number of parameter estimation methods have been proposed for loss tomography of networks with a tree structure as well as a general topological structure. However, these methods suffer from either high computational cost or insufficient use of information in the data. In this paper, we provide both theoretical results and practical algorithms for parameter estimation in loss tomography. By introducing a group of novel statistics and alternative parameter systems, we find that the likelihood function of the observed data from loss tomography keeps exactly the same mathematical formulation for tree and general topologies, revealing that networks with different topologies share the same mathematical nature for loss tomography. More importantly, we discover that a reparametrization of the likelihood function belongs to the standard exponential family, which is convex and has a unique mode under regularity conditions. Based on these theoretical results, novel algorithms to find the MLE are developed. Compared to existing methods in the literature, the proposed methods enjoy great computational advantages.
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    On-chip zero-index metamaterials
    (Nature Publishing Group, 2015) Li, Yang; Kita, Shota; Camayd-Munoz, Phil; Reshef, Orad; Vulis, Daryl; Yin, Mei; Loncar, Marko; Mazur, Eric
    Metamaterials with a refractive index of zero exhibit physical properties such as infinite phase velocity and wavelength. However, there is no way to implement these materials on a photonic chip, restricting the investigation and application of zero-index phenomena to simple shapes and small scales. We designed and fabricated an on-chip integrated metamaterial with a refractive index of zero in the optical regime. Light refracts perpendicular to the facets of a prism made of this metamaterial, directly demonstrating that the index of refraction is zero. The metamaterial consists of low-aspect-ratio silicon pillar arrays embedded in a polymer matrix and clad by gold films. This structure can be fabricated using standard planar processes over a large area in arbitrary shapes and can efficiently couple to photonic integrated circuits and other optical elements. This novel on-chip metamaterial platform opens the door to exploring the physics of zero index and its applications in integrated optics.