Network hierarchy evolution and system vulnerability in power grids

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.Peer ReviewedPostprint (author's final draft

Dilations for Systems of Imprimitivity acting on Banach Spaces

Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-kown result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. The dilated space in general can not be taken as a Hilbert space. However, it can be taken as a Hilbert space for positive operator valued systems of imprimitivity. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces.Comment: 21 page

Dilations of frames, operator valued measures and bounded linear maps

We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator valued measures acting on Banach spaces where operator-valued measures (or maps) are not necessarily completely bounded. The main results state that any operator-valued measure, not necessarily completely bounded, always has a dilation to a projection-valued measure acting on a Banach space, and every bounded linear map, again not necessarily completely bounded, on a Banach algebra has a bounded homomorphism dilation acting on a Banach space. Here the dilation space often needs to be a Banach space even if the underlying space is a Hilbert space, and the projections are idempotents that are not necessarily self-adjoint. These results lead to some new connections between frame theory and operator algebras, and some of them can be considered as part of the investigation about "noncommutative" frame theory.Comment: Contemporary Mathematics, 21 pages. arXiv admin note: substantial text overlap with arXiv:1110.583

Free spectral range electrical tuning of a high quality on-chip microcavity

Reconfigurable photonic circuits have applications ranging from next-generation computer architectures to quantum networks, coherent radar and optical metamaterials. However, complete reconfigurability is only currently practical on millimetre-scale device footprints. Here, we overcome this barrier by developing an on-chip high quality microcavity with resonances that can be electrically tuned across a full free spectral range (FSR). FSR tuning allows resonance with any source or emitter, or between any number of networked microcavities. We achieve it by integrating nanoelectronic actuation with strong optomechanical interactions that create a highly strain-dependent effective refractive index. This allows low voltages and sub-nanowatt power consumption. We demonstrate a basic reconfigurable photonic network, bringing the microcavity into resonance with an arbitrary mode of a microtoroidal optical cavity across a telecommunications fibre link. Our results have applications beyond photonic circuits, including widely tuneable integrated lasers, reconfigurable optical filters for telecommunications and astronomy, and on-chip sensor networks.Comment: Main text: 7 pages, 3 figures. Supplementary information: 7 pages, 9 figure

High-Q exterior whispering gallery modes in a metal-coated microresonator

We propose a kind of plasmonic whispering gallery modes highly localized on the exterior surface of a metal-coated microresonator. This exterior (EX) surface mode possesses high quality factors at room temperature, and can be efficiently excited by a tapered fiber. The EX mode can couple to an interior (IN) mode and this coupling produces a strong anti-crossing behavior, which not only allows conversion of IN to EX modes, but also forms a long-lived anti-symmetric mode. As a potential application, the EX mode could be used for a biosensor with a sensitivity high up to 500 nm per refraction index unit, a large figure of merit, and a wide detection range