38,013 research outputs found

    Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

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    It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space HpH^p, 1p<1 \leq p < \infty, is also compact on the Bergman space {\mathfrak B}^p = L^p_a (\D). In this survey, after having described the above known results, we consider Hardy-Orlicz HΨH^\Psi and Bergman-Orlicz BΨ{\mathfrak B}^\Psi spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on HΨH^\Psi but not on BΨ{\mathfrak B}^\Psi

    Advances in Synthetic Gauge Fields for Light Through Dynamic Modulation

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    Photons are weak particles that do not directly couple to magnetic fields. However, it is possible to generate a photonic gauge field by breaking reciprocity such that the phase of light depends on its direction of propagation. This non-reciprocal phase indicates the presence of an effective magnetic field for the light itself. By suitable tailoring of this phase it is possible to demonstrate quantum effects typically associated with electrons, and as has been recently shown, non-trivial topological properties of light. This paper reviews dynamic modulation as a process for breaking the time-reversal symmetry of light and generating a synthetic gauge field, and discusses its role in topological photonics, as well as recent developments in exploring topological photonics in higher dimensions.Comment: 20 pages, 3 figure

    A Theory of Pricing Private Data

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    Personal data has value to both its owner and to institutions who would like to analyze it. Privacy mechanisms protect the owner's data while releasing to analysts noisy versions of aggregate query results. But such strict protections of individual's data have not yet found wide use in practice. Instead, Internet companies, for example, commonly provide free services in return for valuable sensitive information from users, which they exploit and sometimes sell to third parties. As the awareness of the value of the personal data increases, so has the drive to compensate the end user for her private information. The idea of monetizing private data can improve over the narrower view of hiding private data, since it empowers individuals to control their data through financial means. In this paper we propose a theoretical framework for assigning prices to noisy query answers, as a function of their accuracy, and for dividing the price amongst data owners who deserve compensation for their loss of privacy. Our framework adopts and extends key principles from both differential privacy and query pricing in data markets. We identify essential properties of the price function and micro-payments, and characterize valid solutions.Comment: 25 pages, 2 figures. Best Paper Award, to appear in the 16th International Conference on Database Theory (ICDT), 201