39,152 research outputs found
Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces
It is known, from results of B. MacCluer and J. Shapiro (1986), that every
composition operator which is compact on the Hardy space , , 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 and Bergman-Orlicz 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 but not on
Advances in Synthetic Gauge Fields for Light Through Dynamic Modulation
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
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
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