Dynamic Sampling from a Discrete Probability Distribution with a Known Distribution of Rates

In this paper, we consider a number of efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular the maximum and minimum rate, and where the number of possible outcomes N is large. We consider three basic data structures, the Acceptance-Rejection method, the Complete Binary Tree and the Alias Method. These can be used as building blocks in a multi-level data structure, where at each of the levels, one of the basic data structures can be used. Depending on assumptions on the distribution of the rates of outcomes, different combinations of the basic structures can be used. We prove that for particular data structures the expected time of sampling and update is constant, when the rates follow a non-decreasing distribution, log-uniform distribution or an inverse polynomial distribution, and show that for any distribution, an expected time of sampling and update of $O\left(\log\log{r_{max}}/{r_{min}}\right)$ is possible, where $r_{max}$ is the maximum rate and $r_{min}$ the minimum rate. We also present an experimental verification, highlighting the limits given by the constraints of a real-life setting

Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory

The full structuration of light in the transverse plane, including intensity, phase and polarization, holds the promise of unprecedented capabilities for applications in classical optics as well as in quantum optics and information sciences. Harnessing special topologies can lead to enhanced focusing, data multiplexing or advanced sensing and metrology. Here we experimentally demonstrate the storage of such spatio-polarization-patterned beams into an optical memory. A set of vectorial vortex modes is generated via liquid crystal cell with topological charge in the optic axis distribution, and preservation of the phase and polarization singularities is demonstrated after retrieval, at the single-photon level. The realized multiple-degree-of-freedom memory can find applications in classical data processing but also in quantum network scenarios where structured states have been shown to provide promising attributes, such as rotational invariance

Photonic polarization gears for ultra-sensitive angular measurements

Quantum metrology bears a great promise in enhancing measurement precision, but is unlikely to become practical in the near future. Its concepts can nevertheless inspire classical or hybrid methods of immediate value. Here, we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a "photonic gear", converting, for each photon, a mechanical rotation of an angle {\theta} into an amplified rotation of the optical polarization by m{\theta}, corresponding to a "super-resolving" Malus' law. We show that this effect leads to single-photon angular measurements with the same precision of polarization-only quantum strategies with m photons, but robust to photon losses. Moreover, we combine the gear effect with the quantum enhancement due to entanglement, thus exploiting the advantages of both approaches. The high "gear ratio" m boosts the current state-of-the-art of optical non-contact angular measurements by almost two orders of magnitude.Comment: 10 pages, 4 figures, + supplementary information (10 pages, 3 figures

The future of microarray technology: networking the genome search

In recent years microarray technology has been increasingly used in both basic and clinical research, providing substantial information for a better understanding of genome‐environment interactions responsible for diseases, as well as for their diagnosis and treatment. However, in genomic research using microarray technology there are several unresolved issues, including scientific, ethical and legal issues. Networks of excellence like GA2LEN may represent the best approach for teaching, cost reduction, data repositories, and functional studies implementation