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We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cramér–Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of radiometer and expectation–maximization (EM) algorithms in the estimation of the force noise power. When applied to experimental data, the EM estimator is found to have the lowest error and follow the Cramér–Rao bound most closely. Our analytic results are envisioned to be valuable to optomechanical experiment design, while the EM algorithm, with its ability to estimate most of the system parameters, is envisioned to be useful for optomechanical sensing, atomic magnetometry and fundamental tests of quantum mechanics. [ABSTRACT FROM AUTHOR]

How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the susceptible-infected-recovered model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability ω- and then get infected -with probability β. However, when the fraction of immunized individuals reaches a threshold VL, the vaccination stops, after which only the infection is possible. In the steady state, besides the critical points βc and ωc that separate a non-epidemic from an epidemic phase, we find for a range of VL another transition points, β* > βc and ω* < ωc, which correspond to a novel discontinuous phase transition. This critical value separates a phase where the amount of vaccines is sufficient, from a phase where the disease is strong enough to exhaust all the vaccination units. For a disease with fixed β, the vaccination probability ω can be controlled in order to drastically reduce the number of infected individuals, using efficiently the available vaccines. Furthermore, the temporal evolution of the system close to β* or ω*, shows that after a peak of infection the system enters into a quasi-stationary state, with only a few infected cases. But if there are no more vaccines, these few infected individuals could originate a second outbreak, represented by a second peak of infection. This state of apparent calm, could be dangerous since it may lead to misleading conclusions and to an abandon of the strategies to control the disease. [ABSTRACT FROM AUTHOR]

We introduce a discrete-time distributed consensus process on multi-layered complex networks represented by multiplex graphs. The proposed consensus process can be characterized with a multiplex Markov chain (MC) composed of a mixture of interlayer and intralayer MCs. The interlayer MC is characterized by a parameter which represents the probability that the chain will switch between different layers of the multiplex network. Surprisingly, for large regions of the parameter space the convergence speed of the multiplex MC is determined only by the convergence speed of the interlayer MC. Moreover, as the number of layers in the network is increased, these regions increase until they encompass the whole parameter space. We also show that for some regions of the parameter space, the multiplex MC has a faster convergence speed than the MCs on top of the individual layers, thus complementing previous results on diffusion on multiplex networks. [ABSTRACT FROM AUTHOR]