Control of one-dimensional guided formations using coarse information

Motivated by applications in intelligent highway systems, the paper studies the problem of guiding mobile agents in a one-dimensional formation to their desired relative positions. Only coarse information is used which is communicated from a guidance system that monitors in real time the agents' motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.Comment: 13 pages, 4 figure

Tuning a magnetic Feshbach resonance with spatially modulated laser light

We theoretically investigate the control of a magnetic Feshbach resonance using a bound-to-bound molecular transition driven by spatially modulated laser light. Due to the spatially periodic coupling between the ground and excited molecular states, there exists a band structure of bound states, which can uniquely be characterized by some extra bumps in radio-frequency spectroscopy. With the increasing of coupling strength, the series of bound states will cross zero energy and directly result in a number of scattering resonances, whose position and width can be conveniently tuned by the coupling strength of the laser light and the applied magnetic field (i.e., the detuning of the ground molecular state). In the presence of the modulated laser light, universal two-body bound states near zero-energy threshold still exist. However, compared with the case without modulation, the regime for such universal states is usually small. An unified formula which embodies the influence of the modulated coupling on the resonance width is given. The spatially modulated coupling also implies a local spatially varying interaction between atoms. Our work proposes a practical way of optically controlling interatomic interactions with high spatial resolution and negligible atomic loss.Comment: 9pages, 5figur

Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues---relationships among differing results and levels of accuracy---by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. When compared to the 56 real-world networks, the epidemic threshold obtained by the DMP method is closer to the actual epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in some scenarios---such as networks with positive degree-degree correlations, with an eigenvector localized on the high $k$-core nodes, or with a high level of clustering---the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input parameter, performs better than the other two methods. We also find that the performances of the three predictions are irregular versus modularity

Shape reconstructions by using plasmon resonances

We study the shape reconstruction of a dielectric inclusion from the faraway measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude's model of the dielectric parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme