Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting electrons in two-dimensions (2D), in a uniform magnetic field, where the probes are external solenoids with a magnetic flux that is a fraction of the flux quantum. The Hamiltonian could also be implemented in an ultracold (fermionic) atomic gas in 2D, in a uniform synthetic magnetic field, where the probes are lasers giving rise to synthetic solenoid gauge potentials. We find analytically and numerically the ground state of this system when only the lowest Landau level states are occupied. It is shown that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules of synthetic anyons are discussed for different microscopic realizations of the fusion process.
Composites formed from charged particles and magnetic flux tubes, proposed by Wilczek, are one model for anyons-particles obeying fractional statistics. Here we propose a scheme for realizing charged flux tubes, in which a charged object with an intrinsic magnetic dipole moment is placed between two semi-infinite blocks of a high-permeability (μ_{r}) material, and the images of the magnetic moment create an effective flux tube. We show that the scheme can lead to a realization of Wilczek's anyons, when a two-dimensional electron system, which exhibits the integer quantum Hall effect, is sandwiched between two blocks of the high-μ_{r} material with a temporally fast response (in the cyclotron and Larmor frequency range). The signature of Wilczek's anyons is a slight shift of the resistivity at the plateau of the IQHE. Thus, the quest for high-μ_{r} materials at high frequencies, which is underway in the field of metamaterials, and the quest for anyons, are here found to be on the same avenue.
Various distance-based clustering algorithms have been reported, but the core component of all of them is a similarity or distance measure for classification of data. Rather than setting the priority to comparison of the performance of different clustering algorithms, it may be worthy to analyze the influence of different similarity measures on the results of clustering algorithms. The main contribution of this work is a comparative study of the impact of 9 similarity measures on similarity-based trajectory clustering using DBSCAN algorithm for commercial flight dataset. The novelty in this comparison is exploring the robustness of the clustering algorithm with respect to algorithm parameter. We evaluate the accuracy of clustering, accuracy of anomaly detection, algorithmic efficiency, and we determine the behavior profile for each measure. We show that DTW and Frechet distance lead to the best clustering results, while LCSS and Hausdorff Cosine should be avoided for this task.
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