The Tightness of Multipartite Coherence from Spectrum Estimation

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the l1-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods by using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228 (2021)]. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation.

Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models

In recent years, the research into cluster-weighted models has been intense. However, estimating the covariance matrix of the maximum likelihood estimator under a cluster-weighted model is still an open issue. Here, an approach is developed in which information-based estimators of such a covariance matrix are obtained from the incomplete data log-likelihood of the multivariate Gaussian linear cluster-weighted model. To this end, analytical expressions for the score vector and Hessian matrix are provided. Three estimators of the asymptotic covariance matrix of the maximum likelihood estimator, based on the score vector and Hessian matrix, are introduced. The performances of these estimators are numerically evaluated using simulated datasets in comparison with a bootstrap-based estimator; their usefulness is illustrated through a study aiming at evaluating the link between tourism flows and attendance at museums and monuments in two Italian regions.

Jensen–Shannon Divergence-Based k-Medoids Clustering

Several conventional clustering methods use the squared L2-norm as the dissimilarity. The squared L2-norm is calculated from only the object coordinates and obtains a linear cluster boundary. To extract meaningful cluster partitions from a set of massive objects, it is necessary to obtain cluster partitions that consisting of complex cluster boundaries. In this study, a JS-divergence-based k-medoids (JSKMdd) is proposed. In the proposed method, JS-divergence, which is calculated from the object distribution, is considered as the dissimilarity. The object distribution is estimated from kernel density estimation to calculate the dissimilarity based on both the object coordinates and their neighbors. Numerical experiments were conducted using five artificial datasets to verify the effectiveness of the proposed method. In the numerical experiments, the proposed method was compared with the k-means clustering, k-medoids clustering, and spectral clustering. The results show that the proposed method yields better results in terms of clustering performance than other conventional methods.

Typology of the traditional settlementof the Kinh folk in the areas of North Vietnam

Types of traditional settlement structures of the Kinh folk in the Northern Vietnam are examined. Autonomy and the economy of self-sufficiency in traditional villages have greatly influenced their settlement structure. Such factors as landscape, topography, along with the development over time, have formed the following seven types of settlement structures: compact, one-sided linear, bilateral linear, branched linear, cluster, radial and closed settlements.

Sequential generation of linear cluster states from a single photon emitter

Light states composed of multiple entangled photons—such as cluster states—are essential for developing and scaling-up quantum computing networks. Photonic cluster states can be obtained from single-photon sources and entangling gates, but so far this has only been done with probabilistic sources constrained to intrinsically low efficiencies, and an increasing hardware overhead. Here, we report the resource-efficient generation of polarization-encoded, individually-addressable photons in linear cluster states occupying a single spatial mode. We employ a single entangling-gate in a fiber loop configuration to sequentially entangle an ever-growing stream of photons originating from the currently most efficient single-photon source technology—a semiconductor quantum dot. With this apparatus, we demonstrate the generation of linear cluster states up to four photons in a single-mode fiber. The reported architecture can be programmed for linear-cluster states of any number of photons, that are required for photonic one-way quantum computing schemes.

Comparison of Spatial Layout of Tall Buildings Clustered in Circular, Rectangular, and Linear Geographical Areas and Impact on Skyline

Modern cities with tall building clusters can create powerful and distinctive features on the skyline more so than those with scattered tall buildings. In terms of their role in the city, tall building clusters can improve the image of the city, provide for high population density, and distinguish the urban centers. However, the planning of tall building clusters needs to be conducted using in-depth analysis in response to the spatial context to create an attractive skyline. This research attempts to compare different layouts of tall building clusters organized in circular, rectangular, and linear geographical areas. Their impact on the skyline was determined by analyzing the visibility and height transitions of these tall building clusters. Grasshopper was used to calculate the degree of surface visibility of these tall buildings from observers in urban spaces. To quantify the height transition of the cluster, the obstructed buildings were identified and mapped on the skyline viewed from a specific viewpoint. The results showed that the linear cluster had high visibility, followed by the circular and rectangular clusters. Decreasing the heights from the center to the periphery supported the focal point of the cluster.