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Map projection is an important research content of cartography. However, distortions are inevitable for any map projection. To evaluate the distortions of map projections, averaged ratio between complementary profiles and spherical great circle arcs based shape and area metrics are proposed. By using Bonne projection as an example and exploiting correlation analyses, it is indicated that great circle arcs based indicators simplify the calculation process of small circle arcs based indicators (i.e., the averaged ratio between complementary profiles),and both great and small circle arcs based indicators are highly correlated with each other. Great circle arcs based indicators are also highly correlated with classical differential calculation based indicators(the Pearson product-moment correlation coefficient between them is greater than 0.988), while the proposed metrics are independent on the differential calculation. By utilizing the method of regression analyses, small regression errors are also achieved(the mean error of linear regression is less than 1.10‰). Finally, in order to reduce the number of sampling points and avoid the inconsistency of sampling points for different map projections, this paper also proposes and verifies a random sampling based calculating process. In all word,great circle arcs based indicators could effectively evaluate the distortions of map projections.

We studied the numerical approximation problem of distortion in map projections. Most widely used differential methods calculate area distortion and maximum angular distortion using partial derivatives of forward equations of map projections. However, in certain map projections, partial derivatives are difficult to calculate because of the complicated forms of forward equations, e.g., equations with iterations, integrations, or multi-way branches. As an alternative, the spherical great circle arcs–based metric employs the inverse equations of map projections to transform sample points from the projection plane to the spherical surface, and then calculates a differential-independent distortion metric for the map projections. We introduce a novel forward interpolated version of the previous spherical great circle arcs–based metric, solely dependent on the forward equations of map projections. In our proposed numerical solution, a rational function–based regression is also devised and applied to our metric to obtain an approximate metric of angular distortion. The statistical and graphical results indicate that the errors of the proposed metric are fairly low, and a good numerical estimation with high correlation to the differential-based metric can be achieved.

Code, data, and plots for a novel numerical approximation metric (i.e., FWD-GCA-based metric) of distortion in map projections.FWD-GCA-based metric was introduced in this study:Jin Yan, Tiansheng Xu, Ni Li, and Guanghong Gong. "Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs���Based Distortion Metric of Map Projections" ISPRS International Journal of Geo-Information 10, no. 10: 649. https://doi.org/10.3390/ijgi10100649### Prerequisite ###Install dependencies in Julia:using PkgPkg.add("CSV")Pkg.add("DataFrames")Pkg.add("Proj4")Pkg.add("ForwardDiff")Install dependencies in Python:pip install numpy scipy matplotlib### Links to codes ###Julia code of GCA-based and the proposed FWD-GCA-based metrics:10.6084/m9.figshare.15022092Julia code of traditional differential-based metrics for more than 85 map projections:10.6084/m9.figshare.15022074Some auxiliary functions in Julia and Python for calculations, analyses, and plots.10.6084/m9.figshare.15022095### Links to data ###Approximately 200k sample points (CSV file) on sphere for evaluating differential-based, GCA, and FWD-GCA metrics:10.6084/m9.figshare.15022071Results (CSV format in ZIP files) of angular and area distortions for 200k sample points:[angular] 10.6084/m9.figshare.16681864[area] 10.6084/m9.figshare.16681867Coordinates of approximately 1 million 2-D sample points (CSV format in ZIP files) on projection plane for each map projection to draw plots:10.6084/m9.figshare.15035457### Links to plots ###Plots of area and angular distortions for all map projections we evaluated:[angular] 10.6084/m9.figshare.16681909[area] 10.6084/m9.figshare.16681912

In this paper, we propose an optimized modeling method based on hierarchical reconstruction for 3D building point cloud. In contrast to existing approaches, this method can make full use of the geometric information of the original building facade point cloud and roof point cloud, which will provide a more complete description for the model of buildings. Firstly, we segment and extract the facade and the roof point cloud of the building based on the difference in planar slices. Further, we use the P-Linkage algorithm to segment the facade point cloud into planar patches, and cluster the planar patches to layer the facade point cloud. Therefore, we reduce the complexity of reconstruction from three-dimensional to two-dimensional. Then we reconstruct the building facade based on the hierarchical reconstruction method and the building roof based on the block reconstruction method. Finally, we merge the facade model and roof model and clip unnecessary polygons, leading to the final model. We experiment with different data and the results compared with the commercial modeling software show that the method is feasible and can improve the three-dimensional building modeling effect.

Automatic recognition methods for non-stationary EEG data collected from EEG sensors play an essential role in neurological detection. The integrative approaches proposed in this study consists of Symlet wavelet processing, a gradient boosting machine, and a grid search optimizer for a three-level classification scheme for normal subjects, intermittent epilepsy, and continuous epilepsy. Fourth-order Symlet wavelets were adopted to decompose the EEG data into five time-frequency sub-bands, whose statistical features were computed and used as classification features. The grid search optimizer was used to automatically find the optimal parameters for training the classifier. The classification accuracy of the gradient boosting machine was compared with that of a support vector machine and a random forest classifier constructed according to previous descriptions. Multiple-index were used to evaluate the Symlet wavelet transform-gradient boosting machine-grid search optimizer classification scheme, which provided better classification accuracy and detection effectiveness than has recently reported in other work on three-level classification of EEG data.

The development process of a complex project involves many tasks, organizations and persons. Therefore, how to assign tasks reasonably to the corresponding organizations or persons will substantially affect the project development results. Based on the summary of the main factors that influence the decision-making behaviors, this paper analyzes the characteristics of tasks and persons. Firstly, the importance of tasks is defined and prioritized. Secondly, this paper identified the cooperative inertia factors. Then the person cooperation model is established. Furthermore, the task assignment algorithm based on the organizational evolution model is proposed. Finally, the simulation results demonstrate the rationality of the proposed task assignment model. It can be employed to perform the quantitative analysis of tasks assignment and help managers make decisions.