Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.

Forest above-ground biomass (AGB) can be estimated based on light detection and ranging (LiDAR) point clouds. This paper introduces an accurate and detailed quantitative structure model (AdQSM), which can estimate the AGB of large tropical trees. AdQSM is based on the reconstruction of 3D tree models from terrestrial laser scanning (TLS) point clouds. It represents a tree as a set of closed and complete convex polyhedra. We use AdQSM to model 29 trees of various species (total 18 species) scanned by TLS from three study sites (the dense tropical forests of Peru, Indonesia, and Guyana). The destructively sampled tree geometry measurement data is used as reference values to evaluate the accuracy of diameter at breast height (DBH), tree height, tree volume, branch volume, and AGB estimated from AdQSM. After AdQSM reconstructs the structure and volume of each tree, AGB is derived by combining the wood density of the specific tree species from destructive sampling. The AGB estimation from AdQSM and the post-harvest reference measurement data show a satisfying agreement. The coefficient of variation of root mean square error (CV-RMSE) and the concordance correlation coefficient (CCC) are 20.37% and 0.97, respectively. AdQSM provides accurate tree volume estimation, regardless of the characteristics of the tree structure, without major systematic deviations. We compared the accuracy of AdQSM and TreeQSM in modeling the volume of 29 trees. The tree volume from AdQSM is compared with the reference value, and the determination coefficient (R2), relative bias (rBias), and CV-RMSE of tree volume are 0.96, 6.98%, and 22.62%, respectively. The tree volume from TreeQSM is compared with the reference value, and the R2, relative Bias (rBias), and CV-RMSE of tree volume are 0.94, −9.69%, and 23.20%, respectively. The CCCs between the volume estimates based on AdQSM, TreeQSM, and the reference values are 0.97 and 0.96. AdQSM also models the branches in detail. The volume of branches from AdQSM is compared with the destructive measurement reference data. The R2, rBias, and CV-RMSE of the branches volume are 0.97, 12.38%, and 36.86%, respectively. The DBH and height of the harvested trees were used as reference values to test the accuracy of AdQSM’s estimation of DBH and tree height. The R2, rBias, and CV-RMSE of DBH are 0.94, −5.01%, and 9.06%, respectively. The R2, rBias, and CV-RMSE of the tree height were 0.95, 1.88%, and 5.79%, respectively. This paper provides not only a new QSM method for estimating AGB based on TLS point clouds but also the potential for further development and testing of allometric equations.

We propose a deep learning-based method for object detection in UAV-borne thermal images that have the capability of observing scenes in both day and night. Compared with visible images, thermal images have lower requirements for illumination conditions, but they typically have blurred edges and low contrast. Using a boundary-aware salient object detection network, we extract the saliency maps of the thermal images to improve the distinguishability. Thermal images are augmented with the corresponding saliency maps through channel replacement and pixel-level weighted fusion methods. Considering the limited computing power of UAV platforms, a lightweight combinational neural network ComNet is used as the core object detection method. The YOLOv3 model trained on the original images is used as a benchmark and compared with the proposed method. In the experiments, we analyze the detection performances of the ComNet models with different image fusion schemes. The experimental results show that the average precisions (APs) for pedestrian and vehicle detection have been improved by 2%~5% compared with the benchmark without saliency map fusion and MobileNetv2. The detection speed is increased by over 50%, while the model size is reduced by 58%. The results demonstrate that the proposed method provides a compromise model, which has application potential in UAV-borne detection tasks.

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed.

We establish by exact, nonperturbative methods a universality for the correlation functions in Kraichnan's``rapid-change''model of a passively advected scalar field. We show that the solutions for separated points in the convective range of scales are unique and independent of the particular mechanism of the scalar dissipation. Any non-universal dependences therefore must arise from the large length-scale features. The main step in the proof is to show that solutions of the model equations are unique even in the idealized case of zero diffusivity, under a very modest regularity requirement (square-integrability). Within this regularity class the only zero-modes of the global many-body operators are shown to be trivial ones (ie constants). In a bounded domain of size L , with physical boundary conditions, the``ground-state energy''is strictly positive and scales as L with an exponent L .