Provably non-stiff implementation of weak coupling conditions for hyperbolic problems

In the context of coupling hyperbolic problems, the maximum stable time step of an explicit numerical scheme may depend on the design of the coupling procedure. If this is the case, the coupling procedure is sensitive to changes in model parameters independent of the Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades the performance of a numerical scheme. To overcome this problem, we present a systematic and general procedure for weakly imposing coupling conditions via penalty terms in a provably non-stiff manner. The procedure can be used to construct both energy conservative and dissipative couplings, and the user is given control over the amount of dissipation desired. The resulting formulation is simple to implement and dual consistent. The penalty coefficients take the form of projection matrices based on the coupling conditions. Numerical experiments demonstrate that this procedure results in both optimal spectral radii and superconvergent linear functionals.

Vegetation Removal on 3D Point Cloud Reconstruction of Cut-Slopes Using U-Net

The 3D point cloud reconstruction from photos taken by an unmanned aerial vehicle (UAV) is a promising tool for monitoring and managing risks of cut-slopes. However, surface changes on cut-slopes are likely to be hidden by seasonal vegetation variations on the cut-slopes. This paper proposes a vegetation removal method for 3D reconstructed point clouds using (1) a 2D image segmentation deep learning model and (2) projection matrices available from photogrammetry. For a given point cloud, each 3D point of it is reprojected into the image coordinates by the projection matrices to determine if it belongs to vegetation or not using the 2D image segmentation model. The 3D points belonging to vegetation in the 2D images are deleted from the point cloud. The effort to build a 2D image segmentation model was significantly reduced by using U-Net with the dataset prepared by the colour index method complemented by manual trimming. The proposed method was applied to a cut-slope in Doam Dam in South Korea, and showed that vegetation from the two point clouds of the cut-slope at winter and summer was removed successfully. The M3C2 distance between the two vegetation-removed point clouds showed a feasibility of the proposed method as a tool to reveal actual change of cut-slopes without the effect of vegetation.

Biomarker Extraction Based on Subspace Learning for the Prediction of Mild Cognitive Impairment Conversion

Accurate recognition of progressive mild cognitive impairment (MCI) is helpful to reduce the risk of developing Alzheimer’s disease (AD). However, it is still challenging to extract effective biomarkers from multivariate brain structural magnetic resonance imaging (MRI) features to accurately differentiate the progressive MCI from stable MCI. We develop novel biomarkers by combining subspace learning methods with the information of AD as well as normal control (NC) subjects for the prediction of MCI conversion using multivariate structural MRI data. Specifically, we first learn two projection matrices to map multivariate structural MRI data into a common label subspace for AD and NC subjects, where the original data structure and the one-to-one correspondence between multiple variables are kept as much as possible. Afterwards, the multivariate structural MRI features of MCI subjects are mapped into a common subspace according to the projection matrices. We then perform the self-weighted operation and weighted fusion on the features in common subspace to extract the novel biomarkers for MCI subjects. The proposed biomarkers are tested on Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset. Experimental results indicate that our proposed biomarkers outperform the competing biomarkers on the discrimination between progressive MCI and stable MCI. And the improvement from the proposed biomarkers is not limited to a particular classifier. Moreover, the results also confirm that the information of AD and NC subjects is conducive to predicting conversion from MCI to AD. In conclusion, we find a good representation of brain features from high-dimensional MRI data, which exhibits promising performance for predicting conversion from MCI to AD.

Tuning Database-Friendly Random Projection Matrices for Improved Distance Preservation on Specific Data

Random Projection is one of the most popular and successful dimensionality reduction algorithms for large volumes of data. However, given its stochastic nature, different initializations of the projection matrix can lead to very different levels of performance. This paper presents a guided random search algorithm to mitigate this problem. The proposed method uses a small number of training data samples to iteratively adjust a projection matrix, improving its performance on similarly distributed data. Experimental results show that projection matrices generated with the proposed method result in a better preservation of distances between data samples. Conveniently, this is achieved while preserving the database-friendliness of the projection matrix, as it remains sparse and comprised exclusively of integers after being tuned with our algorithm. Moreover, running the proposed algorithm on a consumer-grade CPU requires only a few seconds.

Forest Structure and Projections of Avicennia germinans (L.) L. at Three Levels of Perturbation in a Southwestern Gulf of Mexico Mangrove

Mangrove forests have declined worldwide and understanding the key drivers of regeneration at different perturbation levels can help manage and preserve these critical ecosystems. For example, the Ramsar site # 1602, located at the Tampamachoco lagoon, Veracruz, México, consists of a dense forest of medium-sized trees composed of three mangrove species. Due to several human activities, including the construction of a power plant around the 1990s, an area of approximately 2.3 km2 has suffered differential levels of perturbation: complete mortality, partial tree loss (divided into two sections: main and isolated patch), and apparently undisturbed sites. The number and size of trees, from seedlings to adults, were measured using transects and quadrats. With a matrix of the abundance of trees by size categories and species, an ordination (nMDS) showed three distinct groups corresponding to the degree of perturbation. Projection matrices based on the size structure of Avicennia germinans showed transition probabilities that varied according to perturbation levels. Lambda showed growing populations except on the zone that showed partial tree loss; a relatively high abundance of seedlings is not enough to ensure stable mangrove dynamics or start regeneration; and the survival of young trees and adult trees showed high sensitivity.

Semi-Supervised Cross-Modal Retrieval Based on Discriminative Comapping

Most cross-modal retrieval methods based on subspace learning just focus on learning the projection matrices that map different modalities to a common subspace and pay less attention to the retrieval task specificity and class information. To address the two limitations and make full use of unlabelled data, we propose a novel semi-supervised method for cross-modal retrieval named modal-related retrieval based on discriminative comapping (MRRDC). The projection matrices are obtained to map multimodal data into a common subspace for different tasks. In the process of projection matrix learning, a linear discriminant constraint is introduced to preserve the original class information in different modal spaces. An iterative optimization algorithm based on label propagation is presented to solve the proposed joint learning formulations. The experimental results on several datasets demonstrate the superiority of our method compared with state-of-the-art subspace methods.

The formal demography of kinship II: Multistate models, parity, and sibship

BackgroundRecent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem.ObjectivesOur aim is to develop a multistate kinship model, classifying individuals jointly by age and other criteria (generically, “stages”).MethodsWe use the vec-permutation method to create multistate projection matrices including age- and stage-dependent survival, fertility, and transitions. These matrices operate on block-structured population vectors that describe the age×stage structure of each kind of kin, at each age of a focal individual.ResultsThe new matrix formulation is directly comparable to, and greatly extends, the recent age-classified kinship model of Caswell (2019a). As an application, we derive a model that includes age and parity. We obtain, for all types of kin, the joint age×parity structure, the marginal age and parity structures, and the (normalized) parity distributions, at every age of the focal individual. We show how to use the age×parity distributions to calculate the distributions of sibship sizes of kin.As an example, we apply the model to Slovakia (1960–2014). The results include a dramatic shift in the parity distribution as the frequency of low-parity kin increased and that of high-parity kin decreased.ContributionThe new model extends the formal demographic analysis of kinship to age×stage-classified models. In addition to parity, other stage classifications, including marital status, maternal age effects, and sex are now open to analysis.