Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger and López (J. Optim. Theory Appl. 154(2), 2012), and is mainly focused on the application of the stationarity criteria to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements—normals and/or subdifferentials.

Spatiotemporal characteristics of the Huangtupo landslide in the Three Gorges region (China) constrained by radar interferometry

The Huangtupo landslide is one of the largest in the Three Gorges region, China. The county-seat town of Badong, located on the south shore between the Xiling and Wu gorges of the Yangtze River, was moved to this unstable slope prior to the construction of the Three Gorges Project, since the new Three Gorges reservoir completely submerged the location of the old city. The instability of the slope is affecting the new town by causing residential safety problems. The Huangtupo landslide provides scientists an opportunity to understand landslide response to fluctuating river water level and heavy rainfall episodes, which is essential to decide upon appropriate remediation measures. Interferometric Synthetic Aperture Radar (InSAR) techniques provide a very useful tool for the study of superficial and spatially variable displacement phenomena. In this paper, three sets of radar data have been processed to investigate the Huangtupo landslide. Results show that maximum displacements are affecting the northwest zone of the slope corresponding to Riverside slumping mass I#. The other main landslide bodies (i.e. Riverside slumping mass II#, Substation landslide and Garden Spot landslide) exhibit a stable behaviour in agreement with in situ data, although some active areas have been recognized in the foot of the Substation landslide and Garden Spot landslide. InSAR has allowed us to study the kinematic behaviour of the landslide and to identify its active boundaries. Furthermore, the analysis of the InSAR displacement time-series has helped recognize the different displacement patterns on the slope and their relationships with various triggering factors. For those persistent scatterers, which exhibit long-term displacements, they can be decomposed into a creep model (controlled by geological conditions) and a superimposed recoverable term (dependent on external factors), which appears closely correlated with reservoir water level changes close to the river's edge. These results, combined with in situ data, provide a comprehensive analysis of the Huangtupo landslide, which is essential for its management.

Constrained self-organizing feature map to preserve feature extraction topology

In many classification problems, it is necessary to consider the specific location of an n-dimensional space from which features have been calculated. For example, considering the location of features extracted from specific areas of a two-dimensional space, as an image, could improve the understanding of a scene for a video surveillance system. In the same way, the same features extracted from different locations could mean different actions for a 3D HCI system. In this paper, we present a self-organizing feature map able to preserve the topology of locations of an n-dimensional space in which the vector of features have been extracted. The main contribution is to implicitly preserving the topology of the original space because considering the locations of the extracted features and their topology could ease the solution to certain problems. Specifically, the paper proposes the n-dimensional constrained self-organizing map preserving the input topology (nD-SOM-PINT). Features in adjacent areas of the n-dimensional space, used to extract the feature vectors, are explicitly in adjacent areas of the nD-SOM-PINT constraining the neural network structure and learning. As a study case, the neural network has been instantiate to represent and classify features as trajectories extracted from a sequence of images into a high level of semantic understanding. Experiments have been thoroughly carried out using the CAVIAR datasets (Corridor, Frontal and Inria) taken into account the global behaviour of an individual in order to validate the ability to preserve the topology of the two-dimensional space to obtain high-performance classification for trajectory classification in contrast of non-considering the location of features. Moreover, a brief example has been included to focus on validate the nD-SOM-PINT proposal in other domain than the individual trajectory. Results confirm the high accuracy of the nD-SOM-PINT outperforming previous methods aimed to classify the same datasets.