Euclidean distance matrix optimization with ordinal constraints (ED-MOC) has found important applications in sensor network localization and molecular conformation. It can also be viewed as a matrix formulation of multidimensional scaling, which is to embed n points in a r-dimensional space such that the resulting distances follow the ordinal constraints. The ordinal constraints, though proved to be quite useful, may result in only zero solution when too many are added, leaving the feasibility of EDMOC as a question. In this paper, we first study the feasibility of EDMOC systematically. We show that if r ≥ n − 2, EDMOC always admits a nontrivial solution. Otherwise, it may have only zero solution. The latter interprets the numerical observations of 'crowding phenomenon'. Next we overcome two obstacles in designing fast algorithms for EDMOC, i.e., the low-rankness and the potential huge number of ordinal constraints. We apply the technique developed in [35] to take the low rank constraint as the conditional positive semidefinite cone with rank cut. This leads to a majorization penalty approach. The ordinal constraints are left to the subproblem, which is exactly the weighted isotonic regression, and can be solved by the enhanced implementation of Pool Adjacent Violators Algorithm (PAVA). Extensive numerical results demonstrate the superior performance of the proposed approach over some state-of-the-art solvers.

Safety and automatic control are extremely important when operating manipulators. For large engineering manipulators, the main challenge is to accurately recognize the posture of all arm segments. In classical sensing methods, the accuracy of an inclinometer is easily affected by the elastic deformation in the manipulator's arms. This results in big error accumulations when sensing the angle of joints between arms one by one. In addition, the sensing method based on machine vision is not suitable for such kind of outdoor working situation yet. In this paper, we propose a novel posture positioning method for multi-joint manipulators based on wireless sensor network localization. The posture sensing problem is formulated as a Nearest-Euclidean-Distance-Matrix (NEDM) model. The resulting approach is referred to as EDM-based posture positioning approach (EPP) and it satisfies the following guiding principles: (i) The posture of each arm segment on a multi-joint manipulator must be estimated as accurately as possible; (ii) The approach must be computationally fast; (iii) The designed approach should not be susceptible to obstructions. To further improve accuracy, we explore the inherent structure of manipulators, i.e., fixed-arm length. This is naturally presented as linear constraints in the NEDM model. For concrete pumps, a typical multi-joint manipulator, the mechanical property that all arm segments always lie in a 2D plane is used for dimension-reduction operation. Simulation and experimental results show that the proposed method provides efficient solutions for posture sensing problem and can obtain preferable localization performance with faster speed than applying the existing localization methods.

Multidimensional scaling (MDS) is to recover a set of points by making use of noised pairwise Euclidean distances. In some situations, the observed Euclidean distances may contain large errors or even missing values. In such cases, the order of the distances is far more important than their magnitude. Non-metric multidimensional scaling (NMDS) is then to deal with this problem by taking use of the ordinal information. The challenge of NMDS is to tackle the large number of ordinal constraints on distances (for [Formula: see text] points, this will be of [Formula: see text]), which will slow down existing numerical algorithms. In this paper, we propose an ordinal weighted Euclidean distance matrix model for NMDS. By designing an ordinal weighted matrix, we get rid of the large number of ordinal constraints and tackle the ordinal constraints in a soft way. We then apply our model to image ranking. The key insight is to view the image ranking problem as NMDS in the kernel space. We conduct extensive numerical test on two state-of-the-art datasets: FG-NET aging dataset and MSRA-MM dataset. The results show the improvement of the proposed approach over the existing methods.

No abstract

Background Breast cancer is the most common cancer among women in China; however, a routine screening programme is currently not available. The aim of this study was to develop a novel model to estimate the effectiveness and cost-effectiveness of several screening strategies for women living in urban areas.Methods We developed a state-transition natural history model of breast cancer and validated the model with multiple outcomes for Chinese women living in urban areas. A total of 23 screening scenarios were considered with different screening techniques, ages, and frequencies. We evaluated the reduction of breast cancer mortality for each screening scenario compared with no screening. By integrating population-specific cost and utility scores, we calculated the incremental cost-effectiveness ratio (ICER) in terms of the cost per quality-adjusted life-year gained.