Iterative Chebyshev approximation method for optimal control problems.

We present a novel numerical approach for solving nonlinear constrained optimal control problems (NCOCPs). Instead of directly solving the NCOCPs, we start by linearizing the constraints and dynamic system, which results in a sequence of sub-problems. For each sub-problem, we use finite number of Chebyshev polynomials to estimate the control and state vectors. To eliminate the errors at non-collocation points caused by conventional collocation methods, we additionally estimate the coefficient functions involved in the linear constraints and dynamic system by Chebyshev polynomials. By leveraging the characteristics of Chebyshev polynomials, the approximate sub-problem is changed into an equivalent nonlinear optimization problem with linear equality constraints. Consequently, any feasible point of the approximate sub-problem will satisfy the constraints and dynamic system throughout the entire time scale. To validate the efficacy of the new method, we solve three examples and assess the accuracy of the method through the computation of its approximation error. Numerical results obtained show that our approach achieves lower approximation error when compared to the Chebyshev pseudo-spectral method. The proposed method is particularly suitable for scenarios that require high-precision approximation, such as aerospace and precision instrument production.

Bifunctional fusion protein targeting both FXIIa and FXIa displays potent anticoagulation effects.

AIMS: Anticoagulation in disease treatment has been wildly studied in recent years. The intrinsic coagulation pathway is attracting attention of research community due to its low bleeding risk, and inhibitors against intrinsic coagulation factor XIIa (FXIIa) or XIa (FXIa) have been extensively studied. However, studies to develop anticoagulant inhibitors simultaneous targeting FXIIa and FXIa have not been reported. Our study aimed to evaluate the anticoagulation effect of the dual targeting of FXIIa and FXIa. MAIN METHODS: A fusion protein Infestin-PN2KPI (IP) was designed by linking FXIIa inhibitor Infesin4 and FXIa inhibitor PN2KPI through a rigid linker, and was cloned, expressed and characterized. The binding of IP to FXIIa and FXIa was verified by SPR, and inhibitory ability of IP against FXIIa and FXIa was verified by chromogenic substrate method. And then, the anticoagulation and antithrombotic functions of IP were extensively evaluated by aPTT assay, FeCl3-induced carotid artery thrombosis model and transient occlusion of the middle cerebral artery model. KEY FINDINGS: IP significantly prolonged aPTT, inhibited thrombosis and prevented stroke at a dose of at least 1/2 lower than the effective dose of its component Infestin4 or PN2KPI, and did not cause bleed risk. SIGNIFICANCE: The bifunctional fusion protein IP showed good anticoagulation effects, and simultaneous targeting FXIIa and FXIa is a promising strategy for anticoagulation drug development.

Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications.

The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.

Nonlinear Semi-Supervised Metric Learning Via Multiple Kernels and Local Topology.

Changing the metric on the data may change the data distribution, hence a good distance metric can promote the performance of learning algorithm. In this paper, we address the semi-supervised distance metric learning (ML) problem to obtain the best nonlinear metric for the data. First, we describe the nonlinear metric by the multiple kernel representation. By this approach, we project the data into a high dimensional space, where the data can be well represented by linear ML. Then, we reformulate the linear ML by a minimization problem on the positive definite matrix group. Finally, we develop a two-step algorithm for solving this model and design an intrinsic steepest descent algorithm to learn the positive definite metric matrix. Experimental results validate that our proposed method is effective and outperforms several state-of-the-art ML methods.