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The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

Pulsed direct current electric barrier (EB) technology has been widely used to repel invasive species, guide fish away from dangerous areas, and direct them towards favourable locations, such as bypass channels. The effectiveness of an EB is influenced by many factors, and there is no consensus concerning what are the primary and secondary effects of the factors that influence fish response to EBs. In this study, Experiment 1 was conducted to investigate primary and secondary effects. It consisted of static water tests in which four factors were varied (electrode arrangement (EA), pulse voltage (PV), pulse frequency (PF), pulse width (PW)), each taking one of three values, in three phases of electrode activation (Phase I, before activating the pulsed power supply; Phase II, during the period of electrification; Phase III, after deactivating the power supply). Since the experimental design was orthogonal, nine treatments were designed and used in each phase. Experiment 2 was to identify whether there was any difference in barrier effectiveness and fish injury at different water velocities (0 m s-1, 0.3 m s-1,and 0.5 m s-1). The result showed that times of silver carp successfully passing the barrier in Phase I were significantly greater than in Phase II or Phase III for each treatment (P < 0.05), and there were no significant differences in times of successful passage among the nine treatments in phase II (P > 0.05). The primary and secondary effects of the four factors on the blocking rate and the number of fish injuries were EA > PV > PW > PF. Barrier obstruction rate and the number of fish injuries increased as fish body length increased. There was no significant difference (P > 0.05) in blocking rate or in fish injury rate as water velocity increased. The study will provide a foundational baseline for conserving fish stocks and preventing the cross-regional spread of invasive fish species. • The primary and secondary effects on barrier and fish injury were determined. • Silver carp had a high avoidance response to electric barrier. • Fish injuries can be minimized by modifying the electrode arrangement. • The blocking rate and fish injuries were positively relation with the size of fish. • Low-velocity flows does not affect the blocking effect of electric barrier. [ABSTRACT FROM AUTHOR]

Graph-based semi-supervised learning (G-SSL) methods play an increasingly important role in machine learning systems. Recently, latent low-rank representation (LatLRR) graph has gained great success in subspace clustering. However, LatLRR only considers the global structure, while the local geometric information, which is often important to many real applications, is ignored. In this paper, we propose a locality regularized LatLRR model (LR-LatLRR) for semi-supervised subspace clustering problems. This model incorporates two regularization terms into LatLRR by taking the local structure of data into account. Then, we develop an efficient splitting algorithm for solving LR-LatLRR. In addition, we also prove the global convergence of the proposed algorithm. Furthermore, we extend the LR-LatLRR model to a case of including the non-negative constraint. Finally, we conduct experiments on a synthetic data and several real data sets for the semi-supervised clustering problems. Experimental results show that our method can obtain high classification accuracy and outperforms several state-of-the-art G-SSL methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optimal trade-off model for portfolio selection with the effect of systematic risk diversification, measured by the maximum marginal systematic risk of all the risk contributors. First, the classical portfolio selection model with constraints on allocation of systematic risk is shown to be equivalent to our trade-off model under certain conditions. Then, we transform the trade-off model into a special non-convex and non-smooth composite problem equivalently. Thus a modified accelerated gradient (AG) algorithm can be introduced to solve the composite problem. The efficiency of the algorithm for solving the composite problem is demonstrated by theoretical results on both the convergence rate and the iteration complexity bound. Finally, empirical analysis demonstrates that the proposed model is a preferred tool for active portfolio risk management when compared with the existing models. We also carry out a series of numerical experiments to compare the performance of the modified AG algorithm with the other three first-order algorithms. [ABSTRACT FROM AUTHOR]

Abstract The control parameterization method used together with the time-scaling transformation is an effective approach to approximating optimal control problems into optimal parameter selection problems when no time delays are involved. The approximate problems can then be solved by gradient-based optimization algorithms. However, the time-scaling transformation, which works well for optimizing variable switching times of the approximate piecewise constant/linear control functions obtained after the application of the control parameterization method, is not applicable to optimal control problems with time delays. In this paper, we consider a class of nonlinear optimal control problems with multiple time delays subject to canonical equality and inequality constraints. Our aim is to develop a novel transformation procedure that converts a given time-delay system into an equivalent system – defined on a new time horizon – in which the control switching times are fixed, but the dynamic system contains multiple variable time delays expressed in terms of the durations between the switching times for each of the approximate control functions in the original time horizon. On this basis, we show that an optimal control policy for the equivalent system can be obtained efficiently using gradient-based optimization techniques. This optimal control policy can then be used to determine the optimal switching times and optimal control variables for the original system. We conclude the paper by solving two example problems. [ABSTRACT FROM AUTHOR]

Semi-supervised support vector machine is a popular method in the research area of machine learning. Considering a large amount of unlabeled data points in real-life world, the semi-supervised support machine has the ability of good generalization for dealing with nonlinear classification problems. In this paper, a proximal quadratic surface support vector machine model is proposed for semi-supervised binary classification. The main advantage of our new model is that the proximal quadratic surfaces are constructed directly for nonlinear classification instead of using the kernel function, which avoids the tasks of choosing kernels and tuning their parameters. We reformulate this proposed model as an unconstrained mixed-integer quadratic programming problem. Semi-definite relaxation is then adopted, and a primal alternating direction method is further proposed for fast computation. We test the proposed method on some artificial and public benchmark data sets. Preliminary results indicate that our method outperforms some well-known methods for semi-supervised classification in terms of the efficiency and classifying accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a sparse quadratic kernel-free least squares semi-supervised support vector machine model by adding an L 1 norm regularization term to the objective function and using the least squares method, which results in a nonconvex and nonsmooth quadratic programming problem. For computational considerations, we use the smoothing technique and consensus technique. Then we adopt the proximal alternating direction method of multipliers (P-ADMM) to solve it, as well as propose a strategy of parameter selection. Then we not only derive the convergence analysis of algorithm, but also estimate the convergence rate as o ( 1 / k ) , where k is the number of iteration. This gives the best bound of P-ADMM known so far for nonconvex consensus problem. To demonstrate the efficiency of our model, we compare the proposed method with several state-of-the-art methods. The numerical results show that our model can achieve both better accuracy and sparsity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose a new splitting augmented Lagrangian method (SALM) for solving a class of optimization problems with both cardinality constraint and semicontinuous variables constraint. The proposed approach, inspired by the penalty decomposition method in [Z.S. Lu and Y. Zhang, Sparse approximation via penalty decomposition methods,SIAM J. Optim.23(4) (2013), pp. 2448–2478], splits the problem into two subproblems using auxiliary variables. SALM solves two subproblems alternatively. Furthermore, we prove the convergence of SALM, under certain assumptions. Finally, SALM is implemented on the portfolio selection problem and the compressed sensing problem, respectively. Numerical results show that SALM outperforms the well-known tailored approach in CPLEX 12.6 and the penalty decomposition method, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concept of maximum relative marginal risk (MRMR) to measure the effect of risk diversification under the mean–variance portfolio selection. Then we develop an optimal trade-off model between the total risk and the MRMR. Since the MRMR is described as a maximum fractional quadratic functions, we convert it into a quadratic function in terms of auxiliary variables and transform it as a constraint. Then it turns to a non-convex quadratically constrained quadratic problems (QCQP). To solve this non-convex QCQP, we relax and approximate the optimal trade-off model, respectively, and obtain both second-order cone relaxation and inner approximation. Both of them provide a lower bound and an upper bound for the original non-convex QCQP. Furthermore, we solve the QCQP by using an efficient and globally convergence branch-and-bound solution algorithm proposed by Li et al. [Active allocation of systematic risk and control of risk sensitivity in portfolio optimization, Eur. J. Oper. Res. 228 (2013), pp. 556–570]. In the process of solution we only branch the variables related to the MRMR and reduce the numbers of branch largely. Finally, our model is illustrated and demonstrated by empirical analysis. The numerical results show that our model outperforms the existing models to deal with the risks between the total risk and the relative marginal risk in portfolio selection. [ABSTRACT FROM PUBLISHER]

Semi-supervised support vector machines arise in machine learning as a model of mixed integer programming problem for classification. In this paper, we propose two convex conic relaxations for the original mixed integer programming problem. The first one is a new semi-definite relaxation, and its possibly maximal ratio of the optimal value is estimated approximately. The second one is a doubly nonnegative relaxation, which is relaxed from a well-known conic programming problem called completely positive programming problem that is equivalent to the original problem. Furthermore, we prove that the doubly nonnegative relaxation is tighter than the semi-definite relaxation. Finally, the numerical results show that two proposed relaxations not only generate proper classifiers but also outperform some existing methods in classification accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of a simple locally kernel function. As an application, we present a full-step interior-point algorithm for second-order cone optimization (SOCO). The algorithm uses the simple locally kernel function to determine the search direction and define the neighbourhood of central path. The full step used in the algorithm has local quadratic convergence property according to the proximity function which is constructed by the simple locally kernel function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bound for SOCO. [ABSTRACT FROM AUTHOR]

In portfolio optimization, non-convex regularization has recently been recognized as an important approach to promote sparsity, while countervailing the shortcomings of convex penalty. In this paper, we customize the non-convex piecewise quadratic approximation (PQA) function considering the background of portfolio management and present the PQA regularized mean–variance model (PMV). By exposing the feature of PMV, we prove that a KKT point of PMV is a local minimizer if the regularization parameter satisfies a mild condition. Besides, the theoretical sparsity of PMV is analysed, which is associated with the regularization parameter and the weight parameter. To solve this model, we introduce the accelerated proximal gradient (APG) algorithm, whose improved linear convergence rate compared with proximal gradient (PG) algorithm is developed. Moreover, the optimal accelerated parameter of APG algorithm for PMV is attained. These theoretical results are further illustrated with numerical experiments. Finally, empirical analysis demonstrates that the proposed model has a better out-of-sample performance and a lower turnover than many other existing models on the tested datasets. [ABSTRACT FROM AUTHOR]

[Display omitted] • Social media has been an instant source of information for natural disasters. • Physical harm was assessed employing existing damage dictionary databases. • The evaluation of flood sensitivity levels in all districts was carried out. • Analysis comprised the investigation of emotional damage using data from tweets. • Sentiment analysis of ex-post disaster evaluation for future flood mitigation. Social media has been an instant source of information for natural disasters, such as urban floods, throughout the world. Ex-post evaluation of the information is considered more important after a flood disaster with devastating consequences on critical infrastructure, the environment, and the well-being of the society. Research proposes an evaluation framework for integrating the disorganized online public opinion on urban flood disaster events towards emotional and conceptual characteristics for better ex-post analysis and public participation. Social media posts on an urban flood were acquired using a search engine, and then sentiment analysis, topic modeling, and spatial–temporal analysis were performed to generate measures of online public opinion about the urban flood crisis. Twitter (X) is the most popular microblogging service presently available. As per the methodology, we analyzed all tweets regarding the 2022 urban flood in the cosmopolitan city (Karachi) of Pakistan from users all over the world. The evaluation results demonstrated that the distribution patterns of post intensities and emotion polarity in response to the floods emphasized crucial aspects with contradictory emotions and highlighted the strategic implications. Experimental results on real datasets show relatively better performance than the baseline and state-of-the-art approaches and achieved the highest 91% score. Online public opinion is a valuable supplement to ex post-disaster evaluation as it helps the project (e.g., flood management) better perform and provides suggestions for future flood mitigation, especially public participation management. [ABSTRACT FROM AUTHOR]

In this paper we study the spectra of uniform hypertrees by using the generalized weighted incident matrix. We show that λ is a nonzero eigenvalue of the hypertree H corresponding to an eigenvector with all elements nonzero if and only if λ is a root of the polynomial φ ( H ) = ∑ i = 0 m ( − 1 ) i | M i | x ( m − i ) r , where | M i | is the number of matchings of order i in H . [ABSTRACT FROM AUTHOR]

In this paper, the adjacency tensor of a general hypergraph is investigated. We study the Perron–Frobenius theorem for the general hypergraphs and obtain some relevant results based on it. In particular, the techniques of weighted incidence matrix and moving edge are extended to general hypergraphs for determining the structure with the maximum spectral radius. A nearly m -uniform supertree is both connected and acyclic, in which each edge contains either m − 1 or m vertices. To begin with, the structures obtaining the maximum spectral radius in two classes of nearly uniform supertrees are determined, where one class is with given number of edges and the other is with given number of vertices. [ABSTRACT FROM AUTHOR]

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. 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, FeCl 3 -induced carotid artery thrombosis model and transient occlusion of the middle cerebral artery model. 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. The bifunctional fusion protein IP showed good anticoagulation effects, and simultaneous targeting FXIIa and FXIa is a promising strategy for anticoagulation drug development. [ABSTRACT FROM AUTHOR]