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In this paper, a computational method based on parameterizing state and control variables is presented for solving Stochastic Optimal Control (SOC) problems. By using Chebyshev wavelets with unknown coefficients, state and control variables are parameterized, and then a stochastic optimal control problem is converted to a stochastic optimization problem. The expected cost functional of the resulting stochastic optimization problem is approximated by sample average approximation thereby the problem can be solved by optimization methods more easily. For facilitating and guaranteeing convergence of the presented method, a new theorem is proved. Finally, the proposed method is implemented based on a newly designed algorithm for solving one of the well-known problems in mathematical finance, the Merton portfolio allocation problem in finite horizon. The simulation results illustrate the improvement of the constructed portfolio return. [ABSTRACT FROM AUTHOR]

In machine learning, models are derived from labeled training data where labels signify classes and features define sample attributes. However, noise from data collection can impair the algorithm's performance. Blanco, Japón, and Puerto proposed mixed-integer programming (MIP) models within support vector machines (SVM) to handle label noise in training datasets. Nonetheless, it is imperative to underscore that their models demonstrate an observable escalation in the number of variables as sample size increases. The nonparallel support vector machine (NPSVM) is a binary classification method that merges the strengths of both SVM and twin SVM. It accomplishes this by determining two nonparallel hyperplanes by solving two optimization problems. Each hyperplane is strategically positioned to be closer to one of the classes while maximizing its distance from the other class. In this paper, to take advantage of NPSVM's features, NPSVM-based relabeling (RENPSVM) MIP models are developed to deal with the label noises in the dataset. The proposed model adjusts observation labels and seeks optimal solutions while minimizing computational costs by selectively focusing on class-relevant observations within an ε-intensive tube. Instances exhibiting similarities to the other class are excluded from this ε-intensive tube. Experiments on 10 UCI datasets show that the proposed NPSVM-based MIP models outperform their counterparts in accuracy and learning time on the majority of datasets. [ABSTRACT FROM AUTHOR]

The fuzzy-C-means (FCM) algorithm is one of the most famous fuzzy clustering algorithms, but it gets stuck in local optima. In addition, this algorithm requires the number of clusters. Also, the density-based spatial of the application with noise (DBSCAN) algorithm, which is a density-based clustering algorithm, unlike the FCM algorithm, should not be pre-numbered. If the clusters are specific and depend on the number of clusters, then it can determine the number of clusters. Another advantage of the DBSCAN clustering algorithm over FCM is its ability to cluster data of different shapes. In this paper, in order to overcome these limitations, a hybrid approach for clustering is proposed, which uses FCM and DBSCAN algorithms. In this method, the optimal number of clusters and the optimal location for the centers of the clusters are determined based on the changes that take place according to the data set in three phases by predicting the possibility of the problems stated in the FCM algorithm. With this improvement, the values of none of the initial parameters of the FCM algorithm are random, and in the first phase, it has been tried to replace these random values to the optimal in the FCM algorithm, which has a significant effect on the convergence of the algorithm because it helps to reduce iterations. The proposed method has been examined on the Iris flower and compared the results with basic FCM algorithm and another algorithm. Results shows the better performance of the proposed method. [ABSTRACT FROM AUTHOR]

Motifs have critical impacts on the behavioral and structural characteristics of RNA sequences. Understanding and predicting the functionalities and interactions of an RNA sequence requires discovering and identifying its motifs. Due to the importance of motif discovery in bioinformatics, a significant corpus of techniques and algorithms have been proposed, each of which has various advantages and limitations and hence, are suitable for specific applications. To understand these techniques and algorithms, compare them, and choose the most suitable one for a particular application scenario, it is crucial to have a clear understanding of the different vital aspects that characterize these algorithms. The lack of such a framework to study these aspects is a serious existing challenge in the literature that needs further investigation. In this paper, we propose a taxonomy and a framework to address this issue. We define the concept of motif discovery process and three aspects that characterize such a process, which are motif type, discovery technique, and application. We then study the literature and classify the existing approaches along with these aspects. This will give the reader a broader view and more precise understanding of what these techniques and algorithms do, how they do it, and what is the most suitable application for each of them. We then present the possible gaps and challenges foreseen to be the future directions of the area. [ABSTRACT FROM AUTHOR]

In recent years, several algorithms with different time complexities have been proposed for the construction of greedy spanners. However, a not so apparently suitable algorithm with running time complexity O(n³ log n), namely the FG algorithm, is proved to be practically the fastest algorithm known for this task. One of the common bottlenecks in the greedy spanner construction algorithms is their use of the shortest path search operation (usually using Dijkstra's algorithm). In this paper, we propose some improvements to the FG algorithm in order to reduce the imposed costs of the shortest path search operation, and therefore to reduce the time required for the construction of greedy spanners. In the first improvement, we reduce the number of this operation calls and in the second one, we reduce the cost of each run of the operation. Experimental results show these improvements are able to significantly accelerate the construction of greedy spanners, compared to the other existing algorithms, especially when the stretch factor gets close to 1. [ABSTRACT FROM AUTHOR]

Numerical solution of conjugate heat transfer (CHT) problems in multi-region domains is a challenging issue in terms of efficiency and stability due to inherent coupling between governing equations in separate sub-domains. This paper aims at comparing two distinct strategies for coupling energy equations at interface of regions: partitioned and monolithic. While the former enforces strong coupling via iterative procedures, the latter suggests simultaneous solution of energy equation throughout all regions at once. More precisely, the primary objective of this study is to compare computational costs for three finite volume- based CHT solvers which share a same method for handling pressure-velocity coupling in the fluid, i.e. semi-implicit projection method, and are distinguished from the coupling strategy for energy equation at interface of interacting sub-domains. The first method applies simultaneous solution of energy equation across all regions while second and third ones use separate solver for each region with difference in handling iterative loops. The accuracy and convergence rate of three algorithms are assessed via transient solution of conjugate free convection in fluid and conduction in vertical wall. Finally, it is concluded that, in contrast to partitioned solver in OpenFOAM for CHT problems, employing a separate loop to enforce energy-energy coupling per iteration, can be much more beneficial in terms of computational costs. [ABSTRACT FROM AUTHOR]

This article investigates a particular version of the cutting angle method for finding the global minimizer of sub-topical (increasing and plus sub-homogeneous) functions over a simplex. The algorithm is based on the abstract convexity of sub-topical functions. Furthermore, we discuss the proof of convergence of the algorithm and provide results from numerical experiments. [ABSTRACT FROM AUTHOR]

The article employs a reinforcement learning method to design a real controller for controlling an inverted pendulum modeled in simmechanics while a force is applied to its cart. The aim of reinforcement learning is to find the best action for each state, in which the process which wants to shift to Q-Learning is a simple algorithm.