Lupaş post quantum Bernstein operators over arbitrary compact intervals

This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

Parsimonious Optimization of Multitask Neural Network Hyperparameters

Neural networks are rapidly gaining popularity in chemical modeling and Quantitative Structure–Activity Relationship (QSAR) thanks to their ability to handle multitask problems. However, outcomes of neural networks depend on the tuning of several hyperparameters, whose small variations can often strongly affect their performance. Hence, optimization is a fundamental step in training neural networks although, in many cases, it can be very expensive from a computational point of view. In this study, we compared four of the most widely used approaches for tuning hyperparameters, namely, grid search, random search, tree-structured Parzen estimator, and genetic algorithms on three multitask QSAR datasets. We mainly focused on parsimonious optimization and thus not only on the performance of neural networks, but also the computational time that was taken into account. Furthermore, since the optimization approaches do not directly provide information about the influence of hyperparameters, we applied experimental design strategies to determine their effects on the neural network performance. We found that genetic algorithms, tree-structured Parzen estimator, and random search require on average 0.08% of the hours required by grid search; in addition, tree-structured Parzen estimator and genetic algorithms provide better results than random search.

A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

EVALUATING THE COMPLEXITY OF IMPLEMENTING DATA PROCESSING ON IOT-DEVICES

A method for implementing data processing in the Internet of Things systems, based on the end device, is considered. While existing approaches are based on the Cloud or Edge paradigm, processing on the end device of the IoT system allows you to reduce the amount of data transmitted at the initial stage. Correlation processing is an effective way to detect signals, however, practical implementations with a long pulse response duration are not suitable for low-power devices. The paper compares a number of implementations with an estimate of the number of computational operations, as well as an improved approach that reduces not only the number of operations, but also the processing delay. In addition, the implementation study is carried out when implementing on the basis of field programmable gate arrays (FPGA). The directions related to the research of signal processing directly on intermediate devices and, especially, on end devices (on-sensor processing) are represented to a lesser extent. This fact is due to the fundamental limitations of the end devices and systems of the Internet of Things, as well as the contradictory requirements. First of all, the devices should be as cheap as possible, autonomous, compact and at the same time have low power consumption. These requirements limit the performance of end devices. The network, in turn, must provide the required quality of service (QoS) and the speed and reliability of data transmission. The implementation of data processing on end devices in IoT systems is of great scientific and practical interest. This article will consider an approach based on correlation processing (consistent filtering). The traditional approach with large orders of filters on low-power, from a computational point of view, devices is redundant and not always feasible.

A New Edge betweenness Measure Using a Game Theoretical Approach : An Application to Hierarchical Community Detection

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

Benchmarking Studies Aimed at Clustering and Classification Tasks Using K-Means, Fuzzy C-Means and Evolutionary Neural Networks

Clustering is a widely used unsupervised learning technique across data mining and machine learning applications and finds frequent use in diverse fields ranging from astronomy, medical imaging, search and optimization, geology, geophysics, and sentiment analysis, to name a few. It is therefore important to verify the effectiveness of the clustering algorithm in question and to make reasonably strong arguments for the acceptance of the end results generated by the validity indices that measure the compactness and separability of clusters. This work aims to explore the successes and limitations of two popular clustering mechanisms by comparing their performance over publicly available benchmarking data sets that capture a variety of data point distributions as well as the number of attributes, especially from a computational point of view by incorporating techniques that alleviate some of the issues that plague these algorithms. Sensitivity to initialization conditions and stagnation to local minima are explored. Further, an implementation of a feedforward neural network utilizing a fully connected topology in particle swarm optimization is introduced. This serves to be a guided random search technique for the neural network weight optimization. The algorithms utilized here are studied and compared, from which their applications are explored. The study aims to provide a handy reference for practitioners to both learn about and verify benchmarking results on commonly used real-world data sets from both a supervised and unsupervised point of view before application in more tailored, complex problems.

On Polynomial Solutions of Pell’s Equation

Polynomial Pell’s equation is x 2 − D y 2 = ± 1 , where D is a quadratic polynomial with integer coefficients and the solutions X , Y must be quadratic polynomials with integer coefficients. Let D = a 2 x 2 + a 1 x + a 0 be a polynomial in Z x . In this paper, some quadratic polynomial solutions are given for the equation x 2 − D y 2 = ± 1 which are significant from computational point of view.

Computational Study of Halogen-Halogen Interactions in Polyhalide Ionic Liquids

Recent years have seen many specific applications of polyhalide ionic liquids (ILs) such as oxidizing solvents for metals and alloys, immersion fluids for optical mineralogy, and electrolyte components for dye-sensitized solar cells. In this work, interhalogen interactions in a set of polyhalide ILs composed of polyhalide anions, [X3]−, [X5]− and [X7]− (X = I or Br), with two typical cations, tetramethylammonium [NMe4]+ and 1,3-dimethylimidazolium [DMIM]+, were thoroughly studied from a computational point of view. In addition, a halogen-bonded supramolecular anion, [C6F13-I∙∙∙I∙∙∙I-C6F13]−, was also taken into account for comparison. Unlike those in bare polyhalide ions, halogen-halogen interactions in ionic pairs for the investigated ILs are somewhat asymmetric caused by the interactions between the cations and the anions. Most interhalogen contacts in ionic pairs have some covalent content, while I∙∙∙I interactions in the complexes of the supramolecular anion are purely noncovalent. In general, there are two classes of interhalogen bonds in ionic pairs: one class with longer X∙∙∙X distances shows primarily ionic character, while the other with shorter distances has a larger degree of covalency, i.e. intermediate ionic/covalent nature.

Constrained regulation problem for continuous-time stochastic systems under state and control constraints

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.

An Overview of the Basic NLP Resources Towards Building the Assamese-English Machine Translation

Machine Translation (MT) is the process of automatically converting one natural language into another, preserving the exact meaning of the input text to the output text. It is one of the classical problems in the Natural Language Processing (NLP) domain and there is a wide application in our daily life. Though the research in MT in English and some other language is relatively in an advanced stage, but for most of the languages, it is far from the human-level performance in the translation task. From the computational point of view, for MT a lot of preprocessing and basic NLP tools and resources are needed. This study gives an overview of the available basic NLP resources in the context of Assamese-English machine translation.