Division Algorithm Research Articles

METHOD OF DETERMINATION OF THERMODYNAMIC AND FILTRATION PARAMETERS FOR HYDRODYNAMIC COMPOSITIONAL MODELS

The calculation of phase behavior is important for choosing a rational mode of development of oil and gas fields. However, solving equations of state and material balance by traditional methods is associated with difficulties: Cardano’s formula allows finding only the roots of a cubic equation, the dichotomy method requires the selection of a segment on which there is only one root. Newton’s iterative method allows finding only one root under given conditions. Another important problem in hydrodynamic simulation is the uncertainty of the relative phase permeability of oil during three-phase filtration. It is proposed for the first time to use the algorithm of sequential division of Euclidean polynomials and Sturm’s theorem to calculate phase behavior. The aim of the work is to develop a methodology for calculating phase behavior and determining the area of increased uncertainty of relative phase permeability of oil. This area is defined as a set of phase saturation values at which relative phase permeabilities of oil according to Stone 1st and 2d models differ by more than 10%. The proposed methodology makes it possible to predict areas of metastable states. The possibility of calculating the roots of material balance equations that do not have physical meaning is excluded. For a model three-phase system, an area of increased uncertainty of relative phase permeability of oil is determined. It is shown that it is possible to determine all real roots of the equations. The proposed metho­dology makes it possible to refine forecast calculations for gas condensate fields.

Cognitive Complexity Beyond Generalization: A Subjective Rating for the Human Comprehension

The cognitive complexity of a software determines the comprehension effort of a particular individual faces when designing, developing and maintaining a software. The comprehension level tends to be varied with each human resulting the cognitive complexity a subjective measurement. Expressing the cognitive complexity as a form of metric quantifies the comprehensibility as a generic value, which does not imply the subjectivity of human factor. This study elaborates the significance of expressing the cognitive complexity as a form of a subjective rating. The cognitive complexity rating has been pioneered with respect to the human and programming dependent factors related to human cognition. The Divisive hierarchical clustering algorithm has been used to train and predict the cognition rating per user. It has been clearly elaborated the subjectivity of the cognitive ratings over the quantitative and static complexity values of current cognitive and software complexity metrics. Thereby, the concept of cognition rates has been proposed as a preliminary step of determining and expressing the cognitive complexity.

Adaptive Resonance Theory-Based Topological Clustering With a Divisive Hierarchical Structure Capable of Continual Learning

Adaptive Resonance Theory (ART) is considered as an effective approach for realizing continual learning thanks to its ability to handle the plasticity-stability dilemma. In general, however, the clustering performance of ART-based algorithms strongly depends on the specification of a similarity threshold, i.e., a vigilance parameter, which is data-dependent and specified by hand. This paper proposes an ART-based topological clustering algorithm with a mechanism that automatically estimates a similarity threshold from the distribution of data points. In addition, for improving information extraction performance, a divisive hierarchical clustering algorithm capable of continual learning is proposed by introducing a hierarchical structure to the proposed algorithm. Experimental results demonstrate that the proposed algorithm has high clustering performance comparable with recently-proposed state-of-the-art hierarchical clustering algorithms.

2-D Frequency Autofocus for Squint Spotlight SAR Imaging With Extended Omega-K

In the existing time-domain autofocus algorithms, the azimuth deramping operation will change the azimuth-independent phase into the azimuth-dependent phase, which may greatly reduce the accuracy of autofocus processing in squint spotlight synthetic aperture radar (SAR). In contrast, the frequency-domain autofocus algorithms can avoid this problem because it does not involve the azimuth deramping operation. However, the existing frequency-domain autofocus algorithms are proposed based on the assumption of broadside mode, which cannot be directly applied to the squint mode. Therefore, this article extends the existing frequency-domain autofocus algorithm to the squint mode combined with the extended Omega-K (EOK) algorithm. Furthermore, a space division (SD) algorithm is embedded into the proposed algorithm as preprocessing, which can effectively compensate for the azimuth-dependent motion error. The simulation and real data are processed to verify the effectiveness of the algorithm.

Microwave Photonic SAR High-Precision Imaging Based on Optimal Subaperture Division

Microwave photonic synthetic aperture radar (MWP-SAR) offers a larger signal bandwidth than conventional SAR, and its theoretical resolution can be improved to centimeter level. To achieve same order of magnitude resolution in azimuth direction, long synthetic aperture is always required, which results in extremely high requirements for the accuracy of imaging procedure. Compared with conventional SAR imaging algorithms, two major problems should be considered: 1) The scattering characteristics of target might vary from the frequency of signal and the angle of incidence, which seriously affects the coherence of received echo. 2) The imaging of MWP-SAR system is more sensitive to motion errors and therefore requires higher accuracy of motion compensation processing. To solve the above issues, a high-precision imaging method for MWP-SAR is proposed. First, based on the attribute scattering center(ASC) model, this paper analyzes the target-scattering characteristics with different frequencies and incident angles. Then, according to the influence of scattering phase on MWP-SAR imaging, an optimal sub-aperture division algorithm is proposed to guarantee the coherence of each sub-aperture data and better imaging results. Furthermore, to compensate for the effects of high-order motion errors, this paper proposes a motion error estimation algorithm based on sub-image registration, where the full aperture high-order motion errors can be divided into multiple linear components, and the flight trajectory of platform can be accurately reconstructed. Finally, a full-aperture time-domain high-precision imaging method is presented, and the effectiveness of the proposed formation is verified by both simulation and actual airborne MWP-SAR data processing.

HELP-WSN-A Novel Adaptive Multi-Tier Hybrid Intelligent Framework for QoS Aware WSN-IoT Networks

Wireless Sensor Network is considered as the intermediate layer in the paradigm of Internet of things (IoT) and its effectiveness depends on the mode of deployment without sacrificing the performance and energy efficiency. WSN provides ubiquitous access to location, the status of different entities of the environment and data acquisition for long term IoT monitoring. Achieving the high performance of the WSN-IoT network remains to be a real challenge since the deployment of these networks in the large area consumes more power which in turn degrades the performance of the networks. So, developing the robust and QoS (quality of services) aware energy-efficient routing protocol for WSN assisted IoT devices needs its brighter light of research to enhance the network lifetime. This paper proposed a Hybrid Energy Efficient Learning Protocol (HELP). The proposed protocol leverages the multi-tier adaptive framework to minimize energy consumption. HELP works in a two-tier mechanism in which it integrates the powerful Extreme Learning Machines for clustering framework and employs the zonal based optimization technique which works on hybrid Whale-dragonfly algorithms to achieve high QoS parameters. The proposed framework uses the sub-area division algorithm to divide the network area into different zones. Extreme learning machines (ELM) which are employed in this framework categories the Zone's Cluster Head (ZCH) based on distance and energy. After categorizing the zone's cluster head, the optimal routing path for an energy-efficient data transfer will be selected based on the new hybrid whale-swarm algorithms. The extensive simulations were carried out using OMNET++-Python user-defined plugins by injecting the dynamic mobility models in networks to make it a more realistic environment. Furthermore, the effectiveness of the proposed HELP is examined against the existing protocols such as LEACH, M-LEACH, SEP, EACRP and SEEP and results show the proposed framework has outperformed other techniques in terms of QoS parameters such as network lifetime, energy, latency.

Rough‐Set‐Based Real‐Time Interest Label Extraction over Large‐Scale Social Networks

Labels provide a quick and effective solution to obtain people interesting content from large‐scale social network information. The current interest label extraction method based on the subgraph stream proves the feasibility of the subgraph stream for user label extraction. However, it is extremely time‐consuming for constructing subgraphs. As an effective mathematical method to deal with fuzzy and uncertain information, rough set‐based representations for subgraph stream construction are capable of capturing the uncertainties of the social network. Therefore, we propose an effective approach called RS_UNITE_SS (namely, rough‐set‐based user‐networked interest topic extraction in the form of subgraph stream), which is suitable for large‐scale social network user interest label extraction. Specifically, we first propose the subgraph division algorithm to construct a subgraph stream by incorporating a rough set. Then, the algorithm for user real‐time interest label extraction based on upper approximation (RILE) is proposed by using sequentially characteristics of the subgraph. Empirically, we evaluate RS_UNITE_SS over real‐world datasets, and experimental results demonstrate that our proposed approach is more computationally efficient than existing methods while achieving higher precision value and MRR value.

An efficient multiphysics solid shell based finite element approach for modeling thin sheet metal forming processes

The main objective of this paper is to provide a numerical approach to study thin sheet metals involved in multiphysics manufacturing processes. The proposed approach also accounts for anisotropic plastic deformations in the context of modeling of deep drawing process. In this work, different constitutive models are implemented with a prismatic solid shell element to simulate these applications. Moreover, a new element assembly technique has been developed to permit the assembly of prismatic elements in a tetrahedral element-based finite element code. This technique splits the prism into multiple tetrahedral elements in such a way that all the cross terms are accounted for. The numerical approach has been validated using multiple tests that involve different non-linearities: geometric, material and contact. Then, more complex sheet metal processes have been simulated. The performance of the solid shell element with one element through the thickness is very comparable to the results obtained with more refined mesh of a tetrahedral element. This reduction in the number of elements accelerates the simulation, especially in the deep drawing problem and the coupled magnetic-mechanical simulation used for the magnetic pulse forming process. • Solid shell finite element implementation in tetrahedral based finite element software. • Prism division algorithm into multiple overlapping tetrahedral elements. • Solid-shell element showed better performance than MINI element in modeling thin structures problems. • Incorporate anisotropic plastic behavior in the simulation of deep drawing process. • Electromagnetic pulse forming simulation using solid shell element reduces time of simulation and maintain good accuracy.

PENGELOMPOKAN DESA ATAU KELURAHAN DI KUTAI KARTANEGARA MENGGUNAKAN ALGORITMA DIVISIVE ANALYSIS

Potential Villages (PODES) provide data on the existence, availability and development of the potential of each government administrative area. In order to make it easier for governments to make policies for a region, it is necessary to group the village and sub-districts. Cluster analysis is an analysis that aims to group objects based on the information that found in the data. One of the cluster analysis methods is the divisive analysis, which is a hierarchical grouping method with a top-down approach, where all objects are placed in one cluster and then sequentially divided into separate groups. This research aim to group villages or sub-districts in Kutai Kartanegara based on the determinants of village backwardness and obtaining the silhouette coefficient value from the optimal cluster analysis using the divisive analysis algorithm. The data used is the 2018 PODES data in Kutai Kartanegara and used 15 variables from natural and environmental factors, facilities infrastructure and access factors as well as socio-economic factors of the population. The results of the optimal cluster formed in the grouping of villages or sub-districts in Kutai Kartanegara using the divisive analysis method are 2 clusters. Cluster 1 consisting of 230 villages or sub-districts and cluster 2 consisting of 2 sub-districts. Silhouette coefficient value for data validation from clustering village or sub-districts in Kutai Kartanegara using the divisive analysis method produces 2 clusters is 0,744 which states that the cluster structure formed in this grouping is a strong structure.

Computer Algorithms Support Physician Decisions in Traumatic Head Injury.

Computer Algorithms Support Physician Decisions in Traumatic Head Injury.

Economic Management Data Envelopes Based on the Clustering of Incomplete Data

In this paper, the economic management data envelope is analyzed by an algorithm for clustering incomplete data, a local search method based on reference vectors is designed in the algorithm to improve the accuracy of the algorithm, and a final solution selection method based on integrated clustering is proposed to obtain the final clustering results from the last generation of the solution set. The proposed algorithm and various aspects of it are tested in comparison using benchmark datasets and other comparison algorithms. A time-series domain partitioning method based on fuzzy mean clustering and information granulation is proposed, and a time series prediction method is proposed based on the domain partitioning results. Firstly, the fuzzy mean clustering method is applied to initially divide the theoretical domain of the time series, and then, the optimization algorithm of the theoretical domain division based on information granulation is proposed. It combines the clustering algorithm and the information granulation method to divide the theoretical domain and improves the accuracy and interpretability of sample data division. This article builds an overview of data warehouse, data integration, and rule engine. It introduces the business data integration of the economic management information system data warehouse and the data warehouse model design, taking tax as an example. The fuzzy prediction method of time series is given for the results of the theoretical domain division after the granulation of time-series information, which transforms the precise time-series data into a time series composed of semantic values conforming to human cognitive forms. It describes the dynamic evolution process of time series by constructing the fuzzy logical relations to these semantic values to obtain their fuzzy change rules and make predictions, which improves the comprehensibility of prediction results. Finally, the prediction experiments are conducted on the weighted stock price index dataset, and the experimental results show that applying the proposed time-series information granulation method for time series prediction can improve the accuracy of the prediction results.

Optimization of wind/solar energy microgrid by division algorithm considering human health and environmental impacts for power-water cogeneration

Although freshwater is necessary for the well-being of humankind, increasing population growth and limited resources lead to a serious crisis to supply freshwater. Since the Earth is surrounded by seawater, desalination based on electrical power is introduced as a promising technology to provide freshwater. It is well documented that the connection of remote areas that usually do not have access to freshwater into the electricity grid is not affordable and eco-friendly. Hence, the efforts to design and construct high reliability, cost-effective, and eco-friendly stand-alone hybrid renewable energy system in remote areas. In line with this, this paper describes a novel energy management system for the optimized operation of a stand-alone hybrid energy system based on photovoltaic panels, wind turbines, batteries, and diesel generator. For this purpose, a multi-objective optimization problem is formulated by combining three objective functions, i.e., minimum the total life cycle cost as well as environmental impacts on human health and ecosystems and the maximum system reliability that can conflict with each. To solve the multi-objective optimization problem, a division algorithm is proposed that is more flexible and faster compared with conventional algorithms such as genetic algorithm. In order to show the proposed framework, a real case study in Larak Island, Iran, with appropriate solar and wind is considered. The effectiveness of the applied approach compared with optimization results of genetic algorithm and the artificial bee swarm optimization algorithm that was previously used successfully to solve optimization problems related to desalination integrated with the renewable energy system. The optimization is performed based on different diesel fuel price amounts (0.2, 0.5, and 1 $/liter). It is seen that at fuel price set to 0.2 and 0.5 $/liter, the seawater reverses osmosis desalination/photovoltaic/diesel generator/battery is the most cost-effective energy system, and when fuel price is 1 $/liter, the seawater reverses osmosis desalination/photovoltaic/wind turbine/diesel generator/battery is the most cost-effective hybrid system. While at fuel price set to 0.2, 0.5, and 1 $/liter, the seawater reverse osmosis desalination /photovoltaic/wind turbine/diesel generator/battery is the most eco-friendly. Finally, the results of this study show proposed algorithm is faster and more accurate (100 iterations, 98.36% accuracy) than the genetic algorithm (1000 iterations, 83.03% accuracy) and the artificial bee swarm optimization (300 iterations, 95.49% accuracy).

Dynamic order Markov model for categorical sequence clustering

Markov models are extensively used for categorical sequence clustering and classification due to their inherent ability to capture complex chronological dependencies hidden in sequential data. Existing Markov models are based on an implicit assumption that the probability of the next state depends on the preceding context/pattern which is consist of consecutive states. This restriction hampers the models since some patterns, disrupted by noise, may be not frequent enough in a consecutive form, but frequent in a sparse form, which can not make use of the information hidden in the sequential data. A sparse pattern corresponds to a pattern in which one or some of the state(s) between the first and last one in the pattern is/are replaced by wildcard(s) that can be matched by a subset of values in the state set. In this paper, we propose a new model that generalizes the conventional Markov approach making it capable of dealing with the sparse pattern and handling the length of the sparse patterns adaptively, i.e. allowing variable length pattern with variable wildcards. The model, named Dynamic order Markov model (DOMM), allows deriving a new similarity measure between a sequence and a set of sequences/cluster. DOMM builds a sparse pattern from sub-frequent patterns that contain significant statistical information veiled by the noise. To implement DOMM, we propose a sparse pattern detector (SPD) based on the probability suffix tree (PST) capable of discovering both sparse and consecutive patterns, and then we develop a divisive clustering algorithm, named DMSC, for Dynamic order Markov model for categorical sequence clustering. Experimental results on real-world datasets demonstrate the promising performance of the proposed model.

Power optimization of binary division based on FPGA

In modern very large scale integrated (VLSI) digital systems, power consumption has become a critical concern of VLSI designers. As size shrinks and density increases in chips, it will be a challenge to design high performance and low-power digital systems. Therefore, VLSI designers are trying to reduce power dissipation in these systems by using power optimization techniques. Different mathematical operations can be found in the architectures of most digital systems. The focus of this paper is division. In comparison to other basic computational operations, division requires more iterations, takes a long time, covers a large area, and consumes more power from the digital system. As a result, the system's design requires high speed and a low-power divider in order to improve its overall performance. This paper focuses on dynamic power dissipation. In order to determine which design consumes the lowest dynamic power, different system designs of digit-recurrence division algorithms, such as restoring division and non-restoring division are suggested. An innovative power-optimization technique, the very hardware descriptions language (VHDL) technique, is utilized to the suggested system designs. The VHDL technique achieved the higher optimization in dynamic power, at 93.66% for non-restoring division with internal-loop iteration, than traditional approaches.

Application of Probabilistic Neural Networks Using High-Frequency Components’ Differential Current for Transformer Protection Schemes to Discriminate between External Faults and Internal Winding Faults in Power Transformers

Internal and external faults in a power transformer are discriminated in this paper using an algorithm based on a combination of a discrete wavelet transform (DWT) and a probabilistic neural network (PNN). DWT decomposes high-frequency fault components using the maximum coefficients of a ¼ cycle DWT as input patterns for the training process in a decision algorithm. A division algorithm between a zero sequence of post-fault differential current waveforms and the differential current coefficient in the ¼ cycle DWT is used to detect the maximum ratio and faults. The simulation system uses various study cases based on Thailand’s electricity transmission and distribution systems. The simulation results demonstrated that the PNN and BPNN are effectively implemented and perform fault detection with satisfactory accuracy. However, the PNN method is most suitable for detecting internal and external faults, and the maximum coefficient algorithm is the most effective in detecting the fault. This study will be useful in differential protection for power transformers.

A blockchain bee colony double inhibition labor division algorithm for spatio-temporal coupling task with application to UAV swarm task allocation

It is difficult for the double suppression division algorithm of bee colony to solve the spatio-temporal coupling or have higher dimensional attributes and undertake sudden tasks. Using the idea of clustering, after clustering tasks according to spatio-temporal attributes, the clustered groups are linked into task sub-chains according to similarity. Then, based on the correlation between clusters, the child chains are connected to form a task chain. Therefore, the limitation is solved that the task chain in the bee colony algorithm can only be connected according to one dimension. When a sudden task occurs, a method of inserting a small number of tasks into the original task chain and a task chain reconstruction method are designed according to the relative relationship between the number of sudden tasks and the number of remaining tasks. Through the above improvements, the algorithm can be used to process tasks with spatio-temporal coupling and burst tasks. In order to reflect the efficiency and applicability of the algorithm, a task allocation model for the unmanned aerial vehicle (UAV) group is constructed, and a one-to-one correspondence between the improved bee colony double suppression division algorithm and each attribute in the UAV group is proposed. Task assignment has been constructed. The study uses the self-adjusting characteristics of the bee colony to achieve task allocation. Simulation verification and algorithm comparison show that the algorithm has stronger planning advantages and algorithm performance.

Evaluation of Three Iterative Algorithms for Phase Modulation Regarding Their Application in Concentrating Light Inside Biological Tissues for Laser Induced Photothermal Therapy

The focusing of light through turbid media like biological tissues is strongly hindered by the scattering of light which limits its safe practice and application in medicine. In order to control this phenomenon, we shaped the incident wavefront using three algorithms including a four-element division algorithm, a partitioning algorithm, and simulated annealing to control, iteratively, a spatial light modulator (SLM). We have tested two different convergence criteria to achieve a focal point inside a turbid environment, made up of a mixture of agar and milk, set to mimic a specific depth of human skin, and provide comparison results. A camera and a lens are used to visualize the focal area and give feedback information to the algorithms. A discussion on the use of these algorithms and convergence criteria is presented, being focused on its convergence time and performance. Depending on the algorithm and operational parameters, improvements of 29% to 46% of the irradiance in the region of interest were accomplished.

From how to why: A quest for the common mathematical meanings behind two different division algorithms

During their education cycle in mathematics, students are exposed to algorithms as early as primary school. Several studies show how students frequently learn to perform these algorithms without controlling the mathematical meanings behind them. On the other hand, several National Standards have highlighted the need to construct meanings in mathematics from the first cycle of education. In this paper we focus on division algorithms, investigating to what extent 6th graders can be guided to understanding the whys behind an algorithm, through the comparison of two different algorithms for integer division. Our results suggest, on the one hand, that “it could work!”, and on the other hand, that the exposure to different algorithms for the same mathematical operation seems particularly significant for bringing out the whys behind such algorithms, as well as for capturing the difference between a mathematical operation and algorithms for calculating the result of such an operation.

Discrete control algorithm of simulation load division based on complex network flow

Discrete control algorithm of simulation load division based on complex network flow

Mathematical Specialized Knowledge of a Mathematics Teacher Educator for Teaching Divisibility


 
 
 The knowledge of Mathematics teachers has been a very prominent focus of attention in the last decades. However, it leaves aside one of the dimensions involved in the development of this type of knowledge, specifically the knowledge of Mathematics teacher educators. In this paper, we discuss a mathematics teacher educator’s knowledge in the context of classes on Euclid’s division algorithm theorem in a Number Theory course for prospective secondary teachers. Some indicators of this specialized knowledge of mathematics teacher educators are presented and discussed.