Search results for: K-means clustering algorithm

Authors: Sana Ansari, Sirus Mohammadi

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In distribution systems, shunt capacitors are used to reduce power losses, to improve voltage profile, and to increase the maximum flow through cables and transformers. This paper presents a new method to determine the optimal locations and economical sizing of fixed and/or switched shunt capacitors with a view to power losses reduction and voltage stability enhancement. General Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with Linear Programming (LP). The proposed method is tested on 33 node distribution system and the results show that the algorithm suitable for practical implementation on real systems with any size.

Keywords: power losses, voltage stability, radial distribution systems, capacitor

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Authors: Shamsundar Kulkarni

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Video capturing by non-professionals will lead to unanticipated effects. Such as image distortion, image blurring etc. Hence, many researchers study such drawbacks to enhance the quality of videos. In this paper, an algorithm is proposed to stabilize jittery videos .A stable output video will be attained without the effect of jitter which is caused due to shaking of handheld camera during video recording. Firstly, salient points from each frame from the input video are identified and processed followed by optimizing and stabilize the video. Optimization includes the quality of the video stabilization. This method has shown good result in terms of stabilization and it discarded distortion from the output videos recorded in different circumstances.

Keywords: video stabilization, point feature matching, salient points, image quality measurement

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Isa Moazen, Ali Nahvi

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Driver drowsiness is a major cause of vehicle accidents, and facial images are highly valuable to detect drowsiness. In this paper, we perform our research via a thermal camera to record drivers' facial images on a driving simulator. A robust real-time algorithm extracts the features using horizontal and vertical integration projection, contours, contour orientations, and cropping tools. The features are included four target areas on the cheeks and forehead. Qt compiler and OpenCV are used with two cameras with different resolutions. A high-resolution thermal camera is used for fifteen subjects, and a low-resolution one is used for a person. The results are investigated by four temperature plots and evaluated by observer rating of drowsiness.

Keywords: advanced driver assistance systems, thermal imaging, driver drowsiness detection, feature extraction

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Authors: Brian E. Usibe

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This paper addresses the problem of a linear crack located in the middle of a homogeneous elastic media under normal tension-compression harmonic loading. The problem of deformation of the fractured media is solved using the direct finite element numerical procedure, including the analysis of the dynamic field variables of the problem. A finite element algorithm that satisfies the unilateral Signorini contact constraint is also presented for the solution of the contact interaction of the crack faces and how this accounts for the qualitative and quantitative changes in the solution when determining the dynamic fracture parameter.

Keywords: harmonic loading, linear crack, fracture parameter, wave number, FEA, contact interaction

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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Authors: Asif Zaman, Moinul Islam Zaber, Amin Ahsan Ali

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In recent years of industrialization, the South Asian countries are being affected by air pollution due to a severe increase in fine particulate matter 2.5 (PM₂.₅). Among them, Bangladesh is one of the most polluting countries. In this paper, statistical analyses were conducted on the time series of PM₂.₅ from various districts in Bangladesh, mostly around Dhaka city. Research has been conducted on the dynamic interactions and relationships between PM₂.₅ concentrations in different zones. The study is conducted toward understanding the characteristics of PM₂.₅, such as spatial-temporal characterization, correlation of other contributors behind air pollution such as human activities, driving factors and environmental casualties. Clustering on the data gave an insight on the districts groups based on their AQI frequency as representative districts. Seasonality analysis on hourly and monthly frequency found higher concentration of fine particles in nighttime and winter season, respectively. Cross correlation analysis discovered a phenomenon of correlations among cities based on time-lagged series of air particle readings and visualization framework is developed for observing interaction in PM₂.₅ concentrations between cities. Significant time-lagged correlations were discovered between the PM₂.₅ time series in different city groups throughout the country by cross correlation analysis. Additionally, seasonal heatmaps depict that the pooled series correlations are less significant in warmer months, and among cities of greater geographic distance as well as time lag magnitude and direction of the best shifted correlated particulate matter time series among districts change seasonally. The geographic map visualization demonstrates spatial behaviour of air pollution among districts around Dhaka city and the significant effect of wind direction as the vital actor on correlated shifted time series. The visualization framework has multipurpose usage from gathering insight of general and seasonal air quality of Bangladesh to determining the pathway of regional transportation of air pollution.

Keywords: air quality, particles, cross correlation, seasonality

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Authors: Kostas Metaxiotis, Kostas Liagkouras

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This study presents an Expert System specially designed to be used with Multiobjective Evolutionary Algorithms (MOEAs) for the solution of the portfolio selection problem. The validation of the proposed hybrid System is done by using data sets from Hang Seng 31 in Hong Kong, DAX 100 in Germany and FTSE 100 in UK. The performance of the proposed system is assessed in comparison with the Non-dominated Sorting Genetic Algorithm II (NSGAII). The evaluation of the performance is based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it. The results show that the proposed hybrid system is efficient for the solution of this kind of problems.

Keywords: expert systems, multi-objective optimization, evolutionary algorithms, portfolio selection

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Authors: Supriya H. S., Chandrakala B. M.

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Deep learning based models have been recently successful adoption for network traffic prediction. However, training a deep learning model for various prediction tasks is considered one of the critical tasks due to various reasons. This research work develops Multi-Layer Hybrid Network (MLHN) for network traffic prediction and analysis; MLHN comprises the three distinctive networks for handling the different inputs for custom feature extraction. Furthermore, an optimized and efficient parameter-tuning algorithm is introduced to enhance parameter learning. MLHN is evaluated considering the “Big Data Challenge” dataset considering the Mean Absolute Error, Root Mean Square Error and R^2as metrics; furthermore, MLHN efficiency is proved through comparison with a state-of-art approach.

Keywords: MLHN, network traffic prediction

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Authors: L. Matlawe, E. S. Idemudia

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The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modeling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they were designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: emotional abuse, employees, mental health, self-concept

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Authors: András Rövid, Takeshi Hashimoto

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The paper focuses on the problem of the point correspondence matching in stereo images. The proposed matching algorithm is based on the combination of simpler methods such as normalized sum of squared differences (NSSD) and a more complex phase correlation based approach, by considering the noise and other factors, as well. The speed of NSSD and the preciseness of the phase correlation together yield an efficient approach to find the best candidate point with sub-pixel accuracy in stereo image pairs. The task of the NSSD in this case is to approach the candidate pixel roughly. Afterwards the location of the candidate is refined by an enhanced phase correlation based method which in contrast to the NSSD has to run only once for each selected pixel.

Keywords: stereo matching, sub-pixel accuracy, phase correlation, SVD, NSSD

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Boukhatem Mohamed Belkaid, Lahdi Mourad

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In this paper, we propose a new encryption system for security issues medical images. The hybrid encryption scheme is based on AES and RSA algorithms to validate the three security services are authentication, integrity, and confidentiality. Privacy is ensured by AES, authenticity is ensured by the RSA algorithm. Integrity is assured by the basic function of the correlation between adjacent pixels. Our system generates a unique password every new session of encryption, that will be used to encrypt each frame of the medical image basis to strengthen and ensure his safety. Several metrics have been used for various tests of our analysis. For the integrity test, we noticed the efficiencies of our system and how the imprint cryptographic changes at reception if a change affects the image in the transmission channel.

Keywords: AES, RSA, integrity, confidentiality, authentication, medical images, encryption, decryption, key, correlation

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Authors: Iris Vogeler, Rogerio Cichota, Armin Werner

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Dairy farms are under pressure to increase productivity while reducing environmental impacts. Effective fertiliser management practices are critical to achieve this. Determination of optimum nitrogen (N) fertilisation rates which maximise pasture growth and minimise N losses is challenging due to variability in plant requirements and likely near-future supply of N by the soil. Remote sensing can be used for mapping N nutrition status of plants and to rapidly assess the spatial variability within a field. An algorithm is, however, lacking which relates the N status of the plants to the expected yield response to additions of N. The aim of this simulation study was to develop a multi-variate model for determining N fertilisation rate for a target percentage of the maximum achievable yield based on the pasture N concentration (ii) use of an algorithm for guiding fertilisation rates, and (iii) evaluation of the model regarding pasture yield and N losses, including N leaching, denitrification and volatilisation. A simulation study was carried out using the Agricultural Production Systems Simulator (APSIM). The simulations were done for an irrigated ryegrass pasture in the Canterbury region of New Zealand. A multi-variate model was developed and used to determine monthly required N fertilisation rates based on pasture N content prior to fertilisation and targets of 50, 75, 90 and 100% of the potential monthly yield. These monthly optimised fertilisation rules were evaluated by running APSIM for a ten-year period to provide yield and N loss estimates from both nonurine and urine affected areas. Comparison with typical fertilisation rates of 150 and 400 kg N/ha/year was also done. Assessment of pasture yield and leaching from fertiliser and urine patches indicated a large reduction in N losses when N fertilisation rates were controlled by the multi-variate model. However, the reduction in leaching losses was much smaller when taking into account the effects of urine patches. The proposed approach based on biophysical modelling to develop a multi-variate model for determining optimum N fertilisation rates dependent on pasture N content is very promising. Further analysis, under different environmental conditions and validation is required before the approach can be used to help adjust fertiliser management practices to temporal and spatial N demand based on the nitrogen status of the pasture.

Keywords: APSIM modelling, optimum N fertilization rate, pasture N content, ryegrass pasture, three dimensional surface response function.

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Authors: H. Gonzalez-Rivera, J. L. Palmeros-Torres

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This paper describes the application of traditional computer vision techniques as a procedure for automatic measurement of the secondary dendrite arm spacing (SDAS) from microscopic images. The algorithm is capable of finding the lineal or curve-shaped secondary column of the main microstructure, measuring its length size in a micro-meter and counting the number of spaces between dendrites. The automatic characterization was compared with a set of 1728 manually characterized images, leading to an accuracy of −0.27 µm for the length size determination and a precision of ± 2.78 counts for dendrite spacing counting, also reducing the characterization time from 7 hours to 2 minutes.

Keywords: dendrite arm spacing, microstructure inspection, pattern recognition, polynomial regression

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Authors: Ali Mashayekh, Mahdiye Khorasani, Thomas weyh

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The demand for battery electric vehicles (BEV) is steadily increasing, and it can be assumed that electric mobility will dominate the market for individual transportation in the future. Regarding BEVs, the focus of state-of-the-art research and development is on vehicle batteries since their properties primarily determine vehicles' characteristic parameters, such as price, driving range, charging time, and lifetime. State-of-the-art battery packs consist of invariable configurations of battery cells, connected in series and parallel. A promising alternative is battery systems based on multilevel inverters, which can alter the configuration of the battery cells during operation via semiconductor switches. The main benefit of such topologies is that a three-phase AC voltage can be directly generated from the battery pack, and no separate power inverters are required. Therefore, modular battery systems based on different multilevel inverter topologies and reconfigurable battery systems are currently under investigation. Another advantage of the multilevel concept is that the possibility to reconfigure the battery pack allows battery cells with different states of charge (SoC) to be connected in parallel, and thus low-loss balancing can take place between such cells. In contrast, in conventional battery systems, parallel connected (hard-wired) battery cells are discharged via bleeder resistors to keep the individual SoCs of the parallel battery strands balanced, ultimately reducing the vehicle range. Different multilevel inverter topologies and reconfigurable batteries have been described in the available literature that makes the before-mentioned advantages possible. However, what has not yet been described is how an intelligent operating algorithm needs to look like to keep the SoCs of the individual battery strands of a modular battery system with integrated power electronics balanced. Therefore, this paper suggests an SoC balancing approach for Battery Modular Multilevel Management (BM3) converter systems, which can be similarly used for reconfigurable battery systems or other multilevel inverter topologies with parallel connectivity. The here suggested approach attempts to simultaneously utilize all converter modules (bypassing individual modules should be avoided) because the parallel connection of adjacent modules reduces the phase-strand's battery impedance. Furthermore, the presented approach tries to reduce the number of switching events when changing the switching state combination. Thereby, the ohmic battery losses and switching losses are kept as low as possible. Since no power is dissipated in any designated bleeder resistors and no designated active balancing circuitry is required, the suggested approach can be categorized as a proactive balancing approach. To verify the algorithm's validity, simulations are used.

Keywords: battery management system, BEV, battery modular multilevel management (BM3), SoC balancing

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Authors: Riona Dighe

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This research attempts to identify an alternative approach to the measurement of Gross National Happiness (GNH). It uses artificial intelligence (AI), incorporating natural language processing (NLP) and sentiment analysis to measure GNH. We use ‘off the shelf’ NLP models responsible for the sentiment analysis of a sentence as a building block for this research. We constructed an algorithm using NLP models to derive a sentiment analysis score against sentences. This was then tested against a sample of 20 respondents to derive a sentiment analysis score. The scores generated resembled human responses. By utilising the MLP classifier, decision tree, linear model, and K-nearest neighbors, we were able to obtain a test accuracy of 89.97%, 54.63%, 52.13%, and 47.9%, respectively. This gave us the confidence to use the NLP models against sentences in websites to measure the GNH of a country.

Keywords: artificial intelligence, NLP, sentiment analysis, gross national happiness

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Authors: Sa’adu Mafara Abubakar, Muhammad Nuraddeen Danjuma, Adewole Tomiwa Adetunji, Richard Mundembe, Salisu Mohammed, Francis Bayo Lewu, Joseph I. Kiok

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Pearl millet is the most drought tolerant of all domesticated cereals, is cultivated extensively to feed millions of people who mainly live in hash agroclimatic zones. It serves as a major source of food for more than 40 million smallholder farmers living in the marginal agricultural lands of Northern Nigeria. Pearl millet grain is more nutritious than other cereals like maize, is also a principal source of energy, protein, vitamins, and minerals for millions of poorest people in the regions where it is cultivated. Pearl millet has recorded relatively little research attention compared with other crops and no sufficient work has analyzed its genetic diversity in north-western Nigeria. Therefore, this study was undertaken with the objectives to analyze the genetic diversity of pearl millet accessions using SSR marker and to analyze the extent of evolutionary relationship among pearl millet accessions at the molecular level. The result of the present study confirmed diversity among accessions of pearl millet in the study area. Simple Sequence Repeats (SSR) markers were used for genetic analysis and evolutionary relationship of the accessions of pearl millet. To analyze the level of genetic diversity, 8 polymorphic SSR markers were used to screen 69 accessions collected based on three maturity periods. SSR markers result reveal relationships among the accessions in terms of genetic similarities, evolutionary and ancestral origin, it also reveals a total of 53 alleles recorded with 8 microsatellites and an average of 6.875 per microsatellite, the range was from 3 to 9 alleles in PSMP2248 and PSMP2080 respectively. Moreover, both the factorial analysis and the dendrogram of phylogeny tree grouping patterns and cluster analysis were almost in agreement with each other that diversity is not clustering according to geographical patterns but, according to similarity, the result showed maximum similarity among clusters with few numbers of accessions. It has been recommended that other molecular markers should be tested in the same study area.

Keywords: pearl millet, genetic diversity, simple sequence repeat (SSR)

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Authors: Yayun Hsu, Henry Horng-Shing Lu

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This paper proposes a data-driven, biology-inspired neural segmentation method of 3D drosophila Brainbow images. We use Bayesian Sequential Partitioning algorithm for probabilistic modeling, which can be used to detect somas and to eliminate cross talk effects. This work attempts to develop an automatic methodology for neuron image segmentation, which nowadays still lacks a complete solution due to the complexity of the image. The proposed method does not need any predetermined, risk-prone thresholds since biological information is inherently included in the image processing procedure. Therefore, it is less sensitive to variations in neuron morphology; meanwhile, its flexibility would be beneficial for tracing the intertwining structure of neurons.

Keywords: brainbow, 3D imaging, image segmentation, neuron morphology, biological data mining, non-parametric learning

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Authors: Damanjit Kaur, Avani Bhatia

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Color constancy is significant for human vision since color is a pictorial cue that helps in solving different visions tasks such as tracking, object recognition, or categorization. Therefore, several computational methods have tried to simulate human color constancy abilities to stabilize machine color representations. Two different kinds of methods have been used, i.e., normalization and constancy. While color normalization creates a new representation of the image by canceling illuminant effects, color constancy directly estimates the color of the illuminant in order to map the image colors to a canonical version. Color constancy is the capability to determine colors of objects independent of the color of the light source. This research work studies the most of the well-known color constancy algorithms like white point and gray world.

Keywords: color constancy, gray world, white patch, modified white patch

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Authors: Meiling Yang, Shuguo Xie, Yilong Zhu

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Nowadays, due to diverse electric products and complex electromagnetic environment, the localization and troubleshooting of the electromagnetic radiation source is urgent and necessary especially on the condition of far field. However, based on the existing DOA positioning method, the system or devices are complex, bulky and expensive. To address this issue, this paper proposes a single antenna radiation source localization method. A single antenna moves to form a virtual antenna array combined with DOA and MUSIC algorithm to position accurately, meanwhile reducing the cost and simplify the equipment. As shown in the results of simulations and experiments, the virtual antenna array DOA estimation modeling is correct and its positioning is credible.

Keywords: virtual antenna array, DOA, localization, far field

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Vahid Bayrami Rad

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Ever since humans developed a collective way of life to the development of urbanization, the concern of security has always been considered one of the most important challenges of life. To protect property, locks have always been a practical tool. With the advancement of technology, the form of locks has changed from mechanical to electric. One of the most widely used fields of using artificial intelligence is its application in the technology of surveillance security systems. Currently, the technologies used in smart anti-theft door handles are one of the most potential fields for using artificial intelligence. Artificial intelligence has the possibility to learn, calculate, interpret and process by analyzing data with the help of algorithms and mathematical models and make smart decisions. We will use Arduino board to process data.

Keywords: arduino board, artificial intelligence, image processing, solenoid lock

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Authors: M. Jebali, M. Jemni

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This work is the part of vision based hand gesture recognition system for Natural Human Computer Interface. Hand tracking and segmentation are the primary steps for any hand gesture recognition system. The aim of this paper is to develop robust and efficient hand segmentation algorithm such as an input to another system which attempt to bring the HCI performance nearby the human-human interaction, by modeling an intelligent sign language recognition system based on prediction in the context of dialogue between the system (avatar) and the interlocutor. For the purpose of hand segmentation, an overcoming occlusion approach has been proposed for superior results for detection of hand from an image.

Keywords: HCI, sign language recognition, object tracking, hand segmentation

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Kyunghee Oh, Dooho Choi

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Although there is no theoretical weakness in a cryptographic algorithm, Side Channel Analysis can find out some secret data from the physical implementation of a cryptosystem. The analysis is based on extra information such as timing information, power consumption, electromagnetic leaks or even sound which can be exploited to break the system. Differential Power Analysis is one of the most popular analyses, as computing the statistical correlations of the secret keys and power consumptions. It is usually necessary to calculate huge data and takes a long time. It may take several weeks for some devices with countermeasures. We suggest and evaluate the methods to shorten the time to analyze cryptosystems. Our methods include distributed computing and parallelized processing.

Keywords: DPA, distributed computing, parallelized processing, side channel analysis

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model

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Authors: Sahar Mobeen, Anam Rafique, Irum Baig

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Acoustic echo cancellation in multichannel is a system identification application. In real time environment, signal changes very rapidly which required adaptive algorithms such as Least Mean Square (LMS), Leaky Least Mean Square (LLMS), Normalized Least Mean square (NLMS) and average (AFA) having high convergence rate and stable. LMS and NLMS are widely used adaptive algorithm due to less computational complexity and AFA used of its high convergence rate. This research is based on comparison of acoustic echo (generated in a room) cancellation thorough LMS, LLMS, NLMS, AFA and newly proposed average normalized leaky least mean square (ANLLMS) adaptive filters.

Keywords: LMS, LLMS, NLMS, AFA, ANLLMS

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Authors: Epaminondas G. Kyriakidis, Theodosis D. Dimitrakos, Constantinos C. Karamatsoukis

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The vehicle routing problem (VRP) is a well-known problem in Operations Research and has been widely studied during the last fifty-five years. The context of the VRP is that of delivering products located at a central depot to customers who are scattered in a geographical area and have placed orders for these products. A vehicle or a fleet of vehicles start their routes from the depot and visit the customers in order to satisfy their demands. Special attention has been given to the capacitated VRP in which the vehicles have limited carrying capacity of the goods that must be delivered. In the present work, we present a specific capacitated stochastic vehicle routing problem which has realistic applications to distributions of materials to shops or to healthcare facilities or to military units. A vehicle starts its route from a depot loaded with items of two similar but not identical products. We name these products, product 1 and product 2. The vehicle must deliver the products to N customers according to a predefined sequence. This means that first customer 1 must be serviced, then customer 2 must be serviced, then customer 3 must be serviced and so on. The vehicle has a finite capacity and after servicing all customers it returns to the depot. It is assumed that each customer prefers either product 1 or product 2 with known probabilities. The actual preference of each customer becomes known when the vehicle visits the customer. It is also assumed that the quantity that each customer demands is a random variable with known distribution. The actual demand is revealed upon the vehicle’s arrival at customer’s site. The demand of each customer cannot exceed the vehicle capacity and the vehicle is allowed during its route to return to the depot to restock with quantities of both products. The travel costs between consecutive customers and the travel costs between the customers and the depot are known. If there is shortage for the desired product, it is permitted to deliver the other product at a reduced price. The objective is to find the optimal routing strategy, i.e. the routing strategy that minimizes the expected total cost among all possible strategies. It is possible to find the optimal routing strategy using a suitable stochastic dynamic programming algorithm. It is also possible to prove that the optimal routing strategy has a specific threshold-type structure, i.e. it is characterized by critical numbers. This structural result enables us to construct an efficient special-purpose dynamic programming algorithm that operates only over those routing strategies having this structure. The findings of the present study lead us to the conclusion that the dynamic programming method may be a very useful tool for the solution of specific vehicle routing problems. A problem for future research could be the study of a similar stochastic vehicle routing problem in which the vehicle instead of delivering, it collects products from ordered customers.

Keywords: collection of similar products, dynamic programming, stochastic demands, stochastic preferences, vehicle routing problem

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