Search results for: Linear Predictive Coefficients.

Authors: O. Takakuwa, Y. Mano, H. Soyama

Abstract:

This paper reveals the interaction between hydrogen and surface stress in austenitic stainless steel by X-ray diffraction stress measurement and thermal desorption analysis before and after being charged with hydrogen. The surface residual stress was varied by surface finishing using several disc polishing agents. The obtained results show that the residual stress near surface had a significant effect on hydrogen absorption behavior, that is, tensile residual stress promoted the hydrogen absorption and compressive one did opposite. Also, hydrogen induced equi-biaxial stress and this stress has a linear correlation with hydrogen content.

Keywords: Hydrogen embrittlement, Residual stress, Surface finishing, Stainless steel.

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Authors: Shobha Sharma, Amita Dev

Abstract:

This research paper presents highly optimized barrel shifter at 22nm Hi K metal gate strained Si technology node. This barrel shifter is having a unique combination of static and dynamic body bias which gives lowest power delay product. This power delay product is compared with the same circuit at same technology node with static forward biasing at ‘supply/2’ and also with normal reverse substrate biasing and still found to be the lowest. The power delay product of this barrel sifter is .39362X10-17J and is lowered by approximately 78% to reference proposed barrel shifter at 32nm bulk CMOS technology. Power delay product of barrel shifter at 22nm Hi K Metal gate technology with normal reverse substrate bias is 2.97186933X10-17J and can be compared with this design’s PDP of .39362X10-17J. This design uses both static and dynamic substrate biasing and also has approximately 96% lower power delay product compared to only forward body biased at half of supply voltage. The NMOS model used are predictive technology models of Arizona state university and the simulations to be carried out using HSPICE simulator.

Keywords: Dynamic body biasing, highly optimized barrel shifter, PDP, Static body biasing.

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Authors: Mohamed A. El-Kady, Badr M. Alshammari

Abstract:

In a recent major industry-supported research and development study, a novel framework was developed and applied for assessment of reliability and quality performance levels in reallife power systems with practical large-scale sizes. The new assessment methodology is based on three metaphors (dimensions) representing the relationship between available generation capacities and required demand levels. The paper shares the results of the successfully completed stud and describes the implementation of the new methodology on practical zones in the Saudi electricity system.

Keywords: Power systems; large-scale analysis, reliability; performance assessment, linear programming.

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Authors: P. Kowalska, P. Gabka, K. Kamieniarz, M. Kamieniarz, W. Stryla, P. Guzik, T. Krauze

Abstract:

We have developed a computer program consisting of 6 subtests assessing the children hand dexterity applicable in the rehabilitation medicine. We have carried out a normative study on a representative sample of 285 children aged from 7 to 15 (mean age 11.3) and we have proposed clinical standards for three age groups (7-9, 9-11, 12-15 years). We have shown statistical significance of differences among the corresponding mean values of the task time completion. We have also found a strong correlation between the task time completion and the age of the subjects, as well as we have performed the test-retest reliability checks in the sample of 84 children, giving the high values of the Pearson coefficients for the dominant and non-dominant hand in the range 0.740.97 and 0.620.93, respectively. A new MATLAB-based programming tool aiming at analysis of cardiologic RR intervals and blood pressure descriptors, is worked out, too. For each set of data, ten different parameters are extracted: 2 in time domain, 4 in frequency domain and 4 in Poincaré plot analysis. In addition twelve different parameters of baroreflex sensitivity are calculated. All these data sets can be visualized in time domain together with their power spectra and Poincaré plots. If available, the respiratory oscillation curves can be also plotted for comparison. Another application processes biological data obtained from BLAST analysis.

Keywords: Biomedical data base processing, Computer software, Hand dexterity, Heart rate and blood pressure variability.

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Authors: A. Ramdane, F.Naceri, S. Ramdane

Abstract:

in this work, we present a new strategy of direct adaptive control denoted: Extended minimal controller synthesis (EMCS). This algorithm is designed for an induction motor, which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The main motivation of the EMCS control is to enhance the robustness of the MRAC algorithms, i.e. the rejection of bounded effects of rapidly varying external disturbances.

Keywords: Adaptive Control, Simple model reference adaptive control (SMRAC), Extended Minimal Controller synthesis (EMCS), Induction Motor (IM)

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Authors: Filiz Ersoz, Taner Ersoz, Tugrul Bayraktar

Abstract:

Renewable energy is referred to as "clean energy" and common popular support for the use of renewable energy (RE) is to provide electricity with zero carbon dioxide emissions. This study provides useful insight into the European Union (EU) RE, especially, into electricity generation obtained from renewables, and their targets. The objective of this study is to identify groups of European countries, using multivariate statistical analysis and selected indicators. The hierarchical clustering method is used to decide the number of clusters for EU countries. The conducted statistical hierarchical cluster analysis is based on the Ward’s clustering method and squared Euclidean distances. Hierarchical cluster analysis identified eight distinct clusters of European countries. Then, non-hierarchical clustering (k-means) method was applied. Discriminant analysis was used to determine the validity of the results with data normalized by Z score transformation. To explore the relationship between the selected indicators, correlation coefficients were computed. The results of the study reveal the current situation of RE in European Union Member States.

Keywords: Share of electricity generation, CO2 emission, targets, multivariate methods, hierarchical clustering, K-means clustering, discriminant analyzed, correlation, EU member countries.

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Authors: Ming-Tsang Wu

Abstract:

The purpose of this study was to explore the correlation between leisure participation and perceived wellness, with the students of a nursing college in southern Taiwan as the subjects. One thousand six hundred and ninety-six (1,696) surveys were sent, and 1,408 surveys were received for an 83.02% valid response rate. Using canonical correlation analysis to analyze the data, the results showed that the linear combination of the two sets of variable produces five significant canonical variates. Out of the five canonical variates, only the first has sufficient explanatory power. The canonical correlation coefficient of first canonical variate is 0.660. This indicated that leisure participation and perceived wellness are significantly correlated.

Keywords: Leisure, perceived wellness.

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Authors: C. Villegas-Quezada, J. Climent

Abstract:

Several works regarding facial recognition have dealt with methods which identify isolated characteristics of the face or with templates which encompass several regions of it. In this paper a new technique which approaches the problem holistically dispensing with the need to identify geometrical characteristics or regions of the face is introduced. The characterization of a face is achieved by randomly sampling selected attributes of the pixels of its image. From this information we construct a set of data, which correspond to the values of low frequencies, gradient, entropy and another several characteristics of pixel of the image. Generating a set of “p" variables. The multivariate data set with different polynomials minimizing the data fitness error in the minimax sense (L∞ - Norm) is approximated. With the use of a Genetic Algorithm (GA) it is able to circumvent the problem of dimensionality inherent to higher degree polynomial approximations. The GA yields the degree and values of a set of coefficients of the polynomials approximating of the image of a face. By finding a family of characteristic polynomials from several variables (pixel characteristics) for each face (say Fi ) in the data base through a resampling process the system in use, is trained. A face (say F ) is recognized by finding its characteristic polynomials and using an AdaBoost Classifier from F -s polynomials to each of the Fi -s polynomials. The winner is the polynomial family closer to F -s corresponding to target face in data base.

Keywords: AdaBoost Classifier, Holistic Face Recognition, Minimax Multivariate Approximation, Genetic Algorithm.

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Authors: Yudia Mailani Putri, Martalena Purba, B. J. Istiti Kandarina

Abstract:

Background: Obesity has been recognized as a global health problem. Individuals classified as overweight and obese are increasing at an alarming rate. This condition is associated with psychological and physiological problems. as a person reaches adulthood, somatic growth ceases. At this stage, the human body has developed fully, to a stable state. As the capital of Riau Province in Indonesia, Pekanbaru is dominated by Malay ethnic population habitually consuming cholesterol-rich fatty foods as a daily menu, a trigger to the onset of obesity resulting in high prevalence of degenerative diseases. Research objectives: The aim of this study is elaborating the relationship between high-fat consumption pattern, stress level, physical activity and the incidence of obesity in adult women in Pekanbaru city. Research Methods: Among the combined research methods applied in this study, the first stage is quantitative observational, analytical cross-sectional research design with adult women aged 20-40 living in Pekanbaru city. The sample consists of 200 women with BMI≥25. Sample data is processed with univariate, bivariate (correlation and simple linear regression) and multivariate (multiple linear regression) analysis. The second phase is qualitative descriptive study purposive sampling by in-depth interviews. six participants withdrew from the study. Results: According to the results of the bivariate analysis, there are relationships between the incidence of obesity and the pattern of high fat foods consumption (energy intake (p≤0.000; r = 0.536), protein intake (p≤0.000; r=0.307), fat intake (p≤0.000; r=0.416), carbohydrate intake (p≤0.000; r=0.430), frequency of fatty food consumption (p≤0.000; r=0.506) and frequency of viscera foods consumption (p≤0.000; r=0.535). There is a relationship between physical activity and incidence of obesity (p≤0.000; r=-0.631). However, there is no relationship between the level of stress (p=0.741; r=0.019-) and the incidence of obesity. Physical activity is a predominant factor in the incidence of obesity in adult women in Pekanbaru city. Conclusion: There are relationships between high-fat food consumption pattern, physical activity and the incidence of obesity in Pekanbaru city whereas physical activity is a predominant factor in the occurrence of obesity, supported by the unchangeable pattern of high-fat foods consumption.

Keywords: Obesity, adult, high in fat, stress, physical activity, consumption pattern.

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Authors: Swarniv Chandra, Basudev Ghosh

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Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

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A model based fault detection and diagnosis technique for DC motor is proposed in this paper. Fault detection using Kalman filter and its different variants are compared. Only incipient faults are considered for the study. The Kalman Filter iterations and all the related computations required for fault detection and fault confirmation are presented. A second order linear state space model of DC motor is used for this work. A comparative assessment of the estimates computed from four different observers and their relative performance is evaluated.

Keywords: DC motor model, Fault detection and diagnosis Kalman Filter, Unscented Kalman Filter

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Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

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Authors: Husna Hasan, Norfatin Salam, Mohd Bakri Adam

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Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is linear for the location parameters. The return level is the level of events (maximum temperature) which is expected to be exceeded once, on average, in a given number of years, is obtained.

Keywords: Extreme temperature, extreme value, return level.

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Authors: Komeil Jahanifar, Zahra Abedi, Yaghob Zeraatkish

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This research was conducted for the first time at the southeastern coasts of the Caspian Sea in order to evaluate the performance of osteichthyes cooperatives through production (catch) function. Using one of the indirect valuation methods in this research, contributory factors in catch were identified and were inserted into the function as independent variables. In order to carry out this research, the performance of 25 Osteichthyes catching cooperatives in the utilization year of 2009 which were involved in fishing in Miankale wildlife refuge region. The contributory factors in catch were divided into groups of economic, ecological and biological factors. In the mentioned function, catch rate of the cooperative were inserted into as the dependant variable and fourteen partial variables in terms of nine general variables as independent variables. Finally, after function estimation, seven variables were rendered significant at 99 percent reliably level. The results of the function estimation indicated that human resource (fisherman quantity) had the greatest positive effect on catch rate with an influence coefficient of 1.7 while weather conditions had the greatest negative effect on the catch rate of cooperatives with an influence coefficient of -2.07. Moreover, factors like member's share, experience and fisherman training and fishing effort played the main roles in the catch rate of cooperative with influence coefficients of 0.81, 0.5 and 0.21, respectively.

Keywords: Production Function, Coefficient, Variable, Osteichthyes, Caspian Sea

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Authors: Chimaobi V. Okolo, Afamefuna J. Ani, Ebere U. Okolo

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This paper seeks to assess the implications of insurance to foreign direct investment inflow in Nigeria. Multiple linear regression technique and correlation matrix test were employed to measure the extent to which foreign direct investment was influenced. The result showed that insurance premium (IP), asset size of insurance industry (AS), and total investment of the industry (TI) impacted significantly and positively on foreign direct investment inflow in Nigeria. There should be effective risk transfer mechanism and financial intermediation, which gives the investor confidence in the risk management strength of the host country.

Keywords: Foreign direct investment, insurance.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

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Authors: Mefleh S. Hamideen

Abstract:

In this investigation, activity concentration of 226Ra, 232Th, and 40K, of some ceramic tile materials used in the local market of Jordan for interior decoration were determined by making use of High Purity Germanium (HPGe) detector. Twenty samples of different country of origin and sizes used in Jordan were analyzed. The concentration values of the last-mentioned radionuclides ranged from 30 Bq.kg-1 (Sample from Jordan) to 98 Bq.kg-1 (Sample from China) for 226Ra, 31 Bq.kg-1 (Sample from Italy) to 98 Bq.kg-1 (Sample from China) for 232Th, and 129 Bq.kg-1 (Sample from Spain) to 679 Bq.kg-1 (Sample from Italy) for 40K. Based on the calculated activity concentrations, some radiological parameters have been calculated to test the radiation hazards in the ceramic tiles. In this work, the following parameters: Total absorbed dose rate (DR), Annual effective dose rate (HR), Radium equivalent activity (Raeq), Radon emanation coefficient F (%) and Radon mass exhalation rate (Em) were calculated for all ceramic tiles and listed in the body of the work. Fortunately, the average calculated values of all parameters are less than the recommended values for each parameter. Consequently, almost all the examined ceramic materials appear to have low radon emanation coefficients. As a result of that investigation, no problems on people can appear by using those ceramic tiles in Jordan.

Keywords: radon emanation coefficient, radon mass exhalation rate, total annual effective dose, radon level

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Authors: Mei-Se Chien, Chien-Chiang Lee, Sin-Jie Cai

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The main purpose of this paper is to investigate thelong-run equilibrium and short-run dynamics of international housing prices when macroeconomic variables change. We apply the Pedroni’s, panel cointegration, using the unbalanced panel data analysis of 33 countries over the period from 1980Q1 to 2013Q1, to examine the relationships among house prices and macroeconomic variables. Our empirical results of panel data cointegration tests support the existence of a cointegration among these macroeconomic variables and house prices. Besides, the empirical results of panel DOLS further present that a 1% increase in economic activity, long-term interest rates, and construction costs cause house prices to respectively change 2.16%, -0.04%, and 0.22% in the long run.Furthermore, the increasing economic activity and the construction cost would cause strongerimpacts on the house prices for lower income countries than higher income countries.The results lead to the conclusion that policy of house prices growth can be regarded as economic growth for lower income countries. Finally, in America region, the coefficient of economic activity is the highest, which displays that increasing economic activity causes a faster rise in house prices there than in other regions. There are some special cases whereby the coefficients of interest rates are significantly positive in America and Asia regions.

Keywords: House prices, Macroeconomic Variables, Panel cointegration, Dynamic OLS.

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Authors: Atman Jbari, Abdellah Adib, Driss Aboutajdine

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This paper addresses the problem of blind source separation (BSS). To recover original signals, from linear instantaneous mixtures, we propose a new contrast function based on the use of a double referenced system. Our approach assumes statistical independence sources. The reference vectors will be incrusted in the cumulant to evaluate the independence. The estimation of the separating matrix will be performed in two steps: whitening observations and joint diagonalization of a set of referenced cumulant matrices. Computer simulations are presented to demonstrate the effectiveness of the suggested approach.

Keywords: Blind source separation, Referenced Cumulant, Contrast, Joint Diagonalization.

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Authors: Liton Jude Rozario, Mohammad Reduanul Haque, Md. Ziarul Islam, Mohammad Shorif Uddin

Abstract:

Face recognition is a technique to automatically identify or verify individuals. It receives great attention in identification, authentication, security and many more applications. Diverse methods had been proposed for this purpose and also a lot of comparative studies were performed. However, researchers could not reach unified conclusion. In this paper, we are reporting an extensive quantitative accuracy analysis of four most widely used face recognition algorithms: Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA) and Support Vector Machine (SVM) using AT&T, Sheffield and Bangladeshi people face databases under diverse situations such as illumination, alignment and pose variations.

Keywords: PCA, ICA, LDA, SVM, face recognition, noise.

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Authors: M. Ouassaid, M. Cherkaoui, A. Nejmi, M. Maaroufi

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This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Sameena Tarannum, S. Pranesh

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The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: Gravity modulation, Oldroyd-B liquid, triple diffusive convection, Venezian approach.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

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Authors: Anirudha Narain, Dinesh Chandra, Ravindra K. S.

Abstract:

A computationally simple approach of model order reduction for single input single output (SISO) and linear timeinvariant discrete systems modeled in frequency domain is proposed in this paper. Denominator of the reduced order model is determined using fuzzy C-means clustering while the numerator parameters are found by matching time moments and Markov parameters of high order system.

Keywords: Model Order reduction, Discrete-time system, Fuzzy C-Means Clustering, Padé approximation.

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Authors: Md. Emaj Uddin

Abstract:

This study compares family communication patterns in association with family socio-cultural status, especially marriage and family pattern, and couples- socio-economic status between Muslim and Santal communities in rural Bangladesh. A total of 288 couples, 145 couples from the Muslim and 143 couples from the Santal were randomly selected through cluster sampling procedure from Kalna village situated in Tanore Upazila of Rajshahi district of Bangladesh, where both the communities dwell as neighbors. In order to collect data from the selected samples, interview method with semistructural questionnaire schedule was applied. The responses given by the respondents were analyzed by Pearson-s chi-squire test and bivariate correlation techniques. The results of Pearson-s chi-squire test revealed that family communication patterns (X2= 25. 90, df= 2, p<0.01, p>0.05) were significantly different between the Muslim and Santal communities. In addition, Spearman-s bivariate correlation coefficients suggested that among the exogenous factors, family type (rs=.135, p<0.05) and occupation of both husband (rs= .197, p<0.01) and wife (rs= .265, p<0.01) were significantly positive associations, and marital arrangement (rs= -.177, p<0.01), education of husband (rs= -.108, p<0.05) and wife (rs= -.142, p<0.01 & p<0.05), and family income (rs= -.164, p<0.01) were significantly negative relations with the family communication patterns followed between the two communities, although age difference between husband and wife, family head and residence patterns were not significant relations with ones.

Keywords: Bangladesh, Cross-Cultural Comparison, Family Communication Patterns, Family Socio-Cultural Status, Muslim, Santal.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

Abstract:

This paper deals with the problem of stability of neural networks with leakage, discrete and distributed delays. A new Lyapunov functional which contains some new double integral terms are introduced. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay system, and by making use of some inequality techniques, delay-dependent criteria are developed to guarantee the stability of the considered system. Finally, numerical examples are provided to illustrate the usefulness of the proposed main results.

Keywords: Neural networks, Stability, Time-varying delays, Linear matrix inequality.

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Authors: Celso L. Fernando, Toshio Yoshii, Takahiro Tsubota

Abstract:

Understanding the causes of a road accident and predicting their occurrence is key to prevent deaths and serious injuries from road accident events. Traditional statistical methods such as the Poisson and the Logistics regressions have been used to find the association of the traffic environmental factors with the accident occurred; recently, an artificial neural network, ANN, a computational technique that learns from historical data to make a more accurate prediction, has emerged. Although the ability to make accurate predictions, the ANN has difficulty dealing with highly unbalanced attribute patterns distribution in the training dataset; in such circumstances, the ANN treats the minority group as noise. However, in the real world data, the minority group is often the group of interest; e.g., in the road traffic accident data, the events of the accident are the group of interest. This study proposes a combination of the k-means with the ANN to improve the predictive ability of the neural network model by alleviating the effect of the unbalanced distribution of the attribute patterns in the training dataset. The results show that the proposed method improves the ability of the neural network to make a prediction on a highly unbalanced distributed attribute patterns dataset; however, on an even distributed attribute patterns dataset, the proposed method performs almost like a standard neural network. 

Keywords: Accident risks estimation, artificial neural network, deep learning, K-mean, road safety.

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Authors: Yilun Shang

Abstract:

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

Keywords: subgraph, expander, random graph, giant component, percolation.

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