Search results for: time series regression.

Authors: Paria Soleimani, Arezoo Neshati

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Myocardial infarction is one of the leading causes of death in the world. Some of these deaths occur even before the patient reaches the hospital. Myocardial infarction occurs as a result of impaired blood supply. Because the most of these deaths are due to coronary artery disease, hence the awareness of the warning signs of a heart attack is essential. Some heart attacks are sudden and intense, but most of them start slowly, with mild pain or discomfort, then early detection and successful treatment of these symptoms is vital to save them. Therefore, importance and usefulness of a system designing to assist physicians in early diagnosis of the acute heart attacks is obvious. The main purpose of this study would be to enable patients to become better informed about their condition and to encourage them to seek professional care at an earlier stage in the appropriate situations. For this purpose, the data were collected on 711 heart patients in Iran hospitals. 28 attributes of clinical factors can be reported by patients; were studied. Three logistic regression models were made on the basis of the 28 features to predict the risk of heart attacks. The best logistic regression model in terms of performance had a C-index of 0.955 and with an accuracy of 94.9%. The variables, severe chest pain, back pain, cold sweats, shortness of breath, nausea and vomiting, were selected as the main features.

Keywords: Coronary heart disease, acute heart attacks, prediction, logistic regression.

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Authors: Sotiris B. Kotsiantis

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Bagging and boosting are among the most popular re-sampling ensemble methods that generate and combine a diversity of regression models using the same learning algorithm as base-learner. Boosting algorithms are considered stronger than bagging on noise-free data. However, there are strong empirical indications that bagging is much more robust than boosting in noisy settings. For this reason, in this work we built an ensemble using an averaging methodology of bagging and boosting ensembles with 10 sub-learners in each one. We performed a comparison with simple bagging and boosting ensembles with 25 sub-learners on standard benchmark datasets and the proposed ensemble gave better accuracy.

Keywords: Regressors, statistical learning.

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Authors: Jeng-Wen Lin, Simon Chien-Yuan Chen

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Based on assumptions of neo-classical economics and rational choice / public choice theory, this paper investigates the regulation of industrial land use in Taiwan by homeowners associations (HOAs) as opposed to traditional government administration. The comparison, which applies the transaction cost theory and a polynomial regression analysis, manifested that HOAs are superior to conventional government administration in terms of transaction costs and overall efficiency. A case study that compares Taiwan-s commonhold industrial park, NangKang Software Park, to traditional government counterparts using limited data on the costs and returns was analyzed. This empirical study on the relative efficiency of governmental and private institutions justified the important theoretical proposition. Numerical results prove the efficiency of the established model.

Keywords: Homeowners Associations, Institutional Efficiency, Polynomial Regression, Transaction Cost.

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Authors: Abhishek Kumar Chandra, Kaushal Kishor, Wasim Khan, Dhananjay Singh, M. S. Alam

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Single phase fluid flow through series of uniform microchannels connected via transition section (converging-diverging section with or without throat) was analytically and numerically studied to characterize the flow within the channel and in the transition sections. Three sets of microchannels of diameters 100, 184, and 249 μm were considered for investigation. Each set contains 10 numbers of microchannels of length 20 mm, connected to each other in series via transition sections. Transition section consists of either converging-diverging section with throat or without throat. The effect of non-uniformity in microchannels on pressure drop was determined by passing water/air through the set of channels for Reynolds number 50 to 1000. Compressibility and rarefaction effects in transition sections were also tested analytically and numerically for air flow. The analytical and numerical results show that these configurations can be used in enhancement of transport processes. However, converging-diverging section without throat shows superior performance over with throat configuration.

Keywords: Contraction-expansion flow, integrated microchannel, microchannel network, single phase flow.

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Authors: Müzeyyen Balçikanli, Erdoğan Özbay, Hakan Tacettin Türker, Okan Karahan, Cengiz Duran Atiş

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In this research, effect of curing time (TC), curing temperature (CT), sodium concentration (SC) and silicate modules (SM) on the compressive strength, chloride ion permeability, and water absorption capacity of alkali activated slag (AAS) concretes were investigated. For maximization of compressive strength while for minimization of chloride ion permeability and water absorption capacity of AAS concretes, best possible combination of CT, CTime, SC and SM were determined. An experimental program was conducted by using the central composite design method. Alkali solution-slag ratio was kept constant at 0.53 in all mixture. The effects of the independent parameters were characterized and analyzed by using statistically significant quadratic regression models on the measured properties (dependent parameters). The proposed regression models are valid for AAS concretes with the SC from 0.1% to 7.5%, SM from 0.4 to 3.2, CT from 20 °C to 94 °C and TC from 1.2 hours to 25 hours. The results of test and analysis indicate that the most effective parameter for the compressive strength, chloride ion permeability and water absorption capacity is the sodium concentration.

Keywords: Alkali activation, slag, rapid chloride permeability, water absorption capacity.

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Authors: D. Mondal, A. Chakrabarti, A. Sengupta

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This paper aims to select the optimal location and setting parameters of TCSC (Thyristor Controlled Series Compensator) controller using Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) to mitigate small signal oscillations in a multimachine power system. Though Power System Stabilizers (PSSs) are prime choice in this issue, installation of FACTS device has been suggested here in order to achieve appreciable damping of system oscillations. However, performance of any FACTS devices highly depends upon its parameters and suitable location in the power network. In this paper PSO as well as GA based techniques are used separately and compared their performances to investigate this problem. The results of small signal stability analysis have been represented employing eigenvalue as well as time domain response in face of two common power system disturbances e.g., varying load and transmission line outage. It has been revealed that the PSO based TCSC controller is more effective than GA based controller even during critical loading condition.

Keywords: Genetic Algorithm, Particle Swarm Optimization, Small Signal Stability, Thyristor Controlled Series Compensator.

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Authors: Norasiah Muhammad, Yupiter HP Manurung

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This paper investigates the development of weld zone in Resistance Spot Welding (RSW) which focuses on weld nugget and Heat Affected Zone (HAZ). The effects of four factors namely weld current, weld time, electrode force and hold time were studied using a general 24 factorial design augmented by five centre points. The results of the analysis showed that all selected factors except hold time exhibit significant effect on weld nugget radius and HAZ size. Optimization of the welding parameters (weld current, weld time and electrode force) to normalize weld nugget and to minimize HAZ size was then conducted using Central Composite Design (CCD) in Response Surface Methodology (RSM) and the optimum parameters were determined. A regression model for radius of weld nugget and HAZ size was developed and its adequacy was evaluated. The experimental results obtained under optimum operating conditions were then compared with the predicted values and were found to agree satisfactorily with each other

Keywords: Factorial design, Optimization, Resistance Spot Welding (RSW), Response Surface Methodology (RSM).

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Authors: Ahmet Oguz Akturk, Kemal Izci, Gurbuz Caliskan, Ismail Sahin

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Rapid developments in technology in the present age have made it necessary for communities to follow technological developments and adapt themselves to these developments. One of the fields that are most rapidly affected by these developments is undoubtedly education. Determination of the attitudes of preservice teachers, who live in an age of technology and get ready to raise future individuals, is of paramount importance both educationally and professionally. The purpose of this study was to analyze attitudes of preservice teachers towards technology and some variables that predict these attitudes (gender, daily duration of internet use, and the number of technical devices owned). 329 preservice teachers attending the education faculty of a large university in central Turkey participated, on a volunteer basis, in this study, where relational survey model was used as the research method. Research findings reveal that preservice teachers’ attitudes towards technology are positive and at the same time, the attitudes of male preservice teachers towards technology are more positive than their female counterparts. As a result of the stepwise multiple regression analysis where factors predicting preservice teachers’ attitudes towards technology, it was found that duration of daily internet use was the strongest predictor of attitudes towards technology.

Keywords: Attitudes towards technology, preservice teachers, gender, stepwise multiple regression analysis.

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Authors: Chaudhuri Manoj Kumar Swain, Susmita Das

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This paper explores a detailed procedure of predicting a path loss (PL) model and its application in estimating the coverage probability in a WiMAX network. For this a hybrid approach is followed in predicting an empirical PL model of a 2.65 GHz WiMAX network deployed in a suburban environment. Data collection, statistical analysis, and regression analysis are the phases of operations incorporated in this approach and the importance of each of these phases has been discussed properly. The procedure of collecting data such as received signal strength indicator (RSSI) through experimental set up is demonstrated. From the collected data set, empirical PL and RSSI models are predicted with regression technique. Furthermore, with the aid of the predicted PL model, essential parameters such as PL exponent as well as the coverage probability of the network are evaluated. This research work may assist in the process of deployment and optimisation of any cellular network significantly.

Keywords: WiMAX, RSSI, path loss, coverage probability, regression analysis.

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Authors: Antoni Wibowo, Harry Pujianto, Dewi Retno Sari Saputro

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The stock market can provide huge profits in a relatively short time in financial sector; however, it also has a high risk for investors and traders if they are not careful to look the factors that affect the stock market. Therefore, they should give attention to the dynamic fluctuations and movements of the stock market to optimize profits from their investment. In this paper, we present a nonlinear autoregressive exogenous model (NARX) to predict the movements of stock market; especially, the movements of the closing price index. As case study, we consider to predict the movement of the closing price in Indonesia composite index (IHSG) and choose the best structures of NARX for IHSG’s prediction.

Keywords: NARX, prediction, stock market, time series.

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Authors: F. Rasi Maezabadi, M. Masdari, M. R. Soltani

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Series of experimental tests were conducted on a section of a 660 kW wind turbine blade to measure the pressure distribution of this model oscillating in plunging motion. In order to minimize the amount of data required to predict aerodynamic loads of the airfoil, a General Regression Neural Network, GRNN, was trained using the measured experimental data. The network once proved to be accurate enough, was used to predict the flow behavior of the airfoil for the desired conditions. Results showed that with using a few of the acquired data, the trained neural network was able to predict accurate results with minimal errors when compared with the corresponding measured values. Therefore with employing this trained network the aerodynamic coefficients of the plunging airfoil, are predicted accurately at different oscillation frequencies, amplitudes, and angles of attack; hence reducing the cost of tests while achieving acceptable accuracy.

Keywords: Airfoil, experimental, GRNN, Neural Network, Plunging.

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Authors: Chiung-Ju Huang

Abstract:

This study utilizes the quantile regression analysis to examine the impact of governance (including democratic quality and technical quality) on happiness in 101 countries worldwide, classified as “developed countries” and “developing countries”. The empirical results show that the impact of democratic quality and technical quality on happiness is significantly positive for “developed countries”, while is insignificant for “developing countries”. The results suggest that the authorities in developed countries can enhance the level of individual happiness by means of improving the democracy quality and technical quality. However, for developing countries, promoting the quality of governance in order to enhance the level of happiness may not be effective. Policy makers in developed countries may pay more attention on increasing real GDP per capita instead of promoting the quality of governance to enhance individual happiness.

Keywords: Governance, happiness, multiple regression, quantile regression.

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Authors: Maria V. Morozova, Yulia V. Emelyanova, Anastasia A. Levina, Elena S. Buyanova, Zoya A. Mikhaylovskaya, Sofia A. Petrova

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The solid solutions of lanthanum niobates substituted by yttrium, bismuth and tungsten were synthesized. The structure of the solid solutions is either LaNbO₄-based monoclinic or BiNbO₄-based triclinic. The series where niobium is substituted by tungsten on B site reveals phase-modulated structure. The values of cell parameters decrease with increasing the dopant concentration for all samples except the tungsten series although the latter show higher total conductivity.

Keywords: Impedance spectroscopy, LaNbO4, lanthanum ortho-niobates.

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Authors: Francisco Miranda

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The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: Ricardo Espinosa

Abstract:

The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise

Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Johan Fredin, Anders Jönsson

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Abrasive waterjet cutting (AWJ) is a highly efficient method for cutting almost any type of material. When holes shall be cut the waterjet first needs to pierce the material.This paper presents a vast experimental analysis of piercing parameters effect on piercing time. Results from experimentation on feed rates, work piece thicknesses, abrasive flow rates, standoff distances and water pressure are also presented as well as studies on three methods for dynamic piercing. It is shown that a large amount of time and resources can be saved by choosing the piercing parameters in a correct way. The large number of experiments puts demands on the experimental setup. An automated experimental setup including piercing detection is presented to enable large series of experiments to be carried out efficiently.

Keywords: Waterjet cutting, Piercing, Experimentation

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Authors: Tahseen A. Jilani, Huda Yasin, Madiha Yasin, C. Ardil

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In this paper we use data mining techniques to investigate factors that contribute significantly to enhancing the risk of acute coronary syndrome. We assume that the dependent variable is diagnosis – with dichotomous values showing presence or  absence of disease. We have applied binary regression to the factors affecting the dependent variable. The data set has been taken from two different cardiac hospitals of Karachi, Pakistan. We have total sixteen variables out of which one is assumed dependent and other 15 are independent variables. For better performance of the regression model in predicting acute coronary syndrome, data reduction techniques like principle component analysis is applied. Based on results of data reduction, we have considered only 14 out of sixteen factors.

Keywords: Acute coronary syndrome (ACS), binary logistic regression analyses, myocardial ischemia (MI), principle component analysis, unstable angina (U.A.).

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Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay

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In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.

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Authors: Hanane Ondella, Pierre Ladet, David Ferrand, Pat Sloan

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In the micro and nano-technology industry, the «clean-rooms» dedicated to manufacturing chip, are equipped with the most sophisticated equipment-tools. There use a large number of resources in according to strict specifications for an optimum working and result. The distribution of «utilities» to the production is assured by teams who use a supervision tool. The studies show the interest to control the various parameters of production or/and distribution, in real time, through a reliable and effective supervision tool. This document looks at a large part of the functions that the supervisor must assure, with complementary functionalities to help the diagnosis and simulation that prove very useful in our case where the supervised installations are complexed and in constant evolution.

Keywords: Control-Command, evolution, non regression, performances, real time, simulation, supervision.

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Authors: R. B. Knudsen, O. T. Rasmussen, R. A. Alphinas

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The reason for conducting this research is to develop an algorithm that is capable of classifying news articles from the automobile industry, according to the competitive actions that they entail, with the use of Text Mining (TM) methods. It is needed to test how to properly preprocess the data for this research by preparing pipelines which fits each algorithm the best. The pipelines are tested along with nine different classification algorithms in the realm of regression, support vector machines, and neural networks. Preliminary testing for identifying the optimal pipelines and algorithms resulted in the selection of two algorithms with two different pipelines. The two algorithms are Logistic Regression (LR) and Artificial Neural Network (ANN). These algorithms are optimized further, where several parameters of each algorithm are tested. The best result is achieved with the ANN. The final model yields an accuracy of 0.79, a precision of 0.80, a recall of 0.78, and an F1 score of 0.76. By removing three of the classes that created noise, the final algorithm is capable of reaching an accuracy of 94%.

Keywords: Artificial neural network, competitive dynamics, logistic regression, text classification, text mining.

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Authors: Xiaolei Hu, Enrico Ferrera, Riccardo Tomasi, Claudio Pastrone

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Load Forecasting plays a key role in making today's and future's Smart Energy Grids sustainable and reliable. Accurate power consumption prediction allows utilities to organize in advance their resources or to execute Demand Response strategies more effectively, which enables several features such as higher sustainability, better quality of service, and affordable electricity tariffs. It is easy yet effective to apply Load Forecasting at larger geographic scale, i.e. Smart Micro Grids, wherein the lower available grid flexibility makes accurate prediction more critical in Demand Response applications. This paper analyses the application of short-term load forecasting in a concrete scenario, proposed within the EU-funded GreenCom project, which collect load data from single loads and households belonging to a Smart Micro Grid. Three short-term load forecasting techniques, i.e. linear regression, artificial neural networks, and radial basis function network, are considered, compared, and evaluated through absolute forecast errors and training time. The influence of weather conditions in Load Forecasting is also evaluated. A new definition of Gain is introduced in this paper, which innovatively serves as an indicator of short-term prediction capabilities of time spam consistency. Two models, 24- and 1-hour-ahead forecasting, are built to comprehensively compare these three techniques.

Keywords: Short-term load forecasting, smart micro grid, linear regression, artificial neural networks, radial basis function network, Gain.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

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Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant.

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Authors: Babakina Alexandra, Yong Soo Kim

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In this study, we analyzed the factors that affect research funds using linear regression analysis to increase the effectiveness of investments in national research projects. We collected 7,916 items of data on research projects that were in the process of being finished or were completed between 2010 and 2011. Data pre-processing and visualization were performed to derive statistically significant results. We identified factors that affected funding using analysis of fit distributions and estimated increasing or decreasing tendencies based on these factors.

Keywords: R&D funding, Cost estimation, Linear regression, Preliminary feasibility study.

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Authors: Chiung-Ju Huang, Yuan-Hong Ho

Abstract:

This paper develops the fiscal health index of 21 local governments in Taiwan over the 1984 to 2010 period. A quantile regression analysis was used to explore the extent that economic variables, political budget cycles, and legislative checks and balances, impact different quantiles of fiscal health index for a country over a sample period of time. Our findings suggest that local governments at the lower quantile are significantly benefited from political budget cycles and the increase in central government revenues, while legislative effective checks and balances and the increase in central government expenditures have a significantly negative effect on local fiscal health. When local governments are in the upper tail of the distribution, legislative checks and balances and growth in macroeconomics have significant and adverse effects on the fiscal health of local governments. However, increases in central government revenues have significant and positive effects on the health status of local government in Taiwan.

Keywords: Fiscal health, political budget cycles, legislative checks and balances, quantile regression.

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Authors: S. Padma, Dr. R. Lakshmipathi, K. Ramash Kumar, P. Nandagopal

Abstract:

The power system network is becoming more complex nowadays and it is very difficult to maintain the stability of the system. Today-s enhancement of technology makes it possible to include new energy storage devices in the electric power system. In addition, with the aid of power electronic devices, it is possible to independently exchange active and reactive power flow with the utility grid. The main purpose of this paper proposes a Proportional – Integral (PI) control based 48 – pulse Inverter based Static Synchronous Series Compensator (SSSC) with and without Superconducting Magnetic Energy Storage (SMES) used for enhancing the transient stability and regulating power flow in automatic mode. Using a test power system through the dynamic simulation in Matlab/Simulink platform validates the performance of the proposed SSSC with and without SMES system.

Keywords: Flexible AC transmission system (FACTS), PIControl, Superconducting Magnetic Energy Storage (SMES), Static Synchronous Series Compensator (SSSC).

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Authors: Mária Stachová, Lukáš Sobíšek

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Data mining incorporates a group of statistical methods used to analyze a set of information, or a data set. It operates with models and algorithms, which are powerful tools with the great potential. They can help people to understand the patterns in certain chunk of information so it is obvious that the data mining tools have a wide area of applications. For example in the theoretical chemistry data mining tools can be used to predict moleculeproperties or improve computer-assisted drug design. Classification analysis is one of the major data mining methodologies. The aim of thecontribution is to create a classification model, which would be able to deal with a huge data set with high accuracy. For this purpose logistic regression, Bayesian logistic regression and random forest models were built using R software. TheBayesian logistic regression in Latent GOLD software was created as well. These classification methods belong to supervised learning methods. It was necessary to reduce data matrix dimension before construct models and thus the factor analysis (FA) was used. Those models were applied to predict the biological activity of molecules, potential new drug candidates.

Keywords: data mining, classification, drug design, QSAR

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Authors: M. M. Hossain, M. Z. Hasan, M. Alauddin, S. Akhter

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Climate change has become a major concern across the world as the intensity along with quantity of the rainfall, mean surface temperature and other climatic parameters have been changed not only in Bangladesh but also in the entire globe. Bangladesh has already experienced many natural hazards. Among them changing of rainfall pattern, erratic and heavy rainfalls are very common. But changes of rainfall pattern and its amount is still in question to some extent. This study aimed to unfold how the historical rainfalls varied over time and how would be their future trends. In this context, historical rainfall data (1975-2014) were collected from Bangladesh Metrological Department (BMD) and then a time series model was developed using Box-Jenkins algorithm in IBM SPSS to forecast the future rainfall. From the historical data analysis, this study revealed that the amount of rainfall decreased over the time and shifted to the post monsoons. Forecasted rainfall shows that the pre-monsoon and early monsoon will get drier in future whereas late monsoon and post monsoon will show huge fluctuations in rainfall magnitudes with temporal variations which means Bangladesh will get comparatively drier seasons in future which may be a serious problem for the country as it depends on agriculture.

Keywords: Monsoon, Pre-monsoon, rainfall, pattern, variations, IBM-SPSS.

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Authors: Vipin Kumar Verma, Praveen Saraswat

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The development of double stenosis in an artery can have serious consequences and can disrupt the normal functioning of the circulatory system. It has been realized that various hydrodynamics effects (i.e. wall shear, pressure distribution etc.) play important role in the development of this disease. Generally in the literature, the cross-section of the artery is assumed to be uniform with a single stenosis. However, in real situation the multiple stenosis develops in series along the length of artery whose cross-section varies slowly. Therefore, the flow of blood is laminar through a small diameter artery with axisymmetric identical double stenosis in series.

Keywords: Wall shear, multiple stenosis, artery.

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