Search results for: classification problem

Authors: I. Davies, O. L. C. Haas

Abstract:

In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.

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Authors: Marc Solé, Francesc Giné, Magda Valls, Nina Bijedic

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What people say on social media has turned into a rich source of information to understand social behavior. Specifically, the growing use of Twitter social media for political communication has arisen high opportunities to know the opinion of large numbers of politically active individuals in real time and predict the global political tendencies of a specific country. It has led to an increasing body of research on this topic. The majority of these studies have been focused on polarized political contexts characterized by only two alternatives. Unlike them, this paper tackles the challenge of forecasting Spanish political trends, characterized by multiple political parties, by means of analyzing the Twitters Users political tendency. According to this, a new strategy, named Tweets Analysis Strategy (TAS), is proposed. This is based on analyzing the users tweets by means of discovering its sentiment (positive, negative or neutral) and classifying them according to the political party they support. From this individual political tendency, the global political prediction for each political party is calculated. In order to do this, two different strategies for analyzing the sentiment analysis are proposed: one is based on Positive and Negative words Matching (PNM) and the second one is based on a Neural Networks Strategy (NNS). The complete TAS strategy has been performed in a Big-Data environment. The experimental results presented in this paper reveal that NNS strategy performs much better than PNM strategy to analyze the tweet sentiment. In addition, this research analyzes the viability of the TAS strategy to obtain the global trend in a political context make up by multiple parties with an error lower than 23%.

Keywords: Political tendency, prediction, sentiment analysis, Twitter.

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Authors: R. Fan, Q. Wan, H. Chen, Y.L. Liu, Y.P. Liu

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In the paper, a fast high-resolution range profile synthetic algorithm called orthogonal matching pursuit with sensing dictionary (OMP-SD) is proposed. It formulates the traditional HRRP synthetic to be a sparse approximation problem over redundant dictionary. As it employs a priori that the synthetic range profile (SRP) of targets are sparse, SRP can be accomplished even in presence of data lost. Besides, the computation complexity decreases from O(MNDK) flops for OMP to O(M(N + D)K) flops for OMP-SD by introducing sensing dictionary (SD). Simulation experiments illustrate its advantages both in additive white Gaussian noise (AWGN) and noiseless situation, respectively.

Keywords: GTD-based model, HRRP, orthogonal matching pursuit, sensing dictionary.

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Authors: N. Arulanand, P. Dhara

Abstract:

Optimizing the parameters in the controller plays a vital role in the control theory and its applications. Optimizing the PID parameters is finding out the best value from the feasible solutions. Finding the optimal value is an optimization problem. Inverted Pendulum is a very good platform for control engineers to verify and apply different logics in the field of control theory. It is necessary to find an optimization technique for the controller to tune the values automatically in order to minimize the error within the given bounds. In this paper, the algorithmic concepts of Harmony search (HS) and Genetic Algorithm (GA) have been analyzed for the given range of values. The experimental results show that HS performs well than GA.

Keywords: Genetic Algorithm, Harmony Search Algorithm, Inverted Pendulum, PID Controller.

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Authors: Y.Ben Jemaa, M.Jaidane

Abstract:

In wireless communication system, a Decision Feedback Equalizer (DFE) to cancel the intersymbol interference (ISI) is required. In this paper, an exact convergence analysis of the (DFE) adapted by the Least Mean Square (LMS) algorithm during the training phase is derived by taking into account the finite alphabet context of data transmission. This allows us to determine the shortest training sequence that allows to reach a given Mean Square Error (MSE). With the intention of avoiding the problem of ill-convergence, the paper proposes an initialization strategy for the blind decision directed (DD) algorithm. This then yields a semi-blind DFE with high speed and good convergence.

Keywords: Adaptive Decision Feedback Equalizer, PerformanceAnalysis, Finite Alphabet Case, Ill-Convergence, Convergence speed.

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Authors: Phyoung Jung Kim, Seogyun Kim

Abstract:

In mobile computing environments, there are many new non existing problems in the distributed system, which is consisted of stationary hosts because of host mobility, sudden disconnection by handoff in wireless networks, voluntary disconnection for efficient power consumption of a mobile host, etc. To solve the problems, we proposed the architecture of Partial Connection Manager (PCM) in this paper. PCM creates the limited number of mobile agents according to priority, sends them in parallel to servers, and combines the results to process the user request rapidly. In applying the proposed PCM to the mobile market agent service, we understand that the mobile agent technique could be suited for the mobile computing environment and the partial connection problem management.

Keywords: Mobile agent, mobile computing, partial connection

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Authors: A. Schuchter, M. Promegger

Abstract:

The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: Flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning.

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

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This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: Chaos, chaotic trajectories, differential mobile robot, Henons map, Khepera III robot, patrolling applications.

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Authors: R. Manimaran

Abstract:

CFD simulations are carried out in arterial stenoses with 48 % areal occlusion. Non-newtonian fluid model is selected for the blood flow as the same problem has been solved before with Newtonian fluid model. Studies on flow resistance with the presence of surface irregularities are carried out. Investigations are also performed on the pressure drop at various Reynolds numbers. The present study revealed that the pressure drop across a stenosed artery is practically unaffected by surface irregularities at low Reynolds numbers, while flow features are observed and discussed at higher Reynolds numbers.

Keywords: Blood flow, Roughness, Computational fluid dynamics, Bio fluid mechanics.

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Authors: B. Vahdani, S. M. Mousavi, R. Tavakkoli-Moghaddam

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Nowadays, the plant location selection has a critical impact on the performance of numerous companies. In this paper, a methodology is presented to solve this problem. The three decision making methods, namely Delphi, AHP and improved VIKOR, are hybridized in order to make the best use of information available based on the decision makers or experts. In this respect, the aim of using Delphi is to select the most influential criteria by a few decision makers. The AHP is utilized to give weights of the selected criteria. Finally, the improved VIKOR method is applied to rank alternatives. At the end of paper, an application example demonstrates the applicability of the proposed methodology.

Keywords: Decision making, Plant location selection, Delphi, AHP, Improved VIKOR.

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Authors: M. Khouil, N. Saber, M. Mestari

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In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: Collision identification, fixed time, convex polyhedra, neural network, AMAXNET.

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Authors: Awais Adnan, Muhammad Ali, Amir Hanif Dar

Abstract:

Image Searching was always a problem specially when these images are not properly managed or these are distributed over different locations. Currently different techniques are used for image search. On one end, more features of the image are captured and stored to get better results. Storing and management of such features is itself a time consuming job. While on the other extreme if fewer features are stored the accuracy rate is not satisfactory. Same image stored with different visual properties can further reduce the rate of accuracy. In this paper we present a new concept of using polynomials of sorted histogram of the image. This approach need less overhead and can cope with the difference in visual features of image.

Keywords: Sorted Histogram, Polynomial Curves, feature pointsof images, Grayscale, visual properties of image.

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Authors: Lukasz Peronski, Roy Bratley, Derek B. Ingham, Lin Ma, Mohamed Pourkashanian, StephenTaylor

Abstract:

The aim of the study was to investigate the possible use of commercial Computational Fluid Dynamics (CFD) software in the design process of a domestic gas boiler. Because of the limited computational resources some simplifications had to be made in order to contribute to the design in a reasonable timescale. The porous media model was used in order to simulate the influence of the pressure drop characteristic of particular elements of a heat transfer system on the water-flow distribution in the system. Further, a combination of CFD analyses and spread sheet calculations was used in order to solve the flow distribution problem.

Keywords: CFD, domestic gas boilers, flow distribution, heatexchanger, porous media

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Authors: Mohammed T. Shukri

Abstract:

The failure of bridges due to excessive local scour during floods poses a challenging problem to hydraulic engineers. The failure of bridges piers is due to many reasons such as localized scour combined with general riverbed degradation. In this paper, we try to estimate the temporal variation of scour depth at nonuniform cylindrical bridge pier, by experimental work conducted in hydraulic laboratories of Gaziantep University Civil Engineering Department on a flume having dimensions of 8.3 m length, 0.8 m width and 0.9 m depth. The experiments will be carried on 20 cm depth of sediment layer having d₅₀=0.4 mm. Three bridge pier shapes having different scaled models will be constructed in a 1.5m of test section in the channel.

Keywords: Scour, local scour, bridge piers, scour depth.

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Authors: Mark Harmon, Abdolghani Ebrahimi, Patrick Lucey, Diego Klabjan

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In this paper, we predict the likelihood of a player making a shot in basketball from multiagent trajectories. To approach this problem, we present a convolutional neural network (CNN) approach where we initially represent the multiagent behavior as an image. To encode the adversarial nature of basketball, we use a multichannel image which we then feed into a CNN. Additionally, to capture the temporal aspect of the trajectories we use “fading.” We find that this approach is superior to a traditional FFN model. By using gradient ascent, we were able to discover what the CNN filters look for during training. Last, we find that a combined FFN+CNN is the best performing network with an error rate of 39%.

Keywords: basketball, computer vision, image processing, convolutional neural network

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Authors: Aditya Khanna, Andrei Kotousov

Abstract:

A novel method is presented for obtaining the stress field induced by an edge dislocation in a multilayered composite. To demonstrate the applications of the obtained solution, we consider the problem of an interfacial crack in a periodically layered bimaterial medium. The crack is modelled as a continuous distribution of edge dislocations and the Distributed Dislocation Technique (DDT) is utilized to obtain numerical results for the energy release rate (ERR). The numerical implementation of the dislocation solution in MATLAB is also provided.

Keywords: Distributed dislocation technique, Edge dislocation, Elastic field, Interfacial crack, Multi-layered composite.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

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This paper proposes a solution to the motion planning and control problem of a point-mass robot which is required to move safely to a designated target in a priori known workspace cluttered with fixed elliptical obstacles of arbitrary position and sizes. A tailored and unique algorithm for target convergence and obstacle avoidance is proposed that will work for any number of fixed obstacles. The control laws proposed in this paper also ensures that the equilibrium point of the given system is asymptotically stable. Computer simulations with the proposed technique and applications to a planar (RP) manipulator will be presented.

Keywords: Point-mass Robot, Asymptotic stability, Motionplanning, Planar Robot Arm.

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Authors: K. Nirmala Devi, V. Murali Bhaskaran

Abstract:

Traditional document representation for classification follows Bag of Words (BoW) approach to represent the term weights. The conventional method uses the Vector Space Model (VSM) to exploit the statistical information of terms in the documents and they fail to address the semantic information as well as order of the terms present in the documents. Although, the phrase based approach follows the order of the terms present in the documents rather than semantics behind the word. Therefore, a semantic concept based approach is used in this paper for enhancing the semantics by incorporating the ontology information. In this paper a novel method is proposed to forecast the intraday stock market price directional movement based on the sentiments from Twitter and money control news articles. The stock market forecasting is a very difficult and highly complicated task because it is affected by many factors such as economic conditions, political events and investor’s sentiment etc. The stock market series are generally dynamic, nonparametric, noisy and chaotic by nature. The sentiment analysis along with wisdom of crowds can automatically compute the collective intelligence of future performance in many areas like stock market, box office sales and election outcomes. The proposed method utilizes collective sentiments for stock market to predict the stock price directional movements. The collective sentiments in the above social media have powerful prediction on the stock price directional movements as up/down by using Granger Causality test.

Keywords: Bag of Words, Collective Sentiments, Ontology, Semantic relations, Sentiments, Social media, Stock Prediction, Twitter, Vector Space Model and wisdom of crowds.

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Authors: Mikhail V. Khachaturyan, Inga A. Koryagina, Maria Nikishova

Abstract:

The study investigates the impact of the ongoing financial crisis, started in the 2^nd half of 2014, on marketing budgets spent by Fast-moving consumer goods companies. In these conditions, special importance is given to efficient possessory risk management systems. The main objective for establishing and developing possessory risk management systems for FMCG companies in a crisis is to analyze the data relating to the external environment and consumer behavior in a crisis. Another important objective for possessory risk management systems of FMCG companies is to develop measures and mechanisms to maintain and stimulate sales. In this regard, analysis of risks and threats which consumers define as the main reasons affecting their level of consumption become important. It is obvious that in crisis conditions the effective risk management systems responsible for development and implementation of strategies for consumer demand stimulation, as well as the identification, analysis, assessment and management of other types of risks of economic security will be the key to sustainability of a company. In terms of financial and economic crisis, the problem of forming and developing possessory risk management systems becomes critical not only in the context of management models of FMCG companies, but for all the companies operating in other sectors of the Russian economy. This study attempts to analyze the specifics of formation and development of company possessory risk management systems. In the modern economy, special importance among all the types of owner’s risks has the risk of reduction in consumer activity. This type of risk is common not only for the consumer goods trade. Study of consumer activity decline is especially important for Russia due to domestic market of consumer goods being still in the development stage, despite its significant growth. In this regard, it is especially important to form and develop possessory risk management systems for FMCG companies. The authors offer their own interpretation of the process of forming and developing possessory risk management systems within owner’s management models of FMCG companies as well as in Russian economy in general. Proposed methods and mechanisms of problem analysis of formation and development of possessory risk management systems in FMCG companies and the results received can be helpful for researchers interested in problems of consumer goods market development in Russia and overseas.

Keywords: FMCG companies, marketing budget, risk management, owner, Russian economy, organization, formation, development, system.

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Authors: Maciej Norberciak

Abstract:

Timetabling problems are often hard and timeconsuming to solve. Most of the methods of solving them concern only one problem instance or class. This paper describes a universal method for solving large, highly constrained timetabling problems from different domains. The solution is based on evolutionary algorithm-s framework and operates on two levels – first-level evolutionary algorithm tries to find a solution basing on given set of operating parameters, second-level algorithm is used to establish those parameters. Tabu search is employed to speed up the solution finding process on first level. The method has been used to solve three different timetabling problems with promising results.

Keywords: Evolutionary algorithms, tabu search, timetabling.

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Authors: Valentina Koliskina, Inta Volodko

Abstract:

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

Keywords: Transient eddy currents, Laplace transform, double conductor line.

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Authors: Gholamreza Habibi

Abstract:

In order to study seed yield and seed yield components in bean under reduced irrigation condition and assessment drought tolerance of genotypes, 15 lines of White beans were evaluated in two separate RCB design with 3 replications under stress and non stress conditions. Analysis of variance showed that there were significant differences among varieties in terms of traits under study, indicating the existence of genetic variation among varieties. The results indicate that drought stress reduced seed yield, number of seed per plant, biological yield and number of pod in White been. In non stress condition, yield was highly correlated with the biological yield, whereas in stress condition it was highly correlated with harvest index. Results of stepwise regression showed that, selection can we done based on, biological yield, harvest index, number of seed per pod, seed length, 100 seed weight. Result of path analysis showed that the highest direct effect, being positive, was related to biological yield in non stress and to harvest index in stress conditions. Factor analysis were accomplished in stress and nonstress condition a, there were 4 factors that explained more than 76 percent of total variations. We used several selection indices such as Stress Susceptibility Index ( SSI ), Geometric Mean Productivity ( GMP ), Mean Productivity ( MP ), Stress Tolerance Index ( STI ) and Tolerance Index ( TOL ) to study drought tolerance of genotypes, we found that the best Stress Index for selection tolerance genotypes were STI, GMP and MP were the greatest correlations between these Indices and seed yield under stress and non stress conditions. In classification of genotypes base on phenotypic characteristics, using cluster analysis ( UPGMA ), all allels classified in 5 separate groups in stress and non stress conditions.

Keywords: Cluster analysis, factor analysis, path analysis, selection index, White bean

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Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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Authors: G. M. Mir, N. A. Shah, Moinuddin

Abstract:

Guard channels improve the probability of successful handoffs by reserving a number of channels exclusively for handoffs. This concept has the risk of underutilization of radio spectrum due to the fact that fewer channels are granted to originating calls even if these guard channels are not always used, when originating calls are starving for the want of channels. The penalty is the reduction of total carried traffic. The optimum number of guard channels can help reduce this problem. This paper presents fuzzy logic based guard channel scheme wherein guard channels are reorganized on the basis of traffic density, so that guard channels are provided on need basis. This will help in incorporating more originating calls and hence high throughput of the radio spectrum

Keywords: Free channels, fuzzy logic, guard channels, Handoff

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Authors: Dj. Cherifi, Y. Miloud, A. Tahri

Abstract:

The primary objective of this paper is to elimination of the problem of sensitivity to parameter variation of induction motor drive. The proposed sensorless strategy is based on an algorithm permitting a better simultaneous estimation of the rotor speed and the stator resistance including an adaptive mechanism based on the lyaponov theory. To study the reliability and the robustness of the sensorless technique to abnormal operations, some simulation tests have been performed under several cases.

The proposed sensorless vector control scheme showed a good performance behavior in the transient and steady states, with an excellent disturbance rejection of the load torque.

Keywords: Induction Motor Drive, field-oriented control, adaptive speed observer, stator resistance estimation.

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Authors: Kyong-min Lee, Moon Soo Chang, PooGyeon Park

Abstract:

In this paper, we propose a geometric modeling of illumination on the patterned image containing etching transistor. This image is captured by a commercial camera during the inspection of a TFT-LCD panel. Inspection of defect is an important process in the production of LCD panel, but the regional difference in brightness, which has a negative effect on the inspection, is due to the uneven illumination environment. In order to solve this problem, we present a geometric modeling of illumination consisting of an interpolation using the least squares method and 3D modeling using bezier surface. Our computational time, by using the sampling method, is shorter than the previous methods. Moreover, it can be further used to correct brightness in every patterned image.

Keywords: Bezier, defect, geometric modeling, illumination, inspection, LCD, panel.

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Authors: Jinn-Yi Yeh, Tai-Hsi Wu

Abstract:

Hemodialysis patients might suffer from unhealthy care behaviors or long-term dialysis treatments. Ultimately they need to be hospitalized. If the hospitalization rate of a hemodialysis center is high, its quality of service would be low. Therefore, how to decrease hospitalization rate is a crucial problem for health care. In this study we combined temporal abstraction with data mining techniques for analyzing the dialysis patients' biochemical data to develop a decision support system. The mined temporal patterns are helpful for clinicians to predict hospitalization of hemodialysis patients and to suggest them some treatments immediately to avoid hospitalization.

Keywords: Hemodialysis, Temporal abstract, Data mining, Healthcare quality.

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Authors: Siripen Yiamjanya, Kevin Wongleedee

Abstract:

This research paper aims to identify travel motivation by push and pull factors that affected decision making of international tourists in selecting Thailand as their destination choice. A total of 200 international tourists who traveled to Thailand during January and February, 2014 were used as the sample in this study. A questionnaire was employed as a tool in collecting the data, conducted in Bangkok. The list consisted of 30 attributes representing both psychological factors as “push- based factors” and destination factors as “pull-based factors”. Mean and standard deviation were used in order to find the top ten travel motives that were important determinants in the respondents’ decision making process to select Thailand as their destination choice. The finding revealed the top ten travel motivations influencing international tourists to select Thailand as their destination choice included [i] getting experience in foreign land; [ii] Thai food; [iii] learning new culture; [iv] relaxing in foreign land; [v] wanting to learn new things; [vi] being interested in Thai culture, and traditional markets; [vii] escaping from same daily life; [viii] enjoying activities; [ix] adventure; and [x] good weather. Classification of push- based and pull- based motives suggested that getting experience in foreign land was the most important push motive for international tourists to travel, while Thai food portrayed its highest significance as pull motive. Discussion and suggestions were also made for tourism industry of Thailand.

Keywords: Decision Making, Destination Choice, International Tourist, Pull Factor, Push Factor, Thailand, Travel Motivation.

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Authors: Hui Liu, Haiyang Quan

Abstract:

This paper To get the angle value with a MEMS rate gyroscope in some specific field, the usual method is to make an integral operation to the rate output, which will lead the error cumulating effect. So the rate gyro is not suitable. MEMS rate integrating gyroscope (MRIG) will solve this problem. A DSP system has been developed to implement the control arithmetic. The system can measure the angle of rotation directly by the control loops that make the sensor work in whole-angle mode. Modeling the system with MATLAB, desirable results of angle outputs are got, which prove the feasibility of the control arithmetic.

Keywords: Rate gyroscope, Rate integrating gyroscope, Whole angle mode, MATLAB modeling, DSP control.

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Authors: Qamar Saeed, Vali Uddin, Reza Katebi

Abstract:

In this paper multivariable predictive PID controller has been implemented on a multi-inputs multi-outputs control problem i.e., quadruple tank system, in comparison with a simple multiloop PI controller. One of the salient feature of this system is an adjustable transmission zero which can be adjust to operate in both minimum and non-minimum phase configuration, through the flow distribution to upper and lower tanks in quadruple tank system. Stability and performance analysis has also been carried out for this highly interactive two input two output system, both in minimum and non-minimum phases. Simulations of control system revealed that better performance are obtained in predictive PID design.

Keywords: Proportional-integral-derivative Control, GeneralizedPredictive Control, Predictive PID Control, Multivariable Systems

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