Search results for: non-negative integer sampling.

Authors: Jamal Laaouine, Mohammed Elhassani Charkani

Abstract:

Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: Igor Luiz Bernardes de Moura, Luan Carlos de Sena Monteiro Ozelim, Fabiano Araujo Soares

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The development of an low cost acquisition system of S-EMG signals which are reliable, comfortable for the user and with high mobility shows to be a relevant proposition in modern biomedical engineering scenario. In the study, the sampling capacity of the Arduino microcontroller Atmel Atmega328 with an A / D converter with 10-bit resolution and its reconstructing capability of a signal of surface electromyography is analyzed. An electronic circuit to capture the signal through two differential channels was designed, signals from Biceps Brachialis of a healthy man of 21 years was acquired to test the system prototype. ARV, MDF, MNF and RMS estimators were used to compare de acquired signals with physiological values. The Arduino was configured with a sampling frequency of 1.5kHz for each channel, and the tests with the circuit designed offered a SNR of 20.57dB.

Keywords: Eletromyography, Arduino, Low-Cost, Atmel Atmega328 microcontroller.

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Authors: Ghada A. Alfattni

Abstract:

Analysing unbalanced datasets is one of the challenges that practitioners in machine learning field face. However, many researches have been carried out to determine the effectiveness of the use of the synthetic minority over-sampling technique (SMOTE) to address this issue. The aim of this study was therefore to compare the effectiveness of the SMOTE over different models on unbalanced datasets. Three classification models (Logistic Regression, Support Vector Machine and Nearest Neighbour) were tested with multiple datasets, then the same datasets were oversampled by using SMOTE and applied again to the three models to compare the differences in the performances. Results of experiments show that the highest number of nearest neighbours gives lower values of error rates. 

Keywords: Imbalanced datasets, SMOTE, machine learning, logistic regression, support vector machine, nearest neighbour.

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Authors: Hisham Md Suhadi, Faaizah Shahbodin, Jamaluddin Hashim

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The study is the way to identify the problems that occur in organizing short course’s lifelong learning in the information and communication technology (ICT) education which are faced by the lecturer and staff at the Mara Skill Institute and Industrial Training Institute in Pahang Malaysia. The important aspects of these issues are classified to five which are selecting the courses administrative. Fifty lecturers and staff were selected as a respondent. The sample is selected by using the non-random sampling method purpose sampling. The questionnaire is used as a research instrument and divided into five main parts. All the data that gain from the questionnaire are analyzed by using the SPSS in term of mean, standard deviation and percentage. The findings showed, there are the problems occur in organizing the short course for lifelong learning in ICT education.

Keywords: Lifelong education, information and communication technology (ICT), short course, ICT education, courses administrative.

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Authors: Florin Leon, Silvia Curteanu

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Developing complete mechanistic models for polymerization reactors is not easy, because complex reactions occur simultaneously; there is a large number of kinetic parameters involved and sometimes the chemical and physical phenomena for mixtures involving polymers are poorly understood. To overcome these difficulties, empirical models based on sampled data can be used instead, namely regression methods typical of machine learning field. They have the ability to learn the trends of a process without any knowledge about its particular physical and chemical laws. Therefore, they are useful for modeling complex processes, such as the free radical polymerization of methyl methacrylate achieved in a batch bulk process. The goal is to generate accurate predictions of monomer conversion, numerical average molecular weight and gravimetrical average molecular weight. This process is associated with non-linear gel and glass effects. For this purpose, an adaptive sampling technique is presented, which can select more samples around the regions where the values have a higher variation. Several machine learning methods are used for the modeling and their performance is compared: support vector machines, k-nearest neighbor, k-nearest neighbor and random forest, as well as an original algorithm, large margin nearest neighbor regression. The suggested method provides very good results compared to the other well-known regression algorithms.

Keywords: Adaptive sampling, batch bulk methyl methacrylate polymerization, large margin nearest neighbor regression, machine learning.

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Authors: Ying-Wen Bai, Ju-Maw Chen

Abstract:

To successfully provide a fast FIR filter with FTT algorithms, overlapped-save algorithms can be used to lower the computational complexity and achieve the desired real-time processing. As the length of the input block increases in order to improve the efficiency, a larger volume of zero padding will greatly increase the computation length of the FFT. In this paper, we use the overlapped block digital filtering to construct a parallel structure. As long as the down-sampling (or up-sampling) factor is an exact multiple lengths of the impulse response of a FIR filter, we can process the input block by using a parallel structure and thus achieve a low-complex fast FIR filter with overlapped-save algorithms. With a long filter length, the performance and the throughput of the digital filtering system will also be greatly enhanced.

Keywords: FIR Filter, Overlapped-save Algorithm, ParallelStructure

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Authors: Elena Castillo-López, Raúl Pereda, Julio Manuel de Luis, Rubén Pérez, Felipe Piña

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Sediments are an important source of accumulation of toxic contaminants within the aquatic environment. Bioassays are a powerful tool for the study of sediments in relation to their toxicity, but they can be expensive. This article presents a methodology to estimate the main physical property of intertidal sediments in coastal zones: heavy metals concentration. This study, which was developed in the Bay of Santander (Spain), applies classical and robust statistic to CASI-2 hyperspectral images to estimate heavy metals presence and ecotoxicity (TOC). Simultaneous fieldwork (radiometric and chemical sampling) allowed an appropriate atmospheric correction to CASI-2 images.

Keywords: Remote sensing, intertidal sediment, airborne sensors, heavy metals, ecotoxicity, robust statistic, estimation.

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Authors: H. V. Chen

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Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They have the property that each vertex label and edge label appears only once in the set of positive integers {c, . . . , c+6m- 1}. Here, we show how to construct certain c-Erdösian of m paths with 2 and 3 vertices by using Skolem sequences.

Keywords: c-Erdösian, Skolem sequences, magic labelling

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Authors: Ali Shatnawi

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Signal processing applications which are iterative in nature are best represented by data flow graphs (DFG). In these applications, the maximum sampling frequency is dependent on the topology of the DFG, the cyclic dependencies in particular. The determination of the iteration bound, which is the reciprocal of the maximum sampling frequency, is critical in the process of hardware implementation of signal processing applications. In this paper, a novel technique to compute the iteration bound is proposed. This technique is different from all previously proposed techniques, in the sense that it is based on the natural flow of tokens into the DFG rather than the topology of the graph. The proposed algorithm has lower run-time complexity than all known algorithms. The performance of the proposed algorithm is illustrated through analytical analysis of the time complexity, as well as through simulation of some benchmark problems.

Keywords: Data flow graph, Iteration period bound, Rateoptimalscheduling, Recursive DSP algorithms.

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Authors: Mojisola F. Oyewole, Franscisca T. Adetoro, Nkiru T. Meludu

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Moringa oleifera is a nutritious vegetable tree with varieties of potential uses, as almost every part of the Moringa oleifera tree can be used for food. This study was conducted in Oyo State, Nigeria, to find out the level of acceptability of Moringa oleifera diversified products among rural and urban dwellers. Purposive sampling was used to select two local governments’ areas. Stratified sampling technique was also used to select one community each from rural and urban areas while snowball sampling technique was used to select ten respondents each from the two communities, making a total number of forty respondents. Data were analyzed using frequencies, percentages, Chi-square, Pearson Product Moment Correlation and regression analysis. Result from the study revealed that majority of the respondents (80%) fell within the age range of 20-49 years and 55% of them were male, 55% were married, 70% of them were Christians, 80% of them had tertiary education. The result also showed that 85% were aware of the Moringa plant and (65%) of them have consumed Moringa oleifera and the perception statements on the benefits of Moringa oleifera indicated that (52.5%) of the respondents rated Moringa oleifera to be favorable, most of them had high acceptability for Moringa egusi soup, Moringa tea, Moringa pap and yam pottage with Moringa. The result of the hypotheses testing showed that there is a significant relationship between sex of the respondents and acceptability of the diversified Moringa oleifera products (x2=6.465, p = 0.011). There is also a significant relationship between family size of the respondents level of acceptability of the Moringa oleifera products (r = 0.327, p = 0.040). Based on the level of acceptability of Moringa oleifera diversified products; the plant is of great economic importance to the populace. Therefore, there should be more public awareness through the media to enlighten people on the beneficial effects of Moringa oleifera.

Keywords: Acceptability, Moringa oleifera, Diversified, Product, Dwellers.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: W. T. Hsu, H. L. Tsai

Abstract:

The rapid aging of the population is a common trend in the world. However, the progress of modern medical technology has increased the average life expectancy. The global population structure has changed dramatically, and the elderly population has risen rapidly. In the face of rapid population growth, it must be noted issues of the aging population must face up to, which are the physiological, psychological, and social problems associated with aging. This study aims to investigate how insurance agents are actively dealing with an aging society, their own aging anxiety, and their exercise habits. Purposive sampling was the sampling method of this study, a total of 204 respondents were surveyed and 204 valid surveys were returned. The returned valid ratio was 100%. Statistical method included descriptive statistics, t-test, and one-way ANOVA. The results of the study found that the insurance agent’s age, seniority, exercise habits to aging anxiety are significantly different.

Keywords: Insurance agent, aging anxiety, exercise habits, elderly.

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

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This paper describes a new efficient blind source separation method; in this method we uses a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation (BSS), estimates, full-band, mixtures, Sub-band.

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Authors: Shuhana Shamsuddin, Nur Rasyiqah Abu Hassan, Ahmad Bashri Sulaiman

Abstract:

Liveable city is referred to as the quality of life in an area that contributes towards a safe, healthy and enjoyable place. This paper discusses the role of the streets- activities in making Kuala Lumpur a liveable city and the happiness level of the residents towards the city-s street activities. The study was conducted using the residents of Kuala Lumpur. A mixed method technique is used with the quantitative data as a main data and supported by the qualitative data. Data were collected using questionnaires, observation and also an interview session with a sample of residents of Kuala Lumpur. The sampling technique is based on multistage cluster data sampling. The findings revealed that, there is still no significant relationship between the length of stay of the resident in Kuala Lumpur with the happiness level towards the street activities that occurred in the city.

Keywords: Liveable city, activities, urban design quality, quality of life, happiness level.

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Authors: D. I. De Souza, G. P. Azevedo, D. R. Fonseca

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In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Inverse Weibull sampling distribution. The location parameter or minimum life will be considered equal to zero. Once again we will provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null hypothesis H0; or obtain additional information by making another observation. The product being analyzed is a new electronic component. There is little information available about the possible values the parameters of the corresponding Inverse Weibull underlying sampling distribution could have.To estimate the shape and the scale parameters of the underlying Inverse Weibull model we will use a maximum likelihood approach for censored failure data. A new example will further develop the proposed sequential life testing approach.

Keywords: Sequential Life Testing, Inverse Weibull Model, Maximum Likelihood Approach, Hypothesis Testing.

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Authors: T.C. Manjunath, B. Bandyopadhyay

Abstract:

This paper features the modeling and design of a Fast Output Sampling (FOS) Feedback control technique for the Active Vibration Control (AVC) of a smart flexible aluminium cantilever beam for a Single Input Single Output (SISO) case. Controllers are designed for the beam by bonding patches of piezoelectric layer as sensor / actuator to the master structure at different locations along the length of the beam by retaining the first 2 dominant vibratory modes. The entire structure is modeled in state space form using the concept of piezoelectric theory, Euler-Bernoulli beam theory, Finite Element Method (FEM) and the state space techniques by dividing the structure into 3, 4, 5 finite elements, thus giving rise to three types of systems, viz., system 1 (beam divided into 3 finite elements), system 2 (4 finite elements), system 3 (5 finite elements). The effect of placing the sensor / actuator at various locations along the length of the beam for all the 3 types of systems considered is observed and the conclusions are drawn for the best performance and for the smallest magnitude of the control input required to control the vibrations of the beam. Simulations are performed in MATLAB. The open loop responses, closed loop responses and the tip displacements with and without the controller are obtained and the performance of the proposed smart system is evaluated for vibration control.

Keywords: Smart structure, Finite element method, State spacemodel, Euler-Bernoulli theory, SISO model, Fast output sampling, Vibration control, LMI

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Authors: Adil AL-Rammahi

Abstract:

When we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

Keywords: Linear Systems, Image Encryption, Calculus.

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Authors: Roger L Goodwin

Abstract:

This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, ”first-glance” correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve.

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Authors: Oğuzhan Hasançebi, Saeid Kazemzadeh Azad

Abstract:

Keywords: Structural design optimization, optimal sizing, metaheuristics, self-adaptive step-size search, steel trusses, steel frames.}

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Authors: Seung-Jun Yu, Jang-Kyun Ahn, Eui-Young Lee, Hyoung-Kyu Song

Abstract:

Space-time block codes (STBC) and spatial multiplexing (SM) are promising techniques that effectively exploit multipleinput multiple-output (MIMO) transmission to achieve more reliable communication and a higher multiplexing rate, respectively. In this paper, we study a practical design for hybrid scheme with multi-input multi-output orthogonal frequency division multiplexing (MIMOOFDM) systems to flexibly maximize the tradeoff between diversity and multiplexing gains. Unlike the existing STBC and SM designs which are suitable for the integer multiplexing rate, the proposed design can achieve arbitrary number of multiplexing rate.

Keywords: Space-Time Block Codes, Spatial Multiplexing, MIMO-OFDM.

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Authors: Pongchanun Luangpaiboon, Wanwisa Sarasang

Abstract:

In this paper, performances of shuffled frog leaping algorithm was investigated on the stealth laser dicing process. Effect of problem on the performance of the algorithm was based on the tolerance of meandering data. From the customer specification it could be less than five microns with the target of zero microns. Currently, the meandering levels are unsatisfactory when compared to the customer specification. Firstly, the two-level factorial design was applied to preliminarily study the statistically significant effects of five process variables. In this study one influential process variable is integer. From the experimental results, the new operating condition from the algorithm was superior when compared to the current manufacturing condition.

Keywords: Stealth Laser Dicing Process, Meandering, Metaheuristics, Shuffled Frog Leaping Algorithm.

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Authors: Freeman Ntuli

Abstract:

An overview of the important aspects of managing and controlling industrial effluent discharges to public sewers namely sampling, characterization, quantification and legislative controls has been presented. The findings have been validated by means of a case study covering three industrial sectors namely, tanning, textile finishing and food processing industries. Industrial effluents discharges were found to be best monitored by systematic and automatic sampling and quantified using water meter readings corrected for evaporative and consumptive losses. Based on the treatment processes employed in the public owned treatment works and the chemical oxygen demand and biochemical oxygen demand levels obtained, the effluent from all the three industrial sectors studied were found to lie in the toxic zone. Thus, physico-chemical treatment of these effluents is required to bring them into the biodegradable zone. KL values (quoted to base e) were greater than 0.50 day-1 compared to 0.39 day-1 for typical municipality wastewater.

Keywords: biodegradability, industrial effluent, pollution control, public sewers

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Authors: Xiaohua Liu, Juan F. Beltran, Nishant Mohanchandra, Godfried T. Toussaint

Abstract:

Support vector machines (SVMs) are considered to be the best machine learning algorithms for minimizing the predictive probability of misclassification. However, their drawback is that for large data sets the computation of the optimal decision boundary is a time consuming function of the size of the training set. Hence several methods have been proposed to speed up the SVM algorithm. Here three methods used to speed up the computation of the SVM classifiers are compared experimentally using a musical genre classification problem. The simplest method pre-selects a random sample of the data before the application of the SVM algorithm. Two additional methods use proximity graphs to pre-select data that are near the decision boundary. One uses k-Nearest Neighbor graphs and the other Relative Neighborhood Graphs to accomplish the task.

Keywords: Machine learning, data mining, support vector machines, proximity graphs, relative-neighborhood graphs, k-nearestneighbor graphs, random sampling, training data condensation.

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Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: Tanzeel bin Abdul Rauf Patker, Saba Mateen

Abstract:

This research investigates the impact of Brand Loyalty on the product performance and the factors those are considered more important in brand reputation. Variables selected for this research are Brand quality, Brand Equity, Brand Reputation to explore the impact of these variables on Product performance. For this purpose, primary research has been conducted. The questionnaire survey for this research study was administered among the population mainly at the shopping malls. For this research study, a sample size of 250 respondents has been taken into consideration. Customers from the shopping malls and university students constitute the sample for this research study using random sampling (non-probabilistic) used as a sampling technique for conducting the research survey. According to the results obtained from the collected data, it is interpreted that product performance shares a direct relationship with brand quality, brand quality, and brand reputation. Result also showed that brand quality and brand equity has a significant effect on product performance, whereas brand reputation has an insignificant effect on product performance.

Keywords: Product performance, brand quality, brand equity and brand reputation.

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Authors: Ahmet Tekcan, Arzu Özkoç

Abstract:

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the first section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some specific values of Q and P.

Keywords: Quadratic irrationals, quadratic ideals, indefinite quadratic forms, extended modular group.

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Authors: Pei-Te Chiueh, Hsiao-Ting Wu, Shang-Lien Lo

Abstract:

Protecting is the sources of drinking water is the first barrier of contamination of drinking water. The Feitsui Reservoir watershed of Taiwan supplies domestic water for around 5 million people in the Taipei metropolitan area. Understanding the spatial patterns of water quality trends in this watershed is an important agenda for management authorities. This study examined 7 sites in the watershed for water quality parameters regulated in the standard for drinking water source. The non-parametric seasonal Mann-Kendall-s test was used to determine significant trends for each parameter. Significant trends of increasing pH occurred at the sampling station in the uppermost stream watershed, and in total phosphorus at 4 sampling stations in the middle and downstream watershed. Additionally, the multi-scale land cover assessment and average land slope were used to explore the influence on the water quality in the watershed. Regression models for predicting water quality were also developed.

Keywords: Seasonal Mann-Kendall's test, Flow-adjusted concentrations, Water quality trends, Land-use

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Authors: Maryam Kargar, Neamatolah Khorasani, Mahmoud Karami, Gholam-Reza Rafiee, Reza Naseh

Abstract:

Interpolated contour maps drawn for aluminum, copper and molybdenum in downstream monitoring boreholes of water dam in Miduk Copper Complex and the values of pH, redox potential (Eh) and distance from water dam indicate different trends of variation and behavior of these three elements in downward groundwater resources. As these maps exhibit, aluminum is dominant in the most alkaline (pH = 9-11) borehole (MB5) to water dam. The highest concentration of molybdenum is found in the nearest borehole (MB6) to water dam. Main concentration of copper is observed in the most oxidized borehole (MB3 with Eh=293.2mV). The spatial difference among sampling stations can be attributed to the existence of faults and diaclases in the geologic structure of Miduk region which causes the groundwater sampling sites to be impressed by different contamination sources (toe seepage and upper seepage water originated from different zones of tailings dump).

Keywords: Contour maps, Monitoring borehole, Toe seepage, Upper seepage.

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Authors: Y. Wu

Abstract:

Today-s business has inevitably been set in the global supply chain management environment. International transportation has never played such an important role in the global supply chain network, because movement of shipments from one country to another tends to be more frequent than ever before. This paper studies international transportation problems experienced by an international transportation company. Because of the limited fleet capacity, the transportation company has to hire additional trucks from two countries in advance. However, customer-s shipment information is uncertain, and decisions have to be made before accurate information can be obtained. This paper proposes a stochastic mixed 0-1 programming model to solve the international transportation problems under uncertain demand. A series of experiments demonstrate the effectiveness of the proposed stochastic model.

Keywords: Global supply chain management, international transportation, stochastic programming.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: Multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, Importance sampling, approximate posterior distribution, Marginal likelihood evidence.

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