Search results for: Gaussian process priors

Authors: Yang Laixia, Deng Jun, Li Dichen, Bai Yang

Abstract:

The forming process parameters of Selective Laser Sintering(SLS) directly affect the forming efficiency and forming quality. Therefore, to determine reasonable process parameters is particularly important. In this paper, the weight of each target of the forming quality and efficiency is firstly calculated with the Analytic Hierarchy Process. And then the size of each target is measured by orthogonal experiment. Finally, the sum of the product of each target with the weight is compared to the process parameters in each group and obtained the optimal molding process parameters.

Keywords: Analytic Hierarchy Process, Multi-objective optimization, Orthogonal test, Selective Laser Sintering

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Authors: Sandipan Chakroborty, Anindya Roy, Goutam Saha

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A state of the art Speaker Identification (SI) system requires a robust feature extraction unit followed by a speaker modeling scheme for generalized representation of these features. Over the years, Mel-Frequency Cepstral Coefficients (MFCC) modeled on the human auditory system has been used as a standard acoustic feature set for SI applications. However, due to the structure of its filter bank, it captures vocal tract characteristics more effectively in the lower frequency regions. This paper proposes a new set of features using a complementary filter bank structure which improves distinguishability of speaker specific cues present in the higher frequency zone. Unlike high level features that are difficult to extract, the proposed feature set involves little computational burden during the extraction process. When combined with MFCC via a parallel implementation of speaker models, the proposed feature set outperforms baseline MFCC significantly. This proposition is validated by experiments conducted on two different kinds of public databases namely YOHO (microphone speech) and POLYCOST (telephone speech) with Gaussian Mixture Models (GMM) as a Classifier for various model orders.

Keywords: Complementary Information, Filter Bank, GMM, IMFCC, MFCC, Speaker Identification, Speaker Recognition.

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Authors: M.K. Bhuyan, Aragala Jagan.

Abstract:

Current image-based individual human recognition methods, such as fingerprints, face, or iris biometric modalities generally require a cooperative subject, views from certain aspects, and physical contact or close proximity. These methods cannot reliably recognize non-cooperating individuals at a distance in the real world under changing environmental conditions. Gait, which concerns recognizing individuals by the way they walk, is a relatively new biometric without these disadvantages. The inherent gait characteristic of an individual makes it irreplaceable and useful in visual surveillance. In this paper, an efficient gait recognition system for human identification by extracting two features namely width vector of the binary silhouette and the MPEG-7-based region-based shape descriptors is proposed. In the proposed method, foreground objects i.e., human and other moving objects are extracted by estimating background information by a Gaussian Mixture Model (GMM) and subsequently, median filtering operation is performed for removing noises in the background subtracted image. A moving target classification algorithm is used to separate human being (i.e., pedestrian) from other foreground objects (viz., vehicles). Shape and boundary information is used in the moving target classification algorithm. Subsequently, width vector of the outer contour of binary silhouette and the MPEG-7 Angular Radial Transform coefficients are taken as the feature vector. Next, the Principal Component Analysis (PCA) is applied to the selected feature vector to reduce its dimensionality. These extracted feature vectors are used to train an Hidden Markov Model (HMM) for identification of some individuals. The proposed system is evaluated using some gait sequences and the experimental results show the efficacy of the proposed algorithm.

Keywords: Gait Recognition, Gaussian Mixture Model, PrincipalComponent Analysis, MPEG-7 Angular Radial Transform.

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Authors: Sanaz Gharehzadeh Shirazi, Subira Gharehzadeh Shirazi, Fariba Jafari

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The present article comprises a theoretical study of structures Performat radical (HCO3) with H2O molecule. We make use of ab initio quantum chemical methods. Unrestricted Hartee-Fock (UHF) with the basis set6-311+g(2df,2p) and density functional theory (B3LYP) with the basis set 6-311+g(2df,2p) and also we done atoms in molecules (AIM) theory for them. We have found four stable geometries the PerformatRadical(HCO3) with H2O.

Keywords: Hydrogen binding, Performat Radical, Water, Gaussian, Atoms in molecules (AIM) theory

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Authors: Bekim Fetaji, Majlinda Fetaji, Mirlinda Ebibi

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The objective of the research was focused on the design, development and evaluation of a sustainable web based network system to be used as an interoperable environment for University process workflow and document management. In this manner the most of the process workflows in Universities can be entirely realized electronically and promote integrated University. Definition of the most used University process workflows enabled creating electronic workflows and their execution on standard workflow execution engines. Definition or reengineering of workflows provided increased work efficiency and helped in having standardized process through different faculties. The concept and the process definition as well as the solution applied as Case study are evaluated and findings are reported.

Keywords: design process workflows, workflow and documentmanagement, Business Process, software engineering

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Authors: Jorge Cardoso

Abstract:

Process measurement is the task of empirically and objectively assigning numbers to the properties of business processes in such a way as to describe them. Desirable attributes to study and measure include complexity, cost, maintainability, and reliability. In our work we will focus on investigating process complexity. We define process complexity as the degree to which a business process is difficult to analyze, understand or explain. One way to analyze a process- complexity is to use a process control-flow complexity measure. In this paper, an attempt has been made to evaluate the control-flow complexity measure in terms of Weyuker-s properties. Weyuker-s properties must be satisfied by any complexity measure to qualify as a good and comprehensive one.

Keywords: Business process measurement, workflow, complexity.

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Authors: Abbas Al-Refaie

Abstract:

This study optimized the performance of plastic extrusion process of drip irrigation pipes using fuzzy goal programming. Two main responses were of main interest; roll thickness and hardness. Four main process factors were studied. The L₁₈ array was then used for experimental design. The individual-moving range control charts were used to assess the stability of the process, while the process capability index was used to assess process performance. Confirmation experiments were conducted at the obtained combination of optimal factor setting by fuzzy goal programming. The results revealed that process capability was improved significantly from -1.129 to 0.8148 for roll thickness and from 0.0965 to 0.714 and hardness. Such improvement results in considerable savings in production and quality costs.

Keywords: Fuzzy goal programming, extrusion process, process capability, irrigation plastic pipes.

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Authors: I. Hosni, L. Bennaceur Farah, N. Saber, R Bennaceur

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Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.

Keywords: Multiscale, bi-dimensional, wavelets, SPM, backscattering, multilayer, air pockets, vegetable.

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Authors: Zahra Mohammadnazari, Fateme Rostambeygi, Fatemeh Dehrouyeh, Hwang Ki-Soon, Amir Aghsami

Abstract:

Corporations have always prioritized efforts to examine and improve processes. Various metrics, such as the cost and time required to implement the process and can be specified in this regard. Process improvement can be defined as an improvement of these indicators. This is accomplished by looking at prospective adjustments to the current executive process model or the resources allotted to it. Research has been conducted in this paper to the improve the procurement process and aims to explore assessment prospects in the project using a combination of process mining and simulation (benefiting from Play-In and Play-Out methodologies). To run the simulation, we will need to complete the control flow diagram, institution settings, resource settings, and activity settings. The process of mining event logs yields the process control flow. However, both the entry of institutions and the distribution of resources must be modeled. The rate of admission of institutions and the distribution of time for the implementation of activities will be determined in the next step.

Keywords: Business reengineering, Petri net, process-based simulation, process mining.

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Authors: V. Subramanyan Namboodiri, Sajan. D. George, Steffen Hardt

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Polystyrene particles of different sizes are optically trapped with a gaussian beam from a He-Cd laser operating at 442 nm. The particles are observed to exhibit luminescence after a certain trapping time followed by an escape from the optical trap. The observed luminescence is explained in terms of the photodegradation of the polystyrene backbone. It is speculated that these chemical modifications also play a role for the escape of the particles from the trap. Variations of the particle size and the laser power show that these parameters have a great influence on the observed phenomena.

Keywords: Photodegradation, Polystyrene particles, Opticaltrapping

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Authors: Pavol Tanuska, Pavel Vazan, Michal Kebisek, Dominika Jurovata

Abstract:

The paper gives the results of the project that was oriented on the usage of knowledge discoveries from production systems for needs of the hierarchical process control. One of the main project goals was the proposal of knowledge discovery model for process control. Specifics data mining methods and techniques was used for defined problems of the process control. The gained knowledge was used on the real production system thus the proposed solution has been verified. The paper documents how is possible to apply the new discovery knowledge to use in the real hierarchical process control. There are specified the opportunities for application of the proposed knowledge discovery model for hierarchical process control.

Keywords: Hierarchical process control, knowledge discovery from databases, neural network.

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Authors: Burcu Kaya, Jan-Martin Kaiser, Karl-Friedrich Becker, Tanja Braun, Klaus-Dieter Lang

Abstract:

Quality of the molded packages is strongly influenced by the process parameters of the transfer molding. To achieve a better package quality and a stable transfer molding process, it is necessary to understand the influence of the process parameters on the package quality. This work aims to comprehend the relationship between the process parameters, and to identify the optimum process parameters for the transfer molding process in order to achieve less voids and wire sweep. To achieve this, a DoE is executed for process optimization and a regression analysis is carried out. A systematic approach is represented to generate models which enable an estimation of the number of voids and wire sweep. Validation experiments are conducted to verify the model and the results are presented.

Keywords: Epoxy molding compounds, optimization, regression analysis, transfer molding process, voids, wire sweep.

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Authors: Ali Ridho Barakbah, Yasushi Kiyoki

Abstract:

This paper presents a new approach for image segmentation by applying Pillar-Kmeans algorithm. This segmentation process includes a new mechanism for clustering the elements of high-resolution images in order to improve precision and reduce computation time. The system applies K-means clustering to the image segmentation after optimized by Pillar Algorithm. The Pillar algorithm considers the pillars- placement which should be located as far as possible from each other to withstand against the pressure distribution of a roof, as identical to the number of centroids amongst the data distribution. This algorithm is able to optimize the K-means clustering for image segmentation in aspects of precision and computation time. It designates the initial centroids- positions by calculating the accumulated distance metric between each data point and all previous centroids, and then selects data points which have the maximum distance as new initial centroids. This algorithm distributes all initial centroids according to the maximum accumulated distance metric. This paper evaluates the proposed approach for image segmentation by comparing with K-means and Gaussian Mixture Model algorithm and involving RGB, HSV, HSL and CIELAB color spaces. The experimental results clarify the effectiveness of our approach to improve the segmentation quality in aspects of precision and computational time.

Keywords: Image segmentation, K-means clustering, Pillaralgorithm, color spaces.

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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: Felix Baumann, Aleksandar Milutinovic, Dieter Roller

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Up to this point business process management projects in general and business process modelling projects in particular could not rely on a practical and scientifically validated method to estimate cost and effort. Especially the model development phase is not covered by a cost estimation method or model. Further phases of business process modelling starting with implementation are covered by initial solutions which are discussed in the literature. This article proposes a method of filling this gap by deriving a cost estimation method from available methods in similar domains namely software development or software engineering. Software development is regarded as closely similar to process modelling as we show. After the proposition of this method different ideas for further analysis and validation of the method are proposed. We derive this method from COCOMO II and Function Point which are established methods of effort estimation in the domain of software development. For this we lay out similarities of the software development process and the process of process modelling which is a phase of the Business Process Management life-cycle.

Keywords: Cost Estimation, Effort Estimation, Process Modelling, Business Process Management, COCOMO.

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Authors: Mazin Z. Othman, Maan M. Shaker, Mohammed F. Abdullah

Abstract:

This study introduces a new method for detecting, sorting, and localizing spikes from multiunit EEG recordings. The method combines the wavelet transform, which localizes distinctive spike features, with Super-Paramagnetic Clustering (SPC) algorithm, which allows automatic classification of the data without assumptions such as low variance or Gaussian distributions. Moreover, the method is capable of setting amplitude thresholds for spike detection. The method makes use of several real EEG data sets, and accordingly the spikes are detected, clustered and their times were detected.

Keywords: EEG time localizations, EEG spike detection, superparamagnetic algorithm, wavelet transform.

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Authors: Hanieh Jalali, Ahmad Baraani

Abstract:

Nowaday-s, many organizations use systems that support business process as a whole or partially. However, in some application domains, like software development and health care processes, a normative Process Aware System (PAS) is not suitable, because a flexible support is needed to respond rapidly to new process models. On the other hand, a flexible Process Aware System may be vulnerable to undesirable and fraudulent executions, which imposes a tradeoff between flexibility and security. In order to make this tradeoff available, a genetic-based anomaly detection model for logs of Process Aware Systems is presented in this paper. The detection of an anomalous trace is based on discovering an appropriate process model by using genetic process mining and detecting traces that do not fit the appropriate model as anomalous trace; therefore, when used in PAS, this model is an automated solution that can support coexistence of flexibility and security.

Keywords: Anomaly Detection, Genetic Algorithm, ProcessAware Systems, Process Mining.

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Authors: O. P. Sharma, V. Janyani, S. Sancheti

Abstract:

Data rate, tolerable bit error rate or frame error rate and range & coverage are the key performance requirement of a communication link. In this paper performance of MFSK link is analyzed in terms of bit error rate, number of errors and total number of data processed. In the communication link model proposed, which is implemented using MATLAB block set, an improvement in BER is observed. Different parameters which effects and enables to keep BER low in M-ary communication system are also identified.

Keywords: Additive White Gaussian Noise (AWGN), Bit Error Rate (BER), Frequency Shift Keying (FSK), Orthogonal Signaling.

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Authors: D. D. Vaziri, D. DeOliveira

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This article concerns with the accessibility of Business process modelling tools (BPMo tools) and business process modelling languages (BPMo languages). Therefore the reader will be introduced to business process management and the authors' motivation behind this inquiry. Afterwards, the paper will reflect problems when applying inaccessible BPMo tools. To illustrate these problems the authors distinguish between two different categories of issues and provide practical examples. Finally the article will present three approaches to improve the accessibility of BPMo tools and BPMo languages.

Keywords: Accessibility, Business Process Management, BPM, Event Process Chains, Modelling Languages

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

Abstract:

Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: Katalina Grigorova, Kaloyan Mironov

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The paper focuses on the benefits of business process modeling. Although this discipline is developing for many years, there is still necessity of creating new opportunities to meet the ever increasing users’ needs. Because one of these needs is related to the conversion of business process models from one standard to another, the authors have developed a converter between BPMN and EPC standards using workflow patterns as intermediate tool. Nowadays there are too many systems for business process modeling. The variety of output formats is almost the same as the systems themselves. This diversity additionally hampers the conversion of the models. The presented study is aimed at discussing problems due to differences in the output formats of various modeling environments.

Keywords: Business process modeling, business process modeling standards, workflow patterns, converting models.

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Authors: Ayyaz Mahmood

Abstract:

A new approach for the improvement of coding gain in channel coding using Advanced Encryption Standard (AES) and Maximum A Posteriori (MAP) algorithm is proposed. This new approach uses the avalanche effect of block cipher algorithm AES and soft output values of MAP decoding algorithm. The performance of proposed approach is evaluated in the presence of Additive White Gaussian Noise (AWGN). For the verification of proposed approach, computer simulation results are included.

Keywords: Advanced Encryption Standard (AES), Avalanche Effect, Maximum A Posteriori (MAP), Soft Input Decryption (SID).

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Authors: Heejung Lee

Abstract:

In a highly competitive environment, it becomes more important to shorten the whole business process while delivering or even enhancing the business value to the customers and suppliers. Although the workflow management systems receive much attention for its capacity to practically support the business process enactment, the effective workflow modeling method remain still challenging and the high degree of process complexity makes it more difficult to gain the short lead time. This paper presents a workflow structuring method in a holistic way that can reduce the process complexity using activity-needs and formal concept analysis, which eventually enhances the key performance such as quality, delivery, and cost in business process.

Keywords: Workflow management, reengineering, formal concept analysis.

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Authors: Zenon Chaczko, Essam Rahali, Rizwan Tariq

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This paper introduces a process for the module level integration of computer based systems. It is based on the Six Sigma Process Improvement Model, where the goal of the process is to improve the overall quality of the system under development. We also present a conceptual framework that shows how this process can be implemented as an integration solution. Finally, we provide a partial implementation of key components in the conceptual framework.

Keywords: Software Quality, Six Sigma, System Integration, 3SI Process, 3SI Conceptual Framework.

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Authors: Chih-Feng Chuang, Shih-Ching Shiu, Chao-Jen Cheng

Abstract:

The purpose of this study was to investigate the relationships among students- process of study, creative self-efficacy and creativity while attending college. A total of 60 students enrolled in Hsiuping Institute of Technology in central Taiwan were selected as samples for the study. The instruments for this study included three questionnaires to explore the aforesaid aspects. This researchers tested creative self-efficacy and process of study, and creativity with Pearson correlation and hierarchical regression analyses. The major findings of this research are (1) the process of study had direct positive predictability on creativity, and (2) the relationship between process of study and creativity is partially mediated by creative self-efficacy.

Keywords: Process of study, Creative self-efficacy, Creativity

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Authors: T.A. Adegbola, IEA Aghachi, E.R. Sadiku

Abstract:

To investigates the effect of fiberglass clamping process improvement on drape simulation prediction. This has great effect on the mould and the fiber during manufacturing process. This also, improves the fiber strain, the quality of the fiber orientation in the area of folding and wrinkles formation during the press-forming process. Drape simulation software tool was used to digitalize the process, noting the formation problems on the contour sensitive part. This was compared with the real life clamping processes using single and double frame set-ups to observe the effects. Also, restrains are introduced by using clips, and the G-clamps with predetermine revolution to; restrain the fabric deformation during the forming process.The incorporation of clamping and fabric restrain deformation improved on the prediction of the simulation tool. Therefore, for effective forming process, incorporation of clamping process into the drape simulation process will assist in the development of fiberglass application in manufacturing process.

Keywords: clamping, fiberglass, drape simulation, pressforming.

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Authors: Davit Mirzoyan, Ararat Khachatryan

Abstract:

A process corner monitoring circuit (PCMC) is presented in this work. The circuit generates a signal, the logical value of which depends on the process corner only. The signal can be used in both digital and analog circuits for testing and compensation of process variations (PV). The presented circuit uses only metal-oxide-semiconductor (MOS) transistors, which allow increasing its detection accuracy, decrease power consumption and area. Due to its simplicity the presented circuit can be easily modified to monitor parametrical variations of only n-type and p-type MOS (NMOS and PMOS, respectively) transistors, resistors, as well as their combinations. Post-layout simulation results prove correct functionality of the proposed circuit, i.e. ability to monitor the process corner (equivalently die-to-die variations) even in the presence of within-die variations.

Keywords: Detection, monitoring, process corner, process variation.

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Authors: Bernhard G. Humm, Janina Fengel

Abstract:

Business process modeling has become an accepted means for designing and describing business operations. Thereby, consistency of business process models, i.e., the absence of modeling faults, is of upmost importance to organizations. This paper presents a concept and subsequent implementation for detecting faults in business process models and for computing a measure of their consistency. It incorporates not only syntactic consistency but also semantic consistency, i.e., consistency regarding the meaning of model elements from a business perspective.

Keywords: Business process modeling, model analysis, semantic consistency, Semantic Web

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Authors: Marcos Devaner, Marcela Alves, Cledson Braga, Fabiano Alves, Wilton Bezerra

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This article discusses the inclusion of people with disabilities in the process of testing an accessible system solution for distance education. The accessible system, team profile, methodologies and techniques covered in the testing process are presented. The testing process shown in this paper was designed from the experience with user. The testing process emerged from lessons learned from past experiences and the end user is present at all stages of the tests. Also, lessons learned are reported and how it was possible the maturing of the team and the methods resulting in a simple, productive and effective process.

Keywords: Experience report, accessible systems, software testing, testing process, systems, e-learning.

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Authors: Appanah Rao Appadu, Muhammad Zaid Dauhoo

Abstract:

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

Keywords: Optimised time derivative, dissipation, dispersion, cfl number, Nomenclature: k : time step, h : spatial step, β :advection velocity, r: cfl/Courant number, hkrβ= , w =θ, h : exact wave number, n :time level, RPE : Relative phase error per unit time step, AFM :modulus of amplification factor

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