Search results for: Propagation of Error.

Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Christhu Raj M. R., Rajeev Sukumaran

Abstract:

Underwater acoustic networks have attracted great attention in the last few years because of its numerous applications. High data rate can be achieved by efficiently modeling the physical layer in the network protocol stack. In Acoustic medium, propagation speed of the acoustic waves is dependent on many parameters such as temperature, salinity, density, and depth. Acoustic propagation speed cannot be modeled using standard empirical formulas such as Urick and Thorp descriptions. In this paper, we have modeled the acoustic channel using real time data of temperature, salinity, and speed of Bay of Bengal (Indian Coastal Region). We have modeled the acoustic channel by using Mackenzie speed equation and real time data obtained from National Institute of Oceanography and Technology. It is found that acoustic propagation speed varies between 1503 m/s to 1544 m/s as temperature and depth differs. The simulation results show that temperature, salinity, depth plays major role in acoustic propagation and data rate increases with appropriate data sets substituted in the simulated model.

Keywords: Underwater Acoustics, Mackenzie Speed Equation, Temperature, Salinity.

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Khine Phyu, Aung Myint Aye

Abstract:

This paper presents results of measurements campaign carried out at a carrier frequency of 24GHz with the help of TPLINK router in indoor line-of-sight (LOS) scenarios. Firstly, the radio wave propagation strategies are analyzed in some rooms with router of point to point Ad hoc network. Then floor attenuation is defined for 3 floors in experimental region. The free space model and dual slope models are modified by considering the influence of corridor conditions on each floor. Using these models, indoor signal attenuation can be estimated in modeling of indoor radio wave propagation. These results and modified models can also be used in planning the networks of future personal communications services.

Keywords: radio wave signal analyzing, LOS radio wavepropagation, indoor radio wave propagation, free space model, tworay model and indoor attenuation.

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Authors: Phornpat Chewasoonthorn, Surat Kwanmuang

Abstract:

Indoor positioning technologies have been evolved rapidly. They augment the Global Positioning System (GPS) which requires line-of-sight to the sky to track the location of people or objects. In this study, we developed an error correction method for an indoor real-time location system (RTLS) based on an ultra-wideband (UWB) sensor from Decawave. Multiple stationary nodes (anchor) were installed throughout the workspace. The distance between stationary and moving nodes (tag) can be measured using a two-way-ranging (TWR) scheme. The result has shown that the uncorrected ranging error from the sensor system can be as large as 1 m. To reduce ranging error and thus increase positioning accuracy, we present an online correction algorithm using the Kalman filter. The results from experiments have shown that the system can reduce ranging error down to 5 cm.

Keywords: Indoor positioning, ultra-wideband, error correction, Kalman filter.

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

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Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: M. Ali, K. Masood

Abstract:

In this paper methodology to exploit creeping wave for body area network BAN communication reliability are described. Creeping wave propagation effects are visualized & analyzed. During this work Dipole, IA antennas various antennas were redesigned using existing designs and their propagation characteristics were verified for optimum performance when used on BANs. These antennas were then applied on body shapes-including rectangular, spherical and cylindrical so that all the effects of actual human body can be taken nearly into account. Parametric simulation scheme was devised so that on Body channel characterization can be visualized at front, curved and back region. In the next phase multiple inputs multiple output MIMO scheme was introduced where virtual antennas were used in order to diminish the effects of antennas on the propagation of waves. Results were, extracted and analyzed at different heights. Finally based on comparative measurement and analysis it was concluded that on body propagation can be exploited to gain spatial diversity.

Keywords: BAN, Creeping Wave, MIMO, WIAs.

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Authors: Jehnming Lin

Abstract:

In the laser cleavage of glass, the laser is mostly adopted as a heat source to generate a thermal stress state on the substrates. The crack propagation of the soda-lime glass in the laser thermal cleavage with the straight-turning paths was investigated in this study experimentally and numerically. The crack propagation was visualized by a high speed camera with the off-line examination on the micro-crack propagation. The temperature and stress distributions induced by the laser heat source were calculated by ANSYS software based on the finite element method (FEM). With the cutting paths in various turning directions, the experimental and numerical results were in comparison and verified. The fracture modes due to the normal and shear stresses were verified at the turning point of the laser cleavage path. It shows a significant variation of the stress profiles along the straight-turning paths and causes a change on the fracture modes.

Keywords: Laser cleavage, glass, fracture, stress analysis.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

Abstract:

On the basis of the theory of nonlinear elasticity, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: Acoustoelasticity, dispersion, finite deformation, lamb waves.

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Authors: Irina Pyrlina

Abstract:

This article presents the results of a study conducted to identify operational risks for information systems (IS) with service-oriented architecture (SOA). Analysis of current approaches to risk and system error classifications revealed that the system error classes were never used for SOA risk estimation. Additionally system error classes are not normallyexperimentally supported with realenterprise error data. Through the study several categories of various existing error classifications systems are applied and three new error categories with sub-categories are identified. As a part of operational risks a new error classification scheme is proposed for SOA applications. It is based on errors of real information systems which are service providers for application with service-oriented architecture. The proposed classification approach has been used to classify SOA system errors for two different enterprises (oil and gas industry, metal and mining industry). In addition we have conducted a research to identify possible losses from operational risks.

Keywords: Enterprise architecture, Error classification, Oil&Gas and Metal&Mining industries, Operational risks, Serviceoriented architecture

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Authors: Ε. Giovanis

Abstract:

In this paper we present an autoregressive model with neural networks modeling and standard error backpropagation algorithm training optimization in order to predict the gross domestic product (GDP) growth rate of four countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final optimum weights from input-hidden layer after the training process. The forecasts are compared with those of the ordinary autoregressive model and we conclude that the proposed regression-s forecasting results outperform significant those of autoregressive model in the out-of-sample period. The idea behind this approach is to propose a parametric regression with weighted variables in order to test for the statistical significance and the magnitude of the estimated autoregressive coefficients and simultaneously to estimate the forecasts.

Keywords: Autoregressive model, Error back-propagation Feed-Forward neural networks, , Gross Domestic Product

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Authors: Achela K. Fernando, Xiujuan Zhang, Peter F. Kinley

Abstract:

A feed-forward, back-propagation Artificial Neural Network (ANN) model has been used to forecast the occurrences of wastewater overflows in a combined sewerage reticulation system. This approach was tested to evaluate its applicability as a method alternative to the common practice of developing a complete conceptual, mathematical hydrological-hydraulic model for the sewerage system to enable such forecasts. The ANN approach obviates the need for a-priori understanding and representation of the underlying hydrological hydraulic phenomena in mathematical terms but enables learning the characteristics of a sewer overflow from the historical data. The performance of the standard feed-forward, back-propagation of error algorithm was enhanced by a modified data normalizing technique that enabled the ANN model to extrapolate into the territory that was unseen by the training data. The algorithm and the data normalizing method are presented along with the ANN model output results that indicate a good accuracy in the forecasted sewer overflow rates. However, it was revealed that the accurate forecasting of the overflow rates are heavily dependent on the availability of a real-time flow monitoring at the overflow structure to provide antecedent flow rate data. The ability of the ANN to forecast the overflow rates without the antecedent flow rates (as is the case with traditional conceptual reticulation models) was found to be quite poor.

Keywords: Artificial Neural Networks, Back-propagationlearning, Combined sewer overflows, Forecasting.

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Authors: Guang Zou, Kian Banisoleiman, Arturo González

Abstract:

Crack initiation and propagation threatens structural integrity of welded joints and normally inspections are assigned based on crack propagation models. However, the approach based on crack propagation models may not be applicable for some high-quality welded joints, because the initial flaws in them may be so small that it may take long time for the flaws to develop into a detectable size. This raises a concern regarding the inspection planning of high-quality welded joins, as there is no generally acceptable approach for modeling the whole fatigue process that includes the crack initiation period. In order to address the issue, this paper reviews treatment methods for crack initiation period and initial crack size in crack propagation models applied to inspection planning. Generally, there are four approaches, by: 1) Neglecting the crack initiation period and fitting a probabilistic distribution for initial crack size based on statistical data; 2) Extrapolating the crack propagation stage to a very small fictitious initial crack size, so that the whole fatigue process can be modeled by crack propagation models; 3) Assuming a fixed detectable initial crack size and fitting a probabilistic distribution for crack initiation time based on specimen tests; and, 4) Modeling the crack initiation and propagation stage separately using small crack growth theories and Paris law or similar models. The conclusion is that in view of trade-off between accuracy and computation efforts, calibration of a small fictitious initial crack size to S-N curves is the most efficient approach.

Keywords: Crack initiation, fatigue reliability, inspection planning, welded joints.

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Authors: Qun-Feng Zhang, Pan-Pan Yan, Jun Li, Jun-Qing Lei

Abstract:

Numerical investigation of hammershock propagation in the S-bend intake caused by engine surge has been conducted by using Improved Delayed Detach-Eddy Simulation (IDDES). The effects of surge signatures on hammershock characteristics are obtained. It was shown that once the hammershock is produced, it moves upward to the intake entrance quickly with constant speed, however, the strength of hammershock keeps increasing. Meanwhile, being influenced by the centrifugal force, the hammershock strength on the larger radius side is much larger. Hammershock propagation speed and strength are sensitive to the ramp upgradient of surge signature. A larger ramp up gradient results in higher propagation speed and greater strength. Nevertheless, ramp down profile of surge signature have no obvious effect on the propagation speed and strength of hammershock. Increasing the maximum value of surge signature leads to enhance in the intensity of hammershock, they approximately match quadratic function distribution law.

Keywords: Hammershock, IDDES, S-bend, surge signature.

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Authors: Jinho Kim, Dongik Shin, Deokwon Yun, Changsoo Han

Abstract:

Rotating stages in semiconductor, display industry and many other fields require challenging accuracy to perform their functions properly. Especially, Axis of rotation error on rotary system is significant; such as the spindle error motion of the aligner, wire bonder and inspector machine which result in the poor state of manufactured goods. To evaluate and improve the performance of such precision rotary stage, unessential movements on the other 5 degrees of freedom of the rotary stage must be measured and analyzed. In this paper, we have measured the three translations and two tilt motions of a rotating stage with high precision capacitive sensors. To obtain the radial error motion from T.I.R (Total Indicated Reading) of radial direction, we have used Donaldson's reversal technique. And the axial components of the spindle tilt error motion can be obtained accurately from the axial direction outputs of sensors by Estler face motion reversal technique. Further more we have defined and measured the sensitivity of positioning error to the five error motions.

Keywords: Donaldson's reversal methods, Estler face motionreversal method, Error motion, sensitivity, T.I.R (Total IndicatedReading).

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Authors: S. Anna Durai, E. Anna Saro

Abstract:

In general the images used for compression are of different types like dark image, high intensity image etc. When these images are compressed using Counter Propagation Neural Network, it takes longer time to converge. The reason for this is that the given image may contain a number of distinct gray levels with narrow difference with their neighborhood pixels. If the gray levels of the pixels in an image and their neighbors are mapped in such a way that the difference in the gray levels of the neighbor with the pixel is minimum, then compression ratio as well as the convergence of the network can be improved. To achieve this, a Cumulative Distribution Function is estimated for the image and it is used to map the image pixels. When the mapped image pixels are used the Counter Propagation Neural Network yield high compression ratio as well as it converges quickly.

Keywords: Correlation, Counter Propagation Neural Networks, Cummulative Distribution Function, Image compression.

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Authors: P. Prema, B. Ramadoss

Abstract:

Testing is an activity that is required both in the development and maintenance of the software development life cycle in which Integration Testing is an important activity. Integration testing is based on the specification and functionality of the software and thus could be called black-box testing technique. The purpose of integration testing is testing integration between software components. In function or system testing, the concern is with overall behavior and whether the software meets its functional specifications or performance characteristics or how well the software and hardware work together. This explains the importance and necessity of IT for which the emphasis is on interactions between modules and their interfaces. Software errors should be discovered early during IT to reduce the costs of correction. This paper introduces a new type of integration error, presenting an overview of Integration Testing techniques with comparison of each technique and also identifying which technique detects what type of error.

Keywords: Integration Error, Integration Error Types, Integration Testing Techniques, Software Testing

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Authors: Kollarama Subramanyam, Nisha Kuruvilla, J. P. Raina

Abstract:

Novel compact expressions for propagation constant (γ) of SWCNT and bundled SWCNTs interconnect, in terms of physical parameters such as length, operating frequency and diameter of CNTs is proposed in this work. These simplified expressions enable physical insight and accurate estimation of signal attenuation level and its phase change at any length for a particular frequency. The proposed expressions are validated against SPICE simulated results of lumped as well as distributed equivalent electrical RLC nets of CNT interconnect. These expressions also help us to evaluate the cut off frequencies of SWCNTs for different interconnect lengths.

Keywords: Attenuation constant, Bundled SWCNT, CNT interconnects, Propagation Constant.

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Authors: Mohamed Adnan Landolsi, Ali F. Almutairi

Abstract:

The paper addresses the problem of line-of-sight (LOS) vs. non-line-of-sight (NLOS) propagation link identification in ultra-wideband (UWB) wireless networks, which is necessary for improving the accuracy of radiolocation and positioning applications. A LOS/NLOS likelihood hypothesis testing approach is applied based on exploiting distinctive statistical features of the channel impulse response (CIR) using parameters related to the “skewness” of the CIR and its root mean square (RMS) delay spread. A log-normal fit is presented for the probability densities of the CIR parameters. Simulation results show that different environments (residential, office, outdoor, etc.) have measurable differences in their CIR parameters’ statistics, which is then exploited in determining the nature of the propagation channels. Correct LOS/NLOS channel identification rates exceeding 90% are shown to be achievable for most types of environments. Additional improvement is also obtained by combining both CIR skewness and RMS delay statistics.

Keywords: Ultra-wideband, propagation, line-of-sight, non-line-of-sight, identification.

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Authors: Ammar Elyas babiker, M.Nordin B. Zakaria, Hassan Yosif, Samir B. Ibrahim

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Variable channel conditions in underwater networks, and variable distances between sensors due to water current, leads to variable bit error rate (BER). This variability in BER has great effects on energy efficiency of error correction techniques used. In this paper an efficient energy adaptive hybrid error correction technique (AHECT) is proposed. AHECT adaptively changes error technique from pure retransmission (ARQ) in a low BER case to a hybrid technique with variable encoding rates (ARQ & FEC) in a high BER cases. An adaptation algorithm depends on a precalculated packet acceptance rate (PAR) look-up table, current BER, packet size and error correction technique used is proposed. Based on this adaptation algorithm a periodically 3-bit feedback is added to the acknowledgment packet to state which error correction technique is suitable for the current channel conditions and distance. Comparative studies were done between this technique and other techniques, and the results show that AHECT is more energy efficient and has high probability of success than all those techniques.

Keywords: Underwater communication, wireless sensornetworks, error correction technique, energy efficiency

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Authors: E. E. Mantilla, C. R. Reyes, B. G. Ramos

Abstract:

This paper describes the development of a WLAN propagation model, using Spectral Analyzer measurements. The signal is generated by two Access Points (APs) on the base floor at the administrative Communication School of ESPOL building. In general, users do not have a Q&S reference about a wireless network; however, this depends on the level signal as a function of frequency, distance and other path conditions between receiver and transmitter. Then, power density of the signal decrease as it propagates through space and data transfer rate is affected. This document evaluates and implements empirical mathematical formulation for the characterization of WLAN radio wave propagation on two aisles of the building base floor.

Keywords: frequency, Spectral Analyzer, transmitter, WLAN.

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Authors: Rameswar Debnath, Haruhisa Takahashi

Abstract:

An evolutionary method whose selection and recombination operations are based on generalization error-bounds of support vector machine (SVM) can select a subset of potentially informative genes for SVM classifier very efficiently [7]. In this paper, we will use the derivative of error-bound (first-order criteria) to select and recombine gene features in the evolutionary process, and compare the performance of the derivative of error-bound with the error-bound itself (zero-order) in the evolutionary process. We also investigate several error-bounds and their derivatives to compare the performance, and find the best criteria for gene selection and classification. We use 7 cancer-related human gene expression datasets to evaluate the performance of the zero-order and first-order criteria of error-bounds. Though both criteria have the same strategy in theoretically, experimental results demonstrate the best criterion for microarray gene expression data.

Keywords: support vector machine, generalization error-bound, feature selection, evolutionary algorithm, microarray data

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Authors: M.V Rajesh, Archana R, A Unnikrishnan, R Gopikakumari, Jeevamma Jacob

Abstract:

The System Identification problem looks for a suitably parameterized model, representing a given process. The parameters of the model are adjusted to optimize a performance function based on error between the given process output and identified process output. The linear system identification field is well established with many classical approaches whereas most of those methods cannot be applied for nonlinear systems. The problem becomes tougher if the system is completely unknown with only the output time series is available. It has been reported that the capability of Artificial Neural Network to approximate all linear and nonlinear input-output maps makes it predominantly suitable for the identification of nonlinear systems, where only the output time series is available. [1][2][4][5]. The work reported here is an attempt to implement few of the well known algorithms in the context of modeling of nonlinear systems, and to make a performance comparison to establish the relative merits and demerits.

Keywords: Multilayer neural networks, Radial Basis Functions, Clustering algorithm, Back Propagation training, Extended Kalmanfiltering, Mean Square Error, Nonlinear Modeling, Cramer RaoLower Bound.

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Authors: Jaeyoon Lee, Dongweon Yoon, Hoon Yoo, Sanggoo Kim

Abstract:

Orthogonal frequency division multiplexing (OFDM) has developed into a popular scheme for wideband digital communications used in consumer applications such as digital broadcasting, wireless networking and broadband internet access. In the OFDM system, carrier frequency offset (CFO) causes intercarrier interference (ICI) which significantly degrades the system error performance. In this paper we provide an exact evaluation method for error performance analysis of arbitrary 2-D modulation OFDM systems with CFO, and analyze the effect of CFO on error performance.

Keywords: Carrier frequency offset, Probability of error, Inter-channel interference, Orthogonal frequency division multiplexing

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Authors: Eric Filiol, Edouard Franc, Alessandro Gubbioli, Benoit Moquet, Guillaume Roblot

Abstract:

Worm propagation profiles have significantly changed since 2003-2004: sudden world outbreaks like Blaster or Slammer have progressively disappeared and slower but stealthier worms appeared since, most of them for botnets dissemination. Decreased worm virulence results in more difficult detection. In this paper, we describe a stealth worm propagation model which has been extensively simulated and analysed on a huge virtual network. The main features of this model is its ability to infect any Internet-like network in a few seconds, whatever may be its size while greatly limiting the reinfection attempt overhead of already infected hosts. The main simulation results shows that the combinatorial topology of routing may have a huge impact on the worm propagation and thus some servers play a more essential and significant role than others. The real-time capability to identify them may be essential to greatly hinder worm propagation.

Keywords: Combinatorial worm, worm spreading, worm virulence, stealth worm, spreading simulation, vertex cover, networktopology, WAST simulator, SuWAST simulator.

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Authors: A. Bumbová, J. Kellner, J. Navrátil, D. Pluskal, M. Kozubková, E. Kozubek

Abstract:

The paper deals with the possibilities of modelling vapour propagation of explosive substances in the FLUENT software. With regard to very low tensions of explosive substance vapours the experiment has been verified as exemplified by mononitrotoluene. Either constant or time variable meteorological conditions have been used for calculation. Further, it has been verified that the eluent source may be time-dependent and may reflect a real situation or the liberation rate may be constant. The execution of the experiment as well as evaluation were clear and it could also be used for modelling vapour and aerosol propagation of selected explosive substances in the atmospheric boundary layer.

Keywords: atmospheric boundary layer, explosive substances, FLUENT software, modelling of propagation

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Authors: Jaroslav Polec, Viliam Hirner, Michal Martinovič, Kvetoslava Kotuliaková

Abstract:

In this paper we present a novel error model for packet loss and subsequent error description. The proposed model simulates the error performance of wireless communication link. The model is designed as two independent Markov chains, where the first one is used for packet generation and the second one generates correctly and incorrectly transmitted bits for received packets from the first chain. The statistical analyses of real communication on the wireless link are used for determination of model-s parameters. Using the obtained parameters and the implementation of the generator, we collected generated traffic. The obtained results generated by proposed model are compared with the real data collection.

Keywords: Wireless channel, error model, Markov chain, Elliot model, Gilbert model, generator, IEEE 802.11.

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Authors: Wen-Tsann Lin, Yung-Tsan Jou, Yih-Chuan Wu, Yuan-Du Hsiao

Abstract:

The Emergency Department of a medical center in Taiwan cooperated to conduct the research. A predictive model of triage system is contracted from the contract procedure, selection of parameters to sample screening. 2,000 pieces of data needed for the patients is chosen randomly by the computer. After three categorizations of data mining (Multi-group Discriminant Analysis, Multinomial Logistic Regression, Back-propagation Neural Networks), it is found that Back-propagation Neural Networks can best distinguish the patients- extent of emergency, and the accuracy rate can reach to as high as 95.1%. The Back-propagation Neural Networks that has the highest accuracy rate is simulated into the triage acuity expert system in this research. Data mining applied to the predictive model of the triage acuity expert system can be updated regularly for both the improvement of the system and for education training, and will not be affected by subjective factors.

Keywords: Back-propagation Neural Networks, Data Mining, Emergency Department, Triage System.

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: Embedded Runge-Kutta-Fehlberg method, Initial value problem.

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