Search results for: Error estimates.

Authors: Vijay Shankar

Abstract:

Evapotranspiration (ET) is a major component of the hydrologic cycle and its accurate estimation is essential for hydrological studies. In past, various estimation methods have been developed for different climatological data, and the accuracy of these methods varies with climatic conditions. Reference crop evapotranspiration (ET0) is a key variable in procedures established for estimating evapotranspiration rates of agricultural crops. Values of ET0 are used with crop coefficients for many aspects of irrigation and water resources planning and management. Numerous methods are used for estimating ET0. As per internationally accepted procedures outlined in the United Nations Food and Agriculture Organization-s Irrigation and Drainage Paper No. 56(FAO-56), use of Penman-Monteith equation is recommended for computing ET0 from ground based climatological observations. In the present study, seven methods have been selected for performance evaluation. User friendly software has been developed using programming language visual basic. The visual basic has ability to create graphical environment using less coding. For given data availability the developed software estimates reference evapotranspiration for any given area and period for which data is available. The accuracy of the software has been checked by the examples given in FAO-56.The developed software is a user friendly tool for estimating ET0 under different data availability and climatic conditions.

Keywords: Crop coefficient, Crop evapotranspiration, Field moisture, Irrigation Scheduling.

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Authors: E. Dabbour, S. M. Easa

Abstract:

Most of the collision warning systems currently available in the automotive market are mainly designed to warn against imminent rear-end and lane-changing collisions. No collision warning system is commercially available to warn against imminent turning collisions at intersections, especially for left-turn collisions when a driver attempts to make a left-turn at either a signalized or non-signalized intersection, conflicting with the path of other approaching vehicles traveling on the opposite-direction traffic stream. One of the major factors that lead to left-turn collisions is the human error and misjudgment of the driver of the turning vehicle when perceiving the speed and acceleration of other vehicles traveling on the opposite-direction traffic stream; therefore, using a properly-designed collision warning system will likely reduce, or even eliminate, this type of collisions by reducing human error. This paper introduces perceptual framework for a proposed collision warning system that can detect imminent left-turn collisions at intersections. The system utilizes a commercially-available detection sensor (either a radar sensor or a laser detector) to detect approaching vehicles traveling on the opposite-direction traffic stream and calculate their speeds and acceleration rates to estimate the time-tocollision and compare that time to the time required for the turning vehicle to clear the intersection. When calculating the time required for the turning vehicle to clear the intersection, consideration is given to the perception-reaction time of the driver of the turning vehicle, which is the time required by the driver to perceive the message given by the warning system and react to it by engaging the throttle. A regression model was developed to estimate perception-reaction time based on age and gender of the driver of the host vehicle. Desired acceleration rate selected by the driver of the turning vehicle, when making the left-turn movement, is another human factor that is considered by the system. Another regression model was developed to estimate the acceleration rate selected by the driver of the turning vehicle based on driver-s age and gender as well as on the location and speed of the nearest approaching vehicle along with the maximum acceleration rate provided by the mechanical characteristics of the turning vehicle. By comparing time-to-collision with the time required for the turning vehicle to clear the intersection, the system displays a message to the driver of the turning vehicle when departure is safe. An application example is provided to illustrate the logic algorithm of the proposed system.

Keywords: Collision warning systems, intelligent transportationsystems, vehicle safety.

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Authors: Sunita Verma , Divya Tiwari, Ajay Verma

Abstract:

Water samples were collected from river Pandu at six stations where human and animal activities were high. Composite samples were analyzed for dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD) , pH values during dry and wet seasons as well as the harmattan period. The total data points were used to establish relationships between the parameters and data were also subjected to statistical analysis and expressed as mean ± standard error of mean (SEM) at a level of significance of p<0.05. Regression analysis was carried out to establish relationships if any between studied parameters and relationships in form of scatter plots were obtained between DO/BOD, COD/DO, BOD/COD, COD/pH, BOD/pH and DO/pH. The high to moderate correlation coefficient observed, R2 ranged from 0.68 to 0.15 between these parameters.

Keywords: BOD, DO, COD, pH, Regression analysis.

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Authors: P. Prudtikul, S. Pathomsiri

Abstract:

Most, if not all, public hospitals in Thailand have encountered a common problem regarding the increasing demand for medical services. The increasing number of patients causes so much strain on the hospital-s services, over-crowded, overloaded working hours, staff fatigue, medical error and long waiting time. This research studied the characteristics of operational processes of the medical care services at the medicine department in a large public university hospital. The research focuses on details regarding methods, procedures, processes, resources, and time management in overall processes. The simulation model is used as a tool to analyze the impact of various improvement strategies.

Keywords: Patient flow, medicine department, simulation, outpatient department.

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Authors: Seung-Jun Yu, Yong-Jun Kim, Jung-In Baik, Hyoung-Kyu Song

Abstract:

In this paper, a dual-hop relay based on channel state is studied. In the conventional relay scheme, a relay uses the same modulation method without reference to channel state. But, a relay uses an adaptive modulation method with reference to channel state. If the channel state is poor, a relay eliminates latter 2 bits and uses Quadrature Phase Shift Keying (QPSK) modulation. If channel state is good, a relay modulates the received symbols with 16-QAM symbols by using 4 bits. The performance of the proposed scheme for Symbol Error Rate (SER) and throughput is analyzed.

Keywords: Adaptive transmission, channel state, dual-hop, hierarchical modulation, relay.

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Authors: Pandian Elavarasan, Kishore Kondamudi, Sreedevi Upadhyayula

Abstract:

Ionic liquids are well known as green solvents, reaction media and catalysis. Here, three different sulfonic acid functional ionic liquids prepared in the laboratory are used as catalysts in alkylation of p-cresol with tert-butyl alcohol. The kinetics on each of the catalysts was compared and a kinetic model was developed based on the product distribution over these catalysts. The kinetic parameters were estimated using Marquadt's algorithm to minimize the error function. The Arrhenius plots show a curvature which is best interpreted by the extended Arrhenius equation.

Keywords: Alkylation, p-cresol, tert-butyl alcohol, kinetics, activation parameter, extended Arrhenius equation.

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Authors: Seiyed Hamid Zareh, Atabak Sarrafan, Kambiz Ghaemi Osgouie

Abstract:

This paper will first describe predictor controllers when the proportional-integral-derivative (PID) controllers are inactive for procedures that have large delay time (LDT) in transfer stage. Therefore in those states, the predictor controllers are better than the PID controllers, then compares three types of predictor controllers. The value of these controller-s parameters are obtained by trial and error method, so here an effort has been made to obtain these parameters by Ziegler-Nichols method. Eventually in this paper Ziegler-Nichols method has been described and finally, a PIP controller has been designed for a thermal system, which circulates hot air to keep the temperature of a chamber constant.

Keywords: Proportional-integral-predictive controller, Transferfunction, Delay time, Transport-lag.

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Authors: Ali Zifan, Mohammad Hassan Moradi, Sohrab Saberi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG-s. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna-s two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna-s method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise DerivativeDynamic Time Warping.

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Authors: Mohammad Reza Farzami Pour

Abstract:

Determination of genetic variation is useful for plant breeding and hence production of more efficient plant species under different conditions, like drought stress. In this study a sample of 28 recombinant inbred lines (RILs) of wheat developed from the cross of Norstar and Zagross varieties, together with their parents, were evaluated for two years (2010-2012) under normal and water stress conditions using split plot design with three replications. Main plots included two irrigation treatments of 70 and 140 mm evaporation from Class A pan and sub-plots consisted of 30 genotypes. The effect of genotypes and interaction of genotypes with years and water regimes were significant for all characters. Significant genotypic effect implies the existence of genetic variation among the lines under study. Heritability estimates were high for 1000 grain weight (0.87). Biomass and grain yield showed the lowest heritability values (0.42 and 0.50, respectively). Highest genotypic and phenotypic coefficients of variation (GCV and PCV) belonged to harvest index. Moderate genetic advance for most of the traits suggested the feasibility of selection among the RILs under investigation. Some RILs were higher yielding than either parent at both environments.

Keywords: Wheat, genetic gain, heritability, recombinant inbred lines.

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Authors: Riddhi Parmar, Shilpi Gupta, Upena Dalal

Abstract:

Orthogonal Frequency Division Multiplexing (OFDM) is one of the techniques for high speed data rate communication with main consideration for 4G and 5G systems. In OFDM, there are several mapping schemes which provide a way of parallel transmission. In this paper, comparisons of mapping schemes used by some standards have been made and also has been discussed about the performance of the non-conventional modulation technique. The Comparisons of Bit Error Rate (BER) performances for conventional and non-conventional modulation schemes have been done using MATLAB software. Mentioned schemes used in OFDM system can be selected on the basis of the requirement of power or spectrum efficiency and BER analysis.

Keywords: BER, π/4 differential quadrature phase shift keying (Pi/4 DQPSK), OFDM, phase shift keying, quadrature phase shift keying.

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Authors: Chao Wang, Zuxue Xia, Wenhai Xia, Rui Wang, Jiayuan Hu, Rui Cheng

Abstract:

Aiming at the application of indoor personnel positioning under smog conditions, this paper proposes a 3D positioning method based on the IWR1443 millimeter wave radar sensor. The problem that millimeter-wave radar cannot effectively form contours in 3D point cloud imaging is solved. The results show that the method can effectively achieve indoor positioning and scene construction, and the maximum positioning error of the system is 0.130 m.

Keywords: indoor positioning, millimeter wave radar, IWR1443 sensor, point cloud imaging

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Authors: Ali Zifan, Sohrab Saberi, Mohammad Hassan Moradi, Farzad Towhidkhah

Abstract:

Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG's. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna's two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna's method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise Derivative Dynamic Time Warping.

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Authors: Han Bing, Yin Zhenjie

Abstract:

In order to analyze the status of a diesel engine, as well as conduct fault prediction, a new prediction model based on a gray system is proposed in this paper, which takes advantage of the neural network and the genetic algorithm. The proposed GBPGA prediction model builds on the GM (1.5) model and uses a neural network, which is optimized by a genetic algorithm to construct the error compensator. We verify our proposed model on the diesel faulty simulation data and the experimental results show that GBPGA has the potential to employ fault prediction on diesel.

Keywords: Fault prediction, Neural network, GM (1.5), Genetic algorithm, GBPGA.

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Authors: Jin Sup Kim, Woo Young Jung, Minho Kwon

Abstract:

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Keywords: Dynamic, α-Method, P-Method, PC α-Method, Newmark method.

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Authors: Naveed Ur Rehman, Rehan Jamil, Irfan Jamil

Abstract:

In this paper, we regard as a coded transmission over a frequency-selective channel. We plan to study analytically the convergence of the turbo-detector using a maximum a posteriori (MAP) equalizer and a MAP decoder. We demonstrate that the densities of the maximum likelihood (ML) exchanged during the iterations are e-symmetric and output-symmetric. Under the Gaussian approximation, this property allows to execute a one-dimensional scrutiny of the turbo-detector. By deriving the analytical terminology of the ML distributions under the Gaussian approximation, we confirm that the bit error rate (BER) performance of the turbo-detector converges to the BER performance of the coded additive white Gaussian noise (AWGN) channel at high signal to noise ratio (SNR), for any frequency selective channel.

Keywords: MAP, ML, SNR, Decoder, BER, Coded transmission.

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Authors: M. Kollar, A. Zieba

Abstract:

In this paper, we present a method for a time synchronization between the two eNodeBs (eNBs) in E-UTRAN (Evolved Universal Terrestrial Radio Access) network. The two eNBs are cooperating in so-called inter eNB CA (Carrier Aggregation) case and connected via asymmetrical IP network. We solve the problem by using broadcasting signals generated in E-UTRAN as synchronization signals. The results show that the time synchronization with the proposed method is possible with the error significantly less than 1 ms which is sufficient considering the time transmission interval is 1 ms in E-UTRAN. This makes this method (with low complexity) more suitable than Network Time Protocol (NTP) in the mobile applications with generated broadcasting signals where time synchronization in asymmetrical network is required.

Keywords: E-UTRAN, IP scheduled throughput, initial burst delay, synchronization, NTP, delay, asymmetric network.

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Authors: Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung Kang, Soo-Ho Kim

Abstract:

This paper presents an iterative algorithm to find a inverse kinematic solution of 5-DOF robot. The algorithm is to minimize the iteration number. Since the 5-DOF robot cannot give full orientation of tool. Only z-direction of tool is satisfied while rotation of tool is determined by kinematic constraint. This work therefore described how to specify the tool direction and let the tool rotation free. The simulation results show that this algorithm effectively worked. Using the proposed iteration algorithm, error due to inverse kinematics converged to zero rapidly in 5 iterations. This algorithm was applied in real welding robot and verified through various practical works.

Keywords: 5-DOF manipulator, Inverse kinematics, Iterative algorithm, Wrist offset.

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Authors: ML. Benmessaoud, A. Lamrani, K. Nemra, AK. Souici

Abstract:

This paper presents an Extended Kaman Filter implementation of a single-camera Visual Simultaneous Localization and Mapping algorithm, a novel algorithm for simultaneous localization and mapping problem widely studied in mobile robotics field. The algorithm is vision and odometry-based, The odometry data is incremental, and therefore it will accumulate error over time, since the robot may slip or may be lifted, consequently if the odometry is used alone we can not accurately estimate the robot position, in this paper we show that a combination of odometry and visual landmark via the extended Kalman filter can improve the robot position estimate. We use a Pioneer II robot and motorized pan tilt camera models to implement the algorithm.

Keywords: Mobile Robot, Navigation, vSLAM, EKF, monocular.

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Authors: Z. Feng, V. Viswanathan, D. Navarro, I. O'Connor

Abstract:

This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.

Keywords: CMOS image sensor, high speed simulation, image sensor matrix simulation.

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Authors: Supattra Aomumpai, Chutima Prommak

Abstract:

This paper presents a studyof the impact of reference node locations on the accuracy of the indoor positioning systems. In particular, we analyze the localization accuracy of the RSSI database mapping techniques, deploying on the IEEE 802.15.4 wireless networks. The results show that the locations of the reference nodes used in the positioning systems affect the signal propagation characteristics in the service area. Thisin turn affects the accuracy of the wireless indoor positioning system. We found that suitable location of reference nodes could reduce the positioning error upto 35 %.

Keywords: Indoor positioning systems, IEEE 802.15.4 wireless networks, Signal propagation characteristics

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Authors: Al-Falahi Amir, Yusoff M. Z, Yusaf T

Abstract:

The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN" in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wide range of Mach number. The developed solver uses second order accurate cell-vertex finite volume spatial discretization and forth order accurate Runge-Kutta temporal integration and it is designed to simulate the flow process for similar driver/driven gases (e.g. air-air as working fluids). The solver is validated against analytical solution and experimental measurements in the high speed flow test facility. Further investigations were made on the flow process inside the shock tube by using the solver. The shock wave motion, reflection and interaction were investigated and their influence on the performance of the shock tube was determined. The results provide very good estimates for both shock speed and shock pressure obtained after diaphragm rupture. Also detailed information on the gasdynamic processes over the full length of the facility is available. The agreements obtained have been reasonable.

Keywords: shock tunnel, shock tube, shock wave, CFD.

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Authors: S. Thirumurugan, D. R. Prince Williams

Abstract:

Software Reliability is one of the key factors in the software development process. Software Reliability is estimated using reliability models based on Non Homogenous Poisson Process. In most of the literature the Software Reliability is predicted only in testing phase. So it leads to wrong decision-making concept. In this paper, two Software Reliability concepts, testing and operational phase are studied in detail. Using S-Shaped Software Reliability Growth Model (SRGM) and Exponential SRGM, the testing and operational reliability values are obtained. Finally two reliability values are compared and optimal release time is investigated.

Keywords: Error Detection Rate, Estimation of Parameters, Instantaneous Failure Rate, Mean Value Function, Non Homogenous Poisson Process (NHPP), Software Reliability.

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Authors: An Hong Nguyen, Chatpan Chintanapakdee, Toshiro Hayashikawa

Abstract:

Presented herein is an assessment of current nonlinear static procedures (NSPs) for seismic evaluation of bucklingrestrained braced frames (BRBFs) which have become a favorable lateral-force resisting system for earthquake resistant buildings. The bias and accuracy of modal, improved modal pushover analysis (MPA, IMPA) and mass proportional pushover (MPP) procedures are comparatively investigated when they are applied to BRBF buildings subjected to two sets of strong ground motions. The assessment is based on a comparison of seismic displacement demands such as target roof displacements, peak floor/roof displacements and inter-story drifts. The NSP estimates are compared to 'exact' results from nonlinear response history analysis (NLRHA). The response statistics presented show that the MPP procedure tends to significantly overestimate seismic demands of lower stories of tall buildings considered in this study while MPA and IMPA procedures provide reasonably accurate results in estimating maximum inter-story drift over all stories of studied BRBF systems.

Keywords: Buckling-restrained braced frames, nonlinearresponse history analysis, nonlinear static procedure, seismicdemands.

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

Abstract:

This paper proposes an efficient lattice-reduction-aided detection (LRD) scheme to improve the detection performance of MIMO-OFDM system. In this proposed scheme, V candidate symbols are considered at the first layer, and V probable streams are detected with LRD scheme according to the first detected V candidate symbols. Then, the most probable stream is selected through a ML test. Since the proposed scheme can more accurately detect initial symbol and can reduce transmission of error to rest symbols, the proposed scheme shows more improved performance than conventional LRD with very low complexity.

Keywords: Lattice reduction aided detection, MIMO-OFDM, QRD-M, V-BLAST.

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Authors: M. Harir, A. Bendiabdellah, A. Chaouch, N. Benouzza

Abstract:

This paper deals with the modelling and simulation of the squirrel cage induction motor by taking into account all space harmonic components as well as the introduction of the bars skew in the calculation of the linear evolution of the magnetomotive force (MMF) between the slots extremities. The model used is based on multiple coupled circuits and the modified winding function approach (MWFA). The effect of skewing is included in the calculation of motors inductances with an axial asymmetry in the rotor. The simulation results in both time and spectral domains show the effectiveness and merits of the model and the error that may be caused if the skew of the bars are neglected.

Keywords: Modelling, MWFA, Skew effect, Squirrel cage induction motor, Spectral domain.

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Authors: Axay J Mehta, Hema A Mehta, T.C.Manjunath, C. Ardil

Abstract:

In this paper, the modelling and design of artificial neural network architecture for load forecasting purposes is investigated. The primary pre-requisite for power system planning is to arrive at realistic estimates of future demand of power, which is known as Load Forecasting. Short Term Load Forecasting (STLF) helps in determining the economic, reliable and secure operating strategies for power system. The dependence of load on several factors makes the load forecasting a very challenging job. An over estimation of the load may cause premature investment and unnecessary blocking of the capital where as under estimation of load may result in shortage of equipment and circuits. It is always better to plan the system for the load slightly higher than expected one so that no exigency may arise. In this paper, a load-forecasting model is proposed using a multilayer neural network with an appropriately modified back propagation learning algorithm. Once the neural network model is designed and trained, it can forecast the load of the power system 24 hours ahead on daily basis and can also forecast the cumulative load on daily basis. The real load data that is used for the Artificial Neural Network training was taken from LDC, Gujarat Electricity Board, Jambuva, Gujarat, India. The results show that the load forecasting of the ANN model follows the actual load pattern more accurately throughout the forecasted period.

Keywords: Power system, Load forecasting, Neural Network, Neuron, Stabilization, Network structure, Load.

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Authors: Yu-Chun Lin

Abstract:

We identify clawback triggers from firms- proxy statements (Form DEF 14A) and use the likelihood of restatements to proxy for financial reporting quality. Based on a sample of 578 U.S. firms that voluntarily adopt clawback provisions during 2003-2009, when restatement-based triggers could be decomposed into two types: fraud and unintentional error, and we do observe the evidence that using fraud triggers is associated with high financial reporting quality. The findings support that fraud triggers can enhance deterrent effect of clawback provision by establishing a viable disincentive against fraud, misconduct, and otherwise harmful acts. These results are robust to controlling for the compensation components, to different sample specifications and to a number of sensitivity.

Keywords: Accruals quality, Clawback provisions, Compensation, Restatements.

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Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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Authors: Mamoun F. Abdel-Hafez

Abstract:

In this paper, the detection of a fault in the Global Positioning System (GPS) measurement is addressed. The class of faults considered is a bias in the GPS pseudorange measurements. This bias is modeled as an unknown constant. The fault could be the result of a receiver fault or signal fault such as multipath error. A bias bank is constructed based on set of possible fault hypotheses. Initially, there is equal probability of occurrence for any of the biases in the bank. Subsequently, as the measurements are processed, the probability of occurrence for each of the biases is sequentially updated. The fault with a probability approaching unity will be declared as the current fault in the GPS measurement. The residual formed from the GPS and Inertial Measurement Unit (IMU) measurements is used to update the probability of each fault. Results will be presented to show the performance of the presented algorithm.

Keywords: Estimation and filtering, Statistical data analysis, Faultdetection and identification.

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Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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