Search results for: mean-square error.

Authors: Chieh-Yuan Tsai, Chuang-Cheng Chiu

Abstract:

Biclustering aims at identifying several biclusters that reveal potential local patterns from a microarray matrix. A bicluster is a sub-matrix of the microarray consisting of only a subset of genes co-regulates in a subset of conditions. In this study, we extend the motif of subspace clustering to present a K-biclusters clustering (KBC) algorithm for the microarray biclustering issue. Besides minimizing the dissimilarities between genes and bicluster centers within all biclusters, the objective function of the KBC algorithm additionally takes into account how to minimize the residues within all biclusters based on the mean square residue model. In addition, the objective function also maximizes the entropy of conditions to stimulate more conditions to contribute the identification of biclusters. The KBC algorithm adopts the K-means type clustering process to efficiently make the partition of K biclusters be optimized. A set of experiments on a practical microarray dataset are demonstrated to show the performance of the proposed KBC algorithm.

Keywords: Microarray, Biclustering, Subspace clustering, Meansquare residue model.

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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: 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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Authors: Shamsuddin Ahmed, M. G. M. Khan, Biman Prasad, Avlin Prasad

Abstract:

The focus of this paper is to construct daily time series exchange rate forecast models of Samoan Tala/USD and Tala/AUD during the year 2008 to 2012 with neural network The performance of the models was measured by using varies error functions such as Root Square mean error (RSME), Mean absolute error (MAE), and Mean absolute percentage error (MAPE). Our empirical findings suggest that AR (1) model is an effective tool to forecast the Tala/USD and Tala/AUD.

Keywords: Neural Network Forecasting Model, Autoregressive time series, Exchange rate, Tala/AUD, winters model.

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Authors: Dinesh Inamadar, R. Venugopalan, K. Padmini

Abstract:

An attempt has been made in the present communication to elucidate the efficacy of robust ANOVA methods to analyse horticultural field experimental data in the presence of outliers. Results obtained fortify the use of robust ANOVA methods as there was substantiate reduction in error mean square, and hence the probability of committing Type I error, as compared to the regular approach.

Keywords: Outliers, robust ANOVA, horticulture, Cook distance, Type I error.

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Authors: R. Sabre

Abstract:

This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: Spectral density, stable processes, aliasing, p-adic.

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Authors: Mohammad Rakibul Islam

Abstract:

Link reliability and transmitted power are two important design constraints in wireless network design. Error control coding (ECC) is a classic approach used to increase link reliability and to lower the required transmitted power. It provides coding gain, resulting in transmitter energy savings at the cost of added decoder power consumption. But the choice of ECC is very critical in the case of wireless sensor network (WSN). Since the WSNs are energy constraint in nature, both the BER and power consumption has to be taken into count. This paper develops a step by step approach in finding suitable error control codes for WSNs. Several simulations are taken considering different error control codes and the result shows that the RS(31,21) fits both in BER and power consumption criteria.

Keywords: Error correcting code, RS, BCH, wireless sensor networks.

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Authors: Richard W. Longman

Abstract:

Iterative learning control aims to achieve zero tracking error of a specific command. This is accomplished by iteratively adjusting the command given to a feedback control system, based on the tracking error observed in the previous iteration. One would like the iterations to converge to zero tracking error in spite of any error present in the model used to design the learning law. First, this need for stability robustness is discussed, and then the need for robustness of the property that the transients are well behaved. Methods of producing the needed robustness to parameter variations and to singular perturbations are presented. Then a method involving reverse time runs is given that lets the world behavior produce the ILC gains in such a way as to eliminate the need for a mathematical model. Since the real world is producing the gains, there is no issue of model error. Provided the world behaves linearly, the approach gives an ILC law with both stability robustness and good transient robustness, without the need to generate a model.

Keywords: Iterative learning control, stability robustness, monotonic convergence.

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Authors: Bashar Albaalbaki, Roger E. Khayat

Abstract:

This work is a comparative study on the effect of Delaunay triangulation algorithms on discretization error for conduction-convection conservation problems. A structured triangulation and many unstructured Delaunay triangulations using three popular algorithms for node placement strategies are used. The numerical method employed is the vertex-centered finite volume method. It is found that when the computational domain can be meshed using a structured triangulation, the discretization error is lower for structured triangulations compared to unstructured ones for only low Peclet number values, i.e. when conduction is dominant. However, as the Peclet number is increased and convection becomes more significant, the unstructured triangulations reduce the discretization error. Also, no statistical correlation between triangulation angle extremums and the discretization error is found using 200 samples of randomly generated Delaunay and non-Delaunay triangulations. Thus, the angle extremums cannot be an indicator of the discretization error on their own and need to be combined with other triangulation quality measures, which is the subject of further studies.

Keywords: Conduction-convection problems, Delaunay triangulation, discretization error, finite volume method.

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Authors: Ahmed Abdolkhalig, Rastko Zivanovic

Abstract:

This paper evaluates the Total Vector Error of an estimated Phasor as define in IEEE C37.118 standard within different medium access in Local Area Networks (LAN). Three different LAN models (CSMA/CD, CSMA/AMP and Switched Ethernet) are evaluated. The Total Vector Error of the estimated Phasor has been evaluated for the effect of Nodes Number under the standardized network Band-width values defined in IEC 61850-9-2 communication standard (i.e. 0.1, 1 and 10 Gbps).

Keywords: Phasor, Local Area Network, Total Vector Error, IEEE C37.118, IEC 61850.

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Authors: Thomas Odaker, Dieter Kranzlmueller, Jens Volkert

Abstract:

We present an approach to triangle mesh simplification designed to be executed on the GPU. We use a quadric error metric to calculate an error value for each vertex of the mesh and order all vertices based on this value. This step is followed by the parallel removal of a number of vertices with the lowest calculated error values. To allow for the parallel removal of multiple vertices we use a set of per-vertex boundaries that prevent mesh foldovers even when simplification operations are performed on neighbouring vertices. We execute multiple iterations of the calculation of the vertex errors, ordering of the error values and removal of vertices until either a desired number of vertices remains in the mesh or a minimum error value is reached. This parallel approach is used to speed up the simplification process while maintaining mesh topology and avoiding foldovers at every step of the simplification.

Keywords: Computer graphics, half edge collapse, mesh simplification, precomputed simplification, topology preserving.

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Authors: T. Hirner, J. Polec

Abstract:

This paper presents an approach for an unequal error protection of facial features of personal ID images coding. We consider unequal error protection (UEP) strategies for the efficient progressive transmission of embedded image codes over noisy channels. This new method is based on the progressive image compression embedded zerotree wavelet (EZW) algorithm and UEP technique with defined region of interest (ROI). In this case is ROI equal facial features within personal ID image. ROI technique is important in applications with different parts of importance. In ROI coding, a chosen ROI is encoded with higher quality than the background (BG). Unequal error protection of image is provided by different coding techniques and encoding LL band separately. In our proposed method, image is divided into two parts (ROI, BG) that consist of more important bytes (MIB) and less important bytes (LIB). The proposed unequal error protection of image transmission has shown to be more appropriate to low bit rate applications, producing better quality output for ROI of the compresses image. The experimental results verify effectiveness of the design. The results of our method demonstrate the comparison of the UEP of image transmission with defined ROI with facial features and the equal error protection (EEP) over additive white gaussian noise (AWGN) channel.

Keywords: Embedded zerotree wavelet (EZW), equal error protection (EEP), facial features, personal ID images, region of interest (ROI), unequal error protection (UEP)

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Authors: Cinna Soltanpur, Mohammad Ghamari, Behzad Momahed Heravi, Fatemeh Zare

Abstract:

Low-density parity-check (LDPC) codes have been shown to deliver capacity approaching performance; however, problematic graphical structures (e.g. trapping sets) in the Tanner graph of some LDPC codes can cause high error floors in bit-error-ratio (BER) performance under conventional sum-product algorithm (SPA). This paper presents a serial concatenation scheme to avoid the trapping sets and to lower the error floors of LDPC code. The outer code in the proposed concatenation is the LDPC, and the inner code is a high rate array code. This approach applies an interactive hybrid process between the BCJR decoding for the array code and the SPA for the LDPC code together with bit-pinning and bit-flipping techniques. Margulis code of size (2640, 1320) has been used for the simulation and it has been shown that the proposed concatenation and decoding scheme can considerably improve the error floor performance with minimal rate loss.

Keywords: Concatenated coding, low–density parity–check codes, array code, error floors.

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Authors: M. O. Welcome, Y. E. Razvodovsky, E. V. Pereverzeva, V. A. Pereverzev

Abstract:

The error monitoring and processing system, EMPS is the system located in the substantia nigra of the midbrain, basal ganglia and cortex of the forebrain, and plays a leading role in error detection and correction. The main components of EMPS are the dopaminergic system and anterior cingulate cortex. Although, recent studies show that alcohol disrupts the EMPS, the ways in which alcohol affects this system are poorly understood. Based on current literature data, here we suggest a hypothesis of alcohol-related glucose-dependent system of error monitoring and processing, which holds that the disruption of the EMPS is related to the competency of glucose homeostasis regulation, which in turn may determine the dopamine level as a major component of EMPS. Alcohol may indirectly disrupt the EMPS by affecting dopamine level through disorders in blood glucose homeostasis regulation.

Keywords: Alcohol related disruption, Error monitoring andprocessing system, Mechanism.

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Authors: Mahdi Yaghobi, Mohammad Haeri

Abstract:

The current methods of predictive controllers are utilized for those processes in which the rate of output variations is not high. For such processes, therefore, stability can be achieved by implementing the constrained predictive controller or applying infinite prediction horizon. When the rate of the output growth is high (e.g. for unstable nonminimum phase process) the stabilization seems to be problematic. In order to avoid this, it is suggested to change the method in the way that: first, the prediction error growth should be decreased at the early stage of the prediction horizon, and second, the rate of the error variation should be penalized. The growth of the error is decreased through adjusting its weighting coefficients in the cost function. Reduction in the error variation is possible by adding the first order derivate of the error into the cost function. By studying different examples it is shown that using these two remedies together, the closed-loop stability of unstable nonminimum phase process can be achieved.

Keywords: GPC, Stability, Varying Weighting Coefficients.

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Authors: S. Swain, P. S Khuntia

Abstract:

In this paper, the unstable angle of attack of a FOXTROT aircraft is controlled by using Genetic Algorithm based flight controller and the result is compared with the conventional techniques like Tyreus-Luyben (TL), Ziegler-Nichols (ZN) and Interpolation Rule (IR) for tuning the PID controller. In addition, the performance indices like Mean Square Error (MSE), Integral Square Error (ISE), and Integral Absolute Time Error (IATE) etc. are improved by using Genetic Algorithm. It was established that the error by using GA is very less as compared to the conventional techniques thereby improving the performance indices of the dynamic system.

Keywords: Angle of Attack, Genetic Algorithm, Performance Indices, PID Controller.

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Authors: Chaiwat Tantarangsee

Abstract:

The purposes of this study are 1) to study the effects of participatory error correction process and 2) to find out the students’ satisfaction of such error correction process. This study is a Quasi Experimental Research with single group, in which data is collected 5 times preceding and following 4 experimental studies of participatory error correction process including providing coded indirect corrective feedback in the students’ texts with error treatment activities. Samples include 52 2nd year English Major students, Faculty of Humanities and Social Sciences, Suan Sunandha Rajabhat University. Tool for experimental study includes the lesson plan of the course; Reading and Writing English for Academic Purposes II, and tools for data collection include 5 writing tests of short texts and a questionnaire. Based on formative evaluation of the students’ writing ability prior to and after each of the 4 experiments, the research findings disclose the students’ higher scores with statistical difference at 0.00. Moreover, in terms of the effect size of such process, it is found that for mean of the students’ scores prior to and after the 4 experiments; d equals 0.6801, 0.5093, 0.5071, and 0.5296 respectively. It can be concluded that participatory error correction process enables all of the students to learn equally well and there is improvement in their ability to write short texts. Finally the students’ overall satisfaction of the participatory error correction process is in high level (Mean = 4.39, S.D. = 0.76).

Keywords: Coded indirect corrective feedback, participatory error correction process, error treatment.

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Authors: Ondrej Baran, Miroslav Kasal, Petr Vagner, Tomas Urbanec

Abstract:

This paper deals with the modeling and the evaluation of a multiplicative phase noise influence on the bit error ratio in a general space communication system. Our research is focused on systems with multi-state phase shift keying modulation techniques and it turns out, that the phase noise significantly affects the bit error rate, especially for higher signal to noise ratios. These results come from a system model created in Matlab environment and are shown in a form of constellation diagrams and bit error rate dependencies. The change of a user data bit rate is also considered and included into simulation results. Obtained outcomes confirm theoretical presumptions.

Keywords: Additive thermal noise, AWGN, BER, bit error rate, multiplicative phase noise, phase shift keying.

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Authors: Anjana Choudhary

Abstract:

The ad hoc networks are the future of wireless technology as everyone wants fast and accurate error free information so keeping this in mind Bit Error Rate (BER) and power is optimized in this research paper by using the Genetic Algorithm (GA). The digital modulation techniques used for this paper are Binary Phase Shift Keying (BPSK), M-ary Phase Shift Keying (M-ary PSK), and Quadrature Amplitude Modulation (QAM). This work is implemented on Wireless Ad Hoc Networks (WLAN). Then it is analyze which modulation technique is performing well to optimize the BER and power of WLAN.

Keywords: Bit Error Rate, Genetic Algorithm, Power, Phase Shift Keying, Quadrature Amplitude Modulation, Signal to Noise Ratio, Wireless Ad Hoc Networks.

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Authors: M. Arulvizhi

Abstract:

In Multiuser MIMO communication systems, interuser interference has a strong impact on the transmitted signals. Precoding technique schemes are employed for multiuser broadcast channels to suppress an interuser interference. Different Linear and nonlinear precoding schemes are there. For the massive system dimension, it is difficult to design an appropriate precoding algorithm with low computational complexity and good error rate performance at the same time over fading channels. This paper describes the error rate performance of precoding schemes over fading channels with the assumption of perfect channel state information at the transmitter. To estimate the bit error rate performance, different propagation environments namely, Rayleigh, Rician and Nakagami fading channels have been offered. This paper presents the error rate performance comparison of these fading channels based on precoding methods like Channel Inversion and Dirty paper coding for multiuser broadcasting system. MATLAB simulation has been used. It is observed that multiuser system achieves better error rate performance by Dirty paper coding over Rayleigh fading channel.

Keywords: Multiuser MIMO, channel inversion precoding, dirty paper coding, fading channels, BER.

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Authors: Abhijit Mitra

Abstract:

A special case of floating point data representation is block floating point format where a block of operands are forced to have a joint exponent term. This paper deals with the finite wordlength properties of this data format. The theoretical errors associated with the error model for block floating point quantization process is investigated with the help of error distribution functions. A fast and easy approximation formula for calculating signal-to-noise ratio in quantization to block floating point format is derived. This representation is found to be a useful compromise between fixed point and floating point format due to its acceptable numerical error properties over a wide dynamic range.

Keywords: Block floating point, Roundoff error, Block exponent dis-tribution fuction, Signal factor.

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Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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Authors: Shiraz Ahmad, Zhe-Ming Lu

Abstract:

An effective visual error concealment method has been presented by employing a robust rotation, scale, and translation (RST) invariant partial patch matching model (RSTI-PPMM) and exemplar-based inpainting. While the proposed robust and inherently feature-enhanced texture synthesis approach ensures the generation of excellent and perceptually plausible visual error concealment results, the outlier pruning property guarantees the significant quality improvements, both quantitatively and qualitatively. No intermediate user-interaction is required for the pre-segmented media and the presented method follows a bootstrapping approach for an automatic visual loss recovery and the image and video error concealment.

Keywords: Exemplar-based image and video inpainting, outlierpruning, RST-invariant partial patch matching model (RSTI-PPMM), visual error concealment.

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Authors: Fangfang Meng, Shuang Cong

Abstract:

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

Keywords: Implicit Lyapunov control, state error, degenerate cases, convergence.

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Authors: Kamil Ďurana, Robert Černý

Abstract:

An electrical apparatus for measuring moisture content was developed by our laboratory and uses dependence of electrical properties on water content in studied material. Error analysis of the apparatus was run by measuring different volumes of water in a simplified specimen, i.e. hollow plexiglass block, in order to avoid as many side-effects as possible. Obtained data were processed using both basic and advanced statistics and results were compared with each other. The influence of water content on accuracy of measured data was studied as well as the influence of variation of apparatus' proper arrangement or factual methodics of its usage. The overall coefficient of variation was 4%. There was no trend found in results of error dependence on water content. Comparison with current surveys led to a conclusion, that the studied apparatus can be used for indirect measurement of water content in porous materials, with expectable error and under known conditions. Factual experiments with porous materials are not involved, but are currently under investigation.

Keywords: device, capacitance method, error analysis, moisture meter

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Authors: R. Sabre, W. Horrigue, J. C. Simon

Abstract:

This paper is interested in two difficulties encountered in practice when observing a continuous time process. The first is that we cannot observe a process over a time interval; we only take discrete observations. The second is the process frequently observed with a constant additive error. It is important to give an estimator of the spectral density of such a process taking into account the additive observation error and the choice of the discrete observation times. In this work, we propose an estimator based on the spectral smoothing of the periodogram by the polynomial Jackson kernel reducing the additive error. In order to solve the aliasing phenomenon, this estimator is constructed from observations taken at well-chosen times so as to reduce the estimator to the field where the spectral density is not zero. We show that the proposed estimator is asymptotically unbiased and consistent. Thus we obtain an estimate solving the two difficulties concerning the choice of the instants of observations of a continuous time process and the observations affected by a constant error.

Keywords: Spectral density, stable processes, aliasing, periodogram.

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Authors: Jun Sung Go, Jong Kang Park, Jong Tae Kim

Abstract:

As semi-conductor manufacturing technology evolves; the single event transient problem becomes more significant issue. Single event transient has a critical impact on both combinational and sequential logic circuits, so it is important to evaluate the soft error tolerance of the circuits at the design stage. In this paper, we present a soft error detecting simulation using scan chain. The simulation model generates a single event transient randomly in the circuit, and detects the soft error during the execution of the test patterns. We verified this model by inserting a scan chain in an 8051 microprocessor using 65 nm CMOS technology. While the test patterns generated by ATPG program are passing through the scan chain, we insert a single event transient and detect the number of soft errors per sub-module. The experiments show that the soft error rates per cell area of the SFR module is 277% larger than other modules.

Keywords: Scan chain, single event transient, soft error, 8051 processor.

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Authors: Chaiwat Tantarangsee

Abstract:

The purposes of this study are 1) to study the frequent English writing errors of students registering the course: Reading and Writing English for Academic Purposes II, and 2) to find out the results of writing error correction by using coded indirect corrective feedback and writing error treatments. Samples include 28 2nd year English Major students, Faculty of Education, Suan Sunandha Rajabhat University. Tool for experimental study includes the lesson plan of the course; Reading and Writing English for Academic Purposes II, and tool for data collection includes 4 writing tests of short texts. The research findings disclose that frequent English writing errors found in this course comprise 7 types of grammatical errors, namely Fragment sentence, Subject-verb agreement, Wrong form of verb tense, Singular or plural noun endings, Run-ons sentence, Wrong form of verb pattern and Lack of parallel structure. Moreover, it is found that the results of writing error correction by using coded indirect corrective feedback and error treatment reveal the overall reduction of the frequent English writing errors and the increase of students’ achievement in the writing of short texts with the significance at .05.

Keywords: Coded indirect corrective feedback, error correction, error treatment, frequent English writing errors.

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Authors: Johann Barbier, Guillaume Sicot, Sebastien Houcke

Abstract:

In this paper we present a generic approach for the problem of the blind estimation of the parameters of linear and convolutional error correcting codes. In a non-cooperative context, an adversary has only access to the noised transmission he has intercepted. The intercepter has no knowledge about the parameters used by the legal users. So, before having acess to the information he has first to blindly estimate the parameters of the error correcting code of the communication. The presented approach has the main advantage that the problem of reconstruction of such codes can be expressed in a very simple way. This allows us to evaluate theorical bounds on the complexity of the reconstruction process but also bounds on the estimation rate. We show that some classical reconstruction techniques are optimal and also explain why some of them have theorical complexities greater than these experimentally observed.

Keywords: Blind estimation parameters, error correcting codes, non-cooperative context, reconstruction algorithm

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Authors: Chaiwat Tantarangsee

Abstract:

The purposes of this study are 1) to study the frequent English writing errors of students registering the course: Reading and Writing English for Academic Purposes II, and 2) to find out the results of writing error correction by using coded indirect corrective feedback and writing error treatments. Samples include 28 2nd year English Major students, Faculty of Education, Suan Sunandha Rajabhat University. Tool for experimental study includes the lesson plan of the course; Reading and Writing English for Academic Purposes II, and tool for data collection includes 4 writing tests of short texts. The research findings disclose that frequent English writing errors found in this course comprise 7 types of grammatical errors, namely Fragment sentence, Subject-verb agreement, Wrong form of verb tense, Singular or plural noun endings, Run-ons sentence, Wrong form of verb pattern and Lack of parallel structure. Moreover, it is found that the results of writing error correction by using coded indirect corrective feedback and error treatment reveal the overall reduction of the frequent English writing errors and the increase of students’ achievement in the writing of short texts with the significance at .05.

Keywords: Coded indirect corrective feedback, error correction, and error treatment.

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