Search results for: recursive least squares.

Authors: Boontee Kruatrachue, Narongchai Moongfangklang, Kritawan Siriboon

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This paper describes fast and efficient method for page segmentation of document containing nonrectangular block. The segmentation is based on edge following algorithm using small window of 16 by 32 pixels. This segmentation is very fast since only border pixels of paragraph are used without scanning the whole page. Still, the segmentation may contain error if the space between them is smaller than the window used in edge following. Consequently, this paper reduce this error by first identify the missed segmentation point using direction information in edge following then, using X-Y cut at the missed segmentation point to separate the connected columns. The advantage of the proposed method is the fast identification of missed segmentation point. This methodology is faster with fewer overheads than other algorithms that need to access much more pixel of a document.

Keywords: Contour Direction Technique, Missed SegmentationPoints, Page Segmentation, Recursive X-Y Cut Technique

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Authors: Carlos Huertas, Reyes Juarez-Ramirez

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Public health is one of the most critical issues today; therefore, there is great interest to improve technologies in the area of diseases detection. With machine learning and feature selection, it has been possible to aid the diagnosis of several diseases such as cancer. In this work, we present an extension to the Heat Map Based Feature Selection algorithm, this modification allows automatic threshold parameter selection that helps to improve the generalization performance of high dimensional data such as mass spectrometry. We have performed a comparison analysis using multiple cancer datasets and compare against the well known Recursive Feature Elimination algorithm and our original proposal, the results show improved classification performance that is very competitive against current techniques.

Keywords: Feature selection, mass spectrometry, biomarker discovery, cancer.

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Authors: Sanjeeb Kumar Kar

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The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: J. B. V. Subrahmanyam, C. Radhakrishna

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This paper presents a simple three phase power flow method for solution of three-phase unbalanced radial distribution system (RDN) with voltage dependent loads. It solves a simple algebraic recursive expression of voltage magnitude, and all the data are stored in vector form. The algorithm uses basic principles of circuit theory and can be easily understood. Mutual coupling between the phases has been included in the mathematical model. The proposed algorithm has been tested with several unbalanced radial distribution networks and the results are presented in the article. 8- bus and IEEE 13 bus unbalanced radial distribution system results are in agreements with the literature and show that the proposed model is valid and reliable.

Keywords: radial distribution networks, load flow, circuitmodel, three-phase four-wire, unbalance.

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Authors: Khin May Win, Nan Sai Moon Kham

Abstract:

Identification of cancer genes that might anticipate the clinical behaviors from different types of cancer disease is challenging due to the huge number of genes and small number of patients samples. The new method is being proposed based on supervised learning of classification like support vector machines (SVMs).A new solution is described by the introduction of the Maximized Margin (MM) in the subset criterion, which permits to get near the least generalization error rate. In class prediction problem, gene selection is essential to improve the accuracy and to identify genes for cancer disease. The performance of the new method was evaluated with real-world data experiment. It can give the better accuracy for classification.

Keywords: Microarray data, feature selection, recursive featureelimination, support vector machines.

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Authors: N.B. Adams

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This article discusses the concept of student ownership of knowledge and seeks to determine how to move students from knowledge acquisition to knowledge application and ultimately to knowledge generation in a virtual setting. Instructional strategies for fostering student engagement in a virtual environment are critical to the learner-s strategic ownership of the knowledge. A number of relevant theories that focus on learning, affect, needs and adult concerns are presented to provide a basis for exploring the transfer of knowledge from teacher to learner. A model under development is presented that combines the dimensions of knowledge approach, the teacher-student relationship with regards to knowledge authority and teaching approach to demonstrate the recursive and scaffolded design for creation of virtual learning environments.

Keywords: Virtual learning environments, learning theory, teaching model, online learning.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel

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We present our ongoing work on the development of a new quadrotor aerial vehicle which has a tilt-wing mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using Newton-Euler formulation. Linear and nonlinear controllers for the stabilization of attitude of the vehicle and control of its altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide satisfactory performance in achieving desired maneuvers.

Keywords: UAV, VTOL, dynamic model, stabilization, LQR, SMC

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Authors: O.M. Mohamed vall, M. Radhi

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This work presents a recursive identification algorithm. This algorithm relates to the identification of closed loop system with Variable Structure Controller. The approach suggested includes two stages. In the first stage a genetic algorithm is used to obtain the parameters of switching function which gives a control signal rich in commutations (i.e. a control signal whose spectral characteristics are closest possible to those of a white noise signal). The second stage consists in the identification of the system parameters by the instrumental variable method and using the optimal switching function parameters obtained with the genetic algorithm. In order to test the validity of this algorithm a simulation example is presented.

Keywords: Closed loop identification, variable structure controller, pseud-random binary sequence, genetic algorithms.

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Authors: Mohammad Shams Esfand Abadi, Nader Hadizadeh Kashani, Vahid Mehrdad

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In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.

Keywords: Adaptive filter, affine projection, selective regressor.

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Authors: Fateme Ashari-Ghomi, Najme Khorasani, Abbas Nowzari-Dalini

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In this paper, we present two new ranking and unranking algorithms for k-ary trees represented by x-sequences in Gray code order. These algorithms are based on a gray code generation algorithm developed by Ahrabian et al.. In mentioned paper, a recursive backtracking generation algorithm for x-sequences corresponding to k-ary trees in Gray code was presented. This generation algorithm is based on Vajnovszki-s algorithm for generating binary trees in Gray code ordering. Up to our knowledge no ranking and unranking algorithms were given for x-sequences in this ordering. we present ranking and unranking algorithms with O(kn2) time complexity for x-sequences in this Gray code ordering

Keywords: k-ary Tree Generation, Ranking, Unranking, Gray Code.

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Authors: Aizzat Mohd. Nasurdin, Noor Hazlina Ahmad, Cheng Ling Tan

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This study aims to examine the role of career advancement and job security as predictors of employee commitment to their organization. Data was collected from 580 frontline employees attached to two departments of 29 luxury hotels in Peninsular Malaysia. Statistical results using Partial Least Squares technique provided support for the proposed hypotheses. In view of the findings, theoretical and practical implications are discussed.

Keywords: Organizational commitment, career advancement, job security, frontline employees, luxury hotels, Malaysia.

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Authors: Karandeep Singh, Baibing Li

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Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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Authors: Baoguang Tian, Nan Chen

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A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Horia Păunescu

Abstract:

Purpose: The study aimed to assess the depressant or antidepressant effects of several Nonsteroidal Anti-Inflammatory Drugs (NSAIDs) in mice: the selective cyclooxygenase-2 (COX-2) inhibitor meloxicam, and the non-selective COX-1 and COX-2 inhibitors lornoxicam, sodium metamizole, and ketorolac. The current literature data regarding such effects of these agents are scarce. Materials and methods: The study was carried out on NMRI mice weighing 20-35 g, kept in a standard laboratory environment. The study was approved by the Ethics Committee of the University of Medicine and Pharmacy „Carol Davila”, Bucharest. The study agents were injected intraperitoneally, 10 mL/kg body weight (bw) 1 hour before the assessment of the locomotor activity by cage testing (n=10 mice/ group) and 2 hours before the forced swimming tests (n=15). The study agents were dissolved in normal saline (meloxicam, sodium metamizole), ethanol 11.8% v/v in normal saline (ketorolac), or water (lornoxicam), respectively. Negative and positive control agents were also given (amitryptilline in the forced swimming test). The cage floor used in the locomotor activity assessment was divided into 20 equal 10 cm squares. The forced swimming test involved partial immersion of the mice in cylinders (15/9cm height/diameter) filled with water (10 cm depth at 28C), where they were left for 6 minutes. The cage endpoint used in the locomotor activity assessment was the number of treaded squares. Four endpoints were used in the forced swimming test (immobility latency for the entire 6 minutes, and immobility, swimming, and climbing scores for the final 4 minutes of the swimming session), recorded by an observer that was „blinded” to the experimental design. The statistical analysis used the Levene test for variance homogeneity, ANOVA and post-hoc analysis as appropriate, Tukey or Tamhane tests. Results: No statistically significant increase or decrease in the number of treaded squares was seen in the locomotor activity assessment of any mice group. In the forced swimming test, amitryptilline showed an antidepressant effect in each experiment, at the 10 mg/kg bw dosage. Sodium metamizole was depressant at 100 mg/kg bw (increased the immobility score, p=0.049, Tamhane test), but not in lower dosages as well (25 and 50 mg/kg bw). Ketorolac showed an antidepressant effect at the intermediate dosage of 5 mg/kg bw, but not so in the dosages of 2.5 and 10 mg/kg bw, respectively (increased the swimming score, p=0.012, Tamhane test). Meloxicam and lornoxicam did not alter the forced swimming endpoints at any dosage level. Discussion: 1) Certain NSAIDs caused changes in the forced swimming patterns without interfering with locomotion. 2) Sodium metamizole showed a depressant effect, whereas ketorolac proved antidepressant. Conclusion: NSAID-induced mood changes are not class effects of these agents and apparently are independent of the type of inhibited cyclooxygenase (COX-1 or COX-2). Disclosure: This paper was co-financed from the European Social Fund, through the Sectorial Operational Programme Human Resources Development 2007-2013, project number POSDRU /159 /1.5 /S /138907 "Excellence in scientific interdisciplinary research, doctoral and postdoctoral, in the economic, social and medical fields -EXCELIS", coordinator The Bucharest University of Economic Studies.

Keywords: Antidepressant, depressant, forced swim, NSAIDs.

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Authors: Shazia Javed, Noor Atinah Ahmad

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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Jac W. Andrews, J. B. Hale

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Effective practicing psychologists require ongoing skill development that is constructivist and recursive in nature, with mentor, colleague, co-worker, and patient feedback critical to successful acquisition and maintenance of professional competencies. This paper will provide an overview of the nature and scope of psychologist skill development through multisource feedback (MSF) or 360 degree evaluation, present a rationale for its use for assessing practicing psychologist performance, and advocate its use in psychology given the demonstrated model utility in other health professions. The paper will conclude that an international research design is needed to assess the feasibility, reliability, and validity of MSF system ratings intended to solicit feedback from mentors, colleagues, coworkers, and patients about psychologist competencies. If adopted, the MSF model could lead to enhanced skill development that fosters patient satisfaction within and across countries.

 

Keywords: Psychologist, multisource feedback, psychologist competency, professionalism.

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Authors: Abder-Rahman Ali, Adélaïde Albouy-Kissi, Manuel Grand-Brochier, Viviane Ladan-Marcus, Christine Hoeffl, Claude Marcus, Antoine Vacavant, Jean-Yves Boire

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In this paper, we present a new segmentation approach for focal liver lesions in contrast enhanced ultrasound imaging. This approach, based on a two-cluster Fuzzy C-Means methodology, considers type-II fuzzy sets to handle uncertainty due to the image modality (presence of speckle noise, low contrast, etc.), and to calculate the optimum inter-cluster threshold. Fine boundaries are detected by a local recursive merging of ambiguous pixels. The method has been tested on a representative database. Compared to both Otsu and type-I Fuzzy C-Means techniques, the proposed method significantly reduces the segmentation errors.

Keywords: Defuzzification, fuzzy clustering, image segmentation, type-II fuzzy sets.

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Authors: Khalid M. Aamir, Mohammad A. Maud

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Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.

Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.

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Authors: Ali Shatnawi

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

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

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Authors: Ming-Hui Lee, Tsung-Chien Chen, Yuh-Shiou Tai

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The intelligent fuzzy input estimator is used to estimate the input force of the rigid bar structural system in this study. The fuzzy Kalman filter without the input term and the fuzzy weighting recursive least square estimator are two main portions of this method. The practicability and accuracy of the proposed method were verified with numerical simulations from which the input forces of a rigid bar structural system were estimated from the output responses. In order to examine the accuracy of the proposed method, a rigid bar structural system is subjected to periodic sinusoidal dynamic loading. The excellent performance of this estimator is demonstrated by comparing it with the use of difference weighting function and improper the initial process noise covariance. The estimated results have a good agreement with the true values in all cases tested.

Keywords: Fuzzy Input Estimator, Kalman Filter, RecursiveLeast Square Estimator.

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Authors: Esra E. Aleisa, Li Lin

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Complex engineering design problems consist of numerous factors of varying criticalities. Considering fundamental features of design and inferior details alike will result in an extensive waste of time and effort. Design parameters should be introduced gradually as appropriate based on their significance relevant to the problem context. This motivates the representation of design parameters at multiple levels of an abstraction hierarchy. However, developing abstraction hierarchies is an area that is not well understood. Our research proposes a novel hierarchical abstraction methodology to plan effective engineering designs and processes. It provides a theoretically sound foundation to represent, abstract and stratify engineering design parameters and tasks according to causality and criticality. The methodology creates abstraction hierarchies in a recursive and bottom-up approach that guarantees no backtracking across any of the abstraction levels. The methodology consists of three main phases, representation, abstraction, and layering to multiple hierarchical levels. The effectiveness of the developed methodology is demonstrated by a design problem.

Keywords: Hierarchies, Abstraction, Loop-free, Engineering Design

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Authors: Yang Zhang, Yuncai Liu

Abstract:

Accurately predicting non-peak traffic is crucial to daily traffic for all forecasting models. In the paper, least squares support vector machines (LS-SVMs) are investigated to solve such a practical problem. It is the first time to apply the approach and analyze the forecast performance in the domain. For comparison purpose, two parametric and two non-parametric techniques are selected because of their effectiveness proved in past research. Having good generalization ability and guaranteeing global minima, LS-SVMs perform better than the others. Providing sufficient improvement in stability and robustness reveals that the approach is practically promising.

Keywords: Parametric and Nonparametric Techniques, Non-peak Traffic Forecasting

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Authors: Xinjian Kou, Linlin Li, Yongju Zhou, Jimian Song

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We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

Keywords: Structural robustness, structural reliability, redundancy component, redundancy matrix.

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Authors: S. Kavitha, Nirmala P. Ratchagar

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This paper presents the novel deterministic dynamic programming approach for solving optimization problem with quadratic objective function with linear equality and inequality constraints. The proposed method employs backward recursion in which computations proceeds from last stage to first stage in a multi-stage decision problem. A generalized recursive equation which gives the exact solution of an optimization problem is derived in this paper. The method is purely analytical and avoids the usage of initial solution. The feasibility of the proposed method is demonstrated with a practical example. The numerical results show that the proposed method provides global optimum solution with negligible computation time.

Keywords: Backward recursion, Dynamic programming, Multi-stage decision problem, Quadratic objective function.

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Authors: F. Yaghobian, R. Stosch, B. Güttler

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This study aims to demonstrate the quantification of peptides based on isotope dilution surface enhanced Raman scattering (IDSERS). SERS spectra of phenylalanine (Phe), leucine (Leu) and two peptide sequences TGQIFK (T13) and YSFLQNPQTSLCFSESIPTPSNR (T6) as part of the 22-kDa human growth hormone (hGH) were obtained on Ag-nanoparticle covered substrates. On the basis of the dominant Phe and Leu vibrational modes, precise partial least squares (PLS) prediction models were built enabling the determination of unknown T13 and T6 concentrations. Detection of hGH in its physiological concentration in order to investigate the possibility of protein quantification has been achieved.

Keywords: Surface Enhanced Raman Scattering, Quantification, Peptides.

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Authors: T Panigrahi, G Panda, Mulgrew

Abstract:

This paper introduces a new approach for the performance analysis of adaptive filter with error saturation nonlinearity in the presence of impulsive noise. The performance analysis of adaptive filters includes both transient analysis which shows that how fast a filter learns and the steady-state analysis gives how well a filter learns. The recursive expressions for mean-square deviation(MSD) and excess mean-square error(EMSE) are derived based on weighted energy conservation arguments which provide the transient behavior of the adaptive algorithm. The steady-state analysis for co-related input regressor data is analyzed, so this approach leads to a new performance results without restricting the input regression data to be white.

Keywords: Error saturation nonlinearity, transient analysis, impulsive noise.

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Authors: B. Sudhakar, K. A. Ponnusamy

Abstract:

In India cotton was the major commercial crop and cultivating all the states. In recent years, area of cotton declined due to pest and disease attack, drought, lower price for the produces etc. The first reason as pest and disease attack will be the challenges and it is of utmost importance that in future the insect problems would have to be tackled through Integrated Pest Management (IPM). The present study deals with principle knowledge of IPM adopting cotton cultivators in irrigated and rainfed conditions. Under irrigated conditions, among cultural practices, all respondents had principle knowledge about growing high yielding and pest resistant hybrids, sowing quality and certified seeds and avoiding cotton ratoon cropping. Regarding mechanical practices all respondents had principle knowledge about collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 93% of them had principle knowledge about spraying neem oil, followed by 82% about tying Trichogramma eggcard. Among chemical practices, more than 90% of the respondents had principle knowledge about of spraying herbicide (96%), identifying ETL (Economic Threshold Level) for cotton pests (94%), and applying safe insecticides (90%). Under rainfed condition, among cultural practices, all respondents had principle knowledge about sowing quality and certified seeds and growing high yielding and pest resistant hybrids seeds. Regarding mechanical practices hundred percentage of the respondents had principle knowledge on the mechanical practices viz., collecting and destroying egg, larvae and pupae of pests and removing and destroying pest and disease infected cotton squares, flowers and other shed materials. With regard to biological practices, 96% of the respondents had correct in principle knowledge about spraying neem oil, followed by 89% about tying Trichogramma eggcard. With regard to chemical practices, more than 90% of the respondents had principle knowledge of applying safe insecticides (95%), avoiding repeated use of the same insecticides (95%), identifying ETL for cotton pests (94%) and applying granular insecticides (90%).

Keywords: Biological practices, chemical practices, cultural practices, mechanical practices, integrated pest management.

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Authors: N. Azadi-Tinat, H. Oraizi

Abstract:

Design of compact UWB multilayered microstrip filter with E-shape resonator is presented, which provides wide stopband up to 20 GHz and arbitrary impedance matching. The design procedure is developed based on the method of least squares and theory of N-coupled transmission lines. The dimensions of designed filter are about 11 mm × 11 mm and the three E-shape resonators are placed among four dielectric layers. The average insertion loss in the passband is less than 1 dB and in the stopband is about 30 dB up to 20 GHz. Its group delay in the UWB region is about 0.5 ns. The performance of the optimized filter design perfectly agrees with the microwave simulation softwares.

Keywords: Ultra-wideband, method of least square, multilayer microstrip filter, n-coupled transmission lines.

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Authors: Kaewkarn Phuangsombat, Arthit Phuangsombat, Anupun Terdwongworakul

Abstract:

Hard seeds will not grow and can cause mold in sprouting process. Thus, the hard seeds need to be separated from the normal seeds. Near infrared hyperspectral imaging in a range of 900 to 1700 nm was implemented to develop a model by partial least squares discriminant analysis to discriminate the hard seeds from the normal seeds. The orientation of the seeds was also studied to compare the performance of the models. The model based on hilum-up orientation achieved the best result giving the coefficient of determination of 0.98, and root mean square error of prediction of 0.07 with classification accuracy was equal to 100%.

Keywords: Mung bean, near infrared, germinatability, hard seed.

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Authors: Taweechai Nuntawisuttiwong, Natasha Dejdumrong

Abstract:

Geometric modeling plays an important role in the constructions and manufacturing of curve, surface and solid modeling. Their algorithms are critically important not only in the automobile, ship and aircraft manufacturing business, but are also absolutely necessary in a wide variety of modern applications, e.g., robotics, optimization, computer vision, data analytics and visualization. The calculation and display of geometric objects can be accomplished by these six techniques: Polynomial basis, Recursive, Iterative, Coefficient matrix, Polar form approach and Pyramidal algorithms. In this research, the coefficient matrix (simply called monomial form approach) will be used to model polynomial rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and NB1 surfaces. Some examples of the monomial forms for these surface modeling are illustrated in many aspects, e.g., construction, derivatives, model transformation, degree elevation and degress reduction.

Keywords: Monomial form, rectangular surfaces, CAGD curves, monomial matrix applications.

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