Search results for: Fast Haar Transform

Authors: Pyung-Soo Kim, Jeong Hun Choi

Abstract:

In this paper, to resolve the problem of existing schemes, an alternative fast handover Proxy Mobile IPv6 (PMIPv6) scheme using the IEEE 802.21 Media Independent Handover (MIH) function is proposed for heterogeneous wireless networks. The proposed scheme comes to support fast handover for the mobile node (MN) irrespective of the presence or absence of MIH functionality as well as L3 mobility functionality, whereas the MN in existing schemes has to implement MIH functionality. That is, the proposed scheme does not require the MN to be involved in MIH related signaling required for handover procedure. The base station (BS) with MIH functionality performs handover on behalf of the MN. Therefore, the proposed scheme can reduce burden and power consumption of MNs with limited resource and battery power since MNs are not required to be involved for the handover procedure. In addition, the proposed scheme can reduce considerably traffic overhead over wireless links between MN and BS since signaling messages are reduced.

Keywords: Fast handover, PMIPv6, MIH.

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Authors: Guo Xiuhua, Sun Tao, Wu Haifeng, He Wen, Liang Zhigang, Zhang Mengxia, Guo Aimin, Wang Wei

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Purpose: To explore the use of Curvelet transform to extract texture features of pulmonary nodules in CT image and support vector machine to establish prediction model of small solitary pulmonary nodules in order to promote the ratio of detection and diagnosis of early-stage lung cancer. Methods: 2461 benign or malignant small solitary pulmonary nodules in CT image from 129 patients were collected. Fourteen Curvelet transform textural features were as parameters to establish support vector machine prediction model. Results: Compared with other methods, using 252 texture features as parameters to establish prediction model is more proper. And the classification consistency, sensitivity and specificity for the model are 81.5%, 93.8% and 38.0% respectively. Conclusion: Based on texture features extracted from Curvelet transform, support vector machine prediction model is sensitive to lung cancer, which can promote the rate of diagnosis for early-stage lung cancer to some extent.

Keywords: CT image, Curvelet transform, Small pulmonary nodules, Support vector machines, Texture extraction.

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Authors: Cheng-Ying Lo

Abstract:

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Keywords: Differential transform, hyperbolic heat transfer, thin film, ultrashort-pulsed laser.

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Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine

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In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.

Keywords: Color image, grayscale image, singular values decomposition, lifting wavelet transform, image watermarking, watermark, secure.

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Authors: Kamrul Hasan Talukder, Koichi Harada

Abstract:

The scientific community has invested a great deal of effort in the fields of discrete wavelet transform in the last few decades. Discrete wavelet transform (DWT) associated with the vector quantization has been proved to be a very useful tool for the compression of image. However, the DWT is very computationally intensive process requiring innovative and computationally efficient method to obtain the image compression. The concurrent transformation of the image can be an important solution to this problem. This paper proposes a model of concurrent DWT for image compression. Additionally, the formal verification of the model has also been performed. Here the Symbolic Model Verifier (SMV) has been used as the formal verification tool. The system has been modeled in SMV and some properties have been verified formally.

Keywords: Computation Tree Logic, Discrete WaveletTransform, Formal Verification, Image Compression, Symbolic Model Verifier.

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Authors: V. Swarnalatha, A. V. Narasimha Rao, P. Pal

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The present research reports the investigation of fast etching of silicon for the fabrication of microelectromechanical systems (MEMS) structures using silicon wet bulk micromachining. Low concentration tetramethyl-ammonium hydroxide (TMAH) and hydroxylamine (NH₂OH) are used as main etchant and additive, respectively. The concentration of NH₂OH is varied to optimize the composition to achieve best etching characteristics such as high etch rate, significantly high undercutting at convex corner for the fast release of the microstructures from the substrate, and improved etched surface morphology. These etching characteristics are studied on Si{100} and Si{110} wafers as they are most widely used in the fabrication of MEMS structures as wells diode, transistors and integrated circuits.

Keywords: KOH, MEMS, micromachining, silicon, TMAH, wet anisotropic etching.

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Authors: Nedeljko Cvejic, Tapio Sepp

Abstract:

A study of the obtainable watermark data rate for information hiding algorithms is presented in this paper. As the perceptual entropy for wideband monophonic audio signals is in the range of four to five bits per sample, a significant amount of additional information can be inserted into signal without causing any perceptual distortion. Experimental results showed that transform domain watermark embedding outperforms considerably watermark embedding in time domain and that signal decompositions with a high gain of transform coding, like the wavelet transform, are the most suitable for high data rate information hiding. Keywords?Digital watermarking, information hiding, audio watermarking, watermark data rate.

Keywords: Digital watermarking, information hiding, audio watermarking, watermark data rate.

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Authors: Mohammed Amroune, Hadi Sebaa, Tarek Bouktir

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Reactive power limit of power system is one of the major causes of voltage instability. The only way to save the system from voltage instability is to reduce the reactive power load or add additional reactive power to reaching the point of voltage collapse. In recent times, the application of FACTS devices is a very effective solution to prevent voltage instability due to their fast and very flexible control. In this paper, voltage stability assessment with SVC and TCSC devices is investigated and compared in the modified IEEE 30-bus test system. The fast voltage stability indicator (FVSI) is used to identify weakest bus and to assess the voltage stability of power system.

Keywords: SVC, TCSC, Voltage stability, Fast Voltage Stability Index (FVSI), Reactive power.

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Authors: Driss Guerchi, Fatiha Djebbar

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In this work we introduce an efficient method to limit the impact of the hiding process on the quality of the cover speech. Vector quantization of the speech spectral information reduces drastically the number of the secret speech parameters to be embedded in the cover signal. Compared to scalar hiding, vector quantization hiding technique provides a stego signal that is indistinguishable from the cover speech. The objective and subjective performance measures reveal that the current hiding technique attracts no suspicion about the presence of the secret message in the stego speech, while being able to recover an intelligible copy of the secret message at the receiver side.

Keywords: Speech steganography, LSF vector quantization, fast Fourier transform

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Authors: Madina Hamiane, May Hashim Ali

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This paper presents the processing and analysis of ECG signals. The study is based on wavelet transform and uses exclusively the MATLAB environment. This study includes removing Baseline wander and further de-noising through wavelet transform and metrics such as signal-to noise ratio (SNR), Peak signal-to-noise ratio (PSNR) and the mean squared error (MSE) are used to assess the efficiency of the de-noising techniques. Feature extraction is subsequently performed whereby signal features such as heart rate, rise and fall levels are extracted and the QRS complex was detected which helped in classifying the ECG signal. The classification is the last step in the analysis of the ECG signals and it is shown that these are successfully classified as Normal rhythm or Abnormal rhythm.  The final result proved the adequacy of using wavelet transform for the analysis of ECG signals.

Keywords: ECG Signal, QRS detection, thresholding, wavelet decomposition, feature extraction.

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Authors: Hee-Choul Kwon, Heeyong Kwon

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Image rotation is one of main pre-processing steps for image processing or image pattern recognition. It is implemented with a rotation matrix multiplication. It requires a lot of floating point arithmetic operations and trigonometric calculations, so it takes a long time to execute. Therefore, there has been a need for a high speed image rotation algorithm without two major time-consuming operations. However, the rotated image has a drawback, i.e. distortions. We solved the problem using an augmented two-step shear transform. We compare the presented algorithm with the conventional rotation with images of various sizes. Experimental results show that the presented algorithm is superior to the conventional rotation one.

Keywords: High speed rotation operation, image rotation, transform matrix, image processing, pattern recognition.

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Authors: A. Izadbakhsh, M. M. Fateh, M. A. Sadrnia

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A multivariable discontinuous feedback linearization approach is proposed to position control of an electrically driven fast robot manipulator. A desired performance is achieved by selecting a useful controller and suitable sampling rate and considering saturation for actuators. There is a high flexibility to apply the proposed control approach on different electrically driven manipulators. The control approach can guarantee the stability and satisfactory tracking performance. A PUMA 560 robot driven by geared permanent magnet dc motors is simulated. The simulation results show a desired performance for control system under technical specifications.

Keywords: Fast robot, feedback linearization, multivariabledigital control, PUMA560.

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Authors: Praseeda Lekshmi.V, Dr.M.Sasikumar

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Facial expression analysis is rapidly becoming an area of intense interest in computer science and human-computer interaction design communities. The most expressive way humans display emotions is through facial expressions. In this paper we present a method to analyze facial expression from images by applying Gabor wavelet transform (GWT) and Discrete Cosine Transform (DCT) on face images. Radial Basis Function (RBF) Network is used to classify the facial expressions. As a second stage, the images are preprocessed to enhance the edge details and non uniform down sampling is done to reduce the computational complexity and processing time. Our method reliably works even with faces, which carry heavy expressions.

Keywords: Face Expression, Radial Basis Function, GaborWavelet Transform, Human Computer Interaction.

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: Yu-Wei Chen, Li-Ren Han

Abstract:

In this paper, we employ the approach of linear programming to propose a new interactive broadcast method. In our method, a film S is divided into n equal parts and broadcast via k channels. The user simultaneously downloads these segments from k channels into the user-s set-top-box (STB) and plays them in order. Our method assumes that the initial p segments will not have fast-forwarding capabilities. Every time the user wants to initiate d times fast-forwarding, according to our broadcasting strategy, the necessary segments already saved in the user-s STB or are just download on time for playing. The proposed broadcasting strategy not only allows the user to pause and rewind, but also to fast-forward.

Keywords: Broadcasting, Near Video-on-Demand (VOD), Linear Programming, Video-Cassette-Recorder (VCR) Functions, Waiting Time.

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Authors: Sherif. S. Nafee, Ameer. K. Al-Ramady, Salem. A. Shaheen

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The analytical prediction of the decay heat results from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team from King Abdulaziz University (KAU), Saudi Arabia, and supervised by Argonne National Laboratory (ANL) has collaborated with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic comparisons with the measurements reported by the University of Tokyo, in YAYOI reactor.

Keywords: Decay heat, fast neutron fission, and Numerical Solution of Linear Differential Equations.

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Authors: H. Kelkoul, Y. Zaz

Abstract:

Nowadays, the vigorous popularity of video processing techniques has resulted in an explosive growth of multimedia data illegal use. So, watermarking security has received much more attention. The purpose of this paper is to explore some watermarking techniques in order to observe their specificities and select the finest methods to apply in digital cinema domain against movie piracy by creating an invisible watermark that includes the date, time and the place where the hacking was done. We have studied three principal watermarking techniques in the frequency domain: Spread spectrum, Wavelet transform domain and finally the digital cinema watermarking transform domain. In this paper, a detailed technique is presented where embedding is performed using direct sequence spread spectrum technique in DWT transform domain. Experiment results shows that the algorithm provides high robustness and good imperceptibility.

Keywords: Digital cinema, watermarking, wavelet, spread spectrum, JPEG2000.

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Authors: Chun-Yao Lee, Yao-chen Lee

Abstract:

This paper describes a method of signal process applied on an end effects of Hilbert-Huang transform (HHT) to provide an improvement in the reality of spectrum. The method is based on back-propagation network (BPN). To improve the effect, the end extension of the original signal is obtained by back-propagation network. A full waveform including origin and its extension is decomposed by using empirical mode decomposition (EMD) to obtain intrinsic mode functions (IMFs) of the waveform. Then, the Hilbert transform (HT) is applied to the IMFs to obtain the Hilbert spectrum of the waveform. As a result, the method is superiority of the processing of end effect of HHT to obtain the real frequency spectrum of signals.

Keywords: Neural network, back-propagation network, Hilbert-Huang transform

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Authors: Rafiullah Chamlawi, Asifullah Khan, Adnan Idris, Zahid Munir

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Authentication of multimedia contents has gained much attention in recent times. In this paper, we propose a secure semi-fragile watermarking, with a choice of two watermarks to be embedded. This technique operates in integer wavelet domain and makes use of semi fragile watermarks for achieving better robustness. A self-recovering algorithm is employed, that hides the image digest into some Wavelet subbands to detect possible malevolent object manipulation undergone by the image (object replacing and/or deletion). The Semi-fragility makes the scheme tolerant for JPEG lossy compression as low as quality of 70%, and locate the tempered area accurately. In addition, the system ensures more security because the embedded watermarks are protected with private keys. The computational complexity is reduced using parameterized integer wavelet transform. Experimental results show that the proposed scheme guarantees the safety of watermark, image recovery and location of the tempered area accurately.

Keywords: Integer Wavelet Transform (IWT), Discrete Cosine Transform (DCT), JPEG Compression, Authentication and Self- Recovery.

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Authors: P. S. Gomathi, B. Kalaavathi

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The process in which the complementary information from multiple images is integrated to provide composite image that contains more information than the original input images is called image fusion. Medical image fusion provides useful information from multimodality medical images that provides additional information to the doctor for diagnosis of diseases in a better way. This paper represents the wavelet based medical image fusion algorithm on different multimodality medical images. In order to fuse the medical images, images are decomposed using Redundant Wavelet Transform (RWT). The high frequency coefficients are convolved with morphological operator followed by the maximum-selection (MS) rule. The low frequency coefficients are processed by MS rule. The reconstructed image is obtained by inverse RWT. The quantitative measures which includes Mean, Standard Deviation, Average Gradient, Spatial frequency, Edge based Similarity Measures are considered for evaluating the fused images. The performance of this proposed method is compared with Pixel averaging, PCA, and DWT fusion methods. When compared with conventional methods, the proposed framework provides better performance for analysis of multimodality medical images.

Keywords: Discrete Wavelet Transform (DWT), Image Fusion, Morphological Processing, Redundant Wavelet Transform (RWT).

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Authors: Shang-Lin Hsieh, Lung-Yao Hsu, I-Ju Tsai

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This paper proposes a copyright protection scheme for color images using secret sharing and wavelet transform. The scheme contains two phases: the share image generation phase and the watermark retrieval phase. In the generation phase, the proposed scheme first converts the image into the YCbCr color space and creates a special sampling plane from the color space. Next, the scheme extracts the features from the sampling plane using the discrete wavelet transform. Then, the scheme employs the features and the watermark to generate a principal share image. In the retrieval phase, an expanded watermark is first reconstructed using the features of the suspect image and the principal share image. Next, the scheme reduces the additional noise to obtain the recovered watermark, which is then verified against the original watermark to examine the copyright. The experimental results show that the proposed scheme can resist several attacks such as JPEG compression, blurring, sharpening, noise addition, and cropping. The accuracy rates are all higher than 97%.

Keywords: Color image, copyright protection, discrete wavelet transform, secret sharing, watermarking.

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Authors: Ken-Lin Chang, Jun-Hong Lin, Shui-Tein Chen

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In this study, we used a two-stage process and potassium hydroxide (KOH) to transform waste biomass (rice straw) into activated carbon and then evaluated the adsorption capacity of the waste for removing carbofuran from an aqueous solution. Activated carbon was fast and effective for the removal of carbofuran because of its high surface area. The native and carbofuran-loaded adsorbents were characterized by elemental analysis. Different adsorption parameters, such as the initial carbofuran concentration, contact time, temperature and pH for carbofuran adsorption, were studied using a batch system. This study demonstrates that rice straw can be very effective in the adsorption of carbofuran from bodies of water.

Keywords: Rice straw, Carbofuran, Activated carbon

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Authors: Sunil Dehipawala, Aregama Sirisumana, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden T. Cheung

Abstract:

The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, Fourier Transform, metalloproteins, XANES.

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Authors: Liu Dan, Wang Xue, Wang Guiqin, Qian Zhihong

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The burst noise is a kind of noises that are destructive and frequently found in semiconductor devices and ICs, yet detecting and removing the noise has proved challenging for IC designers or users. According to the properties of burst noise, a methodological approach is presented (proposed) in the paper, by which the burst noise can be analysed and detected in time domain. In this paper, principles and properties of burst noise are expounded first, Afterwards, feasibility (viable) of burst noise detection by means of wavelet transform in the time domain is corroborated in the paper, and the multi-resolution characters of Gaussian noise, burst noise and blurred burst noise are discussed in details by computer emulation. Furthermore, the practical method to decide parameters of wavelet transform is acquired through a great deal of experiment and data statistics. The methodology may yield an expectation in a wide variety of applications.

Keywords: Burst noise, detection, wavelet transform

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Authors: Michael Zimba

Abstract:

A duplicated image region may be subjected to a number of attacks such as noise addition, compression, reflection, rotation, and scaling with the intention of either merely mating it to its targeted neighborhood or preventing its detection. In this paper, we present an effective and robust method of detecting duplicated regions inclusive of those affected by the various attacks. In order to reduce the dimension of the image, the proposed algorithm firstly performs discrete wavelet transform, DWT, of a suspicious image. However, unlike most existing copy move image forgery (CMIF) detection algorithms operating in the DWT domain which extract only the low frequency subband of the DWT of the suspicious image thereby leaving valuable information in the other three subbands, the proposed algorithm simultaneously extracts features from all the four subbands. The extracted features are not only more accurate representation of image regions but also robust to additive noise, JPEG compression, and affine transformation. Furthermore, principal component analysis-eigenvalue decomposition, PCA-EVD, is applied to reduce the dimension of the features. The extracted features are then sorted using the more computationally efficient Radix Sort algorithm. Finally, same affine transformation selection, SATS, a duplication verification method, is applied to detect duplicated regions. The proposed algorithm is not only fast but also more robust to attacks compared to the related CMIF detection algorithms. The experimental results show high detection rates. 

Keywords: Affine Transformation, Discrete Wavelet Transform, Radix Sort, SATS.

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: Yu Bin, Zhang Yan

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The prediction of transmembrane helical segments (TMHs) in membrane proteins is an important field in the bioinformatics research. In this paper, a new method based on discrete wavelet transform (DWT) has been developed to predict the number and location of TMHs in membrane proteins. PDB coded as 1KQG was chosen as an example to describe the prediction of the number and location of TMHs in membrane proteins by using this method. To access the effect of the method, 80 proteins with known 3D-structure from Mptopo database are chosen at random as the test objects (including 325 TMHs), 308 of which can be predicted accurately, the average predicted accuracy is 96.3%. In addition, the above 80 membrane proteins are divided into 13 groups according to their function and type. In particular, the results of the prediction of TMHs of the 13 groups are satisfying.

Keywords: discrete wavelet transform, hydrophobicity, membrane protein, transmembrane helical segments

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Moneeb Gohar, Seok Joo Koh, Tae-Won Um, Hyun-Woo Lee

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This paper proposes a fast tree join scheme to provide seamless multicast handover in the mobile networks based on the Fast Mobile IPv6 (FMIPv6). In the existing FMIPv6-based multicast handover scheme, the bi-directional tunnelling or the remote subscription is employed with the packet forwarding from the previous access router (AR) to the new AR. In general, the remote subscription approach is preferred to the bi-directional tunnelling one, since in the remote subscription scheme we can exploit an optimized multicast path from a multicast source to many mobile receivers. However, in the remote subscription scheme, if the tree joining operation takes a long time, the amount of data packets to be forwarded and buffered for multicast handover will increase, and thus the corresponding buffer may overflow, which results in severe packet losses. In order to reduce these costs associated with packet forwarding and buffering, this paper proposes the fast join to multicast tree, in which the new AR will join the multicast tree as fast as possible, so that the new multicast data packets can also arrive at the new AR, by which the packet forwarding and buffering costs can be reduced. From numerical analysis, it is shown that the proposed scheme can give better performance than the existing FMIPv6-based multicast handover schemes in terms of the multicast packet delivery costs.

Keywords: Mobile Multicast, FMIPv6, Seamless Handover, Fast Tree Join.

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Authors: Zahra Yaghoubi, Nooshin Bigdeli, Karim Afshar

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This paper at first presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. After that a drive-response synchronization method with linear output error feedback is presented for “generalized projective synchronization" for a class of fractional-order chaotic systems via a scalar transmitted signal. Genesio_Tesi and Duffing systems are used to illustrate the effectiveness of the proposed synchronization method.

Keywords: Generalized projective synchronization; Fractionalorder;Chaos; Caputo derivative; Differential transform method

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