Search results for: Laplacian Pyramid

Authors: Ayşe Dilek Maden

Abstract:

For a given a simple connected graph, we present some new bounds via a new approach for a special topological index given by the sum of the real number power of the non-zero normalized Laplacian eigenvalues. To use this approach presents an advantage not only to derive old and new bounds on this topic but also gives an idea how some previous results in similar area can be developed.

Keywords: Degree Kirchhoff index, normalized Laplacian eigenvalue, spanning tree.

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Authors: Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

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As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Keywords: periodic solution, neutral Rayleigh equation, variable sign, Deviating argument, p-Laplacian, Mawhin’s continuation.

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Authors: Li Xiguang

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In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.

Keywords: p-Laplacian, cone, fixed point theorem, positive solution.

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Authors: Yanling Zhu, Kai Wang

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By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Mahdi Nouri

Abstract:

In this paper we introduce an efficient solution method for the Eigen-decomposition of bisymmetric and per symmetric matrices of symmetric structures. Here we decompose adjacency and Laplacian matrices of symmetric structures to submatrices with low dimension for fast and easy calculation of eigenvalues and eigenvectors. Examples are included to show the efficiency of the method.

Keywords: Graphs theory, Eigensolution, adjacency and Laplacian matrix, Canonical forms, bisymmetric, per symmetric.

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Authors: K. Idir, H. Merouani, Y. Tlili.

Abstract:

An effective method for the early detection of breast cancer is the mammographic screening. One of the most important signs of early breast cancer is the presence of microcalcifications. For the detection of microcalcification in a mammography image, we propose to conceive a multiagent system based on a dual irregular pyramid. An initial segmentation is obtained by an incremental approach; the result represents level zero of the pyramid. The edge information obtained by application of the Canny filter is taken into account to affine the segmentation. The edge-agents and region-agents cooper level by level of the pyramid by exploiting its various characteristics to provide the segmentation process convergence.

Keywords: Dual Pyramid, Image Segmentation, Multi-agent System, Region/Edge Cooperation.

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Authors: A. A. Abaker Omer, H. B. Mohamed Balh, W. Liu, A. Abas, J. Yu, S. Li, W. Ma, W. El Kolaly, Y. Y. Ahmed Abuker

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We have discovered an important technical solution that could make new approaches in the processing of wet silicon etching, especially in the production of photovoltaic cells. During its inferior light-trapping and structural properties, the inverted pyramid structure outperforms the conventional pyramid textures and black silicone. The traditional pyramid textures and black silicon can only be accomplished with more advanced lithography, laser processing, etc. Importantly, our data demonstrate the feasibility of an inverted pyramidal structure of silicon via one-step Cu-catalyzed chemical etching (CCCE) in Cu (NO₃)₂/HF/H₂O₂/H₂O solutions. The effects of etching time and reaction temperature on surface geometry and light trapping were systematically investigated. The conclusion shows that the inverted pyramid structure has ultra-low reflectivity of ~4.2% in the wavelength of 300~1000 nm; introduce of Cu particles can significantly accelerate the dissolution of the silicon wafer. The etching and the inverted pyramid structure formation mechanism are discussed. Inverted pyramid structure with outstanding anti-reflectivity includes useful applications throughout the manufacture of semi-conductive industry-compatible solar cells, and can have significant impacts on industry colleagues and populations.

Keywords: Cu-catalyzed chemical etching, inverted pyramid nanostructured, reflection, solar cells.

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Authors: Santhosh K. S. Annayappa, Nupur Pruthi

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The region of dentate nucleus is a common site for various pathologies like hematomas, tumours, etc. We aimed to study in detail the relationship of this region with the vermis, especially the pyramid using microscopic fibre dissection technique. To achieve this aim, 20 cerebellar hemispheres were studied from the 11 cerebellums. Dissection was performed using wooden spatulas and micro dissectors under a microscope following Klingler’s preservation technique. The relationship between the pyramid of vermis and the dentate nucleus was studied in detail. A similar relationship was studied on the MRI of randomly selected trigeminal neuralgia patients and correlated with anatomical findings. Results show the mean distance of the lateral margin of the dentate nucleus from the midline on anatomic specimens was 21.4 ± 1.8 mm (19-25 mm) and 23.4 ± 3.4 mm (15-29 mm) on right and left side, respectively. Similar measurements made on the MRI were 22.97 ± 2.0 mm (20.03-26.15 mm) on the right side and 23.98 ± 2.1 mm (21.47-27.67 mm) on the left side. The amount of white matter dissection required to reach the dentate nucleus at the pyramidal attachment area was 7.3 ± 1.0 mm (6-9 mm) on the right side and 6.8 ± 1.4 mm (5-10 mm) on the left side. It was concluded that the pyramid of vermis has a constant relationship with the dentate nucleus and can be used as an excellent landmark during surgery to localise the dentate nucleus on the suboccipital surface.

Keywords: Fiber dissection, micro neurosurgery, dentate nucleus of cerebellum, pyramid of vermis.

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Authors: Salam M. H. Kareem

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Instructional or teaching procedures and their proper sequence are essential for high-quality learning outcomes. These actions are the path that the teacher takes during the learning process after setting the learning objectives. Teachers and specialists in the education field should include teaching procedures with putting in place an effective mechanism for the procedure’s implementation to achieve a logical sequence with the desired output of overall education process. Determining the sequence of these actions may be a strategic process outlined by a strategic educational plan or drawn by teachers with a high level of experience, enabling them to determine those logical procedures. While specific actions may be necessary for a specific form, many Physical Education (PE) teachers can work out on various sports disciplines. This study was conducted to investigate the impact of using the teaching sequence of the teaching pyramid in raising the level of enjoyment in swimming classes. Four months later of teaching swimming skills to the control and experimental groups of the study, we figured that using the tools shown in the teaching pyramid with the experimental group led to statistically significant differences in the positive tendencies of students to participate in the swimming classes by using the traditional procedures of teaching and using of successive procedures in the teaching pyramid, and in favor of the teaching pyramid, The students are influenced by enhancing their tendency to participate in swimming classes when the teaching procedures followed are sensitive to individual differences and are based on the element of pleasure in learning, and less positive levels of the tendency of students when using traditional teaching procedures, by getting the level of skills' requirements higher and more difficult to perform. The level of positive tendencies of students when using successive procedures in the teaching pyramid was increased, by getting the level of skills' requirements higher and more difficult to perform, because of the high level of motivation and the desire to challenge the self-provided by the teaching pyramid.

Keywords: Physical education, swimming classes, teaching process, teaching pyramid.

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Authors: Irfah Najihah Basir Malan, Norhana Salamudin, Noryati Ahmad

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Corporate ownership structure is an important factor influencing firm performance. This study aims to answer the question whether pyramid structure has negative effect on firm value. This study is important because the ownership of public listed companies in Malaysia is highly concentrated. The concentrated ownership such as Malaysia, agency conflict is prevalent between controlling shareholders and minority shareholders. Accordingly, the dominant role of shareholders in firms allows the controlling shareholders (including managers) to expropriate the interest of the minority shareholders for their own private advantage. This research is conducted on pyramidal firms in Malaysia. Applying the Attig Model as the underlying statistical test, it is found that firm value is negatively related to pyramid ownership of Malaysian public listed firms due to the mismatch between cash flow rights and control rights. Future research needs to focus on identifying the heterogeneous factors that improve the generalizability of research.

Keywords: Pyramid structure, Cash flow right, Control right, Firm value, Attig model.

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Authors: Mohamed El Aroussi, Mohammed El Hassouni, Sanaa Ghouzali, Mohammed Rziza, Driss Aboutajdine

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In this paper the problem of face recognition under variable illumination conditions is considered. Most of the works in the literature exhibit good performance under strictly controlled acquisition conditions, but the performance drastically drop when changes in pose and illumination occur, so that recently number of approaches have been proposed to deal with such variability. The aim of this work is to introduce an efficient local appearance feature extraction method based steerable pyramid (SP) for face recognition. Local information is extracted from SP sub-bands using LBP(Local binary Pattern). The underlying statistics allow us to reduce the required amount of data to be stored. The experiments carried out on different face databases confirm the effectiveness of the proposed approach.

Keywords: Face recognition (FR), Steerable pyramid (SP), localBinary Pattern (LBP).

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Authors: Elnaz Lashgari, Emel Demircan

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Electromyography (EMG) is one of the most important interfaces between humans and robots for rehabilitation. Decoding this signal helps to recognize muscle activation and converts it into smooth motion for the robots. Detecting each muscle’s pattern during walking and running is vital for improving the quality of a patient’s life. In this study, EMG data from 10 muscles in 10 subjects at 4 different speeds were analyzed. EMG signals are nonlinear with high dimensionality. To deal with this challenge, we extracted some features in time-frequency domain and used manifold learning and Laplacian Eigenmaps algorithm to find the intrinsic features that represent data in low-dimensional space. We then used the Bayesian classifier to identify various patterns of EMG signals for different muscles across a range of running speeds. The best result for vastus medialis muscle corresponds to 97.87±0.69 for sensitivity and 88.37±0.79 for specificity with 97.07±0.29 accuracy using Bayesian classifier. The results of this study provide important insight into human movement and its application for robotics research.

Keywords: Electrocardiogram, manifold learning, Laplacian Eigenmaps, running pattern.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

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The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Jing Jia, Shanqing Huang, Fang Liu, Qiang Ren, Gui Li, Mengyun Cheng, Chufeng Jin, Yican Wu

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Medical image registration is the key technology in image guided radiation therapy (IGRT) systems. On the basis of the previous work on our IGRT prototype with a biorthogonal x-ray imaging system, we described a method focused on the 2D/2D rigid-body registration using multiresolution pyramid based mutual information in this paper. Three key steps were involved in the method ： firstly, four 2D images were obtained including two x-ray projection images and two digital reconstructed radiographies（DRRs ） as the input for the registration ； Secondly, each pair of the corresponding x-ray image and DRR image were matched using multiresolution pyramid based mutual information under the ITK registration framework ； Thirdly, we got the final couch offset through a coordinate transformation by calculating the translations acquired from the two pairs of the images. A simulation example of a parotid gland tumor case and a clinical example of an anthropomorphic head phantom were employed in the verification tests. In addition, the influence of different CT slice thickness were tested. The simulation results showed that the positioning errors were 0.068±0.070, 0.072±0.098, 0.154±0.176mm along three axes which were lateral, longitudinal and vertical. The clinical test indicated that the positioning errors of the planned isocenter were 0.066, 0.07, 2.06mm on average with a CT slice thickness of 2.5mm. It can be concluded that our method with its verified accuracy and robustness can be effectively used in IGRT systems for patient setup.

Keywords: 2D/2D registration, image guided radiation therapy, multi resolution pyramid, mutual information.

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Authors: Suman Senapati, Goutam Saha

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This work presents a fusion of Log Gabor Wavelet (LGW) and Maximum a Posteriori (MAP) estimator as a speech enhancement tool for acoustical background noise reduction. The probability density function (pdf) of the speech spectral amplitude is approximated by a Generalized Laplacian Distribution (GLD). Compared to earlier estimators the proposed method estimates the underlying statistical model more accurately by appropriately choosing the model parameters of GLD. Experimental results show that the proposed estimator yields a higher improvement in Segmental Signal-to-Noise Ratio (S-SNR) and lower Log-Spectral Distortion (LSD) in two different noisy environments compared to other estimators.

Keywords: Speech Enhancement, Generalized Laplacian Distribution, Log Gabor Wavelet, Bayesian MAP Marginal Estimator.

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Authors: S. Esakkirajan, T. Veerakumar, V. Senthil Murugan, R. Sudhakar

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This paper presents a new fingerprint coding technique based on contourlet transform and multistage vector quantization. Wavelets have shown their ability in representing natural images that contain smooth areas separated with edges. However, wavelets cannot efficiently take advantage of the fact that the edges usually found in fingerprints are smooth curves. This issue is addressed by directional transforms, known as contourlets, which have the property of preserving edges. The contourlet transform is a new extension to the wavelet transform in two dimensions using nonseparable and directional filter banks. The computation and storage requirements are the major difficulty in implementing a vector quantizer. In the full-search algorithm, the computation and storage complexity is an exponential function of the number of bits used in quantizing each frame of spectral information. The storage requirement in multistage vector quantization is less when compared to full search vector quantization. The coefficients of contourlet transform are quantized by multistage vector quantization. The quantized coefficients are encoded by Huffman coding. The results obtained are tabulated and compared with the existing wavelet based ones.

Keywords: Contourlet Transform, Directional Filter bank, Laplacian Pyramid, Multistage Vector Quantization

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Authors: Yasuomi D. Sato, Yasutaka Kuriya

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We here propose improved version of elastic graph matching (EGM) as a face detector, called the multi-scale EGM (MS-EGM). In this improvement, Gabor wavelet-based pyramid reduces computational complexity for the feature representation often used in the conventional EGM, but preserving a critical amount of information about an image. The MS-EGM gives us higher detection performance than Viola-Jones object detection algorithm of the AdaBoost Haar-like feature cascade. We also show rapid detection speeds of the MS-EGM, comparable to the Viola-Jones method. We find fruitful benefits in the MS-EGM, in terms of topological feature representation for a face.

Keywords: Face detection, Gabor wavelet based pyramid, elastic graph matching, topological preservation, redundancy of computational complexity.

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Authors: S.Esakkirajan, T. Veerakumar, V. Senthil Murugan, P.Navaneethan

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In this paper, image compression using hybrid vector quantization scheme such as Multistage Vector Quantization (MSVQ) and Pyramid Vector Quantization (PVQ) are introduced. A combined MSVQ and PVQ are utilized to take advantages provided by both of them. In the wavelet decomposition of the image, most of the information often resides in the lowest frequency subband. MSVQ is applied to significant low frequency coefficients. PVQ is utilized to quantize the coefficients of other high frequency subbands. The wavelet coefficients are derived using lifting scheme. The main aim of the proposed scheme is to achieve high compression ratio without much compromise in the image quality. The results are compared with the existing image compression scheme using MSVQ.

Keywords: Lifting Scheme, Multistage Vector Quantization and Pyramid Vector Quantization.

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Authors: Konghe Xie

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Two consensus problems are considered in this paper. One is the consensus of linear multi-agent systems with weakly connected directed communication topology. The other is the consensus of nonlinear multi-agent systems with strongly connected directed communication topology. For the first problem, a simplified consensus protocol is designed: Each child agent can only communicate with one of its neighbors. That is, the real communication topology is a directed spanning tree of the original communication topology and without any cycles. Then, the necessary and sufficient condition is put forward to the multi-agent systems can be reached consensus. It is worth noting that the given conditions do not need any eigenvalue of the corresponding Laplacian matrix of the original directed communication network. For the second problem, the feedback gain is designed in the nonlinear consensus protocol. Then, the sufficient condition is proposed such that the systems can be achieved consensus. Besides, the consensus interval is introduced and analyzed to solve the consensus problem. Finally, two numerical simulations are included to verify the theoretical analysis.

Keywords: Consensus, multi-agent systems, directed spanning tree, the Laplacian matrix.

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Authors: Omer Cahana, Maya Herman, Ofer Levi

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Magnetic Resonance Imaging (MRI) is a lengthy medical scan that stems from a long acquisition time. Its length is mainly due to the traditional sampling theorem, which defines a lower boundary for sampling. However, it is still possible to accelerate the scan by using a different approach such as Compress Sensing (CS) or Parallel Imaging (PI). These two complementary methods can be combined to achieve a faster scan with high-fidelity imaging. To achieve that, two conditions must be satisfied: i) the signal must be sparse under a known transform domain, and ii) the sampling method must be incoherent. In addition, a nonlinear reconstruction algorithm must be applied to recover the signal. While the rapid advances in Deep Learning (DL) have had tremendous successes in various computer vision tasks, the field of MRI reconstruction is still in its early stages. In this paper, we present an end-to-end method for MRI reconstruction from k-space to image. Our method contains two parts. The first is sensitivity map estimation (SME), which is a small yet effective network that can easily be extended to a variable number of coils. The second is reconstruction, which is a top-down architecture with lateral connections developed for building high-level refinement at all scales. Our method holds the state-of-art fastMRI benchmark, which is the largest, most diverse benchmark for MRI reconstruction.

Keywords: Accelerate MRI scans, image reconstruction, pyramid network, deep learning.

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Authors: Muhammad Azam, Micheal Olaolu Arowolo, Fei He, Mihail Popescu, Dong Xu

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The number of biological papers is growing quickly, which means that the number of biological pathway figures in those papers is also increasing quickly. Each pathway figure shows extensive biological information, like the names of genes and how the genes are related. However, manually annotating pathway figures takes a lot of time and work. Even though using advanced image understanding models could speed up the process of curation, these models still need to be made more accurate. To improve gene name recognition from pathway figures, we applied a Siamese network to map image segments to a library of pictures containing known genes in a similar way to person recognition from photos in many photo applications. We used a triple loss function and a triplet spatial pyramid pooling network by combining the triplet convolution neural network and the spatial pyramid pooling (TSPP-Net). We compared VGG19 and VGG16 as the Siamese network model. VGG16 achieved better performance with an accuracy of 93%, which is much higher than Optical Character Recognition (OCR) results.

Keywords: Biological pathway, image understanding, gene name recognition, object detection, Siamese network, Visual Geometry Group.

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

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Authors: Jooho Hwang, Chang-Kyu Song, Chun-Hong Park

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This paper describes a method to measure and compensate a 4 axes ultra-precision machine tool that generates micro patterns on the large surfaces. The grooving machine is usually used for making a micro mold for many electrical parts such as a light guide plate for LCD and fuel cells. The ultra precision machine tool has three linear axes and one rotational table. Shaping is usually used to generate micro patterns. In the case of 50 μm pitch and 25 μm height pyramid pattern machining with a 90° wedge angle bite, one of linear axis is used for long stroke motion for high cutting speed and other linear axis are used for feeding. The triangular patterns can be generated with many times of long stroke of one axis. Then 90° rotation of work piece is needed to make pyramid patterns with superposition of machined two triangular patterns. To make a two dimensional positioning error, straightness of two axes in out of plane, squareness between the each axis are important. Positioning errors, straightness and squarness were measured by laser interferometer system. Those were compensated and confirmed by ISO230-6. One of difficult problem to measure the error motions is squareness or parallelism of axis between the rotational table and linear axis. It was investigated by simultaneous moving of rotary table and XY axes. This compensation method is introduced in this paper.

Keywords: Ultra-precision machine tool, muti-axis errors, squraness, positioning errors.

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Authors: Abhishek Neogi, Jayesh Verma, Pinaki Pratim Acharjya

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Image segmentation and edge detection is a fundamental section in image processing. In case of noisy images Edge Detection is very less effective if we use conventional Spatial Filters like Sobel, Prewitt, LOG, Laplacian etc. To overcome this problem we have proposed the use of Stochastic Gradient Mask instead of Spatial Filters for generating gradient images. The present study has shown that the resultant images obtained by applying Stochastic Gradient Masks appear to be much clearer and sharper as per Edge detection is considered.

Keywords: Image segmentation, edge Detection, noisy images, spatialfilters, stochastic gradient kernel.

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Authors: Kiyoshi Sawada, Takashi Mitsuishi

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This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth N* = H is obtained by minimizing the total path length which is the sum of lengths of shortest paths between every pair of all nodes.

Keywords: complete K-ary tree, organization structure, shortest path

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: Soham De, Nupur Biswas, Abhijit Sanyal, Pulak Ray, Alokmay Datta

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Particle detection in very noisy and low contrast images is an active field of research in image processing. In this article, a method is proposed for the efficient detection and sizing of subsurface spherical particles, which is used for the processing of softly fused Au nanoparticles. Transmission Electron Microscopy is used for imaging the nanoparticles, and the proposed algorithm has been tested with the two-dimensional projected TEM images obtained. Results are compared with the data obtained by transmission optical spectroscopy, as well as with conventional circular object detection algorithms.

Keywords: Transmission Electron Microscopy, Circular Hough Transform, Au Nanoparticles, Median Filter, Laplacian Sharpening Filter, Canny Edge Detection

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Authors: Le Kang

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According to the nature of the university, as a free and responsible academic community, USR is based on a different foundation —academic responsibility, so the Pyramid and the IC Model of CSR could not fully explain the most distinguished feature of USR. This paper sought to put forward a new model— Ferris Wheel Model, to illustrate the nature of USR and the process of achievement. The Ferris Wheel Model of USR shows the university creates a balanced, fairness and neutrality systemic structure to afford social responsibilities; that makes the organization could obtain a synergistic effect to achieve more extensive interests of stakeholders and wider social responsibilities.

Keywords: USR, Achievement model, Ferris wheel model.

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Authors: V. Geetha, K. S. Aprameya

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Early diagnosis of dental caries is essential for maintaining dental health. In this paper, method for diagnosis of dental caries is proposed using Laplacian filter, adaptive thresholding, texture analysis and Support Vector Machine (SVM) classifier. Analysis of the proposed method is compared with Otsu thresholding, watershed segmentation and active contouring method. Adaptive thresholding has comparatively better performance with 96.9% accuracy and 96.1% precision. The results are validated using statistical method, two-way ANOVA, at significant level of 5%, that shows the interaction of proposed method on performance parameter measures are significant. Hence the proposed technique could be used for detection of dental caries in automated computer assisted diagnosis system.

Keywords: Computer assisted diagnosis, dental caries, dental radiography, image segmentation.

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Authors: Do Phuc, Nguyen Thi Kim Phung

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In this paper, we represent protein structure by using graph. A protein structure database will become a graph database. Each graph is represented by a spectral vector. We use Jacobi rotation algorithm to calculate the eigenvalues of the normalized Laplacian representation of adjacency matrix of graph. To measure the similarity between two graphs, we calculate the Euclidean distance between two graph spectral vectors. To cluster the graphs, we use M-tree with the Euclidean distance to cluster spectral vectors. Besides, M-tree can be used for graph searching in graph database. Our proposal method was tested with graph database of 100 graphs representing 100 protein structures downloaded from Protein Data Bank (PDB) and we compare the result with the SCOP hierarchical structure.

Keywords: Eigenvalues, m-tree, graph database, protein structure, spectra graph theory.

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