Search results for: Adomian’s Decomposition Method

Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

Abstract:

A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: R. Sadykova

Abstract:

This article analyses the peculiarities of Japan’s policy toward the countries of Central Asia. The increasing role of Central Asia in the system of international relations engendered an objective need for understanding of the policy of leading states, including Japan, in the region in the twenty-first century. The purpose of the study is to investigate the peculiarities of the formation and development of Japan policy in Central Asia and to identify the problems and prospects of Japan’s policy toward the countries of the region on the basis of experts’ opinions. In this article, the method of analysis of the situation and a systematic method were used. Prognostic methods, the collective expert assessment and scenarios were used in the study to determine the prospects of Japan’s policy toward the countries of Central Asia.

Keywords: Japan, Central Asia, the Eurasian concept, ‘Central Asia plus Japan’ Dialogue.

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Authors: Chintanu K. Sarmah, Sandhya Samarasinghe, Don Kulasiri, Daniel Catchpoole

Abstract:

Gene expression profiling is rapidly evolving into a powerful technique for investigating tumor malignancies. The researchers are overwhelmed with the microarray-based platforms and methods that confer them the freedom to conduct large-scale gene expression profiling measurements. Simultaneously, investigations into cross-platform integration methods have started gaining momentum due to their underlying potential to help comprehend a myriad of broad biological issues in tumor diagnosis, prognosis, and therapy. However, comparing results from different platforms remains to be a challenging task as various inherent technical differences exist between the microarray platforms. In this paper, we explain a simple ratio-transformation method, which can provide some common ground for cDNA and Affymetrix platform towards cross-platform integration. The method is based on the characteristic data attributes of Affymetrix- and cDNA- platform. In the work, we considered seven childhood leukemia patients and their gene expression levels in either platform. With a dataset of 822 differentially expressed genes from both these platforms, we carried out a specific ratio-treatment to Affymetrix data, which subsequently showed an improvement in the relationship with the cDNA data.

Keywords: Gene expression profiling, microarray, cDNA, Affymetrix, childhood leukaemia.

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Authors: R. Xu, X. Zhao, X. Li, C. Kwan, C.-I Chang

Abstract:

An image texture analysis and target recognition approach of using an improved image texture feature coding method (TFCM) and Support Vector Machine (SVM) for target detection is presented. With our proposed target detection framework, targets of interest can be detected accurately. Cascade-Sliding-Window technique was also developed for automated target localization. Application to mammogram showed that over 88% of normal mammograms and 80% of abnormal mammograms can be correctly identified. The approach was also successfully applied to Synthetic Aperture Radar (SAR) and Ground Penetrating Radar (GPR) images for target detection.

Keywords: Image texture analysis, feature extraction, target detection, pattern classification.

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: E. Khorram, S.M. Mirzababaei

Abstract:

Everyday the usages of the Internet increase and simply a world of the data become accessible. Network providers do not want to let the provided services to be used in harmful or terrorist affairs, so they used a variety of methods to protect the special regions from the harmful data. One of the most important methods is supposed to be the firewall. Firewall stops the transfer of such packets through several ways, but in some cases they do not use firewall because of its blind packet stopping, high process power needed and expensive prices. Here we have proposed a method to find a discriminate function to distinguish between usual packets and harmful ones by the statistical processing on the network router logs. So an administrator can alarm to the user. This method is very fast and can be used simply in adjacent with the Internet routers.

Keywords: Data Mining, Firewall, Optimization, Packetclassification, Statistical Pattern Recognition.

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Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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Authors: Alena Zemanová, Jan Zeman, Michal Šejnoha

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The polymer foil used for manufacturing of laminated glass members behaves in a viscoelastic manner with temperature dependance. This contribution aims at incorporating the time/temperature-dependent behavior of interlayer to our earlier elastic finite element model for laminated glass beams. The model is based on a refined beam theory: each layer behaves according to the finite-strain shear deformable formulation by Reissner and the adjacent layers are connected via the Lagrange multipliers ensuring the inter-layer compatibility of a laminated unit. The time/temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams, Landel, and Ferry. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, we demonstrate that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units.

Keywords: Laminated glass, finite element method, finite-strain Reissner model, Lagrange multipliers, generalized Maxwell model, Williams-Landel-Ferry equation, Newton method.

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Authors: M. R. Naghavi, M. Maleki, S. F. Tabatabaei

Abstract:

In order to study floristic and molecular classification of common wild wheat (Triticum boeoticum Boiss.), an analysis was conducted on populations of the Triticum boeoticum collected from different regions of Iran. Considering all floristic compositions of habitats, six floristic groups (syntaxa) within the populations were identified. A high level of variation of T. boeoticum also detected using SSR markers. Our results showed that molecular method confirmed the grouping of floristic method. In other word, the results from our study indicate that floristic classification are still useful, efficient, and economic tools for characterizing the amount and distribution of genetic variation in natural populations of T. boeoticum. Nevertheless, molecular markers appear as useful and complementary techniques for identification and for evaluation of genetic diversity in studied populations.

Keywords: T. boeoticum, diversity, floristic, SSRs.

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle.

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Authors: Jong-Whoi Shin, Chong-Sun Hwang

Abstract:

Various security APIs (Application Programming Interfaces) are being used in a variety of application areas requiring the information security function. However, these standards are not compatible, and the developer must use those APIs selectively depending on the application environment or the programming language. To resolve this problem, we propose the standard draft of the information security component, while SSL (Secure Sockets Layer) using the confidentiality and integrity component interface has been implemented to verify validity of the standard proposal. The implemented SSL uses the lower-level SSL component when establishing the RMI (Remote Method Invocation) communication between components, as if the security algorithm had been implemented by adding one more layer on the TCP/IP.

Keywords: Component Based Design, Application Programming Interface, Secure Socket Layer, Remote Method Invocation.

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Authors: Valentina Obradović, Josip Mesić, Maja Ergović Ravančić, Kamila Mijowska, Brankica Svitlica

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French oak and American oak barrels are most famous all over the world, but barrels of different origin can also be used for obtaining high quality wines. The aim of this research was to compare the influence of different Slovenian (Croatian) and French oak barrels on the quality of Chardonnay wine. Grapes were grown in the Croatian wine growing region of Kutjevo in 2015. Chardonnay wines were tested for basic oenological parameters (alcohol, extract, reducing sugar, SO₂, acidity), total polyphenols content (Folin-Ciocalteu method), antioxidant activity (ABTS and DPPH method) and colour density. Sensory evaluation was performed by students of viticulture/oenology. Samples produced by classical fermentation and ageing in French oak barrels had better results for polyphenols and sensory evaluation (especially low toasting level) than samples in Slovenian barrels. All tested samples were scored as a “quality” or “premium quality” wines. Sur lie method of fermentation and ageing in Slovenian oak barrel had very good extraction of polyphenols and high antioxidant activity with the usage of authentic yeasts, while commercial yeast strain resulted in worse chemical and sensory parameters.

Keywords: Chardonnay, French oak, Slovenian oak, sur lie.

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Authors: Kasra Majbouri Yazdi, Adel Majbouri Yazdi, Saeid Khodayi, Jingyu Hou, Wanlei Zhou, Saeed Saedy

Abstract:

Fake news and false information are big challenges of all types of media, especially social media. There is a lot of false information, fake likes, views and duplicated accounts as big social networks such as Facebook and Twitter admitted. Most information appearing on social media is doubtful and in some cases misleading. They need to be detected as soon as possible to avoid a negative impact on society. The dimensions of the fake news datasets are growing rapidly, so to obtain a better result of detecting false information with less computation time and complexity, the dimensions need to be reduced. One of the best techniques of reducing data size is using feature selection method. The aim of this technique is to choose a feature subset from the original set to improve the classification performance. In this paper, a feature selection method is proposed with the integration of K-means clustering and Support Vector Machine (SVM) approaches which work in four steps. First, the similarities between all features are calculated. Then, features are divided into several clusters. Next, the final feature set is selected from all clusters, and finally, fake news is classified based on the final feature subset using the SVM method. The proposed method was evaluated by comparing its performance with other state-of-the-art methods on several specific benchmark datasets and the outcome showed a better classification of false information for our work. The detection performance was improved in two aspects. On the one hand, the detection runtime process decreased, and on the other hand, the classification accuracy increased because of the elimination of redundant features and the reduction of datasets dimensions.

Keywords: Fake news detection, feature selection, support vector machine, K-means clustering, machine learning, social media.

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Authors: Salama Meghriche, Amer Draa, Mohammed Boulemden

Abstract:

Heart failure is the most common reason of death nowadays, but if the medical help is given directly, the patient-s life may be saved in many cases. Numerous heart diseases can be detected by means of analyzing electrocardiograms (ECG). Artificial Neural Networks (ANN) are computer-based expert systems that have proved to be useful in pattern recognition tasks. ANN can be used in different phases of the decision-making process, from classification to diagnostic procedures. This work concentrates on a review followed by a novel method. The purpose of the review is to assess the evidence of healthcare benefits involving the application of artificial neural networks to the clinical functions of diagnosis, prognosis and survival analysis, in ECG signals. The developed method is based on a compound neural network (CNN), to classify ECGs as normal or carrying an AtrioVentricular heart Block (AVB). This method uses three different feed forward multilayer neural networks. A single output unit encodes the probability of AVB occurrences. A value between 0 and 0.1 is the desired output for a normal ECG; a value between 0.1 and 1 would infer an occurrence of an AVB. The results show that this compound network has a good performance in detecting AVBs, with a sensitivity of 90.7% and a specificity of 86.05%. The accuracy value is 87.9%.

Keywords: Artificial neural networks, Electrocardiogram(ECG), Feed forward multilayer neural network, Medical diagnosis, Pattern recognitionm, Signal processing.

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Authors: A. Nuric, S. Nuric, L. Kricak, I. Lapandic, R. Husagic

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This paper describes topic of computer simulation with regard to the ground movement above an underground mine. Simulation made with software package ADINA for nonlinear elastic-plastic analysis with finite elements method. The one of representative profiles from Mine 'Stara Jama' in Zenica has been investigated. A collection and selection of both geo-mechanical data and geometric parameters of the mine was necessary for performing these simulations. Results of estimation have been compared with measured values (vertical displacement of surface), and then simulation performed with assumed dynamic and dimensions of excavation, over a period of time. Results are presented with bitmaps and charts.

Keywords: Computer, finite element method, mine, nonlinear analysis, numerical modeling, simulation, subsidence.

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Authors: Mostafa Alinezhad, Mehrdad Ahmadi Kamarposhti

Abstract:

According to the increasing utilization in power system, the transmission lines and power plants often operate in stability boundary and system probably lose its stable condition by over loading or occurring disturbance. According to the reasons that are mentioned, the prediction and recognition of voltage instability in power system has particular importance and it makes the network security stronger.This paper, by considering of power system contingencies based on the effects of them on Mega Watt Margin (MWM) and maximum loading point is focused in order to analyse the static voltage stability using continuation power flow method. The study has been carried out on IEEE 14-Bus Test System using Matlab and Psat softwares and results are presented.

Keywords: Contingency, Continuation Power Flow, Static Voltage Stability, Voltage Collapse.

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Authors: Tetsuro Saeki, Yuichi Kato, Shoutarou Mizuno

Abstract:

STRIM (Statistical Test Rule Induction Method) has been proposed as a method to effectively induct if-then rules from the decision table which is considered as a sample set obtained from the population of interest. Its usefulness has been confirmed by simulation experiments specifying rules in advance, and by comparison with conventional methods. However, scope for future development remains before STRIM can be applied to the analysis of real-world data sets. The first requirement is to determine the size of the dataset needed for inducting true rules, since finding statistically significant rules is the core of the method. The second is to examine the capacity of rule induction from datasets with contaminated attribute values created by missing data and noise, since real-world datasets usually contain such contaminated data. This paper examines the first problem theoretically, in connection with the rule length. The second problem is then examined in a simulation experiment, utilizing the critical size of dataset derived from the first step. The experimental results show that STRIM is highly robust in the analysis of datasets with contaminated attribute values, and hence is applicable to real-world data

Keywords: Rule induction, decision table, missing data, noise.

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Authors: M. Mert, M. T. Ozkan

Abstract:

Pile load tests should be applied to check the bearing capacity calculations and to determine the settlement of the pile corresponding to test load. Strain gauges can be installed into pile in order to determine the shaft resistance of the piles for every soil layer respectively. Detailed results can be obtained by means of strain gauges placed at certain levels into test piles. In the scope of this study, pile load test data obtained from two different projects are examined.  Instrumented static pile load tests were applied on totally 7 test bored piles of different diameters (80 cm, 150 cm, and 200 cm) and different lengths (between 30-76 m) in two different project site. Settlement analysis of test piles is done by using some of load transfer methods and finite element method. Plaxis 3D which is a three-dimensional finite element program is also used for settlement analysis of the test piles. In this study, firstly bearing capacity of test piles are determined and compared with strain gauge data which is required for settlement analysis. Then, settlement values of the test piles are estimated by using load transfer methods developed in recent years and finite element method. The aim of this study is to show similarities and differences between the results obtained from settlement analysis methods and instrumented pile load tests.

Keywords: Failure, finite element method, monitoring and instrumentation, pile, settlement.

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Authors: Daniel Morariu, Lucian N. Vintan, Volker Tresp

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Text categorization is the problem of classifying text documents into a set of predefined classes. After a preprocessing step, the documents are typically represented as large sparse vectors. When training classifiers on large collections of documents, both the time and memory restrictions can be quite prohibitive. This justifies the application of feature selection methods to reduce the dimensionality of the document-representation vector. In this paper, three feature selection methods are evaluated: Random Selection, Information Gain (IG) and Support Vector Machine feature selection (called SVM_FS). We show that the best results were obtained with SVM_FS method for a relatively small dimension of the feature vector. Also we present a novel method to better correlate SVM kernel-s parameters (Polynomial or Gaussian kernel).

Keywords: Feature Selection, Learning with Kernels, SupportVector Machine, and Classification.

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Authors: Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang

Abstract:

One good analysis method in seismic response analysis is direct time integration, which widely adopts Rayleigh damping. An approach is presented for selection of Rayleigh damping coefficients to be used in seismic analyses to produce a response that is consistent with Modal damping response. In the presented approach, the expression of the error of peak response, acquired through complete quadratic combination method, and Rayleigh damping coefficients was set up and then the coefficients were produced by minimizing the error. Two finite element modes of soil layers, excited by 28 seismic waves, were used to demonstrate the feasibility and validity.

Keywords: Rayleigh damping, modal damping, damping coefficients, seismic response analysis.

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Authors: Ardhendu Behera, Denis Lalanne, Rolf Ingold

Abstract:

This paper proposes a method, combining color and layout features, for identifying documents captured from low-resolution handheld devices. On one hand, the document image color density surface is estimated and represented with an equivalent ellipse and on the other hand, the document shallow layout structure is computed and hierarchically represented. Our identification method first uses the color information in the documents in order to focus the search space on documents having a similar color distribution, and finally selects the document having the most similar layout structure in the remaining of the search space.

Keywords: Document color modeling, document visualsignature, kernel density estimation, document identification.

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Authors: Abhijit Mitra

Abstract:

An effective approach for extracting document images from a noisy background is introduced. The entire scheme is divided into three sub- stechniques – the initial preprocessing operations for noise cluster tightening, introduction of a new thresholding method by maximizing the ratio of stan- dard deviations of the combined effect on the image to the sum of weighted classes and finally the image restoration phase by image binarization utiliz- ing the proposed optimum threshold level. The proposed method is found to be efficient compared to the existing schemes in terms of computational complexity as well as speed with better noise rejection.

Keywords: Document image extraction, Preprocessing, Ratio of stan-dard deviations, Bi-level adaptive thresholding.

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Authors: H. Nikzad, S. Yoshitomi

Abstract:

This study investigates and develops the structural optimization method. The effect of size constraints on practical solution of reinforced concrete (RC) building structure with shear wall is proposed. Cross-sections of beam and column, and thickness of shear wall are considered as design variables. The objective function to be minimized is total cost of the structure by using a simple and efficient automated MATLAB platform structural optimization methodology. With modification of mathematical formulations, the result is compared with optimal solution without size constraints. The most suitable combination of section sizes is selected as for the final design application based on linear static analysis. The findings of this study show that defining higher value of upper bound of sectional sizes significantly affects optimal solution, and defining of size constraints play a vital role in finding of global and practical solution during optimization procedures. The result and effectiveness of proposed method confirm the ability and efficiency of optimal solutions for 3D RC shear wall-frame structure.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC shear wall-frame structures.

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Authors: Menglong Su, Shaoyun Shi, Qing Xu

Abstract:

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm

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Authors: Victor Breux, Jérôme Boutet, Alain Goret, Viviane Cattin

Abstract:

Early detection of anomalies in data centers is important to reduce downtimes and the costs of periodic maintenance. However, there is little research on this topic and even fewer on the fusion of sensor data for the detection of abnormal events. The goal of this paper is to propose a method for anomaly detection in data centers by combining sensor data (temperature, humidity, power) and deep learning models. The model described in the paper uses one autoencoder per sensor to reconstruct the inputs. The auto-encoders contain Long-Short Term Memory (LSTM) layers and are trained using the normal samples of the relevant sensors selected by correlation analysis. The difference signal between the input and its reconstruction is then used to classify the samples using feature extraction and a random forest classifier. The data measured by the sensors of a data center between January 2019 and May 2020 are used to train the model, while the data between June 2020 and May 2021 are used to assess it. Performances of the model are assessed a posteriori through F1-score by comparing detected anomalies with the data center’s history. The proposed model outperforms the state-of-the-art reconstruction method, which uses only one autoencoder taking multivariate sequences and detects an anomaly with a threshold on the reconstruction error, with an F1-score of 83.60% compared to 24.16%.

Keywords: Anomaly detection, autoencoder, data centers, deep learning.

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Authors: S. Soltan, A. Zarnani, R. AliMohammadzadeh, M. Rahgozar

Abstract:

XML has become a popular standard for information exchange via web. Each XML document can be presented as a rooted, ordered, labeled tree. The Node label shows the exact position of a node in the original document. Region and Dewey encoding are two famous methods of labeling trees. In this paper, we propose a new insert friendly labeling method named IFDewey based on recently proposed scheme, called Extended Dewey. In Extended Dewey many labels must be modified when a new node is inserted into the XML tree. Our method eliminates this problem by reserving even numbers for future insertion. Numbers generated by Extended Dewey may be even or odd. IFDewey modifies Extended Dewey so that only odd numbers are generated and even numbers can then be used for a much easier insertion of nodes.

Keywords: XML, tree labeling, query processing.

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Authors: Aicha Majda, Abdelhamid El Hassani

Abstract:

Lung CT image segmentation is a prerequisite in lung CT image analysis. Most of the conventional methods need a post-processing to deal with the abnormal lung CT scans such as lung nodules or other lesions. The simplest similarity measure in the standard Graph Cuts Algorithm consists of directly comparing the pixel values of the two neighboring regions, which is not accurate because this kind of metrics is extremely sensitive to minor transformations such as noise or other artifacts problems. In this work, we propose an improved version of the standard graph cuts algorithm based on the Patch-Based similarity metric. The boundary penalty term in the graph cut algorithm is defined Based on Patch-Based similarity measurement instead of the simple intensity measurement in the standard method. The weights between each pixel and its neighboring pixels are Based on the obtained new term. The graph is then created using theses weights between its nodes. Finally, the segmentation is completed with the minimum cut/Max-Flow algorithm. Experimental results show that the proposed method is very accurate and efficient, and can directly provide explicit lung regions without any post-processing operations compared to the standard method.

Keywords: Graph cuts, lung CT scan, lung parenchyma segmentation, patch based similarity metric.

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Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

Abstract:

Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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