Search results for: spatial patterns

Authors: Ramaswamy Palaniappan

Abstract:

This paper reports a new approach on identifying the individuality of persons by using parametric classification of multiple mental thoughts. In the approach, electroencephalogram (EEG) signals were recorded when the subjects were thinking of one or more (up to five) mental thoughts. Autoregressive features were computed from these EEG signals and classified by Linear Discriminant classifier. The results here indicate that near perfect identification of 400 test EEG patterns from four subjects was possible, thereby opening up a new avenue in biometrics.

Keywords: Autoregressive, Biometrics, Electroencephalogram, Linear discrimination, Mental thoughts.

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Authors: Yong-jun Zhao, Heng-li Zhang, Zong-yun Hu

Abstract:

Based on the sources- smoothed rank profile (SRP) and modified minimum description length (MMDL) principle, a method for estimation of the source coherency structure (SCS) and the number of wideband sources is proposed in this paper. Instead of focusing, we first use a spatial smoothing technique to pre-process the array covariance matrix of each frequency for de-correlating the sources and then use smoothed rank profile to determine the SCS and the number of wideband sources. We demonstrate the availability of the method by numerical simulations.

Keywords: Wideband sources, source coherency structure (SCS), smoothed rank profile (SRP).

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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Authors: Jaroslav Burian, Kateřina Sorbiová, Pavel Tuček, Michaela Tučková

Abstract:

The article describes problems of city centers with regard to possibilities of their delimitation in a GIS environment. First the definitions and delimitations of a city centre which are in use are mentioned, furthermore a chosen case study (the historical centre of Olomouc city in the Czech Republic) is employed to describe the methods of delimitation in use. In addition to describing the current state, the article also deals with possibilities of delimitation of a city centre in GIS environment by means of several chosen approaches. The authors describe, compare and discuss the chosen methods and assess the achieved results and also applicability of the designed methods for other cities.

Keywords: analysis, city center, GIS, spatial structures

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Authors: Farhad F. Yusifov

Abstract:

With the explosive growth of data available on the Internet, personalization of this information space become a necessity. At present time with the rapid increasing popularity of the WWW, Websites are playing a crucial role to convey knowledge and information to the end users. Discovering hidden and meaningful information about Web users usage patterns is critical to determine effective marketing strategies to optimize the Web server usage for accommodating future growth. The task of mining useful information becomes more challenging when the Web traffic volume is enormous and keeps on growing. In this paper, we propose a intelligent model to discover and analyze useful knowledge from the available Web log data.

Keywords: Clustering, Self organizing map, Web log files, Web traffic.

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Authors: A. Rahdar, V. Arbabi, H. Ghanbari

Abstract:

ZnS nanoparticles of different size have been synthesized using a colloidal particles method. Zns nanoparticles prepared with capping agent (mercaptoethanol) then were characterized using X-ray diffraction (XRD) and UV-Vis spectroscopy. The particle size of the nanoparticles calculated from the XRD patterns has been found in the range 1.85-2.44nm. Absorption spectra have been obtained using UV-Vis spectrophotometer to find the optical band gap and the obtained values have been founded to being range 3.83-4.59eV. It was also found that energy band gap increase with the increase in molar capping agent solution.

Keywords: ZnS, Nanoparticle, X-ray.

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Authors: Tossaporn Kachanubal, Somkait Udomhunsakul

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In this paper, we proposed a method to classify each type of natural rock texture. Our goal is to classify 26 classes of rock textures. First, we extract five features of each class by using principle component analysis combining with the use of applied spatial frequency measurement. Next, the effective node number of neural network was tested. We used the most effective neural network in classification process. The results from this system yield quite high in recognition rate. It is shown that high recognition rate can be achieved in separation of 26 stone classes.

Keywords: Texture classification, SFM, neural network, rock texture classification.

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Authors: L. Jiang

Abstract:

Since the late 1980s, the new phenomena of 'employment subcentres' or 'polycentricity' has appeared in the metropolises of North American and Western Europe and it has been an interesting topic for academics and researchers. This paper specifically uses one case study-Guangzhou to explore the development and the mechanism of employment subcentres and polycentricity in Chinese metropolises by spatial analysis method on the basis of the first economic census data. In conclusion, the paper regards that the employment subcentres and polycentricity has existed in Chinese metropolises. And that, the mechanism of them is mainly from the secondary industry instead of the tertiary industry in North American and Western Europe

Keywords: Employment Subcentre, Polycentricity, Guangzhou.

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Authors: M. Raciti Castelli, P. Cioppa, E. Benini

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This paper presents a CFD analysis of the flow around a 30° inclined flat plate of infinite span. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a flat plate invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested and flow field characteristics in the neighborhood of the flat plate have been numerically investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a twodimensional inclined plate.

Keywords: CFD, lift, drag, flat plate

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Authors: Adam Rabcewicz

Abstract:

Variational methods for optical flow estimation are known for their excellent performance. The method proposed by Brox et al. [5] exemplifies the strength of that framework. It combines several concepts into single energy functional that is then minimized according to clear numerical procedure. In this paper we propose a modification of that algorithm starting from the spatiotemporal gradient constancy assumption. The numerical scheme allows to establish the connection between our model and the CLG(H) method introduced in [18]. Experimental evaluation carried out on synthetic sequences shows the significant superiority of the spatial variant of the proposed method. The comparison between methods for the realworld sequence is also enclosed.

Keywords: optical flow, variational methods, gradient constancy assumption.

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Authors: Ramin Halavati, Mansour Jamzad, Mahdieh Soleymani

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Persian (Farsi) script is totally cursive and each character is written in several different forms depending on its former and later characters in the word. These complexities make automatic handwriting recognition of Persian a very hard problem and there are few contributions trying to work it out. This paper presents a novel practical approach to online recognition of Persian handwriting which is based on representation of inputs and patterns with very simple visual features and comparison of these simple terms. This recognition approach is tested over a set of Persian words and the results have been quite acceptable when the possible words where unknown and they were almost all correct in cases that the words where chosen from a prespecified list.

Keywords: Image Processing, Pattern Recognition.

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Authors: Ilaha Rzayeva, Emin Alasgarov, Orkhan Karim-Zada

Abstract:

This study attempts to consider the linkage between management and computer sciences in order to develop the software named “IntelSymb” as a demo application to prove data analysis of non-energy^* fields’ diversification, which will positively influence on energy dependency mitigation of countries. Afterward, we analyzed 18 years of economic fields of development (5 sectors) of 13 countries by identifying which patterns mostly prevailed and which can be dominant in the near future. To make our analysis solid and plausible, as a future work, we suggest developing a gateway or interface, which will be connected to all available on-line data bases (WB, UN, OECD, U.S. EIA) for countries’ analysis by fields. Sample data consists of energy (TPES and energy import indicators) and non-energy industries’ (Main Science and Technology Indicator, Internet user index, and Sales and Production indicators) statistics from 13 OECD countries over 18 years (1995-2012). Our results show that the diversification of non-energy industries can have a positive effect on energy sector dependency (energy consumption and import dependence on crude oil) deceleration. These results can provide empirical and practical support for energy and non-energy industries diversification’ policies, such as the promoting of Information and Communication Technologies (ICTs), services and innovative technologies efficiency and management, in other OECD and non-OECD member states with similar energy utilization patterns and policies. Industries, including the ICT sector, generate around 4 percent of total GHG, but this is much higher — around 14 percent — if indirect energy use is included. The ICT sector itself (excluding the broadcasting sector) contributes approximately 2 percent of global GHG emissions, at just under 1 gigatonne of carbon dioxide equivalent (GtCO2eq). Ergo, this can be a good example and lesson for countries which are dependent and independent on energy, and mainly emerging oil-based economies, as well as to motivate non-energy industries diversification in order to be ready to energy crisis and to be able to face any economic crisis as well.

Keywords: Energy policy, energy diversification, “IntelSymb” software, renewable energy.

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Authors: Seung-Jun Yu, Hwan-Jun Choi, Hyoung-Kyu Song

Abstract:

Among spatial diversity scheme, orthogonal space-time block code (OSTBC) and cyclic delay diversity (CDD) have been widely studied for the cooperative wireless relaying system. However, conventional OSTBC and CDD cannot cope with change in the number of relays owing to low throughput or error performance. In this paper, we propose a cooperative cyclic delay diversity (CDD) scheme that use hierarchical modulation at the source and adaptive modulation based on cyclic redundancy check (CRC) code at the relays.

Keywords: Adaptive modulation, Cooperative communication, CDD, OSTBC.

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Authors: A. Aydarous, M. El Ghazaly

Abstract:

The purpose of this study was to investigate the response of the newly released Gafchromic HD-V2 film for alpha particle of 5.5 MeV. Gafchromic HD-V2 was exposed to alpha particles of energy 5 MeV from 241Am for different durations. Then the films were scanned with a flatbed scanner. The dose response curve up to 2200 Gy has been achieved. The film’s reproducibility and sensitivity were evaluated. The results obtained show that the net optical density increases almost exponentially with the increase in the exposure time, and it becomes saturated after prolonged exposure times. The red channel shows the highest sensitivity, with a value of 4 x 10-3 Gy-1 at netOD of 0.4. The inter-film reproducibility was measured and the relative uncertainty found was 1.7 %, 2.1 % and 2.3 % for grey, red and green channels, respectively.

Keywords: Alpha dosimetry, 241Am, Gafchromic film.

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Authors: S.B. Tavakoly Sany, A. Salleh, A.H. Sulaiman, G.H. Monazami

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The coastal sediments of West Port of Malaysia was monitored from Nov. 2009 to Oct. 2010 to assess spatial distribution of heavy metals As, Cu, Cd, Cr, Hg, Ni, Zn and Pb. Sediment samples were collected from 10 stations in dry and rainy season in West Port. The range concentrations measured (Mg/g dry weight ) were from 23.4 to 98.3 for Zn, 22.3 to 80 for Pb, 7.4 to 27.6 Cu, 0.244 to 3.53 for Cd, 7.2 to 22.2 for Ni, 20.2 to 162 for As, 0.11 to 0.409 for Hg and 11.5 to 61.5 for Cr. The geochemical indexes used in this study were Geoaccumulation (Igeo), Contamination Factor (CF) and Pollution Load Index (PLI); these indexes were used to evaluate the levels of sediment contaminations. The results of these indexes show that, the status of West Port sediment quality are moderately polluted by heavy metals except in arsenic which shows the high level of pollution.

Keywords: Heavy metals, Sediment Quality, West Port.

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Authors: Vahid Sabermand, Yousef Hojjat, Majid Hasanzadeh

Abstract:

This paper contains 2 main parts. In the first part of paper we simulated and studied three types of electrode patterns used in various industries for suspension and handling of the semiconductor and glass and we selected the best pattern by evaluating the electrostatic force, which was comb pattern electrode. In the second part we investigated the parameters affecting the amount of electrostatic force such as the gap between surface and electrode (g), the electrode width (w), the gap between electrodes (t), the surface permittivity and electrode length and methods of improvement of adhesion force by changing these values.

Keywords: Electrostatic force, electrostatic adhesion, electrostatic chuck, electrostatic application in industry, Electroadhesive grippers.

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Authors: M. Shakaib, M. Ehtesham-ul Haq, I. Ahmed, R.M. Yunus

Abstract:

Computational fluid dynamics (CFD) simulations carried out in this paper show that spacer orientation has a major influence on temperature patterns and on the heat transfer rates. The local heat flux values significantly vary from high to very low values at each filament when spacer touches the membrane surface. The heat flux profile is more uniform when spacer filaments are not in contact with the membrane thus making this arrangement more beneficial. The temperature polarization is also found to be less in this case when compared to the empty channel.

Keywords: heat transfer, membrane distillation, spacer, temperature polarization.

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Authors: S. Sarumathi, N. Shanthi, S. Vidhya

Abstract:

In the present world, predicting rainfall is considered to be an essential and also a challenging task. Normally, the climate and rainfall are presumed to have non-linear as well as intricate phenomena. For predicting accurate rainfall, we necessitate advanced computer modeling and simulation. When there is an enhanced understanding of the spatial and temporal distribution of precipitation then it becomes enrichment to applications such as hydrologic, climatic and ecological. Conversely, there may be some kind of challenges occur in the community due to some application which results in the absence of consistent precipitation observation in remote and also emerging region. This survey paper provides a multifarious collection of methodologies which are epitomized by various researchers for predicting the rainfall. It also gives information about some technique to forecast rainfall, which is appropriate to all methods like numerical, traditional and statistical.

Keywords: Satellite Image, Segmentation, Feature Extraction, Classification, Clustering, Precipitation Estimation.

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Authors: S. Sarumathi, N. Shanthi

Abstract:

Due to the fast and flawless technological innovation there is a tremendous amount of data dumping all over the world in every domain such as Pattern Recognition, Machine Learning, Spatial Data Mining, Image Analysis, Fraudulent Analysis, World Wide Web etc., This issue turns to be more essential for developing several tools for data mining functionalities. The major aim of this paper is to analyze various tools which are used to build a resourceful analytical or descriptive model for handling large amount of information more efficiently and user friendly. In this survey the diverse tools are illustrated with their extensive technical paradigm, outstanding graphical interface and inbuilt multipath algorithms in which it is very useful for handling significant amount of data more indeed.

Keywords: Classification, Clustering, Data Mining, Machine learning, Visualization.

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Authors: Evgeny Pyshkin, Maxim Mozgovoy, Vladislav Volkov

Abstract:

The paper follows a discourse on computer-assisted language learning. We examine problems of foreign language teaching and learning and introduce a metamodel that can be used to define learning models of language grammar structures in order to support teacher/student interaction. Special attention is paid to the concept of a virtual language lab. Our approach to language education assumes to encourage learners to experiment with a language and to learn by discovering patterns of grammatically correct structures created and managed by a language expert.

Keywords: Computer-assisted instruction, Language learning, Natural language grammar models, HCI.

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Authors: Zarine Avetisyan

Abstract:

The present paper presents the discussion of scholars concerning speech impact, peculiarities of its realization, speech strategies and techniques in particular. Departing from the viewpoints of many prominent linguists, the paper suggests that manipulative argumentation be viewed as a most pervasive speech strategy with a certain set of techniques which are to be found in modern American political discourse. The precedence of their occurrence allows us to regard them as pragmatic patterns of speech impact realization in effective public speaking.

Keywords: Manipulative argumentation, political discourse, speech impact, technique.

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Authors: Sorcha Bennett, Joe Sullivan

Abstract:

Triple-Level Cell (TLC) NAND Flash memory at, and below, 20nm (nanometer) is still largely unexplored by researchers, and with the ever more commonplace existence of Flash in consumer and enterprise applications there is a need for such gaps in knowledge to be filled. At the time of writing, there was little published data or literature on TLC, and more specifically reliability testing, with a further emphasis on both endurance and retention. This paper will give an introduction to NAND Flash memory, followed by an overview of the relevant current research on the reliability of Flash memory, along with the planned future work which will provide results to help characterise the reliability of TLC memory.

Keywords: TLC NAND flash memory, reliability, endurance, retention, trade-off, raw flash, patterns.

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Authors: Afnan T. Bagasi, Donia M. Bettaieb, Abeer Alsobahi

Abstract:

The wayfinding system affects the course of a museum journey for visitors, both directly and indirectly. The design aspects of this system play an important role, making it an effective communication system within the museum space. However, translating the concepts that pertain to its design, and which are based on integration and connectivity in museum space design, such as intelligibility, lacks customization in the form of specific design considerations with reference to the most important approaches. These approaches link the organizational and practical aspects to the semiotic and semantic aspects related to the space syntax by targeting the visual and perceived consistency of visitors. In this context, the present study aims to identify how to apply the concept of intelligibility by employing integration and connectivity to design a wayfinding system in museums as a kind of composite interior space. Using the available plans and images to extrapolate the considerations used to design the wayfinding system in the Saudi National Museum as a case study, a descriptive analytical method was used to understand the basic organizational and Morphological principles of the museum space through the main aspects of space design (the Morphological and the pragmatic). The study’s methodology is based on the description and analysis of the basic organizational and Morphological principles of the museum space at the level of the major Morphological and Pragmatic design layers (based on available pictures and diagrams) and inductive method about applied level of intelligibility in spatial layout in the Hall of Islam and Arabia at the National Museum Saudi Arabia within the framework of a case study through the levels of verification of the properties of the concepts of connectivity and integration. The results indicated that the application of the characteristics of intelligibility is weak on both Pragmatic and Morphological levels. Based on the concept of connective and integration, we conclude the following: (1) High level of reflection of the properties of connectivity on the pragmatic level, (2) Weak level of reflection of the properties of Connectivity at the morphological level (3) Weakness in the level of reflection of the properties of integration in the space sample as a result of a weakness in the application at the morphological and pragmatic level. The study’s findings will assist designers, professionals, and researchers in the field of museum design in understanding the significance of the wayfinding system by delving into it through museum spaces by highlighting the most essential aspects using a clear analytical method.

Keywords: wayfinding system, museum journey, intelligibility, integration, connectivity, interior design

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Authors: F. Pourhasanzade, S. H. Sabzpoushan

Abstract:

The heart tissue is an excitable media. A Cellular Automata is a type of model that can be used to model cardiac action potential propagation. One of the advantages of this approach against the methods based on differential equations is its high speed in large scale simulations. Recent cellular automata models are not able to avoid flat edges in the result patterns or have large neighborhoods. In this paper, we present a new model to eliminate flat edges by minimum number of neighbors.

Keywords: Cellular Automata, Action Potential Simulation, Isotropic Pattern.

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Authors: B. Kubrak J. Wissink H. Herlina

Abstract:

Two-dimensional Direct Numerical Simulation (DNS) of high Schmidt number mass transfer in a convective flow environment (Rayleigh-B'enard) is carried out and results are compared to experimental data. A fourth-order accurate WENO-scheme has been used for scalar transport in order to aim for a high accuracy in areas of high concentration gradients. It was found that the typical spatial distance between downward plumes of cold high concentration water and the eddy size are in good agreement with experiments using a combined PIV-LIF technique for simultaneous and spatially synoptic measurements of 2D velocity and concentration fields.

Keywords: Air-Water Interface, DNS, Gas Transfer, LIF.

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Authors: Hong Choon Ong

Abstract:

Naïve Bayes classifiers are simple probabilistic classifiers. Classification extracts patterns by using data file with a set of labeled training examples and is currently one of the most significant areas in data mining. However, Naïve Bayes assumes the independence among the features. Structural learning among the features thus helps in the classification problem. In this study, the use of structural learning in Bayesian Network is proposed to be applied where there are relationships between the features when using the Naïve Bayes. The improvement in the classification using structural learning is shown if there exist relationship between the features or when they are not independent.

Keywords: Bayesian Network, Classification, Naïve Bayes, Structural Learning.

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Authors: Xu Chen, Zhao Caiqi

Abstract:

In addition to the advantages of light weight, resistant corrosion and ease of processing, aluminum is also applied to the long-span spatial structures. However, the elastic modulus of aluminum is lower than that of the steel. This paper combines the high performance aluminum honeycomb panel with the aluminum latticed shell, forming a new panel-and-rod composite shell structure. Through comparative analysis between the static and dynamic performance, the conclusion that the structure of composite shell is noticeably superior to the structure combined before.

Keywords: Combination of aluminum honeycomb panel and rod latticed shell, dynamic performance, response spectrum analysis, seismic properties.

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Authors: David J. Robbins, R. Stewart Cant, Lynn F. Gladden

Abstract:

A robust AUSM+ upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of state with respect to the IAPWS-IF97 equation of state for water. The algorithm demonstrates a combination of robustness and accuracy over a range of flow conditions, with the stiffened-gas equation tending to overestimate liquid temperature and density profiles.

Keywords: Multiphase flow, AUSM+ scheme, liquid EOS, low Mach number models

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Authors: Shi Chen, Zi Y. Chen, Jian K. Dan, Jian F. Li

Abstract:

Evolution of one-dimensional electron system under high-energy-density (HED) conditions is investigated, using the principle of least-action and variational method. In a single-mode modulation model, the amplitude and spatial wavelength of the modulation are chosen to be general coordinates. Equations of motion are derived by considering energy conservation and force balance. Numerical results show that under HED conditions, electron density modulation could exist. Time dependences of amplitude and wavelength are both positively related to the rate of energy input. Besides, initial loading speed has a significant effect on modulation amplitude, while wavelength relies more on loading duration.

Keywords: Electron density modulation, HED, nonlinearevolution, plasmas.

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Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wavebeam both in elevation and azimuth. In this paper a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: Beamforming, transducer array, BIS-expansion.

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