Search results for: Boolean functions representation

Authors: R. Lokeshkumar, P. Sengottuvelan

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Web mining is to discover and extract useful Information. Different users may have different search goals when they search by giving queries and submitting it to a search engine. The inference and analysis of user search goals can be very useful for providing an experience result for a user search query. In this project, we propose a novel approach to infer user search goals by analyzing search web logs. First, we propose a novel approach to infer user search goals by analyzing search engine query logs, the feedback sessions are constructed from user click-through logs and it efficiently reflect the information needed for users. Second we propose a preprocessing technique to clean the unnecessary data’s from web log file (feedback session). Third we propose a technique to generate pseudo-documents to representation of feedback sessions for clustering. Finally we implement k-medoids clustering algorithm to discover different user search goals and to provide a more optimal result for a search query based on feedback sessions for the user.

Keywords: Data Preprocessing, Session Identification, Web log mining, Web Personalization.

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Authors: Sicheng Liu

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Based on the key issue of the current fourth world studies, the article aims to analyze the features of character-settings in Chinese ethnic minority films. As a generalizable transformation, this feature progresses from a microcosmic representation. It argues that, as the mediation, films note down the current state of people and their surroundings, while the ‘fourth world’ theorization (or the fourth cinema) provides a new perspective to ethnic minority topics in China. Like the ‘fourth cinema’ focusing on the depiction of indigeneity groups, the ethnic minority films portrait the non-Han nationalities in China. Both types possess the motif of returning history-writing to the minority members’ own hand. In this article, the discussion entirely involves three types of cinematic role-settings in Chinese minority themed films, which illustrates that, similar to the creative principle of the fourth film, the themes and narratives of these films are becoming more individualized, with more concern to minority grassroots.

Keywords: Fourth world, Chinese ethnic minority films, ethnicity and culture reflection, mother tongue (muyu), highlighting to individual spirits.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

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This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: Jagannath Aryal, Don Kulasiri, Dishi Liu

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This paper describes the optimization of a complex dairy farm simulation model using two quite different methods of optimization, the Genetic algorithm (GA) and the Lipschitz Branch-and-Bound (LBB) algorithm. These techniques have been used to improve an agricultural system model developed by Dexcel Limited, New Zealand, which describes a detailed representation of pastoral dairying scenarios and contains an 8-dimensional parameter space. The model incorporates the sub-models of pasture growth and animal metabolism, which are themselves complex in many cases. Each evaluation of the objective function, a composite 'Farm Performance Index (FPI)', requires simulation of at least a one-year period of farm operation with a daily time-step, and is therefore computationally expensive. The problem of visualization of the objective function (response surface) in high-dimensional spaces is also considered in the context of the farm optimization problem. Adaptations of the sammon mapping and parallel coordinates visualization are described which help visualize some important properties of the model-s output topography. From this study, it is found that GA requires fewer function evaluations in optimization than the LBB algorithm.

Keywords: Genetic Algorithm, Linux Cluster, LipschitzBranch-and-Bound, Optimization

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: Exchange rate, quantile regression, combining forecasts.

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Authors: Su Hyung Jo, Ki Young Kim, Sang Ho Lee

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Security management has changed from the management of security equipments and useful interface to manager. It analyzes the whole security conditions of network and preserves the network services from attacks. Secure router technology has security functions, such as intrusion detection, IPsec(IP Security) and access control, are applied to legacy router for secure networking. It controls an unauthorized router access and detects an illegal network intrusion. This paper relates to a security engine management of router based on a security policy, which is the definition of security function against a network intrusion. This paper explains the security policy and designs the structure of security engine management framework.

Keywords: Policy server, security engine, security management, security policy

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Authors: Artion Kashuri, Rozana Liko

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In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: R. Babisaraswathi, N. Shanthi, S. S. Kiruthika

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Web search engines are designed to retrieve and extract the information in the web databases and to return dynamic web pages. The Semantic Web is an extension of the current web in which it includes semantic content in web pages. The main goal of semantic web is to promote the quality of the current web by changing its contents into machine understandable form. Therefore, the milestone of semantic web is to have semantic level information in the web. Nowadays, people use different keyword- based search engines to find the relevant information they need from the web. But many of the words are polysemous. When these words are used to query a search engine, it displays the Search Result Records (SRRs) with different meanings. The SRRs with similar meanings are grouped together based on Word Sense Disambiguation (WSD). In addition to that semantic annotation is also performed to improve the efficiency of search result records. Semantic Annotation is the process of adding the semantic metadata to web resources. Thus the grouped SRRs are annotated and generate a summary which describes the information in SRRs. But the automatic semantic annotation is a significant challenge in the semantic web. Here ontology and knowledge based representation are used to annotate the web pages.

Keywords: Ontology, Semantic Web, WordNet, Word Sense Disambiguation.

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Authors: J. Bolzan, C. Marden

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The article proposed intends to analyze the possibility (and conditions) of a media regulation law in a democratic rule of law in the twenty-first century. To do so, will be presented initially the idea of the public sphere (by Jürgen Habermas), showing how it is presented as an interface between the citizen and the state (or the private and public) and how important is it in a deliberative democracy. Based on this paradigm, the traditional perception of the role of public information (such as system functional element) and on the possibility of media regulation will be exposed, due to the public nature of their activity. A critical argument will then be displayed from two different perspectives: a) the formal function of the current media information, considering that the digital age has fragmented the information access; b) the concept of a constructive democracy, which reduces the need for representation, changing the strategic importance of the public sphere. The question to be addressed (based on the comparative law) is if the regulation is justified in a polycentric democracy, especially when it operates under the digital age (with immediate and virtual communication). The proposal is to be presented in the sense that even in a twenty-first century the media in a democratic rule of law still has an extremely important role and may be subject to regulation, but this should be on terms very different (and narrower) from those usually defended.

Keywords: Media regulation, public sphere, digital age, constructive democracy.

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Authors: Chih-Wei Lin, Duen-Ren Liu, Hui-Fang Chen

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Effective knowledge support relies on providing operation-relevant knowledge to workers promptly and accurately. A knowledge flow represents an individual-s or a group-s knowledge-needs and referencing behavior of codified knowledge during operation performance. The flow has been utilized to facilitate organizational knowledge support by illustrating workers- knowledge-needs systematically and precisely. However, conventional knowledge-flow models cannot work well in cooperative teams, which team members usually have diverse knowledge-needs in terms of roles. The reason is that those models only provide one single view to all participants and do not reflect individual knowledge-needs in flows. Hence, we propose a role-based knowledge-flow view model in this work. The model builds knowledge-flow views (or virtual knowledge flows) by creating appropriate virtual knowledge nodes and generalizing knowledge concepts to required concept levels. The customized views could represent individual role-s knowledge-needs in teamwork context. The novel model indicates knowledge-needs in condensed representation from a roles perspective and enhances the efficiency of cooperative knowledge support in organizations.

Keywords: cooperative knowledge support, knowledge flow, knowledge-flow view, role-based models

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Authors: Maninder Jeet Kaur, Moin Uddin, Harsh K. Verma

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The efficient use of available licensed spectrum is becoming more and more critical with increasing demand and usage of the radio spectrum. This paper shows how the use of spectrum as well as dynamic spectrum management can be effectively managed and spectrum allocation schemes in the wireless communication systems be implemented and used, in future. This paper would be an attempt towards better utilization of the spectrum. This research will focus on the decision-making process mainly, with an assumption that the radio environment has already been sensed and the QoS requirements for the application have been specified either by the sensed radio environment or by the secondary user itself. We identify and study the characteristic parameters of Cognitive Radio and use Genetic Algorithm for spectrum allocation. Performance evaluation is done using MATLAB toolboxes.

Keywords: Cognitive Radio, Fitness Functions, Fuzzy Logic, Quality of Service (QoS)

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Authors: Agnieszka Danek, Rafał Pokrzywa

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Approximate tandem repeats in a genomic sequence are two or more contiguous, similar copies of a pattern of nucleotides. They are used in DNA mapping, studying molecular evolution mechanisms, forensic analysis and research in diagnosis of inherited diseases. All their functions are still investigated and not well defined, but increasing biological databases together with tools for identification of these repeats may lead to discovery of their specific role or correlation with particular features. This paper presents a new approach for finding approximate tandem repeats in a given sequence, where the similarity between consecutive repeats is measured using the Hamming distance. It is an enhancement of a method for finding exact tandem repeats in DNA sequences based on the Burrows- Wheeler transform.

Keywords: approximate tandem repeats, Burrows-Wheeler transform, Hamming distance, suffix array

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Authors: Reza Gharehkhani

Abstract:

Sedimentation in reservoirs lowers the quality of consumed water, reduce the volume of reservoir, lowers the controllable amount of flood, increases the risk of water overflow during possible floods and the risk of reversal and reduction of dam's useful life. So in all stages of dam establishment such as cognitive studies, phase-1 studies of design, control, construction and maintenance, the problem of sedimentation in reservoir should be considered. What engineers need to do is examine and develop the methods to keep effective capacity of a reservoir, however engineers should also consider the influences of the methods on the flood disaster, functions of water use facilities and environmental issues.This article first examines the sedimentation in reservoirs and shows how to control it and then discusses the studies about the sedimens in Siazakh Dam.

Keywords: Sedimentation, Reservoir, Sediment Control, Dam

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Authors: Ahmad Fadel Klaib, Zurinahni Zainol, Nurul Hashimah Ahamed, Rosma Ahmad, Wahidah Hussin

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Bioinformatics and Cheminformatics use computer as disciplines providing tools for acquisition, storage, processing, analysis, integrate data and for the development of potential applications of biological and chemical data. A chemical database is one of the databases that exclusively designed to store chemical information. NMRShiftDB is one of the main databases that used to represent the chemical structures in 2D or 3D structures. SMILES format is one of many ways to write a chemical structure in a linear format. In this study we extracted Antimicrobial Structures in SMILES format from NMRShiftDB and stored it in our Local Data Warehouse with its corresponding information. Additionally, we developed a searching tool that would response to user-s query using the JME Editor tool that allows user to draw or edit molecules and converts the drawn structure into SMILES format. We applied Quick Search algorithm to search for Antimicrobial Structures in our Local Data Ware House.

Keywords: Exact String-matching Algorithms, NMRShiftDB, SMILES Format, Antimicrobial Structures.

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Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Samriti Jindal, Shailendra Singh

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Biometric measures of one kind or another have been used to identify people since ancient times, with handwritten signatures, facial features, and fingerprints being the traditional methods. Of late, Systems have been built that automate the task of recognition, using these methods and newer ones, such as hand geometry, voiceprints and iris patterns. These systems have different strengths and weaknesses. This work is a two-section composition. In the starting section, we present an analytical and comparative study of common biometric techniques. The performance of each of them has been viewed and then tabularized as a result. The latter section involves the actual implementation of the techniques under consideration that has been done using a state of the art tool called, MATLAB. This tool aids to effectively portray the corresponding results and effects.

Keywords: Matlab, Recognition, Facial Vectors, Functions.

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Authors: Bo Liu, Qingshan Kong, Weiqing Huang

Abstract:

With the rapid development of modern communication, diagnosing the fiber-optic quality and faults in real-time is widely focused. In this paper, a Labview-based system is proposed for fiber-optic faults detection. The wavelet threshold denoising method combined with Empirical Mode Decomposition (EMD) is applied to denoise the optical time domain reflectometer (OTDR) signal. Then the method based on Gabor representation is used to detect events. Experimental measurements show that signal to noise ratio (SNR) of the OTDR signal is improved by 1.34dB on average, compared with using the wavelet threshold denosing method. The proposed system has a high score in event detection capability and accuracy. The maximum detectable fiber length of the proposed Labview-based system can be 65km.

Keywords: Empirical mode decomposition (EMD), events detection, Gabor transform, optical time domain reflectometer (OTDR), wavelet threshold denoising.

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Authors: Peiangpob Monnuanprang

Abstract:

In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

Keywords: Euler equations, transformation, hyperbolic, elliptic

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Authors: Nur Aisyah Jalalludin, Arwindra Rizqiawan, Goro Fujita

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In this study, we aim to demonstrate a microgrid system experimental simulation for an easy understanding of a large-scale microgrid system. This model is required for industrial training and learning environments. However, in order to create an exact representation of a microgrid system, the laboratory-scale system must fulfill the requirements of a grid-connected inverter, in which power values are assigned to the system to cope with the intermittent output from renewable energy sources. Aside from that, during fluctuations in load capacity, the grid-connected system must be able to supply power from the utility grid side and microgrid side in a balanced manner. Therefore, droop control is installed in the inverter’s control board to maintain a balanced power sharing in both sides. This power control in a stand-alone condition and droop control in a grid-connected condition must be implemented in order to maintain a stabilized system. Based on the experimental results, power control and droop control can both be applied in the system by comparing the experimental and reference values.

Keywords: Droop control, droop characteristic, grid-connected inverter, microgrid, power control.

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Authors: Ritvik Chauhan, Vijay Kumar Baraik

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Women are most vulnerable to crime despite occupying central position in shaping a society as the first teacher of children. In India too, having equal rights and constitutional safeguards, the incidences of crime against them are large and grave. In this context of crime against women, especially rape has been increasing over time. This paper explores the spatial and temporal aspects of crime against women in India with special reference to rape. It also examines the crime against women with its spatial, socio-economic and demographic associates using related data obtained from the National Crime Records Bureau India, Indian Census and other government sources of the Government of India. The simple statistical, choropleth mapping and other cartographic representation methods have been used to see the crime rates, spatio-temporal patterns of crime, and association of crime with its correlates.  The major findings are visible spatial variations across the country and are also in the rising trends in terms of incidence and rates over the reference period. The study also indicates that the geographical associations are somewhat observed. However, selected indicators of socio-economic factors seem to have no significant bearing on crime against women at this level.

Keywords: Crime against women, crime mapping, trend analysis.

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Authors: Yu-Wei Chen, Li-Ren Han

Abstract:

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

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

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Authors: N. Rezaee, M Nayeripour, A. Roosta, T. Niknam

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With the prevalence of computer and development of information technology, Geographic Information Systems (GIS) have long used for a variety of applications in electrical engineering. GIS are designed to support the analysis, management, manipulation and mapping of spatial data. This paper presents several usages of GIS in power utilities such as automated route selection for the construction of new power lines which uses a dynamic programming model for route optimization, load forecasting and optimizing planning of substation-s location and capacity with comprehensive algorithm which involves an accurate small-area electric load forecasting procedure and simulates the different cost functions of substations.

Keywords: Geographic information systems (GIS), optimallocation and capacity, power distribution planning, route selection, spatial load forecasting.

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Authors: Lewis E. Hibell, Honghai Liu, David J. Brown

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This paper presents the results of enhancing images from a left and right stereo pair in order to increase the resolution of a 3D representation of a scene generated from that same pair. A new neural network structure known as a Self Delaying Dynamic Network (SDN) has been used to perform the enhancement. The advantage of SDNs over existing techniques such as bicubic interpolation is their ability to cope with motion and noise effects. SDNs are used to generate two high resolution images, one based on frames taken from the left view of the subject, and one based on the frames from the right. This new high resolution stereo pair is then processed by a disparity map generator. The disparity map generated is compared to two other disparity maps generated from the same scene. The first is a map generated from an original high resolution stereo pair and the second is a map generated using a stereo pair which has been enhanced using bicubic interpolation. The maps generated using the SDN enhanced pairs match more closely the target maps. The addition of extra noise into the input images is less problematic for the SDN system which is still able to out perform bicubic interpolation.

Keywords: Genetic Evolution, Image Enhancement, Neuron Networks, Stereo Vision

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Authors: Leila Graini

Abstract:

In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: All-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator.

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Authors: Paula Verdugo-Hernández, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of Mathematical Working Spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: Convergence, graphical representations, Mathematical Working Spaces, paradigms of real analysis, real number sequences.

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Authors: Abdussamad Ismail, Dong-Sheng Jeng

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A self-evolution algorithm for optimizing neural networks using a combination of PSO and JPSO is proposed. The algorithm optimizes both the network topology and parameters simultaneously with the aim of achieving desired accuracy with less complicated networks. The performance of the proposed approach is compared with conventional back-propagation networks using several synthetic functions, with better results in the case of the former. The proposed algorithm is also implemented on slope stability problem to estimate the critical factor of safety. Based on the results obtained, the proposed self evolving network produced a better estimate of critical safety factor in comparison to conventional BPN network.

Keywords: Neural networks, Topology evolution, Particle swarm optimization.

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Authors: Petr Šimek, Kamil Kostruk

Abstract:

This paper deals with the problem of testing the Electronic Control Unit (ECU) for the specified function validation. Modern ECUs have many functions which need to be tested. This process requires tracking between the test and the specification. The technique discussed in this paper explores the system for automating this process. The paper focuses on the introduction to the problem in general, then it describes the proposed test system concept and its principle. It looks at how the process of the ECU interface specification file for automated interface testing and test tracking works. In the end, the future possible development of the project is discussed.

Keywords: Electronic control unit testing, embedded system, test generate, test automation, process automation, CAN bus, Ethernet.

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Authors: Abdessamad Essaouabi, Ibnelhaj Elhassane

Abstract:

Efficient storage, transmission and use of video information are key requirements in many multimedia applications currently being addressed by MPEG-4. To fulfill these requirements, a new approach for representing video information which relies on an object-based representation, has been adopted. Therefore, objectbased watermarking schemes are needed for copyright protection. This paper proposes a novel blind object watermarking scheme for images and video using the in place lifting shape adaptive-discrete wavelet transform (SA-DWT). In order to make the watermark robust and transparent, the watermark is embedded in the average of wavelet blocks using the visual model based on the human visual system. Wavelet coefficients n least significant bits (LSBs) are adjusted in concert with the average. Simulation results shows that the proposed watermarking scheme is perceptually invisible and robust against many attacks such as lossy image/video compression (e.g. JPEG, JPEG2000 and MPEG-4), scaling, adding noise, filtering, etc.

Keywords: Watermark, visual model, robustness, in place lifting shape adaptive-discrete wavelet transform.

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Authors: Yingjie Zhang

Abstract:

This paper is concerned with an improved algorithm based on the piecewise-smooth Mumford and Shah (MS) functional for an efficient and reliable segmentation. In order to speed up convergence, an additional force, at each time step, is introduced further to drive the evolution of the curves instead of only driven by the extensions of the complementary functions u + and u - . In our scheme, furthermore, the piecewise-constant MS functional is integrated to generate the extra force based on a temporary image that is dynamically created by computing the union of u + and u - during segmenting. Therefore, some drawbacks of the original algorithm, such as smaller objects generated by noise and local minimal problem also are eliminated or improved. The resulting algorithm has been implemented in Matlab and Visual Cµ, and demonstrated efficiently by several cases.

Keywords: Active contours, energy minimization, image segmentation, level sets.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

Abstract:

A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: Priyadarsini P. L. K, Hemalatha T.

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This paper proves that the problem of finding connected vertex cover in a 2-connected planar graph ( CVC-2 ) with maximum degree 4 is NP-complete. The motivation for proving this result is to give a shorter and simpler proof of NP-Completeness of TRA-MLC (the Top Right Access point Minimum-Length Corridor) problem [1], by finding the reduction from CVC-2. TRA-MLC has many applications in laying optical fibre cables for data communication and electrical wiring in floor plans.The problem of finding connected vertex cover in any planar graph ( CVC ) with maximum degree 4 is NP-complete [2]. We first show that CVC-2 belongs to NP and then we find a polynomial reduction from CVC to CVC-2. Let a graph G0 and an integer K form an instance of CVC, where G0 is a planar graph and K is an upper bound on the size of the connected vertex cover in G0. We construct a 2-connected planar graph, say G, by identifying the blocks and cut vertices of G0, and then finding the planar representation of all the blocks of G0, leading to a plane graph G1. We replace the cut vertices with cycles in such a way that the resultant graph G is a 2-connected planar graph with maximum degree 4. We consider L = K -2t+3 t i=1 di where t is the number of cut vertices in G1 and di is the number of blocks for which ith cut vertex is common. We prove that G will have a connected vertex cover with size less than or equal to L if and only if G0 has a connected vertex cover of size less than or equal to K.

Keywords: NP-complete, 2-Connected planar graph, block, cut vertex

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