Search results for: extreme points

Authors: Mojtaba Mahdavi, Mohamad Mahdavi, Maryam Yazdani

Abstract:

A heuristic conceptual model for to develop the Reliability Centered Maintenance (RCM), especially in preventive strategy, has been explored during this paper. In most real cases which complicity of system obligates high degree of reliability, this model proposes a more appropriate reliability function between life time distribution based and another which is based on relevant Extreme Value (EV) distribution. A statistical and mathematical approach is used to estimate and verify these two distribution functions. Then best one is chosen just among them, whichever is more reliable. A numeric Industrial case study will be reviewed to represent the concepts of this paper, more clearly.

Keywords: Lifetime distribution, Reliability, Estimation, Extreme value, Improving model, Series, Parallel.

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Authors: Haruka Mikamori, Koyu Chinen

Abstract:

An optimized design of E/O and O/E for access points of WiMAX RoF was carried out by evaluating RCE. The use of the DFB-LD, a low input-impedance driving, a low distortion PIN-PD, and a high gain EPHEMT amplifier is promising the cost-effective design. For the uplink RoF design, the use of EDFA and EP-HEMT amplifiers is necessity.

Keywords: WiMAX, RoF, RCE, RAU, Access Point

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Authors: V. Tereshchenko, A. Tregubenko

Abstract:

In this study we survey the method for fast finding a minimum link path between two arbitrary points within a simple polygon, which can pass only through the vertices, with preprocessing.

Keywords: Minimum link path, simple polygon, Steiner points, optimal algorithm.

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Authors: Theerawat Songyot, Tham Manjing, Bunyarit Uyyanonvara, Chanjira Sinthanayothin

Abstract:

Corner detection and optical flow are common techniques for feature-based video stabilization. However, these algorithms are computationally expensive and should be performed at a reasonable rate. This paper presents an algorithm for discarding irrelevant feature points and maintaining them for future use so as to improve the computational cost. The algorithm starts by initializing a maintained set. The feature points in the maintained set are examined against its accuracy for modeling. Corner detection is required only when the feature points are insufficiently accurate for future modeling. Then, optical flows are computed from the maintained feature points toward the consecutive frame. After that, a motion model is estimated based on the simplified affine motion model and least square method, with outliers belonging to moving objects presented. Studentized residuals are used to eliminate such outliers. The model estimation and elimination processes repeat until no more outliers are identified. Finally, the entire algorithm repeats along the video sequence with the points remaining from the previous iteration used as the maintained set. As a practical application, an efficient video stabilization can be achieved by exploiting the computed motion models. Our study shows that the number of times corner detection needs to perform is greatly reduced, thus significantly improving the computational cost. Moreover, optical flow vectors are computed for only the maintained feature points, not for outliers, thus also reducing the computational cost. In addition, the feature points after reduction can sufficiently be used for background objects tracking as demonstrated in the simple video stabilizer based on our proposed algorithm.

Keywords: background object tracking, feature point reduction, low cost tracking, video stabilization.

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Authors: Muhammad Naveed, Muhammad Khalid Abdullah, Khalid Rashid, Hafiz Farooq Ahmad

Abstract:

Aspect Oriented Programming promises many advantages at programming level by incorporating the cross cutting concerns into separate units, called aspects. Join Points are distinguishing features of Aspect Oriented Programming as they define the points where core requirements and crosscutting concerns are (inter)connected. Currently, there is a problem of multiple aspects- composition at the same join point, which introduces the issues like ordering and controlling of these superimposed aspects. Dynamic strategies are required to handle these issues as early as possible. State chart is an effective modeling tool to capture dynamic behavior at high level design. This paper provides methodology to formulate the strategies for multiple aspect composition at high level, which helps to better implement these strategies at coding level. It also highlights the need of designing shared join point at high level, by providing the solutions of these issues using state chart diagrams in UML 2.0. High level design representation of shared join points also helps to implement the designed strategy in systematic way.

Keywords: Aspect Oriented Software Development, Shared Join Points.

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Authors: Miika Toivanen, Jouko Lampinen

Abstract:

This paper presents an online method that learns the corresponding points of an object from un-annotated grayscale images containing instances of the object. In the first image being processed, an ensemble of node points is automatically selected which is matched in the subsequent images. A Bayesian posterior distribution for the locations of the nodes in the images is formed. The likelihood is formed from Gabor responses and the prior assumes the mean shape of the node ensemble to be similar in a translation and scale free space. An association model is applied for separating the object nodes and background nodes. The posterior distribution is sampled with Sequential Monte Carlo method. The matched object nodes are inferred to be the corresponding points of the object instances. The results show that our system matches the object nodes as accurately as other methods that train the model with annotated training images.

Keywords: Bayesian modeling, Gabor filters, Online learning, Sequential Monte Carlo.

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Authors: Chaw Su Mon

Abstract:

Abstract— The paper presents a preliminary study on modeling and estimation of basic wind speed ( extreme wind gusts ) for the consideration of vulnerability and design of building in Ayeyarwady Region. The establishment of appropriate design wind speeds is a critical step towards the calculation of design wind loads for structures. In this paper the extreme value analysis of this prediction work is based on the anemometer data (1970-2009) maintained by the department of meteorology and hydrology of Pathein. Statistical and probabilistic approaches are used to derive formulas for estimating 3-second gusts from recorded data (10-minute sustained mean wind speeds).

Keywords: Basic Wind Speed, Building, Gusts, Statistical and probabilistic approaches

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Authors: Xing Xiong, Byung-Jae Choi

Abstract:

It is important for an autonomous mobile robot to know where it is in any time in an indoor environment. In this paper, we design a relative self-localization algorithm. The algorithm compare the interest point in two images and compute the relative displacement and orientation to determent the posture. Firstly, we use the SURF algorithm to extract the interest points of the ceiling. Second, in order to reduce amount of calculation, a replacement SURF is used to extract orientation and description of the interest points. At last, according to the transformation of the interest points in two images, the relative self-localization of the mobile robot will be estimated greatly.

Keywords: Relative Self-Localization Posture, SURF, Natural Landmark, Interest Point.

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Authors: Rampal Singh, S. Balasundaram

Abstract:

In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Nemir Al-Azzawi, Harsa A. Mat Sakim, Wan Ahmed K. Wan Abdullah, Yasmin Mohd Yacob

Abstract:

Feature-based registration is an effective technique for clinical use, because it can greatly reduce computational costs. However, this technique, which estimates the transformation by using feature points extracted from two images, may cause misalignments. To handle with this limitation, we propose to extract the salient edges and extracted control points (CP) of medical images by using efficiency of multiresolution representation of data nonsubsampled contourlet transform (NSCT) that finds the best feature points. The MR images were first decomposed using the NSCT, and then Edge and CP were extracted from bandpass directional subband of NSCT coefficients and some proposed rules. After edge and CP extraction, mutual information was adopted for the registration of feature points and translation parameters are calculated by using particle swarm optimization (PSO). The experimental results showed that the proposed method produces totally accurate performance for registration medical CT-MR images.

Keywords: Feature-based registration, mutual information, nonsubsampled contourlet transform, particle swarm optimization.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

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In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Jae Moon Lee

Abstract:

In general, algorithms to find continuous k-nearest neighbors have been researched on the location based services, monitoring periodically the moving objects such as vehicles and mobile phone. Those researches assume the environment that the number of query points is much less than that of moving objects and the query points are not moved but fixed. In gaming environments, this problem is when computing the next movement considering the neighbors such as flocking, crowd and robot simulations. In this case, every moving object becomes a query point so that the number of query point is same to that of moving objects and the query points are also moving. In this paper, we analyze the performance of the existing algorithms focused on location based services how they operate under gaming environments.

Keywords: Flocking behavior, heterogeneous agents, similarity, simulation.

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Authors: Tang Hong, Zhang Lufeng, Chen Hua, Zhang Jianbo

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Today many developers use the Java components collected from the Internet as external LIBs to design and develop their own software. However, some unknown security bugs may exist in these components, such as SQL injection bug may comes from the components which have no specific check for the input string by users. To check these bugs out is very difficult without source code. So a novel method to check the bugs in Java bytecode based on points-to dataflow analysis is in need, which is different to the common analysis techniques base on the vulnerability pattern check. It can be used as an assistant tool for security analysis of Java bytecode from unknown softwares which will be used as extern LIBs.

Keywords: Java bytecode, points-to dataflow, vulnerability analysis

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Authors: Ziad Abdeldayem, Jakub Markiewicz, Kunal Kansara, Laura Edwards

Abstract:

Airborne Laser Scanning (ALS) is one of the main technologies for generating high-resolution digital terrain models (DTMs). DTMs are crucial to several applications, such as topographic mapping, flood zone delineation, geographic information systems (GIS), hydrological modelling, spatial analysis, etc. Laser scanning system generates irregularly spaced three-dimensional cloud of points. Raw ALS data are mainly ground points (that represent the bare earth) and non-ground points (that represent buildings, trees, cars, etc.). Removing all the non-ground points from the raw data is referred to as filtering. Filtering heavily forested areas is considered a difficult and challenging task as the canopy stops laser pulses from reaching the terrain surface. This research presents an approach for removing non-ground points from raw ALS data in densely forested areas. Smoothing splines are exploited to interpolate and fit the noisy ALS data. The presented filter utilizes a weight function to allocate weights for each point of the data. Furthermore, unlike most of the methods, the presented filtering algorithm is designed to be automatic. Three different forested areas in the United Kingdom are used to assess the performance of the algorithm. The results show that the generated DTMs from the filtered data are accurate (when compared against reference terrain data) and the performance of the method is stable for all the heavily forested data samples. The average root mean square error (RMSE) value is 0.35 m.

Keywords: Airborne laser scanning, digital terrain models, filtering, forested areas.

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Authors: Stephen Karungaru, Minoru Fukumi, Norio Akamatsu

Abstract:

In this paper, we propose a morphing method by which face color images can be freely transformed. The main focus of this work is the transformation of one face image to another. This method is fully automatic in that it can morph two face images by automatically detecting all the control points necessary to perform the morph. A face detection neural network, edge detection and medium filters are employed to detect the face position and features. Five control points, for both the source and target images, are then extracted based on the facial features. Triangulation method is then used to match and warp the source image to the target image using the control points. Finally color interpolation is done using a color Gaussian model that calculates the color for each particular frame depending on the number of frames used. A real coded Genetic algorithm is used in both the image warping and color blending steps to assist in step size decisions and speed up the morphing. This method results in ''very smooth'' morphs and is fast to process.

Keywords: color transition, genetic algorithms morphing, warping

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Authors: Dong Ming, Chen Haipeng

Abstract:

POS (also been called DGPS/IMU) technique can obtain the Exterior Orientation Elements of aerial photo, so the triangulation and DLG production using POS can save large numbers of ground control points (GCP), and this will improve the produce efficiency of DLG and reduce the cost of collecting GCP. This paper mainly research on POS technique in production of 1:10 000 scale DLG on GCP distribution. We designed 23 kinds of ground control points distribution schemes, using integrated sensor direction method to do the triangulation experiments, based on the results of triangulation, we produce a map with the scale of 1:10 000 and test its accuracy. This paper put forward appropriate GCP distributing schemes by experiments and research above, and made preparations for the application of POS technique on photogrammetry 4D data production.

Keywords: POS, IMU, DGPS, DLG, ground control point, triangulation

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Authors: Adnan Abdul-Aziz Gutub, Manal Mohammad Fattani

Abstract:

This paper presents a new steganography approach suitable for Arabic texts. It can be classified under steganography feature coding methods. The approach hides secret information bits within the letters benefiting from their inherited points. To note the specific letters holding secret bits, the scheme considers the two features, the existence of the points in the letters and the redundant Arabic extension character. We use the pointed letters with extension to hold the secret bit 'one' and the un-pointed letters with extension to hold 'zero'. This steganography technique is found attractive to other languages having similar texts to Arabic such as Persian and Urdu.

Keywords: Arabic text, Cryptography, Feature coding, Information security, Text steganography, Text watermarking.

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Authors: Rana Yousef, Khalil el Hindi

Abstract:

The behavior of Radial Basis Function (RBF) Networks greatly depends on how the center points of the basis functions are selected. In this work we investigate the use of instance reduction techniques, originally developed to reduce the storage requirements of instance based learners, for this purpose. Five Instance-Based Reduction Techniques were used to determine the set of center points, and RBF networks were trained using these sets of centers. The performance of the RBF networks is studied in terms of classification accuracy and training time. The results obtained were compared with two Radial Basis Function Networks: RBF networks that use all instances of the training set as center points (RBF-ALL) and Probabilistic Neural Networks (PNN). The former achieves high classification accuracies and the latter requires smaller training time. Results showed that RBF networks trained using sets of centers located by noise-filtering techniques (ALLKNN and ENN) rather than pure reduction techniques produce the best results in terms of classification accuracy. The results show that these networks require smaller training time than that of RBF-ALL and higher classification accuracy than that of PNN. Thus, using ALLKNN and ENN to select center points gives better combination of classification accuracy and training time. Our experiments also show that using the reduced sets to train the networks is beneficial especially in the presence of noise in the original training sets.

Keywords: Radial basis function networks, Instance-based reduction, PNN.

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Authors: J. Witzany, T. Čejka, R. Zigler

Abstract:

With respect to the dissipation of energy through plastic deformation of joints of prefabricated wall units, the paper points out the principal importance of efficient reinforcement of the prefabricated system at its joints. The method, quality and amount of reinforcement are essential for reaching the necessary degree of joint ductility. The paper presents partial results of experimental research of vertical joints of prefabricated units exposed to monotonously rising loading and repetitive shear force and formulates a conclusion that the limit state of the structure as a whole is preceded by the disintegration of joints, or that the structure tends to pass from linearly elastic behaviour to non-linearly elastic to plastic behaviour by exceeding the proportional elastic limit in joints.Experimental verification on a model of a 7-storey prefabricated structure revealed weak points in its load-bearing systems, mainly at places of critical points around openings situated in close proximity to vertical joints of mutually perpendicularly oriented walls.

Keywords: dissipative energy, dynamic and cycling load repetitive load, working diagrams of joints

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Authors: Ibrahim Gomaa, Hoda M. O. Mokhtar

Abstract:

Although most of the existing skyline queries algorithms focused basically on querying static points through static databases; with the expanding number of sensors, wireless communications and mobile applications, the demand for continuous skyline queries has increased. Unlike traditional skyline queries which only consider static attributes, continuous skyline queries include dynamic attributes, as well as the static ones. However, as skyline queries computation is based on checking the domination of skyline points over all dimensions, considering both the static and dynamic attributes without separation is required. In this paper, we present an efficient algorithm for computing continuous skyline queries without discriminating between static and dynamic attributes. Our algorithm in brief proceeds as follows: First, it excludes the points which will not be in the initial skyline result; this pruning phase reduces the required number of comparisons. Second, the association between the spatial positions of data points is examined; this phase gives an idea of where changes in the result might occur and consequently enables us to efficiently update the skyline result (continuous update) rather than computing the skyline from scratch. Finally, experimental evaluation is provided which demonstrates the accuracy, performance and efficiency of our algorithm over other existing approaches.

Keywords: Continuous query processing, dynamic database, moving object, skyline queries.

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Authors: Petra Balla, Gabor Manhertz, Akos Antal

Abstract:

Nowadays spinal deformities are very frequent problems among teenagers. Scheuermann disease is a one dimensional deformity of the spine, but it has prevalence over 11% of the children. A traditional technology, the moiré method was used by us for screening and diagnosing this type of spinal deformity. A LabVIEW program has been developed to evaluate the moiré pictures of patients with Scheuermann disease. Two different solutions were tested in this computer program, the extreme and the inflexion point calculation methods. Effects using these methods were compared and according to the results both solutions seemed to be appropriate. Statistical results showed better efficiency in case of the extreme search method where the average difference was only 6,09⁰.

Keywords: Spinal deformity, picture evaluation, moiré method, Scheuermann disease, curve detection, moiré topography.

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Authors: Amjad Abdullah, Amjad Yahya, Bushra Aljohani, Amani S. Alghamdi

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Change point detection is an important part of data analysis. The presence of a change point refers to a significant change in the behavior of a time series. In this article, we examine the detection of multiple change points of parameters of the exponential Lomax distribution, which is broad and flexible compared with other distributions while fitting data. We used the Schwarz information criterion and binary segmentation to detect multiple change points in publicly available data on the average temperature in the ozone layer. The change points were successfully located.

Keywords: Binary segmentation, change point, exponential Lomax distribution, information criterion.

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Authors: Nishant Shrivastava, D. K. Sehgal

Abstract:

In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.

Keywords: Finite element, Lagrangian, optimal stress location, serendipity.

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Authors: V. Tereshchenko, V. Muravitskiy

Abstract:

We consider the methods of construction simple polygons for a set S of n points and applying them for searching the minimal area polygon. In this paper we propose the approximate algorithm, which generates the simple polygonalizations of a fixed set of points and finds the minimal area polygon, in O (n3) time and using O(n2) memory.

Keywords: simple polygon, approximate algorithm, minimal area polygon, polygonalizations

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Authors: F. Yildiz, S. Y. Oturanc

Abstract:

Advances technology in the field of photogrammetry replaces analog cameras with reflection on aircraft GPS/IMU system with a digital aerial camera. In this system, when determining the position of the camera with the GPS, camera rotations are also determined by the IMU systems. All around the world, digital aerial cameras have been used for the photogrammetry applications in the last ten years. In this way, in terms of the work done in photogrammetry it is possible to use time effectively, costs to be reduced to a minimum level, the opportunity to make fast and accurate. Geo-referencing techniques that are the cornerstone of the GPS / INS systems, photogrammetric triangulation of images required for balancing (interior and exterior orientation) brings flexibility to the process. Also geo-referencing process; needed in the application of photogrammetry targets to help to reduce the number of ground control points. In this study, the use of direct and indirect georeferencing techniques on the accuracy of the points was investigated in the production of photogrammetric mapping.

Keywords: Photogrammetry, GPS/IMU Systems, Geo- Referencing.

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Authors: Nisha Budhwar, Sunita Daniel

Abstract:

In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: Susceptible, exposed, infective, recovered, infective immigrants, reproduction number, Lyapunov function, equilibrium points, global stability.

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Authors: Olugbara O.O., Adebiyi A.A.

Abstract:

Most standard software development methodologies are often not applied to software projects in many developing countries of the world. The approach generally practice is close to what eXtreme Programming (XP) is likely promoting, just keep coding and testing as the requirement evolves. XP is an agile software process development methodology that has inherent capability for improving efficiency of Business Software Development (BSD). XP can facilitate Business-to-Development (B2D) relationship due to its customer-oriented advocate. From practitioner point of view, we applied XP to BSD and result shows that customer involvement has positive impact on productivity, but can as well frustrate the success of the project. In an effort to promote software engineering practice in developing countries of Africa, we present the experiment performed, lessons learned, problems encountered and solution adopted in applying XP methodology to BSD.

Keywords: Requirements engineering, Requirements elicitation, Extreme programming, Mobile Work force

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Authors: F. Rotaru, S. Bejinariu, C. D. Niţâ, R. Luca, I. Pâvâloi, C. Lazâr

Abstract:

The paper presents a technique suitable in robot vision applications where it is not possible to establish the object position from one view. Usually, one view pose calculation methods are based on the correspondence of image features established at a training step and exactly the same image features extracted at the execution step, for a different object pose. When such a correspondence is not feasible because of the lack of specific features a new method is proposed. In the first step the method computes from two views the 3D pose of feature points. Subsequently, using a registration algorithm, the set of 3D feature points extracted at the execution phase is aligned with the set of 3D feature points extracted at the training phase. The result is a Euclidean transform which have to be used by robot head for reorientation at execution step.

Keywords: features correspondence, registration algorithm, robot vision, triangulation method.

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Authors: Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that a collineation of M(A) preserve cross-ratio. Also, we obtain some results about harmonic points.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonic points.

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Authors: Taimur Qureshi, Djamel A Zighed

Abstract:

Many supervised induction algorithms require discrete data, even while real data often comes in a discrete and continuous formats. Quality discretization of continuous attributes is an important problem that has effects on speed, accuracy and understandability of the induction models. Usually, discretization and other types of statistical processes are applied to subsets of the population as the entire population is practically inaccessible. For this reason we argue that the discretization performed on a sample of the population is only an estimate of the entire population. Most of the existing discretization methods, partition the attribute range into two or several intervals using a single or a set of cut points. In this paper, we introduce a technique by using resampling (such as bootstrap) to generate a set of candidate discretization points and thus, improving the discretization quality by providing a better estimation towards the entire population. Thus, the goal of this paper is to observe whether the resampling technique can lead to better discretization points, which opens up a new paradigm to construction of soft decision trees.

Keywords: Bootstrap, discretization, resampling, soft decision trees.

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