Search results for: metric dimension

Authors: Nisha Goyal, R.K. Gupta

Abstract:

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

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

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Authors: Nedeljko Cvejic, Artur Łoza, David Bull, Nishan Canagarajah

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In this paper, we present a novel objective nonreference performance assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented by the fused image. The metric is based on the Universal Image Quality Index and uses the similarity between blocks of pixels in the input images and the fused image as the weighting factors for the metrics. Experimental results confirm that the values of the proposed metrics correlate well with the subjective quality of the fused images, giving a significant improvement over standard measures based on mean squared error and mutual information.

Keywords: Fusion performance measures, image fusion, non-reference quality measures, objective quality measures.

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Authors: Jianqin Qu

Abstract:

This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: Covariant point, point matching, dimension free, rigid registration.

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Authors: Nedeljko Cvejic, Artur Łoza, David Bull, Nishan Canagarajah

Abstract:

In this paper, we present a novel objective nonreference performance assessment algorithm for image fusion. It takes into account local measurements to estimate how well the important information in the source images is represented by the fused image. The metric is based on the Universal Image Quality Index and uses the similarity between blocks of pixels in the input images and the fused image as the weighting factors for the metrics. Experimental results confirm that the values of the proposed metrics correlate well with the subjective quality of the fused images, giving a significant improvement over standard measures based on mean squared error and mutual information.

Keywords: Fusion performance measures, image fusion, nonreferencequality measures, objective quality measures.

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Gong Jie, Yu Qianxu, Liu Min, Shan Weiwei

Abstract:

The design of methods of the 20 K large dimension cold shield used for infrared radiation demarcating in space environment simulation test were introduced in this paper. The cold shield were cooled by five G-M cryocoolers , and the dimension of the cold shield is the largest in our country.Cold shield installation and distribution and compensator for contraction on cooling were introduced detailedly. The temperature distribution and cool-down time of cold shield surface were also calculated and analysed in this paper. The design of cold shield resolves the difficulty of compensator for contraction on cooling successfully. Test results show that the actual technical performance indicators of cold shield met and exceeded the design requirements.

Keywords: cold shield, G-M cryocooler，infrared radiometer demarcating, satellite, space environment simulation equipments

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Authors: Dimitrios J. Dimitriou, Maria F. Sartzetaki

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Air Transport links markets and individuals, making regions more competitive and promoting social and economic development. The assessment of social contribution is the key objective of this paper, focusing on the definition of the components of social dimension and welfare metrics in the national scale. According to a top-down approach, the key dimensions that affect the social welfare are presented. Conventional wisdom is to provide estimations on added value to social issues caused by the air transport development and present the methodology framework for measuring the contribution of transport development in social value chain. Greece is the case study of this paper, providing results from the contribution of air transport infrastructures in national welfare. The application key findings are essential for managers and decision makers to support actions and plans towards economic recovery of an economy presenting strong seasonal characteristics (because of tourism) and suffering from recession.

Keywords: Air transport, social dimension, social coherence, resilient business development, socioeconomic impact.

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Authors: Julia Kucerova, Jaroslav Polec, Darina Tarcsiova

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Visual information is very important in human perception of surrounding world. Video is one of the most common ways to capture visual information. The video capability has many benefits and can be used in various applications. For the most part, the video information is used to bring entertainment and help to relax, moreover, it can improve the quality of life of deaf people. Visual information is crucial for hearing impaired people, it allows them to communicate personally, using the sign language; some parts of the person being spoken to, are more important than others (e.g. hands, face). Therefore, the information about visually relevant parts of the image, allows us to design objective metric for this specific case. In this paper, we present an example of an objective metric based on human visual attention and detection of salient object in the observed scene.

Keywords: sign language, objective video quality, visual attention, saliency

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: Jaroslav Polec, Petra Heribanová, Tomáš Hirner

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In this paper we proposed a method for finding video frames representing one sign in the finger alphabet. The method is based on determining hands location, segmentation and the use of standard video quality evaluation metrics. Metric calculation is performed only in regions of interest. Sliding mechanism for finding local extrema and adaptive threshold based on local averaging is used for key frames selection. The success rate is evaluated by recall, precision and F1 measure. The method effectiveness is compared with metrics applied to all frames. Proposed method is fast, effective and relatively easy to realize by simple input video preprocessing and subsequent use of tools designed for video quality measuring.

Keywords: Key frame, video, quality, metric, MSE, MSAD, SSIM, VQM, sign language, finger alphabet.

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Authors: B. S. Raghavendra, D. Narayana Dutt

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In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In addition, some properties of the FD are discussed.

Keywords: Box-counting, Fractal dimension, Higuchi method, Katz method, Parametric fractal signals, Sevcik method.

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Authors: Taehan Lee

Abstract:

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: Integer programming, multicommodity network design, routing, shortest path.

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Authors: Mehdi Seifbarghy, Sajjad Jalali, Seyed Habib A. Rahmati

Abstract:

This paper provides a framework in order to incorporate reliability issue as a sign of disruption in distribution systems and partial covering theory as a response to limitation in coverage radios and economical preferences, simultaneously into the traditional literatures of capacitated facility location problems. As a result we develop a bi-objective model based on the discrete scenarios for expected cost minimization and demands coverage maximization through a three echelon supply chain network by facilitating multi-capacity levels for provider side layers and imposing gradual coverage function for distribution centers (DCs). Additionally, in spite of objectives aggregation for solving the model through LINGO software, a branch of LP-Metric method called Min- Max approach is proposed and different aspects of corresponds model will be explored.

Keywords: Reliability Cost, Partial Covering, LP-Metric

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Authors: Parvinder S. Sandhu, Harpreet Kaur, Amanpreet Singh

Abstract:

Automatic reusability appraisal is helpful in evaluating the quality of developed or developing reusable software components and in identification of reusable components from existing legacy systems; that can save cost of developing the software from scratch. But the issue of how to identify reusable components from existing systems has remained relatively unexplored. In this research work, structural attributes of software components are explored using software metrics and quality of the software is inferred by different Neural Network based approaches, taking the metric values as input. The calculated reusability value enables to identify a good quality code automatically. It is found that the reusability value determined is close to the manual analysis used to be performed by the programmers or repository managers. So, the developed system can be used to enhance the productivity and quality of software development.

Keywords: Neural Network, Software Reusability, Software Metric, Accuracy, MAE, RMSE.

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Authors: Gitanjali Devi, Kandarpa Kumar Sarma, Pranayee Datta, Anjana Kakoti Mahanta

Abstract:

Cosmic showers, from their places of origin in space, after entering earth generate secondary particles called Extensive Air Shower (EAS). Detection and analysis of EAS and similar High Energy Particle Showers involve a plethora of experimental setups with certain constraints for which soft-computational tools like Artificial Neural Network (ANN)s can be adopted. The optimality of ANN classifiers can be enhanced further by the use of Multiple Classifier System (MCS) and certain data - dimension reduction techniques. This work describes the performance of certain data dimension reduction techniques like Principal Component Analysis (PCA), Independent Component Analysis (ICA) and Self Organizing Map (SOM) approximators for application with an MCS formed using Multi Layer Perceptron (MLP), Recurrent Neural Network (RNN) and Probabilistic Neural Network (PNN). The data inputs are obtained from an array of detectors placed in a circular arrangement resembling a practical detector grid which have a higher dimension and greater correlation among themselves. The PCA, ICA and SOM blocks reduce the correlation and generate a form suitable for real time practical applications for prediction of primary energy and location of EAS from density values captured using detectors in a circular grid.

Keywords: EAS, Shower, Core, ANN, Location.

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Authors: S. Mahmoodzadeh, J. Shahrabi, M. A. Torkamani, J. Sabaghzadeh Ghomi

Abstract:

Recognizing behavioral patterns of financial markets is essential for traders. Japanese candlestick chart is a common tool to visualize and analyze such patterns in an economic time series. Since the world was introduced to Japanese candlestick charting, traders saw how combining this tool with intelligent technical approaches creates a powerful formula for the savvy investors. This paper propose a generalization to box counting method of Grassberger-Procaccia, which is based on computing the correlation dimension of Japanese candlesticks instead commonly used 'close' points. The results of this method applied on several foreign exchange rates vs. IRR (Iranian Rial). Satisfactorily show lower chaotic dimension of Japanese candlesticks series than regular Grassberger-Procaccia method applied merely on close points of these same candles. This means there is some valuable information inside candlesticks.

Keywords: Chaos, Japanese candlestick, generalized box counting, strange attractor.

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Authors: M. A Anjum, M. Y. Javed, A. Basit

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In this paper a new approach to face recognition is presented that achieves double dimension reduction making the system computationally efficient with better recognition results. In pattern recognition techniques, discriminative information of image increases with increase in resolution to a certain extent, consequently face recognition results improve with increase in face image resolution and levels off when arriving at a certain resolution level. In the proposed model of face recognition, first image decimation algorithm is applied on face image for dimension reduction to a certain resolution level which provides best recognition results. Due to better computational speed and feature extraction potential of Discrete Cosine Transform (DCT) it is applied on face image. A subset of coefficients of DCT from low to mid frequencies that represent the face adequately and provides best recognition results is retained. A trade of between decimation factor, number of DCT coefficients retained and recognition rate with minimum computation is obtained. Preprocessing of the image is carried out to increase its robustness against variations in poses and illumination level. This new model has been tested on different databases which include ORL database, Yale database and a color database. The proposed technique has performed much better compared to other techniques. The significance of the model is two fold: (1) dimension reduction up to an effective and suitable face image resolution (2) appropriate DCT coefficients are retained to achieve best recognition results with varying image poses, intensity and illumination level.

Keywords: Biometrics, DCT, Face Recognition, Feature extraction.

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Authors: K. S. Jasmine, R. Vasantha

Abstract:

The overriding goal of software engineering is to provide a high quality system, application or a product. To achieve this goal, software engineers must apply effective methods coupled with modern tools within the context of a mature software process [2]. In addition, it is also must to assure that high quality is realized. Although many quality measures can be collected at the project levels, the important measures are errors and defects. Deriving a quality measure for reusable components has proven to be challenging task now a days. The results obtained from the study are based on the empirical evidence of reuse practices, as emerged from the analysis of industrial projects. Both large and small companies, working in a variety of business domains, and using object-oriented and procedural development approaches contributed towards this study. This paper proposes a quality metric that provides benefit at both project and process level, namely defect removal efficiency (DRE).

Keywords: Software Reuse, Defect density, Reuse metrics, Defect Removal efficiency.

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Authors: Pongsiri K.

Abstract:

This research aimed to study the market feasibility for new brand coffee house, the case study of Thailand.. This study is a mixed methods research combining quantitative research and the qualitative research. Primary data 350 sets of questionnaires were distributed, and the high quality completed questionnaires of 320 sets returned. Research samples are identified as customers’ of Hi-end department stores in Thailand. The sources of secondary data were critical selected from highly reliable sources, both from public and private sectors. The results were used to classify the customer group into two main groups, the younger than 25 and the older than 25years old. Results of the younger group, are give priority to the dimension of coffee house and its services dimension more than others, then branding dimension and the product dimension respectively. On the other hand, the older group give the difference result as they rate the important of the branding, coffee house and its services, then the product respectively. Coffee consuming is not just the trend but it has become part of people lifestyle. And the new cultures also created by the wise businessman. Coffee was long produced and consumed in Thailand. But it is surprisingly the hi-end brand coffee houses in Thai market are mostly imported brands. The café business possibility for Thai brand coffee house in Thai market were discussed in the paper.

Keywords: Coffee House, Café, Coffee Consuming and new entry branding, market feasibility

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Authors: Smriti H. Bhandari, S. M. Deshpande

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Surface metrology with image processing is a challenging task having wide applications in industry. Surface roughness can be evaluated using texture classification approach. Important aspect here is appropriate selection of features that characterize the surface. We propose an effective combination of features for multi-scale and multi-directional analysis of engineering surfaces. The features include standard deviation, kurtosis and the Canny edge detector. We apply the method by analyzing the surfaces with Discrete Wavelet Transform (DWT) and Dual-Tree Complex Wavelet Transform (DT-CWT). We used Canberra distance metric for similarity comparison between the surface classes. Our database includes the surface textures manufactured by three machining processes namely Milling, Casting and Shaping. The comparative study shows that DT-CWT outperforms DWT giving correct classification performance of 91.27% with Canberra distance metric.

Keywords: Dual-tree complex wavelet transform, surface metrology, surface roughness, texture classification.

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Authors: Ho-Hyun Park, Woosik Kim, Miae Woo

Abstract:

It is expected that ubiquitous era will come soon. A ubiquitous environment has features like peer-to-peer and nomadic environments. Such features can be represented by peer-to-peer systems and mobile ad-hoc networks (MANETs). The features of P2P systems and MANETs are similar, appealing for implementing P2P systems in MANET environment. It has been shown that, however, the performance of the P2P systems designed for wired networks do not perform satisfactorily in mobile ad-hoc environment. Subsequently, this paper proposes a method to improve P2P performance using cross-layer design and the goodness of a node as a peer. The proposed method uses routing metric as well as P2P metric to choose favorable peers to connect. It also utilizes proactive approach for distributing peer information. According to the simulation results, the proposed method provides higher query success rate, shorter query response time and less energy consumption by constructing an efficient overlay network.

Keywords: Ad-hoc Networks, Cross-layer, Peer-to-Peer, Performance Analysis.

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Authors: Peña Aguilar Juan M., Valencia Luis, Pastrana Alberto, Nava Estefany, Martinez A., Vivanco M., Castañeda A.

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This paper seeks to compare the innovation of Mexico from an economic and human perspective, with the seven most innovative countries according to the Global Innovation Index 2013, done by the World Intellectual Property Organization (WIPO). The above analysis suggests nine dimensions: Expenditure on R & D, intellectual property, appropriate environment to conduct business, economic stability, triple helix for R & D, ICT Infrastructure, education, human resources and quality of life. Each dimension is represented by an indicator which is later used to construct a radial graph that compares the innovative capacity of the countries analyzed. As a result, it is proposed a new indicator of innovation called The Area of Innovation. Observations are made from the results, and finally as a conclusion, those items or dimensions in which Mexico suffers lag in innovation are identify.

Keywords: Dimension, measure, innovation level, economy, radar chart.

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Authors: Michal Mardiak, Jaroslav Polec

Abstract:

In this paper we proposed comparison of four content based objective metrics with results of subjective tests from 80 video sequences. We also include two objective metrics VQM and SSIM to our comparison to serve as “reference” objective metrics because their pros and cons have already been published. Each of the video sequence was preprocessed by the region recognition algorithm and then the particular objective video quality metric were calculated i.e. mutual information, angular distance, moment of angle and normalized cross-correlation measure. The Pearson coefficient was calculated to express metrics relationship to accuracy of the model and the Spearman rank order correlation coefficient to represent the metrics relationship to monotonicity. The results show that model with the mutual information as objective metric provides best result and it is suitable for evaluating quality of video sequences.

Keywords: Objective quality metrics, mutual information, region recognition, content based metrics

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Authors: Razib M. Othman, Safaai Deris, Rosli M. Illias, Zalmiyah Zakaria, Saberi M. Mohamad

Abstract:

Nowadays, Gene Ontology has been used widely by many researchers for biological data mining and information retrieval, integration of biological databases, finding genes, and incorporating knowledge in the Gene Ontology for gene clustering. However, the increase in size of the Gene Ontology has caused problems in maintaining and processing them. One way to obtain their accessibility is by clustering them into fragmented groups. Clustering the Gene Ontology is a difficult combinatorial problem and can be modeled as a graph partitioning problem. Additionally, deciding the number k of clusters to use is not easily perceived and is a hard algorithmic problem. Therefore, an approach for solving the automatic clustering of the Gene Ontology is proposed by incorporating cohesion-and-coupling metric into a hybrid algorithm consisting of a genetic algorithm and a split-and-merge algorithm. Experimental results and an example of modularized Gene Ontology in RDF/XML format are given to illustrate the effectiveness of the algorithm.

Keywords: Automatic clustering, cohesion-and-coupling metric, gene ontology; genetic algorithm, split-and-merge algorithm.

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Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

Abstract:

Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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Authors: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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Authors: Seyedeh Belin Tavakoly Sany, H. Rosli, R. Majid, S. Aishah

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In this study, water monitoring was performed from Nov. 2012 to Oct. 2013 to assess water quality and evaluate the spatial and temporal distribution of physicochemical and biological variables in water. Water samples were collected from 10 coastal water stations of West Port. In the case of water-quality assessment, multi-metric indices and operational indicators have been proposed to classify the trophic status at different stations. The trophic level of West Port coastal water ranges from eutrophic to hypertrophic. Chl-a concentration was used to estimate the biological response of phytoplankton biomass and indicated eutrophic conditions in West Port and mesotrophic conditions at the control site. During the study period, no eutrophication events or secondary symptoms occurred, which may be related to hydrodynamic turbulence and water exchange, which prevent the development of eutrophic conditions in the West Port.

Keywords: Water quality, multi-metric indices, operational indicator, Malaysia, West Port.

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Authors: Ali Anaissi, Paul J. Kennedy, Madhu Goyal

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Analysis and visualization of microarraydata is veryassistantfor biologists and clinicians in the field of diagnosis and treatment of patients. It allows Clinicians to better understand the structure of microarray and facilitates understanding gene expression in cells. However, microarray dataset is a complex data set and has thousands of features and a very small number of observations. This very high dimensional data set often contains some noise, non-useful information and a small number of relevant features for disease or genotype. This paper proposes a non-linear dimensionality reduction algorithm Local Principal Component (LPC) which aims to maps high dimensional data to a lower dimensional space. The reduced data represents the most important variables underlying the original data. Experimental results and comparisons are presented to show the quality of the proposed algorithm. Moreover, experiments also show how this algorithm reduces high dimensional data whilst preserving the neighbourhoods of the points in the low dimensional space as in the high dimensional space.

Keywords: Linear Dimension Reduction, Non-Linear Dimension Reduction, Principal Component Analysis, Biologists.

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Authors: Weifeng Pan

Abstract:

The stability of a software system is one of the most important quality attributes affecting the maintenance effort. Many techniques have been proposed to support the analysis of software stability at the architecture, file, and class level of software systems, but little effort has been made for that at the feature (i.e., method and attribute) level. And the assumptions the existing techniques based on always do not meet the practice to a certain degree. Considering that, in this paper, we present a novel metric, Stability of Software (SoS), to measure the stability of object-oriented software systems by software change propagation analysis using a simulation way in software dependency networks at feature level. The approach is evaluated by case studies on eight open source Java programs using different software structures (one employs design patterns versus one does not) for the same object-oriented program. The results of the case studies validate the effectiveness of the proposed metric. The approach has been fully automated by a tool written in Java.

Keywords: Software stability, change propagation, design pattern, software maintenance, object-oriented (OO) software.

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Authors: Loai AbdAllah, Ilan Shimshoni

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Missing values in data are common in real world applications. Since the performance of many data mining algorithms depend critically on it being given a good metric over the input space, we decided in this paper to define a distance function for unlabeled datasets with missing values. We use the Bhattacharyya distance, which measures the similarity of two probability distributions, to define our new distance function. According to this distance, the distance between two points without missing attributes values is simply the Mahalanobis distance. When on the other hand there is a missing value of one of the coordinates, the distance is computed according to the distribution of the missing coordinate. Our distance is general and can be used as part of any algorithm that computes the distance between data points. Because its performance depends strongly on the chosen distance measure, we opted for the k nearest neighbor classifier to evaluate its ability to accurately reflect object similarity. We experimented on standard numerical datasets from the UCI repository from different fields. On these datasets we simulated missing values and compared the performance of the kNN classifier using our distance to other three basic methods. Our  experiments show that kNN using our distance function outperforms the kNN using other methods. Moreover, the runtime performance of our method is only slightly higher than the other methods.

Keywords: Missing values, Distance metric, Bhattacharyya distance.

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