Search results for: spatial point patterns

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: Taras Agryzkov, Almudena Nolasco-Cirugeda, Jos´e L. Oliver, Leticia Serrano-Estrada, Leandro Tortosa, Jos´e F. Vicent

Abstract:

This paper aims to represent the commercial activity of a city taking as source data the social network Foursquare. The city of Murcia is selected as case study, and the location-based social network Foursquare is the main source of information. After carrying out a reorganisation of the user-generated data extracted from Foursquare, it is possible to graphically display on a map the various city spaces and venues especially those related to commercial, food and entertainment sector businesses. The obtained visualisation provides information about activity patterns in the city of Murcia according to the people‘s interests and preferences and, moreover, interesting facts about certain characteristics of the town itself.

Keywords: Social networks, Foursquare, spatial analysis, data visualization, geocomputation.

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Authors: Kayun Chantarasathaporn, Chonawat Srisa-an

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Design Patterns have gained more and more acceptances since their emerging in software development world last decade and become another de facto standard of essential knowledge for Object-Oriented Programming developers nowadays. Their target usage, from the beginning, was for regular computers, so, minimizing power consumption had never been a concern. However, in this decade, demands of more complicated software for running on mobile devices has grown rapidly as the much higher performance portable gadgets have been supplied to the market continuously. To get along with time to market that is business reason, the section of software development for power conscious, battery, devices has shifted itself from using specific low-level languages to higher level ones. Currently, complicated software running on mobile devices are often developed by high level languages those support OOP concepts. These cause the trend of embracing Design Patterns to mobile world. However, using Design Patterns directly in software development for power conscious systems is not recommended because they were not originally designed for such environment. This paper demonstrates the adapted Design Pattern for power limitation system. Because there are numerous original design patterns, it is not possible to mention the whole at once. So, this paper focuses only in creating Energy Conscious version of existing regular "Builder Pattern" to be appropriated for developing low power consumption software.

Keywords: Design Patterns, Builder Pattern, Low Power Consumption, Object Oriented Programming, Power Conscious System, Software.

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Authors: J. Ruiz-Pinales, J. J. Acosta-Reyes, A. Salazar-Garibay, R. Jaime-Rivas

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In this paper, we present a new method for incorporating global shift invariance in support vector machines. Unlike other approaches which incorporate a feature extraction stage, we first scale the image and then classify it by using the modified support vector machines classifier. Shift invariance is achieved by replacing dot products between patterns used by the SVM classifier with the maximum cross-correlation value between them. Unlike the normal approach, in which the patterns are treated as vectors, in our approach the patterns are treated as matrices (or images). Crosscorrelation is computed by using computationally efficient techniques such as the fast Fourier transform. The method has been tested on the ORL face database. The tests indicate that this method can improve the recognition rate of an SVM classifier.

Keywords: Face recognition, support vector machines, shiftinvariance, image registration.

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Authors: B. Sanchez, D. Zambrana-Vasquez, J. Fresner, C. Krenn, F. Morea, L. Mercatelli

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Local administrations are facing established targets on sustainable development from different disciplines at the heart of different city departments. Nevertheless, some of these targets, such as CO₂ reduction, relate to two or more disciplines, as it is the case of sustainable mobility and energy plans (SUMP & SECAP/SEAP). This opens up the possibility to efficiently cooperate among different city departments and to create and develop harmonized spatial plans by using available resources and together achieving more ambitious goals in cities. The steps of the harmonization processes developed result in the identification of areas to achieve common strategic objectives. Harmonization, in other words, helps different departments in local authorities to work together and optimize the use or resources by sharing the same vision, involving key stakeholders, and promoting common data assessment to better optimize the resources. A methodology to promote resilient city planning via the harmonization of sustainable mobility and energy plans is presented in this paper. In order to validate the proposed methodology, a representative city engaged in an innovation process in efficient spatial planning is used as a case study. The harmonization process of sustainable mobility and energy plans covers identifying matching targets between different fields, developing different spatial plans with dual benefit and common indicators guaranteeing the continuous improvement of the harmonized plans. The proposed methodology supports local administrations in consistent spatial planning, considering both energy efficiency and sustainable mobility. Thus, municipalities can use their human and economic resources efficiently. This guarantees an efficient upgrade of land use plans integrating energy and mobility aspects in order to achieve sustainability targets, as well as to improve the wellbeing of its citizens.

Keywords: Harmonized planning, spatial planning, sustainable energy, sustainable mobility, SECAP, SUMP.

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Authors: Ali Essam El Shazly

Abstract:

The social logic of 'Sequina' slum area in Alexandria details the integral measure of space syntax at the room-level of twenty-building samples. The essence of spatial structure integrates the central 'visitor' domain with the 'living' frontage of the 'children' zone against the segregated privacy of the opposite 'parent' depth. Meanwhile, the multifunctioning of shallow rooms optimizes the integral 'visitor' structure through graph and visibility dimensions in contrast to the 'inhabitant' structure of graph-tails out of sight. Common theme of the layout integrity increases in compensation to the decrease of room visibility. Despite the 'pheno-type' of collective integration, the individual layouts observe 'geno-type' structure of spatial diversity per room adjoins. In this regard, the layout integrity alternates the cross-correlation of the 'kitchen & living' rooms with the 'inhabitant & visitor' domains of 'motherhood' dynamic structure. Moreover, the added 'grandparent' restructures the integral measure to become the deepest space, but opens to the 'living' of 'household' integrity. Some isomorphic layouts change the integral structure just through the 'balcony' extension of access, visual or ignored 'ringiness' of space syntax. However, the most integrated or segregated layouts invert the 'geno-type' into a shallow 'inhabitant' centrality versus the remote 'visitor' structure. Overview of the multivariate social logic of spatial integrity could never clarify without the micro-data analysis.

Keywords: Alexandria, Sequina slum, spatial integration, space syntax.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: Olfa.Ben Ahmed, Mahmoud. Mejdoub, Chokri. Ben Amar

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Recognizing human action from videos is an active field of research in computer vision and pattern recognition. Human activity recognition has many potential applications such as video surveillance, human machine interaction, sport videos retrieval and robot navigation. Actually, local descriptors and bag of visuals words models achieve state-of-the-art performance for human action recognition. The main challenge in features description is how to represent efficiently the local motion information. Most of the previous works focus on the extension of 2D local descriptors on 3D ones to describe local information around every interest point. In this paper, we propose a new spatio-temporal descriptor based on a spacetime description of moving points. Our description is focused on an Accordion representation of video which is well-suited to recognize human action from 2D local descriptors without the need to 3D extensions. We use the bag of words approach to represent videos. We quantify 2D local descriptor describing both temporal and spatial features with a good compromise between computational complexity and action recognition rates. We have reached impressive results on publicly available action data set

Keywords: Accordion, Bag of Features, Human action, Motion, Moving point, Space-Time Descriptor, SIFT, Video.

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Authors: Akrem Sellami, Imed Riadh Farah

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Hyperspectral imagery (HSI) typically provides a wealth of information captured in a wide range of the electromagnetic spectrum for each pixel in the image. Hence, a pixel in HSI is a high-dimensional vector of intensities with a large spectral range and a high spectral resolution. Therefore, the semantic interpretation is a challenging task of HSI analysis. We focused in this paper on object classification as HSI semantic interpretation. However, HSI classification still faces some issues, among which are the following: The spatial variability of spectral signatures, the high number of spectral bands, and the high cost of true sample labeling. Therefore, the high number of spectral bands and the low number of training samples pose the problem of the curse of dimensionality. In order to resolve this problem, we propose to introduce the process of dimensionality reduction trying to improve the classification of HSI. The presented approach is a semi-supervised band selection method based on spatial hypergraph embedding model to represent higher order relationships with different weights of the spatial neighbors corresponding to the centroid of pixel. This semi-supervised band selection has been developed to select useful bands for object classification. The presented approach is evaluated on AVIRIS and ROSIS HSIs and compared to other dimensionality reduction methods. The experimental results demonstrate the efficacy of our approach compared to many existing dimensionality reduction methods for HSI classification.

Keywords: Hyperspectral image, spatial hypergraph, dimensionality reduction, semantic interpretation, band selection, feature extraction.

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Authors: Abbas Siefi, Mohammad Javad Karimifar

Abstract:

We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.

Keywords: Spatial design of experiments, maximum entropy sampling, computer experiments, genetic algorithm.

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Authors: B. L. Ho, L. Shi, D. F. Wang, V. C. T. Mok

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The brain’s functional connectivity while temporally non-stationary does express consistency at a macro spatial level. The study of stable resting state connectivity patterns hence provides opportunities for identification of diseases if such stability is severely perturbed. A mathematical model replicating the brain’s spatial connections will be useful for understanding brain’s representative geometry and complements the empirical model where it falls short. Empirical computations tend to involve large matrices and become infeasible with fine parcellation. However, the proposed analytical model has no such computational problems. To improve replicability, 92 subject data are obtained from two open sources. The proposed methodology, inspired by financial theory, uses multivariate regression to find relationships of every cortical region of interest (ROI) with some pre-identified hubs. These hubs acted as representatives for the entire cortical surface. A variance-covariance framework of all ROIs is then built based on these relationships to link up all the ROIs. The result is a high level of match between model and empirical correlations in the range of 0.59 to 0.66 after adjusting for sample size; an increase of almost forty percent. More significantly, the model framework provides an intuitive way to delineate between systemic drivers and idiosyncratic noise while reducing dimensions by more than 30 folds, hence, providing a way to conduct attribution analysis. Due to its analytical nature and simple structure, the model is useful as a standalone toolkit for network dependency analysis or as a module for other mathematical models.

Keywords: Functional magnetic resonance imaging, multivariate regression, network hubs, resting state functional connectivity.

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Authors: Hamed Rafiei, Masoud Rabbani

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This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: Eric Kojo Wu Aikins

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This paper examines the relationships between and among the various drivers of climate change that have both climatic and ecological consequences for vegetation and land cover change in arctic areas, particularly in arctic Alaska. It discusses the various processes that have created spatial and climatic structures that have facilitated observable vegetation and land cover changes in the Arctic. Also, it indicates that the drivers of both climatic and ecological changes in the Arctic are multi-faceted and operate in a system with both positive and negative feedbacks that largely results in further increases or decreases of the initial drivers of climatic and vegetation change mainly at the local and regional scales. It demonstrates that the impact of arctic warming on land cover change and the Arctic ecosystems is not unidirectional and one dimensional in nature but it represents a multi-directional and multi-dimensional forces operating in a feedback system.

Keywords: Arctic Vegetation Change, Climate Change, Feedback System, Spatial Process and Structure.

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Authors: Maya Rupert, Salima Hassas, Carlos Li, John Sherwood

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Online Communities are an example of sociallyaware, self-organising, complex adaptive computing systems. The multi-agent systems (MAS) paradigm coordinated by self-organisation mechanisms has been used as an effective way for the simulation and modeling of such systems. In this paper, we propose a model for simulating an online health community using a situated multi-agent system approach, governed by the co-evolution of the social and spatial organisations of the agents.

Keywords: multi-agent systems, organizations, online communities.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

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Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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Authors: Y. Chaiko

Abstract:

It is important to provide possibility of so called “handover" for the mobile subscriber from GSM network to Wi-Fi network and back. To solve specified problem it is necessary to estimate connection time between base station and wireless access point. Difficulty to estimate this parameter is that it doesn-t described in specifications of the standard and, hence, no recommended value is given. In this paper, the analytical model is presented that allows the estimating connection time between base station and IEEE 802.11 access point.

Keywords: Access point, connection procedure, Wi-Fi network.

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Authors: Menglong Su, Shaoyun Shi, Qing Xu

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

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

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Authors: Amir Shafeeq, Ayyaz Muhammad, Noman Hassan, Rofice Dickson

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Different vegetable oil based biodiesel (FAMES) were prepared by alkaline transesterification using refined oils as well as waste frying oil (WFO). Methanol and sodium hydroxide are used as catalyst under similar reaction conditions. To ensure the quality of biodiesel produced, a series of different ASTM Standard tests were carried out. In this context, various testwere done including viscosity, carbon residue, specific gravity, corrosion test, flash point, cloud point and pour point. Results revealed that characteristics of biodiesel depend on the feedstock and it is far better than petroleum diesel.

Keywords: Biodiesel, Edible oils, Separation.

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Authors: G. Revathi, P. Saikrishnan

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An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.

Keywords: Boundary layer, suction, mass transfer, rotating sphere.

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Authors: Christina Volioti, Sotiris Manitsaris, Eleni Katsouli, Vasiliki Tsekouropoulou, Leontios J. Hadjileontiadis

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The piano sonatas of Beethoven represent part of the Intangible Cultural Heritage. The aims of this research were to further explore this intangibility by placing emphasis on defining emotional normative ratings for the “Waldstein” (Op. 53) and “Tempest” (Op. 31) Sonatas of Beethoven. To this end, a musicological analysis was conducted on these particular sonatas and referential patterns in these works of Beethoven were defined. Appropriate interactive questionnaires were designed in order to create a statistical normative rating that describes the emotional status when an individual listens to these musical excerpts. Based on these ratings, it is possible for emotional annotations for these same referential patterns to be created and integrated into the music score.

Keywords: Emotional annotations, intangible cultural heritage, musicological analysis, normative ratings.

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Authors: R.Balamurugan, S.Subramanian

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This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.

Keywords: Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.

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Authors: Benshi Zhu

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In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method.

Keywords: Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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Authors: Li Feng

Abstract:

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.

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Authors: Harleen Kaur

Abstract:

Knowledge Discovery in Databases (KDD) is the process of extracting previously unknown, hidden and interesting patterns from a huge amount of data stored in databases. Data mining is a stage of the KDD process that aims at selecting and applying a particular data mining algorithm to extract an interesting and useful knowledge. It is highly expected that data mining methods will find interesting patterns according to some measures, from databases. It is of vital importance to define good measures of interestingness that would allow the system to discover only the useful patterns. Measures of interestingness are divided into objective and subjective measures. Objective measures are those that depend only on the structure of a pattern and which can be quantified by using statistical methods. While, subjective measures depend only on the subjectivity and understandability of the user who examine the patterns. These subjective measures are further divided into actionable, unexpected and novel. The key issues that faces data mining community is how to make actions on the basis of discovered knowledge. For a pattern to be actionable, the user subjectivity is captured by providing his/her background knowledge about domain. Here, we consider the actionability of the discovered knowledge as a measure of interestingness and raise important issues which need to be addressed to discover actionable knowledge.

Keywords: Data Mining Community, Knowledge Discovery inDatabases (KDD), Interestingness, Subjective Measures, Actionability.

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Authors: J. Areerut, F. Samuel

Abstract:

The purpose of this research is to analyze the pattern of television commercials and how they encourage non-governmental organizations to build their image in Thailand. It realizes how public relations can impact an organization's image. It is a truth that bad public relations management can cause hurt a reputation. On the other hand, a very small amount of work in public relations helps your organization to be recognized broadly and eventually accepted even wider. The main idea in this paper is to study and analyze patterns of television commercials that could impact non-governmental organization's images in a greater way. This research uses questionnaires and content analysis to summarize results. The findings show the aspects of how patterns of television commercials that are suited to non-governmental organization work in Thailand. It will be useful for any non-governmental organization that wishes to build their image through television commercials and also for further work based on this research.

Keywords: Television Commercial (TVC), Organization Image, Non-Governmental Organization: NGO, Public Relation.

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Authors: Nguyen Viet Tan

Abstract:

The Bahnar is one of 11 indigenous groups living in the Central Highlands of Vietnam. It is one among the four most popular groups in this area, including the Mnong who speak the same language of Mon Khmer family, while both groups of the Jrai and the Rhade belong to the Malayo-Polynesian language family. These groups once captured fertile plateaus, left their cultural and artistic heritage which affected the remaining small groups. Despite the difference in ethnic origins, these groups seem to share similar beliefs, customs and related folk arts after a very long time living beside each other. However, through an in-depth study, this paper points out the fact that the decorative patterns used by the Bahnar are different from the other ethnic groups, especially in color. Based on historical materials from the local museums and some studies in 1980s when all of the ethnic groups in this area had still lived in self-sufficient condition, this paper characterizes the traditional color scheme used by the Bahnar and identifies the difference in decorative motifs of this group compared to the others by pointing out they do not use green in their usual decorative patterns. Moreover, combined with some field surveys recently, through comparative analysis, it also discovers stylistic variations of these patterns in the process of cultural exchange with the other ethnic groups, both in and out of the region, in modern living conditions. This study helps to preserve and promote the traditional values and cultural identity of the Bahnar people in the Central Highlands of Vietnam, avoiding the fusion of styles among groups during the cultural exchange.

Keywords: Bahnar ethic group, decorative patterns, the central highland of Vietnam, traditional color scheme.

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Authors: Rima Hleiss, Elie Bitar, Mahmoud Hassan, Mohamad Khalil

Abstract:

A comprehensive study of object recognition in the human brain requires combining both spatial and temporal analysis of brain activity. Here, we are mainly interested in three issues: the time perception of visual objects, the ability of discrimination between two particular categories (objects vs. animals), and the possibility to identify a particular spatial representation of visual objects. Our experiment consisted of acquiring dense electroencephalographic (EEG) signals during a picture-naming task comprising a set of objects and animals’ images. These EEG responses were recorded from nine participants. In order to determine the time perception of the presented visual stimulus, we analyzed the Event Related Potentials (ERPs) derived from the recorded EEG signals. The analysis of these signals showed that the brain perceives animals and objects with different time instants. Concerning the discrimination of the two categories, the support vector machine (SVM) was applied on the instantaneous EEG (excellent temporal resolution: on the order of millisecond) to categorize the visual stimuli into two different classes. The spatial differences between the evoked responses of the two categories were also investigated. The results showed a variation of the neural activity with the properties of the visual input. Results showed also the existence of a spatial pattern of electrodes over particular regions of the scalp in correspondence to their responses to the visual inputs.

Keywords: Brain activity, dense EEG, evoked responses, spatiotemporal analysis, SVM, perception.

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Authors: Jooho Hwang, Chang-Kyu Song, Chun-Hong Park

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This paper describes a method to measure and compensate a 4 axes ultra-precision machine tool that generates micro patterns on the large surfaces. The grooving machine is usually used for making a micro mold for many electrical parts such as a light guide plate for LCD and fuel cells. The ultra precision machine tool has three linear axes and one rotational table. Shaping is usually used to generate micro patterns. In the case of 50 μm pitch and 25 μm height pyramid pattern machining with a 90° wedge angle bite, one of linear axis is used for long stroke motion for high cutting speed and other linear axis are used for feeding. The triangular patterns can be generated with many times of long stroke of one axis. Then 90° rotation of work piece is needed to make pyramid patterns with superposition of machined two triangular patterns. To make a two dimensional positioning error, straightness of two axes in out of plane, squareness between the each axis are important. Positioning errors, straightness and squarness were measured by laser interferometer system. Those were compensated and confirmed by ISO230-6. One of difficult problem to measure the error motions is squareness or parallelism of axis between the rotational table and linear axis. It was investigated by simultaneous moving of rotary table and XY axes. This compensation method is introduced in this paper.

Keywords: Ultra-precision machine tool, muti-axis errors, squraness, positioning errors.

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