Search results for: hierarchical structure model.

Authors: G. M. Mir, Moinuddin, N. A. Shah

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In the age of global communications, heterogeneous networks are seen to be the best choice of strategy to ensure continuous and uninterruptible services. This will allow mobile terminal to stay in connection even they are migrating into different segment coverage through the handoff process. With the increase of teletraffic demands in mobile cellular system, hierarchical cellular systems have been adopted extensively for more efficient channel utilization and better QoS (Quality of Service). This paper presents a bidirectional call overflow scheme between two layers of microcells and macrocells, where handoffs are decided by the velocity of mobile making the call. To ensure that handoff calls are given higher priorities, it is assumed that guard channels are assigned in both macrocells and microcells. A hysteresis value introduced in mobile velocity is used to allow mobile roam in the same cell if its velocity changes back within the set threshold values. By doing this the number of handoffs is reduced thereby reducing the processing overhead and enhancing the quality of service to the end user.

Keywords: Hierarchical cellular systems, hysteresis, overflow, threshold.

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Authors: Wiem Daoud Ben Amor, Luis Martínez López, Jr., Hela Moalla Frikha

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Most of the multi-criteria group decision making (MCGDM) problems dealing with qualitative criteria require consideration of the large background of expert information. It is common that experts have different degrees of knowledge for giving their alternative assessments according to criteria. So, it seems logical that they use different evaluation scales to express their judgment, i.e., multi granular linguistic scales. In this context, we propose the extension of the classical additive ratio assessment (ARAS) method to the case of a hierarchical linguistics term for managing multi granular linguistic scales in uncertain context where uncertainty is modeled by means in linguistic information. The proposed approach is called the extended hierarchical linguistics-ARAS method (ELH-ARAS). Within the ELH-ARAS approach, the decision maker (DMs) can diagnose the results (the ranking of the alternatives) in a decomposed style i.e., not only at one level of the hierarchy but also at the intermediate ones. Also, the developed approach allows a feedback transformation i.e., the collective final results of all experts are able to be transformed at any level of the extended linguistic hierarchy that each expert has previously used. Therefore, the ELH-ARAS technique makes it easier for decision-makers to understand the results. Finally, an MCGDM case study is given to illustrate the proposed approach.

Keywords: Additive ratio assessment, extended hierarchical linguistic, multi-criteria group decision making problems, multi granular linguistic contexts.

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Authors: Tan Kian Lam, Abdullah Zawawi bin Haji Talib, Mohd. Azam Osman

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This paper describes a method of modeling to model shadow play puppet using sophisticated computer graphics techniques available in OpenGL in order to allow interactive play in real-time environment as well as producing realistic animation. This paper proposes a novel real-time method is proposed for modeling of puppet and its shadow image that allows interactive play of virtual shadow play using texture mapping and blending techniques. Special effects such as lighting and blurring effects for virtual shadow play environment are also developed. Moreover, the use of geometric transformations and hierarchical modeling facilitates interaction among the different parts of the puppet during animation. Based on the experiments and the survey that were carried out, the respondents involved are very satisfied with the outcomes of these techniques.

Keywords: Animation, blending, hierarchical modeling, interactive play, real-time, shadow play, visual simulation.

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Authors: Manisha Kankarej

Abstract:

The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, Integrability condition & Nijenhuis tensor.

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Authors: Rui Antunes, Fernando V. Coito

Abstract:

This article presents the development of a neural network cognitive model for the classification and detection of different frequency signals. The basic structure of the implemented neural network was inspired on the perception process that humans generally make in order to visually distinguish between high and low frequency signals. It is based on the dynamic neural network concept, with delays. A special two-layer feedforward neural net structure was successfully implemented, trained and validated, to achieve minimum target error. Training confirmed that this neural net structure descents and converges to a human perception classification solution, even when far away from the target.

Keywords: Neural Networks, Signal Classification, Adaptative Filters, Cognitive Neuroscience

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Authors: N. K. Sharma, J. Nayak, D. K. Sehgal, R. K. Pandey

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Bone material is treated as heterogeneous and hierarchical in nature therefore appropriate size of bone specimen is required to analyze its tensile properties at a particular hierarchical level. Tensile properties of cortical bone are important to investigate the effect of drug treatment, disease and aging as well as for development of computational and analytical models. In the present study tensile properties of buffalo as well as goat femoral and tibiae cortical bone are analyzed using sub-size tensile specimens. Femoral cortical bone was found to be stronger in tension as compared to the tibiae cortical bone and the tensile properties obtained using sub-size specimens show close resemblance with the tensile properties of full-size cortical specimens. A two dimensional finite element (FE) modal was also applied to simulate the tensile behavior of sub-size specimens. Good agreement between experimental and FE model was obtained for sub-size tensile specimens of cortical bone.

Keywords: Cortical bone, sub-size specimen, full size specimen, finite element modeling.

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Authors: Zhidong Zhang, Zhi-Chao Zhang

Abstract:

This study examined the mental health and behavioral problems in early adolescence with the instrument of Achenbach System of Empirically Based Assessment (ASEBA). The purpose of the study was stratified sampling method was used to collect data from 1975 participants. Multiple regression models and hierarchical regression models were applied to examine the relations between the background variables and internalizing problems, and the ones between students’ performance and internalizing problems. The results indicated that several background variables as predictors could significantly predict the anxious/depressed problem; reading and social study scores could significantly predict the anxious/depressed problem. However the class as a hierarchical macro factor did not indicate the significant effect. In brief, the majority of these models represented that the background variables, behaviors and academic performance were significantly related to the anxious/depressed problem.

Keywords: Behavioral problems, anxious/depression problems, empirical-based assessment, hierarchical modeling.

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Authors: Hermenegilde Nkurunziza, Albrecht Gebhardt, Juergen Pilz

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The focus in this work is to assess which method allows a better forecasting of malaria cases in Bujumbura ( Burundi) when taking into account association between climatic factors and the disease. For the period 1996-2007, real monthly data on both malaria epidemiology and climate in Bujumbura are described and analyzed. We propose a hierarchical approach to achieve our objective. We first fit a Generalized Additive Model to malaria cases to obtain an accurate predictor, which is then used to predict future observations. Various well-known forecasting methods are compared leading to different results. Based on in-sample mean average percentage error (MAPE), the multiplicative exponential smoothing state space model with multiplicative error and seasonality performed better.

Keywords: Burundi, Forecasting, Malaria, Regressionmodel, State space model.

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Authors: G. Schuh, A. Kampker, A. Hoeschen, T. Jasinski

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Today-s manufacturing companies are facing multiple and dynamic customer-supplier-relationships embedded in nonhierarchical production networks. This complex environment leads to problems with delivery reliability and wasteful turbulences throughout the entire network. This paper describes an operational model based on a theoretical framework which improves delivery reliability of each individual customer-supplier-relationship within non-hierarchical production networks of the European machinery and equipment industry. By developing a non-centralized coordination mechanism based on determining the value of delivery reliability and derivation of an incentive system for suppliers the number of in time deliveries can be increased and thus the turbulences in the production network smoothened. Comparable to an electronic stock exchange the coordination mechanism will transform the manual and nontransparent process of determining penalties for delivery delays into an automated and transparent market mechanism creating delivery reliability.

Keywords: delivery reliability, machinery and equipmentindustry, non-hierarchical production networks, supply chainmanagement

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Authors: Yasmin Mohd Yacob, Harsa A. Mat Sakim, Nor Ashidi Mat Isa

Abstract:

Feature selection study is gaining importance due to its contribution to save classification cost in terms of time and computation load. In search of essential features, one of the methods to search the features is via the decision tree. Decision tree act as an intermediate feature space inducer in order to choose essential features. In decision tree-based feature selection, some studies used decision tree as a feature ranker with a direct threshold measure, while others remain the decision tree but utilized pruning condition that act as a threshold mechanism to choose features. This paper proposed threshold measure using Manhattan Hierarchical Cluster distance to be utilized in feature ranking in order to choose relevant features as part of the feature selection process. The result is promising, and this method can be improved in the future by including test cases of a higher number of attributes.

Keywords: Feature ranking, decision tree, hierarchical cluster, Manhattan distance.

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

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Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear identification, NNARX.

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Authors: Haidar Safa, Hassan Artail, Ahmad Mehio, Hicham Zahr, Ziad Matragi

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The Mobile IP Standard has been developed to support mobility over the Internet. This standard contains several drawbacks as in the cases where packets are routed via sub-optimal paths and significant amount of signaling messages is generated due to the home registration procedure which keeps the network aware of the current location of the mobile nodes. Recently, a dynamic hierarchical mobility management strategy for mobile IP networks (DHMIP) has been proposed to reduce home registrations costs. However, this strategy induces a packet delivery delay and increases the risk of packet loss. In this paper, we propose an enhanced version of the dynamic hierarchical strategy that reduces the packet delivery delay and minimizes the risk of packet loss. Preliminary results obtained from simulations are promising. They show that the enhanced version outperforms the original dynamic hierarchical mobility management strategy version.

Keywords: Location management, Mobile IP (MIP), Home Agent, Foreign Agent.

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Authors: Oh Hyeon Jeon, WooYoung Jung

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In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

Keywords: Weir structure, seepage, flood disaster fragility, probabilistic risk assessment, Monte-Carlo Simulation, permeability coefficient.

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Authors: Mohammad Reza Oftadeh

Abstract:

The purpose of the article is to describe project objective structure (POS) concept that was developed on research activities and experiences about project management, Balanced Scorecard (BSC) and European Foundation Quality Management Excellence Model (EFQM Excellence Model). Furthermore, this paper tries to define a balanced, systematic, and integrated measurement approach to meet project objectives and project strategic goals based on a process-oriented model. In this paper, POS is suggested in order to measure project performance in the project life cycle. After using the POS model, the project manager can ensure in order to achieve the project objectives on the project charter. This concept can help project managers to implement integrated and balanced monitoring and control project work.

Keywords: Project objectives, project performance management, PMBOK, key performance indicators, integration management.

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Authors: R. AliMohammadzadeh, M. Rahgozar, A. Zarnani

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The inherent flexibilities of XML in both structure and semantics makes mining from XML data a complex task with more challenges compared to traditional association rule mining in relational databases. In this paper, we propose a new model for the effective extraction of generalized association rules form a XML document collection. We directly use frequent subtree mining techniques in the discovery process and do not ignore the tree structure of data in the final rules. The frequent subtrees based on the user provided support are split to complement subtrees to form the rules. We explain our model within multi-steps from data preparation to rule generation.

Keywords: XML, Data Mining, Association Rule Mining.

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Authors: Zongyan Li, Matt Best

Abstract:

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: Correlation analysis, F-ratio, Levenberg-Marquardt, MSE, NARX, neural network, optimisation.

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Authors: Seung-Jun Yu, Young-Min Ko, Hyoung-Kyu Song

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Recently developed cooperative diversity scheme enables a terminal to get transmit diversity through the support of other terminals. However, most of the introduced cooperative schemes have a common fault of decreased transmission rate because the destination should receive the decodable compositions of symbols from the source and the relay. In order to achieve high data rate, we propose a cooperative scheme that employs hierarchical modulation. This scheme is free from the rate loss and allows seamless cooperative communication.

Keywords: Cooperative communication, hierarchical modulation, high data rate, transmission scheme.

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Authors: Han-Soo Kim, Jae-Gyun Ahn, Hyo-Seung Ahn

Abstract:

Though nonlinear dynamic analysis using a specialized hydro-code such as AUTODYN is accurate and useful tool for progressive collapse assessment of a multi-story building subjected to blast load, it takes too much time to be applied to a practical simulation of progressive collapse of a tall building. In this paper, blast analysis of a RC frame structure using a simplified model with Reinforcement Contact technique provided in Ansys Workbench was introduced and investigated on its accuracy. Even though the simplified model has a fraction of elements of the detailed model, the simplified model with this modeling technique shows similar structural behavior under the blast load to the detailed model. The proposed modeling method can be effectively applied to blast loading progressive collapse analysis of a RC frame structure.

Keywords: Autodyn, Blast Load, Progressive Collapse, Reinforcement Contact.

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Authors: Minsoo Lee, Yun-mi Kim, Yoon-kyung Lee

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XML data consists of a very flexible tree-structure which makes it difficult to support the storing and retrieving of XML data. The node numbering scheme is one of the most popular approaches to store XML in relational databases. Together with the node numbering storage scheme, structural joins can be used to efficiently process the hierarchical relationships in XML. However, in order to process a tree-structured XPath query containing several hierarchical relationships and conditional sentences on XML data, many structural joins need to be carried out, which results in a high query execution cost. This paper introduces mechanisms to reduce the XPath queries including branch nodes into a much more efficient form with less numbers of structural joins. A two step approach is proposed. The first step merges duplicate nodes in the tree-structured query and the second step divides the query into sub-queries, shortens the paths and then merges the sub-queries back together. The proposed approach can highly contribute to the efficient execution of XML queries. Experimental results show that the proposed scheme can reduce the query execution cost by up to an order of magnitude of the original execution cost.

Keywords: XML, Xpath, tree-structured query, query reduction.

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Authors: Riaz A. Bhatti, Wang Yanrong

Abstract:

Particle damping is a technique to reduce the structural vibrations by means of placing small metallic particles inside a cavity that is attached to the structure at location of high vibration amplitudes. In this paper, we have presented an analytical model to simulate the particle damping of two dimensional transient vibrations in structure operating under high centrifugal loads. The simulation results show that this technique remains effective as long as the ratio of the dynamic acceleration of the structure to the applied centrifugal load is more than 0.1. Particle damping increases with the increase of particle to structure mass ratio. However, unlike to the case of particle damping in the absence of centrifugal loads where the damping efficiency strongly depends upon the size of the cavity, here this dependence becomes very weak. Despite the simplicity of the model, the simulation results are considerably in good agreement with the very scarce experimental data available in the literature for particle damping under centrifugal loads.

Keywords: Impact damping, particle damping, vibration control, vibration suppression.

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Authors: Le Kang

Abstract:

According to the nature of the university, as a free and responsible academic community, USR is based on a different foundation —academic responsibility, so the Pyramid and the IC Model of CSR could not fully explain the most distinguished feature of USR. This paper sought to put forward a new model— Ferris Wheel Model, to illustrate the nature of USR and the process of achievement. The Ferris Wheel Model of USR shows the university creates a balanced, fairness and neutrality systemic structure to afford social responsibilities; that makes the organization could obtain a synergistic effect to achieve more extensive interests of stakeholders and wider social responsibilities.

Keywords: USR, Achievement model, Ferris wheel model.

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Authors: Lenka Ševelová, Aleš Florian

Abstract:

Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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Authors: Hong Pan, Yaping Zhu, Liang Zheng Xia

Abstract:

We propose a fast and robust hierarchical face detection system which finds and localizes face images with a cascade of classifiers. Three modules contribute to the efficiency of our detector. First, heterogeneous feature descriptors are exploited to enrich feature types and feature numbers for face representation. Second, a PSO-Adaboost algorithm is proposed to efficiently select discriminative features from a large pool of available features and reinforce them into the final ensemble classifier. Compared with the standard exhaustive Adaboost for feature selection, the new PSOAdaboost algorithm reduces the training time up to 20 times. Finally, a three-stage hierarchical classifier framework is developed for rapid background removal. In particular, candidate face regions are detected more quickly by using a large size window in the first stage. Nonlinear SVM classifiers are used instead of decision stump functions in the last stage to remove those remaining complex nonface patterns that can not be rejected in the previous two stages. Experimental results show our detector achieves superior performance on the CMU+MIT frontal face dataset.

Keywords: Adaboost, Face detection, Feature selection, PSO

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Authors: Christian P. Crisostomo, Chrysline Margus N. Piñol

Abstract:

A zero-field ferromagnetic Ising model is utilized to simulate the propagation of infection in a population that assumes a square lattice structure. The rate of infection increases with temperature. The disease spreads faster among individuals with low J values. Such effect, however, diminishes at higher temperatures.

Keywords: Epidemiology, Ising model, lattice models

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Authors: Goh Chin Hock, Chandan Kumar Chakrabarty, Mohammad Hadi Badjian, Sanjay Devkumar

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This paper presents a microstrip meandered open circuited stub with bandstop characteristic. The proposed structure is designed on a high frequency laminate with dielectric constant of 4.0 and board thickness of 0.508 millimeters. The scattering parameters and electromagnetic field distributions at various frequencies are investigated by modeling the structure with three dimensional electromagnetic simulation tool. In order to describe the resonant and bandstop characteristic of the meandered open circuited stub, a Smith chart as well as electric field at various frequencies and phases is illustrated accordingly. The structure can be an alternative method in suppressing the harmonic response of a bandpass filter.

Keywords: Bandstop, Equivalent Lumped Element Model, Electromagnetic Model, Meandered Open Circuited Stub

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Authors: M. K. Witek-Hajduk, T. M. Napiórkowski

Abstract:

A number of studies discussed the topic of benefits of retailers-manufacturers cooperation and coopetition. However, there are only few publications focused on the benefits of cooperation and coopetition between retailers and their suppliers of durable consumer goods; especially in the context of business model of cooperating partners. This paper aims to provide a clustering approach to segment retailers selling consumer durables according to the benefits they obtain from their cooperation with key manufacturers and differentiate the said retailers’ in term of the business models of cooperating partners. For the purpose of the study, a survey (with a CATI method) collected data on 603 consumer durables retailers present on the Polish market. Retailers are clustered both, with hierarchical and non-hierarchical methods. Five distinctive groups of consumer durables’ retailers are (based on the studied benefits) identified using the two-stage clustering approach. The clusters are then characterized with a set of exogenous variables, key of which are business models employed by the retailer and its partnering key manufacturer. The paper finds that the a combination of a medium sized retailer classified as an Integrator with a chiefly domestic capital and a manufacturer categorized as a Market Player will yield the highest benefits. On the other side of the spectrum is medium sized Distributor retailer with solely domestic capital – in this case, the business model of the cooperating manufactrer appears to be irreleveant. This paper is the one of the first empirical study using cluster analysis on primary data that defines the types of cooperation between consumer durables’ retailers and manufacturers – their key suppliers. The analysis integrates a perspective of both retailers’ and manufacturers’ business models and matches them with individual and joint benefits.

Keywords: Business model, cooperation, cluster analysis, retailer-manufacturer relationships.

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Authors: Kamal K.Bharadwaj, Rekha Kandwal

Abstract:

An important structuring mechanism for knowledge bases is building clusters based on the content of their knowledge objects. The objects are clustered based on the principle of maximizing the intraclass similarity and minimizing the interclass similarity. Clustering can also facilitate taxonomy formation, that is, the organization of observations into a hierarchy of classes that group similar events together. Hierarchical representation allows us to easily manage the complexity of knowledge, to view the knowledge at different levels of details, and to focus our attention on the interesting aspects only. One of such efficient and easy to understand systems is Hierarchical Production rule (HPRs) system. A HPR, a standard production rule augmented with generality and specificity information, is of the following form Decision If < condition> Generality Specificity . HPRs systems are capable of handling taxonomical structures inherent in the knowledge about the real world. In this paper, a set of related HPRs is called a cluster and is represented by a HPR-tree. This paper discusses an algorithm based on cumulative learning scenario for dynamic structuring of clusters. The proposed scheme incrementally incorporates new knowledge into the set of clusters from the previous episodes and also maintains summary of clusters as Synopsis to be used in the future episodes. Examples are given to demonstrate the behaviour of the proposed scheme. The suggested incremental structuring of clusters would be useful in mining data streams.

Keywords: Cumulative learning, clustering, data mining, hierarchical production rules.

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Authors: P. Puustinen, A. Kanto

Abstract:

This paper proposes a new procedure for analyzing means-end chain data in marketing research. Most commonly the collected data is summarized in the Hierarchical Value Map (HVM) illustrating the main attribute-consequence-value linkages. This paper argues that traditionally constructed HVM may give an erroneous impression of the results of a means-end study. To justify the arguments, an alternative procedure to (1) determine the dominant attribute-consequence-value linkages and (2) construct HVM in a precise manner is presented. The current approach makes a contribution to means-end analysis, allowing marketers to address a set of marketing problems, such as advertising strategy.

Keywords: Means-end chain analysis, Laddering, Hierarchical Value Map.

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Authors: Adla Bentellis, Zizette Boufaïda

Abstract:

Nowadays, the pace of business change is such that, increasingly, new functionality has to be realized and reliably installed in a matter of days, or even hours. Consequently, more and more business processes are prone to a continuous change. The objective of the research in progress is to use the MAP model, in a conceptual modeling method for flexible and adaptive business process. This method can be used to capture the flexibility dimensions of a business process; it takes inspiration from modularity concept in the object oriented paradigm to establish a hierarchical construction of the BP modeling. Its intent is to provide a flexible modeling that allows companies to quickly adapt their business processes.

Keywords: Business Process, Business process modeling, flexibility, MAP Model.

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Authors: Dali Zhang, Baoqun Yin, Hongsheng Xi

Abstract:

In this paper, we propose a single sample path based algorithm with state aggregation to optimize the average rewards of singularly perturbed Markov reward processes (SPMRPs) with a large scale state spaces. It is assumed that such a reward process depend on a set of parameters. Differing from the other kinds of Markov chain, SPMRPs have their own hierarchical structure. Based on this special structure, our algorithm can alleviate the load in the optimization for performance. Moreover, our method can be applied on line because of its evolution with the sample path simulated. Compared with the original algorithm applied on these problems of general MRPs, a new gradient formula for average reward performance metric in SPMRPs is brought in, which will be proved in Appendix, and then based on these gradients, the schedule of the iteration algorithm is presented, which is based on a single sample path, and eventually a special case in which parameters only dominate the disturbance matrices will be analyzed, and a precise comparison with be displayed between our algorithm with the old ones which is aim to solve these problems in general Markov reward processes. When applied in SPMRPs, our method will approach a fast pace in these cases. Furthermore, to illustrate the practical value of SPMRPs, a simple example in multiple programming in computer systems will be listed and simulated. Corresponding to some practical model, physical meanings of SPMRPs in networks of queues will be clarified.

Keywords: Singularly perturbed Markov processes, Gradient of average reward, Differential reward, State aggregation, Perturbed close network.

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