Search results for: Existing concept
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2943

Search results for: Existing concept

2283 Detection of Diabetic Symptoms in Retina Images Using Analog Algorithms

Authors: Daniela Matei, Radu Matei

Abstract:

In this paper a class of analog algorithms based on the concept of Cellular Neural Network (CNN) is applied in some processing operations of some important medical images, namely retina images, for detecting various symptoms connected with diabetic retinopathy. Some specific processing tasks like morphological operations, linear filtering and thresholding are proposed, the corresponding template values are given and simulations on real retina images are provided.

Keywords: Diabetic retinopathy, pathology detection, cellular neural networks, analog algorithms.

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2282 A Case of Study for 3D Stereoscopic Conversion in Visual Effects Industry

Authors: Jin Zhi

Abstract:

This paper covered a series of key points in terms of 2D to 3D stereoscopic conversion. A successfully applied stereoscopic conversion approach in current visual effects industry was presented. The purpose of this paper is to cover a detailed workflow and concept, which has been successfully used in 3D stereoscopic conversion for feature films in visual effects industry, and therefore to clarify the process in stereoscopic conversion production and provide a clear idea for those entry-level artists to improve an overall understanding of 3D stereoscopic in digital compositing field as well as to the higher education factor of visual effects and hopefully inspire further collaboration and participants particularly between academia and industry.

Keywords: Clean plates, Mattes, Stereoscopic conversion, 3Dprojection, Z-depth.

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2281 Fuzzy Power Controller Design for Purdue University Research Reactor-1

Authors: Oktavian Muhammad Rizki, Appiah Rita, Lastres Oscar, Miller True, Chapman Alec, Tsoukalas Lefteri H.

Abstract:

The Purdue University Research Reactor-1 (PUR-1) is a 10 kWth pool-type research reactor located at Purdue University’s West Lafayette campus. The reactor was recently upgraded to use entirely digital instrumentation and control systems. However, currently, there is no automated control system to regulate the power in the reactor. We propose a fuzzy logic controller as a form of digital twin to complement the existing digital instrumentation system to monitor and stabilize power control using existing experimental data. This work assesses the feasibility of a power controller based on a Fuzzy Rule-Based System (FRBS) by modelling and simulation with a MATLAB algorithm. The controller uses power error and reactor period as inputs and generates reactivity insertion as output. The reactivity insertion is then converted to control rod height using a logistic function based on information from the recorded experimental reactor control rod data. To test the capability of the proposed fuzzy controller, a point-kinetic reactor model is utilized based on the actual PUR-1 operation conditions and a Monte Carlo N-Particle simulation result of the core to numerically compute the neutronics parameters of reactor behavior. The Point Kinetic Equation (PKE) was employed to model dynamic characteristics of the research reactor since it explains the interactions between the spatial and time varying input and output variables efficiently. The controller is demonstrated computationally using various cases: startup, power maneuver, and shutdown. From the test results, it can be proved that the implemented fuzzy controller can satisfactorily regulate the reactor power to follow demand power without compromising nuclear safety measures.

Keywords: Fuzzy logic controller, power controller, reactivity, research reactor.

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2280 Research of Data Cleaning Methods Based on Dependency Rules

Authors: Yang Bao, Shi Wei Deng, Wang Qun Lin

Abstract:

This paper introduces the concept and principle of data cleaning, analyzes the types and causes of dirty data, and proposes several key steps of typical cleaning process, puts forward a well scalability and versatility data cleaning framework, in view of data with attribute dependency relation, designs several of violation data discovery algorithms by formal formula, which can obtain inconsistent data to all target columns with condition attribute dependent no matter data is structured (SQL) or unstructured (NoSql), and gives 6 data cleaning methods based on these algorithms.

Keywords: Data cleaning, dependency rules, violation data discovery, data repair.

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2279 Comparative Study of Intuitionistic and Generalized Neutrosophic Soft Sets

Authors: Debabrata Mandal

Abstract:

The aim of this paper is to define several operations such as Intersection, Union, OR, AND operations of intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Maji and compare these with intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Said et al via examples. At the end of the paper, a new concept - extension is introduced, which can be used to refine our choices in case of decision making.

Keywords: AND, OR, Union, Intersection, Extension, Decision making.

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2278 Analysis of Explosive Shock Wave and its Application in Snow Avalanche Release

Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

Avalanche velocity (from start to track zone) has been estimated in the present model for an avalanche which is triggered artificially by an explosive devise. The initial development of the model has been from the concept of micro-continuum theories [1], underwater explosions [2] and from fracture mechanics [3] with appropriate changes to the present model. The model has been computed for different slab depth R, slope angle θ, snow density ¤ü, viscosity μ, eddy viscosity η*and couple stress parameter η. The applicability of the present model in the avalanche forecasting has been highlighted.

Keywords: Snow avalanche velocity, avalanche zones, shockwave, couple stress fluids.

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2277 IFC-Based Construction Engineering Domain Otology Development

Authors: Jin Si, Yanzhong Wang

Abstract:

The essence of the 21st century is knowledge economy. Knowledge has become the key resource of economic growth and social development. Construction industry is no exception. Because of the characteristic of complexity, project manager can't depend only on information management. The only way to improve the level of construction project management is to set up a kind of effective knowledge accumulation mechanism. This paper first introduced the IFC standard and the concept of ontology. Then put forward the construction method of the architectural engineering domain ontology based on IFC. And finally build up the concepts, properties and the relationship between the concepts of the ontology. The deficiency of this paper is also pointed out.

Keywords: Construction Engineering, IFC, Ontology

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2276 Ontologies for Complex Event Processing

Authors: Irina Astrova, Arne Koschel, Jan Lukanowski, Jose Luis Munoz Martinez, Valerij Procenko, Marc Schaaf

Abstract:

In this paper, five ontologies are described, which include the event concepts. The paper provides an overview and comparison of existing event models. The main criteria for comparison are that there should be possibilities to model events with stretch in the time and location and participation of objects; however, there are other factors that should be taken into account as well. The paper also shows an example of using ontologies in complex event processing.

Keywords: Ontologies, events, complex event processing (CEP).

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2275 Routing Algorithm for a Clustered Network

Authors: Hemanth KumarA.R, Sudhakara G., Satyanarayana B.S.

Abstract:

The Cluster Dimension of a network is defined as, which is the minimum cardinality of a subset S of the set of nodes having the property that for any two distinct nodes x and y, there exist the node Si, s2 (need not be distinct) in S such that ld(x,s1) — d(y, s1)1 > 1 and d(x,s2) < d(x,$) for all s E S — {s2}. In this paper, strictly non overlap¬ping clusters are constructed. The concept of LandMarks for Unique Addressing and Clustering (LMUAC) routing scheme is developed. With the help of LMUAC routing scheme, It is shown that path length (upper bound)PLN,d < PLD, Maximum memory space requirement for the networkMSLmuAc(Az) < MSEmuAc < MSH3L < MSric and Maximum Link utilization factor MLLMUAC(i=3) < MLLMUAC(z03) < M Lc

Keywords: Metric dimension, Cluster dimension, Cluster.

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2274 Barriers and Conflicts in Relationships of Small Firms – Insights from Central Europe

Authors: Maciej Mitręga

Abstract:

This paper contributes to our knowledge about buyerseller relations by identifying barriers and conflict situations associated with maintaining and developing durable business relationships by small companies. The contribution of prior studies with regard to negative aspects of marketing relationships is presented in the first section. The international research results are discussed with regard to the existing conceptualizations and main research implications identified at the end.

Keywords: Relationship marketing, barriers, conflict, SME, international research.

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2273 Trust and Security in Electronic Payments: What We Have and Need to Know?

Authors: Theodosios Tsiakis, George Stephanides, George Pekos

Abstract:

The growth of open networks created the interest to commercialise it. The establishment of an electronic business mechanism must be accompanied by a digital-electronic payment system to transfer the value of transactions. Financial organizations are requested to offer a secure e-payment synthesis with equivalent levels of trust and security served in conventional paper-based payment transactions. The paper addresses the challenge of the first trade problem in e-commerce, provides a brief literature review on electronic payment and attempts to explain the underlying concept and method of trust in relevance to electronic payment.

Keywords: Electronic payment, security, trust, electronic business mechanism.

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2272 Models and Metamodels for Computer-Assisted Natural Language Grammar Learning

Authors: Evgeny Pyshkin, Maxim Mozgovoy, Vladislav Volkov

Abstract:

The paper follows a discourse on computer-assisted language learning. We examine problems of foreign language teaching and learning and introduce a metamodel that can be used to define learning models of language grammar structures in order to support teacher/student interaction. Special attention is paid to the concept of a virtual language lab. Our approach to language education assumes to encourage learners to experiment with a language and to learn by discovering patterns of grammatically correct structures created and managed by a language expert.

Keywords: Computer-assisted instruction, Language learning, Natural language grammar models, HCI.

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2271 Educational Robotics Constructivism and Modeling of Robots using Reverse Engineering

Authors: David G. Maxínez, A. Ferreyra Ramírez, Ismael Echenique Álvarez, Francisco Javier Sánchez Rangel, Guillermo Castillo Tapia, Petra Baldivia Noyola, María Antonieta García Galván

Abstract:

The project describes the modeling of various architectures mechatronics specifically morphologies of robots in an educational environment. Each structure developed by students of pre-school, primary and secondary was created using the concept of reverse engineering in a constructivist environment, to later be integrated in educational software that promotes the teaching of educational Robotics in a virtual and economic environment.

Keywords: Modeling, constructivist, engineering, reverse, robotics education, virtual, morphology.

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2270 Discovery of Production Rules with Fuzzy Hierarchy

Authors: Fadl M. Ba-Alwi, Kamal K. Bharadwaj

Abstract:

In this paper a novel algorithm is proposed that integrates the process of fuzzy hierarchy generation and rule discovery for automated discovery of Production Rules with Fuzzy Hierarchy (PRFH) in large databases.A concept of frequency matrix (Freq) introduced to summarize large database that helps in minimizing the number of database accesses, identification and removal of irrelevant attribute values and weak classes during the fuzzy hierarchy generation.Experimental results have established the effectiveness of the proposed algorithm.

Keywords: Data Mining, Degree of subsumption, Freq matrix, Fuzzy hierarchy.

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2269 Object Detection in Digital Images under Non-Standardized Conditions Using Illumination and Shadow Filtering

Authors: Waqqas-ur-Rehman Butt, Martin Servin, Marion Pause

Abstract:

In recent years, object detection has gained much attention and very encouraging research area in the field of computer vision. The robust object boundaries detection in an image is demanded in numerous applications of human computer interaction and automated surveillance systems. Many methods and approaches have been developed for automatic object detection in various fields, such as automotive, quality control management and environmental services. Inappropriately, to the best of our knowledge, object detection under illumination with shadow consideration has not been well solved yet. Furthermore, this problem is also one of the major hurdles to keeping an object detection method from the practical applications. This paper presents an approach to automatic object detection in images under non-standardized environmental conditions. A key challenge is how to detect the object, particularly under uneven illumination conditions. Image capturing conditions the algorithms need to consider a variety of possible environmental factors as the colour information, lightening and shadows varies from image to image. Existing methods mostly failed to produce the appropriate result due to variation in colour information, lightening effects, threshold specifications, histogram dependencies and colour ranges. To overcome these limitations we propose an object detection algorithm, with pre-processing methods, to reduce the interference caused by shadow and illumination effects without fixed parameters. We use the Y CrCb colour model without any specific colour ranges and predefined threshold values. The segmented object regions are further classified using morphological operations (Erosion and Dilation) and contours. Proposed approach applied on a large image data set acquired under various environmental conditions for wood stack detection. Experiments show the promising result of the proposed approach in comparison with existing methods.

Keywords: Image processing, Illumination equalization, Shadow filtering, Object detection, Colour models, Image segmentation.

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2268 Stereotype Student Model for an Adaptive e-Learning System

Authors: Ani Grubišić, Slavomir Stankov, Branko Žitko

Abstract:

This paper describes a concept of stereotype student model in adaptive knowledge acquisition e-learning system. Defined knowledge stereotypes are based on student's proficiency level and on Bloom's knowledge taxonomy. The teacher module is responsible for the whole adaptivity process: the automatic generation of courseware elements, their dynamic selection and sorting, as well as their adaptive presentation using templates for statements and questions. The adaptation of courseware is realized according to student-s knowledge stereotype.

Keywords: Adaptive e-learning systems, adaptive courseware, stereotypes, Bloom's knowledge taxonomy.

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2267 Experimental Characterization of a Thermoacoustic Travelling-Wave Refrigerator

Authors: M. Pierens, J.-P. Thermeau, T. Le Pollès, P. Duthil

Abstract:

The performances of a thermoacoustic travelling-wave refrigerator are presented. Developed in the frame of the European project called THATEA, it is designed for providing 600 W at a temperature of 233 K with an efficiency of 40 % relative to the Carnot efficiency. This paper presents the device and the results of the first measurements. For a cooling power of 210 W, a coefficient of performance relative to Carnot of 30 % is achieved when the refrigerator is coupled with an existing standing-wave engine.

Keywords: Refrigeration, sustainable energy, thermoacoustics, travelling-wave type heat pump

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2266 Mobile Cloud Middleware: A New Service for Mobile Users

Authors: K. Akherfi, H. Harroud

Abstract:

Cloud computing (CC) and mobile cloud computing (MCC) have advanced rapidly the last few years. Today, MCC undergoes fast improvement and progress in terms of hardware (memory, embedded sensors, power consumption, touch screen, etc.) software (more and more sophisticated mobile applications) and transmission (higher data transmission rates achieved with different technologies such as 3Gs). This paper presents a review on the concept of CC and MCC. Then, it discusses what has been done regarding middleware in cloud and mobile cloud computing. Later, it shows the architecture of our proposed middleware along with its functionalities which will be provided to mobile clients in order to overcome the well known problems (such as low battery power, slow CPU speed and little memory…).

Keywords: Context-aware, cloud computing, middleware, mobile cloud.

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2265 A New Approach for Controlling Overhead Traveling Crane Using Rough Controller

Authors: Mazin Z. Othman

Abstract:

This paper presents the idea of a rough controller with application to control the overhead traveling crane system. The structure of such a controller is based on a suggested concept of a fuzzy logic controller. A measure of fuzziness in rough sets is introduced. A comparison between fuzzy logic controller and rough controller has been demonstrated. The results of a simulation comparing the performance of both controllers are shown. From these results we infer that the performance of the proposed rough controller is satisfactory.

Keywords: Accuracy measure, Fuzzy Logic Controller (FLC), Overhead Traveling Crane (OTC), Rough Set Theory (RST), Roughness measure

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2264 Stroke Extraction and Approximation with Interpolating Lagrange Curves

Authors: Bence Kővári, ZSolt Kertész

Abstract:

This paper proposes a stroke extraction method for use in off-line signature verification. After giving a brief overview of the current ongoing researches an algorithm is introduced for detecting and following strokes in static images of signatures. Problems like the handling of junctions and variations in line width and line intensity are discussed in detail. Results are validated by both using an existing on-line signature database and by employing image registration methods.

Keywords: Stroke extraction, spline fitting, off-line signatureverification, image registration.

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2263 Cluster Based Energy Efficient and Fault Tolerant n-Coverage in Wireless Sensor Network

Authors: D. Satish Kumar, N. Nagarajan

Abstract:

Coverage conservation and extend the network lifetime are the primary issues in wireless sensor networks. Due to the large variety of applications, coverage is focus to a wide range of interpretations. The applications necessitate that each point in the area is observed by only one sensor while other applications may require that each point is enclosed by at least sensors (n>1) to achieve fault tolerance. Sensor scheduling activities in existing Transparent and non- Transparent relay modes (T-NT) Mobile Multi-Hop relay networks fails to guarantee area coverage with minimal energy consumption and fault tolerance. To overcome these issues, Cluster based Energy Competent n- coverage scheme called (CEC n-coverage scheme) to ensure the full coverage of a monitored area while saving energy. CEC n-coverage scheme uses a novel sensor scheduling scheme based on the n-density and the remaining energy of each sensor to determine the state of all the deployed sensors to be either active or sleep as well as the state durations. Hence, it is attractive to trigger a minimum number of sensors that are able to ensure coverage area and turn off some redundant sensors to save energy and therefore extend network lifetime. In addition, decisive a smallest amount of active sensors based on the degree coverage required and its level. A variety of numerical parameters are computed using ns2 simulator on existing (T-NT) Mobile Multi-Hop relay networks and CEC n-coverage scheme. Simulation results showed that CEC n-coverage scheme in wireless sensor network provides better performance in terms of the energy efficiency, 6.61% reduced fault tolerant in terms of seconds and the percentage of active sensors to guarantee the area coverage compared to exiting algorithm.

Keywords: Wireless Sensor network, Mobile Multi-Hop relay networks, n-coverage, Cluster based Energy Competent, Transparent and non- Transparent relay modes, Fault Tolerant, sensor scheduling.

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2262 Demystifying Full-Stack Observability: Mastering Visibility, Insight, and Action in the Modern Digital Landscape

Authors: Ashly Joseph

Abstract:

In the era of digital transformation, full-stack observability has emerged as a crucial aspect of administering modern application stacks. This research paper presents the concept of full-stack observability, its significance in the context of contemporary application stacks, and the challenges posed by swiftly evolving digital environments. In addition, it describes how full-stack observability intends to provide complete visibility and actionable insights by correlating telemetry across multiple domains.

Keywords: Actionable insights, digital transformation, full-stack observability, performance metrics.

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2261 Indoor Air Quality Analysis for Renovating Building: A Case Study of Student Studio, Department of Landscape, Chiangmai, Thailand

Authors: Warangkana Juangjandee

Abstract:

The rapidly increasing number of population in the limited area creates an effect on the idea of the improvement of the area to suit the environment and the needs of people. Faculty of architecture Chiang Mai University is also expanding in both variety fields of study and quality of education. In 2020, the new department will be introduced in the faculty which is Department of Landscape Architecture. With the limitation of the area in the existing building, the faculty plan to renovate some parts of its school for anticipates the number of students who will join the program in the next two years. As a result, the old wooden workshop area is selected to be renovated as student studio space. With such condition, it is necessary to study the restriction and the distinctive environment of the site prior to the improvement in order to find ways to manage the existing space due to the fact that the primary functions that have been practiced in the site, an old wooden workshop space and the new function, studio space, are too different. 72.9% of the annual times in the room are considered to be out of the thermal comfort condition with high relative humidity. This causes non-comfort condition for occupants which could promote mould growth. This study aims to analyze thermal comfort condition in the Landscape Learning Studio Area for finding the solution to improve indoor air quality and respond to local conditions. The research methodology will be in two parts: 1) field gathering data on the case study 2) analysis and finding the solution of improving indoor air quality. The result of the survey indicated that the room needs to solve non-comfort condition problem. This can be divided into two ways which are raising ventilation and indoor temperature, e.g. improving building design and stack driven ventilation, using fan for enhancing more internal ventilation.

Keywords: Relative humidity, renovation, temperature, thermal comfort.

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2260 Performance Modeling for Web based J2EE and .NET Applications

Authors: Shankar Kambhampaty, Venkata Srinivas Modali

Abstract:

When architecting an application, key nonfunctional requirements such as performance, scalability, availability and security, which influence the architecture of the system, are some times not adequately addressed. Performance of the application may not be looked at until there is a concern. There are several problems with this reactive approach. If the system does not meet its performance objectives, the application is unlikely to be accepted by the stakeholders. This paper suggests an approach for performance modeling for web based J2EE and .Net applications to address performance issues early in the development life cycle. It also includes a Performance Modeling Case Study, with Proof-of-Concept (PoC) and implementation details for .NET and J2EE platforms.

Keywords: Performance Measures, Performance Modeling, Performance Testing, Resource Utilization, Response Time, Throughput.

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2259 Enhancing the e-Government Functionality using Knowledge Management

Authors: Mohammad Al Rawajbeh, Ahmad Haboush

Abstract:

The primary aim of the e-government applications is the fast citizen service and the accomplishment of governmental functions. This paper discusses the knowledge management for egovernment development in the needs and role. The paper focused on analyzing the advantages of using knowledge management by using the existing IT technologies to maximize the government functions efficiency. The proposed new approach of providing government services is based on using Knowledge management as a part of e-government system.

Keywords: E-government, knowledge management, e-service, etools, governmental functions.

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2258 The Image as an Initial Element of the Cognitive Understanding of Words

Authors: S. Pesina, T. Solonchak

Abstract:

An analysis of word semantics focusing on the invariance of advanced imagery in several pressing problems. Interest in the language of imagery is caused by the introduction, in the linguistics sphere, of a new paradigm, the center of which is the personality of the speaker (the subject of the language). Particularly noteworthy is the question of the place of the image when discussing the lexical, phraseological values ​​and the relationship of imagery and metaphors. In part, the formation of a metaphor, as an interaction between two intellective entities, occurs at a cognitive level, and it is the category of the image, having cognitive roots, which aides in the correct interpretation of the results of this process on the lexical-semantic level.

Keywords: Image, metaphor, concept, creation of a metaphor, cognitive linguistics, erased image, vivid image.

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2257 Conditions on Blind Source Separability of Linear FIR-MIMO Systems with Binary Inputs

Authors: Jiashan Tang

Abstract:

In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the proposed criteria is weaker than that in the literature which requires that the channel matrix is irreducible/invertible or reversible.

Keywords: Blind source separable, FIR-MIMO system, Binary input, Bezout equality.

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2256 A Proposed Optimized and Efficient Intrusion Detection System for Wireless Sensor Network

Authors: Abdulaziz Alsadhan, Naveed Khan

Abstract:

In recent years intrusions on computer network are the major security threat. Hence, it is important to impede such intrusions. The hindrance of such intrusions entirely relies on its detection, which is primary concern of any security tool like Intrusion detection system (IDS). Therefore, it is imperative to accurately detect network attack. Numerous intrusion detection techniques are available but the main issue is their performance. The performance of IDS can be improved by increasing the accurate detection rate and reducing false positive. The existing intrusion detection techniques have the limitation of usage of raw dataset for classification. The classifier may get jumble due to redundancy, which results incorrect classification. To minimize this problem, Principle component analysis (PCA), Linear Discriminant Analysis (LDA) and Local Binary Pattern (LBP) can be applied to transform raw features into principle features space and select the features based on their sensitivity. Eigen values can be used to determine the sensitivity. To further classify, the selected features greedy search, back elimination, and Particle Swarm Optimization (PSO) can be used to obtain a subset of features with optimal sensitivity and highest discriminatory power. This optimal feature subset is used to perform classification. For classification purpose, Support Vector Machine (SVM) and Multilayer Perceptron (MLP) are used due to its proven ability in classification. The Knowledge Discovery and Data mining (KDD’99) cup dataset was considered as a benchmark for evaluating security detection mechanisms. The proposed approach can provide an optimal intrusion detection mechanism that outperforms the existing approaches and has the capability to minimize the number of features and maximize the detection rates.

Keywords: Particle Swarm Optimization (PSO), Principle component analysis (PCA), Linear Discriminant Analysis (LDA), Local Binary Pattern (LBP), Support Vector Machine (SVM), Multilayer Perceptron (MLP).

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2255 2D Image Processing for DSO Astrophotography

Authors: R. Suszynski, K. Wawryn, R. Wirski

Abstract:

The new concept of two–dimensional (2D) image processing implementation for auto-guiding system is shown in this paper. It is dedicated to astrophotography and operates with astronomy CCD guide cameras or with self-guided dual-detector CCD cameras and ST4 compatible equatorial mounts. This idea was verified by MATLAB model, which was used to test all procedures and data conversions. Next the circuit prototype was implemented at Altera MAX II CPLD device and tested for real astronomical object images. The digital processing speed of CPLD prototype board was sufficient for correct equatorial mount guiding in real-time system.

Keywords: DSO astrophotography, image processing, twodimensionalconvolution method, two-dimensional filtering.

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2254 Applications of Trigonometic Measures of Fuzzy Entropy to Geometry

Authors: Om Parkash, C.P.Gandhi

Abstract:

In the literature of fuzzy measures, there exist many well known parametric and non-parametric measures, each with its own merits and limitations. But our main emphasis is on applications of these measures to a variety of disciplines. To extend the scope of applications of these fuzzy measures to geometry, we need some special fuzzy measures. In this communication, we have introduced two new fuzzy measures involving trigonometric functions and simultaneously provided their applications to obtain the basic results already existing in the literature of geometry.

Keywords: Entropy, Uncertainty, Fuzzy Entropy, Concavity, Symmetry.

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