Search results for: Decision Support System.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 10452

Search results for: Decision Support System.

6342 The Analysis of Different Classes of Weighted Fuzzy Petri Nets and Their Features

Authors: Yurii Bloshko, Oksana Olar

Abstract:

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: Fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms.

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6341 Effects of Initial State on Opinion Formation in Complex Social Networks with Noises

Authors: Yi Yu, Vu Xuan Nguyen, Gaoxi Xiao

Abstract:

Opinion formation in complex social networks may exhibit complex system dynamics even when based on some simplest system evolution models. An interesting and important issue is the effects of the initial state on the final steady-state opinion distribution. By carrying out extensive simulations and providing necessary discussions, we show that, while different initial opinion distributions certainly make differences to opinion evolution in social systems without noises, in systems with noises, given enough time, different initial states basically do not contribute to making any significant differences in the final steady state. Instead, it is the basal distribution of the preferred opinions that contributes to deciding the final state of the systems. We briefly explain the reasons leading to the observed conclusions. Such an observation contradicts with a long-term belief on the roles of system initial state in opinion formation, demonstrating the dominating role that opinion mutation can play in opinion formation given enough time. The observation may help to better understand certain observations of opinion evolution dynamics in real-life social networks.

Keywords: Opinion formation, Deffuant model, opinion mutation, consensus making.

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6340 IRIS: An Interactive Video Game for Children with Long-Term Illness in Hospitals

Authors: Ganetsou Evanthia, Koutsikos Emmanouil, Austin Anna Maria

Abstract:

Information technology has long served the needs of individuals for learning and entertainment, but much less for children in sickness. The aim of the proposed online video game is to provide immersive learning opportunities as well as essential social and emotional scenarios for hospital-bound children with long-term illness. Online self-paced courses on chosen school subjects, including specialized software and multisensory assessments, aim at enhancing children’s academic achievement and sense of inclusion, while doctor minigames familiarize and educate young patients on their medical conditions. Online ethical dilemmas will offer children opportunities to contemplate on the importance of medical procedures and following assigned medication, often challenging for young patients; they will therefore reflect on their condition, re-evaluate their perceptions about hospitalization, and assume greater personal responsibility for their progress. Children’s emotional and psychosocial needs are addressed by engaging in social conventions, such as interactive, daily, collaborative mini games with other hospitalized peers, like virtual competitive sports games, weekly group psychodrama sessions, and online birthday parties or sleepovers. Social bonding is also fostered by having a virtual pet to interact with and take care of, as well as a virtual nurse to discuss and reflect on the mood of the day, engage in constructive dialogue and perspective-taking, and offer reminders. Access to the platform will be available throughout the day depending on the patient’s health status. The program is designed to minimize escapism and feelings of exclusion and can flexibly be adapted to offer post-treatment and a support online system at home.

Keywords: Hospitalized children, interactive games, long-term illness, cognitive enhancement, socioemotional development.

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6339 Meta Random Forests

Authors: Praveen Boinee, Alessandro De Angelis, Gian Luca Foresti

Abstract:

Leo Breimans Random Forests (RF) is a recent development in tree based classifiers and quickly proven to be one of the most important algorithms in the machine learning literature. It has shown robust and improved results of classifications on standard data sets. Ensemble learning algorithms such as AdaBoost and Bagging have been in active research and shown improvements in classification results for several benchmarking data sets with mainly decision trees as their base classifiers. In this paper we experiment to apply these Meta learning techniques to the random forests. We experiment the working of the ensembles of random forests on the standard data sets available in UCI data sets. We compare the original random forest algorithm with their ensemble counterparts and discuss the results.

Keywords: Random Forests [RF], ensembles, UCI.

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6338 A New Nonlinear PID Controller and its Parameter Design

Authors: Yongping Ren, Zongli Li, Fan Zhang

Abstract:

A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme.

Keywords: Nonlinear PID controller, stability, gain equivalence, dissipative, T-Passivity.

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6337 Experimental Investigation on Excess Pore Water Pressure in Soft Soil-Foundations under Minor Shocks

Authors: Zhiying Zhang, Chongdu Cho, Qiang Pan, Xilin Lu

Abstract:

In this study, shaking table tests are performed to investigate the behavior of excess pore water pressure in different soft soil-foundations of soil-structure interaction (SSI) system. The variation of the behaviors under cycled minor shock is observed. Moreover, The generation and variation mechanism of excess pore water pressure under earthquake excitation in different soft soilfoundations are analyzed and discussed.

Keywords: Excess pore water pressure, shaking table tests, soft soil foundation, SSI system.

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6336 Developing a Structured and Strategically Focused Performance Assessment System

Authors: Isabel Duarte de Almeida, João Vilas-Boas, Ana Abrantes Cabral

Abstract:

The number and adequacy of Performance-Indicators (PIs) for organisational purposes are core to the success of organisations and a major concern to the sponsor of this research. This assignment developed a procedure to improve a firm’s performance assessment system, by identifying two key-PIs out of 28 initial ones, and by setting criteria and their relative importance to validate and rank the adequacy and the right number of operational metrics. The Analytical-Hierarchy-Process was used with a synthesismethod to treat data coming from the management inquiries. Although organisational alignment has been achieved, business processes should also be targeted and PIs continuously revised.

Keywords: Strategic performance assessment systems, Key Performance Indicators (KPIs), Analytical Hierarchy Process (AHP).

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6335 Plug and Play Interferometer Configuration using Single Modulator Technique

Authors: Norshamsuri Ali, Hafizulfika, Salim Ali Al-Kathiri, Abdulla Al-Attas, Suhairi Saharudin, Mohamed Ridza Wahiddin

Abstract:

We demonstrate single-photon interference over 10 km using a plug and play system for quantum key distribution. The quality of the interferometer is measured by using the interferometer visibility. The coding of the signal is based on the phase coding and the value of visibility is based on the interference effect, which result a number of count. The setup gives full control of polarization inside the interferometer. The quality measurement of the interferometer is based on number of count per second and the system produces 94 % visibility in one of the detectors.

Keywords: single photon, interferometer, quantum key distribution.

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6334 Choosing an Ontology Language

Authors: Anna V. Zhdanova, Uwe Keller

Abstract:

We summarize information that facilitates choosing an ontology language for knowledge intensive applications. This paper is a short version of the ontology language state-of-the-art and evolution analysis carried out for choosing an ontology language in the IST Esperonto project. At first, we analyze changes and evolution that took place in the filed of Semantic Web languages during the last years, in particular, around the ontology languages of the RDF/S and OWL family. Second, we present current trends in development of Semantic Web languages, in particular, rule support extensions for Semantic Web languages and emerging ontology languages such as WSMO languages.

Keywords: OWL, RDF/S, Semantic Web Languages, WSML

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6333 Application of Phase Change Materials (PCMs) in Maintaining Comfort Temperature inside an Automobile

Authors: A. Jamekhorshid, S. M. Sadrameli

Abstract:

This paper presents the modeling results of an innovative system for the temperature control in the interior compartment of a stationary automobile facing the solar energy from the sun. A very thin layer of PCM inside a pouch placed in the ceiling of the car in which the heating energy is absorbed and release with melting and solidification of phase change materials. As a result the temperature of the car interior is maintained in the comfort condition. The amount of required PCM has been calculated to be about 755 g. The PCM-temperature controlling system is simple and has a potential to be implemented as a practical solution to prevent undesirable heating of the automobile-s cabin.

Keywords: Phase Change Material (PCM), automobile's cabin, temperature control

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6332 Forecasting Rainfall in Thailand: A Case Study of Nakhon Ratchasima Province

Authors: N. Sopipan

Abstract:

In this paper, we study the rainfall using a time series for weather stations in Nakhon Ratchasima province in Thailand by various statistical methods to enable us to analyse the behaviour of rainfall in the study areas. Time-series analysis is an important tool in modelling and forecasting rainfall. The ARIMA and Holt-Winter models were built on the basis of exponential smoothing. All the models proved to be adequate. Therefore it is possible to give information that can help decision makers establish strategies for the proper planning of agriculture, drainage systems and other water resource applications in Nakhon Ratchasima province. We obtained the best performance from forecasting with the ARIMA Model(1,0,1)(1,0,1)12.

Keywords: ARIMA Models, Exponential Smoothing, Holt- Winter model.

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6331 Multi-Agent Approach for Monitoring and Control of Biotechnological Processes

Authors: Ivanka Valova

Abstract:

This paper is aimed at using a multi-agent approach to monitor and diagnose a biotechnological system in order to validate certain control actions depending on the process development and the operating conditions. A multi-agent system is defined as a network of interacting software modules that collectively solve complex tasks. Remote monitoring and control of biotechnological processes is a necessity when automated and reliable systems operating with no interruption of certain activities are required. The advantage of our approach is in its flexibility, modularity and the possibility of improving by acquiring functionalities through the integration of artificial intelligence.

Keywords: Multi-agent approach, artificial intelligence, biotechnological processes, anaerobic biodegradation.

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6330 Multi-Rate Exact Discretization based on Diagonalization of a Linear System - A Multiple-Real-Eigenvalue Case

Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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6329 Optimization Based Obstacle Avoidance

Authors: R. Dariani, S. Schmidt, R. Kasper

Abstract:

Based on a non-linear single track model which describes the dynamics of vehicle, an optimal path planning strategy is developed. Real time optimization is used to generate reference control values to allow leading the vehicle alongside a calculated lane which is optimal for different objectives such as energy consumption, run time, safety or comfort characteristics. Strict mathematic formulation of the autonomous driving allows taking decision on undefined situation such as lane change or obstacle avoidance. Based on position of the vehicle, lane situation and obstacle position, the optimization problem is reformulated in real-time to avoid the obstacle and any car crash.

Keywords: Autonomous driving, Obstacle avoidance, Optimal control, Path planning.

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6328 Experimental Study of Thermal Environment in a Room with Mixing Ventilation

Authors: Dong-Mei Pan, Liang XIA, Ming-Yin Chan

Abstract:

This paper reports an experimental study on a sleeping thermal manikin in a room equipped with a mixing ventilation system. In the experimental work, heat loss from the sleeping thermal manikin was measured under different conditions. The supply air temperature was in a range of 17°C to 27°C. Apart from the heat loss of the sleeping thermal manikin, the velocity distributions and temperature distributions were also measured in the experiments for subsequent analysis.

Keywords: Sleeping Environment, Mixing Ventilation System

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6327 Method for Auto-Calibrate Projector and Color-Depth Systems for Spatial Augmented Reality Applications

Authors: R. Estrada, A. Henriquez, R. Becerra, C. Laguna

Abstract:

Spatial Augmented Reality is a variation of Augmented Reality where the Head-Mounted Display is not required. This variation of Augmented Reality is useful in cases where the need for a Head-Mounted Display itself is a limitation. To achieve this, Spatial Augmented Reality techniques substitute the technological elements of Augmented Reality; the virtual world is projected onto a physical surface. To create an interactive spatial augmented experience, the application must be aware of the spatial relations that exist between its core elements. In this case, the core elements are referred to as a projection system and an input system, and the process to achieve this spatial awareness is called system calibration. The Spatial Augmented Reality system is considered calibrated if the projected virtual world scale is similar to the real-world scale, meaning that a virtual object will maintain its perceived dimensions when projected to the real world. Also, the input system is calibrated if the application knows the relative position of a point in the projection plane and the RGB-depth sensor origin point. Any kind of projection technology can be used, light-based projectors, close-range projectors, and screens, as long as it complies with the defined constraints; the method was tested on different configurations. The proposed procedure does not rely on a physical marker, minimizing the human intervention on the process. The tests are made using a Kinect V2 as an input sensor and several projection devices. In order to test the method, the constraints defined were applied to a variety of physical configurations; once the method was executed, some variables were obtained to measure the method performance. It was demonstrated that the method obtained can solve different arrangements, giving the user a wide range of setup possibilities.

Keywords: Color depth sensor, human computer interface, interactive surface, spatial augmented reality.

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6326 Application of Rapid Prototyping to Create Additive Prototype Using Computer System

Authors: Meftah O. Bashir, Fatma A. Karkory

Abstract:

Rapid prototyping is a new group of manufacturing processes, which allows fabrication of physical of any complexity using a layer by layer deposition technique directly from a computer system. The rapid prototyping process greatly reduces the time and cost necessary to bring a new product to market. The prototypes made by these systems are used in a range of industrial application including design evaluation, verification, testing, and as patterns for casting processes. These processes employ a variety of materials and mechanisms to build up the layers to build the part. The present work was to build a FDM prototyping machine that could control the X-Y motion and material deposition, to generate two-dimensional and three-dimensional complex shapes. This study focused on the deposition of wax material. This work was to find out the properties of the wax materials used in this work in order to enable better control of the FDM process. This study will look at the integration of a computer controlled electro-mechanical system with the traditional FDM additive prototyping process. The characteristics of the wax were also analysed in order to optimise the model production process. These included wax phase change temperature, wax viscosity and wax droplet shape during processing.

Keywords: Rapid prototyping, wax, manufacturing processes, additive prototyping.

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6325 Low-complexity Integer Frequency Offset Synchronization for OFDMA System

Authors: Young-Jae Kim, Young-Hwan You

Abstract:

This paper presents a integer frequency offset (IFO) estimation scheme for the 3GPP long term evolution (LTE) downlink system. Firstly, the conventional joint detection method for IFO and sector cell index (CID) information is introduced. Secondly, an IFO estimation without explicit sector CID information is proposed, which can operate jointly with the proposed IFO estimation and reduce the time delay in comparison with the conventional joint method. Also, the proposed method is computationally efficient and has almost similar performance in comparison with the conventional method over the Pedestrian and Vehicular channel models.

Keywords: LTE, OFDMA, primary synchronization signal (PSS), IFO, CID

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6324 Solving SPDEs by a Least Squares Method

Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.

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6323 Explorations in the Role of Emotion in Moral Judgment

Authors: Arthur Yan

Abstract:

Recent theorizations on the cognitive process of moral judgment have focused on the role of intuitions and emotions, marking a departure from previous emphasis on conscious, step-by-step reasoning. My study investigated how being in a disgusted mood state affects moral judgment. Participants were induced to enter a disgusted mood state through listening to disgusting sounds and reading disgusting descriptions. Results shows that they, when compared to control who have not been induced to feel disgust, are more likely to endorse actions that are emotionally aversive but maximizes utilitarian return The result is analyzed using the 'emotion-as-information' approach to decision making. The result is consistent with the view that emotions play an important role in determining moral judgment.

Keywords: Disgust, mood induction, moral judgment, emotion-as-information.

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6322 Comparison of Valuation Techniques for Bone Age Assessment

Authors: N. Olarte L, A. Rubiano F, A. Mejía F.

Abstract:

This comparison of valuation techniques for bone age assessment is a work carried out by the Telemedicine Research Group of the Military University - TIGUM, as a preliminary to the Design and development a treatment system of hand and wrist radiological images for children aged 0-6 years to bone age assessment . In this paper the techniques mentioned for decades have been the most widely used and the statistically significant. Althought, initially with the current project, it wants to work with children who have limit age, this comparison and evaluation techniques work will help in the future to expand the study subject in the system to bone age assessment, implementing more techniques, tools and deeper analysis to accomplish this purpose.

Keywords: Atlas, Bone Age Assessment, Hand and Wrist Radiograph, Image Processing

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6321 Unified Structured Process for Health Analytics

Authors: Supunmali Ahangama, Danny Chiang Choon Poo

Abstract:

Health analytics (HA) is used in healthcare systems for effective decision making, management and planning of healthcare and related activities. However, user resistances, unique position of medical data content and structure (including heterogeneous and unstructured data) and impromptu HA projects have held up the progress in HA applications. Notably, the accuracy of outcomes depends on the skills and the domain knowledge of the data analyst working on the healthcare data. Success of HA depends on having a sound process model, effective project management and availability of supporting tools. Thus, to overcome these challenges through an effective process model, we propose a HA process model with features from rational unified process (RUP) model and agile methodology.

Keywords: Agile methodology, health analytics, unified process model, UML.

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6320 Simulation for Input-Output Energy Structure in Agriculture: Bangladesh

Authors: M. S. Alam, M. R. Alam, Nusrat Jahan Imu

Abstract:

This paper presents a computer simulation model based on system dynamics methodology for analyzing the dynamic characteristics of input energy structure in agriculture and Bangladesh is used here as a case study for model validation. The model provides an input energy structure linking the major energy flows with human energy and draft energy from cattle as well as tractors and/or power tillers, irrigation, chemical fertilizer and pesticide. The evaluation is made in terms of different energy dependent indicators. During the simulation period, the energy input to agriculture increased from 6.1 to 19.15 GJ/ha i.e. 2.14 fold corresponding to energy output in terms of food, fodder and fuel increase from 71.55 to 163.58 GJ/ha i.e. 1.28 fold from the base year. This result indicates that the energy input in Bangladeshi agricultural production is increasing faster than the energy output. Problems such as global warming, nutrient loading and pesticide pollution can associate with this increasing input. For an assessment, a comparative statement of input energy use in agriculture of developed countries (DCs) and least developed countries (LDCs) including Bangladesh has been made. The performance of the model is found satisfactory to analyze the agricultural energy system for LDCs

Keywords: Agriculture, energy indicator, system dynamics, energy flows.

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6319 A New Method of Adaptation in Integrated Learning Environment

Authors: Ildar Galeev, Renat Mustaphin, C. Ardil

Abstract:

A new method of adaptation in a partially integrated learning environment that includes electronic textbook (ET) and integrated tutoring system (ITS) is described. The algorithm of adaptation is described in detail. It includes: establishment of Interconnections of operations and concepts; estimate of the concept mastering level (for all concepts); estimate of student-s non-mastering level on the current learning step of information on each page of ET; creation of a rank-order list of links to the e-manual pages containing information that require repeated work.

Keywords: Adaptation, Integrated Learning Environment, Integrated Tutoring System, Electronic Textbook.

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6318 Survey on Arabic Sentiment Analysis in Twitter

Authors: Sarah O. Alhumoud, Mawaheb I. Altuwaijri, Tarfa M. Albuhairi, Wejdan M. Alohaideb

Abstract:

Large-scale data stream analysis has become one of the important business and research priorities lately. Social networks like Twitter and other micro-blogging platforms hold an enormous amount of data that is large in volume, velocity and variety. Extracting valuable information and trends out of these data would aid in a better understanding and decision-making. Multiple analysis techniques are deployed for English content. Moreover, one of the languages that produce a large amount of data over social networks and is least analyzed is the Arabic language. The proposed paper is a survey on the research efforts to analyze the Arabic content in Twitter focusing on the tools and methods used to extract the sentiments for the Arabic content on Twitter.

Keywords: Big Data, Social Networks, Sentiment Analysis.

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6317 A Survey of Discrete Facility Location Problems

Authors: Z. Ulukan, E. Demircioğlu

Abstract:

Facility location is a complex real-world problem which needs a strategic management decision. This paper provides a general review on studies, efforts and developments in Facility Location Problems which are classical optimization problems having a wide-spread applications in various areas such as transportation, distribution, production, supply chain decisions and telecommunication. Our goal is not to review all variants of different studies in FLPs or to describe very detailed computational techniques and solution approaches, but rather to provide a broad overview of major location problems that have been studied, indicating how they are formulated and what are proposed by researchers to tackle the problem. A brief, elucidative table based on a grouping according to “General Problem Type” and “Methods Proposed” used in the studies is also presented at the end of the work.

Keywords: Discrete location problems, exact methods, heuristic algorithms, single source capacitated facility location problems.

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6316 System Detecting Border Gateway Protocol Anomalies Using Local and Remote Data

Authors: A. Starczewska, A. Nawrat, K. Daniec, J. Homa, K. Hołda

Abstract:

Border Gateway Protocol (BGP) is the main routing protocol that enables routing establishment between all autonomous systems, which are the basic administrative units of the internet. Due to the poor protection of BGP, it is important to use additional BGP security systems. Many solutions to this problem have been proposed over the years, but none of them have been implemented on a global scale. This article describes a system capable of building images of real-time BGP network topology in order to detect BGP anomalies. Our proposal performs a detailed analysis of BGP messages that come into local network cards supplemented by information collected by remote collectors in different localizations.

Keywords: Border Gateway Protocol, BGP, BGP hijacking, cybersecurity, detection.

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6315 Cooperative CDD Scheme Based On Adaptive Modulation in Wireless Communication System

Authors: Seung-Jun Yu, Hwan-Jun Choi, Hyoung-Kyu Song

Abstract:

Among spatial diversity scheme, orthogonal space-time block code (OSTBC) and cyclic delay diversity (CDD) have been widely studied for the cooperative wireless relaying system. However, conventional OSTBC and CDD cannot cope with change in the number of relays owing to low throughput or error performance. In this paper, we propose a cooperative cyclic delay diversity (CDD) scheme that use hierarchical modulation at the source and adaptive modulation based on cyclic redundancy check (CRC) code at the relays.

Keywords: Adaptive modulation, Cooperative communication, CDD, OSTBC.

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6314 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case

Authors: Salim Ibrir

Abstract:

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

Keywords: Singular systems, Discrete-time systems, Regularization, LMIs

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6313 Modeling Language for Machine Learning

Authors: Tsuyoshi Okita, Tatsuya Niwa

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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