Search results for: 3 edit σ rule

Authors: M. S. Annie Christi

Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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Authors: Ghulam Nabi Naz

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After independence, the popular belief that Gandhian will not indulge in corruption got a setback, post-independence setup paved the way for heavy corruption. The menace which would have dealt with strong legal provisions has become a way of life of Indian society. Corruption is recognized as the single biggest problem facing the country today. It undermines democracy and rule of law, violates human rights, distorts market and corrodes the moral fibre of people. The paper discusses the causes and possible remedial measures of corruption and response of people in Indian society. It emphasizes the factors which provide fertile ground for growth of corruption like, degradation of moral values, absence of a strong anti-corruption law and its effective enforcement, accountability, consistency and a defective system of fighting elections. The paper also highlights the reforms necessary for fighting corruption in India.

Keywords: Embezzlement, colonial, licence Raj, good governance, misappropriation, Sangh ideologue, Anna movement.

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Authors: Kaveh PourAkbar Saffar, Nima JamilPour, Ahmad Raeisi Najafi, Gholamreza Rouhi, Ahmad Reza Arshi, Abdolhossein Fereidoon

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The presence of chemical bonding between functionalized carbon nanotubes and matrix in carbon nanotube reinforced composites is modeled by elastic beam elements representing covalent bonding characteristics. Neglecting other reinforcing mechanisms in the composite such as relatively weak interatomic Van der Waals forces, this model shows close results to the Rule of Mixtures model-s prediction for effective Young-s modulus of a Representative Volume Element of composite for small volume fractions (~1%) and high aspect ratios (L/D>200) of CNTs.

Keywords: Beam Element, Carbon Nanotube Reinforced Composite, Cross-link, Young's modulus.

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Authors: F. Raja, M. Rahgozar, F. Oroumchian

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XML is a markup language which is becoming the standard format for information representation and data exchange. A major purpose of XML is the explicit representation of the logical structure of a document. Much research has been performed to exploit logical structure of documents in information retrieval in order to precisely extract user information need from large collections of XML documents. In this paper, we describe an XML information retrieval weighting scheme that tries to find the most relevant elements in XML documents in response to a user query. We present this weighting model for information retrieval systems that utilize plausible inferences to infer the relevance of elements in XML documents. We also add to this model the Dempster-Shafer theory of evidence to express the uncertainty in plausible inferences and Dempster-Shafer rule of combination to combine evidences derived from different inferences.

Keywords: Dempster-Shafer theory, plausible inferences, XMLinformation retrieval.

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Authors: Katarzyna Strzała-Osuch

Abstract:

Environmental investments, including ecological projects, relating to the protection of atmosphere are today a need. However, investing in the environment should be based on rational management rules. This comes across a problem of selecting a method to assess substances reduced during projects. Therefore, a method allowing for the assessment of decision rationality has to be found. The purpose of this article is to present and systematise pollution reduction assessment methods and illustrate theoretical analyses with empirical data. Empirical results confirm theoretical considerations, which proved that the only method for judging pollution reduction, free of apparent disadvantages, is the Eco 99-ratio method. To make decisions on environmental projects, financing institutions should take into account a rationality rule. Therefore the Eco 99-ratio method could be applied to make decisions relating to environmental investments in the area of air protection.

Keywords: Assessment of pollution reduction, costs of environmental protection, efficiency of environmental investments.

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Authors: Hossein Sahoolizadeh, Alishir Moradi Kordalivand, Zargham Heidari

Abstract:

In first stage of each microwave receiver there is Low Noise Amplifier (LNA) circuit, and this stage has important rule in quality factor of the receiver. The design of a LNA in Radio Frequency (RF) circuit requires the trade-off many importance characteristics such as gain, Noise Figure (NF), stability, power consumption and complexity. This situation Forces desingners to make choices in the desing of RF circuits. In this paper the aim is to design and simulate a single stage LNA circuit with high gain and low noise using MESFET for frequency range of 5 GHz to 6 GHz. The desing simulation process is down using Advance Design System (ADS). A single stage LNA has successfully designed with 15.83 dB forward gain and 1.26 dB noise figure in frequency of 5.3 GHz. Also the designed LNA should be working stably In a frequency range of 5 GHz to 6 GHz.

Keywords: Advance Design System, Low Noise Amplifier, Radio Frequency, Noise Figure.

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Authors: Asil Y. Zureigat, Ayat A. Oudat

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Analyzing the old and bringing in the new is an ever-ongoing process in driving innovations in architecture. This paper looks at the excessive use of stone in apartment buildings in Amman and speculates on the existing possibilities of changing the cladding material. By looking at architectural exceptions present in Amman, the paper seeks to make the exception the rule, by adding new materials to the architectural library of Amman and in turn, project a series of possible new identities to the existing stone scape. Through distributing a survey, conducting a photographic study on exceptional buildings and shedding light on the historical narrative of stone, the paper highlights the ways in which new finishing materials such as plaster, paint and stone variations could be introduced in an attempt to project a new architectural identity to Amman.

Keywords: Architectural city identity, cladding materials, façade architecture, image of the city.

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Authors: César Garza

Abstract:

In supervised binary classification and regression problems, it is well-known that learnability is equivalent to uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.

Keywords: Statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization.

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Authors: K. Muthukannan, P. Latha

Abstract:

In addition to environmental parameters like rain, temperature diseases on crop is a major factor which affects production quality & quantity of crop yield. Hence disease management is a key issue in agriculture. For the management of disease, it needs to be detected at early stage. So, treat it properly & control spread of the disease. Now a day, it is possible to use the images of diseased leaf to detect the type of disease by using image processing techniques. This can be achieved by extracting features from the images which can be further used with classification algorithms or content based image retrieval systems. In this paper, color image is used to extract the features such as mean and standard deviation after the process of region cropping. The selected features are taken from the cropped image with different image size samples. Then, the extracted features are taken in to the account for classification using Fuzzy Inference System (FIS).

Keywords: Image Cropping, Classification, Color, Fuzzy Rule, Feature Extraction.

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Authors: Chien-Hua Wang, Wei-Hsuan Lee, Chin-Tzong Pang

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In data mining, the association rules are used to find for the associations between the different items of the transactions database. As the data collected and stored, rules of value can be found through association rules, which can be applied to help managers execute marketing strategies and establish sound market frameworks. This paper aims to use Fuzzy Frequent Pattern growth (FFP-growth) to derive from fuzzy association rules. At first, we apply fuzzy partition methods and decide a membership function of quantitative value for each transaction item. Next, we implement FFP-growth to deal with the process of data mining. In addition, in order to understand the impact of Apriori algorithm and FFP-growth algorithm on the execution time and the number of generated association rules, the experiment will be performed by using different sizes of databases and thresholds. Lastly, the experiment results show FFPgrowth algorithm is more efficient than other existing methods.

Keywords: Data mining, association rule, fuzzy frequent patterngrowth.

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Authors: Payam Parvasi, Mohammad Hossein Sedaghat, Reza Janamiri, Amir Hatampour

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In this work, several ASP solutions were flooded into fractured models initially saturated with heavy oil at a constant flow rate and different geometrical characteristics of fracture. The ASP solutions are constituted from 2 polymers i.e. a synthetic polymer, hydrolyzed polyacrylamide as well as a biopolymer, a surfactant and 2types of alkaline. The results showed that using synthetic hydrolyzed polyacrylamide polymer increases ultimate oil recovery; however, type of alkaline does not play a significant rule on oil recovery. In addition, position of the injection well respect to the fracture system has remarkable effects on ASP flooding. For instance increasing angle of fractures with mean flow direction causes more oil recovery and delays breakthrough time. This work can be accounted as a comprehensive survey on ASP flooding which considers most of effective factors in this chemical EOR method.

Keywords: ASP Flooding, Fractured System, Displacement, Heavy Oil.

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Authors: Ayman M. Mansour

Abstract:

In this paper, we propose a multi-agent intelligent system that is used for monitoring the health conditions of elderly people. Monitoring the health condition of elderly people is a complex problem that involves different medical units and requires continuous monitoring. Such expert system is highly needed in rural areas because of inadequate number of available specialized physicians or nurses. Such monitoring must have autonomous interactions between these medical units in order to be effective. A multi-agent system is formed by a community of agents that exchange information and proactively help one another to achieve the goal of elderly monitoring. The agents in the developed system are equipped with intelligent decision maker that arms them with the rule-based reasoning capability that can assist the physicians in making decisions regarding the medical condition of elderly people.

Keywords: Fuzzy Logic, Inference system, Monitoring system, Multi-agent system.

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Authors: Amal Elmzabi, Mostafa Bellafkih, Mohammed Ramdani

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The Chiu-s method which generates a Takagi-Sugeno Fuzzy Inference System (FIS) is a method of fuzzy rules extraction. The rules output is a linear function of inputs. In addition, these rules are not explicit for the expert. In this paper, we develop a method which generates Mamdani FIS, where the rules output is fuzzy. The method proceeds in two steps: first, it uses the subtractive clustering principle to estimate both the number of clusters and the initial locations of a cluster centers. Each obtained cluster corresponds to a Mamdani fuzzy rule. Then, it optimizes the fuzzy model parameters by applying a genetic algorithm. This method is illustrated on a traffic network management application. We suggest also a Mamdani fuzzy rules generation method, where the expert wants to classify the output variables in some fuzzy predefined classes.

Keywords: Fuzzy entropy, fuzzy inference systems, genetic algorithms, network management, subtractive clustering.

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Authors: Hassan M. Elragal

Abstract:

This paper discusses a method for improving accuracy of fuzzy-rule-based classifiers using particle swarm optimization (PSO). Two different fuzzy classifiers are considered and optimized. The first classifier is based on Mamdani fuzzy inference system (M_PSO fuzzy classifier). The second classifier is based on Takagi- Sugeno fuzzy inference system (TS_PSO fuzzy classifier). The parameters of the proposed fuzzy classifiers including premise (antecedent) parameters, consequent parameters and structure of fuzzy rules are optimized using PSO. Experimental results show that higher classification accuracy can be obtained with a lower number of fuzzy rules by using the proposed PSO fuzzy classifiers. The performances of M_PSO and TS_PSO fuzzy classifiers are compared to other fuzzy based classifiers

Keywords: Fuzzy classifier, Optimization of fuzzy systemparameters, Particle swarm optimization, Pattern classification.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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Authors: Vasudha Bhatnagar, Ahmed Sultan Al-Hegami, Naveen Kumar

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Rule Discovery is an important technique for mining knowledge from large databases. Use of objective measures for discovering interesting rules leads to another data mining problem, although of reduced complexity. Data mining researchers have studied subjective measures of interestingness to reduce the volume of discovered rules to ultimately improve the overall efficiency of KDD process. In this paper we study novelty of the discovered rules as a subjective measure of interestingness. We propose a hybrid approach based on both objective and subjective measures to quantify novelty of the discovered rules in terms of their deviations from the known rules (knowledge). We analyze the types of deviation that can arise between two rules and categorize the discovered rules according to the user specified threshold. We implement the proposed framework and experiment with some public datasets. The experimental results are promising.

Keywords: Knowledge Discovery in Databases (KDD), Interestingness, Subjective Measures, Novelty Index.

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Authors: Ying Zhao

Abstract:

Keystroke authentication is a new access control system to identify legitimate users via their typing behavior. In this paper, machine learning techniques are adapted for keystroke authentication. Seven learning methods are used to build models to differentiate user keystroke patterns. The selected classification methods are Decision Tree, Naive Bayesian, Instance Based Learning, Decision Table, One Rule, Random Tree and K-star. Among these methods, three of them are studied in more details. The results show that machine learning is a feasible alternative for keystroke authentication. Compared to the conventional Nearest Neighbour method in the recent research, learning methods especially Decision Tree can be more accurate. In addition, the experiment results reveal that 3-Grams is more accurate than 2-Grams and 4-Grams for feature extraction. Also, combination of attributes tend to result higher accuracy.

Keywords: Keystroke Authentication, Pattern recognition, MachineLearning, Instance-based Learning, Bayesian, Decision Tree.

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Authors: S. Chokri

Abstract:

Load modeling is one of the central functions in power systems operations. Electricity cannot be stored, which means that for electric utility, the estimate of the future demand is necessary in managing the production and purchasing in an economically reasonable way. A majority of the recently reported approaches are based on neural network. The attraction of the methods lies in the assumption that neural networks are able to learn properties of the load. However, the development of the methods is not finished, and the lack of comparative results on different model variations is a problem. This paper presents a new approach in order to predict the Tunisia daily peak load. The proposed method employs a computational intelligence scheme based on the Fuzzy neural network (FNN) and support vector regression (SVR). Experimental results obtained indicate that our proposed FNN-SVR technique gives significantly good prediction accuracy compared to some classical techniques.

Keywords: Neural network, Load Forecasting, Fuzzy inference, Machine learning, Fuzzy modeling and rule extraction, Support Vector Regression.

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Authors: Hidemi Ogasawara, Kiyoshi Akama, Hiroshi Mabuchi

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The purpose of this paper is to propose a framework for constructing correct parallel processing programs based on Equivalent Transformation Framework (ETF). ETF regards computation as In the framework, a problem-s domain knowledge and a query are described in definite clauses, and computation is regarded as transformation of the definite clauses. Its meaning is defined by a model of the set of definite clauses, and the transformation rules generated must preserve meaning. We have proposed a parallel processing method based on “specialization", a part of operation in the transformations, which resembles substitution in logic programming. The method requires “Memo-tree", a history of specialization to maintain correctness. In this paper we proposes the new method for the specialization-base parallel processing without Memo-tree.

Keywords: Parallel processing, Program correctness, Equivalent transformation, Specializer generation rule

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Authors: Margaret F. Shipley

Abstract:

Fuzzy logic can be used when knowledge is incomplete or when ambiguity of data exists. The purpose of this paper is to propose a proactive fuzzy set- based model for reacting to the risk inherent in investment activities relative to a complete view of portfolio management. Fuzzy rules are given where, depending on the antecedents, the portfolio size may be slightly or significantly decreased or increased. The decision maker considers acceptable bounds on the proportion of acceptable risk and return. The Fuzzy Controller model allows learning to be achieved as 1) the firing strength of each rule is measured, 2) fuzzy output allows rules to be updated, and 3) new actions are recommended as the system continues to loop. An extension is given to the fuzzy controller that evaluates potential financial loss before adjusting the portfolio. An application is presented that illustrates the algorithm and extension developed in the paper.

Keywords: Portfolio Management, Financial Market Monitoring, Fuzzy Controller, Fuzzy Logic,

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Authors: Chen Wu, Youquan Xu, Dandan Li, Ronghua Yang, Lijuan Wang

Abstract:

In rough set models, tolerance relation, similarity relation and limited tolerance relation solve different situation problems for incomplete information systems in which there exists a phenomenon of missing value. If two objects have the same few known attributes and more unknown attributes, they cannot distinguish them well. In order to solve this problem, we presented two improved limited and variable precision rough set models. One is symmetric, the other one is non-symmetric. They all use more stringent condition to separate two small probability equivalent objects into different classes. The two models are needed to engage further study in detail. In the present paper, we newly form object classes with a different respect comparing to the first suggested model. We overcome disadvantages of non-symmetry regarding to the second suggested model. We discuss relationships between or among several models and also make rule generation. The obtained results by applying the second model are more accurate and reasonable.

Keywords: Incomplete information system, rough set, symmetry, variable precision.

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Authors: Imran Sarwar Bajwa

Abstract:

Internet is one of the major sources of information for the person belonging to almost all the fields of life. Major language that is used to publish information on internet is language. This thing becomes a problem in a country like Pakistan, where Urdu is the national language. Only 10% of Pakistan mass can understand English. The reason is millions of people are deprived of precious information available on internet. This paper presents a system for translation from English to Urdu. A module LESSA is used that uses a rule based algorithm to read the input text in English language, understand it and translate it into Urdu language. The designed approach was further incorporated to translate the complete website from English language o Urdu language. An option appears in the browser to translate the webpage in a new window. The designed system will help the millions of users of internet to get benefit of the internet and approach the latest information and knowledge posted daily on internet.

Keywords: Natural Language Translation, Text Understanding, Knowledge extraction, Text Processing

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Authors: A. Zerkane, K. El Bikri, R. Benamar

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The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.

Keywords: Nonlinear vibrations, functionally graded materials, homogenization procedure.

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Authors: D. Prangchumpol

Abstract:

Server provisioning is one of the most attractive topics in virtualization systems. Virtualization is a method of running multiple independent virtual operating systems on a single physical computer. It is a way of maximizing physical resources to maximize the investment in hardware. Additionally, it can help to consolidate servers, improve hardware utilization and reduce the consumption of power and physical space in the data center. However, management of heterogeneous workloads, especially for resource utilization of the server, or so called provisioning becomes a challenge. In this paper, a new concept for managing workloads based on user behavior is presented. The experimental results show that user behaviors are different in each type of service workload and time. Understanding user behaviors may improve the efficiency of management in provisioning concept. This preliminary study may be an approach to improve management of data centers running heterogeneous workloads for provisioning in virtualization system.

Keywords: association rule, provisioning, server virtualization.

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Authors: Besa Muslimi, Miriam A. M. Capretz, Jagath Samarabandu

Abstract:

Artificial neural networks (ANN) have the ability to model input-output relationships from processing raw data. This characteristic makes them invaluable in industry domains where such knowledge is scarce at best. In the recent decades, in order to overcome the black-box characteristic of ANNs, researchers have attempted to extract the knowledge embedded within ANNs in the form of rules that can be used in inference systems. This paper presents a new technique that is able to extract a small set of rules from a two-layer ANN. The extracted rules yield high classification accuracy when implemented within a fuzzy inference system. The technique targets industry domains that possess less complex problems for which no expert knowledge exists and for which a simpler solution is preferred to a complex one. The proposed technique is more efficient, simple, and applicable than most of the previously proposed techniques.

Keywords: fuzzy rule extraction, fuzzy systems, knowledgeacquisition, pattern recognition, artificial neural networks.

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Authors: G. Lavanya Devi, Allam Appa Rao, A. Damodaram, GR Sridhar, G. Jaya Suma

Abstract:

Cluster analysis divides data into groups that are meaningful, useful, or both. Analysis of biological data is creating a new generation of epidemiologic, prognostic, diagnostic and treatment modalities. Clustering of protein sequences is one of the current research topics in the field of computer science. Linear relation is valuable in rule discovery for a given data, such as if value X goes up 1, value Y will go down 3", etc. The classical linear regression models the linear relation of two sequences perfectly. However, if we need to cluster a large repository of protein sequences into groups where sequences have strong linear relationship with each other, it is prohibitively expensive to compare sequences one by one. In this paper, we propose a new technique named General Regression Model Technique Clustering Algorithm (GRMTCA) to benignly handle the problem of linear sequences clustering. GRMT gives a measure, GR*, to tell the degree of linearity of multiple sequences without having to compare each pair of them.

Keywords: Clustering, General Regression Model, Protein Sequences, Similarity Measure.

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

Abstract:

In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: Carbon nanotubes, vibration control, piezoelectric layers, elastic foundation.

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Authors: M. Ovinis, D. Kerr, K. Bouazza-Marouf, M. Vloeberghs

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In this paper, algorithms for the automatic localisation of two anatomical soft tissue landmarks of the head the medial canthus (inner corner of the eye) and the tragus (a small, pointed, cartilaginous flap of the ear), in CT images are describet. These landmarks are to be used as a basis for an automated image-to-patient registration system we are developing. The landmarks are localised on a surface model extracted from CT images, based on surface curvature and a rule based system that incorporates prior knowledge of the landmark characteristics. The approach was tested on a dataset of near isotropic CT images of 95 patients. The position of the automatically localised landmarks was compared to the position of the manually localised landmarks. The average difference was 1.5 mm and 0.8 mm for the medial canthus and tragus, with a maximum difference of 4.5 mm and 2.6 mm respectively.The medial canthus and tragus can be automatically localised in CT images, with performance comparable to manual localisation

Keywords: Anatomical soft tissue landmarks, automatic localisation, Computed Tomography (CT)

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Authors: Vanda Božić, Željko Nikač

Abstract:

The wars and armed conflicts have often resulted in violations of international humanitarian law, and often commit the most serious international crimes such as war crimes, crimes against humanity, aggression and genocide. However, only in the XX century the rule was articulated idea of establishing a body of international criminal justice in order to prosecute these crimes and their perpetrators. The first steps in this field have been made by establishing the International military tribunals for war crimes at Nuremberg and Tokyo, and the formation of ad hoc tribunals for the former Yugoslavia and Rwanda. In the end, The International Criminal Court was established in Rome in 1998 with the aim of justice and in order to give satisfaction the victims of crimes and their families. The aim of the paper was to provide a historical and comparative analysis of the institutions of international criminal justice based on which these institutions de lege lata fulfilled the goals of individual criminal responsibility and justice. Furthermore, the authors suggest de lege ferenda that the Permanent International Criminal Tribunal, in addition to the prospective case, also takes over the current ICTY and ICTR cases.

Keywords: International crimes, international criminal justice, prosecution of crimes, Ad Hoc tribunal, the International Criminal Court.

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Authors: Stanislav Aryeh V. Fradkin, Sharif E.Guseynov

Abstract:

There is a complex situation on the transport environment in the cities of the world. For the analysis and prevention of environmental problems an accurate calculation hazardous substances concentrations at each point of the investigated area is required. In the turbulent atmosphere of the city the wellknown methods of mathematical statistics for these tasks cannot be applied with a satisfactory level of accuracy. Therefore, to solve this class of problems apparatus of mathematical physics is more appropriate. In such models, because of the difficulty as a rule the influence of uneven land surface on streams of air masses in the turbulent atmosphere of the city are not taken into account. In this paper the influence of the surface roughness, which can be quite large, is mathematically shown. The analysis of this problem under certain conditions identified the possibility of areas appearing in the atmosphere with pressure tending to infinity, i.e. so-called "wall effect".

Keywords: Air pollution, concentration of harmful substances, physical-mathematical model, urban area.

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