Search results for: relation

Authors: Qingjiang Li, Hui Xu, Haijun Liu, Xiaobo Tian

Abstract:

To judge whether the memristor can be interpreted as the fourth fundamental circuit element, we propose a variable-relation criterion of fundamental circuit elements. According to the criterion, we investigate the nature of three fundamental circuit elements and the memristor. From the perspective of variables relation, the memristor builds a direct relation between the voltage across it and the current through it, instead of a direct relation between the magnetic flux and the charge. Thus, it is better to characterize the memristor and the resistor as two special cases of the same fundamental circuit element, which is the memristive system in Chua-s new framework. Finally, the definition of memristor is refined according to the difference between the magnetic flux and the flux linkage.

Keywords: Memristor, Fundamental, Variable-Relation Criterion, Memristive system

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Authors: Tharini N. de Silva, Xiao Zhibo, Zhao Rui, Mao Kezhi

Abstract:

Causal relation identification is a crucial task in information extraction and knowledge discovery. In this work, we present two approaches to causal relation identification. The first is a classification model trained on a set of knowledge-based features. The second is a deep learning based approach training a model using convolutional neural networks to classify causal relations. We experiment with several different convolutional neural networks (CNN) models based on previous work on relation extraction as well as our own research. Our models are able to identify both explicit and implicit causal relations as well as the direction of the causal relation. The results of our experiments show a higher accuracy than previously achieved for causal relation identification tasks.

Keywords: Causal relation identification, convolutional neural networks, natural Language Processing, Machine Learning.

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Authors: Lidia Obojska

Abstract:

This paper has, as its point of departure, the foundational axiomatic theory of E. De Giorgi (1996, Scuola Normale Superiore di Pisa, Preprints di Matematica 26, 1), based on two primitive notions of quality and relation. With the introduction of a unary relation, we develop a system totally based on the sole primitive notion of relation. Such a modification enables a definition of the concept of dynamic unary relation. In this way we construct a simple language capable to express other well known theories such as Robinson-s arithmetic or a piece of a theory of concatenation. A key role in this system plays an abstract relation designated by “( )", which can be interpreted in different ways, but in this paper we will focus on the case when we can perform computations and obtain results.

Keywords: language, unary relations, arithmetic, computability

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Authors: Ke Lu, Tetsuya Furukawa

Abstract:

Data objects are usually organized hierarchically, and the relations between them are analyzed based on a corresponding concept hierarchy. The relation between data objects, for example how similar they are, are usually analyzed based on the conceptual distance in the hierarchy. If a node is an ancestor of another node, it is enough to analyze how close they are by calculating the distance vertically. However, if there is not such relation between two nodes, the vertical distance cannot express their relation explicitly. This paper tries to fill this gap by improving the analysis method for data objects based on hierarchy. The contributions of this paper include: (1) proposing an improved method to evaluate the vertical distance between concepts; (2) defining the concept horizontal distance and a method to calculate the horizontal distance; and (3) discussing the methods to confine a range by the horizontal distance and the vertical distance, and evaluating the relation between concepts.

Keywords: Concept Hierarchy, Horizontal Distance, Relation Analysis, Vertical Distance

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Authors: Wongvisarut Khuangsatung, Pakkinee Chitsakul

Abstract:

In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.

Keywords: Geodesic, Surface of revolution, Clairaut's relation, Clairaut parameterization.

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Authors: Pham Ba Quang, Nguyen Tien Dat, Huynh Quyet Thang

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In this paper, we generalize several techniques in developing Fault Tolerant Software. We introduce property “Correctness" in evaluating N-version Systems and compare it to some commonly used properties such as reliability or availability. We also find out the relation between this property and the number of versions of system. Our experiments to verify the correctness and the applicability of the relation are also presented.

Keywords: Correctness, Fault Tolerant Software, N-versionSystems

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Authors: Ayşe Yurdakul, Eckehard Schnieder

Abstract:

Because of the increasing multidisciplinarity and multilinguality, communication problems in different technical fields grow more and more. Therefore, each technical field has its own specific language, terminology which is characterized by the different definition of terms. In addition to definition problems, there are also relation problems between terms. Among these problems of relation, there are the synonymy, antonymy, hypernymy/hyponymy, ambiguity, risk of confusion and translation problems etc.

Thus, the terminology management system iglos of the Institute for Traffic Safety and Automation Engineering of the Technische Universität Braunschweig has the target to solve these problems by a methodological standardisation of term definitions with the aid of the iglos sign model and iglos relation types. The focus of this paper should be on solving definition and relation problems between terms in English navigation terminology.

Keywords: Iglos, iglos sign model, methodological resolutions, navigation terminology, common language, technical language, positioning, definition problems, relation problems.

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Authors: Xiuqin Ma, Norrozila Binti Sulaiman, Hongwu Qin

Abstract:

In the research field of Rough Set, few papers concern the significance of attribute set. However, there is important relation between the significance of single attribute and that of attribute set, which should not be ignored. In this paper, we draw conclusions by case analysis that (1) the attribute set including single attributes with high significance is certainly significant, while, (2)the attribute set which consists of single attributes with low significance possibly has high significance. We validate the conclusions on discernibility matrix and the results demonstrate the contribution of our conclusions.

Keywords: relation, attribute set, single attribute, rough set, significance

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Authors: Daniel A. Montoya, Marta L. Tostes

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This investigation aims at analyzing and determining the relation between two very important variables in the human resource management: The organizational climate and the performance assessment. This study aims at contributing with knowledge in the search of the relation between the mentioned variables because the literature still does not provide solid evidence to this respect and the cases revised are incipient to reach conclusions enabling a typology about this relation.To this regard, a correlational and cross-sectional perspective was adopted in which quantitative and qualitative techniques were chosen with the total of the workers of the tourist service company PTS Peru. In order to measure the organizational climate, the OCQ (Organization Climate Questionnaire) from was used; it has 50 items and measures 9 dimensions of the Organizational Climate. Also, to assess performance, a questionnaire with 21 items and 6 dimensions was designed. As a means of assessment, a focus group was prepared and was applied to a worker in every area of the company. Additionally, interviews to human resources experts were conducted. The results of the investigation show a clear relation between the organizational climate and the personnel performance assessment as well as a relation between the nine dimensions of the organizational climate and the work performance in general and with some of its dimensions.

Keywords: Job performance, human resource management, organization climate, performance assessment.

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Authors: A.Nagoor Gani, J.Malarvizhi

Abstract:

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed.

Keywords: complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

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Authors: Suguru Yoshioka, Seiichi Tani, Seinosuke Toda

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In historical science and social science, the influence of natural disaster upon society is a matter of great interest. In recent years, some archives are made through many hands for natural disasters, however it is inefficiency and waste. So, we suppose a computer system to create a historical natural disaster archive. As the target of this analysis, we consider newspaper articles. The news articles are considered to be typical examples that prescribe the temporal relations of affairs for natural disaster. In order to do this analysis, we identify the occurrences in newspaper articles by some index entries, considering the affairs which are specific to natural disasters, and show the temporal relation between natural disasters. We designed and implemented the automatic system of “extraction of the occurrences of natural disaster" and “temporal relation table for natural disaster."

Keywords: Database, digital library, corpus, historical natural disaster, temporal relation

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Authors: Chen Wu, Xiaohua Hu

Abstract:

This paper proposes rough set models with three different level knowledge granules in incomplete information system under tolerance relation by similarity between objects according to their attribute values. Through introducing dominance relation on the discourse to decompose similarity classes into three subclasses: little better subclass, little worse subclass and vague subclass, it dismantles lower and upper approximations into three components. By using these components, retrieving information to find naturally hierarchical expansions to queries and constructing answers to elaborative queries can be effective. It illustrates the approach in applying rough set models in the design of information retrieval system to access different granular expanded documents. The proposed method enhances rough set model application in the flexibility of expansions and elaborative queries in information retrieval.

Keywords: Incomplete information system, Rough set model, tolerance relation, dominance relation, approximation, decomposition, elaborative query.

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Authors: Wan Norhasniah Wan Husin, Mohd Ridhuan Tee Abdullah

Abstract:

Towards the end of 19th century, the discovery of tin and the growing importance of rubber, had led Malaya to once again become the centre of attraction to western colonization, which later on caused the region to be influxed by cheap labour from China and India. One of the factors which attracted the alien communities was the characteristics of social relation offered by the Malays. If one analyzes the history of social relation of the Malays either among themselves or their relation with alien communities, it is apparent that the community places high regards to values such as tolerant, cooperative, respectful and helpful with each other. In fact, all these values are deeply rooted in the value of 'budi'. With the arrival of Islam, the value of 'budi' had been well assimilated with Islamic values thus giving birth to the value of 'budi-Islam'. Through 'budi- Islam', the Malay conducted their dealings with British as well the other communities during the time of peace or conflict. This value is well nurtured due to the geographical circumstances like the fertile, naturally rich land and bountiful marine life. Besides, a set of Malay customs known as 'adat' custom contributed in enhancing the values of budi.

Keywords: Adat System, budi and Islam, Chinese community, Malay community

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Authors: N. Samarinas, C. Evangelides, C. Vrekos

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The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: Classification, fuzzy logic, tolerance relations, rainfall data.

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Authors: A. Arjomand Kermani, N. Charbgoo, M. Alalhesabi

Abstract:

In the situation of great acceleration of changes and the need for new developments in the cities on one hand and conservation and regeneration approaches on the other hand, place identity and its relation with heritage context have taken on new importance. This relation is generally mutual and complex one. The significant point in this relation is that the process of identifying something as heritage rather than just historical  phenomena, brings that which may be inherited into the realm of identity. In planning and urban design as well as environmental psychology and phenomenology domain, place identity and its attributes and components were studied and discussed. However, the relation between physical environment (especially heritage) and identity has been neglected in the planning literature. This article aims to review the knowledge on this field and develop a model on the influence and relation of these two major concepts (heritage and identity). To build this conceptual model, we draw on available literature in environmental psychology as well as planning on place identity and heritage environment using a descriptive-analytical methodology to understand how they can inform the planning strategies and governance policies. A cross-disciplinary analysis is essential to understand the nature of place identity and heritage context and develop a more holistic model of their relationship in order to be employed in planning process and decision making. Moreover, this broader and more holistic perspective would enable both social scientists and planners to learn from one another’s expertise for a fuller understanding of community dynamics. The result indicates that a combination of these perspectives can provide a richer understanding—not only of how planning impacts our experience of place, but also how place identity can impact community planning and development.

Keywords: heritage, Inter-disciplinary study, Place identity, planning

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Authors: Afonso, S. C., Fernandes, P. O., Monte, A. P.

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Modern times call organizations to have an active role in the social arena, through Corporate Social Responsibility (CSR). The objective of this research was to test the hypothesis that there is a positive relation between social performance and economic performance, and if there is a positive correlation between social performance and financial-economic performance. To test these theories a measure of social performance, based on the Green Book of Commission of the European Community, was used in a group of nineteen Portuguese top companies, listed on the PSI 20 index, through a period of five years, since 2005 to 2009. A clusters analysis was applied to group companies by their social performance and to compare and correlate their economic performance. Results indicate that companies that had a better social performance are not the ones who had a better economic performance, and suggest that the middle path might provide a good relation CSR-Economic performance, as a basis to a sustainable development.

Keywords: Corporate Social Responsibility, Economic Performance, Win-Win relationship

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Authors: Fujian Wang, Shubin Ruan, Meiwei Dai

Abstract:

Speed dispersion has tight relation to traffic safety. In this paper, several kinds of indicating parameters (the standard speed deviation, the coefficient of variation, the deviation of V85 and V15, the mean speed deviations, and the difference between adjacent car speeds) are applied to investigate the characteristics of speed dispersion, where V85 and V15 are 85th and 15th percentile speed, respectively. Their relationships are into full investigations and the results show that: there exists a positive relation (linear) between mean speed and the deviation of V85 and V15; while a negative relation (quadratic) between traffic flow and standard speed deviation. The mean speed deviation grows exponentially with mean speed while the absolute speed deviation between adjacent cars grows linearly with the headway. The results provide some basic information for traffic management.

Keywords: Headway, indicating parameters, speed dispersion, urban expressway.

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Authors: Bita Mashayekhi, Zeynab Lotfi Aghel

Abstract:

The determinants of Earnings Response Coefficient (ERC), including firm size, earnings growth, and earnings persistence are studied in this research. These determinants are supposed to be moderator variables that affect ERC and Return Response Coefficient. The research sample contains 82 Iranian listed companies in Tehran Stock Exchange (TSE) from 2001 to 2012. Gathered data have been processed by EVIEWS Software. Results show a significant positive relation between firm size and ERC, and also between earnings growth and ERC; however, there is no significant relation between earnings persistence and ERC. Also, the results show that ERC will be increased by firm size and earnings growth, but there is no relation between earnings persistence and ERC.

Keywords: Earnings response coefficient, return response coefficient, firm size, earnings growth, earnings persistence.

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Authors: Khelood A. Mkalaf, Peter Gibson, John Flanagan

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This study investigates the relationship between the reliability of critical medical equipment (CME) and the effectiveness of CME maintenance management strategies in relation to patient outcomes in 84 public hospitals of a top 20 OECD country. The work has examined the effectiveness of CME maintenance management strategies used by the public hospital system of a large state run health organization. The conceptual framework was designed to examine the significance of the relationship between six variables: (1) types of maintenance management strategies, (2) maintenance services, (3) maintenance practice, (4) medical equipment reliability, (5) maintenance costs and (6) patient outcomes. The results provide interesting insights into the effectiveness of the maintenance strategies used. For example, there appears to be about a 1 in 10 000 probability of failure of anesthesia equipment, but these seem to be confined to specific maintenance situations. There are also some findings in relation to outsourcing of maintenance. For each of the variables listed, results are reported in relation to the various types of maintenance strategies and services. Decision-makers may use these results to evaluate more effective maintenance strategies for their CME and generate more effective patient outcomes.

Keywords: Critical medical equipment, maintenance strategy, patient outcomes, reliability.

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Authors: Frantisek Bozek, Lenka Jesonkova, Jiri Dvorak, Milos Bozek, Eduard Bakos

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The contents of nitrates and nitrites were monitored in 15 ground water resources of a selected region earmarked for the emergency supply of population. The resources have been selected on the basis of previous assessment of natural conditions and the exploitation of territory in the infiltration area as well as the surroundings of water resources. The health risk analysis carried out in relation to nitrates and nitrites, which were found to be the most serious water contaminants, proved, that 14 resources met the health standards in relation to the assessed criterion and could be included in crisis plans. Water quality of ground resources may be assessed in the same way with regard to other contaminants.

Keywords: Drinking water, health risks, methemoglobinemia, nitrates, nitrites, water pollution.

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Authors: Isaac K. E. Ampomah, Seong-Bae Park, Sang-Jo Lee

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Over the past decade, there have been promising developments in Natural Language Processing (NLP) with several investigations of approaches focusing on Recognizing Textual Entailment (RTE). These models include models based on lexical similarities, models based on formal reasoning, and most recently deep neural models. In this paper, we present a sentence encoding model that exploits the sentence-to-sentence relation information for RTE. In terms of sentence modeling, Convolutional neural network (CNN) and recurrent neural networks (RNNs) adopt different approaches. RNNs are known to be well suited for sequence modeling, whilst CNN is suited for the extraction of n-gram features through the filters and can learn ranges of relations via the pooling mechanism. We combine the strength of RNN and CNN as stated above to present a unified model for the RTE task. Our model basically combines relation vectors computed from the phrasal representation of each sentence and final encoded sentence representations. Firstly, we pass each sentence through a convolutional layer to extract a sequence of higher-level phrase representation for each sentence from which the first relation vector is computed. Secondly, the phrasal representation of each sentence from the convolutional layer is fed into a Bidirectional Long Short Term Memory (Bi-LSTM) to obtain the final sentence representations from which a second relation vector is computed. The relations vectors are combined and then used in then used in the same fashion as attention mechanism over the Bi-LSTM outputs to yield the final sentence representations for the classification. Experiment on the Stanford Natural Language Inference (SNLI) corpus suggests that this is a promising technique for RTE.

Keywords: Deep neural models, natural language inference, recognizing textual entailment, sentence-to-sentence relation.

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Authors: Prasertsak Ekphisutsuntorn, Prungchan Wongwises, Chaiyuth Chinnarasri, Usa Humphries, Suphat Vongvisessomjai

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In this paper, the significant wave height at the Upper Gulf of Thailand and the changing of wave height at Bangkhuntien shoreline were simulated by using the Simulating WAves Nearshore Model (SWAN) version 40.51. The simulated results indicated that the significant wave height by SWAN model corresponded with the observed data. The results showed that the maximum significant wave height at the Bangkhuntien shoreline were 1.06-2.05 m. and the average significant wave height at the Bangkhuntien shoreline were 0.30-0.47 m. The significant wave height can be used to calculate the erosion through the Bangkhuntien shoreline. The erosion rates at the Bangkhuntien shoreline were prepared by using the aerial photo and they were about 1.80 m/yr. from 1980- 1986, 4.75 m/yr from 1987-1993, 15.28 m/yr from 1994-1996 and 10.03 m/yr from 1997-2002. The relation between the wave energy and the erosion were in good agreement. Therefore, the significant wave height was one of the major factors of the erosion at the Bangkhuntien shoreline.

Keywords: significant wave height, erosion, SWAN, relation, Bangkhuntien shoreline

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Authors: A. R. Shahani, E. Mahdavi, M. Amidpour

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Environment-assisted cracking (EAC) is one of the most serious causes of structural failure over a broad range of industrial applications including offshore structures. In EAC condition there is not a definite relation such as Paris equation in Linear Elastic Fracture Mechanics (LEFM). According to studying and searching a lot what the researchers said either a material has contact with hydrogen or any other corrosive environment, phenomenon of electrical and chemical reactions of material with its environment will be happened. In the literature, there are many different works to consider fatigue crack growing and solve it but they are experimental works. Thus, in this paper, authors have an aim to evaluate mathematically the pervious works in LEFM. Obviously, if an environment is more sour and corrosive, the changes of stress intensity factor is more and the calculation of stress intensity factor is difficult. A mathematical relation to deal with the stress intensity factor during the diffusion of sour environment especially hydrogen in a marine pipeline is presented. By using this relation having and some experimental relation an analytical formulation will be presented which enables the fatigue crack growth and critical crack length under cyclic loading to be predicted. In addition, we can calculate KSCC and stress intensity factor in the pipeline caused by EAC.

Keywords: Embrittlement, Fracture mechanics, Hydrogen diffusion, Stress intensity factor.

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Authors: Chen Wu, Lijuan Wang

Abstract:

Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.

Keywords: Incomplete information system, rough set, tolerance relation, knowledge dependence, attribute reduction.

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Authors: Loredana Drobot

Abstract:

A therapeutic success is the aim of any therapeutic intervention, but a therapeutic failure is the other side of the same coin. The purpose of this study is to present the activity of a personal development group, composed of 14 participants (psychologists, doctors and a priest) registered for a 2 days course of integrative psychotherapy. The objectives of this study are centred on: the management of the personal development group breaking moment realized by the therapist/trainer; the analysis of the trainer’s personal situation and of some group participants and the brief presentation of the main work methods applied on participants in the repairing of the therapeutic relation and in the counter transfer management. The therapist’s orientation is an integrative one and the demarche realized includes T.A. techniques, role play, Gestalt and family systemic psychotherapy. The conclusions obtained represent landmarks for the future activity within that group and strengthen the therapeutic relation with the group.

Keywords: Therapeutic success, therapeutic failure.

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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: Safiah A. Madkhali

Abstract:

The grammatical relation object has not attracted the same attention in the literature as subject has. Where there is a clearly monotransitive verb such as kick, the criteria for identifying the grammatical relation may converge. However, the term object is also used to refer to phenomena that do not subsume all, or even most, of the recognized properties of the canonical object. Instances of such phenomena include non-canonical objects such as the ones in the so-called double-object construction i.e., the indirect object and the direct object as in (He bought his dog a new collar). In this paper, it is demonstrated how criteria of identifying the grammatical relation object that are found in the theoretical and typological literature can be applied to Arabic. Also, further language-specific criteria are here derived from the regularities of the canonical object in the language. The criteria established in this way are then applied to the non-canonical objects to demonstrate how far they conform to, or diverge from, the canonical object. Contrary to the claim that the direct object is more similar to the canonical object than is the indirect object, it was found that it is, in fact, the indirect object rather than the direct object that shares most of the aspects of the canonical object in monotransitive clauses.

Keywords: Canonical objects, double-object constructions, direct object, indirect object, non-canonical objects.

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Authors: Ekachai Phaisangittisagul, Rapeepol Chongprachawat

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Obtaining labeled data in supervised learning is often difficult and expensive, and thus the trained learning algorithm tends to be overfitting due to small number of training data. As a result, some researchers have focused on using unlabeled data which may not necessary to follow the same generative distribution as the labeled data to construct a high-level feature for improving performance on supervised learning tasks. In this paper, we investigate the impact of the relationship between unlabeled and labeled data for classification performance. Specifically, we will apply difference unlabeled data which have different degrees of relation to the labeled data for handwritten digit classification task based on MNIST dataset. Our experimental results show that the higher the degree of relation between unlabeled and labeled data, the better the classification performance. Although the unlabeled data that is completely from different generative distribution to the labeled data provides the lowest classification performance, we still achieve high classification performance. This leads to expanding the applicability of the supervised learning algorithms using unsupervised learning.

Keywords: Autoencoder, high-level feature, MNIST dataset, selftaught learning, supervised learning.

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Authors: João V. Staub de Melo, Glicério Trichês, Liseane P. Thives

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This paper presents the results of the development of asphalt nanocomposites containing carbon nanotubes (CNTs) with high resistance to permanent deformation, aiming to increase the performance of asphalt surfaces in relation to the rutting problem. Asphalt nanocomposites were prepared with the addition of different proportions of CNTs (1%, 2% and 3%) in relation to the weight of asphalt binder. The base binder used was a conventional binder (50-70 penetration) classified as PG 58-22. The optimum percentage of CNT addition in the asphalt binder (base) was determined through the evaluation of the rheological and empirical characteristics of the nanocomposites produced. In order to evaluate the contribution and the effects of the nanocomposite (optimized) in relation to the rutting, the conventional and nanomodified asphalt mixtures were tested in a French traffic simulator (Orniéreur). The results obtained demonstrate the efficient contribution of the asphalt nanocomposite containing CNTs to the resistance to permanent deformation of the asphalt mixture.

Keywords: Asphalt nanocomposites, asphalt mixtures, carbon nanotubes, nanotechnology, permanent deformation.

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Authors: G.K.Panda, S.S.Rout

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The balancing numbers are natural numbers n satisfying the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) + (n + 2) + · · · + (n + r); r is the balancer corresponding to the balancing number n.The nth balancing number is denoted by Bn and the sequence {Bn}1 n=1 satisfies the recurrence relation Bn+1 = 6Bn-Bn-1. The balancing numbers posses some curious properties, some like Fibonacci numbers and some others are more interesting. This paper is a study of recurrent sequence {xn}1 n=1 satisfying the recurrence relation xn+1 = Axn - Bxn-1 and possessing some curious properties like the balancing numbers.

Keywords: Recurrent sequences, Balancing numbers, Lucas balancing numbers, Binet form.

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