Search results for: semantic algebra

Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang

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The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.

Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications

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Authors: Muna Tabuni

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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

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Authors: Michael Lousis

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The kind of the most important and conspicuous errors the students made during the three-years of testing of their progress in Algebra are presented in this article. The way these students’ errors changed over three-years of school Algebra learning also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students, who were purposefully culled according to their participation in each occasion of testing in the development of the three-year Kassel Project in England and Greece, in both domains at once of Arithmetic and Algebra. Hence, for each of these English and Greek students, six test-scripts were available and corresponded to the three occasions of testing in both Arithmetic and Algebra respectively.

Keywords: algebra, errors, Kassel Project, progress of learning

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Sharjeel Aslam, Vassil Vassilev, Karim Ouazzane

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Ontologies and various semantic repositories became a convenient approach for implementing model-driven architectures of distributed systems on the Web. SPARQL is the standard query language for querying such. However, although SPARQL is well-established standard for querying semantic repositories in RDF and OWL format and there are commonly used APIs which supports it, like Jena for Java, its parallel option is not incorporated in them. This article presents a complete framework consisting of an object algebra for parallel RDF and an index-based implementation of the parallel query engine capable of dealing with the distributed RDF ontologies which share common vocabulary. It has been implemented in Java, and for validation of the algorithms has been applied to the problem of organizing virtual exhibitions on the Web.

Keywords: distributed ontologies, parallel querying, semantic indexing, shared vocabulary, SPARQL

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Authors: Alireza Gilani

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In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice.

Keywords: BCK-algebra, pseudo-BCK algebra, pseudo-ideal, implicative pseudo-ideal

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Authors: Zarine Avetisyan

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Concepts are part and parcel of everyday text and talk. Their ubiquity predetermines the topicality of the given research which aims at the semantic decomposition of concepts in general and the concept of joy in particular, as well as the study of lexico-semantic variants as means of realization of a certain concept in different “semantic settings”, namely in a certain context. To achieve the stated aim, the given research departs from the methods of componential and contextual analysis, studying lexico-semantic variants /LSVs/ of the concept of joy and the semantic signs embedded in those LSVs, such as the semantic sign of intensity, supporting emotions, etc. in the context of Modern English fiction.

Keywords: concept, context, lexico-semantic variant, semantic sign

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Authors: Salvatore Triolo

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We discuss the possibility of extending the well-known Gelfand-Naimark-Segal representation to modules over a C*algebra. We focus our attention on the case of Hilbert modules. We consider, in particular, the problem of the existence of a faithful representation. Non-commutative Lᵖ-spaces are shown to constitute examples of a class of CQ*-algebras. Finally, we have shown that any semisimple proper CQ*-algebra (X, A#), with A# a W*-algebra can be represented as a CQ*-algebra of measurable operators in Segal’s sense.

Keywords: Gelfand-Naimark-Segal representation, CQ*-algebras, faithful representation, non-commutative Lᵖ-spaces, operator in Hilbert spaces

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Authors: Yassir I. Dinar

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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.

Keywords: lie algebra, root systems, representation theory, nilpotent orbits

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Natalia Pacheco Rego

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The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.

Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation

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Authors: Sahar Maâlej Dammak, Anis Jedidi, Rafik Bouaziz

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With the great mass of pages managed through the world, and especially with the advent of the Web, their manual annotation is impossible. We focus, in this paper, on the semiautomatic annotation of the web pages. We propose an approach and a framework for semantic annotation of web pages entitled “Querying Web”. Our solution is an enhancement of the first result of annotation done by the “Semantic Radar” Plug-in on the web resources, by annotations using an enriched domain ontology. The concepts of the result of Semantic Radar may be connected to several terms of the ontology, but connections may be uncertain. We represent annotations as possibility distributions. We use the hierarchy defined in the ontology to compute degrees of possibilities. We want to achieve an automation of the fuzzy semantic annotation of web resources.

Keywords: fuzzy semantic annotation, semantic web, domain ontologies, querying web

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Authors: Wagneur Edouard

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Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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Authors: T. G. Asmitha Chandini

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Web-based image search re-ranking, as an successful method to get better the results. In a query keyword, the first stair is store the images is first retrieve based on the text-based information. The user to select a query keywordimage, by using this query keyword other images are re-ranked based on their visual properties with images.Now a day to day, people projected to match images in a semantic space which is used attributes or reference classes closely related to the basis of semantic image. though, understanding a worldwide visual semantic space to demonstrate highly different images from the web is difficult and inefficient. The re-ranking images, which automatically offline part learns dissimilar semantic spaces for different query keywords. The features of images are projected into their related semantic spaces to get particular images. At the online stage, images are re-ranked by compare their semantic signatures obtained the semantic précised by the query keyword image. The query-specific semantic signatures extensively improve both the proper and efficiency of image re-ranking.

Keywords: Query, keyword, image, re-ranking, semantic, signature

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Paria Tajabor, Azin Azarbani

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The purpose of this research study is exploring two kind of semantic repositories with regards to various factors to find the best approaches that an artificial manager can use to produce ontology in a system based on their interaction, association and research. To this end, as the best way to evaluate each system and comparing with others is analysis, several benchmarking over these two repositories were examined. These two semantic repositories: OWLIM and AllegroGraph will be the main core of this study. The general objective of this study is to be able to create an efficient and cost-effective manner reports which is required to support decision making in any large enterprise.

Keywords: OWLIM, allegrograph, RDF, reasoning, semantic repository, semantic-web, SPARQL, ontology, query

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Authors: Wiem Ben Khalifa, Dalila Souilem, Mahmoud Neji

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The evolutions of Social Web and Semantic Web lead us to ask ourselves about the way of supporting the personalization of learning by means of intelligent filtering of educational resources published in the digital networks. We recommend personalized courses of learning articulated around a first educational course defined upstream. Resuming the context and the stakes in the personalization, we also suggest anchoring the personalization of learning in a community of interest within a group of learners enrolled in the same training. This reflection is supported by the display of an active and semantic system of learning dedicated to the constitution of personalized to measure courses and in the due time.

Keywords: Semantic Web, semantic system, ontology, evaluation, e-learning

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Authors: Hadeel Al Obaidy, Amani Al Heela

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The main purpose of this paper is to examine the concept of semantic web and the role that ontology and semantic annotation plays in the development of semantic web services. The paper focuses on semantic web infrastructure illustrating how ontology and annotation work to provide the learning capabilities for building content semantically. To improve productivity and quality of software, the paper applies approaches, notations and techniques offered by software engineering. It proposes a conceptual model to develop semantic web services for the infrastructure of web information retrieval system of digital libraries. The developed system uses ontology and annotation to build a knowledge based system to define and link the meaning of a web content to retrieve information for users’ queries. The results are more relevant through keywords and ontology rule expansion that will be more accurate to satisfy the requested information. The level of results accuracy would be enhanced since the query semantically analyzed work with the conceptual architecture of the proposed system.

Keywords: semantic web services, software engineering, semantic library, knowledge representation, ontology

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Authors: Hiroshi Yamaguchi, Phillip C. Y. Sheu, Ryo Fujita, Shigeo Tsujii

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In this paper, the secure BioSemantic Scheme is presented to bridge biological/biomedical research problems and computational solutions via semantic computing. Due to the diversity of problems in various research fields, the semantic capability description language (SCDL) plays and important role as a common language and generic form for problem formalization. SCDL is expected the essential for future semantic and logical computing in Biosemantic field. We show several example to Biomedical problems in this paper. Moreover, in the coming age of cloud computing, the security problem is considered to be crucial issue and we presented a practical scheme to cope with this problem.

Keywords: biomedical applications, private information retrieval (PIR), semantic capability description language (SCDL), semantic computing

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Authors: Zarine Avetisyan

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The paradigm of Modern Linguistics incorporates disciplines which allow to analyze both language and discourse units and to demonstrate the multi-layeredness of lingo-cultural consciousness. By implementing lingo-cognitive approach to discourse and communication studies, the present paper tries to create the integral linguistic picture of the concept of joy and to analyze the lexico-semantic groups and relevant lexico-semantic variants of its realization in the context of Modern English fiction.

Keywords: concept of joy, lexico-semantic variant, semantic sign, cognition

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Rihab Ben Lamine, Raoudha Ben Jemaa, Ikram Amous Ben Amor

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This paper proposes a graph planning technique for semantic adaptable Web Services composition. First, we use an ontology based context model for extending Web Services descriptions with information about the most suitable context for its use. Then, we transform the composition problem into a semantic context aware graph planning problem to build the optimal service composition based on user's context. The construction of the planning graph is based on semantic context aware Web Service discovery that allows for each step to add most suitable Web Services in terms of semantic compatibility between the services parameters and their context similarity with the user's context. In the backward search step, semantic and contextual similarity scores are used to find best composed Web Services list. Finally, in the ranking step, a score is calculated for each best solution and a set of ranked solutions is returned to the user.

Keywords: semantic web service, web service composition, adaptation, context, graph planning

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Authors: S. Alansary, M. Nagi

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This paper presents an approach of conducting semantic annotation of Arabic corpus using the Universal Networking Language (UNL) framework. UNL is intended to be a promising strategy for providing a large collection of semantically annotated texts with formal, deep semantics rather than shallow. The result would constitute a semantic resource (semantic graphs) that is editable and that integrates various phenomena, including predicate-argument structure, scope, tense, thematic roles and rhetorical relations, into a single semantic formalism for knowledge representation. The paper will also present the Interactive Analysis​ tool for automatic semantic annotation (IAN). In addition, the cornerstone of the proposed methodology which are the disambiguation and transformation rules, will be presented. Semantic annotation using UNL has been applied to a corpus of 20,000 Arabic sentences representing the most frequent structures in the Arabic Wikipedia. The representation, at different linguistic levels was illustrated starting from the morphological level passing through the syntactic level till the semantic representation is reached. The output has been evaluated using the F-measure. It is 90% accurate. This demonstrates how powerful the formal environment is, as it enables intelligent text processing and search.

Keywords: semantic analysis, semantic annotation, Arabic, universal networking language

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Authors: Skiker Kaoutar, Mounir Maouene

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Neuroimaging studies indicate that a large fronto-parieto-temporal network support nouns and their features, with some areas store semantic knowledge (visual, auditory, olfactory, gustatory,…), other areas store lexical representation and other areas are implicated in general semantic processing. However, it is not well understood how this fronto-parieto-temporal network can be modulated by different semantic tasks and different semantic relations between nouns. In this study, we combine a behavioral semantic network, functional MRI studies involving object’s related nouns and brain network studies to explain how different semantic tasks and different semantic relations between nouns can modulate the activity within the brain network of nouns and their features. We first describe how nouns and their features form a large scale brain network. For this end, we examine the connectivities between areas recruited during the processing of nouns to know which configurations of interaction areas are possible. We can thus identify if, for example, brain areas that store semantic knowledge communicate via functional/structural links with areas that store lexical representations. Second, we examine how this network is modulated by different semantic tasks involving nouns and finally, we examine how category specific activation may result from the semantic relations among nouns. The results indicate that brain network of nouns and their features is highly modulated and flexible by different semantic tasks and semantic relations. At the end, this study can be used as a guide to help neurosientifics to interpret the pattern of fMRI activations detected in the semantic processing of nouns. Specifically; this study can help to interpret the category specific activations observed extensively in a large number of neuroimaging studies and clinical studies.

Keywords: nouns, features, network, category specificity

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Authors: Réka Sárközi, Péter Iványi, Attila B. Széll

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The aim of this paper is to present the adaptation of the dome construction tool for formex algebra to the parametric design software Grasshopper. Formex algebra is a mathematical system, primarily used for planning structural systems such like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used and the dome structures are defined in spherical coordinate system. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and also additional dome-based structures using special coordinate-system solutions based on spherical coordinate systems. It also contains additional structural possibilities like making double layer grids in all geometry forms. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.

Keywords: parametric design, structural morphology, space structures, spherical coordinate system

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Authors: Aïcha Ben Salem, Faouzi Boufares, Sebastiao Correia

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The subject covered in this paper aims at assisting the user in its quality approach. The goal is to better extract, mix, interpret and reuse data. It deals with the semantic schema recognition of a data source. This enables the extraction of data semantics from all the available information, inculding the data and the metadata. Firstly, it consists of categorizing the data by assigning it to a category and possibly a sub-category, and secondly, of establishing relations between columns and possibly discovering the semantics of the manipulated data source. These links detected between columns offer a better understanding of the source and the alternatives for correcting data. This approach allows automatic detection of a large number of syntactic and semantic anomalies.

Keywords: schema recognition, semantic data profiling, meta-categorisation, semantic dependencies inter columns

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Authors: Ricardo Avila, Gabriel Lopes, Vania Vidal, Jose Macedo

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This article offers a approach to the automatic discovery of semantic concepts and links in the domain of Oil Exploration and Production (E&P). Machine learning methods combined with textual pre-processing techniques were used to detect local patterns in texts and, thus, generate new concepts and new semantic links. Even using more specific vocabularies within the oil domain, our approach has achieved satisfactory results, suggesting that the proposal can be applied in other domains and languages, requiring only minor adjustments.

Keywords: semantic links, data mining, linked data, SKOS

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Authors: Lin Huo, Xianwei Liu, Jingxiong Zhou

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Recently, due to the existence of semantic gap between image visual features and human concepts, the semantic of image auto-annotation has become an important topic. Firstly, by extract low-level visual features of the image, and the corresponding Hash method, mapping the feature into the corresponding Hash coding, eventually, transformed that into a group of binary string and store it, image auto-annotation by search is a popular method, we can use it to design and implement a method of image semantic auto-annotation. Finally, Through the test based on the Corel image set, and the results show that, this method is effective.

Keywords: image auto-annotation, color correlograms, Hash code, image retrieval

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Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista

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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.

Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom

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