Search results for: Knowledge representation

Authors: Dhruvit S. Berawala, Jann R. Ursin, Obrad Slijepcevic

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Shale gas is one of the most rapidly growing forms of natural gas. Unconventional natural gas deposits are difficult to characterize overall, but in general are often lower in resource concentration and dispersed over large areas. Moreover, gas is densely packed into the matrix through adsorption which accounts for large volume of gas reserves. Gas production from tight shale deposits are made possible by extensive and deep well fracturing which contacts large fractions of the formation. The conventional reservoir modelling and production forecasting methods, which rely on fluid-flow processes dominated by viscous forces, have proved to be very pessimistic and inaccurate. This paper presents a new approach to forecast shale gas production by detailed modeling of gas desorption, diffusion and non-linear flow mechanisms in combination with statistical representation of these processes. The representation of the model involves a cube as a porous media where free gas is present and a sphere (SiC: Sphere in Cube model) inside it where gas is adsorbed on to the kerogen or organic matter. Further, the sphere is considered consisting of many layers of adsorbed gas in an onion-like structure. With pressure decline, the gas desorbs first from the outer most layer of sphere causing decrease in its molecular concentration. The new available surface area and change in concentration triggers the diffusion of gas from kerogen. The process continues until all the gas present internally diffuses out of the kerogen, gets adsorbs onto available surface area and then desorbs into the nanopores and micro-fractures in the cube. Each SiC idealizes a gas pathway and is characterized by sphere diameter and length of the cube. The diameter allows to model gas storage, diffusion and desorption; the cube length takes into account the pathway for flow in nanopores and micro-fractures. Many of these representative but general cells of the reservoir are put together and linked to a well or hydraulic fracture. The paper quantitatively describes these processes as well as clarifies the geological conditions under which a successful shale gas production could be expected. A numerical model has been derived which is then compiled on FORTRAN to develop a simulator for the production of shale gas by considering the spheres as a source term in each of the grid blocks. By applying SiC to field data, we demonstrate that the model provides an effective way to quickly access gas production rates from shale formations. We also examine the effect of model input properties on gas production.

Keywords: Sphere in Cube Grid Approach to Modelling of Shale Gas Production Using Non-Linear Flow Mechanisms

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Authors: Jagmohan Mago, Parvinder S. Sandhu, Neeru Chawla

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In this paper, a Bayesian Network (BN) based system is presented for providing clinical decision support to healthcare practitioners in rural or remote areas of India for young infants or children up to the age of 5 years. The government is unable to appoint child specialists in rural areas because of inadequate number of available pediatricians. It leads to a high Infant Mortality Rate (IMR). In such a scenario, Intelligent Pediatric System provides a realistic solution. The prototype of an intelligent system has been developed that involves a knowledge component called an Intelligent Pediatric Assistant (IPA); and User Agents (UA) along with their Graphical User Interfaces (GUI). The GUI of UA provides the interface to the healthcare practitioner for submitting sign-symptoms and displaying the expert opinion as suggested by IPA. Depending upon the observations, the IPA decides the diagnosis and the treatment plan. The UA and IPA form client-server architecture for knowledge sharing.

Keywords: Network, Based Intelligent, Pediatric System

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Authors: Tuisem Shimrah

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One general agreement on climate change is that its causes may be local but the effects are global. Indigenous people are subscribed to “low-carbon” traditional ways of life and as such they have contributed little to causes of climate change. On the contrary they are the most adversely affected by climate change due to their dependence on surrounding rich biological wealth as a source of their livelihood, health care, entertainment and cultural activities This paper deals with the results of the investigation of various adaptation strategies adopted to combat climate change by traditional community. The result shows effective ways of application of traditional knowledge and wisdom applied by Tangkhul traditional community at local and community level in remote areas in Northeast India. Four adaptation measures are being presented in this paper.

Keywords: Climate change, adaptation, Tangkhul, traditional community, policy, Northeast India.

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Authors: M. M. Shahidul Hassan, Omiya Hassan

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Bangladesh has set its goal to reach upper middle-income country status by 2024. To attain this status, the country must satisfy the World Bank requirement of achieving minimum Gross National Income (GNI). Number of youth job seekers in the country is increasing. University graduates are looking for decent jobs. So, the vital issue of this country is to understand how the GNI and jobs can be increased. The objective of this paper is to address these issues and find ways to create more job opportunities for youths at home and abroad which will increase the country’s GNI. The paper studies proportion of different goods Bangladesh exported, and also the percentage of employment in different sectors. The data used here for the purpose of analysis have been collected from the available literature. These data are then plotted and analyzed. Through these studies, it is concluded that growth in sectors like agricultural, ready-made garments (RMG), jute industries and fisheries are declining and the business community is not interested in setting up capital-intensive industries. Under this situation, the country needs to explore other business opportunities for a higher economic growth rate. Knowledge can substitute the physical resource. Since the country consists of the large youth population, higher education will play a key role in economic development. It now needs graduates with higher-order skills with innovative quality. Such dispositions demand changes in a university’s curriculum, teaching and assessment method which will function young generations as active learners and creators. By bringing these changes in higher education, a knowledge-based society can be created. The application of such knowledge and creativity will then become the commodity of Bangladesh which will help to reach its goal as an upper middle-income country.

Keywords: Bangladesh, economic sectors, economic growth, higher education, knowledge-based economy, massifcation of higher education, teaching and learning, universities’ role in society.

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Authors: M. Y. Ismail, M. Inam

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This paper presents equivalent circuit modeling of active planar reflectors which can be used for the detailed analysis and characterization of reflector performance in terms of lumped components. Equivalent circuit representation has been proposed for PIN diodes and liquid crystal based active planar reflectors designed within X-band frequency range. A very close agreement has been demonstrated between equivalent circuit results, 3D EM simulated results as well as measured scattering parameter results. In the case of measured results, a maximum discrepancy of 1.05dB was observed in the reflection loss performance, which can be attributed to the losses occurred during measurement process.

Keywords: Equivalent circuit modelling, planar reflectors, reflectarray antenna, PIN diode, liquid crystal.

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Authors: G. Schuh, S. Aghassi

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In order to bridge the gap between research and industry, promoting technology and knowledge transfer becomes increasingly important. Especially small- and medium-sized enterprises, having only little R&D resources themselves, depend on external technology development activities for remaining innovative. Academia research on the other hand needs potential industrial partners, who are capable and willing to commercialize their technologies as most public funding programs require some sort of technology transfer or dissemination activities. Modern web technologies offer more and more “social” functionalities and open up new ways of user interaction. In the past years several technology transfer platforms were developed, making use of modern web technologies in order to enable and support technology transfer. In this paper we report on the results of a state-of-the art analyses of existing technology transfer platforms, point out their advantages and deficits and give a perspective to the development of an improved technology transfer platform.

Keywords: Knowledge transfer, social software, technology management, technology transfer.

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Authors: Xia Lin

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Concept maps can be generated manually or automatically. It is important to recognize differences of the two types of concept maps. The automatically generated concept maps are dynamic, interactive, and full of associations between the terms on the maps and the underlying documents. Through a specific concept mapping system, Visual Concept Explorer (VCE), this paper discusses how automatically generated concept maps are different from manually generated concept maps and how different applications and learning opportunities might be created with the automatically generated concept maps. The paper presents several examples of learning strategies that take advantages of the automatically generated concept maps for concept learning and exploration.

Keywords: Concept maps, Dynamic concept representation, learning strategies, visual interface, Visual Concept Explorer.

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Authors: Pavan S., Sridhar G., Sridhar V.

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Super resolution is one of the commonly referred inference problems in computer vision. In the case of images, this problem is generally addressed using a graphical model framework wherein each node represents a portion of the image and the edges between the nodes represent the statistical dependencies. However, the large dimensionality of images along with the large number of possible states for a node makes the inference problem computationally intractable. In this paper, we propose a representation wherein each node can be represented as acombination of multiple regression functions. The proposed approach achieves a tradeoff between the computational complexity and inference accuracy by varying the number of regression functions for a node.

Keywords: Belief propagation, Graphical model, Regression, Super resolution.

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Authors: Erika Martinez Ramirez, Rene V. Mayorga

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Nowadays, more engineering systems are using some kind of Artificial Intelligence (AI) for the development of their processes. Some well-known AI techniques include artificial neural nets, fuzzy inference systems, and neuro-fuzzy inference systems among others. Furthermore, many decision-making applications base their intelligent processes on Fuzzy Logic; due to the Fuzzy Inference Systems (FIS) capability to deal with problems that are based on user knowledge and experience. Also, knowing that users have a wide variety of distinctiveness, and generally, provide uncertain data, this information can be used and properly processed by a FIS. To properly consider uncertainty and inexact system input values, FIS normally use Membership Functions (MF) that represent a degree of user satisfaction on certain conditions and/or constraints. In order to define the parameters of the MFs, the knowledge from experts in the field is very important. This knowledge defines the MF shape to process the user inputs and through fuzzy reasoning and inference mechanisms, the FIS can provide an “appropriate" output. However an important issue immediately arises: How can it be assured that the obtained output is the optimum solution? How can it be guaranteed that each MF has an optimum shape? A viable solution to these questions is through the MFs parameter optimization. In this Paper a novel parameter optimization process is presented. The process for FIS parameter optimization consists of the five simple steps that can be easily realized off-line. Here the proposed process of FIS parameter optimization it is demonstrated by its implementation on an Intelligent Interface section dealing with the on-line customization / personalization of internet portals applied to E-commerce.

Keywords: Artificial Intelligence, Fuzzy Logic, Fuzzy InferenceSystems, Nonlinear Optimization.

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Authors: Mohammad Javad Dehghani

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In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.

Keywords: Power quality, S-Transform, Short Time FourierTransform , Wavelet Transform, instantaneous sag, swell.

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Authors: Al-Amin Bhuiyan, Chang Hong Liu

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Gabor-based face representation has achieved enormous success in face recognition. This paper addresses a novel algorithm for face recognition using neural networks trained by Gabor features. The system is commenced on convolving a face image with a series of Gabor filter coefficients at different scales and orientations. Two novel contributions of this paper are: scaling of rms contrast and introduction of fuzzily skewed filter. The neural network employed for face recognition is based on the multilayer perceptron (MLP) architecture with backpropagation algorithm and incorporates the convolution filter response of Gabor jet. The effectiveness of the algorithm has been justified over a face database with images captured at different illumination conditions.

Keywords: Fuzzily skewed filter, Gabor filter, rms contrast, neural network.

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Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical vari-ants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time, in classical CPU and, alternativaly, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, ınpainting, parallel projection methods

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Authors: Mario Kubek, Herwig Unger

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Centroid terms are single words that semantically and topically characterise text documents and so may serve as their very compact representation in automatic text processing. In the present paper, centroids are used to measure the relevance of text documents with respect to a given search query. Thus, a new graphbased paradigm for searching texts in large corpora is proposed and evaluated against keyword-based methods. The first, promising experimental results demonstrate the usefulness of the centroid-based search procedure. It is shown that especially the routing of search queries in interactive and decentralised search systems can be greatly improved by applying this approach. A detailed discussion on further fields of its application completes this contribution.

Keywords: Search algorithm, centroid, query, keyword, cooccurrence, categorisation.

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Authors: Yavar Safaei Mehrabani, Mehdi Hosseinzadeh

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As embedded and portable systems were emerged power consumption of circuits had been major challenge. On the other hand latency as determines frequency of circuits is also vital task. Therefore, trade off between both of them will be desirable. Modulo 2n+1 adders are important part of the residue number system (RNS) based arithmetic units with the interesting moduli set (2n-1,2n, 2n+1). In this manuscript we have introduced novel binary representation to the design of modulo 2n+1 adder. VLSI realization of proposed architecture under 180 nm full static CMOS technology reveals its superiority in terms of area, power consumption and power-delay product (PDP) against several peer existing structures.

Keywords: Computer arithmetic, modulo 2n+1 adders, Residue Number System (RNS), VLSI.

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Authors: Michele V. Carbinatto, Wagner Wey Moreira, Myrian Nunomura; Mariana H. C. Tsukamoto, VilmaLeni Nista-Piccolo

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Sports Sciences has been historically supported by the positivism idea of science, especially by the mechanistic/reductionist and becomes a field that views experimentation and measurement as the mayor research domains. The disposition to simplify nature and the world by parts has fragmented and reduced the idea of bodyathletes as machine. In this paper we intent to re-think this perception lined by Complexity Theory. We come with the idea of athletes as a reflexive and active being (corporeity-body). Therefore, the construction of a training that considers the cultural, biological, psychological elements regarding the experience of the human corporal movements in a circumspect and responsible way could bring better chances of accomplishment. In the end, we hope to help coaches understand the intrinsic complexity of the body they are training, how better deal with it, and, in the field of a deep globalization among the different types of knowledge, to respect and accepted the peculiarities of knowledge that comprise this area.

Keywords: Sport science, body, complexity theory, corporeity.

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Authors: F.S.Tashimova, A. Mirzabekova, Z. Ismagambetova, Y. Massanov, Z. Gabit

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In the globalization process, when the struggle for minds and values of the people is taking place, the impact of the virtual space can cause unexpected effects and consequences in the process of adjustment of young people in this world. Their special significance is defined by unconscious influence on the underlying process of meaning and therefore the values preached by them are much more effective and affect both the personal characteristics and the peculiarities of adjustment process. Related to this the challenge is to identify factors influencing the reflection characteristics of virtual subjects and measures their impact on the personal characteristics of the students.

Keywords: Coping behavior, overcoming, personalization (representation), psychological defense, values, virtual space, virtual subject, subjective reflection.

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Authors: Päivi Aarreniemi-Jokipelto, Merja Alanko-Turunen

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The possibilities of mobile technology generate new demands for vocational teacher trainers to transform their approach to work and to incorporate its usage into their ordinary educational practice. This paper presents findings of a focus discussion group (FDG) session on the usage of iPads within a school of vocational teacher education (SoVTE). It aims to clarify how the teacher trainers are using iPads and what has changed in their work during the usage of iPads. The analytical framework bases on content analysis and expansive learning cycle. It was not only found what kind of a role iPads played in their daily practices but it brought also into attention how a cultural change regarding the usage of social media and mobile technology was desperately needed in the whole work community. Thus, the FGD was abducted for developing the knowledge practices of the community of the SoVTE.

Keywords: iPad, mobile learning, vocational teacher education.

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Authors: Mohammadsadegh Zanganehfar

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Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the 70's until today and has generated significant styles such as deconstructivism and parametricism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals. 

Keywords: Asian architecture, fractal geometry, fractal technique, geometric properties

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Authors: H. Zainuddin, F. Hanafi, M. H. Hairi, A. Aman, M.H.N. Talib

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This paper investigates the effects of knowledge-based acceleration feedback control integrated with Automatic Generation Control (AGC) to enhance the quality of frequency control of governing system. The Intelligent Acceleration Feedback Controller (IAFC) is proposed to counter the over and under frequency occurrences due to major load change in power system network. Therefore, generator tripping and load shedding operations can be reduced. Meanwhile, the integration of IAFC with AGC, a well known Load-Frequency Control (LFC) is essential to ensure the system frequency is restored to the nominal value. Computer simulations of frequency response of governing system are used to optimize the parameters of IAFC. As a result, there is substantial improvement on the LFC of governing system that employing the proposed control strategy.

Keywords: Knowledge-based Supplementary Control, Acceleration Feedback, Load Frequency Control, Automatic Generation Control.

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Authors: Weitao Lin

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To quickly extract adequate information from large-scale unstructured text data, this paper studies the representation of events in Chinese scenarios and performs the regularized abstraction. It proposes a Chinese event detection technique based on dependency parsing and rule matching. The method first performs dependency parsing on the original utterance, then performs pattern matching at the word or phrase granularity based on the results of dependent syntactic analysis, filters out the utterances with prominent non-event characteristics, and obtains the final results. The experimental results show the effectiveness of the method.

Keywords: Natural Language Processing, Chinese event detection, rules matching, dependency parsing.

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Authors: Rinaldo Christian Tanumara, Ming Xie, Chi Kit Au

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Human perceives color in categories, which may be identified using color name such as red, blue, etc. The categorization is unique for each human being. However despite the individual differences, the categorization is shared among members in society. This allows communication among them, especially when using color name. Sociable robot, to live coexist with human and become part of human society, must also have the shared color categorization, which can be achieved through learning. Many works have been done to enable computer, as brain of robot, to learn color categorization. Most of them rely on modeling of human color perception and mathematical complexities. Differently, in this work, the computer learns color categorization through interaction with humans. This work aims at developing the innate ability of the computer to learn the human-like color categorization. It focuses on the representation of color categorization and how it is built and developed without much mathematical complexity.

Keywords: Color categorization, color learning, machinelearning, color naming.

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Authors: Hossein Sahoolizadeh, Davood Sarikhanimoghadam, Hamid Dehghani

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This paper proposes new hybrid approaches for face recognition. Gabor wavelets representation of face images is an effective approach for both facial action recognition and face identification. Perform dimensionality reduction and linear discriminate analysis on the down sampled Gabor wavelet faces can increase the discriminate ability. Nearest feature space is extended to various similarity measures. In our experiments, proposed Gabor wavelet faces combined with extended neural net feature space classifier shows very good performance, which can achieve 93 % maximum correct recognition rate on ORL data set without any preprocessing step.

Keywords: Face detection, Neural Networks, Multi-layer Perceptron, Gabor wavelets.

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Authors: Isabel Díez Vial, Marta Fernández Olmoss

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This research tries to analyze the role that knowledge about foreign markets has in increasing firms- exports in clustered spaces. We consider two interrelated sources of knowledge: firms- direct experience and indirect experience from other clustered firms – export externalities. In particular, it is proposed that firms would improve their export performance by accessing to export externalities if they have some previous direct experience that allows them to identify, understand and exploit them. Also, we propose that this positive influence of previous direct experience on export externalities keeps only up to a point, where it becomes negative, creating an inverted “U" shape. Empirical evidence gathered among wine producers located in La Rioja tends to confirm that firms enjoy of export externalities if they have export experience along several years and countries increase their export performance. While this relationship becomes less relevant as they develop a higher experience, we could not confirm the existence of a curvilinear relationship in their influence on export externalities and export performance.

Keywords: Clusters, curvilinear relationship, absorptive capacity

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Authors: Bin Cai, Shilong Wang, Haibo Hu

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The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Norashikin Ahmad, Damminda Alahakoon

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Self-organizing map (SOM) provides both clustering and visualization capabilities in mining data. Dynamic self-organizing maps such as Growing Self-organizing Map (GSOM) has been developed to overcome the problem of fixed structure in SOM to enable better representation of the discovered patterns. However, in mining large datasets or historical data the hierarchical structure of the data is also useful to view the cluster formation at different levels of abstraction. In this paper, we present a technique to generate concept trees from the GSOM. The formation of tree from different spread factor values of GSOM is also investigated and the quality of the trees analyzed. The results show that concept trees can be generated from GSOM, thus, eliminating the need for re-clustering of the data from scratch to obtain a hierarchical view of the data under study.

Keywords: dynamic self-organizing map, concept formation, clustering.

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Authors: Gishantha Thantulage, Tatiana Kalganova, Manissa Wilson

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Ant Colony Algorithms have been applied to difficult combinatorial optimization problems such as the travelling salesman problem and the quadratic assignment problem. In this paper gridbased and random-based ant colony algorithms are proposed for automatic 3D hose routing and their pros and cons are discussed. The algorithm uses the tessellated format for the obstacles and the generated hoses in order to detect collisions. The representation of obstacles and hoses in the tessellated format greatly helps the algorithm towards handling free-form objects and speeds up computation. The performance of algorithm has been tested on a number of 3D models.

Keywords: Ant colony algorithm, Automatic hose routing, tessellated format, RAPID.

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Authors: Sam, Ng, Lewis Leighton, Sam Atkinson, Carson Yan, Landan Hu, Leslie Cheung, Brian Yap, Kent Lung, Ketat Sarakune

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This paper presents a method for verifying cryptocurrency reserves that balances the need for both transparency and data confidentiality. Our methodology employs cryptographic techniques, including Merkle Trees, Bulletproof, and zkSnark, to verify that total assets equal or exceed total liabilities, represented by customer funds. Notably, this verification is achieved without disclosing sensitive information such as the total asset value, customer count, or cold wallet addresses. We delve into the construction and implementation of this methodology. While the system is robust and scalable, we also identify areas for potential enhancements to improve its efficiency and versatility. As the digital asset landscape continues to evolve, our approach provides a solid foundation for ensuring continued trust and security in digital asset platforms.

Keywords: Cryptocurrency, crypto-currency, proof-of-reserve, por, zero-knowledge, zkpor.

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Authors: Nobuhiko Hishinuma, Jun Igari, Rentaro Yoshioka

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When programming in languages such as C, Java, etc., it is difficult to reconstruct the programmer's ideas only from the program code. This occurs mainly because, much of the programmer's ideas behind the implementation are not recorded in the code during implementation. For example, physical aspects of computation such as spatial structures, activities, and meaning of variables are not required as instructions to the computer and are often excluded. This makes the future reconstruction of the original ideas difficult. AIDA, which is a multimedia programming language based on the cyberFilm model, can solve these problems allowing to describe ideas behind programs using advanced annotation methods as a natural extension to programming. In this paper, a development environment that implements the AIDA language is presented with a focus on the annotation methods. In particular, an actual scientific numerical computation code is created and the effects of the annotation methods are analyzed.

Keywords: cyberFilm, development environment, knowledge engineering, multimedia programming language

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Authors: Nneka Osuchukwu, Leonid Shpanin

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The concept of converting the kinetic energy of quadcopter propellers into electrical energy is considered in this contribution following the feasibility study of the propeller vibrations, theoretical energy conversion, and simulation techniques. Analysis of the propeller vibration performance is presented via graphical representation of calculated and simulated parameters, in order to demonstrate the possibility of recovering the harvested energy from the propeller vibrations of the quadcopter while the quadcopter is in operation. Consideration of using piezoelectric materials in such concept, converting the mechanical energy of the propeller into the electrical energy, is given. Photographic evidence of the propeller in operation is presented and discussed together with experimental results to validate the theoretical concept.

Keywords: Unmanned aerial vehicle, energy harvesting, piezoelectric material, propeller vibration.

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Authors: Serifenur Cebesoy, Yelda Aygar, Elgiz Bairamov

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In this study, we examine some spectral properties of non-selfadjoint matrix-valued difference equations consisting of a polynomial-type Jost solution. The aim of this study is to investigate the eigenvalues and spectral singularities of the difference operator L which is expressed by the above-mentioned difference equation. Firstly, thanks to the representation of polynomial type Jost solution of this equation, we obtain asymptotics and some analytical properties. Then, using the uniqueness theorems of analytic functions, we guarantee that the operator L has a finite number of eigenvalues and spectral singularities.

Keywords: Difference Equations, Jost Functions, Asymptotics, Eigenvalues, Continuous Spectrum, Spectral Singularities.

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