Search results for: digital arithmetic

Authors: Hanh Huu Hoang, Tho Manh Nguyen

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Ever increasing capacities of contemporary storage devices inspire the vision to accumulate (personal) information without the need of deleting old data over a long time-span. Hence the target of SemanticLIFE project is to create a Personal Information Management system for a human lifetime data. One of the most important characteristics of the system is its dedication to retrieve information in a very efficient way. By adopting user demands regarding the reduction of ambiguities, our approach aims at a user-oriented and yet powerful enough system with a satisfactory query performance. We introduce the query system of SemanticLIFE, the Virtual Query System, which uses emerging Semantic Web technologies to fulfill users- requirements.

Keywords: Ontology-based Information Retrieval, Digital Memories, SemanticLIFE.

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Authors: Perumal, V., Hassan, H., Bolong, J., Osman, M. N.

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Film, as an art form playing a vital role and is a powerful tool in documenting, influencing and shaping the society. Films are the collective creation of a large number of separate individuals, each contributing with creative input, unique talents, and technical expertise to the project. Recently, the Malaysian Independent (or “Indie") filmmakers have made their presence felt by winning awards at various international film festivals. Working in the digital video (DV) format, a number of independent filmmakers really hit their stride with a range of remarkably strong titles and international recognition has been quick in coming and their works are now regularly in exhibition or in competition, winning many top prizes at prestigious festivals around the world. The interaction factors among crewmembers are emphasized as imperative for group success. An in-depth interview is conducted to analyze the social interactions and exchanges between filmmakers through Social Exchanges Theory (SET). Certainly the new millennium that was marked as the digital technology revolution has changed the face of filmmaking in Malaysia. There is a clear need to study the Malaysian independent cinema especially from the perspective of understanding what causes the independent filmmakers to work so well given all of the difficulties and constraints.

Keywords: Digital filmmaking, technology, interaction, crewmembers, cinema, independent filmmaker.

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Authors: Yuan-Hsiang Chang, Zhong-Xian Peng, Li-Der Jeng

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Music has always been an integral part of human’s daily lives. But, for the most people, reading musical score and turning it into melody is not easy. This study aims to develop an Automatic music score recognition system using digital image processing, which can be used to read and analyze musical score images automatically. The technical approaches included: (1) staff region segmentation; (2) image preprocessing; (3) note recognition; and (4) accidental and rest recognition. Digital image processing techniques (e.g., horizontal /vertical projections, connected component labeling, morphological processing, template matching, etc.) were applied according to musical notes, accidents, and rests in staff notations. Preliminary results showed that our system could achieve detection and recognition rates of 96.3% and 91.7%, respectively. In conclusion, we presented an effective automated musical score recognition system that could be integrated in a system with a media player to play music/songs given input images of musical score. Ultimately, this system could also be incorporated in applications for mobile devices as a learning tool, such that a music player could learn to play music/songs.

Keywords: Connected component labeling, image processing, morphological processing, optical musical recognition.

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Authors: Hidehiko Okada

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The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks. 

Keywords: Evolutionary algorithms, differential evolution, neural network, neuroevolution, interval arithmetic.

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Authors: Marco Hemmerling

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The paper outlines the relevance of computational geometry within the design and production process of architecture. Based on two case studies, the digital chain - from the initial formfinding to the final realization of spatial concepts - is discussed in relation to geometric principles. The association with the fascinating complexity that can be found in nature and its underlying geometry was the starting point for both projects presented in the paper. The translation of abstract geometric principles into a three-dimensional digital design model – realized in Rhinoceros – was followed by a process of transformation and optimization of the initial shape that integrated aesthetic, spatial and structural qualities as well as aspects of material properties and conditions of production.

Keywords: Architecture, Computer Aided Architectural Design, 3D-Modeling, Rapid Prototyping, CAD/CAM.

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Authors: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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The concept of order reduction by least-squares moment matching and generalised least-squares methods has been extended about a general point ?a?, to obtain the reduced order models for linear, time-invariant dynamic systems. Some heuristic criteria have been employed for selecting the linear shift point ?a?, based upon the means (arithmetic, harmonic and geometric) of real parts of the poles of high order system. It is shown that the resultant model depends critically on the choice of linear shift point ?a?. The validity of the criteria is illustrated by solving a numerical example and the results are compared with the other existing techniques.

Keywords: Integral square error, Least-squares, Markovparameters, Moment matching, Order reduction.

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Authors: M. Lakshmi, J. Senthil Kumar

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Digital cameras to reduce cost, use an image sensor to capture color images. Color Filter Array (CFA) in digital cameras permits only one of the three primary (red-green-blue) colors to be sensed in a pixel and interpolates the two missing components through a method named demosaicking. Captured data is interpolated into a full color image and compressed in applications. Color interpolation before compression leads to data redundancy. This paper proposes a new Vector Quantization (VQ) technique to construct a VQ codebook with Differential Evolution (DE) Algorithm. The new technique is compared to conventional Linde- Buzo-Gray (LBG) method.

Keywords: Color Filter Array (CFA), Biorthogonal Wavelet, Vector Quantization (VQ), Differential Evolution (DE).

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Authors: T. Cholastova, D. Knotova

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Utilization of diverse germplasm is needed to enhance the genetic diversity of cultivars. The objective of this study was to evaluate the genetic relationships of 98 alfalfa germplasm accessions using morphological traits and SSR markers. From the 98 tested populations, 81 were locals originating in Europe, 17 were introduced from USA, Australia, New Zealand and Canada. Three primers generated 67 polymorphic bands. The average polymorphic information content (PIC) was very high (> 0.90) over all three used primer combinations. Cluster analysis using Unweighted Pair Group Method with Arithmetic Means (UPGMA) and Jaccard´s coefficient grouped the accessions into 2 major clusters with 4 sub-clusters with no correlation between genetic and morphological diversity. The SSR analysis clearly indicated that even with three polymorphic primers, reliable estimation of genetic diversity could be obtained.

Keywords: genetic diversity, Medicago sativa L., morphological traits, SSR markers

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Authors: Mathinee Khongsatid, Phusit Phukamchanoad, Sakapas Sangchai

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This research aims to study the democratic political socialization of the 5th and 6th Graders under the Authority of Dusit District Office, Bangkok by using stratified sampling for probability sampling and using purposive sampling for non-probability sampling to collect data toward the distribution of questionnaires to 300 respondents. This covers all of the schools under the authority of Dusit District Office. The researcher analyzed the data by using descriptive statistics which include arithmetic mean and standard deviation. The result shows that 5th and 6th graders under the authority of Dusit District Office, Bangkok, have displayed some characteristics following democratic political socialization both inside and outside classroom as well as outside school. However, the democratic political socialization in classroom through grouping and class participation is much more emphasized.

Keywords: Democratic, Political Socialization

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Authors: Ayse Yayla, Aynur Akar

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Developments in scientific and technical area cause to use new methods and techniques in education, as is the case in all fields. Especially, the internet contributes a variety of new methods to design virtual and real time laboratory applications in education. In this study, a real time virtual laboratory is designed and implemented for analog and digital communications laboratory experiments by using Lab VIEW program for Marmara University Electronics-Communication Department. In this application, students can access the virtual laboratory web site and perform their experiments without any limitation of time and location so as the students can observe the signals by changing the parameters of the experiment and evaluate the results.

Keywords: Virtual laboratory, LabVIEW, ModulationTechniques

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Authors: R. Talebi, A. Abdel-Dayem, J. Johnson

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Three-dimensional reconstruction of small objects has been one of the most challenging problems over the last decade. Computer graphics researchers and photography professionals have been working on improving 3D reconstruction algorithms to fit the high demands of various real life applications. Medical sciences, animation industry, virtual reality, pattern recognition, tourism industry, and reverse engineering are common fields where 3D reconstruction of objects plays a vital role. Both lack of accuracy and high computational cost are the major challenges facing successful 3D reconstruction. Fringe projection has emerged as a promising 3D reconstruction direction that combines low computational cost to both high precision and high resolution. It employs digital projection, structured light systems and phase analysis on fringed pictures. Research studies have shown that the system has acceptable performance, and moreover it is insensitive to ambient light. This paper presents an overview of fringe projection approaches. It also presents an experimental study and implementation of a simple fringe projection system. We tested our system using two objects with different materials and levels of details. Experimental results have shown that, while our system is simple, it produces acceptable results.

Keywords: Digital fringe projection, 3D reconstruction, phase unwrapping, phase shifting.

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Authors: Cyrille Lambert, Tatiana Kalganova, Emanuele Stomeo, Manissa Wilson

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A multi-board run-time reconfigurable (MRTR) system for evolvable hardware (EHW) is introduced with the aim to implement on hardware the bidirectional incremental evolution (BIE) method. The main features of this digital intrinsic EHW solution rely on the multi-board approach, the variable chromosome length management and the partial configuration of the reconfigurable circuit. These three features provide a high scalability to the solution. The design has been written in VHDL with the concern of not being platform dependant in order to keep a flexibility factor as high as possible. This solution helps tackling the problem of evolving complex task on digital configurable support.

Keywords: Evolvable Hardware, Evolutionary Strategy, multiboardFPGA system.

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Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, we propose a new robust and secure system that is based on the combination between two different transforms Discrete wavelet Transform (DWT) and Contourlet Transform (CT). The combined transforms will compensate the drawback of using each transform separately. The proposed algorithm has been designed, implemented and tested successfully. The experimental results showed that selecting the best sub-band for embedding from both transforms will improve the imperceptibility and robustness of the new combined algorithm. The evaluated imperceptibility of the combined DWT-CT algorithm which gave a PSNR value 88.11 and the combination DWT-CT algorithm improves robustness since it produced better robust against Gaussian noise attack. In addition to that, the implemented system shored a successful extraction method to extract watermark efficiently.

Keywords: DWT, CT, Digital Image Watermarking, Copyright Protection.

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Authors: Jason Zalev, Reza Sedaghat

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This paper describes a complex energy signal model that is isomorphic with digital human fingerprint images. By using signal models, the problem of fingerprint matching is transformed into the signal processing problem of finding a correlation between two complex signals that differ by phase-rotation and time-scaling. A technique for minutiae matching that is independent of image translation, rotation and linear-scaling, and is resistant to missing minutiae is proposed. The method was tested using random data points. The results show that for matching prints the scaling and rotation angles are closely estimated and a stronger match will have a higher correlation.

Keywords: Affine Invariant, Fingerprint Recognition, Matching, Minutiae.

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Authors: Hee-Choul Kwon, Heeyong Kwon

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Image rotation is one of main pre-processing steps for image processing or image pattern recognition. It is implemented with a rotation matrix multiplication. It requires a lot of floating point arithmetic operations and trigonometric calculations, so it takes a long time to execute. Therefore, there has been a need for a high speed image rotation algorithm without two major time-consuming operations. However, the rotated image has a drawback, i.e. distortions. We solved the problem using an augmented two-step shear transform. We compare the presented algorithm with the conventional rotation with images of various sizes. Experimental results show that the presented algorithm is superior to the conventional rotation one.

Keywords: High speed rotation operation, image rotation, transform matrix, image processing, pattern recognition.

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Authors: Nurhakimah Ab. Rahman, Lazim Abdullah

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According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

Keywords: Dual fuzzy polynomial equations, Interval type-2, Ranking method, Value.

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Authors: A.A. Amran, S. R. M. Shukri, S. M. Taib

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The role of entrepreneurs in generating the economy is very important. Thus, nurturing entrepreneurship skills among society is very crucial and should start from the early age. One of the methods is to teach through game such as board game. Game provides a fun and interactive platform for players to learn and play. Besides that as today-s world is moving towards Islamic approach in terms of finance, banking and entertainment but Islamic based game is still hard to find in the market especially games on entrepreneurship. Therefore, there is a gap in this segment that can be filled by learning entrepreneurship through game. The objective of this paper is to develop an entrepreneurship digital-based game entitled “Catur Bistari" that is based on Islamic business approach. Knowledge and skill of entrepreneurship and Islamic business approach will be learned through the tasks that are incorporated inside the game.

Keywords: Board game, educational game, entrepreneurship, Islamic finance and simulation.

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Authors: Imran Usman, Asifullah Khan, Rafiullah Chamlawi, Abdul Majid

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Information hiding for authenticating and verifying the content integrity of the multimedia has been exploited extensively in the last decade. We propose the idea of using genetic algorithm and non-deterministic dependence by involving the un-watermarkable coefficients for digital image authentication. Genetic algorithm is used to intelligently select coefficients for watermarking in a DCT based image authentication scheme, which implicitly watermark all the un-watermarkable coefficients also, in order to thwart different attacks. Experimental results show that such intelligent selection results in improvement of imperceptibility of the watermarked image, and implicit watermarking of all the coefficients improves security against attacks such as cover-up, vector quantization and transplantation.

Keywords: Digital watermarking, fragile watermarking, geneticalgorithm, Image authentication.

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Authors: D. Zare, F. Salmanizade, H. Safiyari

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Physical and mechanical properties of Russian olive fruits were measured at moisture content of 14.43% w.b. The results revealed that the mean length, width and thickness of Russian olive fruits were 20.72, 15.73 and 14.69mm, respectively. Mean mass and volume of Russian olive fruits were measured as 1.45 g and 2.55 cm3, respectively. The sphericity, aspect ratio and surface area were calculated as 0.81, 0.72 and 8.96 cm2, respectively, while arithmetic mean diameter, geometric mean diameter and equivalent diameter of Russian olive fruits were 17.05, 16.83 and 16.84 mm, respectively. Whole fruit density, bulk density and porosity of jujube fruits were measured and found to be 1.01 g/cm3, 0.29 g/cm3 and 69.5%, respectively. The values of static coefficient of friction on three surfaces of glass, galvanized iron and plywood were 0.35, 0.36 and 0.43, respectively. The skin color (L*, a*, b*) varied from 9.92 to 16.08; 2.04 to 3.91 and 1.12 to 3.83, respectively. The values of rupture force, deformation, energy absorbed and hardness were found to be between 12.14-16.85 N, 2.16-4.25 mm, 3.42-6.99 N mm and 17.1-23.85 N/mm.

Keywords: Mechanical and Physical properties, Russian olive fruits, friction coefficient

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Authors: D. Krishnaveni, M. Geetha Priya

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Applications of reversible logic gates in the design of complex integrated circuits provide power optimization.  This technique finds a great use in low power CMOS design, optical computing, quantum computing and nanotechnology. This paper proposes a reversible signed division circuit that can divide an n-bit signed dividend with an n-bit signed divisor using non-restoration division logic. The proposed design adequately addresses the ‘delay’ there by improving the efficiency of the circuit. An attempt is made to design a reversible signed division circuit. This paper provides a threshold to build more complex arithmetic systems using reversible logic, thus increasing the performance of computing systems.

Keywords: Low power CMOS, quantum computing, reversible logic gates, shift register, signed division.

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Authors: Gang Li, Ghulam Mubashar Hassan, Arcady Dyskin, Cara MacNish

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Digital image correlation (DIC) is a contactless fullfield displacement and strain reconstruction technique commonly used in the field of experimental mechanics. Comparing with physical measuring devices, such as strain gauges, which only provide very restricted coverage and are expensive to deploy widely, the DIC technique provides the result with full-field coverage and relative high accuracy using an inexpensive and simple experimental setup. It is very important to study the natural patterns effect on the DIC technique because the preparation of the artificial patterns is time consuming and hectic process. The objective of this research is to study the effect of using images having natural pattern on the performance of DIC. A systematical simulation method is used to build simulated deformed images used in DIC. A parameter (subset size) used in DIC can have an effect on the processing and accuracy of DIC and even cause DIC to failure. Regarding to the picture parameters (correlation coefficient), the higher similarity of two subset can lead the DIC process to fail and make the result more inaccurate. The pictures with good and bad quality for DIC methods have been presented and more importantly, it is a systematic way to evaluate the quality of the picture with natural patterns before they install the measurement devices.

Keywords: Digital image correlation (DIC), Deformation simulation, Natural pattern, Subset size.

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Authors: Yasunori Sugita, Toshinori Yoshikawa, Naoyuki Aikawa

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Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.

Keywords: Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple

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Authors: Gizelle K. Vianna, Gabriel V. Cunha, Gustavo S. Oliveira

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Foliage diseases in plants can cause a reduction in both quality and quantity of agricultural production. Intelligent detection of plant diseases is an essential research topic as it may help monitoring large fields of crops by automatically detecting the symptoms of foliage diseases. This work investigates ways to recognize the late blight disease from the analysis of tomato digital images, collected directly from the field. A pair of multilayer perceptron neural network analyzes the digital images, using data from both RGB and HSL color models, and classifies each image pixel. One neural network is responsible for the identification of healthy regions of the tomato leaf, while the other identifies the injured regions. The outputs of both networks are combined to generate the final classification of each pixel from the image and the pixel classes are used to repaint the original tomato images by using a color representation that highlights the injuries on the plant. The new images will have only green, red or black pixels, if they came from healthy or injured portions of the leaf, or from the background of the image, respectively. The system presented an accuracy of 97% in detection and estimation of the level of damage on the tomato leaves caused by late blight.

Keywords: Artificial neural networks, digital image processing, pattern recognition.

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Authors: Muhibul Haque Bhuyan, Md. Refat Sarder

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If a person can monitor his/her oxygen saturation level intermittently then he/she can identify his/her condition early and thus he/she can seek a doctor’s help. This paper reports the design, simulation, and implementation of a low-cost pulse oxygen saturation measurement device based on a reflective photoplethysmography (PPG) system using an integrated circuit sensor as the fundamental component of this health status checking device. The measurement of the physiological parameter is the blood oxygen saturation level (SpO₂) in the peripheral capillary. This work has been implemented using an Arduino Uno R3 microcontroller along with this sensor integrated circuit (IC). The system is designed in the Proteus environment and then simulated to check its performance. After that, the hardware implementation is performed. We used a clipping type optical sensor to sense the arterial oxygen saturation level of blood signal from the fingertips of an individual and then transformed it into the digital data in the microcontroller through its programming its instruction. The designed system was tested by measuring the SpO₂ level for several people of different ages, from 12 to 57 years of age. Besides, the same people were tested using a standard machine purchased from the market. Test results were found very satisfactory as the average percentage of error was very low, 1.59% only.

Keywords: Digital pulse oxygen saturation level, oximeter, measurement, design, simulation, implementation, proteus, Arduino Uno microcontroller.

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Authors: W. S. Barber, S. L. King

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This paper is a qualitative case study analysis of the development of a fully online learning community of graduate students through arts-based community building activities. With increasing numbers and types of online learning spaces, it is incumbent upon educators to continue to push the edge of what best practices look like in digital learning environments. In digital learning spaces, instructors can no longer be seen as purveyors of content knowledge to be examined at the end of a set course by a final test or exam. The rapid and fluid dissemination of information via Web 3.0 demands that we reshape our approach to teaching and learning, from one that is content-focused to one that is process-driven. Rather than having instructors as formal leaders, today’s digital learning environments require us to share expertise, as it is the collective experiences and knowledge of all students together with the instructors that help to create a very different kind of learning community. This paper focuses on innovations pursued in a 36 hour 12 week graduate course in higher education entitled “Critical and Reflective Practice”. The authors chronicle their journey to developing a fully online learning community (FOLC) by emphasizing the elements of social, cognitive, emotional and digital spaces that form a moving interplay through the community. In this way, students embrace anywhere anytime learning and often take the learning, as well as the relationships they build and skills they acquire, beyond the digital class into real world situations. We argue that in order to increase student online engagement, pedagogical approaches need to stem from two primary elements, both creativity and critical reflection, that are essential pillars upon which instructors can co-design learning environments with students. The theoretical framework for the paper is based on the interaction and interdependence of Creativity, Intuition, Critical Reflection, Social Constructivism and FOLCs. By leveraging students’ embedded familiarity with a wide variety of technologies, this case study of a graduate level course on critical reflection in education, examines how relationships, quality of work produced, and student engagement can improve by using creative and imaginative pedagogical strategies. The authors examine their professional pedagogical strategies through the lens that the teacher acts as facilitator, guide and co-designer. In a world where students can easily search for and organize information as self-directed processes, creativity and connection can at times be lost in the digitized course environment. The paper concludes by posing further questions as to how institutions of higher education may be challenged to restructure their credit granting courses into more flexible modules, and how students need to be considered an important part of assessment and evaluation strategies. By introducing creativity and critical reflection as central features of the digital learning spaces, notions of best practices in digital teaching and learning emerge.

Keywords: Online, pedagogy, learning, communities.

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Authors: J.S. Ubhi, M.S. Patterh, T.S. Kamal

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In this paper, the effect of transmission codes on the performance of coherent square M-ary quadrature amplitude modulation (CSMQAM) under hybrid selection/maximal-ratio combining (H-S/MRC) diversity is analysed. The fading channels are modeled as frequency non-selective slow independent and identically distributed Rayleigh fading channels corrupted by additive white Gaussian noise (AWGN). The results for coded MQAM are computed numerically for the case of (24,12) extended Golay code and compared with uncoded MQAM under H-S/MRC diversity by plotting error probabilities versus average signal to noise ratio (SNR) for various values L and N in order to examine the improvement in the performance of the digital communications system as the number of selected diversity branches is increased. The results for no diversity, conventional SC and Lth order MRC schemes are also plotted for comparison. Closed form analytical results derived in this paper are sufficiently simple and therefore can be computed numerically without any approximations. The analytical results presented in this paper are expected to provide useful information needed for design and analysis of digital communication systems over wireless fading channels.

Keywords: Error probability, diversity reception, Rayleigh fading channels, wireless digital communications.

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Authors: Peter U. Eze, P. Udaya, Robin J. Evans

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Data hiding can be achieved by Steganography or invisible digital watermarking. For digital watermarking, both accurate retrieval of the embedded watermark and the integrity of the cover image are important. Medical image security in Teleradiology is one of the applications where the embedded patient record needs to be extracted with accuracy as well as the medical image integrity verified. In this research paper, the Constant Correlation Spread Spectrum digital watermarking for medical image tamper detection and accurate embedded watermark retrieval is introduced. In the proposed method, a watermark bit from a patient record is spread in a medical image sub-block such that the correlation of all watermarked sub-blocks with a spreading code, W, would have a constant value, p. The constant correlation p, spreading code, W and the size of the sub-blocks constitute the secret key. Tamper detection is achieved by flagging any sub-block whose correlation value deviates by more than a small value, ℇ, from p. The major features of our new scheme include: (1) Improving watermark detection accuracy for high-pixel depth medical images by reducing the Bit Error Rate (BER) to Zero and (2) block-level tamper detection in a single computational process with simultaneous watermark detection, thereby increasing utility with the same computational cost.

Keywords: Constant correlation, medical image, spread spectrum, tamper detection, watermarking.

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Authors: SangWon Han, MuWook Pyeon, Sujung Moon, DaeKyo Seo

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Recently, technologies based on three-dimensional (3D) space information are being developed and quality of life is improving as a result. Research on real-time digital map (RDM) is being conducted now to provide 3D space information. RDM is a service that creates and supplies 3D space information in real time based on location/shape detection. Research subjects on RDM include the construction of 3D space information with matching image data, complementing the weaknesses of image acquisition using multi-source data, and data collection methods using big data. Using RDM will be effective for space analysis using 3D space information in a U-City and for other space information utilization technologies.

Keywords: RDM, multi-source data, big data, U-City.

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Authors: T. C. Chu, S.H. Wu

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This paper suggests ranking alternatives under fuzzy MCDM (multiple criteria decision making) via an centroid based ranking approach, where criteria are classified to benefit qualitative, benefit quantitative and cost quantitative ones. The ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. The membership function for the final fuzzy evaluation value of each alternative can be developed through α-cuts and interval arithmetic of fuzzy numbers. The distance between the original point and the relative centroid is applied to defuzzify the final fuzzy evaluation values in order to rank alternatives. Finally a numerical example demonstrates the computation procedure of the proposed model.

Keywords: Fuzzy MCDM, Criteria, Fuzzy number, Ranking, Relative centroid.

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Authors: Feng Cheng Chang

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A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000.

Keywords: Polynomial roots, greatest common divisor, Longhand polynomial division, Euclidean GCD Algorithm.

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