On the Legibility of Mirror-Reflected and Rotated Text*Symmetry* **2017**, *9*(3), 28; doi:10.3390/sym9030028 - 23 February 2017**Abstract **

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We happened to observe that text that was reflected about either the horizontal or vertical axis was more difficult to read than text that was reflected about first one and then the other, which amounts to a 180-degree rotation. In this article, we

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We happened to observe that text that was reflected about either the horizontal or vertical axis was more difficult to read than text that was reflected about first one and then the other, which amounts to a 180-degree rotation. In this article, we review a number of studies that examine the nature of recognizing reflected and inverted letters, and the frequency of mirror reversal errors (e.g., confusing 'b' for 'd') in children and adults. We explore recent ideas linking the acquisition of literacy with the loss of mirror-invariance, not just for text, but for objects in general. We try to connect these various literatures to examine why certain transformations of text are more difficult to read than others for adults.
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Symmetry Analysis and Conservation Laws of the Zoomeron Equation*Symmetry* **2017**, *9*(2), 27; doi:10.3390/sym9020027 - 21 February 2017**Abstract **

In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the ﬁrst

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In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the ﬁrst time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the ﬁrst time, we construct the conservation laws of the underlying equation using the multiplier method.
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A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids*Symmetry* **2017**, *9*(2), 26; doi:10.3390/sym9020026 - 17 February 2017**Abstract **

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In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH) method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda

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In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH) method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient.
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Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression*Symmetry* **2017**, *9*(2), 24; doi:10.3390/sym9020024 - 10 February 2017**Abstract **

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Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many

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Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR). Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR) is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained.
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Deformable Object Matching Algorithm Using Fast Agglomerative Binary Search Tree Clustering*Symmetry* **2017**, *9*(2), 25; doi:10.3390/sym9020025 - 10 February 2017**Abstract **

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Deformable objects have changeable shapes and they require a different method of matching algorithm compared to rigid objects. This paper proposes a fast and robust deformable object matching algorithm. First, robust feature points are selected using a statistical characteristic to obtain the feature

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Deformable objects have changeable shapes and they require a different method of matching algorithm compared to rigid objects. This paper proposes a fast and robust deformable object matching algorithm. First, robust feature points are selected using a statistical characteristic to obtain the feature points with the extraction method. Next, matching pairs are composed by the feature point matching of two images using the matching method. Rapid clustering is performed using the BST (Binary Search Tree) method by obtaining the geometric similarity between the matching pairs. Finally, the matching of the two images is determined after verifying the suitability of the composed cluster. An experiment with five different image sets with deformable objects confirmed the superior robustness and independence of the proposed algorithm while demonstrating up to 60 times faster matching speed compared to the conventional deformable object matching algorithms.
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Erratum: Rauh, A. Coherent States of Harmonic and Reversed Harmonic Oscillator. *Symmetry*, 2016, *8*, 46*Symmetry* **2017**, *9*(2), 23; doi:10.3390/sym9020023 - 9 February 2017**Abstract **
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A Study on Immersion of Hand Interaction for Mobile Platform Virtual Reality Contents*Symmetry* **2017**, *9*(2), 22; doi:10.3390/sym9020022 - 5 February 2017**Abstract **

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This study proposes gaze-based hand interaction, which is helpful for improving the user’s immersion in the production process of virtual reality content for the mobile platform, and analyzes efficiency through an experiment using a questionnaire. First, three-dimensional interactive content is produced for use

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This study proposes gaze-based hand interaction, which is helpful for improving the user’s immersion in the production process of virtual reality content for the mobile platform, and analyzes efficiency through an experiment using a questionnaire. First, three-dimensional interactive content is produced for use in the proposed interaction experiment while presenting an experiential environment that gives users a high sense of immersion in the mobile virtual reality environment. This is designed to induce the tension and concentration of users in line with the immersive virtual reality environment. Additionally, a hand interaction method based on gaze—which is mainly used for the entry of mobile virtual reality content—is proposed as a design method for immersive mobile virtual reality environment. The user satisfaction level of the immersive environment provided by the proposed gaze-based hand interaction is analyzed through experiments in comparison with the general method that uses gaze only. Furthermore, detailed analysis is conducted by dividing the effects of the proposed interaction method on user’s psychology into positive factors such as immersion and interest and negative factors such as virtual reality (VR) sickness and dizziness. In this process, a new direction is proposed for improving the immersion of users in the production of mobile platform virtual reality content.
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Aesthetic Patterns with Symmetries of the Regular Polyhedron*Symmetry* **2017**, *9*(2), 21; doi:10.3390/sym9020021 - 3 February 2017**Abstract **
A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra.
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Acknowledgement to Reviewers of *Symmetry* in 2016*Symmetry* **2017**, *9*(2), 20; doi:10.3390/sym9020020 - 26 January 2017**Abstract **
The editors of *Symmetry *would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]
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Cyclotomic Aperiodic Substitution Tilings*Symmetry* **2017**, *9*(2), 19; doi:10.3390/sym9020019 - 25 January 2017**Abstract **

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The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the $2n$ -th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers

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The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the $2n$ -th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry ${D}_{n}$ or ${D}_{2n}$ , i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry ${D}_{n}$ or ${D}_{2n}$ only by iteration of substitution rules on a single tile.
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Some Invariants of Jahangir Graphs*Symmetry* **2017**, *9*(1), 17; doi:10.3390/sym9010017 - 23 January 2017**Abstract **

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In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs *J*_{n},_{m} for all values of *m* and *n*. From the M-polynomial, we recover many degree-based topological indices such as

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In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs *J*_{n},_{m} for all values of *m* and *n*. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.
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Fully Integrated on-Chip Switched DC–DC Converter for Battery-Powered Mixed-Signal SoCs*Symmetry* **2017**, *9*(1), 18; doi:10.3390/sym9010018 - 22 January 2017**Abstract **

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This paper presents a fully integrated on-chip switched-capacitor (SC) DC–DC converter that supports a programmable regulated power supply ranging from 2.6 to 3.2 V out of a 5 V input supply. The proposed 4-to-3 step-down topology utilizes two conventional 2-to-1 step-down topologies; each

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This paper presents a fully integrated on-chip switched-capacitor (SC) DC–DC converter that supports a programmable regulated power supply ranging from 2.6 to 3.2 V out of a 5 V input supply. The proposed 4-to-3 step-down topology utilizes two conventional 2-to-1 step-down topologies; each of them (*2-to-1_up* and *2-to-1_dw*) has a different flying capacitance to maximize the load current driving capability while minimizing the bottom-plate capacitance loss. The control circuits use a low power supply provided by a small internal low-drop output (LDO) connected to the internal load voltage (*V*_{L_dw}) from the *2-to-1_dw*, and low swing level-shifted gate-driving signals are generated using the internal load voltage (*V*_{L_dw}). Therefore, the proposed implementation reduces control circuit and switching power consumptions. The programmable power supply voltage is regulated by means of a pulse frequency modulation (PFM) technique with the compensated two-stage operational transconductance amplifier (OTA) and the current-starved voltage controlled oscillator (VCO) to maintain high efficiency over a wide range of load currents. The proposed on-chip SC DC–DC converter is designed and simulated using high-voltage 0.35 μm bipolar, complementary metal-oxide-semiconductor (CMOS) and DMOS (BCDMOS) technology. It achieves a peak efficiency of 74% when delivering an 8 mA load current at a 3.2 V supply voltage level, and it provides a maximum output power of 48 mW (*I*_{L} = 15 mA at *V*_{L_up} = 3.2 V) at 70.5% efficiency. The proposed on-chip SC voltage regulator shows better efficiency than the ideal linear regulator over a wide range of output power, from 2.6 mW to 48 mW. The 18-phase interleaving technique enables the worst-case output voltage ripple to be less than 5.77% of the load voltage.
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Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets*Symmetry* **2017**, *9*(1), 12; doi:10.3390/sym9010012 - 21 January 2017**Abstract **

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The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted

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The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of equations resulting from the Crank–Nicolson discretization help us to use the standard pre-conditioner for the iterative matrix solver and reduces the number of iterations to get an accurate option values. In addition, the number of iterations that is required to solve the preconditioned system, resulting from the proposed iterative Crank–Nicolson scheme, does not grow with the size of the system. Thus, we can effectively reduce the order of complexity in multidimensional option pricing. The numerical results are compared to the one with implicit Operator Splitting Method (OSM) to show the effectiveness.
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Generalized Null 2-Type Surfaces in Minkowski 3-Space*Symmetry* **2017**, *9*(1), 14; doi:10.3390/sym9010014 - 20 January 2017**Abstract **

For the mean curvature vector field $\mathbf{H}$ and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition $\Delta \mathbf{H}=f\mathbf{H}+g\mathbf{C}$ is known as a generalized null 2-type, where *f* and *g*

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For the mean curvature vector field $\mathbf{H}$ and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition $\Delta \mathbf{H}=f\mathbf{H}+g\mathbf{C}$ is known as a generalized null 2-type, where *f* and *g* are smooth functions, and $\mathbf{C}$ is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper, we study flat surfaces in the Minkowski 3-space ${\mathbb{L}}^{3}$ and classify generalized null 2-type flat surfaces. In addition, we show that the only generalized null 2-type null scroll in ${\mathbb{L}}^{3}$ is a *B*-scroll.
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An Orthogonal Multi-Swarm Cooperative PSO Algorithm with a Particle Trajectory Knowledge Base*Symmetry* **2017**, *9*(1), 15; doi:10.3390/sym9010015 - 20 January 2017**Abstract **

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A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO) algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an

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A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO) algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an orthogonal initialization mechanism and a particle trajectory knowledge base for multi-dimensional optimization problems, but also conceives a new adaptive cooperation mechanism to accomplish the information interaction among swarms and particles. Experiments are conducted on a set of benchmark functions, and the results show its better performance compared with traditional PSO algorithm in aspects of convergence, computational efficiency and avoiding premature convergence.
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Data-Filtering System to Avoid Total Data Distortion in IoT Networking*Symmetry* **2017**, *9*(1), 16; doi:10.3390/sym9010016 - 20 January 2017**Abstract **

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In the Internet of Things (IoT) networking, numerous objects are connected to a network. They sense events and deliver the sensed information to the cloud. A lot of data is generated in the IoT network, and servers in the cloud gather the sensed

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In the Internet of Things (IoT) networking, numerous objects are connected to a network. They sense events and deliver the sensed information to the cloud. A lot of data is generated in the IoT network, and servers in the cloud gather the sensed data from the objects. Then, the servers analyze the collected data and provide proper intelligent services to users through the results of the analysis. When the server analyzes the collected data, if there exists malfunctioning data, distortional results of the analysis will be generated. The distortional results lead to misdirection of the intelligent services, leading to poor user experience. In the analysis for intelligent services in IoT, malfunctioning data should be avoided because integrity of the collected data is crucial. Therefore, this paper proposes a data-filtering system for the server in the cloud. The proposed data-filtering system is placed in front of the server and firstly receives the sensed data from the objects. It employs the naïve Bayesian classifier and, by learning, classifies the malfunctioning data from among the collected data. Data with integrity is delivered to the server for analysis. Because the proposed system filters the malfunctioning data, the server can obtain accurate analysis results and reduce computing load. The performance of the proposed data-filtering system is evaluated through computer simulation. Through the simulation results, the efficiency of the proposed data-filtering system is shown.
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A (1 + 2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II*Symmetry* **2017**, *9*(1), 13; doi:10.3390/sym9010013 - 20 January 2017**Abstract **

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A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry

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A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is presented. The Lie symmetries obtained are used for reduction of the Cauchy problem to that of (1 + 1)-dimensional. Exact solutions of some (1 + 1)-dimensional problems are constructed. In particular, we have proved that the Cauchy problem for the (1 + 1)-dimensional simplified Keller–Segel system can be linearized and solved in an explicit form. Moreover, additional biologically motivated restrictions were established in order to obtain a unique solution. The Lie symmetry classification of the (1 + 2)-dimensional Neumann problem for the simplified Keller–Segel system is derived. Because Lie symmetry of boundary-value problems depends essentially on geometry of the domain, which the problem is formulated for, all realistic (from applicability point of view) domains were examined. Reduction of the the Neumann problem on a strip is derived using the symmetries obtained. As a result, an exact solution of a nonlinear two-dimensional Neumann problem on a finite interval was found.
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Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components*Symmetry* **2017**, *9*(1), 10; doi:10.3390/sym9010010 - 13 January 2017**Abstract **

In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous Fréchet components in terms of the usual stochastic order, reversed hazard rate order and likelihood ratio order. The partial results established here extend some well-known results in

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In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous Fréchet components in terms of the usual stochastic order, reversed hazard rate order and likelihood ratio order. The partial results established here extend some well-known results in the literature of Gupta et al. Specifically, first, we generalize the result of Theorem 2 from the usual stochastic order to the reversed hazard rate order. Second, we generalize the result of Theorem 3 from the reversed hazard rate order to the likelihood ratio order. Last, we generalize the result of Theorem 4 from the hazard rate order to the likelihood ratio order when shape parameter $0<\alpha \le 1$ .
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Prognosis Essay Scoring and Article Relevancy Using Multi-Text Features and Machine Learning*Symmetry* **2017**, *9*(1), 11; doi:10.3390/sym9010011 - 12 January 2017**Abstract **

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This study develops a model for essay scoring and article relevancy. Essay scoring is a costly process when we consider the time spent by an evaluator. It may lead to inequalities of the effort by various evaluators to apply the same evaluation criteria.

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This study develops a model for essay scoring and article relevancy. Essay scoring is a costly process when we consider the time spent by an evaluator. It may lead to inequalities of the effort by various evaluators to apply the same evaluation criteria. Bibliometric research uses the evaluation criteria to find relevancy of articles instead. Researchers mostly face relevancy issues while searching articles. Therefore, they classify the articles manually. However, manual classification is burdensome due to time needed for evaluation. The proposed model performs automatic essay evaluation using multi-text features and ensemble machine learning. The proposed method is implemented in two data sets: a Kaggle short answer data set for essay scoring that includes four ranges of disciplines (Science, Biology, English, and English language Arts), and a bibliometric data set having IoT (Internet of Things) and non-IoT classes. The efficacy of the model is measured against the Tandalla and AutoP approach using Cohen’s kappa. The model achieves kappa values of 0.80 and 0.83 for the first and second data sets, respectively. Kappa values show that the proposed model has better performance than those of earlier approaches.
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DIaaS: Resource Management System for the Intra-Cloud with On-Premise Desktops*Symmetry* **2017**, *9*(1), 8; doi:10.3390/sym9010008 - 9 January 2017**Abstract **

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Infrastructure as a service with desktops (DIaaS) based on the extensible mark-up language (XML) is herein proposed to utilize surplus resources. DIaaS is a traditional surplus-resource integrated management technology. It is designed to provide fast work distribution and computing services based on user

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Infrastructure as a service with desktops (DIaaS) based on the extensible mark-up language (XML) is herein proposed to utilize surplus resources. DIaaS is a traditional surplus-resource integrated management technology. It is designed to provide fast work distribution and computing services based on user service requests as well as storage services through desktop-based distributed computing and storage resource integration. DIaaS includes a nondisruptive resource service and an auto-scalable scheme to enhance the availability and scalability of intra-cloud computing resources. A performance evaluation of the proposed scheme measured the clustering performance time for surplus resource utilization. The results showed improvement in computing and storage services in a connection of at least two computers compared to the traditional method for high-availability measurement of nondisruptive services. Furthermore, an artificial server error environment was used to create a clustering delay for computing and storage services and for nondisruptive services. It was compared to the Hadoop distributed file system (HDFS).
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