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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Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security*Symmetry* **2017**, *9*(1), 9; doi:10.3390/sym9010009 - 7 January 2017**Abstract **

The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial

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The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ) system of equations, which is a system representing a subclass of multivariate quadratic (MQ) systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA) and chosen ciphertext attack (CCA) is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol.
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First and Second Zagreb Eccentricity Indices of Thorny Graphs*Symmetry* **2017**, *9*(1), 7; doi:10.3390/sym9010007 - 6 January 2017**Abstract **

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let $H$ be a simple graph. The first Zagreb eccentricity index (${E}_{1}\left(H\right)$ ) is defined to be the summation of squares of the eccentricity of vertices,

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The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let $H$ be a simple graph. The first Zagreb eccentricity index (${E}_{1}\left(H\right)$ ) is defined to be the summation of squares of the eccentricity of vertices, i.e., ${E}_{1}\left(H\right)={\sum}_{u\in V\left(H\right)}{\mathsf{\u0190}}_{H}^{2}\left(u\right)$ . The second Zagreb eccentricity index (${E}_{2}\left(H\right)$ ) is the summation of product of the eccentricities of the adjacent vertices, i.e., ${E}_{2}\left(H\right)={\sum}_{uv\in E\left(H\right)}{\mathsf{\u0190}}_{H}\left(u\right){\mathsf{\u0190}}_{H}\left(v\right)$ . We obtain the thorny graph of a graph $H$ by attaching thorns i.e., vertices of degree one to every vertex of $H$ . In this paper, we will find closed formulation for the first Zagreb eccentricity index and second Zagreb eccentricity index of different well known classes of thorny graphs.
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Some Computational Aspects of Boron Triangular Nanotubes*Symmetry* **2017**, *9*(1), 6; doi:10.3390/sym9010006 - 1 January 2017**Abstract **

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The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M‐polynomial of nanotubes produces closed forms of many degree‐based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned

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The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M‐polynomial of nanotubes produces closed forms of many degree‐based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M‐polynomials of boron triangular nanotubes and recover many important topological degree‐based indices of these nanotubes. We also plot surfaces associated with these nanotubes that show the dependence of each topological index on the parameters of the structure.
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Some Algebraic Polynomials and Topological Indices of Generalized Prism and Toroidal Polyhex Networks*Symmetry* **2017**, *9*(1), 5; doi:10.3390/sym9010005 - 29 December 2016**Abstract **

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A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this report, we compute closed forms of first

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A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this report, we compute closed forms of first Zagreb, second Zagreb, and forgotten polynomials of generalized prism and toroidal polyhex networks. We also compute hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and forgotten index of these networks. Moreover we gave graphical representation of our results, showing the technical dependence of each topological index and polynomial on the involved structural parameters.
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Unmanned Aerial Vehicle Flight Point Classification Algorithm Based on Symmetric Big Data*Symmetry* **2017**, *9*(1), 1; doi:10.3390/sym9010001 - 24 December 2016**Abstract **

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Unmanned aerial vehicles (UAVs) with auto-pilot capabilities are often used for surveillance and patrol. Pilots set the flight points on a map in order to navigate to the imaging point where surveillance or patrolling is required. However, there is the limit denoting the

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Unmanned aerial vehicles (UAVs) with auto-pilot capabilities are often used for surveillance and patrol. Pilots set the flight points on a map in order to navigate to the imaging point where surveillance or patrolling is required. However, there is the limit denoting the information such as absolute altitudes and angles. Therefore, it is required to set the information accurately. This paper hereby proposes a method to construct environmental symmetric big data using an unmanned aerial vehicle (UAV) during flight by designating the imaging and non-imaging points for surveillance and patrols. The K-Means-based algorithm proposed in this paper is then employed to divide the imaging points, which is set by the pilot, into K clusters, and K imaging points are determined using these clusters. Flight data are then used to set the points to which the UAV will fly. In our experiment, flight records were gathered through an UAV in order to monitor a stadium and the imaging and non-imaging points were set using the proposed method and compared with the points determined by a traditional K-Means algorithm. Through the proposed method, the cluster centroids and cumulative distance of its members were reduced by 87.57% more than with the traditional K-Means algorithm. With the traditional K-Means algorithm, imaging points were not created in the five points desired by the pilot, and two incorrect points were obtained. However, with the proposed method, two incorrect imaging points were obtained. Due to these two incorrect imaging points, the two points desired by the pilot were not generated.
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Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain*Symmetry* **2017**, *9*(1), 2; doi:10.3390/sym9010002 - 24 December 2016**Abstract **

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Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent $z=1$ , none of the known variants of conformal invariance can act as its dynamical symmetry. In $d=1$ spatial dimensions, its infinite-dimensional dynamic symmetry is

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Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent $z=1$ , none of the known variants of conformal invariance can act as its dynamical symmetry. In $d=1$ spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.
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State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework*Symmetry* **2017**, *9*(1), 4; doi:10.3390/sym9010004 - 24 December 2016**Abstract **

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State of health (SOH) prediction in Li-ion batteries plays an important role in intelligent battery management systems (BMS). However, the existence of capacity regeneration phenomena remains a great challenge for accurately predicting the battery SOH. This paper proposes a novel prognostic framework to

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State of health (SOH) prediction in Li-ion batteries plays an important role in intelligent battery management systems (BMS). However, the existence of capacity regeneration phenomena remains a great challenge for accurately predicting the battery SOH. This paper proposes a novel prognostic framework to predict the regeneration phenomena of the current battery using the data of a historical battery. The global degradation trend and regeneration phenomena (characterized by regeneration amplitude and regeneration cycle number) of the current battery are extracted from its raw SOH time series. Moreover, regeneration information of the historical battery derived from corresponding raw SOH data is utilized in this framework. The global degradation trend and regeneration phenomena of the current battery are predicted, and then the prediction results are integrated together to calculate the overall SOH prediction values. Particle swarm optimization (PSO) is employed to obtain an appropriate regeneration threshold for the historical battery. Gaussian process (GP) model is adopted to predict the global degradation trend, and linear models are utilized to predict the regeneration amplitude and the cycle number of each regeneration region. The proposed framework is validated using experimental data from the degradation tests of Li-ion batteries. The results demonstrate that both the global degradation trend and the regeneration phenomena of the testing batteries can be well predicted. Moreover, compared with the published methods, more accurate SOH prediction results can be obtained under this framework.
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Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities*Symmetry* **2017**, *9*(1), 3; doi:10.3390/sym9010003 - 22 December 2016**Abstract **

Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classification of regular reduction operators is performed with respect to

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Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classification of regular reduction operators is performed with respect to generalized extended equivalence groups. Exact solutions of some nonlinear wave models, which are invariant under certain reduction operators, are also constructed.
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Accurate Dense Stereo Matching Based on Image Segmentation Using an Adaptive Multi-Cost Approach*Symmetry* **2016**, *8*(12), 159; doi:10.3390/sym8120159 - 21 December 2016**Abstract **

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This paper presents a segmentation-based stereo matching algorithm using an adaptive multi-cost approach, which is exploited for obtaining accuracy disparity maps. The main contribution is to integrate the appealing properties of multi-cost approach into the segmentation-based framework. Firstly, the reference image is segmented

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This paper presents a segmentation-based stereo matching algorithm using an adaptive multi-cost approach, which is exploited for obtaining accuracy disparity maps. The main contribution is to integrate the appealing properties of multi-cost approach into the segmentation-based framework. Firstly, the reference image is segmented by using the mean-shift algorithm. Secondly, the initial disparity of each segment is estimated by an adaptive multi-cost method, which consists of a novel multi-cost function and an adaptive support window cost aggregation strategy. The multi-cost function increases the robustness of the initial raw matching costs calculation and the adaptive window reduces the matching ambiguity effectively. Thirdly, an iterative outlier suppression and disparity plane parameters fitting algorithm is designed to estimate the disparity plane parameters. Lastly, an energy function is formulated in segment domain, and the optimal plane label is approximated by belief propagation. The experimental results with the Middlebury stereo datasets, along with synthesized and real-world stereo images, demonstrate the effectiveness of the proposed approach.
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The Method of Linear Determining Equations to Evolution System and Application for Reaction-Diffusion System with Power Diffusivities*Symmetry* **2016**, *8*(12), 157; doi:10.3390/sym8120157 - 20 December 2016**Abstract **

The method of linear determining equations is constructed to study conditional Lie–Bäcklund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for classical Lie symmetry. As an application of the approach, the

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The method of linear determining equations is constructed to study conditional Lie–Bäcklund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for classical Lie symmetry. As an application of the approach, the two-component reaction-diffusion system with power diffusivities is considered. The conditional Lie–Bäcklund symmetries and differential constraints admitted by the reaction-diffusion system are identified. Consequently, the reductions of the resulting system are established due to the compatibility of the corresponding invariant surface conditions and the original system.
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Noether Symmetries Quantization and Superintegrability of Biological Models*Symmetry* **2016**, *8*(12), 155; doi:10.3390/sym8120155 - 20 December 2016**Abstract **

It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that

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It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that was proposed by Basener and Ross (2005), and that describes the dynamics of growth and sudden decrease in the population of Easter Island.
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THD Reduction of Distribution System Based on ASRFC and HVC Method for SVC under EV Charger Condition for Power Factor Improvement*Symmetry* **2016**, *8*(12), 156; doi:10.3390/sym8120156 - 20 December 2016**Abstract **

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Electric vehicles (EVs) have been gaining popularity in recent years due to growing concerns about fuel depletion and increasing petrol prices. Random uncoordinated charging of multiple EVs at residential distribution feeders with moderate penetration levels is expected in the near future. This paper

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Electric vehicles (EVs) have been gaining popularity in recent years due to growing concerns about fuel depletion and increasing petrol prices. Random uncoordinated charging of multiple EVs at residential distribution feeders with moderate penetration levels is expected in the near future. This paper describes a high performance voltage controller for the EVs charging system, and proposes a scheme of asymmetric synchronous reference frame controller (ASRFC) in order to compensate for the voltage distortions and unbalance distribution system due to EVs charger. This paper explores the power factor of distribution and residential network under random EVs charger on the bus load. ASRFC and harmonic voltage compensator (HVC) are employed for static VAR compensator (SVC) in this paper. The proposed scheme can improve the power factor and total harmonic distortion (THD) of the smart grid due to the EVs charger in grid. The effectiveness of the scheme was investigated and verified through computer simulations of a 22.9-kV grid.
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Fluctuating Asymmetry of Human Populations: A Review*Symmetry* **2016**, *8*(12), 154; doi:10.3390/sym8120154 - 16 December 2016**Abstract **

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Fluctuating asymmetry, the random deviation from perfect symmetry, is a widely used population-level index of developmental instability, developmental noise, and robustness. It reflects a population’s state of adaptation and genomic coadaptation. Here, we review the literature on fluctuating asymmetry of human populations. The

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Fluctuating asymmetry, the random deviation from perfect symmetry, is a widely used population-level index of developmental instability, developmental noise, and robustness. It reflects a population’s state of adaptation and genomic coadaptation. Here, we review the literature on fluctuating asymmetry of human populations. The most widely used bilateral traits include skeletal, dental, and facial dimensions; dermatoglyphic patterns and ridge counts; and facial shape. Each trait has its advantages and disadvantages, but results are most robust when multiple traits are combined into a composite index of fluctuating asymmetry (CFA). Both environmental (diet, climate, toxins) and genetic (aneuploidy, heterozygosity, inbreeding) stressors have been linked to population-level variation in fluctuating asymmetry. In general, these stressors increase average fluctuating asymmetry. Nevertheless, there have been many conflicting results, in part because (1) fluctuating asymmetry is a weak signal in a sea of noise; and (2) studies of human fluctuating asymmetry have not always followed best practices. The most serious concerns are insensitive asymmetry indices (correlation coefficient and coefficient of indetermination), inappropriate size scaling, unrecognized mixture distributions, inappropriate corrections for directional asymmetry, failure to use composite indices, and inattention to measurement error. Consequently, it is often difficult (or impossible) to compare results across traits, and across studies.
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A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method*Symmetry* **2016**, *8*(12), 153; doi:10.3390/sym8120153 - 14 December 2016**Abstract **

Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element

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Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modified ranking method is presented. In comparison with the HFS lexicographical ordering method, the modified ranking method is more reasonable in more general cases.
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Continuous Learning Graphical Knowledge Unit for Cluster Identification in High Density Data Sets*Symmetry* **2016**, *8*(12), 152; doi:10.3390/sym8120152 - 14 December 2016**Abstract **

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Big data are visually cluttered by overlapping data points. Rather than removing, reducing or reformulating overlap, we propose a simple, effective and powerful technique for density cluster generation and visualization, where point marker (graphical symbol of a data point) overlap is exploited in

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Big data are visually cluttered by overlapping data points. Rather than removing, reducing or reformulating overlap, we propose a simple, effective and powerful technique for density cluster generation and visualization, where point marker (graphical symbol of a data point) overlap is exploited in an additive fashion in order to obtain bitmap data summaries in which clusters can be identified visually, aided by automatically generated contour lines. In the proposed method, the plotting area is a bitmap and the marker is a shape of more than one pixel. As the markers overlap, the red, green and blue (RGB) colour values of pixels in the shared region are added. Thus, a pixel of a 24-bit RGB bitmap can code up to 2^{24} (over 1.6 million) overlaps. A higher number of overlaps at the same location makes the colour of this area identical, which can be identified by the naked eye. A bitmap is a matrix of colour values that can be represented as integers. The proposed method updates this matrix while adding new points. Thus, this matrix can be considered as an up-to-time knowledge unit of processed data. Results show cluster generation, cluster identification, missing and out-of-range data visualization, and outlier detection capability of the newly proposed method.
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An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks*Symmetry* **2016**, *8*(12), 151; doi:10.3390/sym8120151 - 10 December 2016**Abstract **

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Heterogeneous networks (HetNets) give users the opportunity to access different access points(APs), which will simultaneously affect user performance and system performance, so user association in HetNets plays a critical role in enhancing the load balancing and the system sum-throughput of networks. Meanwhile, the

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Heterogeneous networks (HetNets) give users the opportunity to access different access points(APs), which will simultaneously affect user performance and system performance, so user association in HetNets plays a critical role in enhancing the load balancing and the system sum-throughput of networks. Meanwhile, the incremental sum-throughput currently fails to meet the escalating data demands. Besides, ensuring fairness amongst users constitutes another urgent issue in the radio resource management (RRM) of HetNets. What is more, few works consider the maximum service user number constraint in femtocell access points (FAPs). To solve the aforementioned problem, this paper associates users to APs by considering system sum-throughput and fairness at the same time in HetNets under a maximum service user number constraint of FAPs; accordingly, the user association problem is formulated. By releasing constraint, the optimal user association algorithm is obtained by Lagrangian function, and based on this optimal solution, a low complexity suboptimal user association algorithm is proposed. At last, this paper investigates the relationship between system sum-throughput and maximum service user number of FAPs. Numerical simulation results show that the proposed algorithm can improve sum-throughput and fairness at the same time at a specific maximum service user number of FAPs.
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Morphometric Asymmetry of Frustule Outlines in the Pennate Diatom *Luticola poulickovae* (Bacillariophyceae)*Symmetry* **2016**, *8*(12), 150; doi:10.3390/sym8120150 - 7 December 2016**Abstract **

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Side orientation of cells is usually ambiguous in unicellular organisms, making it impossible to separate components of directional asymmetry (DA) and fluctuating asymmetry (FA). However, frustules of the diatom *Luticola poulickovae* have biradially symmetric outlines, and their central areas bear ornamentation that is

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Side orientation of cells is usually ambiguous in unicellular organisms, making it impossible to separate components of directional asymmetry (DA) and fluctuating asymmetry (FA). However, frustules of the diatom *Luticola poulickovae* have biradially symmetric outlines, and their central areas bear ornamentation that is asymmetric across the apical axis. The goal of this study was to explore differentiation of morphometric asymmetry across the apical axis into DA and FA components. Is there detectable DA of the valve outlines of two *L. poulickovae* strains that may be related to the asymmetric central areas? Given that the life cycle of diatoms involves cell-size diminution, and cell shape is strongly affected by allometry, we also explored the question of whether asymmetry is correlated with cell size. The extent of symmetric variation among individuals in each strain, as well as DA and FA across the apical axis, were quantified using two Procrustes ANOVA models. The results revealed no correlation of either total asymmetry or FA with valve size. DA was significant and considerably more pronounced than FA in both strains, indicating that there is previously unknown systematic asymmetry of valve outlines of *L. poulickovae*, which may be related to the asymmetry of its central area.
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