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Symmetry, Volume 9, Issue 1 (January 2017)

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Research

Open AccessArticle First and Second Zagreb Eccentricity Indices of Thorny Graphs
Symmetry 2017, 9(1), 7; doi:10.3390/sym9010007
Received: 21 November 2016 / Revised: 22 December 2016 / Accepted: 22 December 2016 / Published: 6 January 2017
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Abstract
The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E1(H)) 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 ( H ) ) is defined to be the summation of squares of the eccentricity of vertices, i.e., E 1 ( H ) = u V ( H ) Ɛ H 2 ( u ) . The second Zagreb eccentricity index ( E 2 ( H ) ) is the summation of product of the eccentricities of the adjacent vertices, i.e., E 2 ( H ) = u v E ( H ) Ɛ H ( u ) Ɛ H ( v ) . 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. Full article
(This article belongs to the Special Issue Symmetry in Complex Networks II)
Open AccessArticle Unmanned Aerial Vehicle Flight Point Classification Algorithm Based on Symmetric Big Data
Symmetry 2017, 9(1), 1; doi:10.3390/sym9010001
Received: 27 September 2016 / Revised: 8 December 2016 / Accepted: 14 December 2016 / Published: 24 December 2016
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Abstract
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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Scientific Programming in Practical Symmetric Big Data)
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Open AccessArticle Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain
Symmetry 2017, 9(1), 2; doi:10.3390/sym9010002
Received: 16 October 2016 / Revised: 18 November 2016 / Accepted: 14 December 2016 / Published: 24 December 2016
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Abstract
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. Full article
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Open AccessArticle 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
Received: 31 October 2016 / Revised: 17 December 2016 / Accepted: 21 December 2016 / Published: 24 December 2016
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Abstract
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. Full article
(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)
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Open AccessArticle Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities
Symmetry 2017, 9(1), 3; doi:10.3390/sym9010003
Received: 13 October 2016 / Revised: 13 December 2016 / Accepted: 14 December 2016 / Published: 22 December 2016
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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. Full article
Open AccessArticle Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security
Symmetry 2017, 9(1), 9; doi:10.3390/sym9010009
Received: 23 September 2016 / Revised: 2 December 2016 / Accepted: 28 December 2016 / Published: 7 January 2017
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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. Full article
(This article belongs to the Special Issue Symmetry in Secure Cyber World)
Open AccessArticle Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components
Symmetry 2017, 9(1), 10; doi:10.3390/sym9010010
Received: 5 December 2016 / Revised: 4 January 2017 / Accepted: 6 January 2017 / Published: 13 January 2017
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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 < α 1 . Full article
Open AccessArticle DIaaS: Resource Management System for the Intra-Cloud with On-Premise Desktops
Symmetry 2017, 9(1), 8; doi:10.3390/sym9010008
Received: 24 November 2016 / Revised: 26 December 2016 / Accepted: 4 January 2017 / Published: 9 January 2017
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Abstract
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
[...] Read more.
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). Full article
(This article belongs to the Special Issue Scientific Programming in Practical Symmetric Big Data)
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Open AccessArticle Some Algebraic Polynomials and Topological Indices of Generalized Prism and Toroidal Polyhex Networks
Symmetry 2017, 9(1), 5; doi:10.3390/sym9010005
Received: 1 December 2016 / Revised: 16 December 2016 / Accepted: 20 December 2016 / Published: 29 December 2016
Cited by 2 | PDF Full-text (4501 KB) | HTML Full-text | XML Full-text
Abstract
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. Full article
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Open AccessArticle Some Computational Aspects of Boron Triangular Nanotubes
Symmetry 2017, 9(1), 6; doi:10.3390/sym9010006
Received: 4 November 2016 / Accepted: 28 December 2016 / Published: 1 January 2017
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Abstract
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. Full article
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Open AccessArticle Prognosis Essay Scoring and Article Relevancy Using Multi-Text Features and Machine Learning
Symmetry 2017, 9(1), 11; doi:10.3390/sym9010011
Received: 17 September 2016 / Revised: 3 January 2017 / Accepted: 6 January 2017 / Published: 12 January 2017
Cited by 1 | PDF Full-text (683 KB) | HTML Full-text | XML Full-text
Abstract
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. Full article
(This article belongs to the Special Issue Symmetry in Cooperative Applications II)
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Open AccessArticle Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets
Symmetry 2017, 9(1), 12; doi:10.3390/sym9010012
Received: 29 September 2016 / Revised: 9 January 2017 / Accepted: 13 January 2017 / Published: 21 January 2017
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Abstract
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. Full article
(This article belongs to the Special Issue Scientific Programming in Practical Symmetric Big Data)
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Open AccessFeature PaperArticle A (1 + 2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II
Symmetry 2017, 9(1), 13; doi:10.3390/sym9010013
Received: 31 October 2016 / Revised: 27 December 2016 / Accepted: 10 January 2017 / Published: 20 January 2017
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Abstract
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. Full article
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Open AccessArticle Generalized Null 2-Type Surfaces in Minkowski 3-Space
Symmetry 2017, 9(1), 14; doi:10.3390/sym9010014
Received: 3 December 2016 / Revised: 16 January 2017 / Accepted: 16 January 2017 / Published: 20 January 2017
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Abstract
For the mean curvature vector field H and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition ΔH=fH+gC is known as a generalized null 2-type, where f and g
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For the mean curvature vector field H and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition Δ H = f H + g C is known as a generalized null 2-type, where f and g are smooth functions, and 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 L 3 and classify generalized null 2-type flat surfaces. In addition, we show that the only generalized null 2-type null scroll in L 3 is a B-scroll. Full article
Open AccessArticle An Orthogonal Multi-Swarm Cooperative PSO Algorithm with a Particle Trajectory Knowledge Base
Symmetry 2017, 9(1), 15; doi:10.3390/sym9010015
Received: 18 November 2016 / Revised: 30 December 2016 / Accepted: 13 January 2017 / Published: 20 January 2017
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Abstract
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
[...] Read more.
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. Full article
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Open AccessArticle Data-Filtering System to Avoid Total Data Distortion in IoT Networking
Symmetry 2017, 9(1), 16; doi:10.3390/sym9010016
Received: 30 September 2016 / Revised: 25 December 2016 / Accepted: 16 January 2017 / Published: 20 January 2017
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Abstract
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. Full article
(This article belongs to the Special Issue Symmetry in Secure Cyber World)
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Open AccessArticle Some Invariants of Jahangir Graphs
Symmetry 2017, 9(1), 17; doi:10.3390/sym9010017
Received: 16 December 2016 / Revised: 16 January 2017 / Accepted: 17 January 2017 / Published: 23 January 2017
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Abstract
In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as
[...] Read more.
In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,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. Full article
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Open AccessArticle Fully Integrated on-Chip Switched DC–DC Converter for Battery-Powered Mixed-Signal SoCs
Symmetry 2017, 9(1), 18; doi:10.3390/sym9010018
Received: 6 November 2016 / Revised: 27 December 2016 / Accepted: 10 January 2017 / Published: 22 January 2017
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Abstract
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
[...] Read more.
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 (VL_dw) from the 2-to-1_dw, and low swing level-shifted gate-driving signals are generated using the internal load voltage (VL_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 (IL = 15 mA at VL_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. Full article
(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)
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