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Symmetry
Volume 9
Issue 12
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Symmetry, Volume 9, Issue 12 (December 2017) – 36 articles

Cover Story (view full-size image): The theory of knotoids can be regarded as a refinement of classical knot theory. Knotoids provide a natural topological domain for studying the knotting of physical structures involving open-ended curves, for example, polymers. In analogy, braidoids extend the classical braids and they form a counterpart theory to the theory of knotoids. Any braidoid gives rise to a knotoid via the closure map and any knotoid can be turned into a braidoid whose closure is topologically equivalent to the starting knotoid. Braidoids can be used for encoding the topological information of knotoids in terms of algebraic expressions. View this paper
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3711 KiB  
Article
A Design for Genetically Oriented Rules-Based Incremental Granular Models and Its Application
by Yeong-Hyeon Byeon and Keun-Chang Kwak
Symmetry 2017, 9(12), 324; https://doi.org/10.3390/sym9120324 - 20 Dec 2017
Cited by 3 | Viewed by 3402
Abstract
In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The [...] Read more.
In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The IGM has been successfully applied to various examples. However, the disadvantage of IGM is that the number of clusters in each context is determined, with the same number, by trial and error. Moreover, a weighting exponent is set to the typical value. In order to solve these problems, the goal of this paper is to design an optimized rule-based IGM with the use of a Genetic Algorithm (GA) to simultaneously optimize the number of cluster centers in each context, the number of contexts, and the weighting exponent. The experimental results regarding a coagulant dosing process in a water purification plant, an automobile mpg (miles per gallon) prediction, and a Boston housing data set revealed that the proposed GA-based IGM showed good performance, when compared with the Radial Basis Function Neural Network (RBFNN), LM, Takagi–Sugeno–Kang (TSK)-Linguistic Fuzzy Model (LFM), GA-based LM, and IGM itself. Full article
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<p>Clusters generated by context-free and context-based clustering: (<b>a</b>) context-free clustering; (<b>b</b>) context-based clustering.</p> Full article ">Figure 2
<p>Generation of contexts by statistical distribution of data: (<b>a</b>) histogram; (<b>b</b>) probability density function; (<b>c</b>) conditional density function; (<b>d</b>) contexts.</p> Full article ">Figure 2 Cont.
<p>Generation of contexts by statistical distribution of data: (<b>a</b>) histogram; (<b>b</b>) probability density function; (<b>c</b>) conditional density function; (<b>d</b>) contexts.</p> Full article ">Figure 3
<p>Distribution of data and cluster centers corresponding to the <span class="html-italic">t</span>th context <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">W</mi> <mi mathvariant="normal">t</mi> </msub> </mrow> </semantics> </math>.</p> Full article ">Figure 4
<p>Detailed view of the case of three contexts and two clusters per context.</p> Full article ">Figure 5
<p>Architecture of local Linguistic Model (LM).</p> Full article ">Figure 6
<p>Actual error <math display="inline"> <semantics> <mrow> <msubsup> <mi>e</mi> <mi>k</mi> <mrow/> </msubsup> </mrow> </semantics> </math> and the predicted fuzzy number <math display="inline"> <semantics> <mrow> <mrow> <mo>〈</mo> <mrow> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>k</mi> <mo>−</mo> </mrow> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>k</mi> </msub> <mo>,</mo> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>k</mi> <mo>+</mo> </mrow> </msub> </mrow> <mo>〉</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 7
<p>Architecture of the Incremental Granular Model (IGM). CFCM: Context-based Fuzzy C-Means.</p> Full article ">Figure 8
<p>Representation of encoding scheme (<span class="html-italic">p =</span> 6).</p> Full article ">Figure 9
<p>Producing the next generation in the design of the Genetic Algorithms (GA)-based IGM.</p> Full article ">Figure 10
<p>Contexts generated from the output space (<span class="html-italic">x</span>-axis: error). (<b>a</b>) <span class="html-italic">p =</span> 5; (<b>b</b>) <span class="html-italic">p =</span> 6; (<b>c</b>) <span class="html-italic">p =</span> 7; (<b>d</b>) <span class="html-italic">p =</span> 8.</p> Full article ">Figure 11
<p>Distribution of data and cluster center corresponding to six contexts (<span class="html-italic">x</span>-axis: <math display="inline"> <semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>x</mi> </mstyle> <mrow> <mi>k</mi> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics> </math> <span class="html-italic">y</span>-axis: <math display="inline"> <semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>x</mi> </mstyle> <mrow> <mi>k</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics> </math>).</p> Full article ">Figure 12
<p>Variation of fitness values by generation.</p> Full article ">Figure 13
<p>Approximation capability for training data.</p> Full article ">Figure 14
<p>Generalization capability for testing data.</p> Full article ">Figure 15
<p>Output of the GA-based IGM with interval prediction.</p> Full article ">Figure 16
<p>Error values predicted by IGM as a local granular model.</p> Full article ">
251 KiB  
Article
Boundary Value Problems for Some Important Classes of Recurrent Relations with Two Independent Variables
by Stevo Stević, Bratislav Iričanin and Zdeněk Šmarda
Symmetry 2017, 9(12), 323; https://doi.org/10.3390/sym9120323 - 20 Dec 2017
Cited by 3 | Viewed by 3193
Abstract
It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: [...] Read more.
It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = { ( n , k ) : 0 ? k ? n , k ? N 0 , n ? N } , the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
5843 KiB  
Article
Graph Cellular Automata with Relation-Based Neighbourhoods of Cells for Complex Systems Modelling: A Case of Traffic Simulation
by Krzysztof Małecki
Symmetry 2017, 9(12), 322; https://doi.org/10.3390/sym9120322 - 19 Dec 2017
Cited by 31 | Viewed by 7321
Abstract
A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to [...] Read more.
A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA). The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks) taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process. Full article
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<p>Changing the graph structure: (<b>a</b>) exemplary graph; (<b>b</b>) after vertex removal; (<b>c</b>) after edge removal; (<b>d</b>) after vertex addition; (<b>e</b>) after edge addition.</p> Full article ">Figure 2
<p>An example of a graph describing the relational neighbourhood of objects in a modeled system. The vertices of the graph correspond to the cells of cellular automata (CA).</p> Full article ">Figure 3
<p>Objects and corresponding relations mapped to cells of r–GCA: (<b>a</b>) relation based neighbourhood graph and (<b>b</b>) corresponding activity matrix of CA cells (1: activated cell, 0: deactivated cell).</p> Full article ">Figure 4
<p>Graph and neighbourhood matrix.</p> Full article ">Figure 5
<p>A fragment of a two-way road with sample vehicles.</p> Full article ">Figure 6
<p>A graph made as per the situation in <a href="#symmetry-09-00322-f005" class="html-fig">Figure 5</a>.</p> Full article ">Figure 7
<p>Neighbourhood matrix—<math display="inline"> <semantics> <mrow> <mstyle mathvariant="bold" mathsize="normal"> <mi>A</mi> </mstyle> <mrow> <mo>(</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>G</mi> </mstyle> <mo>)</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 8
<p>Matrix of weights—<math display="inline"> <semantics> <mrow> <mstyle mathvariant="bold" mathsize="normal"> <mi>W</mi> </mstyle> <mrow> <mo>(</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>G</mi> </mstyle> <mo>)</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 9
<p>Overtaking stage—the analysis of weights.</p> Full article ">Figure 10
<p>Constituents of the operation time of a single iteration in the simulation process.</p> Full article ">Figure 11
<p>Comparison of mean minimum speeds of moving vehicles.</p> Full article ">Figure 12
<p>Comparison of mean maximum speeds of moving vehicles.</p> Full article ">Figure 13
<p>Comparing the total simulation time.</p> Full article ">Figure 14
<p>A map of the analysed road.</p> Full article ">Figure 15
<p>Average number of vehicles for different speed limits.</p> Full article ">Figure 16
<p>Types of neighbourhoods in a graph cellular automaton (relation-based graph cellular automation (r–GCA)): analogous to Moore’s (<b>a</b>) or von Neumann’s neighbourhood (<b>b</b>) in a classical CA; in r–GCA independent from the distance in the d-dimensional space of the cells (<b>c</b>,<b>d</b>).</p> Full article ">
7571 KiB  
Article
A Novel String Grammar Unsupervised Possibilistic C-Medians Algorithm for Sign Language Translation Systems
by Atcharin Klomsae, Sansanee Auephanwiriyakul and Nipon Theera-Umpon
Symmetry 2017, 9(12), 321; https://doi.org/10.3390/sym9120321 - 19 Dec 2017
Cited by 8 | Viewed by 5138
Abstract
Sign language is a basic method for solving communication problems between deaf and hearing people. In order to communicate, deaf and hearing people normally use hand gestures, which include a combination of hand positioning, hand shapes, and hand movements. Thai Sign Language is [...] Read more.
Sign language is a basic method for solving communication problems between deaf and hearing people. In order to communicate, deaf and hearing people normally use hand gestures, which include a combination of hand positioning, hand shapes, and hand movements. Thai Sign Language is the communication method for Thai hearing-impaired people. Our objective is to improve the dynamic Thai Sign Language translation method with a video captioning technique that does not require prior hand region detection and segmentation through using the Scale Invariant Feature Transform (SIFT) method and the String Grammar Unsupervised Possibilistic C-Medians (sgUPCMed) algorithm. This work is the first to propose the sgUPCMed algorithm to cope with the unsupervised generation of multiple prototypes in the possibilistic sense for string data. In our experiments, the Thai Sign Language data set (10 isolated sign language words) was collected from 25 subjects. The best average result within the constrained environment of the blind test data sets of signer-dependent cases was 89–91%, and the successful rate of signer semi-independent cases was 81–85%, on average. For the blind test data sets of signer-independent cases, the best average classification rate was 77–80%. The average result of the system without a constrained environment was around 62–80% for the signer-independent experiments. To show that the proposed algorithm can be implemented in other sign languages, the American sign language (RWTH-BOSTON-50) data set, which consists of 31 isolated American Sign Language words, is also used in the experiment. The system provides 88.56% and 91.35% results on the validation set alone, and for both the training and validation sets, respectively. Full article
(This article belongs to the Special Issue Emerging Approaches and Advances in Big Data)
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<p>System overview of Thai sign language translation. FKNN: fuzzy k-nearest neighbour.</p> Full article ">Figure 2
<p>Examples of 31 hand gestures.</p> Full article ">Figure 3
<p>Keypoint descriptor generation (<b>a</b>) keypoints found on a keyframe; keypoint descriptors found on hand gestures (<b>b</b>) “f”, (<b>c</b>) “l”, and (<b>d</b>) “d1”; and the hand gesture (<b>e</b>) “b” assigned to a test image using the SIFT method and test images within a constraint environment, (<b>f</b>) “e” assigned to a test image using the SIFT method and test frames without a constraint environment, and (<b>g</b>) “nh” assigned to a test image using the SIFT method and test frames without a constraint environment.</p> Full article ">Figure 4
<p><span class="html-italic">Avg_Match</span> of symbol. The matched symbol is “b”: (<b>a</b>) hand gestures “b”; (<b>b</b>) Graph of <span class="html-italic">Avg_Match</span> of symbol.</p> Full article ">Figure 5
<p>(<b>a</b>) The best and (<b>b</b>) average ± standard deviation classification rate (%) of the validation set from four-fold cross-validation when trained with data set 1a for FKNN with <span class="html-italic">K</span> = 1, 3, 5, 7, and 9.</p> Full article ">Figure 6
<p>(<b>a</b>) The best and (<b>b</b>) average ± standard deviation classification rate (%) of the validation set from four-fold cross-validation when trained with data set 1a–5a for FKNN with <span class="html-italic">K</span> = 1, 3, 5, 7, and 9.</p> Full article ">Figure 7
<p>(<b>a</b>) The best and (<b>b</b>) average ± standard deviation classification rate (%) of the validation set from four-fold cross-validation when trained with data set 1a–15a for FKNN with <span class="html-italic">K</span> = 1, 3, 5, 7, and 9.</p> Full article ">Figure 8
<p>Classification rate on test sets when trained with data set 1a.</p> Full article ">Figure 9
<p>Classification rate on test sets when trained with data set 1a–5a.</p> Full article ">Figure 10
<p>Classification rate on test sets when trained with data set 1a–15a.</p> Full article ">Figure 11
<p>Classification rate on test sets when trained with data set 1a–15a, and tested with unseen signers against various complex natural backgrounds.</p> Full article ">Figure 12
<p>Example of 81 hand gestures for the RWTH-BOSTON-50 data set.</p> Full article ">Figure 12 Cont.
<p>Example of 81 hand gestures for the RWTH-BOSTON-50 data set.</p> Full article ">Figure 13
<p>Representative frames (Rframes) of Thai sign language words (<b>a</b>) “Grandmother” and (<b>b</b>) “Grandfather”.</p> Full article ">Figure 14
<p>All frames of RWTH-BOSTON-50 word (<b>a</b>) “GO” and (<b>b</b>) “SHOULD”.</p> Full article ">Figure 15
<p>The hand part of similar keyframes (<b>a</b>) “g”, (<b>b</b>) “g2”, and (<b>c</b>) “k” in Thai Sign Language.</p> Full article ">Figure 16
<p>The hand part of similar keyframes (<b>a</b>) “t”, (<b>b</b>) “t1”, (<b>c</b>) “v”, and (<b>d</b>) “v3” in RWTH-BOSTON-50.</p> Full article ">
291 KiB  
Article
Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making
by Agbodah Kobina, Decui Liang and Xin He
Symmetry 2017, 9(12), 320; https://doi.org/10.3390/sym9120320 - 19 Dec 2017
Cited by 68 | Viewed by 4806
Abstract
As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) [...] Read more.
As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
386 KiB  
Article
New Applications of m-Polar Fuzzy Matroids
by Musavarah Sarwar and Muhammad Akram
Symmetry 2017, 9(12), 319; https://doi.org/10.3390/sym9120319 - 18 Dec 2017
Cited by 27 | Viewed by 4611
Abstract
Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when [...] Read more.
Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
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<p>3-polar fuzzy multigraph.</p> Full article ">Figure 2
<p>Wireless communication.</p> Full article ">Figure 3
<p>Communication network with minimum connections.</p> Full article ">
279 KiB  
Article
Algebraic Aspects of the Supersymmetric Minimal Surface Equation
by Alfred Michel Grundland and Alexander Hariton
Symmetry 2017, 9(12), 318; https://doi.org/10.3390/sym9120318 - 18 Dec 2017
Cited by 5 | Viewed by 2827
Abstract
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 [...] Read more.
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version. Full article
4600 KiB  
Article
Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory
by Karolina Taczanowska, Mikołaj Bielański, Luis-Millán González, Xavier Garcia-Massó and José L. Toca-Herrera
Symmetry 2017, 9(12), 317; https://doi.org/10.3390/sym9120317 - 14 Dec 2017
Cited by 26 | Viewed by 6602
Abstract
Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an [...] Read more.
Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS) tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers) collected in Tatra National Park (TNP), Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph). In a second step, the actual use of the area by skiers (functional network; directed graph) was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: ?, ?, ?), movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige) were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure. Full article
(This article belongs to the Special Issue Graph Theory)
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<p>Characteristics of the study area: designated backcountry skiing zones within the border of Tatra National Park (TNP), Poland.</p> Full article ">Figure 2
<p>Translation of the designated backcountry skiing areas system into a structural network (undirected graph). The geographic coordinates (longitude and latitude) were defined in WGS84 spatial reference system and are expressed in decimal degrees.</p> Full article ">Figure 3
<p>Three-dimensional visualization of the structural skiing network (undirected graph). The geographic coordinates (longitude and latitude) were defined in WGS84 spatial reference system and are expressed in decimal degrees. Altitude is expressed in meters above sea level (m.a.s.l.). The elevation data was used only for visualization purposes.</p> Full article ">Figure 4
<p>Example of a skiing route. (<b>a</b>) Recorded GPS track of a TNP visitor; (<b>b</b>) representation of the corresponding directed graph G = (V,E) where the vertices are V = {44,…,66} and the edges are E = {(50, 49), (49, 51), (51, 59), (59,62), (62, 61), (61, 66), (66, 61), (61,54), (54, 53), (53, 58), (58, 60), (60, 54), (54, 48), (48, 44), (44, 45), (45, 49), (49, 50)}. In the final graph the loop, (66, 66) was deleted, since a property of directed graphs is vi ≠ vj.</p> Full article ">Figure 5
<p>Structural network (undirected graph) depicting the designated backcountry skiing system in TNP. The network is composed of 93 nodes and 133 links.</p> Full article ">Figure 6
<p>Functional network (directed graph) of the designated backcountry skiing system; graph based on the recorded visitors’ trip itineraries. Arrows indicate movement direction; color scale (grey scale) illustrates the intensity of skiing traffic. A darker color means higher use intensity.</p> Full article ">Figure 7
<p>Node centrality measures in the structural (<b>a</b>) and functional networks (<b>b</b>) of designated backcountry skiing zones in TNP.</p> Full article ">
17433 KiB  
Article
Tangible Visualization Table for Intuitive Data Display
by Jongyong Kim, Cheongun Lee, Seung-Hyun Yoon and Sanghun Park
Symmetry 2017, 9(12), 316; https://doi.org/10.3390/sym9120316 - 13 Dec 2017
Viewed by 4970
Abstract
We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture [...] Read more.
We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture image is projected onto the shape display. To minimize projection distortions, we present a sophisticated technique for projection mapping. Gesture-based user interfaces facilitate intuitive manipulations of visualization results. We demonstrate the effectiveness of our system by displaying and manipulating various terrain data using gesture-based interfaces. Full article
(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)
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<p>Tangible visualization table: (<b>a</b>) a projector and a Kinect on the upper part; (<b>b</b>) actuator array on the lower part; (<b>c</b>) tangible visualization of terrain data.</p> Full article ">Figure 2
<p>Structure of the tangible visualization system.</p> Full article ">Figure 3
<p>Hardware devices in the lower part of the system: (<b>a</b>) Arduino Due; (<b>b</b>) actuator driver; (<b>c</b>) actuator and (<b>d</b>) LED.</p> Full article ">Figure 4
<p>Hardware devices in the upper part of the system: (<b>a</b>) projector and (<b>b</b>) Kinect V2.</p> Full article ">Figure 5
<p>Software structure of the tangible visualization table.</p> Full article ">Figure 6
<p>Internal structure of Arduino.</p> Full article ">Figure 7
<p>Coordinate mapping: (<b>a</b>) corner points of the RGB camera; (<b>b</b>) corner points of the infrared camera.</p> Full article ">Figure 8
<p>Projected texture: (<b>a</b>) raw texture image; (<b>b</b>) deformed texture image using extrinsic parameters.</p> Full article ">Figure 9
<p>Projection results after texture modification: (<b>a</b>) projected texture image; (<b>b</b>) raw texture image.</p> Full article ">Figure 10
<p>Texture interpolation: (<b>a</b>) deformed texture including noise before interpolation; (<b>b</b>) interpolated texture using the box filter.</p> Full article ">Figure 11
<p>Conceptual gesture interface diagram.</p> Full article ">Figure 12
<p>Comparison of hand recognition: (<b>a</b>) RGB camera; (<b>b</b>) infrared camera; (<b>c</b>) depth camera.</p> Full article ">Figure 13
<p>Gesture recognition: (<b>a</b>) shape definition for palm recognition; (<b>b</b>) gesture interface flowchart.</p> Full article ">Figure 14
<p>Recognition results of input gestures: (<b>a</b>) Open Palm; (<b>b</b>) Close Palm; (<b>c</b>) Ok Sign; (<b>d</b>) Pointing.</p> Full article ">Figure 15
<p>User interface selection flowchart.</p> Full article ">Figure 16
<p>Gesture to open the menu: (<b>a</b>) start of menu opening; (<b>b</b>) menu opening in progress.</p> Full article ">Figure 17
<p>Menu selection: (<b>a</b>) menu selection on standby; (<b>b</b>) data request menu selection; (<b>c</b>) data transformation menu selection; (<b>d</b>) program termination menu selection.</p> Full article ">Figure 18
<p>Graphical illustration of menu selection.</p> Full article ">Figure 19
<p>Data selection: (<b>a</b>) Map Selection 1; (<b>b</b>) Map Selection 2.</p> Full article ">Figure 20
<p>Terrain data manipulation process (1): (<b>a</b>) image of translating terrain data; (<b>b</b>) applied image after translating data.</p> Full article ">Figure 21
<p>Terrain data manipulation process (2): (<b>a</b>) before zooming in; (<b>b</b>) after zooming in.</p> Full article ">Figure 22
<p>Texture data: (<b>a</b>) Jeju island; (<b>b</b>) Seogwipo.</p> Full article ">Figure 23
<p>Projection mapping time in milliseconds.</p> Full article ">Figure 24
<p>Comparison of visualization results between the tangible visualization table and the mobile client: (<b>a</b>) tangible visualization table; (<b>b</b>) monitor display.</p> Full article ">Figure 24 Cont.
<p>Comparison of visualization results between the tangible visualization table and the mobile client: (<b>a</b>) tangible visualization table; (<b>b</b>) monitor display.</p> Full article ">Figure 25
<p>Example of target area in the given task.</p> Full article ">Figure 26
<p>Feedback from users.</p> Full article ">
831 KiB  
Article
Knotoids, Braidoids and Applications
by Neslihan Gügümcü and Sofia Lambropoulou
Symmetry 2017, 9(12), 315; https://doi.org/10.3390/sym9120315 - 12 Dec 2017
Cited by 20 | Viewed by 4589
Abstract
This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to [...] Read more.
This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to the study of proteins. Full article
(This article belongs to the Special Issue Knot Theory and Its Applications)
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Figure 1
<p>The symmetries of the braidoiding moves and the <span class="html-italic">L</span>-moves.</p> Full article ">Figure 2
<p>Examples of knotoid diagrams: (<b>a</b>) trivial knotoid; (<b>b</b>) a non-trivial planar knotoid that is trivial as spherical; (<b>c</b>,<b>d</b>) two proper knotoids; (<b>e</b>) a knot-type knotoid.</p> Full article ">Figure 3
<p>The moves generating isotopy on knotoid diagrams.</p> Full article ">Figure 4
<p>Forbidden knotoid moves.</p> Full article ">Figure 5
<p>The overpass and the underpass closures of a knotoid diagram resulting in different knots.</p> Full article ">Figure 6
<p>Projections of an open space curve as a knotoid diagram.</p> Full article ">Figure 7
<p>Some examples of braidoid diagrams: (<b>a</b>) a braidoid diagram with one free strand; (<b>b</b>–<b>e</b>) braidoid diagrams with two free strands.</p> Full article ">Figure 8
<p>A <math display="inline"> <semantics> <mo>Δ</mo> </semantics> </math>-move on a braidoid diagram.</p> Full article ">Figure 9
<p>Forbidden braidoid moves involving the head.</p> Full article ">Figure 10
<p>A vertical move on <span class="html-italic">h</span>.</p> Full article ">Figure 11
<p>Swing moves.</p> Full article ">Figure 12
<p>The closure of an abstract labeled braidoid diagram.</p> Full article ">Figure 13
<p>Non-isotopic closures in the presence of endpoint alignment.</p> Full article ">Figure 14
<p>An example of non-equivalent labeled closures.</p> Full article ">Figure 15
<p>The braidoiding move and its closure.</p> Full article ">Figure 16
<p>Subdivision of an up-arc.</p> Full article ">Figure 17
<p>Subdivision is a combination of <math display="inline"> <semantics> <mo>Δ</mo> </semantics> </math>-moves.</p> Full article ">Figure 18
<p>The sliding triangles of the up-arc <math display="inline"> <semantics> <mrow> <mi>Q</mi> <mi>P</mi> </mrow> </semantics> </math>.</p> Full article ">Figure 19
<p>A sliding triangle violating the endpoint condition and further subdivision of the up-arc.</p> Full article ">Figure 20
<p>Arranging a crossing with a full twist.</p> Full article ">Figure 21
<p>Arranging a crossing with a half twist.</p> Full article ">Figure 22
<p>The braidoiding move on up-arcs containing an endpoint.</p> Full article ">Figure 23
<p>Applying the braidoiding algorithm.</p> Full article ">Figure 24
<p>After closure an <span class="html-italic">L</span>-move contracts to the braidoid arc on which it is applied.</p> Full article ">Figure 25
<p>The two cases of the underpass connection.</p> Full article ">Figure 26
<p>The choice of the arc connecting the endpoints does not affect the resulting braid up to <span class="html-italic">L</span>-equivalence.</p> Full article ">Figure 27
<p>(<b>a</b>–<b>e</b>): Filling the braidoid diagrams of <a href="#symmetry-09-00315-f007" class="html-fig">Figure 7</a> with implicit points.</p> Full article ">Figure 28
<p>Elementary blocks for braidoids.</p> Full article ">Figure 29
<p>Multiplication of four blocks containing endpoints and implicit points.</p> Full article ">Figure 30
<p>The configuration of the backbone of the protein 3KZN in 3D and its simplified configuration.</p> Full article ">Figure 31
<p>The knotoid of the protein 3KZN and a corresponding braidoid diagram with algebraic expression <math display="inline"> <semantics> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <msubsup> <mi>σ</mi> <mn>1</mn> <mn>3</mn> </msubsup> <msub> <mi>h</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>.</p> Full article ">
203 KiB  
Article
The Exact Evaluation of Some New Lattice Sums
by I. J. Zucker
Symmetry 2017, 9(12), 314; https://doi.org/10.3390/sym9120314 - 11 Dec 2017
Cited by 7 | Viewed by 3685
Abstract
New q-series in the spirit of Jacobi have been found in a publication first published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely [...] Read more.
New q-series in the spirit of Jacobi have been found in a publication first published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here. Full article
(This article belongs to the Special Issue Mathematical Crystallography)
2527 KiB  
Article
Detection of Double-Compressed H.264/AVC Video Incorporating the Features of the String of Data Bits and Skip Macroblocks
by Heng Yao, Saihua Song, Chuan Qin, Zhenjun Tang and Xiaokai Liu
Symmetry 2017, 9(12), 313; https://doi.org/10.3390/sym9120313 - 11 Dec 2017
Cited by 17 | Viewed by 5709
Abstract
Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be [...] Read more.
Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be tampered with in various ways. Therefore, the double compression in the H.264/AVC video can be used as a first step in the study of video-tampering forensics. This paper proposes a simple, but effective, double-compression detection method that analyzes the periodic features of the string of data bits (SODBs) and the skip macroblocks (S-MBs) for all I-frames and P-frames in a double-compressed H.264/AVC video. For a given suspicious video, the SODBs and S-MBs are extracted for each frame. Both features are then incorporated to generate one enhanced feature to represent the periodic artifact of the double-compressed video. Finally, a time-domain analysis is conducted to detect the periodicity of the features. The primary Group of Pictures (GOP) size is estimated based on an exhaustive strategy. The experimental results demonstrate the efficacy of the proposed method. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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<p>The schematic of the double compression for the cases of conversion from an I-frame to a P-frame.</p> Full article ">Figure 2
<p>The comparison of a string of data bits between single and double compressions on the sequence <span class="html-italic">hall</span>. The sizes of the Groups of Pictures (GOPs) for the single and double compressions are 12 and 15, respectively.</p> Full article ">Figure 3
<p>The string of data bits for the double-compressed test sequence of coastguard. The 73rd and 75th frames are an I-P-frame and P-P-frame, respectively.</p> Full article ">Figure 4
<p>The macroblock-type comparison for the I-P and P-P frames. The yellow dots denote the skip macroblocks.</p> Full article ">Figure 5
<p>Schematic diagram of the proposed method.</p> Full article ">Figure 6
<p>A comparison of the string of data bits between the single and double compression on the sequence <span class="html-italic">hall</span> after a key frame suppression. The sizes of the GOPs for the single and double compression are 12 and 15, respectively.</p> Full article ">Figure 7
<p>Screenshots of the standard test sequences used in our experiments.</p> Full article ">Figure 8
<p>Enhanced feature of the string of data bits for the test sequence <span class="html-italic">coastguard</span>. The periodic artifact and primary GOP size are observable in the figure.</p> Full article ">Figure 9
<p>Boxplot of estimation accuracy of the proposed method for six standard test sequences with different settings of <span class="html-italic">R</span><sub>2</sub>.</p> Full article ">
3189 KiB  
Article
Chaotic Dynamical State Variables Selection Procedure Based Image Encryption Scheme
by Zia Bashir, Jarosław Wątróbski, Tabasam Rashid, Sohail Zafar and Wojciech Sałabun
Symmetry 2017, 9(12), 312; https://doi.org/10.3390/sym9120312 - 11 Dec 2017
Cited by 18 | Viewed by 4782
Abstract
Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led [...] Read more.
Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP) to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption. Full article
(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)
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<p>The starting dynamical system variables.</p> Full article ">Figure 2
<p>Flowchart of proposed scheme. CDSVSP, chaotic dynamic state variables selection procedure.</p> Full article ">Figure 3
<p>Key sensitivity in the first case: (<b>a</b>) plain image; (<b>b</b>) cipher image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18</mn> <mo>)</mo> <mo>;</mo> </mrow> </mrow> </semantics> </math> (<b>c</b>) cipher image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25.000000000000001</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.0</mn> <mo>,</mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18</mn> <mo>)</mo> <mo>;</mo> </mrow> </mrow> </semantics> </math> (<b>d</b>) cipher image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.000000000000001</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18</mn> <mo>)</mo> <mo>;</mo> </mrow> </mrow> </semantics> </math> (<b>e</b>) cipher image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121.000000000000001</mn> <mo>,</mo> <mo> </mo> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18</mn> <mo>)</mo> <mo>;</mo> </mrow> </mrow> </semantics> </math> (<b>f</b>) cipher image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121.0</mn> <mo>,</mo> <mo> </mo> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18.000000000000001</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math>.</p> Full article ">Figure 4
<p>Histogram of images: (<b>a</b>) Lena gray scale image; (<b>b</b>) histogram of Lena image; (<b>c</b>) cipher (encrypted) image <math display="inline"> <semantics> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>25.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>15.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>121.0</mn> <mo>,</mo> <mo> </mo> </mrow> </semantics> </math><math display="inline"> <semantics> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mrow> <mo>=</mo> <mo>−</mo> <mn>18</mn> <mo>)</mo> <mo>;</mo> </mrow> </mrow> </semantics> </math> (<b>d</b>) histogram of cipher (encrypted) image.</p> Full article ">Figure 5
<p>Correlation of 3000 adjacent random pixels of the plain image: (<b>a</b>) horizontal adjacent pixels; (<b>b</b>) vertical adjacent pixels; (<b>c</b>) diagonal adjacent pixels.</p> Full article ">Figure 6
<p>Correlation of 3000 adjacent random pixels of the cipher image: (<b>a</b>) horizontal adjacent pixels; (<b>b</b>) vertical adjacent pixels; (<b>c</b>) diagonal adjacent pixels.</p> Full article ">
1911 KiB  
Article
Task-Management Method Using R-Tree Spatial Cloaking for Large-Scale Crowdsourcing
by Yan Li and Byeong-Seok Shin
Symmetry 2017, 9(12), 311; https://doi.org/10.3390/sym9120311 - 10 Dec 2017
Cited by 5 | Viewed by 4331
Abstract
With the development of sensor technology and the popularization of the data-driven service paradigm, spatial crowdsourcing systems have become an important way of collecting map-based location data. However, large-scale task management and location privacy are important factors for participants in spatial crowdsourcing. In [...] Read more.
With the development of sensor technology and the popularization of the data-driven service paradigm, spatial crowdsourcing systems have become an important way of collecting map-based location data. However, large-scale task management and location privacy are important factors for participants in spatial crowdsourcing. In this paper, we propose the use of an R-tree spatial cloaking-based task-assignment method for large-scale spatial crowdsourcing. We use an estimated R-tree based on the requested crowdsourcing tasks to reduce the crowdsourcing server-side inserting cost and enable the scalability. By using Minimum Bounding Rectangle (MBR)-based spatial anonymous data without exact position data, this method preserves the location privacy of participants in a simple way. In our experiment, we showed that our proposed method is faster than the current method, and is very efficient when the scale is increased. Full article
(This article belongs to the Special Issue Advanced in Artificial Intelligence and Cloud Computing)
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<p>Proposed spatial task-management process.</p> Full article ">Figure 2
<p>Magnetization as a function of applied field.</p> Full article ">Figure 3
<p>Rectangle-based crowdsourcing tasks and running time comparison.</p> Full article ">Figure 4
<p>Rectangle-based crowdsourcing tasks and memory usage comparison.</p> Full article ">Figure 5
<p>Center-of-area attack prevention comparison.</p> Full article ">
3495 KiB  
Article
Reconstructing Damaged Complex Networks Based on Neural Networks
by Ye Hoon Lee and Insoo Sohn
Symmetry 2017, 9(12), 310; https://doi.org/10.3390/sym9120310 - 9 Dec 2017
Cited by 9 | Viewed by 4209
Abstract
Despite recent progress in the study of complex systems, reconstruction of damaged networks due to random and targeted attack has not been addressed before. In this paper, we formulate the network reconstruction problem as an identification of network structure based on much reduced [...] Read more.
Despite recent progress in the study of complex systems, reconstruction of damaged networks due to random and targeted attack has not been addressed before. In this paper, we formulate the network reconstruction problem as an identification of network structure based on much reduced link information. Furthermore, a novel method based on multilayer perceptron neural network is proposed as a solution to the problem of network reconstruction. Based on simulation results, it was demonstrated that the proposed scheme achieves very high reconstruction accuracy in small-world network model and a robust performance in scale-free network model. Full article
(This article belongs to the Special Issue Graph Theory)
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<p>Small-world network algorithm.</p> Full article ">Figure 2
<p>Scale-free network algorithm.</p> Full article ">Figure 3
<p>Multiple-layer perceptron neural network (MLPNN) model.</p> Full article ">Figure 4
<p>MLPNN based reconstruction method.</p> Full article ">Figure 5
<p>MLPNN training algorithm.</p> Full article ">Figure 6
<p>Probability of reconstruction error for small-world networks with <span class="html-italic">N</span> = 10, <span class="html-italic">N</span> = 30, <span class="html-italic">N</span> = 50, <span class="html-italic">M</span> = 10, and <span class="html-italic">p</span> = 0.15.</p> Full article ">Figure 7
<p>Probability of reconstruction error for small-world networks with <span class="html-italic">p</span> = 0.3, <span class="html-italic">p</span> = 0.5, <span class="html-italic">p</span> = 0.7, <span class="html-italic">M</span> = 10, and <span class="html-italic">N</span> = 50.</p> Full article ">Figure 8
<p>Probability of reconstruction error for small-world networks with <span class="html-italic">M</span> = 10, <span class="html-italic">M</span> = 30, <span class="html-italic">M</span> = 50, <span class="html-italic">N</span> = 50, and <span class="html-italic">p</span> = 0.15.</p> Full article ">Figure 9
<p>Probability of reconstruction error for scale-free networks with <span class="html-italic">N</span> = 10, <span class="html-italic">N</span> = 30, <span class="html-italic">N</span> = 50, <span class="html-italic">M</span> = 10, and <span class="html-italic">m</span><sub>0</sub> = 2.</p> Full article ">Figure 10
<p>Probability of reconstruction error for scale-free networks with <span class="html-italic">M</span> = 10, <span class="html-italic">M</span> = 30, <span class="html-italic">M</span> = 50, <span class="html-italic">N</span> = 30, and <span class="html-italic">m</span><sub>0</sub> = 2.</p> Full article ">Figure 11
<p>Probability of reconstruction error for scale-free networks with <span class="html-italic">m</span><sub>0</sub> = 2, <span class="html-italic">m</span><sub>0</sub> = 3, <span class="html-italic">m</span><sub>0</sub> = 4, <span class="html-italic">N</span> = 30, and <span class="html-italic">M</span> = 10.</p> Full article ">
3339 KiB  
Article
Graphical Classification in Multi-Centrality-Index Diagrams for Complex Chemical Networks
by Yasutaka Mizui, Tetsuya Kojima, Shigeyuki Miyagi and Osamu Sakai
Symmetry 2017, 9(12), 309; https://doi.org/10.3390/sym9120309 - 9 Dec 2017
Cited by 19 | Viewed by 5430
Abstract
Various sizes of chemical reaction network exist, from small graphs of linear networks with several inorganic species to huge complex networks composed of protein reactions or metabolic systems. Huge complex networks of organic substrates have been well studied using statistical properties such as [...] Read more.
Various sizes of chemical reaction network exist, from small graphs of linear networks with several inorganic species to huge complex networks composed of protein reactions or metabolic systems. Huge complex networks of organic substrates have been well studied using statistical properties such as degree distributions. However, when the size is relatively small, statistical data suffers from significant errors coming from irregular effects by species, and a macroscopic analysis is frequently unsuccessful. In this study, we demonstrate a graphical classification method for chemical networks that contain tens of species. Betweenness and closeness centrality indices of a graph can create a two-dimensional diagram with information of node distribution for a complex chemical network. This diagram successfully reveals systematic sharing of roles among species as a semi-statistical property in chemical reactions, and distinguishes it from the ones in random networks, which has no functional node distributions. This analytical approach is applicable for rapid and approximate understanding of complex chemical network systems such as plasma-enhanced reactions as well as visualization and classification of other graphs. Full article
(This article belongs to the Special Issue Graph Theory)
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<p>Graph for chemical reaction network in silane plasma. (<b>a</b>) Example of formation of nodes and edges for one typical reaction; and (<b>b</b>) whole structure of graph. Nodes represent species in chemical reactions, and edges start from agents and ends at products of each reaction. Chemical reactions are listed in Ref. [<a href="#B11-symmetry-09-00309" class="html-bibr">11</a>]. Closed red diamonds indicate species displayed in <a href="#symmetry-09-00309-f002" class="html-fig">Figure 2</a> and <a href="#symmetry-09-00309-f003" class="html-fig">Figure 3</a>.</p> Full article ">Figure 2
<p>Distributions of in-degree and out-degree of species (or nodes) in silane plasma displayed in <a href="#symmetry-09-00309-f001" class="html-fig">Figure 1</a>. Inset dashed line indicates equal cases of in-degrees and out-degrees.</p> Full article ">Figure 3
<p>Diagram of betweenness-closeness centrality indices of reaction network in silane plasma displayed in <a href="#symmetry-09-00309-f001" class="html-fig">Figure 1</a>. Inset is diagram in linear scales.</p> Full article ">Figure 4
<p>Graph for chemical reaction network in methane plasma. Nodes represent species in chemical reactions, and edges start from agents and ends at products of each reaction. Chemical reactions are listed in Ref. [<a href="#B10-symmetry-09-00309" class="html-bibr">10</a>]. Closed red diamonds indicate species displayed in <a href="#symmetry-09-00309-f004" class="html-fig">Figure 4</a>.</p> Full article ">Figure 5
<p>Diagram of betweenness-closeness centrality indices of reaction network in methane plasma displayed in <a href="#symmetry-09-00309-f003" class="html-fig">Figure 3</a>. Inset is diagram in linear scales.</p> Full article ">Figure 6
<p>Random graphs created randomly in computation (<b>a</b>–<b>c</b>).</p> Full article ">Figure 7
<p>Diagrams of betweenness-closeness centrality indices. (<b>a</b>–<b>c</b>) corresponds to (<b>a</b>–<b>c</b>) in <a href="#symmetry-09-00309-f006" class="html-fig">Figure 6</a>, respectively. Inset is diagram in linear scales.</p> Full article ">Figure 8
<p>Histograms of cumulative probabilities or relative densities as function of betweenness centrality index. Data points are from <a href="#symmetry-09-00309-f003" class="html-fig">Figure 3</a>, <a href="#symmetry-09-00309-f005" class="html-fig">Figure 5</a> and <a href="#symmetry-09-00309-f007" class="html-fig">Figure 7</a>.</p> Full article ">
4040 KiB  
Article
A Block-Based Division Reversible Data Hiding Method in Encrypted Images
by Wei-Liang Liu, Hui-Shih Leng, Chuan-Kuei Huang and Dyi-Cheng Chen
Symmetry 2017, 9(12), 308; https://doi.org/10.3390/sym9120308 - 8 Dec 2017
Cited by 11 | Viewed by 4686
Abstract
Due to the increased digital media on the Internet, data security and privacy protection issue have attracted the attention of data communication. Data hiding has become a topic of considerable importance. Nowadays, a new challenge consists of reversible data hiding in the encrypted [...] Read more.
Due to the increased digital media on the Internet, data security and privacy protection issue have attracted the attention of data communication. Data hiding has become a topic of considerable importance. Nowadays, a new challenge consists of reversible data hiding in the encrypted image because of the correlations of local pixels that are destroyed in an encrypted image; it is difficult to embed secret messages in encrypted images using the difference of neighboring pixels. In this paper, the proposed method uses a block-based division mask and a new encrypted method based on the logistic map and an additive homomorphism to embed data in an encrypted image by histogram shifting technique. Our experimental results show that the proposed method achieves a higher payload than other works and is more immune to attack upon the cryptosystem. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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<p>An example two-way difference histogram shifting. (<b>a</b>) The cover image difference histogram. (<b>b</b>) The difference histogram (after embedding).</p> Full article ">Figure 2
<p>A 6 × 6 example of the mask matrix in the method of Li et al.</p> Full article ">Figure 3
<p>Bifurcation diagram for the logistic map.</p> Full article ">Figure 4
<p>Comparison of explored cases. (<b>a</b>) The method of Li et al.; (<b>b</b>) The proposed method.</p> Full article ">Figure 5
<p>(<b>a</b>–<b>g</b>) Different-sized blocks in the boundary region.</p> Full article ">Figure 6
<p>An example 3 × 3 block-based division encrypting procedure.</p> Full article ">Figure 7
<p>Difference histogram shifting using block division. (<b>a</b>) The cover image difference histogram; (<b>b</b>) The difference histogram (after embedding).</p> Full article ">Figure 8
<p>An example cross-division encryption procedure.</p> Full article ">Figure 9
<p>Difference histogram shifting using cross-division. (<b>a</b>) The cover image difference histogram; (<b>b</b>) The difference histogram (after embedding).</p> Full article ">
1631 KiB  
Article
A Secure Mobility Network Authentication Scheme Ensuring User Anonymity
by Ya-Fen Chang, Wei-Liang Tai and Min-How Hsu
Symmetry 2017, 9(12), 307; https://doi.org/10.3390/sym9120307 - 8 Dec 2017
Cited by 6 | Viewed by 3788
Abstract
With the rapid growth of network technologies, users are used to accessing various services with their mobile devices. To ensure security and privacy in mobility networks, proper mechanisms to authenticate the mobile user are essential. In this paper, a mobility network authentication scheme [...] Read more.
With the rapid growth of network technologies, users are used to accessing various services with their mobile devices. To ensure security and privacy in mobility networks, proper mechanisms to authenticate the mobile user are essential. In this paper, a mobility network authentication scheme based on elliptic curve cryptography is proposed. In the proposed scheme, a mobile user can be authenticated without revealing who he is for user anonymity, and a session key is also negotiated to protect the following communications. The proposed mobility network authentication scheme is analyzed to show that it can ensure security, user anonymity, and convenience. Moreover, Burrows-Abadi-Needham logic (BAN logic) is used to deduce the completeness of the proposed authentication scheme. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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<p>An illustration of mobility networks.</p> Full article ">Figure 2
<p>Registration phase in our scheme.</p> Full article ">Figure 3
<p>Login phase in our scheme.</p> Full article ">Figure 4
<p>Authentication and establishment of the session key phase in our scheme.</p> Full article ">Figure 5
<p>Update session key phase in our scheme.</p> Full article ">Figure 6
<p>Password change phase in our scheme.</p> Full article ">
214 KiB  
Article
Complexity Phenomena Induced by Novel Symmetry and Symmetry-Breakings with Antiscreening at Cosmological Scales—A Tutorial
by Tom T. S. Chang
Symmetry 2017, 9(12), 306; https://doi.org/10.3390/sym9120306 - 7 Dec 2017
Cited by 2 | Viewed by 3157
Abstract
Complexity phenomena in cosmological evolution due to the scale-running of the propagator coupling constant can yield new insights related to virtual particles and antiscreening effects with dark matter consequences. This idea was developed in accordance with the differential-integral functional formulation of the Wilsonian [...] Read more.
Complexity phenomena in cosmological evolution due to the scale-running of the propagator coupling constant can yield new insights related to virtual particles and antiscreening effects with dark matter consequences. This idea was developed in accordance with the differential-integral functional formulation of the Wilsonian renormalization group based on the one-particle irreducible scale-dependent effective action for gravitational evolution. In this tutorial communication, we briefly describe the essence of the result with minimal mathematical details and then consider a few simple examples to provide a basic understanding of such an interesting and intriguing complexity process in terms of fractional calculus. Full article
4801 KiB  
Article
Face Liveness Detection Based on Skin Blood Flow Analysis
by Shun-Yi Wang, Shih-Hung Yang, Yon-Ping Chen and Jyun-We Huang
Symmetry 2017, 9(12), 305; https://doi.org/10.3390/sym9120305 - 7 Dec 2017
Cited by 26 | Viewed by 12054
Abstract
Face recognition systems have been widely adopted for user authentication in security systems due to their simplicity and effectiveness. However, spoofing attacks, including printed photos, displayed photos, and replayed video attacks, are critical challenges to authentication, and these spoofing attacks allow malicious invaders [...] Read more.
Face recognition systems have been widely adopted for user authentication in security systems due to their simplicity and effectiveness. However, spoofing attacks, including printed photos, displayed photos, and replayed video attacks, are critical challenges to authentication, and these spoofing attacks allow malicious invaders to gain access to the system. This paper proposes two novel features for face liveness detection systems to protect against printed photo attacks and replayed attacks for biometric authentication systems. The first feature obtains the texture difference between red and green channels of face images inspired by the observation that skin blood flow in the face has properties that enable distinction between live and spoofing face images. The second feature estimates the color distribution in the local regions of face images, instead of whole images, because image quality might be more discriminative in small areas of face images. These two features are concatenated together, along with a multi-scale local binary pattern feature, and a support vector machine classifier is trained to discriminate between live and spoofing face images. The experimental results show that the performance of the proposed method for face spoof detection is promising when compared with that of previously published methods. Furthermore, the proposed system can be implemented in real time, which is valuable for mobile applications. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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<p>Examples of (<b>a</b>) a live face image, (<b>b</b>) a printed photo, and (<b>c</b>) a photo displayed on a mobile phone.</p> Full article ">Figure 2
<p>Proposed face liveness detection system.</p> Full article ">Figure 3
<p>R–G deviated texture in (<b>a</b>) a live face image and (<b>b</b>) a spoofing face image; (<b>c</b>,<b>d</b>) Graphical representation of the R–G deviated texture in the live and spoofing images.</p> Full article ">Figure 4
<p>Examples of a live face image (<b>first row</b>), spoofing face image used in a printed photo attack (<b>second row</b>), and spoofing face image used in a video replay attack. Images were retrieved from the CASIA database. (<b>a</b>) Face image; (<b>b</b>) Histogram of the hue component; (<b>c</b>) Histogram of the saturation component; (<b>d</b>) Histogram of the value component.</p> Full article ">Figure 5
<p>Samples of live face images (<b>top row</b>) and spoofing face images (<b>bottom row</b>) in the NUAA database.</p> Full article ">Figure 6
<p>Samples of spoofing attack images in the CASIA database. (<b>a</b>) Printed photo attack; (<b>b</b>) Printed photo with perforated eye regions; (<b>c</b>) Video replay attack.</p> Full article ">Figure 7
<p>Face samples in Idiap Replay-Attack. (<b>a</b>) Live face image; (<b>b</b>) Spoofing face image used in printed photo attacks; (<b>c</b>) Spoofing face image used in mobile phone attacks; (<b>d</b>) Spoofing face image used in tablet attacks.</p> Full article ">Figure 8
<p>Face samples in the MSU database that were captured using the cameras in a Google Nexus 5 mobile phone (<b>top row</b>) and MacBook Air (<b>bottom row</b>). (<b>a</b>) Live face images; (<b>b</b>) Spoofing face images replayed on an iPad Air screen; (<b>c</b>) Spoofing face images replayed on an iPhone 5S screen; (<b>d</b>) Spoofing face images used in a printed photo attack.</p> Full article ">Figure 9
<p>Face spoofing detection performance on the (<b>a</b>) NUAA; (<b>b</b>) CASIA; (<b>c</b>) Idiap; and (<b>d</b>) MSU databases, using the MLBP to extract features from various color channels.</p> Full article ">Figure 10
<p>Ten examples of correctly classified images in the NUAA database by using our proposed method.</p> Full article ">Figure 11
<p>Five examples of misclassified spoofing face images in the NUAA database by using our proposed method.</p> Full article ">Figure 12
<p>Ten examples of correctly classified images in the CASIA database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">Figure 13
<p>Ten examples of misclassified images in the CASIA database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">Figure 14
<p>Ten examples of correctly classified images in Idiap database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">Figure 15
<p>Ten examples of misclassified images in Idiap database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">Figure 16
<p>Ten examples of correctly classified images in the MSU database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">Figure 17
<p>Ten examples of misclassified images in the MSU database by using the proposed method. (<b>top row</b>) live face images; (<b>bottom row</b>) spoofing face images.</p> Full article ">
4713 KiB  
Article
Performance Analysis of MIMO System with Single RF Link Based on Switched Parasitic Antenna
by He Yu, Guohui Yang, Fanyi Meng and Yingsong Li
Symmetry 2017, 9(12), 304; https://doi.org/10.3390/sym9120304 - 6 Dec 2017
Cited by 8 | Viewed by 5226
Abstract
This paper introduces the principle and key technology of single radio frequency (RF) link Multiple-Input Multiple-Output (MIMO) system based on a switched parasitic antenna (SPA). The software SystemVue is adopted for signal processing and system-level simulation with merit of strong operability and high [...] Read more.
This paper introduces the principle and key technology of single radio frequency (RF) link Multiple-Input Multiple-Output (MIMO) system based on a switched parasitic antenna (SPA). The software SystemVue is adopted for signal processing and system-level simulation with merit of strong operability and high efficiency, which provides tools for the single RF link MIMO system research. A single RF link of a 2 × 2 MIMO system based on the switch parasitic antenna is proposed in this paper. The binary codes are modulated to the baseband Binary Phase Shift Keying (BPSK) signals and transmitted with a 2.4 GHz carrier frequency. The receiver based on the super-heterodyne prototype adopts the channel equalization algorithm for restoring symbols, and it can effectively reduce the system error rate. The simulation results show that the MIMO system built on the platform can achieve equivalent performance with traditional MIMO system, which validates the effectiveness of the proposed scheme. The switched parasitic antenna and equalization algorithm provide new research ideas for single RF link MIMO system and have theoretical significance for further research. Full article
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<p>Diagram of single radio frequency (RF) link Multiple-Input Multiple-Output (MIMO) system.</p> Full article ">Figure 2
<p>Diagram of single RF link MIMO system in SystemVue.</p> Full article ">Figure 3
<p>Internal structure of modulation module.</p> Full article ">Figure 4
<p>Diagram of transmitter module.</p> Full article ">Figure 5
<p>The input and output spectrum of the transmitter link chain. (<b>a</b>) The input spectrum; (<b>b</b>) The output spectrum.</p> Full article ">Figure 6
<p>Diagram of the receiver module.</p> Full article ">Figure 7
<p>The input and output spectrum of the receiver link chain. (<b>a</b>) The input spectrum; (<b>b</b>) The output spectrum.</p> Full article ">Figure 8
<p>Influence of SPDT characteristics on system error rate. (<b>a</b>) Influence of the switch loss; (<b>b</b>) Influence of the switch isolation.</p> Full article ">Figure 9
<p>The channel capacity of the system varies with the signal to noise ratio.</p> Full article ">Figure 10
<p>Constellation diagram after system demodulation. (<b>a</b>) Non-ideal system; (<b>b</b>) Ideal system.</p> Full article ">Figure 11
<p>Two input signals for spectrum broadening verification. (<b>a</b>) Fixed form symbol; (<b>b</b>) Pseudo random code.</p> Full article ">Figure 12
<p>Output spectrum of the two symbols. (<b>a</b>) Fixed form symbol; (<b>b</b>) Pseudo random code.</p> Full article ">Figure 12 Cont.
<p>Output spectrum of the two symbols. (<b>a</b>) Fixed form symbol; (<b>b</b>) Pseudo random code.</p> Full article ">Figure 13
<p>The regularity of BER change with SNR under different algorithms.</p> Full article ">
994 KiB  
Article
Determinant Formulae of Matrices with Certain Symmetry and Its Applications
by Yongju Bae and In Sook Lee
Symmetry 2017, 9(12), 303; https://doi.org/10.3390/sym9120303 - 6 Dec 2017
Cited by 2 | Viewed by 4275
Abstract
In this paper, we introduce formulae for the determinants of matrices with certain symmetry. As applications, we will study the Alexander polynomial and the determinant of a periodic link which is presented as the closure of an oriented 4-tangle. Full article
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<p>Type of periodic subject.</p> Full article ">Figure 2
<p>A trefoil knot diagram and a Hopf link diagram.</p> Full article ">Figure 3
<p>Reidemeister moves.</p> Full article ">Figure 4
<p><math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>e</mi> </msub> <mo>∩</mo> <msub> <mi>T</mi> <mi>f</mi> </msub> </mrow> </semantics> </math>.</p> Full article ">Figure 5
<p><math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>k</mi> <mo>)</mo> </mrow> </semantics> </math>-tangle, denominator and numerator.</p> Full article ">Figure 6
<p>Orientation of a tangle.</p> Full article ">Figure 7
<p>Three types of denominator <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 8
<p>Applying Reidemeister Move II.</p> Full article ">Figure 9
<p>Seifert graphs for <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>N</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 10
<p>Seifert graph for <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <msup> <mi>T</mi> <mi>n</mi> </msup> <mo>)</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 11
<p>Example for Case II.</p> Full article ">Figure 12
<p><span class="html-italic">T</span><sub>+</sub> and <span class="html-italic">T</span><sub>−</sub>.</p> Full article ">Figure 13
<p>Seifert graphs of <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <msup> <mi>T</mi> <mo>′</mo> </msup> <mo>)</mo> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <msubsup> <mi>T</mi> <mo>+</mo> <mo>′</mo> </msubsup> <mo>)</mo> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <msubsup> <mi>T</mi> <mo>−</mo> <mo>′</mo> </msubsup> <mo>)</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 14
<p>Seifert graph of <math display="inline"> <semantics> <mrow> <mi>D</mi> <mo>(</mo> <msup> <mi>T</mi> <mrow> <mo>′</mo> <mi>n</mi> </mrow> </msup> <mo>)</mo> </mrow> </semantics> </math>.</p> Full article ">Figure 15
<p>Example for Case III.</p> Full article ">Figure 16
<p><math display="inline"> <semantics> <mrow> <msup> <mrow> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi mathvariant="sans-serif">Δ</mi> <mrow> <mi>D</mi> <mo>(</mo> <msub> <mi>T</mi> <mo>+</mo> </msub> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi mathvariant="sans-serif">Δ</mi> <mrow> <mi>D</mi> <mo>(</mo> <msub> <mi>T</mi> <mo>−</mo> </msub> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mo>−</mo> <mn>8</mn> </mrow> </semantics> </math>.</p> Full article ">
592 KiB  
Article
Internet of Things: A Scientometric Review
by Juan Ruiz-Rosero, Gustavo Ramirez-Gonzalez, Jennifer M. Williams, Huaping Liu, Rahul Khanna and Greeshma Pisharody
Symmetry 2017, 9(12), 301; https://doi.org/10.3390/sym9120301 - 6 Dec 2017
Cited by 55 | Viewed by 11809
Abstract
Internet of Things (IoT) is connecting billions of devices to the Internet. These IoT devices chain sensing, computation, and communication techniques, which facilitates remote data collection and analysis. wireless sensor networks (WSN) connect sensing devices together on a local network, thereby eliminating wires, [...] Read more.
Internet of Things (IoT) is connecting billions of devices to the Internet. These IoT devices chain sensing, computation, and communication techniques, which facilitates remote data collection and analysis. wireless sensor networks (WSN) connect sensing devices together on a local network, thereby eliminating wires, which generate a large number of samples, creating a big data challenge. This IoT paradigm has gained traction in recent years, yielding extensive research from an increasing variety of perspectives, including scientific reviews. These reviews cover surveys related to IoT vision, enabling technologies, applications, key features, co-word and cluster analysis, and future directions. Nevertheless, we lack an IoT scientometrics review that uses scientific databases to perform a quantitative analysis. This paper develops a scientometric review about IoT over a data set of 19,035 documents published over a period of 15 years (2002–2016) in two main scientific databases (Clarivate Web of Science and Scopus). A Python script called ScientoPy was developed to perform quantitative analysis of this data set. This provides insight into research trends by investigating a lead author’s country affiliation, most published authors, top research applications, communication protocols, software processing, hardware, operating systems, and trending topics. Furthermore, we evaluate the top trending IoT topics and the popular hardware and software platforms that are used to research these trends. Full article
(This article belongs to the Special Issue Applications of Internet of Things)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Documents per year published (WoS and Scopus) with the search string “Internet of Things” (IoT) for the period 2000 to 2016. (<b>a</b>) before the duplicates-removal filter; (<b>b</b>) after duplicates-removal filter.</p> Full article ">Figure 2
<p>Internet of Things percentage of documents published per year by the top 7 first author’s corresponding address country for the period 2002 to 2016.</p> Full article ">Figure 3
<p>Internet of Things top 5 authors with most documents published per year, for the period 2006 to 2016.</p> Full article ">Figure 4
<p>Internet of Things top authors’ keywords documents published per year, excluding the keywords: Internet of Things, IoT, Internet of Things (IoT), and The Internet of Things, for the period 2006 to 2016.</p> Full article ">Figure 5
<p>Internet of Things top applications based authors’ keywords in documents per year, for the period 2006 to 2016. (<b>a</b>) applications that start with “smart” (<b>b</b>) applications that do not start with “smart”.</p> Full article ">Figure 6
<p>Internet of Things media and host layers communication protocols based on authors’ keywords in documents per year, for the 2006 to 2016 period. (<b>a</b>) media layers’ communications protocols; (<b>b</b>) host layers’ communication protocols.</p> Full article ">Figure 7
<p>Internet of Things software processing techniques based on authors’ keywords in documents per year, for the period 2006 to 2016.</p> Full article ">Figure 8
<p>Internet of Things devices operating systems (OS) and hardware based on authors’ keywords, for the period 2006 to 2016. (<b>a</b>) most used operating systems in authors’ keywords per year; (<b>b</b>) most used hardware in authors’ keywords per year.</p> Full article ">Figure 9
<p>Internet of Things top trending topics based on authors’ keywords, with average growth rate (AGR) for different times periods (2011–2012, 2013–2014, and 2015–2016).</p> Full article ">
5986 KiB  
Article
A Study for Parametric Morphogeometric Operators to Assist the Detection of Keratoconus
by Laurent Bataille, Francisco Cavas-Martínez, Daniel G. Fernández-Pacheco, Francisco J. F. Cañavate and Jorge L. Alio
Symmetry 2017, 9(12), 302; https://doi.org/10.3390/sym9120302 - 5 Dec 2017
Cited by 3 | Viewed by 4899
Abstract
The aim of this study is to describe a new keratoconus detection method based on the analysis of certain parametric morphogeometric operators extracted from a custom patient-specific three-dimensional (3D) model of the human cornea. A corneal geometric reconstruction is firstly performed using zonal [...] Read more.
The aim of this study is to describe a new keratoconus detection method based on the analysis of certain parametric morphogeometric operators extracted from a custom patient-specific three-dimensional (3D) model of the human cornea. A corneal geometric reconstruction is firstly performed using zonal functions and retrospective Scheimpflug tomography data from 107 eyes of 107 patients. The posterior corneal surface is later analysed using an optimised computational geometry technique and the morphology of healthy and keratoconic corneas is characterized by means of geometric variables. The performance of these variables as predictors of a new geometric marker is assessed through a receiver operating characteristic (ROC) curve analysis and their correlations are analysed through Pearson or Spearman coefficients. The posterior apex deviation variable shows the best keratoconus diagnosis capability. However, the strongest correlations in both healthy and pathological corneas are provided by the metrics directly related to the thickness as the sagittal plane area at the apex and the sagittal plane area at the minimum thickness point. A comparison of the screening of keratoconus provided by the Sirius topographer and the detection of corneal ectasia using the posterior apex deviation parameter is also performed, demonstrating the accuracy of this characterization as an effective marker of the diagnosis and ectatic disease progression. Full article
(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)
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<p>Use of patient-specific 3D modelling for the diagnosis of keratoconus.</p> Full article ">Figure 2
<p>Geometric modelling process by using CAD tools.</p> Full article ">Figure 3
<p>Analysis of the point-surface deviation for the posterior surface reconstruction of a cornea with keratoconus (stage I-AK).</p> Full article ">Figure 4
<p>Geometric variables analysed during the study.</p> Full article ">Figure 5
<p>ROC curve modelling sensitivity versus 1-specificity for the variables analysed.</p> Full article ">
302 KiB  
Article
Cohomology Characterizations of Diagonal Non-Abelian Extensions of Regular Hom-Lie Algebras
by Lina Song and Rong Tang
Symmetry 2017, 9(12), 297; https://doi.org/10.3390/sym9120297 - 5 Dec 2017
Cited by 1 | Viewed by 2883
Abstract
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to [...] Read more.
In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out ( h ) . Then for a general Hom-Lie algebra morphism from g to Out ( h ) , we construct a cohomology class as the obstruction of existence of a non-abelian extension that induces the given Hom-Lie algebra morphism. Full article
7383 KiB  
Article
Virtualized Network Function Orchestration System and Experimental Network Based QR Recognition for a 5G Mobile Access Network
by Misun Ahn, SeungGwan Lee and Sungwon Lee
Symmetry 2017, 9(12), 300; https://doi.org/10.3390/sym9120300 - 3 Dec 2017
Cited by 1 | Viewed by 5903
Abstract
This paper proposes a virtualized network function orchestration system based on Network Function Virtualization (NFV), one of the main technologies in 5G mobile networks. This system should provide connectivity between network devices and be able to create flexible network function and distribution. This [...] Read more.
This paper proposes a virtualized network function orchestration system based on Network Function Virtualization (NFV), one of the main technologies in 5G mobile networks. This system should provide connectivity between network devices and be able to create flexible network function and distribution. This system focuses more on access networks. By experimenting with various scenarios of user service established and activated in a network, we examine whether rapid adoption of new service is possible and whether network resources can be managed efficiently. The proposed method is based on Bluetooth transfer technology and mesh networking to provide automatic connections between network machines and on a Docker flat form, which is a container virtualization technology for setting and managing key functions. Additionally, the system includes a clustering and recovery measure regarding network function based on the Docker platform. We will briefly introduce the QR code perceived service as a user service to examine the proposal and based on this given service, we evaluate the function of the proposal and present analysis. Through the proposed approach, container relocation has been implemented according to a network device’s CPU usage and we confirm successful service through function evaluation on a real test bed. We estimate QR code recognition speed as the amount of network equipment is gradually increased, improving user service and confirm that the speed of recognition is increased as the assigned number of network devices is increased by the user service. Full article
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<p>System Model for the Virtualized Network Function oriented 5G Mobile Network.</p> Full article ">Figure 2
<p>The architecture of a virtual machine and a docker.</p> Full article ">Figure 3
<p>Internal structure of a network device applying a docker swarm.</p> Full article ">Figure 4
<p>The structure of a QR code.</p> Full article ">Figure 5
<p>Architecture of the applied proposed networking method and device internal structure.</p> Full article ">Figure 6
<p>Master node’s mesh net control module operational process.</p> Full article ">Figure 7
<p>Member node’s mesh net control module operational process.</p> Full article ">Figure 8
<p>Mesh net controller mutual recognition and information exchange procedure.</p> Full article ">Figure 9
<p>Internal structure of the master node.</p> Full article ">Figure 10
<p>Internal structure of a member node.</p> Full article ">Figure 11
<p>VNF recovery procedure in the proposed orchestration system.</p> Full article ">Figure 12
<p>Operation process of the proposed QR code recognition.</p> Full article ">Figure 13
<p>Operation process based on combining the existing and proposed methods.</p> Full article ">Figure 14
<p>Result of CPU usage for each node in the proposed method.</p> Full article ">Figure 15
<p>Result of wireless link bandwidth test to verify the proposed network</p> Full article ">Figure 16
<p>Sample QR codes for testing the proposed QR identification method.</p> Full article ">Figure 17
<p>QR code similarity graph applied for the proposed recognition method.</p> Full article ">Figure 18
<p>Test of QR code identification for different numbers of databases used.</p> Full article ">
348 KiB  
Article
Continuity of Fuzzified Functions Using the Generalized Extension Principle
by Hsien-Chung Wu
Symmetry 2017, 9(12), 299; https://doi.org/10.3390/sym9120299 - 1 Dec 2017
Cited by 8 | Viewed by 2897
Abstract
To fuzzify the crisp functions, the extension principle has been widely used for performing this fuzzification. The purpose of this paper is to investigate the continuity of fuzzified function using the more generalized extension principle. The Hausdorff metric will be invoked to study [...] Read more.
To fuzzify the crisp functions, the extension principle has been widely used for performing this fuzzification. The purpose of this paper is to investigate the continuity of fuzzified function using the more generalized extension principle. The Hausdorff metric will be invoked to study the continuity of fuzzified function. We also apply the principle of continuity of fuzzified function to the fuzzy topological vector space. Full article
(This article belongs to the Special Issue Fuzzy Sets Theory and Its Applications)
3627 KiB  
Article
A Model for Shovel Capital Cost Estimation, Using a Hybrid Model of Multivariate Regression and Neural Networks
by Abdolreza Yazdani-Chamzini, Edmundas Kazimieras Zavadskas, Jurgita Antucheviciene and Romualdas Bausys
Symmetry 2017, 9(12), 298; https://doi.org/10.3390/sym9120298 - 1 Dec 2017
Cited by 19 | Viewed by 5602
Abstract
Cost estimation is an essential issue in feasibility studies in civil engineering. Many different methods can be applied to modelling costs. These methods can be divided into several main groups: (1) artificial intelligence, (2) statistical methods, and (3) analytical methods. In this paper, [...] Read more.
Cost estimation is an essential issue in feasibility studies in civil engineering. Many different methods can be applied to modelling costs. These methods can be divided into several main groups: (1) artificial intelligence, (2) statistical methods, and (3) analytical methods. In this paper, the multivariate regression (MVR) method, which is one of the most popular linear models, and the artificial neural network (ANN) method, which is widely applied to solving different prediction problems with a high degree of accuracy, have been combined to provide a cost estimate model for a shovel machine. This hybrid methodology is proposed, taking the advantages of MVR and ANN models in linear and nonlinear modelling, respectively. In the proposed model, the unique advantages of the MVR model in linear modelling are used first to recognize the existing linear structure in data, and, then, the ANN for determining nonlinear patterns in preprocessed data is applied. The results with three indices indicate that the proposed model is efficient and capable of increasing the prediction accuracy. Full article
(This article belongs to the Special Issue Civil Engineering and Symmetry)
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<p>A model for an artificial neuron.</p> Full article ">Figure 2
<p>Architecture of a typical artificial neural networks (ANN).</p> Full article ">Figure 3
<p>The approach used in the research.</p> Full article ">Figure 4
<p>The correlation for shovel cost based on the proposed model.</p> Full article ">Figure 5
<p>The comparison of cost estimation models.</p> Full article ">Figure 6
<p>Sensitivity analysis of input parameters.</p> Full article ">
3205 KiB  
Article
Tool-Wear Analysis Using Image Processing of the Tool Flank
by Ovidiu Gheorghe Moldovan, Simona Dzitac, Ioan Moga, Tiberiu Vesselenyi and Ioan Dzitac
Symmetry 2017, 9(12), 296; https://doi.org/10.3390/sym9120296 - 30 Nov 2017
Cited by 34 | Viewed by 7499
Abstract
Flexibility of manufacturing systems is an essential factor in maintaining the competitiveness of industrial production. Flexibility can be defined in several ways and according to several factors, but in order to obtain adequate results in implementing a flexible manufacturing system able to compete [...] Read more.
Flexibility of manufacturing systems is an essential factor in maintaining the competitiveness of industrial production. Flexibility can be defined in several ways and according to several factors, but in order to obtain adequate results in implementing a flexible manufacturing system able to compete on the market, a high level of autonomy (free of human intervention) of the manufacturing system must be achieved. There are many factors that can disturb the production process and reduce the autonomy of the system, because of the need of human intervention to overcome these disturbances. One of these factors is tool wear. The aim of this paper is to present an experimental study on the possibility to determine the state of tool wear in a flexible manufacturing cell environment, using image acquisition and processing methods. Full article
(This article belongs to the Special Issue Civil Engineering and Symmetry)
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<p>Tool-wear monitoring system.</p> Full article ">Figure 2
<p>Tool-wear monitoring system. (<b>a</b>) unworn flank; (<b>b</b>) worn flank.</p> Full article ">Figure 3
<p>Image acquisition system for the automatic determination of tool wear.</p> Full article ">Figure 4
<p>Tool used for the experimental test.</p> Full article ">Figure 5
<p>Workpiece used for the experimental test.</p> Full article ">Figure 6
<p>Images taken at successive times during processing showing the stages of tool wear: (<b>a</b>) new tool; (<b>b</b>) first stage when the wear became visible; and (<b>c</b>) last stage with massive wear.</p> Full article ">Figure 7
<p>Binary black and white (b/w) image of (<b>a</b>) the new and (<b>b</b>) last stage of wear of the tool flank.</p> Full article ">Figure 8
<p>Enhanced and “rotated-to-horizontal” images of (<b>a</b>) the flank of the new tool and (<b>b</b>) tool with wear.</p> Full article ">Figure 9
<p>Euler number diagram for the experimental images set (points corresponding to worn tool flank are marked with red).</p> Full article ">Figure 10
<p>Normalized sum of white pixels (NSP) diagrams for unworn tool flank.</p> Full article ">Figure 11
<p>Normalized sum of white pixels (NSP) diagrams for worn tool flank.</p> Full article ">Figure 12
<p>Normalized sum of white pixels (NSP) diagram for unworn tool flank and the second-order polynomial approximation (blue curve) with maxima at point M.</p> Full article ">Figure 13
<p>Normalized sum of white pixels (NSP) diagram for worn tool flank and the second-order polynomial approximation (blue curve) with maxima at point M.</p> Full article ">Figure 14
<p>Normalized sum of white pixels (NSP) diagram for worn tool flank and the second-order polynomial approximation (blue curve) with maxima at point M.</p> Full article ">Figure 15
<p>Training performance diagram for the artificial neural network (ANN).</p> Full article ">Figure 16
<p>Confusion matrix for the test set.</p> Full article ">Figure 17
<p>Training success rate (TSR) for networks with 10 to 200 neurons in the hidden layer (100 training sessions for each network; each point in the diagram).</p> Full article ">Figure 18
<p>Performance diagram for the artificial neural network (ANN).</p> Full article ">Figure 19
<p>Training success rate (TSR) for networks with 10 to 1000 neurons in the hidden layer (10 training sessions for each network; each point in the diagram).</p> Full article ">Figure 20
<p>Training success rate (TSR) for networks with 10 to 200 neurons in the hidden layer (100 training sessions for each network; each point in the diagram).</p> Full article ">Figure 21
<p>Performance diagram for the second layer of a two-hidden-layer autoencoder artificial neural network (ANN).</p> Full article ">Figure 22
<p>Training success rate (TSR) for networks with 10 to 520 neurons in the first hidden layer and 10 neurons in the second layer (10 training sessions for each network; each point in the diagram).</p> Full article ">Figure 23
<p>Training success rate (TSR) for networks with 300 neurons in the first hidden layer and 10 to 200 neurons in the second layer (10 training sessions for each network; each point in the diagram).</p> Full article ">Figure 24
<p>Number of misclassifications of tool-flank images from the total number of misclassifications.</p> Full article ">Figure 25
<p>Image of sample number 3 from the test set labeled as unworn tool flank but misclassified, in some cases, as worn tool flank.</p> Full article ">
1164 KiB  
Review
Green Cloud Computing: A Literature Survey
by Laura-Diana Radu
Symmetry 2017, 9(12), 295; https://doi.org/10.3390/sym9120295 - 30 Nov 2017
Cited by 78 | Viewed by 27498
Abstract
Cloud computing is a dynamic field of information and communication technologies (ICTs), introducing new challenges for environmental protection. Cloud computing technologies have a variety of application domains, since they offer scalability, are reliable and trustworthy, and offer high performance at relatively low cost. [...] Read more.
Cloud computing is a dynamic field of information and communication technologies (ICTs), introducing new challenges for environmental protection. Cloud computing technologies have a variety of application domains, since they offer scalability, are reliable and trustworthy, and offer high performance at relatively low cost. The cloud computing revolution is redesigning modern networking, and offering promising environmental protection prospects as well as economic and technological advantages. These technologies have the potential to improve energy efficiency and to reduce carbon footprints and (e-)waste. These features can transform cloud computing into green cloud computing. In this survey, we review the main achievements of green cloud computing. First, an overview of cloud computing is given. Then, recent studies and developments are summarized, and environmental issues are specifically addressed. Finally, future research directions and open problems regarding green cloud computing are presented. This survey is intended to serve as up-to-date guidance for research with respect to green cloud computing. Full article
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<p>Types of cloud computing.</p> Full article ">Figure 2
<p>Distribution of surveys over years.</p> Full article ">Figure 3
<p>Distribution of surveys on environmental issues between 2009 and 2016.</p> Full article ">Figure 4
<p>Distribution on categories of green cloud computing surveys.</p> Full article ">Figure 5
<p>Cloud computing characteristics and their influences on the environment.</p> Full article ">
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