Symmetry
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Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 8, Pages 102: A POCS Algorithm Based on Text Features for the Reconstruction of Document Images at Super-Resolution]]>
http://www.mdpi.com/2073-8994/8/10/102
In order to address the problem of the uncertainty of existing noise models and of the complexity and changeability of the edges and textures of low-resolution document images, this paper presents a projection onto convex sets (POCS) algorithm based on text features. The current method preserves the edge details and smooths the noise in text images by adding text features as constraints to original POCS algorithms and converting the fixed threshold to an adaptive one. In this paper, the optimized scale invariant feature transform (SIFT) algorithm was used for the registration of continuous frames, and finally the image was reconstructed under the improved POCS theoretical framework. Experimental results showed that the algorithm can significantly smooth the noise and eliminate noise caused by the shadows of the lines. The lines of the reconstructed text are smoother and the stroke contours of the reconstructed text are clearer, and this largely eliminates the text edge vibration to enhance the resolution of the document image text.Symmetry2016-09-29810Article10.3390/sym81001021022073-89942016-09-29doi: 10.3390/sym8100102Fengmei LiangYajun XuMengxia ZhangLiyuan Zhang<![CDATA[Symmetry, Vol. 8, Pages 103: Cloud-Based Parameter-Driven Statistical Services and Resource Allocation in a Heterogeneous Platform on Enterprise Environment]]>
http://www.mdpi.com/2073-8994/8/10/103
A fundamental key for enterprise users is a cloud-based parameter-driven statistical service and it has become a substantial impact on companies worldwide. In this paper, we demonstrate the statistical analysis for some certain criteria that are related to data and applied to the cloud server for a comparison of results. In addition, we present a statistical analysis and cloud-based resource allocation method for a heterogeneous platform environment by performing a data and information analysis with consideration of the application workload and the server capacity, and subsequently propose a service prediction model using a polynomial regression model. In particular, our aim is to provide stable service in a given large-scale enterprise cloud computing environment. The virtual machines (VMs) for cloud-based services are assigned to each server with a special methodology to satisfy the uniform utilization distribution model. It is also implemented between users and the platform, which is a main idea of our cloud computing system. Based on the experimental results, we confirm that our prediction model can provide sufficient resources for statistical services to large-scale users while satisfying the uniform utilization distribution.Symmetry2016-09-29810Article10.3390/sym81001031032073-89942016-09-29doi: 10.3390/sym8100103Sungju LeeTaikyeong Jeong<![CDATA[Symmetry, Vol. 8, Pages 100: Smartphone User Identity Verification Using Gait Characteristics]]>
http://www.mdpi.com/2073-8994/8/10/100
Smartphone-based biometrics offers a wide range of possible solutions, which could be used to authenticate users and thus to provide an extra level of security and theft prevention. We propose a method for positive identification of smartphone user’s identity using user’s gait characteristics captured by embedded smartphone sensors (gyroscopes, accelerometers). The method is based on the application of the Random Projections method for feature dimensionality reduction to just two dimensions. Then, a probability distribution function (PDF) of derived features is calculated, which is compared against known user PDF. The Jaccard distance is used to evaluate distance between two distributions, and the decision is taken based on thresholding. The results for subject recognition are at an acceptable level: we have achieved a grand mean Equal Error Rate (ERR) for subject identification of 5.7% (using the USC-HAD dataset). Our findings represent a step towards improving the performance of gait-based user identity verification technologies.Symmetry2016-09-29810Article10.3390/sym81001001002073-89942016-09-29doi: 10.3390/sym8100100Robertas DamaševičiusRytis MaskeliūnasAlgimantas VenčkauskasMarcin Woźniak<![CDATA[Symmetry, Vol. 8, Pages 99: Structural Distortion Stabilizing the Antiferromagnetic and Semiconducting Ground State of BaMn2As2]]>
http://www.mdpi.com/2073-8994/8/10/99
We report evidence that the experimentally found antiferromagnetic structure as well as the semiconducting ground state of BaMn 2 As 2 are caused by optimally-localized Wannier states of special symmetry existing at the Fermi level of BaMn 2 As 2 . In addition, we find that a (small) tetragonal distortion of the crystal is required to stabilize the antiferromagnetic semiconducting state. To our knowledge, this distortion has not yet been established experimentally.Symmetry2016-09-28810Article10.3390/sym8100099992073-89942016-09-28doi: 10.3390/sym8100099Ekkehard Krüger<![CDATA[Symmetry, Vol. 8, Pages 101: Maternal Stress Affects Fetal Growth but Not Developmental Instability in Rabbits]]>
http://www.mdpi.com/2073-8994/8/10/101
Developmental instability (DI), often measured by fluctuating asymmetry (FA) or the frequency of phenodeviants (fPD), is thought to increase with stress. However, specifically for stressors of maternal origin, evidence of such negative associations with DI is scarce. Whereas effects of maternal stress on DI have predominately been examined retroactively in humans, very little is known from experiments with well-defined stress levels in animal model systems. The aim of this study was to examine the effects of maternal exposure to three doses (plus a control) of a toxic compound affecting maternal condition on DI of their offspring in rabbits. Presence of maternal stress induced by the treatment was confirmed by a decrease in food consumption and weight gain of gravid females in the medium and high dose. Major abnormalities and mortality were unaffected by dose, suggesting the lack of toxic effects of the compound on the offspring. In spite of string maternal stress, offspring FA did not increase with dose. The treatment did lead to elevated fPD, but most were transient, reflecting growth retardation. Furthermore, a consistent association between fPD and FA was absent. These findings indicate that DI is not increased by maternal stress in this animal model.Symmetry2016-09-27810Article10.3390/sym81001011012073-89942016-09-27doi: 10.3390/sym8100101Jessica BotsMatteo BrenoLuc De SchaepdrijverStefan Van Dongen<![CDATA[Symmetry, Vol. 8, Pages 97: M-Polynomial and Related Topological Indices of Nanostar Dendrimers]]>
http://www.mdpi.com/2073-8994/8/9/97
Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.Symmetry2016-09-2189Article10.3390/sym8090097972073-89942016-09-21doi: 10.3390/sym8090097Mobeen MunirWaqas NazeerShazia RafiqueShin Kang<![CDATA[Symmetry, Vol. 8, Pages 98: Two-Dimensional Hermite Filters Simplify the Description of High-Order Statistics of Natural Images]]>
http://www.mdpi.com/2073-8994/8/9/98
Natural image statistics play a crucial role in shaping biological visual systems, understanding their function and design principles, and designing effective computer-vision algorithms. High-order statistics are critical for conveying local features but they are challenging to study, largely because their number and variety is large. Here, via the use of two-dimensional Hermite (TDH) functions, we identify a covert symmetry in high-order statistics of natural images that simplifies this task. This emerges from the structure of TDH functions, which are an orthogonal set of functions that are organized into a hierarchy of ranks. Specifically, we find that the shape (skewness and kurtosis) of the distribution of filter coefficients depends only on the projection of the function onto a one-dimensional subspace specific to each rank. The characterization of natural image statistics provided by TDH filter coefficients reflects both their phase and amplitude structure, and we suggest an intuitive interpretation for the special subspace within each rank.Symmetry2016-09-2189Article10.3390/sym8090098982073-89942016-09-21doi: 10.3390/sym8090098Qin HuJonathan Victor<![CDATA[Symmetry, Vol. 8, Pages 96: ANFIS-Based Modeling for Photovoltaic Characteristics Estimation]]>
http://www.mdpi.com/2073-8994/8/9/96
Due to the high cost of photovoltaic (PV) modules, an accurate performance estimation method is significantly valuable for studying the electrical characteristics of PV generation systems. Conventional analytical PV models are usually composed by nonlinear exponential functions and a good number of unknown parameters must be identified before using. In this paper, an adaptive-network-based fuzzy inference system (ANFIS) based modeling method is proposed to predict the current-voltage characteristics of PV modules. The effectiveness of the proposed modeling method is evaluated through comparison with Villalva’s model, radial basis function neural networks (RBFNN) based model and support vector regression (SVR) based model. Simulation and experimental results confirm both the feasibility and the effectiveness of the proposed method.Symmetry2016-09-1689Article10.3390/sym8090096962073-89942016-09-16doi: 10.3390/sym8090096Ziqiang BiJieming MaXinyu PanJian WangYu Shi<![CDATA[Symmetry, Vol. 8, Pages 95: Approach to Multi-Criteria Group Decision-Making Problems Based on the Best-Worst-Method and ELECTRE Method]]>
http://www.mdpi.com/2073-8994/8/9/95
This paper proposes a novel approach to cope with the multi-criteria group decision-making problems. We give the pairwise comparisons based on the best-worst-method (BWM), which can decrease comparison times. Additionally, our comparison results are determined with the positive and negative aspects. In order to deal with the decision matrices effectively, we consider the elimination and choice translation reality (ELECTRE III) method under the intuitionistic multiplicative preference relations environment. The ELECTRE III method is designed for a double-automatic system. Under a certain limitation, without bothering the decision-makers to reevaluate the alternatives, this system can adjust some special elements that have the most influence on the group’s satisfaction degree. Moreover, the proposed method is suitable for both the intuitionistic multiplicative preference relation and the interval valued fuzzy preference relations through the transformation formula. An illustrative example is followed to demonstrate the rationality and availability of the novel method.Symmetry2016-09-0989Article10.3390/sym8090095952073-89942016-09-09doi: 10.3390/sym8090095Xinshang YouTong ChenQing Yang<![CDATA[Symmetry, Vol. 8, Pages 94: Lorentz Transformations from Intrinsic Symmetries]]>
http://www.mdpi.com/2073-8994/8/9/94
We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination with the principle of relativity and the presumed nature of Euclidean space and time, the symmetry principle is employed to derive the proper orthochronous Lorentz transformation without assuming the constancy of the speed of light and specific mathematical requirements (such as group property) a priori. We explicitly demonstrate that the constancy of the speed of light in all inertial frames can be derived using the velocity reciprocity property, which is a deductive consequence of the space–time homogeneity and the space isotropy. The FESI or the FETI symmetry remains to be preserved in the Galilean transformation at the non-relativistic limit. Other similar symmetry operations result in either trivial transformations or improper and/or non-orthochronous Lorentz transformations, which do not form groups.Symmetry2016-09-0989Article10.3390/sym8090094942073-89942016-09-09doi: 10.3390/sym8090094Sheng Chao<![CDATA[Symmetry, Vol. 8, Pages 93: Modeling and Optimization of a Tree Based on Virtual Reality for Immersive Virtual Landscape Generation]]>
http://www.mdpi.com/2073-8994/8/9/93
This study proposes a modeling method that can effectively generate multiple diverse digital trees for creating immersive virtual landscape based on virtual reality and an optimization method for real-time rendering. The proposed method simplifies a process of procedures from growth of tree models to the generation of the three-dimensional branch geometric model. Here, the procedural branch graph (PBG) algorithm is proposed, which simultaneously and effectively generates diverse trees that have a similar branch pattern. Moreover, the optimization method is designed in a polygon-based branch model which controls the resolution of tree models according to the distance from the camera to generate a tree model structure that is appropriate for an immersive system based on virtual reality. Finally, a virtual reality system is established based on the Oculus SDK (Software Development Kit) and Unity3D engine. In this process, the image processing-based pixel to tree (PTT) method is proposed as a technique for easily and efficiently generating a virtual landscape by allocating multiple trees on terrain. An immersive virtual landscape that has a stereoscopic perception and spatial impression is created through the proposed method and whether it can deliver experience of nature in virtual reality to the users was checked through an experiment.Symmetry2016-09-0989Article10.3390/sym8090093932073-89942016-09-09doi: 10.3390/sym8090093Jinmo Kim<![CDATA[Symmetry, Vol. 8, Pages 92: Energy Conservation Law in Industrial Architecture: An Approach through Geometric Algebra]]>
http://www.mdpi.com/2073-8994/8/9/92
Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. Using the framework based on complex algebra in non-sinusoidal circuit analysis (frequency domain), the verification of the energy conservation law is only possible in sinusoidal situations. In this case, reactive energy turns out to be proportional to the energy difference between the average electric and magnetic energies stored in the loads and its cancellation is mathematically trivial. However, in industrial architecture, apparent power definition of electric loads (non-sinusoidal conditions) is inconsistent with the energy conservation law. Up until now, in the classical complex algebra approach, this goal is only valid in the case of purely resistive loads. Thus, in this paper, a new circuit analysis approach using geometric algebra is used to develop the most general proof of energy conservation in industrial building loads. In terms of geometric objects, this powerful tool calculates the voltage, current, and apparent power in electrical systems in non-sinusoidal, linear/nonlinear situations. In contrast to the traditional method developed by Steinmetz, the suggested powerful tool extends the concept of phasor to multivector-phasors and is performed in a new Generalized Complex Geometric Algebra structure (CGn), where Gn is the Clifford algebra in n-dimensional real space and C is the complex vector space. To conclude, a numerical example illustrates the clear advantages of the approach suggested in this paper.Symmetry2016-09-0689Article10.3390/sym8090092922073-89942016-09-06doi: 10.3390/sym8090092Juan BravoManuel Castilla<![CDATA[Symmetry, Vol. 8, Pages 90: The Combination of a Fuzzy Analytical Hierarchy Process and the Taguchi Method to Evaluate the Malaysian Users’ Willingness to Pay for Public Transportation]]>
http://www.mdpi.com/2073-8994/8/9/90
This study is an attempt to overcome the lack of reliable estimates on the willingness of Malaysian users to pay for public transportation (particularly buses) through a combined analysis of a fuzzy analytical hierarchy process (F-AHP) and the Taguchi method. This is a ground-breaking study in the attempt to evaluate the bus users’ satisfaction factors based on the F-AHP, and find the pattern for the users’ willingness to pay (WTP) characteristic by reducing the travel time with the Taguchi application. The data were collected from the public transportation users’ intentions in Kelang Valley, Kuala Lumpur, Malaysia. The results convinced us that, for complex data, one requires flexible approaches that can adjust their combination methods to the properties of analyzed datasets. This study is interested in initiating the use of a system combination strategy to have a better understanding of the factors that motivate the public transportation users to be willing to pay for the public transportation’s fare.Symmetry2016-09-0289Article10.3390/sym8090090902073-89942016-09-02doi: 10.3390/sym8090090Hashem Salarzadeh JenatabadiPeyman BabashamsiNur Yusoff<![CDATA[Symmetry, Vol. 8, Pages 91: Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes]]>
http://www.mdpi.com/2073-8994/8/9/91
In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged U ( 1 ) nonlinear CP 1 -model. If 2 π n , n ∈ Z , is the quantized magnetic flux of the two species of BPS vortex solutions, 2 n linearly-independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension 2 n of these stringy topological defects is thus locally shown.Symmetry2016-09-0189Article10.3390/sym8090091912073-89942016-09-01doi: 10.3390/sym8090091Alberto Alonso-IzquierdoJuan Mateos-Guilarte<![CDATA[Symmetry, Vol. 8, Pages 89: Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks]]>
http://www.mdpi.com/2073-8994/8/9/89
User interactions in online social networks (OSNs) enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal aware controlled information diffusion modeling in OSNs. Users interact more frequently when they are close to each other geographically, have similar behaviors, and fall into similar demographic categories. Considering these facts, we propose multicriteria-based social ties relationship and temporal-aware probabilistic information diffusion modeling for controlled information spread maximization in OSNs. The proposed social ties relationship modeling takes into account user spatial information, content trust, opinion similarity, and demographics. We suggest a ranking algorithm that considers the user ties strength with friends and friends-of-friends to rank users in OSNs and select highly influential injection nodes. These nodes are able to improve social content recommendations, minimize information diffusion time, and maximize information spread. Furthermore, the proposed temporal-aware probabilistic diffusion process categorizes the nodes and diffuses the recommended content to only those users who are highly influential and can enhance information dissemination. The experimental results show the effectiveness of the proposed scheme.Symmetry2016-09-0189Article10.3390/sym8090089892073-89942016-09-01doi: 10.3390/sym8090089Farman UllahSungchang Lee<![CDATA[Symmetry, Vol. 8, Pages 88: The Conformal Camera in Modeling Active Binocular Vision]]>
http://www.mdpi.com/2073-8994/8/9/88
Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system.Symmetry2016-08-3189Article10.3390/sym8090088882073-89942016-08-31doi: 10.3390/sym8090088Jacek Turski<![CDATA[Symmetry, Vol. 8, Pages 87: Weyl, Majorana and Dirac Fields from a Unified Perspective]]>
http://www.mdpi.com/2073-8994/8/9/87
A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian methods play no role in the present exposition, which covers several fundamental aspects of relativistic field theory, which are commonly not included in introductory courses when treating fermionic fields via the Dirac equation in the first place.Symmetry2016-08-3089Article10.3390/sym8090087872073-89942016-08-30doi: 10.3390/sym8090087Andreas Aste<![CDATA[Symmetry, Vol. 8, Pages 86: Facial Feature Movements Caused by Various Emotions: Differences According to Sex]]>
http://www.mdpi.com/2073-8994/8/9/86
Facial muscle micro movements for eight emotions were induced via visual and auditory stimuli and were verified according to sex. Thirty-one main facial features were chosen from the Kinect API out of 121 initially obtained facial features; the average change of pixel value was measured after image alignment. The proposed method is advantageous as it allows for comparisons. Facial micro-expressions are analyzed in real time using 31 facial feature points. The amount of micro-expressions for the various emotion stimuli was comparatively analyzed for differences according to sex. Men’s facial movements were similar for each emotion, whereas women’s facial movements were different for each emotion. The six feature positions were significantly different according to sex; in particular, the inner eyebrow of the right eye had a confidence level of p &lt; 0.01. Consequently, discriminative power showed that men’s ability to separate one emotion from the others was lower compared to women’s ability in terms of facial expression, despite men’s average movements being higher compared to women’s. Additionally, the asymmetric phenomena around the left eye region of women appeared more strongly in cases of positive emotions.Symmetry2016-08-3089Article10.3390/sym8090086862073-89942016-08-30doi: 10.3390/sym8090086Kun SuhYoonkyoung KimEui Lee<![CDATA[Symmetry, Vol. 8, Pages 85: A Survey of Public Key Infrastructure-Based Security for Mobile Communication Systems]]>
http://www.mdpi.com/2073-8994/8/9/85
Mobile communication security techniques are employed to guard the communication between the network entities. Mobile communication cellular systems have become one of the most important communication systems in recent times and are used by millions of people around the world. Since the 1990s, considerable efforts have been taken to improve both the communication and security features of the mobile communications systems. However, these improvements divide the mobile communications field into different generations according to the communication and security techniques such as A3, A5 and A8 algorithms for 2G-GSM cellular system, 3G-authentication and key agreement (AKA), evolved packet system-authentication and key agreement (EPS-AKA), and long term evolution-authentication and key agreement (LTE-AKA) algorithms for 3rd generation partnership project (3GPP) systems. Furthermore, these generations have many vulnerabilities, and huge security work is involved to solve such problems. Some of them are in the field of the public key cryptography (PKC) which requires a high computational cost and more network flexibility to be achieved. As such, the public key infrastructure (PKI) is more compatible with the modern generations due to the superior communications features. This paper surveys the latest proposed works on the security of GSM, CDMA, and LTE cellular systems using PKI. Firstly, we present the security issues for each generation of mobile communication systems, then we study and analyze the latest proposed schemes and give some comparisons. Finally, we introduce some new directions for the future scope. This paper classifies the mobile communication security schemes according to the techniques used for each cellular system and covers some of the PKI-based security techniques such as authentication, key agreement, and privacy preserving.Symmetry2016-08-2689Review10.3390/sym8090085852073-89942016-08-26doi: 10.3390/sym8090085Mohammed RamadanGuohong DuFagen LiChunxiang Xu<![CDATA[Symmetry, Vol. 8, Pages 84: The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton]]>
http://www.mdpi.com/2073-8994/8/9/84
This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.Symmetry2016-08-2589Article10.3390/sym8090084842073-89942016-08-25doi: 10.3390/sym8090084Oleg EvsutinAlexander ShelupanovRoman MeshcheryakovDmitry BondarenkoAngelika Rashchupkina<![CDATA[Symmetry, Vol. 8, Pages 83: Revisiting the Optical PT-Symmetric Dimer]]>
http://www.mdpi.com/2073-8994/8/9/83
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT -symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT -symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem.Symmetry2016-08-2489Review10.3390/sym8090083832073-89942016-08-24doi: 10.3390/sym8090083José Huerta MoralesJulio GuerreroServando López-AguayoBlas Rodríguez-Lara<![CDATA[Symmetry, Vol. 8, Pages 82: Decoration of the Truncated Tetrahedron—An Archimedean Polyhedron—To Produce a New Class of Convex Equilateral Polyhedra with Tetrahedral Symmetry]]>
http://www.mdpi.com/2073-8994/8/8/82
The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from a 6.6.6 tiling of hexagons and pasting them onto the full triangular faces of an icosahedron produces icosahedral fullerene cages. Here we show that pasting cutouts from a 6.6.6 tiling onto the full hexagonal and triangular faces of an Archimedean host polyhedron, the truncated tetrahedron, produces two series of tetrahedral (Td) fullerene cages. Cages in the first series have 28n2 vertices (n ≥ 1). Cages in the second (leapfrog) series have 3 × 28n2. We can transform all of the cages of the first series and the smallest cage of the second series into geometrically convex equilateral polyhedra. With tetrahedral (Td) symmetry, these new polyhedra constitute a new class of “convex equilateral polyhedra with polyhedral symmetry”. We also show that none of the other Archimedean polyhedra, six with octahedral symmetry and six with icosahedral, can host full-face cutouts from regular tilings to produce cages with the host’s polyhedral symmetry.Symmetry2016-08-2088Article10.3390/sym8080082822073-89942016-08-20doi: 10.3390/sym8080082Stan ScheinAlexander YehKris CoolsaetJames Gayed<![CDATA[Symmetry, Vol. 8, Pages 81: Cosmological Reflection of Particle Symmetry]]>
http://www.mdpi.com/2073-8994/8/8/81
The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review.Symmetry2016-08-2088Review10.3390/sym8080081812073-89942016-08-20doi: 10.3390/sym8080081Maxim Khlopov<![CDATA[Symmetry, Vol. 8, Pages 80: Superconducting Gap Symmetry of LaFeP(O,F) Observed by Impurity Doping Effect]]>
http://www.mdpi.com/2073-8994/8/8/80
We have investigated Mn, Co and Ni substitution effects on polycrystalline samples of LaFePO0.95F0.05 by resistivity and magnetoresistance measurements. In LaFe1-xMxPO0.95F0.05 (M = Mn, Co and Ni), the superconducting transition temperature (Tc) monotonously decreases with increasing the impurity doping level of x. There is a clear difference of Tc suppression rates among Mn, Co and Ni doping cases, and the decreasing rate of Tc by Mn doping as a magnetic impurity is larger than those by the nonmagnetic doping impurities (Co/Ni). This result indicates that in LaFePO0.95F0.05, Tc is rapidly suppressed by the pair-breaking effect of magnetic impurities, and the pairing symmetry is a full-gapped s-wave. In the nonmagnetic impurity-doped systems, the residual resistivity in the normal state has nearly the same value when Tc becomes zero. The residual resistivity value is almost consistent with the universal value of sheet resistance for two-dimensional superconductors, suggesting that Tc is suppressed by electron localization in Co/Ni-doped LaFePO0.95F0.05.Symmetry2016-08-1788Article10.3390/sym8080080802073-89942016-08-17doi: 10.3390/sym8080080Shigeki MiyasakaSinnosuke SuzukiSetsuko Tajima<![CDATA[Symmetry, Vol. 8, Pages 79: Modeling Bottom-Up Visual Attention Using Dihedral Group D4]]>
http://www.mdpi.com/2073-8994/8/8/79
In this paper, first, we briefly describe the dihedral group D 4 that serves as the basis for calculating saliency in our proposed model. Second, our saliency model makes two major changes in a latest state-of-the-art model known as group-based asymmetry. First, based on the properties of the dihedral group D 4 , we simplify the asymmetry calculations associated with the measurement of saliency. This results is an algorithm that reduces the number of calculations by at least half that makes it the fastest among the six best algorithms used in this research article. Second, in order to maximize the information across different chromatic and multi-resolution features, the color image space is de-correlated. We evaluate our algorithm against 10 state-of-the-art saliency models. Our results show that by using optimal parameters for a given dataset, our proposed model can outperform the best saliency algorithm in the literature. However, as the differences among the (few) best saliency models are small, we would like to suggest that our proposed model is among the best and the fastest among the best. Finally, as a part of future work, we suggest that our proposed approach on saliency can be extended to include three-dimensional image data.Symmetry2016-08-1588Article10.3390/sym8080079792073-89942016-08-15doi: 10.3390/sym8080079Puneet Sharma<![CDATA[Symmetry, Vol. 8, Pages 78: Automatic Frequency Identification under Sample Loss in Sinusoidal Pulse Width Modulation Signals Using an Iterative Autocorrelation Algorithm]]>
http://www.mdpi.com/2073-8994/8/8/78
In this work, we present a simple algorithm to calculate automatically the Fourier spectrum of a Sinusoidal Pulse Width Modulation Signal (SPWM). Modulated voltage signals of this kind are used in industry by speed drives to vary the speed of alternating current motors while maintaining a smooth torque. Nevertheless, the SPWM technique produces undesired harmonics, which yield stator heating and power losses. By monitoring these signals without human interaction, it is possible to identify the harmonic content of SPWM signals in a fast and continuous manner. The algorithm is based in the autocorrelation function, commonly used in radar and voice signal processing. Taking advantage of the symmetry properties of the autocorrelation, the algorithm is capable of estimating half of the period of the fundamental frequency; thus, allowing one to estimate the necessary number of samples to produce an accurate Fourier spectrum. To deal with the loss of samples, i.e., the scan backlog, the algorithm iteratively acquires and trims the discrete sequence of samples until the required number of samples reaches a stable value. The simulation shows that the algorithm is not affected by either the magnitude of the switching pulses or the acquisition noise.Symmetry2016-08-1088Article10.3390/sym8080078782073-89942016-08-10doi: 10.3390/sym8080078Alejandro SaidYasser DavizónPiero Espino-RománRoberto Rodríguez-SaidCarlos Hernández-Santos<![CDATA[Symmetry, Vol. 8, Pages 77: The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements]]>
http://www.mdpi.com/2073-8994/8/8/77
This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to tailor a spherical distribution via orthogonal polynomials to better comply with kurtosis requirements, we provide operational conditions for the positiveness of the resulting multivariate Gram–Charlier-like expansion, together with its kurtosis range. Finally, the approach proposed here is applied to some selected spherical distributions.Symmetry2016-08-0588Article10.3390/sym8080077772073-89942016-08-05doi: 10.3390/sym8080077Luca BagnatoMario FalivaMaria Zoia<![CDATA[Symmetry, Vol. 8, Pages 76: Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras]]>
http://www.mdpi.com/2073-8994/8/8/76
We study almost contact metric structures on 5-dimensional nilpotent Lie algebras and investigate the class of left invariant almost contact metric structures on corresponding Lie groups. We determine certain classes that a five-dimensional nilpotent Lie group can not be equipped with.Symmetry2016-08-0488Article10.3390/sym8080076762073-89942016-08-04doi: 10.3390/sym8080076Nülifer ÖzdemirMehmet SolgunŞirin Aktay<![CDATA[Symmetry, Vol. 8, Pages 74: M&E-NetPay: A Micropayment System for Mobile and Electronic Commerce]]>
http://www.mdpi.com/2073-8994/8/8/74
As an increasing number of people purchase goods and services online, micropayment systems are becoming particularly important for mobile and electronic commerce. We have designed and developed such a system called M&amp;E-NetPay (Mobile and Electronic NetPay). With open interoperability and mobility, M&amp;E-NetPay uses web services to connect brokers and vendors, providing secure, flexible and reliable credit services over the Internet. In particular, M&amp;E-NetPay makes use of a secure, inexpensive and debit-based off-line protocol that allows vendors to interact only with customers, after validating coins. The design of the architecture and protocol of M&amp;E-NetPay are presented, together with the implementation of its prototype in ringtone and wallpaper sites. To validate our system, we have conducted its evaluations on performance, usability and heuristics. Furthermore, we compare our system to the CORBA-based (Common Object Request Broker Architecture) off-line micro-payment systems. The results have demonstrated that M&amp;E-NetPay outperforms the .NET-based M&amp;E-NetPay system in terms of performance and user satisfaction.Symmetry2016-08-0388Article10.3390/sym8080074742073-89942016-08-03doi: 10.3390/sym8080074Xiaodi HuangJinsong BaoXiaoling DaiEdwin SinghWeidong HuangChangqin Huang<![CDATA[Symmetry, Vol. 8, Pages 75: Fuzzy System-Based Face Detection Robust to In-Plane Rotation Based on Symmetrical Characteristics of a Face]]>
http://www.mdpi.com/2073-8994/8/8/75
As face recognition technology has developed, it has become widely used in various applications such as door access control, intelligent surveillance, and mobile phone security. One of its applications is its adoption in TV environments to supply viewers with intelligent services and high convenience. In a TV environment, the in-plane rotation of a viewer’s face frequently occurs because he or she may decide to watch the TV from a lying position, which degrades the accuracy of the face recognition. Nevertheless, there has been little previous research to deal with this problem. Therefore, we propose a new fuzzy system–based face detection algorithm that is robust to in-plane rotation based on the symmetrical characteristics of a face. Experimental results on two databases with one open database show that our method outperforms previous methods.Symmetry2016-08-0388Article10.3390/sym8080075752073-89942016-08-03doi: 10.3390/sym8080075Hyung HongWon LeeYeong KimKi KimDat NguyenKang Park<![CDATA[Symmetry, Vol. 8, Pages 73: Broken versus Non-Broken Time Reversal Symmetry: Irreversibility and Response]]>
http://www.mdpi.com/2073-8994/8/8/73
We review some approaches to macroscopic irreversibility from reversible microscopic dynamics, introducing the contribution of time dependent perturbations within the framework of recent developments in non-equilibrium statistical physics. We show that situations commonly assumed to violate the time reversal symmetry (presence of magnetic fields, rotating reference frames, and some time dependent perturbations) in reality do not violate this symmetry, and can be treated with standard theories and within standard experimental protocols.Symmetry2016-07-2988Article10.3390/sym8080073732073-89942016-07-29doi: 10.3390/sym8080073Sara Dal CengioLamberto Rondoni<![CDATA[Symmetry, Vol. 8, Pages 72: Small-Amplitude Nonlinear Modes under the Combined Effect of the Parabolic Potential, Nonlocality and PT Symmetry]]>
http://www.mdpi.com/2073-8994/8/8/72
We consider nonlinear modes of the nonlinear Schrödinger equation with nonlocal nonlinearities and and PT -symmetric parabolic potential. We show that there exists a set of continuous families of nonlinear modes and study their linear stability in the limit of small nonlinearity. It is demonstrated that either PT symmetry or the nonlocality can be used to manage the stability of the small-amplitude nonlinear modes. The stability properties are also found to depend on the particular shape of the nonlocal kernel. Numerical simulations show that the stability results remain valid not only for the infinitesimally small nonlinear modes, but also for the modes of finite amplitude.Symmetry2016-07-2888Article10.3390/sym8080072722073-89942016-07-28doi: 10.3390/sym8080072Dmitry ZezyulinVladimir Konotop<![CDATA[Symmetry, Vol. 8, Pages 71: SCPL: A Social Cooperative Programming Language to Automate Cooperative Processes in (A)Symmetric Social Networks]]>
http://www.mdpi.com/2073-8994/8/8/71
In recent years, the increasing use of social networks and applications—especially those used in an asymmetric way—has significantly changed the business processes in many organizations. These applications provide new cooperative ways of performing these processes by taking advantage of the interactions among users. However, the high number of these applications has led to a lack of automation in their interactions and, thus, the need of manually connecting to these networks to perform recurrent and repetitive tasks. In order to automate these operations, this paper presents SCPL, a Domain Specific Language (DSL) that enables connectivity among different social networks and applications and provides a way to automate their management. The main contribution of this paper is showing how SCPL can be used to specify collaborative tasks using symmetric and asymmetric social networks in a transparent way.Symmetry2016-07-2888Article10.3390/sym8080071712073-89942016-07-28doi: 10.3390/sym8080071José ConejeroFernando Sánchez-FigueroaRoberto Rodríguez-EcheverríaJuan Preciado<![CDATA[Symmetry, Vol. 8, Pages 70: Unveiling the Dynamics of the Universe]]>
http://www.mdpi.com/2073-8994/8/8/70
We explore the dynamics and evolution of the Universe at early and late times, focusing on both dark energy and extended gravity models and their astrophysical and cosmological consequences. Modified theories of gravity not only provide an alternative explanation for the recent expansion history of the universe, but they also offer a paradigm fundamentally distinct from the simplest dark energy models of cosmic acceleration. In this review, we perform a detailed theoretical and phenomenological analysis of different modified gravity models and investigate their consistency. We also consider the cosmological implications of well motivated physical models of the early universe with a particular emphasis on inflation and topological defects. Astrophysical and cosmological tests over a wide range of scales, from the solar system to the observable horizon, severely restrict the allowed models of the Universe. Here, we review several observational probes—including gravitational lensing, galaxy clusters, cosmic microwave background temperature and polarization, supernova and baryon acoustic oscillations measurements—and their relevance in constraining our cosmological description of the Universe.Symmetry2016-07-2688Review10.3390/sym8080070702073-89942016-07-26doi: 10.3390/sym8080070Pedro AvelinoTiago BarreiroC. CarvalhoAntonio da SilvaFrancisco LoboPrado Martín-MorunoJosé MimosoNelson NunesDiego Rubiera-GarcíaDiego Sáez-GómezLara SousaIsmael TerenoArlindo Trindade<![CDATA[Symmetry, Vol. 8, Pages 69: A Logistic Based Mathematical Model to Optimize Duplicate Elimination Ratio in Content Defined Chunking Based Big Data Storage System]]>
http://www.mdpi.com/2073-8994/8/7/69
Deduplication is an efficient data reduction technique, and it is used to mitigate the problem of huge data volume in big data storage systems. Content defined chunking (CDC) is the most widely used algorithm in deduplication systems. The expected chunk size is an important parameter of CDC, and it influences the duplicate elimination ratio (DER) significantly. We collected two realistic datasets to perform an experiment. The experimental results showed that the current approach of setting the expected chunk size to 4 KB or 8 KB empirically cannot optimize DER. Therefore, we present a logistic based mathematical model to reveal the hidden relationship between the expected chunk size and the DER. This model provides a theoretical basis for optimizing DER by setting the expected chunk size reasonably. We used the collected datasets to verify this model. The experimental results showed that the R2 values, which describe the goodness of fit, are above 0.9, validating the correctness of this mathematic model. Based on the DER model, we discussed how to make DER close to the optimum by setting the expected chunk size reasonably.Symmetry2016-07-2187Article10.3390/sym8070069692073-89942016-07-21doi: 10.3390/sym8070069Longxiang WangXiaoshe DongXingjun ZhangFuliang GuoYinfeng WangWeifeng Gong<![CDATA[Symmetry, Vol. 8, Pages 68: Adaptive Image Matching Using Discrimination of Deformable Objects]]>
http://www.mdpi.com/2073-8994/8/7/68
We propose an efficient image-matching method for deformable-object image matching using discrimination of deformable objects and geometric similarity clustering between feature-matching pairs. A deformable transformation maintains a particular form in the whole image, despite local and irregular deformations. Therefore, the matching information is statistically analyzed to calculate the possibility of deformable transformations, and the images can be identified using the proposed method. In addition, a method for matching deformable object images is proposed, which clusters matching pairs with similar types of geometric deformations. Discrimination of deformable images showed about 90% accuracy, and the proposed deformable image-matching method showed an average 89% success rate and 91% accuracy with various transformations. Therefore, the proposed method robustly matches images, even with various kinds of deformation that can occur in them.Symmetry2016-07-2187Article10.3390/sym8070068682073-89942016-07-21doi: 10.3390/sym8070068Insu WonJaehyup JeongHunjun YangJangwoo KwonDongseok Jeong<![CDATA[Symmetry, Vol. 8, Pages 67: Computing the Surface Area of Three-Dimensional Scanned Human Data]]>
http://www.mdpi.com/2073-8994/8/7/67
An efficient surface area evaluation method is introduced by using smooth surface reconstruction for three-dimensional scanned human body data. Surface area evaluations for various body parts are compared with the results from the traditional alginate-based method, and quite high similarity between the two results is obtained. We expect that our surface area evaluation method can be an alternative to measuring surface area by the cumbersome alginate method.Symmetry2016-07-2087Article10.3390/sym8070067672073-89942016-07-20doi: 10.3390/sym8070067Seung-Hyun YoonJieun Lee<![CDATA[Symmetry, Vol. 8, Pages 66: Relationship between Fractal Dimension and Spectral Scaling Decay Rate in Computer-Generated Fractals]]>
http://www.mdpi.com/2073-8994/8/7/66
Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D) and power spectrum decay rate (β). Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.Symmetry2016-07-1987Article10.3390/sym8070066662073-89942016-07-19doi: 10.3390/sym8070066Alexander BiesCooper BoydstonRichard TaylorMargaret Sereno<![CDATA[Symmetry, Vol. 8, Pages 65: A Model-Driven Framework to Develop Personalized Health Monitoring]]>
http://www.mdpi.com/2073-8994/8/7/65
Both distributed healthcare systems and the Internet of Things (IoT) are currently hot topics. The latter is a new computing paradigm to enable advanced capabilities in engineering various applications, including those for healthcare. For such systems, the core social requirement is the privacy/security of the patient information along with the technical requirements (e.g., energy consumption) and capabilities for adaptability and personalization. Typically, the functionality of the systems is predefined by the patient’s data collected using sensor networks along with medical instrumentation; then, the data is transferred through the Internet for treatment and decision-making. Therefore, systems creation is indeed challenging. In this paper, we propose a model-driven framework to develop the IoT-based prototype and its reference architecture for personalized health monitoring (PHM) applications. The framework contains a multi-layered structure with feature-based modeling and feature model transformations at the top and the application software generation at the bottom. We have validated the framework using available tools and developed an experimental PHM to test some aspects of the functionality of the reference architecture in real time. The main contribution of the paper is the development of the model-driven computational framework with emphasis on the synergistic effect of security and energy issues.Symmetry2016-07-1887Article10.3390/sym8070065652073-89942016-07-18doi: 10.3390/sym8070065Algimantas VenčkauskasVytautas ŠtuikysJevgenijus ToldinasNerijus Jusas<![CDATA[Symmetry, Vol. 8, Pages 64: A Modified GrabCut Using a Clustering Technique to Reduce Image Noise]]>
http://www.mdpi.com/2073-8994/8/7/64
In this paper, a modified GrabCut algorithm is proposed using a clustering technique to reduce image noise. GrabCut is an image segmentation method based on GraphCut starting with a user-specified bounding box around the object to be segmented. In the modified version, the original image is filtered using the median filter to reduce noise and then the quantized image using K-means algorithm is used for the normal GrabCut method for object segmentation. This new process showed that it improved the object segmentation performance a lot and the extract segmentation result compared to the standard method.Symmetry2016-07-1487Article10.3390/sym8070064642073-89942016-07-14doi: 10.3390/sym8070064GangSeong LeeSangHun LeeGaOn KimJongHun ParkYoungSoo Park<![CDATA[Symmetry, Vol. 8, Pages 63: Cubature Formulas of Multivariate Polynomials Arising from Symmetric Orbit Functions]]>
http://www.mdpi.com/2073-8994/8/7/63
The paper develops applications of symmetric orbit functions, known from irreducible representations of simple Lie groups, in numerical analysis. It is shown that these functions have remarkable properties which yield to cubature formulas, approximating a weighted integral of any function by a weighted finite sum of function values, in connection with any simple Lie group. The cubature formulas are specialized for simple Lie groups of rank two. An optimal approximation of any function by multivariate polynomials arising from symmetric orbit functions is discussed.Symmetry2016-07-1487Article10.3390/sym8070063632073-89942016-07-14doi: 10.3390/sym8070063Jiří HrivnákLenka MotlochováJiří Patera<![CDATA[Symmetry, Vol. 8, Pages 62: Image Region Duplication Forgery Detection Based on Angular Radial Partitioning and Harris Key-Points]]>
http://www.mdpi.com/2073-8994/8/7/62
Region duplication forgery where a part of the image itself is copied and pasted onto a different part of the same image grid is becoming more popular in image manipulation. The forgers often apply geometric transformations such as rotation and scaling operations to make the forgery imperceptible. In this study, an image region duplication forgery detection algorithm is proposed based on the angular radial partitioning and Harris key-points. Two standard databases have been used: image data manipulation and MICC-F220 (Media Integration and Communication Center– of the University of Florence) for experimentation. Experiment results demonstrate that the proposed technique can detect rotated regions in multiples of 30 degrees and can detect region duplication with different scaling factors from 0.8, to 1.2. More experimental results are presented to confirm the effectiveness of detecting region duplication that has undergone other changes, such as Gaussian noise, and JPEG compression.Symmetry2016-07-1387Article10.3390/sym8070062622073-89942016-07-13doi: 10.3390/sym8070062Diaa UliyanHamid JalabAinuddin Abdul WahabSomayeh Sadeghi<![CDATA[Symmetry, Vol. 8, Pages 61: Stochastic Cooperative Decision Approach for Studying the Symmetric Behavior of People in Wireless Indoor Location Systems]]>
http://www.mdpi.com/2073-8994/8/7/61
Nowadays, several wireless location systems have been developed in the research world. The goal of these systems has always been to find the greatest accuracy as possible. However, if every node takes data from the environment, we can gather a lot of information, which may help us understand what is happening around our network in a cooperative way. In order to develop this cooperative location and tracking system, we have implemented a sensor network to capture data from user devices. From this captured data we have observed a symmetry behavior in people’s movements at a specific site. By using these data and the symmetry feature, we have developed a statistical cooperative approach to predict the new user’s location. The system has been tested in a real environment, evaluating the next location predicted by the system and comparing it with the next location in the real track, thus getting satisfactory results. Better results have been obtained when the stochastic cooperative approach uses the transition matrix with symmetry.Symmetry2016-07-1387Article10.3390/sym8070061612073-89942016-07-13doi: 10.3390/sym8070061Jesús TomásMiguel Garcia-PinedaAlejandro CánovasJaime Lloret<![CDATA[Symmetry, Vol. 8, Pages 60: Massless Majorana-Like Charged Carriers in Two-Dimensional Semimetals]]>
http://www.mdpi.com/2073-8994/8/7/60
The band structure of strongly correlated two-dimensional (2D) semimetal systems is found to be significantly affected by the spin-orbit coupling (SOC), resulting in SOC-induced Fermi surfaces. Dirac, Weyl and Majorana representations are used for the description of different semimetals, though the band structures of all these systems are very similar. We develop a theoretical approach to the band theory of two-dimensional semimetals within the Dirac–Hartree–Fock self-consistent field approximation. It reveals partially breaking symmetry of the Dirac cone affected by quasi-relativistic exchange interactions for 2D crystals with hexagonal symmetry. Fermi velocity becomes an operator within this approach, and elementary excitations have been calculated in the tight-binding approximation when taking into account the exchange interaction of π ( p z ) -electron with its three nearest π ( p z ) -electrons. These excitations are described by the massless Majorana equation instead of the Dirac one. The squared equation for this field is of the Klein–Gordon–Fock type. Such a feature of the band structure of 2D semimetals as the appearance of four pairs of nodes is shown to be described naturally within the developed formalism. Numerical simulation of band structure has been performed for the proposed 2D-model of graphene and a monolayer of Pb atoms.Symmetry2016-07-0887Article10.3390/sym8070060602073-89942016-07-08doi: 10.3390/sym8070060Halina GrushevskayaGeorge Krylov<![CDATA[Symmetry, Vol. 8, Pages 59: Breathers in Hamiltonian PT -Symmetric Chains of Coupled Pendula under a Resonant Periodic Force]]>
http://www.mdpi.com/2073-8994/8/7/59
We derive a Hamiltonian version of the PT -symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and spectral stability of breathers (time-periodic solutions localized in the lattice) supported near one pair of coupled pendula. Orbital stability or instability of breathers is proved in a subset of the existence region.Symmetry2016-07-0887Article10.3390/sym8070059592073-89942016-07-08doi: 10.3390/sym8070059Alexander ChernyavskyDmitry Pelinovsky<![CDATA[Symmetry, Vol. 8, Pages 58: Power Spectral Deviation-Based Voice Activity Detection Incorporating Teager Energy for Speech Enhancement]]>
http://www.mdpi.com/2073-8994/8/7/58
In this paper, we propose a robust voice activity detection (VAD) algorithm to effectively distinguish speech from non-speech in various noisy environments. The proposed VAD utilizes power spectral deviation (PSD), using Teager energy (TE) to provide a better representation of the PSD, resulting in improved decision performance for speech segments. In addition, the TE-based likelihood ratio and speech absence probability are derived in each frame to modify the PSD for further VAD. We evaluate the performance of the proposed VAD algorithm by objective testing in various environments and obtain better results that those attained by of the conventional methods.Symmetry2016-07-0687Article10.3390/sym8070058582073-89942016-07-06doi: 10.3390/sym8070058Sang-Kyun KimSang-Ick KangYoung-Jin ParkSanghyuk LeeSangmin Lee<![CDATA[Symmetry, Vol. 8, Pages 57: k-Essence Non-Minimally Coupled with Gauss–Bonnet Invariant for Inflation]]>
http://www.mdpi.com/2073-8994/8/7/57
In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss–Bonnet invariant. Examples of canonical scalar field and k-essence to support the early-time acceleration are considered. The formalism to calculate the perturbations in a Friedmann–Robertson–Walker (FRW) universe and to derive the spectral index and the tensor-to-scalar ratio is furnished.Symmetry2016-06-2887Article10.3390/sym8070057572073-89942016-06-28doi: 10.3390/sym8070057Ratbay MyrzakulovLorenzo Sebastiani<![CDATA[Symmetry, Vol. 8, Pages 56: Electrodynamics of a Cosmic Dark Fluid]]>
http://www.mdpi.com/2073-8994/8/7/56
Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium-type representation of the Dark Fluid allows us to involve in its analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar element); respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of 10 models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extended; applications are considered for cosmology and space-times with spherical and pp-wave symmetries. In these applications we focused the attention on three main electromagnetic phenomena induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric Clusters; second, generation of anomalous electromagnetic responses; third, formation of Dark Epochs in the Universe history.Symmetry2016-06-2887Article10.3390/sym8070056562073-89942016-06-28doi: 10.3390/sym8070056Alexander Balakin<![CDATA[Symmetry, Vol. 8, Pages 55: Entangled Harmonic Oscillators and Space-Time Entanglement]]>
http://www.mdpi.com/2073-8994/8/7/55
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of the O ( 3 , 2 ) de Sitter group containing two O ( 3 , 1 ) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the S p ( 4 ) group, which serves as the basic language for two-mode squeezed states. Since the S p ( 4 ) symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.Symmetry2016-06-2887Article10.3390/sym8070055552073-89942016-06-28doi: 10.3390/sym8070055Sibel BaşkalYoung KimMarilyn Noz<![CDATA[Symmetry, Vol. 8, Pages 54: Top-N Recommender Systems Using Genetic Algorithm-Based Visual-Clustering Methods]]>
http://www.mdpi.com/2073-8994/8/7/54
The drastic increase of websites is one of the causes behind the recent information overload on the internet. A recommender system (RS) has been developed for helping users filter information. However, the cold-start and sparsity problems lead to low performance of the RS. In this paper, we propose methods including the visual-clustering recommendation (VCR) method, the hybrid between the VCR and user-based methods, and the hybrid between the VCR and item-based methods. The user-item clustering is based on the genetic algorithm (GA). The recommendation performance of the proposed methods was compared with that of traditional methods. The results showed that the GA-based visual clustering could properly cluster user-item binary images. They also demonstrated that the proposed recommendation methods were more efficient than the traditional methods. The proposed VCR2 method yielded an F1 score roughly three times higher than the traditional approaches.Symmetry2016-06-2487Article10.3390/sym8070054542073-89942016-06-24doi: 10.3390/sym8070054Ukrit MarungNipon Theera-UmponSansanee Auephanwiriyakul<![CDATA[Symmetry, Vol. 8, Pages 53: Three New Classes of Solvable N-Body Problems of Goldfish Type with Many Arbitrary Coupling Constants]]>
http://www.mdpi.com/2073-8994/8/7/53
Three new classes of N-body problems of goldfish type are identified, with N an arbitrary positive integer ( N ≥ 2 ). These models are characterized by nonlinear Newtonian (“accelerations equal forces”) equations of motion describing N equal point-particles moving in the complex z-plane. These highly nonlinear equations feature many arbitrary coupling constants, yet they can be solved by algebraic operations. Some of these N-body problems are isochronous, their generic solutions being all completely periodic with an overall period T independent of the initial data (but quite a few of these solutions are actually periodic with smaller periods T / p with p a positive integer); other models are isochronous for an open region of initial data, while the motions for other initial data are not periodic, featuring instead scattering phenomena with some of the particles incoming from, or escaping to, infinity in the remote past or future.Symmetry2016-06-2487Article10.3390/sym8070053532073-89942016-06-24doi: 10.3390/sym8070053Francesco Calogero<![CDATA[Symmetry, Vol. 8, Pages 52: Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points]]>
http://www.mdpi.com/2073-8994/8/6/52
For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato’s name of an “exceptional point”, t c r i t i c a l = t ( E P ) . In the majority of conventional applications the exceptional point (EP) values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t ( E P ) become real. These values are interpreted as “instants of a catastrophe”, be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology.Symmetry2016-06-2086Article10.3390/sym8060052522073-89942016-06-20doi: 10.3390/sym8060052Miloslav Znojil<![CDATA[Symmetry, Vol. 8, Pages 51: On Classification of Symmetry Reductions for the Eikonal Equation]]>
http://www.mdpi.com/2073-8994/8/6/51
We study the relationship between the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P ( 1 , 4 ) and the types of symmetry reduction of the eikonal equation to ordinary differential equations (ODEs).Symmetry2016-06-1786Article10.3390/sym8060051512073-89942016-06-17doi: 10.3390/sym8060051Vasyl FedorchukVolodymyr Fedorchuk<![CDATA[Symmetry, Vol. 8, Pages 50: Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis]]>
http://www.mdpi.com/2073-8994/8/6/50
The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example) and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions) for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration) for a wide range of values of the model parameters.Symmetry2016-06-1686Article10.3390/sym8060050502073-89942016-06-16doi: 10.3390/sym8060050Roman ChernihaKateryna GozakJacek Waniewski<![CDATA[Symmetry, Vol. 8, Pages 48: Optimal Face-Iris Multimodal Fusion Scheme]]>
http://www.mdpi.com/2073-8994/8/6/48
Multimodal biometric systems are considered a way to minimize the limitations raised by single traits. This paper proposes new schemes based on score level, feature level and decision level fusion to efficiently fuse face and iris modalities. Log-Gabor transformation is applied as the feature extraction method on face and iris modalities. At each level of fusion, different schemes are proposed to improve the recognition performance and, finally, a combination of schemes at different fusion levels constructs an optimized and robust scheme. In this study, CASIA Iris Distance database is used to examine the robustness of all unimodal and multimodal schemes. In addition, Backtracking Search Algorithm (BSA), a novel population-based iterative evolutionary algorithm, is applied to improve the recognition accuracy of schemes by reducing the number of features and selecting the optimized weights for feature level and score level fusion, respectively. Experimental results on verification rates demonstrate a significant improvement of proposed fusion schemes over unimodal and multimodal fusion methods.Symmetry2016-06-1586Article10.3390/sym8060048482073-89942016-06-15doi: 10.3390/sym8060048Omid SharifiMaryam Eskandari<![CDATA[Symmetry, Vol. 8, Pages 49: Neutrino Signals in Electron-Capture Storage-Ring Experiments]]>
http://www.mdpi.com/2073-8994/8/6/49
Neutrino signals in electron-capture decays of hydrogen-like parent ions P in storage-ring experiments at GSI are reconsidered, with special emphasis placed on the storage-ring quasi-circular motion of the daughter ions D in two-body decays P → D + ν e . It is argued that, to the extent that daughter ions are detected, these detection rates might exhibit modulations with periods of order seconds, similar to those reported in the GSI storage-ring experiments for two-body decay rates. New dedicated experiments in storage rings, or using traps, could explore these modulations.Symmetry2016-06-1586Article10.3390/sym8060049492073-89942016-06-15doi: 10.3390/sym8060049Avraham Gal<![CDATA[Symmetry, Vol. 8, Pages 47: A Data Mining Approach for Cardiovascular Disease Diagnosis Using Heart Rate Variability and Images of Carotid Arteries]]>
http://www.mdpi.com/2073-8994/8/6/47
In this paper, we proposed not only an extraction methodology of multiple feature vectors from ultrasound images for carotid arteries (CAs) and heart rate variability (HRV) of electrocardiogram signal, but also a suitable and reliable prediction model useful in the diagnosis of cardiovascular disease (CVD). For inventing the multiple feature vectors, we extract a candidate feature vector through image processing and measurement of the thickness of carotid intima-media (IMT). As a complementary way, the linear and/or nonlinear feature vectors are also extracted from HRV, a main index for cardiac disorder. The significance of the multiple feature vectors is tested with several machine learning methods, namely Neural Networks, Support Vector Machine (SVM), Classification based on Multiple Association Rule (CMAR), Decision tree induction and Bayesian classifier. As a result, multiple feature vectors extracted from both CAs and HRV (CA+HRV) showed higher accuracy than the separative feature vectors of CAs and HRV. Furthermore, the SVM and CMAR showed about 89.51% and 89.46%, respectively, in terms of diagnosing accuracy rate after evaluating the diagnosis or prediction methods using the finally chosen multiple feature vectors. Therefore, the multiple feature vectors devised in this paper can be effective diagnostic indicators of CVD. In addition, the feature vector analysis and prediction techniques are expected to be helpful tools in the decisions of cardiologists.Symmetry2016-06-1386Article10.3390/sym8060047472073-89942016-06-13doi: 10.3390/sym8060047Hyeongsoo KimMusa IshagMinghao PiaoTaeil KwonKeun Ryu<![CDATA[Symmetry, Vol. 8, Pages 46: Coherent States of Harmonic and Reversed Harmonic Oscillator]]>
http://www.mdpi.com/2073-8994/8/6/46
A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of solutions is derived with a time-dependent width parameter. The width of the corresponding probability density fluctuates, or "breathes" periodically with the oscillator frequency. In the case of the RO, one also obtains normalized wave packets which, however, show diffusion through exponential broadening with time. At the initial time, the integration constants give rise to complete sets of coherent states in the three cases considered. The results are applicable to the quantum mechanics of the Kepler-Coulomb problem when transformed to the model of a four-dimensional harmonic oscillator with a constraint. In the classical limit, as was shown recently, the wave packets of the RO basis generate the hyperbolic Kepler orbits, and, by means of analytic continuation, the elliptic orbits are also obtained quantum mechanically.Symmetry2016-06-1386Article10.3390/sym8060046462073-89942016-06-13doi: 10.3390/sym8060046Alexander Rauh<![CDATA[Symmetry, Vol. 8, Pages 45: Fluctuating Charge Order: A Universal Phenomenon in Unconventional Superconductivity?]]>
http://www.mdpi.com/2073-8994/8/6/45
Unconventional superconductors are characterized by various competing ordering phenomena in the normal state, such as antiferromagnetism, charge order, orbital order or nematicity. According to a widespread view, antiferromagnetic fluctuations are the dominant ordering phenomenon in cuprates and Fe based superconductors and are responsible for electron pairing. In contrast, charge order is believed to be subdominant and compete with superconductivity. Here, we argue that fluctuating charge order in the (0,π) direction is a feature shared by the cuprates and the Fe based superconductors alike. Recent data and theoretical models suggest that superconductivity is brought about by charge order excitations independently from spin fluctuations. Thus, quantum fluctuations of charge order may provide an alternative to spin fluctuations as a mechanism of electron pairing in unconventional superconductors.Symmetry2016-06-1086Article10.3390/sym8060045452073-89942016-06-10doi: 10.3390/sym8060045Erminald BertelAlexander Menzel<![CDATA[Symmetry, Vol. 8, Pages 44: On a Reduction Formula for a Kind of Double q-Integrals]]>
http://www.mdpi.com/2073-8994/8/6/44
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey–Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah–Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey–Wilson integral formula.Symmetry2016-06-0886Article10.3390/sym8060044442073-89942016-06-08doi: 10.3390/sym8060044Zhi-Guo Liu<![CDATA[Symmetry, Vol. 8, Pages 43: Investigating the Performance of a Fractal Ultrasonic Transducer Under Varying System Conditions]]>
http://www.mdpi.com/2073-8994/8/6/43
As applications become more widespread there is an ever-increasing need to improve the accuracy of ultrasound transducers, in order to detect at much finer resolutions. In comparison with naturally occurring ultrasound systems the man-made systems have much poorer accuracy, and the scope for improvement has somewhat plateaued as existing transducer designs have been iteratively improved over many years. The desire to bridge the gap between the man-made and naturally occurring systems has led to recent investigation of transducers with a more complex geometry, in order to replicate the complex structure of the natural systems. These transducers have structures representing fractal geometries, and these have been shown to be capable of delivering improved performance in comparison with standard transducer designs. This paper undertakes a detailed investigation of the comparative performance of a standard transducer design, and a transducer based on a fractal geometry. By considering how these performances vary with respect to the key system parameters, a robust assessment of the fractal transducer performance is provided.Symmetry2016-06-0686Article10.3390/sym8060043432073-89942016-06-06doi: 10.3390/sym8060043Euan BarlowEbrahem AlgehyneAnthony Mulholland<![CDATA[Symmetry, Vol. 8, Pages 42: Low Scale Saturation of Effective NN Interactions and Their Symmetries]]>
http://www.mdpi.com/2073-8994/8/6/42
The Skyrme force parameters can be uniquely determined by coarse graining the Nucleon-Nucleon (NN) interactions at a characteristic momentum scale. We show how exact V lowk potentials to second order in momenta are saturated with physical NN scattering threshold parameters at Center of Mass (CM) cut-off scales of about Λ = 250 MeV for the S-waves and Λ = 100 MeV for the P-waves. The pattern of Wigner and Serber symmetries unveiled previously and suggested by Quantum Chromodynamics (QCD) large N c contracted symmetry emerges at these scales.Symmetry2016-06-0186Article10.3390/sym8060042422073-89942016-06-01doi: 10.3390/sym8060042Enrique Ruiz Arriola<![CDATA[Symmetry, Vol. 8, Pages 41: Hybrid Data Hiding Scheme Using Right-Most Digit Replacement and Adaptive Least Significant Bit for Digital Images]]>
http://www.mdpi.com/2073-8994/8/6/41
The goal of image steganographic methods considers three main key issues: high embedding capacity, good visual symmetry/quality, and security. In this paper, a hybrid data hiding method combining the right-most digit replacement (RMDR) with an adaptive least significant bit (ALSB) is proposed to provide not only high embedding capacity but also maintain a good visual symmetry. The cover-image is divided into lower texture (symmetry patterns) and higher texture (asymmetry patterns) areas and these textures determine the selection of RMDR and ALSB methods, respectively, according to pixel symmetry. This paper has three major contributions. First, the proposed hybrid method enhanced the embedding capacity due to efficient ALSB utilization in the higher texture areas of cover images. Second, the proposed hybrid method maintains the high visual quality because RMDR has the closest selection process to generate the symmetry between stego and cover pixels. Finally, the proposed hybrid method is secure against statistical regular or singular (RS) steganalysis and pixel difference histogram steganalysis because RMDR is capable of evading the risk of RS detection attacks due to pixel digits replacement instead of bits. Extensive experimental tests (over 1500+ cover images) are conducted with recent least significant bit (LSB)-based hybrid methods and it is demonstrated that the proposed hybrid method has a high embedding capacity (800,019 bits) while maintaining good visual symmetry (39.00% peak signal-to-noise ratio (PSNR)).Symmetry2016-05-3186Article10.3390/sym8060041412073-89942016-05-31doi: 10.3390/sym8060041Mehdi HussainAinuddin Abdul WahabNoman JavedKi-Hyun Jung<![CDATA[Symmetry, Vol. 8, Pages 38: On Solutions for Linear and Nonlinear Schrödinger Equations with Variable Coefficients: A Computational Approach]]>
http://www.mdpi.com/2073-8994/8/6/38
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the inhomogeneous paraxial wave equation by the Crank-Nicolson scheme with analytical solutions found using Riccati systems. These solutions include oscillating laser beams and Laguerre and Gaussian beams.Symmetry2016-05-2886Article10.3390/sym8060038382073-89942016-05-28doi: 10.3390/sym8060038Gabriel AmadorKiara ColonNathalie LunaGerardo MercadoEnrique PereiraErwin Suazo<![CDATA[Symmetry, Vol. 8, Pages 40: A Methodology and Tool for Investigation of Artifacts Left by the BitTorrent Client]]>
http://www.mdpi.com/2073-8994/8/6/40
The BitTorrent client application is a popular utility for sharing large files over the Internet. Sometimes, this powerful utility is used to commit cybercrimes, like sharing of illegal material or illegal sharing of legal material. In order to help forensics investigators to fight against these cybercrimes, we carried out an investigation of the artifacts left by the BitTorrent client. We proposed a methodology to locate the artifacts that indicate the BitTorrent client activity performed. Additionally, we designed and implemented a tool that searches for the evidence left by the BitTorrent client application in a local computer running Windows. The tool looks for the four files holding the evidence. The files are as follows: *.torrent, dht.dat, resume.dat, and settings.dat. The tool decodes the files, extracts important information for the forensic investigator and converts it into XML format. The results are combined into a single result file.Symmetry2016-05-2686Article10.3390/sym8060040402073-89942016-05-26doi: 10.3390/sym8060040Algimantas VenčkauskasVacius JusasKęstutis PaulikasJevgenijus Toldinas<![CDATA[Symmetry, Vol. 8, Pages 39: A
PT
-Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling]]>
http://www.mdpi.com/2073-8994/8/6/39
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively.Symmetry2016-05-2686Article10.3390/sym8060039392073-89942016-05-26doi: 10.3390/sym8060039Jesús Cuevas-MaraverBoris MalomedPanayotis Kevrekidis<![CDATA[Symmetry, Vol. 8, Pages 37: Optional Frame Selection Algorithm for Adaptive Symmetric Service of Augmented Reality Big Data on Smart Devices]]>
http://www.mdpi.com/2073-8994/8/5/37
Following recent technological advances in diverse mobile devices, including smartphones, tablets and smartwatches, in-depth studies aimed at improving the quality of augmented reality (AR) are currently ongoing. Smartphones feature the essential elements of AR implementation, such as a camera, a processor and a display in a single device. As a result, additional hardware expansion for AR implementation has become unnecessary, popularizing AR technology at the user level. In the early stages, low-level AR technology was used mainly in limited fields, including simple road guides and marker-based recognition. Due to advances in AR technology, the range of usage has expanded as diverse technologies and purposes are combined. Users’ expectations of AR technology have also increased with this trend, and a high quality of service (QoS), with high-resolution, high-quality images, is now available. However, there are limitations in terms of processing speed and graphic treatment with smart devices, which, due to their small size, have inferior performance compared to the desktop environment when processing data for the implementation of high-resolution, high-quality images. This paper proposes an optional frame-selection algorithm (OFSA), which eliminates the unnecessary work involved with redundant frames during rendering for adaptive symmetric service of augmented reality big data on smart devices. Moreover, the memory read-write delay of the internally-operating OFSA, is minimized by adding an adaptive operation function. It is possible to provide adaptive common AR images at an improved frame rate in heterogeneous smart devices with different levels of performance.Symmetry2016-05-2385Article10.3390/sym8050037372073-89942016-05-23doi: 10.3390/sym8050037HwiRim ByunJong ParkYoung-Sik Jeong<![CDATA[Symmetry, Vol. 8, Pages 36: Higher Order Nonclassicality from Nonlinear Coherent States for Models with Quadratic Spectrum]]>
http://www.mdpi.com/2073-8994/8/5/36
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical behaviour of nonlinear coherent states for generalised classes of models corresponding to the generalised ladder operators. A comparative analysis among them indicates that the models with quadratic spectrum are more nonclassical than the others. Our central result is further underpinned by the comparison of the degree of nonclassicality of squeezed states of the corresponding models.Symmetry2016-05-1985Article10.3390/sym8050036362073-89942016-05-19doi: 10.3390/sym8050036Anaelle HertzSanjib DeyVéronique HussinHichem Eleuch<![CDATA[Symmetry, Vol. 8, Pages 35: Symmetry-Based Conflict Detection and Resolution Method towards Web3D-based Collaborative Design]]>
http://www.mdpi.com/2073-8994/8/5/35
In the process of web3D-based collaborative design, it is necessary to completely prevent operation conflicts among designers due to distributed environments and complex 3D models. Therefore, conflict detection and conflict resolution are of great significance to attain an acceptable result. In order to facilitate effective and smooth design work, a symmetry-based collaborative design framework is proposed using the X3D operation models. Combined considerations cover both models and operations, while different operation strategies are utilized for conflict resolution in web-based collaborative design. The strategy can achieve automatic operation, real-time conflict detection based on dynamically adjustable time, and conflict auto-detection and resolution with designers’ customization. A proof-of-concept system is developed for verification. The proposed resolution shows good performance, scalability and interactivity in a case study.Symmetry2016-05-1185Article10.3390/sym8050035352073-89942016-05-11doi: 10.3390/sym8050035Mingjiu YuHongming CaiXiaoming MaLihong Jiang<![CDATA[Symmetry, Vol. 8, Pages 33: Multivariate Krawtchouk Polynomials and Composition Birth and Death Processes]]>
http://www.mdpi.com/2073-8994/8/5/33
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur naturally as spectral orthogonal polynomials in a Karlin and McGregor spectral representation of transition functions in a composition birth and death process. In this Markov composition process in continuous time, there are N independent and identically distributed birth and death processes each with support 0 , 1 , … . The state space in the composition process is the number of processes in the different states 0 , 1 , … . Dealing with the spectral representation requires new extensions of the multivariate Krawtchouk polynomials to orthogonal polynomials on a multinomial distribution with a countable infinity of states.Symmetry2016-05-0985Article10.3390/sym8050033332073-89942016-05-09doi: 10.3390/sym8050033Robert Griffiths<![CDATA[Symmetry, Vol. 8, Pages 34: Ranking Features on Psychological Dynamics of Cooperative Team Work through Bayesian Networks]]>
http://www.mdpi.com/2073-8994/8/5/34
The aim of this study is to rank some features that characterize the psychological dynamics of cooperative team work in order to determine priorities for interventions and formation: leading positive feedback, cooperative manager and collaborative manager features. From a dataset of 20 cooperative sport teams (403 soccer players), the characteristics of the prototypical sports teams are studied using an average Bayesian network (BN) and two special types of BNs, the Bayesian classifiers: naive Bayes (NB) and tree augmented naive Bayes (TAN). BNs are selected as they are able to produce probability estimates rather than predictions. BN results show that the antecessors (the “top” features ranked) are the team members’ expectations and their attraction to the social aspects of the task. The main node is formed by the cooperative behaviors, the consequences ranked at the BN bottom (ratified by the TAN trees and the instantiations made), the roles assigned to the members and their survival inside the same team. These results should help managers to determine contents and priorities when they have to face team-building actions.Symmetry2016-05-0985Article10.3390/sym8050034342073-89942016-05-09doi: 10.3390/sym8050034Pilar Fuster-ParraAlex García-MasJaume CantallopsF. PonsetiYuhua Luo<![CDATA[Symmetry, Vol. 8, Pages 32: The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs]]>
http://www.mdpi.com/2073-8994/8/5/32
Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs) from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.Symmetry2016-05-0685Article10.3390/sym8050032322073-89942016-05-06doi: 10.3390/sym8050032Unil YunGangin LeeChul-Hong Kim<![CDATA[Symmetry, Vol. 8, Pages 31: On Consistent Nonparametric Statistical Tests of Symmetry Hypotheses]]>
http://www.mdpi.com/2073-8994/8/5/31
Being able to formally test for symmetry hypotheses is an important topic in many fields, including environmental and physical sciences. In this paper, one concentrates on a large family of nonparametric tests of symmetry based on Cramér–von Mises statistics computed from empirical distribution and characteristic functions. These tests possess the highly desirable property of being universally consistent in the sense that they detect any kind of departure from symmetry as the sample size becomes large. The asymptotic behaviour of these test statistics under symmetry is deduced from the theory of first-order degenerate V-statistics. The issue of computing valid p-values is tackled using the multiplier bootstrap method suitably adapted to V-statistics, yielding elegant, easy-to-compute and quick procedures for testing symmetry. A special focus is put on tests of univariate symmetry, bivariate exchangeability and reflected symmetry; a simulation study indicates the good sampling properties of these tests. Finally, a framework for testing general symmetry hypotheses is introduced.Symmetry2016-05-0685Article10.3390/sym8050031312073-89942016-05-06doi: 10.3390/sym8050031Jean-François Quessy<![CDATA[Symmetry, Vol. 8, Pages 30: Old Game, New Rules: Rethinking the Form of Physics]]>
http://www.mdpi.com/2073-8994/8/5/30
We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of the simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wavefunction in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.Symmetry2016-05-0685Essay10.3390/sym8050030302073-89942016-05-06doi: 10.3390/sym8050030Christian Baumgarten<![CDATA[Symmetry, Vol. 8, Pages 29: The Reality of Casimir Friction]]>
http://www.mdpi.com/2073-8994/8/5/29
For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with observations, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here, we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.Symmetry2016-04-2885Review10.3390/sym8050029292073-89942016-04-28doi: 10.3390/sym8050029Kimball MiltonJohan HøyeIver Brevik<![CDATA[Symmetry, Vol. 8, Pages 28: An Ultrasonic Lens Design Based on Prefractal Structures]]>
http://www.mdpi.com/2073-8994/8/4/28
The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields.Symmetry2016-04-2184Letter10.3390/sym8040028282073-89942016-04-21doi: 10.3390/sym8040028Sergio Castiñeira-IbáñezDaniel Tarrazó-SerranoConstanza RubioPilar CandelasAntonio Uris<![CDATA[Symmetry, Vol. 8, Pages 27: E-Polytopes in Picard Groups of Smooth Rational Surfaces]]>
http://www.mdpi.com/2073-8994/8/4/27
In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes k 21 . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of 2 k 1 and 1 k 2 via E-type Weyl action.Symmetry2016-04-2084Article10.3390/sym8040027272073-89942016-04-20doi: 10.3390/sym8040027Jae-Hyouk LeeYongJoo Shin<![CDATA[Symmetry, Vol. 8, Pages 25: Spontaneous Breakdown of the Time Reversal Symmetry]]>
http://www.mdpi.com/2073-8994/8/4/25
The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.Symmetry2016-04-2084Article10.3390/sym8040025252073-89942016-04-20doi: 10.3390/sym8040025Janos Polonyi<![CDATA[Symmetry, Vol. 8, Pages 26: Chiral Symmetry and the Nucleon-Nucleon Interaction]]>
http://www.mdpi.com/2073-8994/8/4/26
We review how nuclear forces emerge from low-energy quantum chromodynamics (QCD) via chiral effective field theory (EFT). During the past two decades, this approach has evolved into a powerful tool to derive nuclear two- and many-body forces in a systematic and model-independent way. We then focus on the nucleon-nucleon (N N) interaction and show in detail how, governed by chiral symmetry, the long- and intermediate-range of the N N potential builds up order by order. We proceed up to sixth order in small momenta, where convergence is achieved. The final result allows for a full assessment of the validity of the chiral EFT approach to the N N interaction.Symmetry2016-04-2084Article10.3390/sym8040026262073-89942016-04-20doi: 10.3390/sym8040026Ruprecht Machleidt<![CDATA[Symmetry, Vol. 8, Pages 23: Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566]]>
http://www.mdpi.com/2073-8994/8/4/23
The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach.Symmetry2016-04-1884Commentary10.3390/sym8040023232073-89942016-04-18doi: 10.3390/sym8040023Michael FrewerGeorge Khujadze<![CDATA[Symmetry, Vol. 8, Pages 24: Reply to Frewer et al. Comments on Janocha et al. Lie Symmetry Analysis of the Hopf Functional-Differential Equation. Symmetry 2015, 7, 1536–1566]]>
http://www.mdpi.com/2073-8994/8/4/24
We reply to the comment by Frewer and Khujadze regarding our contribution “Lie Symmetry Analysis of the Hopf Functional-Differential Equation” (Symmetry 2015, 7(3), 1536). The method developed by the present authors considered the Lie group analysis of the Hopf equations with functional derivatives in the equation, not the integro-differential equations in general. It was based on previous contributions (Oberlack and Wacławczyk, Arch. Mech. 2006, 58; Wacławczyk and Oberlack, J. Math. Phys. 2013, 54). In fact, three of the symmetries calculated in (Symmetry 2015, 7(3), 1536) break due to internal consistency constrains and conditions imposed on test functions, the same concerns the corresponding symmetries derived by Frewer and Khujadze and another, spurious symmetry, which was not discussed by Frewer and Khujadze. As a result, the same set of symmetries is obtained with both approaches.Symmetry2016-04-1684Reply10.3390/sym8040024242073-89942016-04-16doi: 10.3390/sym8040024Marta WacławczykDaniel JanochaMartin Oberlack<![CDATA[Symmetry, Vol. 8, Pages 22: Local Dynamics in an Infinite Harmonic Chain]]>
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By the method of recurrence relations, the time evolution in a local variable in a harmonic chain is obtained. In particular, the autocorrelation function is obtained analytically. Using this result, a number of important dynamical quantities are obtained, including the memory function of the generalized Langevin equation. Also studied are the ergodicity and chaos in a local dynamical variable.Symmetry2016-04-1584Article10.3390/sym8040022222073-89942016-04-15doi: 10.3390/sym8040022M. Lee<![CDATA[Symmetry, Vol. 8, Pages 21: Anomalous Mirror Symmetry Generated by Optical Illusion]]>
http://www.mdpi.com/2073-8994/8/4/21
This paper introduces a new concept of mirror symmetry, called “anomalous mirror symmetry”, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown.Symmetry2016-04-0884Article10.3390/sym8040021212073-89942016-04-08doi: 10.3390/sym8040021Kokichi Sugihara<![CDATA[Symmetry, Vol. 8, Pages 20: Resource Symmetric Dispatch Model for Internet of Things on Advanced Logistics]]>
http://www.mdpi.com/2073-8994/8/4/20
Business applications in advanced logistics service are highly concurrent. In this paper, we propose a resource symmetric dispatch model for the concurrent and cooperative tasks of the Internet of Things. In the model, the terminals receive and deliver commands, data, and information with mobile networks, wireless networks, and sensor networks. The data and information are classified and processed by the clustering servers in the cloud service platform. The cluster service, resource dispatch, and load balance are cooperative for management and monitoring of every application case during the logistics service lifecycle. In order to support the high performance of cloud service, resource symmetric dispatch algorithm among clustering servers and load balancing method among multi-cores in one server, including NIO (Non-blocking Input/Output) and RMI (Remote Method Invocation) are utilized to dispatch the cooperation of computation and service resources.Symmetry2016-04-0584Article10.3390/sym8040020202073-89942016-04-05doi: 10.3390/sym8040020Guofeng QinLisheng WangQiyan Li<![CDATA[Symmetry, Vol. 8, Pages 19: Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection]]>
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By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.Symmetry2016-03-3184Article10.3390/sym8040019192073-89942016-03-31doi: 10.3390/sym8040019Pan ZhangLiang Zhang<![CDATA[Symmetry, Vol. 8, Pages 18: Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation]]>
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We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to the discrete problem and stability of the discrete solution. The discretization considered is then known to converge to the viscosity solution but no rate of convergence was known.Symmetry2016-03-2484Article10.3390/sym8040018182073-89942016-03-24doi: 10.3390/sym8040018Gerard Awanou<![CDATA[Symmetry, Vol. 8, Pages 17: Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light]]>
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We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation.Symmetry2016-03-1983Article10.3390/sym8030017172073-89942016-03-19doi: 10.3390/sym8030017Heung-Ryoul Noh<![CDATA[Symmetry, Vol. 8, Pages 16: Pseudospin Symmetry as a Bridge between Hadrons and Nuclei]]>
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Atomic nuclei exhibit approximate pseudospin symmetry. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from the insight that pseudospin symmetry has relativistic origins . We show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei. Since QCD sum rules predict that the sum of the scalar and vector potentials is small, we discuss the quark origins of pseudospin symmetry in nuclei and spin symmetry in hadrons.Symmetry2016-03-1883Article10.3390/sym8030016162073-89942016-03-18doi: 10.3390/sym8030016Joseph Ginocchio<![CDATA[Symmetry, Vol. 8, Pages 14: Status of X(1835) and pp¯ Interaction from Chiral Symmetry]]>
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After the observation of the strong near-threshold enhancement of proton-antiproton mass spectrum in
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decay, lots of theoretical investigations have been available such as new resonance, the final-state
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bound state (or baryonium), glueball, or other exotic (tetra-quark) states. Here, we provide a short review on the current status, especially on the pertinent discussions concerning its relation to
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interaction, for which the emphasis is put on the recently constructed chiral potential.Symmetry2016-03-1783Article10.3390/sym8030014142073-89942016-03-17doi: 10.3390/sym8030014Yong-Feng LiuXian-Wei Kang<![CDATA[Symmetry, Vol. 8, Pages 15: Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations]]>
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A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.Symmetry2016-03-1783Article10.3390/sym8030015152073-89942016-03-17doi: 10.3390/sym8030015Rutwig Campoamor-Stursberg<![CDATA[Symmetry, Vol. 8, Pages 12: Dual Pairs of Holomorphic Representations of Lie Groups from a Vector-Coherent-State Perspective]]>
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It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive pairs of holomorphic representations which are bi-orthogonal duals of each other with respect to a simple Bargmann inner product. It is then shown that the dual of a standard holomorphic representation has an integral expression for its inner product, with a Bargmann measure and a simply-defined kernel, which is not restricted to discrete-series representations. Dual pairs of holomorphic representations also provide practical ways to construct orthonormal bases for unitary irreps which bypass the need for evaluating the integral expressions for their inner products. This leads to practical algorithms for the application of holomorphic representations to model problems with dynamical symmetries in physics.Symmetry2016-03-1683Article10.3390/sym8030012122073-89942016-03-16doi: 10.3390/sym8030012David RoweJoe Repka<![CDATA[Symmetry, Vol. 8, Pages 13: Bézier Triangles with G2 Continuity across Boundaries]]>
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PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces G2 continuity across boundaries while preserving G1 continuity at vertices. The sharpness of the blends can be controlled locally by varying the extent of these blending regions. We demonstrate the effectiveness of our technique by showing several modeling examples.Symmetry2016-03-1583Article10.3390/sym8030013132073-89942016-03-15doi: 10.3390/sym8030013Chang-Ki LeeHae-Do HwangSeung-Hyun Yoon<![CDATA[Symmetry, Vol. 8, Pages 11: A Combinatorial Approach to Time Asymmetry]]>
http://www.mdpi.com/2073-8994/8/3/11
In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a finite probability space. We can then also attempt to compute the probabilities for different kinds of behavior and in particular under certain conditions argue that an asymmetric behavior of the entropy should be much more probable than a symmetric one. This offers an explanation for the asymmetry of time as a broken symmetry in the multiverse. The focus here is on simple models which can be analyzed using methods from combinatorics. Although the computational difficulties rapidly become enormous when the size of the model grows, this still gives hints about how a full-scale model should behave.Symmetry2016-03-1583Article10.3390/sym8030011112073-89942016-03-15doi: 10.3390/sym8030011Martin Tamm<![CDATA[Symmetry, Vol. 8, Pages 10: Polarity Formation in Molecular Crystals as a Symmetry Breaking Effect]]>
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The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin flip invariance—the former being broken by geometric constraints, the latter by the interaction of the first non-zero multipole with the next order multipole. Two different behaviors of the thermal average of the order parameter as a function of position are found. The free energy per lattice site converges to a finite value in the thermodynamic limit showing the consistency of the model in a macroscopic representation.Symmetry2016-03-1183Article10.3390/sym8030010102073-89942016-03-11doi: 10.3390/sym8030010Luigi CannavacciuoloJürg Hulliger<![CDATA[Symmetry, Vol. 8, Pages 9: Duality in Geometric Graphs: Vector Graphs, Kirchhoff Graphs and Maxwell Reciprocal Figures]]>
http://www.mdpi.com/2073-8994/8/3/9
We compare two mathematical theories that address duality between cycles and vertex-cuts of graphs in geometric settings. First, we propose a rigorous definition of a new type of graph, vector graphs. The special case of R2-vector graphs matches the intuitive notion of drawing graphs with edges taken as vectors. This leads to a discussion of Kirchhoff graphs, as originally presented by Fehribach, which can be defined independent of any matrix relations. In particular, we present simple cases in which vector graphs are guaranteed to be Kirchhoff or non-Kirchhoff. Next, we review Maxwell’s method of drawing reciprocal figures as he presented in 1864, using modern mathematical language. We then demonstrate cases in which R2-vector graphs defined from Maxwell reciprocals are “dual” Kirchhoff graphs. Given an example in which Maxwell’s theories are not sufficient to define vector graphs, we begin to explore other methods of developing dual Kirchhoff graphs.Symmetry2016-02-2983Article10.3390/sym803000992073-89942016-02-29doi: 10.3390/sym8030009Tyler ReeseRandy PaffenrothJoseph Fehribach<![CDATA[Symmetry, Vol. 8, Pages 8: New Upper Bound and Lower Bound for Degree-Based Network Entropy]]>
http://www.mdpi.com/2073-8994/8/2/8
The degree-based network entropy which is inspired by Shannon’s entropy concept becomes the information-theoretic quantity for measuring the structural information of graphs and complex networks. In this paper, we study some properties of the degree-based network entropy. Firstly we develop a refinement of Jensen’s inequality. Next we present the new and more accurate upper bound and lower bound for the degree-based network entropy only using the order, the size, the maximum degree and minimum degree of a network. The bounds have desirable performance to restrict the entropy in different kinds of graphs. Finally, we show an application to structural complexity analysis of a computer network modeled by a connected graph.Symmetry2016-02-1982Article10.3390/sym802000882073-89942016-02-19doi: 10.3390/sym8020008Guoxiang LuBingqing LiLijia Wang<![CDATA[Symmetry, Vol. 8, Pages 7: On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map]]>
http://www.mdpi.com/2073-8994/8/2/7
A complex map can give rise to two kinds of fractal sets: the Julia sets and the parameters sets (or the connectivity loci) which represent different connectivity properties of the corresponding Julia sets. In the significative results of (Int. J. Bifurc. Chaos, 2009, 19:2123–2129) and (Nonlinear. Dyn. 2013, 73:1155–1163), the authors presented the two kinds of fractal sets of a class of alternated complex map and left some visually observations to be proved about the boundedness and symmetry properties of these fractal sets. In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.Symmetry2016-01-2682Article10.3390/sym802000772073-89942016-01-26doi: 10.3390/sym8020007Da WangShuTang Liu<![CDATA[Symmetry, Vol. 8, Pages 6: Acknowledgement to Reviewers of Symmetry in 2015]]>
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The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Symmetry2016-01-2181Editorial10.3390/sym801000662073-89942016-01-21doi: 10.3390/sym8010006Symmetry Editorial Office<![CDATA[Symmetry, Vol. 8, Pages 5: Symmetry in Sphere-Based Assembly Configuration Spaces]]>
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Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions.Symmetry2016-01-2181Article10.3390/sym801000552073-89942016-01-21doi: 10.3390/sym8010005Meera SitharamAndrew VinceMenghan WangMiklós Bóna<![CDATA[Symmetry, Vol. 8, Pages 4: Synthesis of Chiral Cyclic Carbonates via Kinetic Resolution of Racemic Epoxides and Carbon Dioxide]]>
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The catalytic synthesis of cyclic carbonates using carbon dioxide as a C1-building block is a highly active area of research. Here, we review the catalytic production of enantiomerically enriched cyclic carbonates via kinetic resolution of racemic epoxides catalysed by metal-containing catalyst systems.Symmetry2016-01-1481Review10.3390/sym801000442073-89942016-01-14doi: 10.3390/sym8010004Xiao WuJosé Castro-OsmaMichael North