Symmetry
http://www.mdpi.com/journal/symmetry
Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 7, Pages 1333-1351: A Framework for Symmetric Part Detection in Cluttered Scenes]]>
http://www.mdpi.com/2073-8994/7/3/1333
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Symmetry2015-07-2073Review10.3390/sym7031333133313512073-89942015-07-20doi: 10.3390/sym7031333Tom LeeSanja FidlerAlex LevinshteinCristian SminchisescuSven Dickinson<![CDATA[Symmetry, Vol. 7, Pages 1289-1332: Computing with Colored Tangles]]>
http://www.mdpi.com/2073-8994/7/3/1289
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated colored tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete and with bounded resources that it can decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.Symmetry2015-07-2073Article10.3390/sym7031289128913322073-89942015-07-20doi: 10.3390/sym7031289Avishy CarmiDaniel Moskovich<![CDATA[Symmetry, Vol. 7, Pages 1275-1288: Development of Network Analysis and Visualization System for KEGG Pathways]]>
http://www.mdpi.com/2073-8994/7/3/1275
Big data refers to informationalization technology for extracting valuable information through the use and analysis of large-scale data and, based on that data, deriving plans for response or predicting changes. With the development of software and devices for next generation sequencing, a vast amount of bioinformatics data has been generated recently. Also, bioinformatics data based big-data technology is rising rapidly as a core technology by the bioinformatician, biologist and big-data scientist. KEGG pathway is bioinformatics data for understanding high-level functions and utilities of the biological system. However, KEGG pathway analysis requires a lot of time and effort because KEGG pathways are high volume and very diverse. In this paper, we proposed a network analysis and visualization system that crawl user interest KEGG pathways, construct a pathway network based on a hierarchy structure of pathways and visualize relations and interactions of pathways by clustering and selecting core pathways from the network. Finally, we construct a pathway network collected by starting with an Alzheimer’s disease pathway and show the results on clustering and selecting core pathways from the pathway network.Symmetry2015-07-1673Article10.3390/sym7031275127512882073-89942015-07-16doi: 10.3390/sym7031275Dongmin SeoMin-Ho LeeSeok Yu<![CDATA[Symmetry, Vol. 7, Pages 1261-1274: In Memoriam: Slavik Jablan 1952–2015]]>
http://www.mdpi.com/2073-8994/7/3/1261
After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. [...]Symmetry2015-07-1573Obituary10.3390/sym7031261126112742073-89942015-07-15doi: 10.3390/sym7031261Donald CroweGyörgy DarvasDirk HuylebrouckJay KappraffLouis KauffmanSofia LambropoulouJozef PrzytyckiLjiljana RadovićRadmila SazdanovicVera de SpinadelAna ZekovićSymmetry Office<![CDATA[Symmetry, Vol. 7, Pages 1211-1260: The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric]]>
http://www.mdpi.com/2073-8994/7/3/1211
The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon positions: AAA and AAC are at 1-distance; codons are maximally at 3-distance.) The CodonPolytope, a 9-dimensional geometric object, is spanned by 64 vertices that represent the codons and the Euclidian distances between these vertices correspond one-to-one with intercodon Hamming distances. The CodonGraph represents the vertices and edges of the polytope; each edge equals a Hamming 1-distance. The mirror reflection symmetry group of the polytope is isomorphic to the largest permutation symmetry group of the codon set that preserves Hamming distances. These groups contain 82,944 symmetries. Many polytope symmetries coincide with the degeneracy and similarity patterns of the genetic code. These code symmetries are strongly related with the face structure of the polytope with smaller faces displaying stronger code symmetries. Splitting the polytope stepwise into smaller faces models an early evolution of the code that generates this hierarchy of code symmetries. The canonical code represents a class of 41,472 codes with equivalent symmetries; a single class among an astronomical number of symmetry classes comprising all possible codes.Symmetry2015-07-1473Article10.3390/sym7031211121112602073-89942015-07-14doi: 10.3390/sym7031211Reijer Lenstra<![CDATA[Symmetry, Vol. 7, Pages 1176-1210: Real Time MODBUS Transmissions and Cryptography Security Designs and Enhancements of Protocol Sensitive Information]]>
http://www.mdpi.com/2073-8994/7/3/1176
Information technology (IT) security has become a major concern due to the growing demand for information and massive development of client/server applications for various types of applications running on modern IT infrastructure. How has security been taken into account and which paradigms are necessary to minimize security issues while increasing efficiency, reducing the influence on transmissions, ensuring protocol independency and achieving substantial performance? We have found cryptography to be an absolute security mechanism for client/server architectures, and in this study, a new security design was developed with the MODBUS protocol, which is considered to offer phenomenal performance for future development and enhancement of real IT infrastructure. This study is also considered to be a complete development because security is tested in almost all ways of MODBUS communication. The computed measurements are evaluated to validate the overall development, and the results indicate a substantial improvement in security that is differentiated from conventional methods.Symmetry2015-07-0273Article10.3390/sym7031176117612102073-89942015-07-02doi: 10.3390/sym7031176Aamir ShahzadMalrey LeeYoung-Keun LeeSuntae KimNaixue XiongJae-Young ChoiYounghwa Cho<![CDATA[Symmetry, Vol. 7, Pages 1164-1175: Hierarchical Clustering Using One-Class Support Vector Machines]]>
http://www.mdpi.com/2073-8994/7/3/1164
This paper presents a novel hierarchical clustering method using support vector machines. A common approach for hierarchical clustering is to use distance for the task. However, different choices for computing inter-cluster distances often lead to fairly distinct clustering outcomes, causing interpretation difficulties in practice. In this paper, we propose to use a one-class support vector machine (OC-SVM) to directly find high-density regions of data. Our algorithm generates nested set estimates using the OC-SVM and exploits the hierarchical structure of the estimated sets. We demonstrate the proposed algorithm on synthetic datasets. The cluster hierarchy is visualized with dendrograms and spanning trees.Symmetry2015-07-0173Article10.3390/sym7031164116411752073-89942015-07-01doi: 10.3390/sym7031164Gyemin Lee<![CDATA[Symmetry, Vol. 7, Pages 1151-1163: Multiple Minimum Support-Based Rare Graph Pattern Mining Considering Symmetry Feature-Based Growth Technique and the Differing Importance of Graph Elements]]>
http://www.mdpi.com/2073-8994/7/3/1151
Frequent graph pattern mining is one of the most interesting areas in data mining, and many researchers have developed a variety of approaches by suggesting efficient, useful mining techniques by integration of fundamental graph mining with other advanced mining works. However, previous graph mining approaches have faced fatal problems that cannot consider important characteristics in the real world because they cannot process both (1) different element importance and (2) multiple minimum support thresholds suitable for each graph element. In other words, graph elements in the real world have not only frequency factors but also their own importance; in addition, various elements composing graphs may require different thresholds according to their characteristics. However, traditional ones do not consider such features. To overcome these issues, we propose a new frequent graph pattern mining method, which can deal with both different element importance and multiple minimum support thresholds. Through the devised algorithm, we can obtain more meaningful graph pattern results with higher importance. We also demonstrate that the proposed algorithm has more outstanding performance compared to previous state-of-the-art approaches in terms of graph pattern generation, runtime, and memory usage.Symmetry2015-06-2673Article10.3390/sym7031151115111632073-89942015-06-26doi: 10.3390/sym7031151Gangin LeeUnil YunHeungmo RyangDonggyu Kim<![CDATA[Symmetry, Vol. 7, Pages 1122-1150: Symmetry-Breaking as a Paradigm to Design Highly-Sensitive Sensor Systems]]>
http://www.mdpi.com/2073-8994/7/2/1122
A large class of dynamic sensors have nonlinear input-output characteristics, often corresponding to a bistable potential energy function that controls the evolution of the sensor dynamics. These sensors include magnetic field sensors, e.g., the simple fluxgate magnetometer and the superconducting quantum interference device (SQUID), ferroelectric sensors and mechanical sensors, e.g., acoustic transducers, made with piezoelectric materials. Recently, the possibilities offered by new technologies and materials in realizing miniaturized devices with improved performance have led to renewed interest in a new generation of inexpensive, compact and low-power fluxgate magnetometers and electric-field sensors. In this article, we review the analysis of an alternative approach: a symmetry-based design for highly-sensitive sensor systems. The design incorporates a network architecture that produces collective oscillations induced by the coupling topology, i.e., which sensors are coupled to each other. Under certain symmetry groups, the oscillations in the network emerge via an infinite-period bifurcation, so that at birth, they exhibit a very large period of oscillation. This characteristic renders the oscillatory wave highly sensitive to symmetry-breaking effects, thus leading to a new detection mechanism. Model equations and bifurcation analysis are discussed in great detail. Results from experimental works on networks of fluxgate magnetometers are also included.Symmetry2015-06-1972Review10.3390/sym7021122112211502073-89942015-06-19doi: 10.3390/sym7021122Antonio PalaciosVisarath InPatrick Longhini<![CDATA[Symmetry, Vol. 7, Pages 1080-1121: An Extended Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets]]>
http://www.mdpi.com/2073-8994/7/2/1080
This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges and internal symmetries provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.Symmetry2015-06-1672Article10.3390/sym7021080108011212073-89942015-06-16doi: 10.3390/sym7021080Sylvester GatesJames ParkerVincent RodgersLeo RodriguezKory Stiffler<![CDATA[Symmetry, Vol. 7, Pages 1061-1079: Symmetry Extraction in High Sensitivity Melanoma Diagnosis]]>
http://www.mdpi.com/2073-8994/7/2/1061
Melanoma diagnosis depends on the experience of doctors. Symmetry is one of the most important factors to measure, since asymmetry shows an uncontrolled growth of cells, leading to melanoma cancer. A system for melanoma detection in diagnosing melanocytic diseases with high sensitivity is proposed here. Two different sets of features are extracted based on the importance of the ABCD rule and symmetry evaluation to develop a new architecture. Support Vector Machines are used to classify the extracted sets by using both an alternative labeling method and a structure divided into two different classifiers which prioritize sensitivity. Although feature extraction is based on former works, the novelty lies in the importance given to symmetry and the proposed architecture, which combines two different feature sets to obtain a high sensitivity, prioritizing the medical aspect of diagnosis. In particular, a database provided by Hospital Universitario de Gran Canaria Doctor Negrín was tested, obtaining a sensitivity of 100% and a specificity of 66.66% using a leave-one-out validation method. These results show that 66.66% of biopsies would be avoided if this system is applied to lesions which are difficult to classify by doctors.Symmetry2015-06-1572Article10.3390/sym7021061106110792073-89942015-06-15doi: 10.3390/sym7021061Elyoenai Guerra-SeguraCarlos Travieso-GonzálezJesús Alonso-HernándezAntonio Ravelo-GarcíaGregorio Carretero<![CDATA[Symmetry, Vol. 7, Pages 1043-1060: Kinematic Skeleton Based Control of a Virtual Simulator for Military Training]]>
http://www.mdpi.com/2073-8994/7/2/1043
Virtual simulation technology has been considered as a highly efficient and cost-effective solution for a soldier training system, and evolved into diverse combinations of hardware and software. To maximize the virtual reality effect within a restricted space, a locomotion interface such as an omni-directional treadmill is introduced as a major component of a virtual simulator, therefore real time interaction between human and the virtual simulator becomes very important. Displacement and heading changes of the trainee are crucial information to control the virtual simulator when we implement highly reactive motion control for the omni-directional treadmill and interaction control of the virtual contents. This paper proposes a control parameter estimation algorithm for the virtual training simulator by using two types of motion capture sensors and presents the experimental results. Kinematic joint positions are analyzed to estimate the trainee’s location and velocity for feedback and feedforward control of the omni-directional treadmill. The accuracy of two approaches is evaluated by comparing with the reference system, which gives a ground truth value.Symmetry2015-06-1172Article10.3390/sym7021043104310602073-89942015-06-11doi: 10.3390/sym7021043Soyeon LeeSangjoon ParkKyoil ChungChoongho Cho<![CDATA[Symmetry, Vol. 7, Pages 1040-1042: Symmetry Best Paper Award 2015]]>
http://www.mdpi.com/2073-8994/7/2/1040
In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:Symmetry2015-06-0872Editorial10.3390/sym7021040104010422073-89942015-06-08doi: 10.3390/sym7021040Sergei Odintsov<![CDATA[Symmetry, Vol. 7, Pages 1028-1039: Development of Patient Status-Based Dynamic Access System for Medical Information Systems]]>
http://www.mdpi.com/2073-8994/7/2/1028
Recently, the hospital information system environment using IT communication technology and utilization of medical information has been increasing. In the medical field, the medical information system only supports the transfer of patient information to medical staff through an electronic health record, without information about patient status. Hence, it needs a method of real-time monitoring for the patient. Also, in this environment, a secure method in approaching healthcare through various smart devices is required. Therefore, in this paper, in order to classify the status of the patients, we propose a dynamic approach of the medical information system in a hospital information environment using the dynamic access control method. Also, we applied the symmetric method of AES (Advanced Encryption Standard). This was the best encryption algorithm for sending and receiving biological information. We can define usefulness as the dynamic access application service based on the final result of the proposed system. The proposed system is expected to provide a new solution for a convenient medical information system.Symmetry2015-06-0872Article10.3390/sym7021028102810392073-89942015-06-08doi: 10.3390/sym7021028Chang JeongVathana BanKwon YoonSu Joo<![CDATA[Symmetry, Vol. 7, Pages 1017-1027: Supersymmetric Displaced Number States]]>
http://www.mdpi.com/2073-8994/7/2/1017
We introduce, generate and study a family of supersymmetric displaced number states (SDNS) that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.Symmetry2015-06-0572Article10.3390/sym7021017101710272073-89942015-06-05doi: 10.3390/sym7021017Fredy Zypman<![CDATA[Symmetry, Vol. 7, Pages 994-1016: Multi-Classifier Based on a Query-by-Singing/Humming System]]>
http://www.mdpi.com/2073-8994/7/2/994
With the increase in the number of music files on various devices, it can be difficult to locate a desired file, especially when the title of the song or the name of the singer is not known. We propose a new query-by-singing/humming (QbSH) system that can find music files that match what the user is singing or humming. This research is novel in the following three ways: first, the Fourier descriptor (FD) method is proposed as the first classifier; it transforms the humming or music waveform into the frequency domain. Second, quantized dynamic time warping (QDTW) using symmetrical search space and quantized linear scaling (QLS) are used as the second and third classifiers, respectively, which increase the accuracy of the QbSH system compared to the conventional DTW and LS methods. Third, five classifiers, which include the three already mentioned along with the conventional DTW using symmetrical search space and LS methods, are combined using score level fusion, which further enhances performance. Experimental results with the 2009 MIR-QbSH corpus and the AFA MIDI 100 databases show that the proposed method outperforms those using a single classifier and other fusion methods.Symmetry2015-06-0472Article10.3390/sym702099499410162073-89942015-06-04doi: 10.3390/sym7020994Gi NamKang Park<![CDATA[Symmetry, Vol. 7, Pages 976-993: Consistent Positive Co-Variation between Fluctuating Asymmetry and Sexual Trait Size: A Challenge to the Developmental Instability-Sexual Selection Hypothesis]]>
http://www.mdpi.com/2073-8994/7/2/976
The developmental instability (DI)-sexual selection hypothesis proposes that large size and symmetry in secondary sexual traits are favored by sexual selection because they reveal genetic quality. A critical prediction of this hypothesis is that there should exist negative correlations between trait fluctuating asymmetry (FA) and size of condition dependent sexual traits; condition dependent traits should reveal an organism’s overall health and vigor, and be influenced by a multitude of genetic loci. Here, we tested for the predicted negative FA-size correlations in the male sex comb of Drosophila bipectinata. Among field-caught males from five widely separated geographic localities, FA-size correlations were consistently positive, despite evidence that sex comb size is condition dependent. After controlling for trait size, FA was significantly negatively correlated with body size within several populations, indicating that developmental instability in the comb may reveal individual genetic quality. We suggest the possibility that condition dependent traits in some cases tap into independent units of the genome (a restricted set of genes), rather than signaling overall genetic properties of the organism. There were pronounced among-population differences in both comb FA and size, and these traits were positively correlated across populations, recapitulating the within-population patterns. We conclude that the results are inconsistent with the DI-sexual selection hypothesis, and discuss potential reasons for positive FA-size co-variation in sexual traits.Symmetry2015-06-0372Article10.3390/sym70209769769932073-89942015-06-03doi: 10.3390/sym7020976Michal PolakKassie HookerFrances Tyler<![CDATA[Symmetry, Vol. 7, Pages 962-975: Characterizations of Network Structures Using Eigenmode Analysis]]>
http://www.mdpi.com/2073-8994/7/2/962
We introduced an analysis to identify structural characterization of two-dimensional regular and amorphous networks. The analysis was shown to be reliable to determine the global network rigidity and can also identify local floppy regions in the mixture of rigid and floppy regions. The eigenmode analysis explores the structural properties of various networks determined by eigenvalue spectra. It is useful to determine the general structural stability of networks that the traditional Maxwell counting scheme based on the statistics of nodes (degrees of freedom) and bonds (constraints) does not provide. A visual characterization scheme was introduced to examine the local structure characterization of the networks. The eigenmode analysis is under development for various practical applications on more general network structures characterized by coordination numbers and nodal connectivity such as graphenes and proteins.Symmetry2015-06-0372Article10.3390/sym70209629629752073-89942015-06-03doi: 10.3390/sym7020962Youngho ParkSangil Hyun<![CDATA[Symmetry, Vol. 7, Pages 949-961: Conservation Laws and Exact Solutions of a Generalized Zakharov–Kuznetsov Equation]]>
http://www.mdpi.com/2073-8994/7/2/949
In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along with the simplest equation method.Symmetry2015-06-0372Article10.3390/sym70209499499612073-89942015-06-03doi: 10.3390/sym7020949Dimpho MothibiChaudry Khalique<![CDATA[Symmetry, Vol. 7, Pages 935-948: Design of a Distributed Personal Information Access Control Scheme for Secure Integrated Payment in NFC]]>
http://www.mdpi.com/2073-8994/7/2/935
At the center of core technologies for a future cyber world, such as Internet of Things (IoT) or big data, is a context-rich system that offers services by using situational information. The field where context-rich systems were first introduced is near-field communication (NFC)-based electronic payments. Near-field Communication (NFC) integrated payment services collect the payment information of the credit card and the location information to generate patterns in the user’s consumption or movement through big data technology. Based on such pattern information, tailored services, such as advertisement, are offered to users. However, there is difficulty in controlling access to personal information, as there is a collaborative relationship focused on the trusted service manager (TSM) that is close knit to shared personal information. Moreover, in the case of Hadoop, among the many big data analytical technologies, it offers access control functions, but not a way to authorize the processing of personal information, making it impossible to grant authority between service providers to process information. As such, this paper proposes a key generation and distribution method, as well as a secure communication protocol. The analysis has shown that the efficiency was greater for security and performance compared to relation works.Symmetry2015-06-0272Article10.3390/sym70209359359482073-89942015-06-02doi: 10.3390/sym7020935Jungho KangJong ParkSangkee Suk<![CDATA[Symmetry, Vol. 7, Pages 843-934: Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications]]>
http://www.mdpi.com/2073-8994/7/2/843
Approximately two decades after the first pioneering analyses, the study of shape asymmetry with the methods of geometric morphometrics has matured and is a burgeoning field. New technology for data collection and new methods and software for analysis are widely available and have led to numerous applications in plants and animals, including humans. This review summarizes the concepts and morphometric methods for studying asymmetry of shape and size. After a summary of mathematical and biological concepts of symmetry and asymmetry, a section follows that explains the methods of geometric morphometrics and how they can be used to analyze asymmetry of biological structures. Geometric morphometric analyses not only tell how much asymmetry there is, but also provide information about the patterns of covariation in the structure under study. Such patterns of covariation in fluctuating asymmetry can provide valuable insight about the developmental basis of morphological integration, and have become important tools for evolutionary developmental biology. The genetic basis of fluctuating asymmetry has been studied from empirical and theoretical viewpoints, but serious challenges remain in this area. There are many promising areas for further research that are only little explored at present.Symmetry2015-06-0272Review10.3390/sym70208438439342073-89942015-06-02doi: 10.3390/sym7020843Christian Klingenberg<![CDATA[Symmetry, Vol. 7, Pages 815-842: Cosmological Probes for Supersymmetry]]>
http://www.mdpi.com/2073-8994/7/2/815
The multi-parameter character of supersymmetric dark-matter models implies the combination of their experimental studies with astrophysical and cosmological probes. The physics of the early Universe provides nontrivial effects of non-equilibrium particles and primordial cosmological structures. Primordial black holes (PBHs) are a profound signature of such structures that may arise as a cosmological consequence of supersymmetric (SUSY) models. SUSY-based mechanisms of baryosynthesis can lead to the possibility of antimatter domains in a baryon asymmetric Universe. In the context of cosmoparticle physics, which studies the fundamental relationship of the micro- and macro-worlds, the development of SUSY illustrates the main principles of this approach, as the physical basis of the modern cosmology provides cross-disciplinary tests in physical and astronomical studies.Symmetry2015-05-2972Review10.3390/sym70208158158422073-89942015-05-29doi: 10.3390/sym7020815Maxim Khlopov<![CDATA[Symmetry, Vol. 7, Pages 788-814: Supersymmetry with Radiatively-Driven Naturalness: Implications for WIMP and Axion Searches]]>
http://www.mdpi.com/2073-8994/7/2/788
By insisting on naturalness in both the electroweak and quantum chromodynamics (QCD) sectors of the minimal supersymmetric standard model (MSSM), the portrait for dark matter production is seriously modified from the usual weakly interacting massive particle (WIMP) miracle picture. In supersymmetry (SUSY) models with radiatively-driven naturalness (radiative natural SUSY or radiative natural SUSY (RNS)) which include a Dine–Fischler–Srednicki–Zhitnitsky (DFSZ)-like solution to the strong charge-conjugation-parity (CP) and SUSY \(\mu\) problems, dark matter is expected to be an admixture of both axions and higgsino-like WIMPs. The WIMP/axion abundance calculation requires simultaneous solution of a set of coupled Boltzmann equations which describe quasi-stable axinos and saxions. In most of parameter space, axions make up the dominant contribution of dark matter although regions of WIMP dominance also occur. We show the allowed range of Peccei-Quinn (PQ) scale \(f_a\) and compare to the values expected to be probed by the axion dark matter search experiment (ADMX) axion detector in the near future. We also show WIMP detection rates, which are suppressed from usual expectations, because now WIMPs comprise only a fraction of the total dark matter. Nonetheless, ton-scale noble liquid detectors should be able to probe the entirety of RNS parameter space. Indirect WIMP detection rates are less propitious since they are reduced by the square of the depleted WIMP abundance.Symmetry2015-05-2872Article10.3390/sym70207887888142073-89942015-05-28doi: 10.3390/sym7020788Kyu BaeHoward BaerVernon BargerMichael SavoyHasan Serce<![CDATA[Symmetry, Vol. 7, Pages 774-787: Flexible Polyhedral Surfaces with Two Flat Poses]]>
http://www.mdpi.com/2073-8994/7/2/774
We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids.Symmetry2015-05-2772Article10.3390/sym70207747747872073-89942015-05-27doi: 10.3390/sym7020774Hellmuth Stachel<![CDATA[Symmetry, Vol. 7, Pages 726-773: Probing Majorana Neutrinos and their CP Violation in Decays of Charged Scalar Mesons π, K, D, Ds, B, Bc]]>
http://www.mdpi.com/2073-8994/7/2/726
Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles. There are different ways to explore these issues. In this article we describe neutrino-mediated decays of charged pseudoscalar mesons such as π± ,K± and B±, in scenarios where extra neutrinos are heavy and can be on their mass shell. We discuss semileptonic and leptonic decays of such kinds. We investigate possible ways of using these decays in order to distinguish between the Dirac and Majorana character of neutrinos. Further, we argue that there are significant possibilities of detecting CP violation in such decays when there are at least two almost degenerate Majorana neutrinos involved. This latter type of scenario fits well into the known neutrino minimal standard model (MSM) which could simultaneously explain the Dark Matter and Baryon Asymmetry of the Universe.Symmetry2015-05-2672Article10.3390/sym70207267267732073-89942015-05-26doi: 10.3390/sym7020726Gorazd CvetičClaudio DibChoong KimJilberto Zamora-Saá<![CDATA[Symmetry, Vol. 7, Pages 714-725: Conservation Laws of Discrete Evolution Equations by Symmetries and Adjoint Symmetries]]>
http://www.mdpi.com/2073-8994/7/2/714
A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for the disadvantage of non-Lagrangian structures in presenting a correspondence between symmetries and conservation laws. Applications are made for the construction of conservation laws of the Volterra lattice equation.Symmetry2015-05-2272Article10.3390/sym70207147147252073-89942015-05-22doi: 10.3390/sym7020714Wen-Xiu Ma<![CDATA[Symmetry, Vol. 7, Pages 689-713: Sensitivity of High-Scale SUSY in Low Energy Hadronic FCNC]]>
http://www.mdpi.com/2073-8994/7/2/689
We discuss the sensitivity of the high-scale supersymmetry (SUSY) at \(10\)–\(1000\) TeV in \(B^0\), \(B_s\), \(K^0\) and \(D\) meson systems together with the neutron electric dipole moment (EDM) and the mercury EDM. In order to estimate the contribution of the squark flavor mixing to these flavor changing neutral currents (FCNCs), we calculate the squark mass spectrum, which is consistent with the recent Higgs discovery. The SUSY contribution in \(\epsilon_K\) could be large, around \(40\%\) in the region of the SUSY scale \(10\)–\(100\) TeV. The neutron EDM and the mercury EDM are also sensitive to the SUSY contribution induced by the gluino-squark interaction. The predicted EDMs are roughly proportional to \(|\epsilon_K^{\rm SUSY}|\). If the SUSY contribution is the level of \({\cal O}(10\%)\) for \(\epsilon_K\), the neutron EDM is expected to be discovered in the region of \(10^{-28}\)–\(10^{-26}\) ecm. The mercury EDM also gives a strong constraint for the gluino-squark interaction. The SUSY contribution of \(\Delta M_D\) is also discussed.Symmetry2015-05-2172Article10.3390/sym70206896897132073-89942015-05-21doi: 10.3390/sym7020689Morimitsu TanimotoKei Yamamoto<![CDATA[Symmetry, Vol. 7, Pages 675-688: Secure Cooperative Spectrum Sensing via a Novel User-Classification Scheme in Cognitive Radios for Future Communication Technologies]]>
http://www.mdpi.com/2073-8994/7/2/675
Future communication networks would be required to deliver data on a far greater scale than is known to us today, thus mandating the maximal utilization of the available radio spectrum using cognitive radios. In this paper, we have proposed a novel cooperative spectrum sensing approach for cognitive radios. In cooperative spectrum sensing, the fusion center relies on reports of the cognitive users to make a global decision. The global decision is obtained by assigning weights to the reports received from cognitive users. Computation of such weights requires prior information of the probability of detection and the probability of false alarms, which are not readily available in real scenarios. Further, the cognitive users are divided into reliable and unreliable categories based on their weighted energy by using some empirical threshold. In this paper, we propose a method to classify the cognitive users into reliable, neutral and unreliable categories without using any pre-defined or empirically-obtained threshold. Moreover, the computation of weights does not require the detection, or false alarm probabilities, or an estimate of these probabilities. Reliable cognitive users are assigned the highest weights; neutral cognitive users are assigned medium weights (less than the reliable and higher than the unreliable cognitive users’ weights); and unreliable users are assigned the least weights. We show the performance improvement of our proposed method through simulations by comparing it with the conventional cooperative spectrum sensing scheme through different metrics, like receiver operating characteristic (ROC) curve and mean square error. For clarity, we also show the effect of malicious users on detection probability and false alarm probability individually through simulations.Symmetry2015-05-1472Article10.3390/sym70206756756882073-89942015-05-14doi: 10.3390/sym7020675Muhammad UsmanKoo Insoo<![CDATA[Symmetry, Vol. 7, Pages 651-674: Harmonic Maps and Biharmonic Maps]]>
http://www.mdpi.com/2073-8994/7/2/651
This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.Symmetry2015-05-1272Article10.3390/sym70206516516742073-89942015-05-12doi: 10.3390/sym7020651Hajime Urakawa<![CDATA[Symmetry, Vol. 7, Pages 625-650: Coupled SU(3)-Structures and Supersymmetry]]>
http://www.mdpi.com/2073-8994/7/2/625
We review coupled SU(3)-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behavior of flows of SU(3)-structures with respect to the coupled condition.Symmetry2015-05-1172Article10.3390/sym70206256256502073-89942015-05-11doi: 10.3390/sym7020625Anna FinoAlberto Raffero<![CDATA[Symmetry, Vol. 7, Pages 599-624: Reduction by Lie Group Symmetries in Diffeomorphic Image Registration and Deformation Modelling]]>
http://www.mdpi.com/2073-8994/7/2/599
We survey the role of reduction by symmetry in the large deformation diffeomorphic metric mapping framework for registration of a variety of data types (landmarks, curves, surfaces, images and higher-order derivative data). Particle relabelling symmetry allows the equations of motion to be reduced to the Lie algebra allowing the equations to be written purely in terms of the Eulerian velocity field. As a second use of symmetry, the infinite dimensional problem of finding correspondences between objects can be reduced for a range of concrete data types, resulting in compact representations of shape and spatial structure. Using reduction by symmetry, we describe these models in a common theoretical framework that draws on links between the registration problem and geometric mechanics. We outline these constructions and further cases where reduction by symmetry promises new approaches to the registration of complex data types.Symmetry2015-05-0772Article10.3390/sym70205995996242073-89942015-05-07doi: 10.3390/sym7020599Stefan SommerHenry Jacobs<![CDATA[Symmetry, Vol. 7, Pages 561-598: Group Theory of Wannier Functions Providing the Basis for a Deeper Understanding of Magnetism and Superconductivity]]>
http://www.mdpi.com/2073-8994/7/2/561
The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger) in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates.Symmetry2015-05-0572Review10.3390/sym70205615615982073-89942015-05-05doi: 10.3390/sym7020561Ekkehard KrügerHorst Strunk<![CDATA[Symmetry, Vol. 7, Pages 546-560: Online Social Snapshots of a Generic Facebook Session Based on Digital Insight Data for a Secure Future IT Environment]]>
http://www.mdpi.com/2073-8994/7/2/546
Physical memory acquisition has been an import facet for digital forensics (DF) specialists due to its volatile characteristics. Nowadays, thousands of millions of global participants utilize online social networking (OSN) mechanisms to expand their social lives, ranging from business-oriented purposes to leisure motivations. Facebook (FB) is one of the most dominant social networking sites (SNS) available today. Unfortunately, it has been a major avenue for cybercriminals to commit illegal activities. Therefore, the digital traces of previous sessions of an FB user play an essential role as the first step for DF experts to pursue the disclosure of the identity of the suspect who was exploiting FB. In this research work, we provide a systematic methodology to reveal a previous session of an FB identity, as well as his/her partial social circle via collecting, analyzing, preserving and presenting the associated digital traces to obtain the online social snapshots of a specific FB user who was utilizing a computing device with Internet Explorer (IE) 10 without turning off the power of the gadget. This novel approach can be a paradigm for how DF specialists ponder the crime scene to conduct the first response in order to avoid the permanent loss of the precious digital evidence in previous FB sessions. The hash values of the image files of the random access memory (RAM) of the computing device have proven to be identical before and after forensics operations, which could be probative evidence in a court of law.Symmetry2015-05-0472Article10.3390/sym70205465465602073-89942015-05-04doi: 10.3390/sym7020546Hai-Cheng ChuJong Park<![CDATA[Symmetry, Vol. 7, Pages 515-545: Some Elementary Aspects of 4-Dimensional Geometry]]>
http://www.mdpi.com/2073-8994/7/2/515
We indicate that Heron’s formula (which relates the square of the area of a triangle to a quartic function of its edge lengths) can be interpreted as a scissors congruence in four-dimensional space. In the process of demonstrating this, we examine a number of decompositions of hypercubes, hyper-parallelograms and other elementary four-dimensional solids.Symmetry2015-05-0472Article10.3390/sym70205155155452073-89942015-05-04doi: 10.3390/sym7020515J. CarterDavid Mullens<![CDATA[Symmetry, Vol. 7, Pages 488-514: Fluctuating and Directional Asymmetry of the Blue Mussel (Mytilus edulis): Improving Methods of Morphological Analysis to Explore Species Performance at the Northern Border of Its Range]]>
http://www.mdpi.com/2073-8994/7/2/488
In this work we examined morphological variation at different levels to study performance and population structuring of the blue mussel Mytilus edulis. Our objectives were: (i) to develop an integrated technique for analyzing morphological variation in blue mussels and, based on this technique; (ii) to perform a morphometric description of mussels from the northern part of their range; and (iii) to verify the hypothesis that populations at the outer range of their distribution have reduced performance due to harsh climatic conditions. Means, directional asymmetry (i.e., systematic differences between left and right structures), fluctuating asymmetry (random deviations from perfect symmetry, a measure of developmental instability), factorial variation (difference between total variance and variance of fluctuating asymmetry, an indirect index of genotypic variation), and measurement error were examined for 14 bilateral characters of muscle scars on mussel shells. Also, we analyzed one non-bilateral character. For the first time directional asymmetry—approaching 13% of the right:left ratio—was described in blue mussels. Measurement error, often ignored in morphometric studies, contributed 26% of total variance. Accurately addressing these methodical challenges is key to further and improved ecological interpretations. Morphological differences were found between (i) samples from estuarine areas in the White and Pechora Seas and (ii) samples from Barents Sea areas with oceanic salinity. Samples from the first group exhibited lower fluctuating asymmetry, indicating higher developmental stability likely due to better feeding conditions and lower factorial variation, which may result from lower genotypic variation. Absence of correlation between fluctuating asymmetry and temperature suggests that low temperatures in the northern border of their range do not degrade the performance of adult blue mussels in this region.Symmetry2015-04-2972Article10.3390/sym70204884885142073-89942015-04-29doi: 10.3390/sym7020488Dmitry LajusMarina KatolikovaPetr StrelkovHerman Hummel<![CDATA[Symmetry, Vol. 7, Pages 464-487: Provable Fair Document Exchange Protocol with Transaction Privacy for E-Commerce]]>
http://www.mdpi.com/2073-8994/7/2/464
Transaction privacy has attracted a lot of attention in the e-commerce. This study proposes an efficient and provable fair document exchange protocol with transaction privacy. Using the proposed protocol, any untrusted parties can fairly exchange documents without the assistance of online, trusted third parties. Moreover, a notary only notarizes each document once. The authorized document owner can exchange a notarized document with different parties repeatedly without disclosing the origin of the document or the identities of transaction participants. Security and performance analyses indicate that the proposed protocol not only provides strong fairness, non-repudiation of origin, non-repudiation of receipt, and message confidentiality, but also enhances forward secrecy, transaction privacy, and authorized exchange. The proposed protocol is more efficient than other works.Symmetry2015-04-2872Article10.3390/sym70204644644872073-89942015-04-28doi: 10.3390/sym7020464Ren-Junn HwangChih-Hua Lai<![CDATA[Symmetry, Vol. 7, Pages 450-463: On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons]]>
http://www.mdpi.com/2073-8994/7/2/450
We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed here in a non-standard way. Thus, two separate two-component Majorana-type field equations for the eigenfields of the charge-conjugation operator are obtained. The corresponding free fields are entirely separated without a gauge field, but remain mixed and coupled together through an electromagnetic field term. For fermions that are charged and, thus, subjected to the gauge field of electrodynamics, these two Majorana fields can be reassembled into a doublet, which is equivalent to a standard four-component Dirac spinor field. In this way, the Dirac equation is retained in a new guise, which is fully equivalent to that equation in its chiral form.Symmetry2015-04-2772Article10.3390/sym70204504504632073-89942015-04-27doi: 10.3390/sym7020450Eckart Marsch<![CDATA[Symmetry, Vol. 7, Pages 427-449: Unsupervised Object Modeling and Segmentation with Symmetry Detection for Human Activity Recognition]]>
http://www.mdpi.com/2073-8994/7/2/427
In this paper we present a novel unsupervised approach to detecting and segmenting objects as well as their constituent symmetric parts in an image. Traditional unsupervised image segmentation is limited by two obvious deficiencies: the object detection accuracy degrades with the misaligned boundaries between the segmented regions and the target, and pre-learned models are required to group regions into meaningful objects. To tackle these difficulties, the proposed approach aims at incorporating the pair-wise detection of symmetric patches to achieve the goal of segmenting images into symmetric parts. The skeletons of these symmetric parts then provide estimates of the bounding boxes to locate the target objects. Finally, for each detected object, the graphcut-based segmentation algorithm is applied to find its contour. The proposed approach has significant advantages: no a priori object models are used, and multiple objects are detected. To verify the effectiveness of the approach based on the cues that a face part contains an oval shape and skin colors, human objects are extracted from among the detected objects. The detected human objects and their parts are finally tracked across video frames to capture the object part movements for learning the human activity models from video clips. Experimental results show that the proposed method gives good performance on publicly available datasets.Symmetry2015-04-2372Article10.3390/sym70204274274492073-89942015-04-23doi: 10.3390/sym7020427Jui-Yuan SuShyi-Chyi ChengDe-Kai Huang<![CDATA[Symmetry, Vol. 7, Pages 412-426: Confluent Supersymmetric Partners of Quantum Systems Emerging from the Spheroidal Equation]]>
http://www.mdpi.com/2073-8994/7/2/412
We construct confluent supersymmetric partners of quantum systems that emerge from the spheroidal equation. Properties of the systems and of their transformed counterparts are discussed.Symmetry2015-04-2272Article10.3390/sym70204124124262073-89942015-04-22doi: 10.3390/sym7020412Axel Schulze-HalbergJie Wang<![CDATA[Symmetry, Vol. 7, Pages 395-411: Motion Key-Frame Extraction by Using Optimized t-Stochastic Neighbor Embedding]]>
http://www.mdpi.com/2073-8994/7/2/395
Key-frame extracting technology has been widely used in the field of human motion synthesis. Efficient and accurate key frames extraction methods can improve the accuracy of motion synthesis. In this paper, we use an optimized t-Stochastic Neighbor Embedding (t-SNE for short) algorithm to reduce the data and on this basis extract the key frames. The experimental results show that the validity of this method is better than the existing methods under the same experimental data.Symmetry2015-04-2172Technical Note10.3390/sym70203953954112073-89942015-04-21doi: 10.3390/sym7020395Qiang ZhangYi YaoDongsheng ZhouRui Liu<![CDATA[Symmetry, Vol. 7, Pages 383-394: The Digital Fingerprinting Analysis Concerning Google Calendar under Ubiquitous Mobile Computing Era]]>
http://www.mdpi.com/2073-8994/7/2/383
Internet Communication Technologies (ICTs) are making progress day by day, driven by the relentless need to utilize them for everything from leisure to business. This inevitable trend has dramatically changed contemporary digital behavior in all aspects. Undoubtedly, digital fingerprints will be at some point unwarily left on crime scenes creating digital information security incidents. On the other hand, corporates in the private sector or governments are on the edge of being exploited in terms of confidential digital information leakages. Some digital fingerprinting is volatile by its nature. Alternatively, once the power of computing devices is no longer sustainable, these digital traces could disappear forever. Due to the pervasive usage of Google Calendar and Safari browser among network communities, digital fingerprinting could be disclosed if forensics is carried out in a sound manner, which could be admitted in a court of law as probative evidences concerning certain cybercrime incidents.Symmetry2015-04-1772Article10.3390/sym70203833833942073-89942015-04-17doi: 10.3390/sym7020383Hai-Cheng ChuGai-Ge WangJong Park<![CDATA[Symmetry, Vol. 7, Pages 376-382: A Development of Hybrid Drug Information System Using Image Recognition]]>
http://www.mdpi.com/2073-8994/7/2/376
In order to prevent drug abuse or misuse cases and avoid over-prescriptions, it is necessary for medicine taker to be provided with detailed information about the medicine. In this paper, we propose a drug information system and develop an application to provide information through drug image recognition using a smartphone. We designed a contents-based drug image search algorithm using the color, shape and imprint of drug. Our convenient application can provide users with detailed information about drugs and prevent drug misuse.Symmetry2015-04-1672Article10.3390/sym70203763763822073-89942015-04-16doi: 10.3390/sym7020376HwaMin LeeDoo-Soon ParkMin-Hyung Choi<![CDATA[Symmetry, Vol. 7, Pages 365-375: Everywhere Equivalent 2-Component Links]]>
http://www.mdpi.com/2073-8994/7/2/365
A link diagram is said to be (orientedly) everywhere equivalent if all the diagramsobtained by switching one crossing represent the same (oriented) link. We classify suchdiagrams of two components.Symmetry2015-04-1372Article10.3390/sym70203653653752073-89942015-04-13doi: 10.3390/sym7020365Alexander Stoimenow<![CDATA[Symmetry, Vol. 7, Pages 354-364: Variation in Fractal Symmetry of Annual Growth in Aspen as an Indicator of Developmental Stability in Trees]]>
http://www.mdpi.com/2073-8994/7/2/354
Fractal symmetry is symmetry across scale. If one looks at a branch of a tree its branching pattern is reminiscent of the tree as a whole. Plants exhibit a number of different symmetries, including bilateral, rotational, translational, and fractal; deviations from each of these types has been associated with organisms developing in stressful environments. Here, we explore the utilization and meaning of fractal analysis on annual growth ring production in woody plants. Early detection of stress in plants is difficult and the compounding effects of multiple or severe stressors can lead to irreversible damage or death. Annual wood production was used to produce a time series for individuals from stands classified as either high vigor or low vigor (a general measure of health). As a measure of symmetry over time, the fractal dimension of each time series was determined and compared among vigor classes. We found that individuals obtained from low vigor sites had a significantly lower fractal dimension than those from high vigor sites. These results agree with patterns found in a variety of other organisms, and we argue that the reduced fractal dimension is related to a loss in system complexity of stressed individuals.Symmetry2015-04-0972Article10.3390/sym70203543543642073-89942015-04-09doi: 10.3390/sym7020354Jordan SinclairDaniel KashianJohn BradfordD. Freeman<![CDATA[Symmetry, Vol. 7, Pages 336-353: The Perception of Symmetry in Depth: Effect of Symmetry Plane Orientation]]>
http://www.mdpi.com/2073-8994/7/2/336
The visual system is sensitive to symmetries in the frontoparallel plane, and bilateral symmetry about a vertical axis has a particular salience. However, these symmetries represent only a subset of the symmetries realizable in three-dimensional space. The retinal image symmetries formed when viewing natural objects are typically the projections of three-dimensional objects—animals, for example—that have a symmetry in depth. To characterize human sensitivity to depth symmetry, experiments measured observers’ ability to discriminate stereo displays that were symmetrically distributed in depth and those that were asymmetrically distributed. Disparity values were distributed about one of four planes passing through the z-axis and differing in frontoparallel orientation. Asymmetrical patterns were generated by perturbing one of these disparities. Symmetrical-asymmetrical discrimination thresholds were lowest for symmetry about the vertical plane and highest for the horizontal plane. Thresholds for discriminating repetitions and non-repetitions of depth values did not differ across the four planes, whereas discriminations for depth gradients differed from both the symmetry and repetition cases. The heightened sensitivity to symmetry in depth about the vertical plane is a 3-D analog of 2-D mirror-image symmetry performance and could be its source.Symmetry2015-04-0372Article10.3390/sym70203363363532073-89942015-04-03doi: 10.3390/sym7020336Bart Farell<![CDATA[Symmetry, Vol. 7, Pages 327-335: A New Fluctuating Asymmetry Index, or the Solution for the Scaling Effect?]]>
http://www.mdpi.com/2073-8994/7/2/327
Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ2p), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability can be tested with an F-test, which is the most common way to compare variances. However, the variance is expected to scale proportionally to the square of the mean as there is a tendency in biological data for σ2p to scale proportionally to the square of the mean ( ): σ2p = Z ξ, where ξ is the scaling exponent, which is expected to be two for pure statistical reasons, is the mean of the trait and Z is a measure of individual-level variability. Because of this scaling effect, the fluctuating asymmetry will be affected, FA is estimated as the variance between the right and the left sides of a trait (σ2r − l = σ2r + σ2l − 2rσrσl), where σ2r and σ2l are the variances of the right and the left trait values, respectively. In this paper, we propose a novel method that allows an exact correction of the scaling effect, which will enable a proper comparison of the degree of fluctuating asymmetry for a trait. The problem of the scaling of the FA with the trait size is quite crucial if FA is to be considered an indicator of fitness or an indicator of environmental or genetic stress, as different stresses or fitness levels are typically accompanied by a change of the traits’ .Symmetry2015-04-0172Brief Report10.3390/sym70203273273352073-89942015-04-01doi: 10.3390/sym7020327Cino PertoldiTorsten Kristensen<![CDATA[Symmetry, Vol. 7, Pages 305-326: Topology of Platonic Spherical Manifolds: From Homotopy to Harmonic Analysis]]>
http://www.mdpi.com/2073-8994/7/2/305
We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the corresponding deck group. We employ the point symmetry of each Platonic manifold to construct its fundamental domain as a spherical orbifold. While the three-sphere supports an orthonormal complete basis for harmonic analysis formed by Wigner polynomials, a given spherical orbifold leads to a selection of a specific subbasis. The resulting selection rules find applications in cosmic topology, probed by the cosmic microwave background.Symmetry2015-03-3172Article10.3390/sym70203053053262073-89942015-03-31doi: 10.3390/sym7020305Peter Kramer<![CDATA[Symmetry, Vol. 7, Pages 294-304: Live Mobile Distance Learning System for Smart Devices]]>
http://www.mdpi.com/2073-8994/7/2/294
In recent years, mobile and ubiquitous computing has emerged in our daily lives, and extensive studies have been conducted in various areas using smart devices, such as tablets, smartphones, smart TVs, smart refrigerators, and smart media devices, in order to realize this computing technology. Especially, the integration of mobile networking technology and intelligent mobile devices has made it possible to develop the advanced mobile distance learning system that supports portable smart devices such as smartphones and tablets for the future IT environment. We present a synchronous mobile learning system that enables both instructor and student to participate in distance learning with their tablets. When an instructor gives a lecture using a tablet with front-face camera by bringing up slides and making annotations on them, students in the distance can watch the instructor and those slides with annotation on their own tablets in real time. A student can also ask a question or have a discussion together using the text chat feature of the system during a learning session. We also show the user evaluation of the system. A user survey shows that about 67% are in favor of the prototype of the system.Symmetry2015-03-2572Article10.3390/sym70202942943042073-89942015-03-25doi: 10.3390/sym7020294Jang LeeDoo-Soon ParkYoung-Sik JeongJong Park<![CDATA[Symmetry, Vol. 7, Pages 284-293: Variation in Measurement Error in Asymmetry Studies: A New Model, Simulations and Application]]>
http://www.mdpi.com/2073-8994/7/2/284
The importance of measurement error in studies of asymmetry has been acknowledged for a long time. It is now common practice to acquire independent repeated measurements of trait values and to estimate the degree of measurement error relative to the amount of asymmetry. Methods also allow obtaining unbiased estimates of asymmetry, both at the population and individual level. One aspect that has been ignored is potential between-individual variation in measurement error. In this paper, I develop a new method to investigate this variation in measurement error and to generate unbiased estimates of individual asymmetries. Simulations show that variation in measurement error can indeed result in biased estimates of individual asymmetry and that the proposed method adequately provides unbiased estimates. The method is applied to two empirical datasets and shows that, at least in some traits, substantial variations in measurement occur. The limitations of the model are discussed.Symmetry2015-03-2472Article10.3390/sym70202842842932073-89942015-03-24doi: 10.3390/sym7020284Stefan Van Dongen<![CDATA[Symmetry, Vol. 7, Pages 269-283: Study on User Authority Management for Safe Data Protection in Cloud Computing Environments]]>
http://www.mdpi.com/2073-8994/7/1/269
In cloud computing environments, user data are encrypted using numerous distributed servers before storing such data. Global Internet service companies, such as Google and Yahoo, recognized the importance of Internet service platforms and conducted self-research and development to create and utilize large cluster-based cloud computing platform technology based on low-priced commercial nodes. As diverse data services become possible in distributed computing environments, high-capacity distributed management is emerging as a major issue. Meanwhile, because of the diverse forms of using high-capacity data, security vulnerability and privacy invasion by malicious attackers or internal users can occur. As such, when various sensitive data are stored in cloud servers and used from there, the problem of data spill might occur because of external attackers or the poor management of internal users. Data can be managed through encryption to prevent such problems. However, existing simple encryption methods involve problems associated with the management of access to data stored in cloud environments. Therefore, in the present paper, a technique for data access management by user authority, based on Attribute-Based Encryption (ABE) and secret distribution techniques, is proposed.Symmetry2015-03-1971Technical Note10.3390/sym70102692692832073-89942015-03-19doi: 10.3390/sym7010269Su-Hyun KimIm-Yeong Lee<![CDATA[Symmetry, Vol. 7, Pages 255-268: Fluctuating Asymmetry of Plant Leaves: Batch Processing with LAMINA and Continuous Symmetry Measures]]>
http://www.mdpi.com/2073-8994/7/1/255
Unlike landmark methods for estimating object asymmetry, continuous symmetry measures (CSM) can be used to measure the symmetry distance (ds) of inconsistent objects, such as plant leaves. Inconsistent objects have no homologous landmarks, no consistent topology, no quantitative consistency, and sometimes no matching points. When CSM is used in conjugation with LAMINA Leaf Shape Determination software, one can quickly and efficiently process a large number of scanned leaves. LAMINA automatically generates equally-spaced points around the perimeter of each leaf and the resulting x-y coordinates are normalized to average centroid size prior to estimating ds using a fold, average, unfold algorithm. We estimated shape asymmetry of leaves of three species of flowering plants: Ligustrum sinense (Chinese Privet), Rubus cuneifolius (blackberry), and Perilla frutescens (Perilla), as well as individual leaves from a few species of oaks (Quercus) and maples (Acer). We found that 100 to 200 equally-spaced points worked well for all three of the main species. Measurement error accounted for a small proportion of the asymmetry variation. Nevertheless, measurement error was great enough to generate some negative size scaling after normalization to average centroid size.Symmetry2015-03-1371Article10.3390/sym70102552552682073-89942015-03-13doi: 10.3390/sym7010255John GrahamMattie WhitesellMark IIHagit Hel-OrEviatar NevoShmuel Raz<![CDATA[Symmetry, Vol. 7, Pages 241-254: Evidence for Obliqueness of Angles as a Cue to Planar Surface Slant Found in Extremely Simple Symmetrical Shapes]]>
http://www.mdpi.com/2073-8994/7/1/241
The Necker cube is a striking example for perceptual dominance of 3D over 2D. Object symmetry and obliqueness of angles are co-varying cues that may underlie the perceived slant of Necker cubes. To investigate the power of the oblique-angle cue, slants were judged of extremely simple symmetrical shapes. Slant computations based on an assumption of orthogonality were made for two abutting lines as a function of vertex angle and the slant of the screen. Computed slants were compared with slants judged by six subjects under binocular viewing conditions. Judged slant was highly correlated with slant specified by the oblique angles under an assumption of orthogonality. The contributions of screen cues, including binocular disparity, were negligible. The consistency of the judgments across subjects indicates the assumption of orthogonality as one of the principles underlying slant perception. Necker cubes illustrate that the visual system can disengage unambiguous cues in favor of ambiguous object-symmetry and oblique-angle cues, if the latter indicate very different slants. Selective disengagement of cues may be the mechanism that underlies the success of 2D images in ancient, as well as modern civilizations.Symmetry2015-03-0971Article10.3390/sym70102412412542073-89942015-03-09doi: 10.3390/sym7010241Casper Erkelens<![CDATA[Symmetry, Vol. 7, Pages 220-240: Inflationary Cosmology in Modified Gravity Theories]]>
http://www.mdpi.com/2073-8994/7/1/220
We review inflationary cosmology in modified gravity such as R2 gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the R2 term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in F(R) gravity is also explained.Symmetry2015-03-0971Review10.3390/sym70102202202402073-89942015-03-09doi: 10.3390/sym7010220Kazuharu BambaSergei Odintsov<![CDATA[Symmetry, Vol. 7, Pages 206-219: Teaching-Learning Activity Modeling Based on Data Analysis]]>
http://www.mdpi.com/2073-8994/7/1/206
Numerous studies are currently being carried out on personalized services based on data analysis to find and provide valuable information about information overload. Furthermore, the number of studies on data analysis of teaching-learning activities for personalized services in the field of teaching-learning is increasing, too. This paper proposes a learning style recency-frequency-durability (LS-RFD) model for quantified analysis on the level of activities of learners, to provide the elements of teaching-learning activities according to the learning style of the learner among various parameters for personalized service. This is to measure preferences as to teaching-learning activity according to recency, frequency and durability of such activities. Based on the results, user characteristics can be classified into groups for teaching-learning activity by categorizing the level of preference and activity of the learner.Symmetry2015-03-0571Article10.3390/sym70102062062192073-89942015-03-05doi: 10.3390/sym7010206Kyungrog KimYoo-Joo ChoiMihui KimJung-Won LeeDoo-Soon ParkNammee Moon<![CDATA[Symmetry, Vol. 7, Pages 193-205: 126 GeV Higgs Boson Associated with D-term Triggered Dynamical Supersymmetry Breaking]]>
http://www.mdpi.com/2073-8994/7/1/193
Continuing with our previous work on \(D\)-term triggered dynamical supersymmetry breaking, , we consider a system in which our generic \({\cal N}=1\) action is minimally extended to include the pair of Higgs doublet superfields charged under the overall \(U(1)\) together with μ and Bμ terms. The gauge group is taken to be \(SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)\). We point out, among other things, that the Higgs mass less than the \(\textit{Z}\)-boson mass at tree level can be pushed up to be around 126 GeV by \(D\)-term contributions of the overall \(U(1)\). This is readily realized by taking a \(U(1)\) gauge coupling to be \({\cal O}(1)\).Symmetry2015-03-0371Article10.3390/sym70101931932052073-89942015-03-03doi: 10.3390/sym7010193Hiroshi ItoyamaNobuhito Maru<![CDATA[Symmetry, Vol. 7, Pages 182-192: Real-Time Projection-Based Augmented Reality System for Dynamic Objects in the Performing Arts]]>
http://www.mdpi.com/2073-8994/7/1/182
This paper describes the case study of applying projection-based augmented reality, especially for dynamic objects in live performing shows, such as plays, dancing, or musicals. Our study aims to project imagery correctly inside the silhouettes of flexible objects, in other words, live actors or the surface of actor’s costumes; the silhouette transforms its own shape frequently. To realize this work, we implemented a special projection system based on the real-time masking technique, that is to say real-time projection-based augmented reality system for dynamic objects in performing arts. We installed the sets on a stage for live performance, and rehearsed particular scenes of a musical. In live performance, using projection-based augmented reality technology enhances technical and theatrical aspects which were not possible with existing video projection techniques. The projected images on the surfaces of actor’s costume could not only express the particular scene of a performance more effectively, but also lead the audience to an extraordinary visual experience.Symmetry2015-02-2771Article10.3390/sym70101821821922073-89942015-02-27doi: 10.3390/sym7010182Jaewoon LeeYeonjin KimMyeong-Hyeon HeoDongho KimByeong-Seok Shin<![CDATA[Symmetry, Vol. 7, Pages 164-181: Symmetry of “Twins”]]>
http://www.mdpi.com/2073-8994/7/1/164
The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D and 3D perception analyses. We start analyzing a pair of twin buildings with projection of the architectural composition elements in 2D picture plane (plane of the composition) and we distinguish four 2D keyframe cases based on the relation between the bilateral symmetry of the twin composition and the bilateral symmetry of each element. In 3D perception for each 2D keyframe case there are two sub-variants, with and without a symmetry plane parallel to the picture plane. The bilateral symmetry is dominant if the corresponding symmetry plane is orthogonal to the picture plane. The essence of the complete classification is relation between the bilateral (dominant) symmetry of the architectural composition and the bilateral symmetry of each element of that composition.Symmetry2015-02-1371Article10.3390/sym70101641641812073-89942015-02-13doi: 10.3390/sym7010164Vladan NikolićLjiljana RadovićBiserka Marković<![CDATA[Symmetry, Vol. 7, Pages 146-163: The Genetic Architecture of Fluctuating Asymmetry of Mandible Size and Shape in a Population of Mice: Another Look]]>
http://www.mdpi.com/2073-8994/7/1/146
Fluctuating asymmetry (FA), typically measured by variation in the differences between right and left sides of bilateral traits, is commonly used to assess developmental instability (DI) in populations. A previous quantitative trait locus (QTL) investigation using an F2 intercross mouse population found little evidence of individual loci affecting FA in mandible size, but an abundance of epistatic interactions between loci. Here we extend this work by testing whether these patterns replicate in an F3 population derived from the same intercross. Using a large number of molecular markers genotyped in over 1200 mice, we uncovered significant interactions between loci (QTLs) affecting FA in mandible size (and shape). Epistasis contributed roughly 20% of the variation in FASIZE and 19% of the variation in FASHAPE at the 0.0001 probability level alone, and was comparable to that previously estimated for the F2 mice, and much greater than that generated from the few single-locus QTLs affecting the mandible FA traits. The positions of the single-locus and epistatic QTLs for FA that we discovered suggested that logical candidate genes for DI are those controlling size or shape in the traits themselves, and that they may be interacting with genes for heat shock proteins.Symmetry2015-02-1171Article10.3390/sym70101461461632073-89942015-02-11doi: 10.3390/sym7010146Larry LeamyChristian KlingenbergEmma SherrattJason WolfJames Cheverud<![CDATA[Symmetry, Vol. 7, Pages 125-145: Crystallography and Magnetic Phenomena]]>
http://www.mdpi.com/2073-8994/7/1/125
This essay describes the development of groups used for the specification of symmetries from ordinary and magnetic point groups to Fedorov and magnetic space groups, as well as other varieties of groups useful in the study of symmetric objects. In particular, we consider the problem of some incorrectness in Vol. A of the International Tables for Crystallography. Some results of tensor calculus are presented in connection with magnetoelectric phenomena, where we demonstrate the use of Ascher’s trinities and Opechowski’s magic relations and their connection. Specific tensor decomposition calculations on the grounds of Clebsch Gordan products are illustrated.Symmetry2015-02-0271Article10.3390/sym70101251251452073-89942015-02-02doi: 10.3390/sym7010125Vojtěch Kopský<![CDATA[Symmetry, Vol. 7, Pages 105-124: Two-Round Password-Only Authenticated Key Exchange in the Three-Party Setting]]>
http://www.mdpi.com/2073-8994/7/1/105
We present the first provably-secure three-party password-only authenticated key exchange (PAKE) protocol that can run in only two communication rounds. Our protocol is generic in the sense that it can be constructed from any two-party PAKE protocol. The protocol is proven secure in a variant of the widely-accepted model of Bellare, Pointcheval and Rogaway (2000) without any idealized assumptions on the cryptographic primitives used. We also investigate the security of the two-round, three-party PAKE protocol of Wang, Hu and Li (2010) and demonstrate that this protocol cannot achieve implicit key authentication in the presence of an active adversary.Symmetry2015-01-2771Article10.3390/sym70101051051242073-89942015-01-27doi: 10.3390/sym7010105Junghyun NamKim-Kwang ChooSangchul HanJuryon PaikDongho Won<![CDATA[Symmetry, Vol. 7, Pages 89-104: Can the Comparisons of Feature Locations Explain the Difficulty in Discriminating Mirror-Reflected Pairs of Geometrical Figures from Disoriented Identical Pairs?]]>
http://www.mdpi.com/2073-8994/7/1/89
The present experiment investigates whether patterns of shifts of feature locations could affect the same/different decisions of simultaneously presented pairs of geometrical figures. A shift of locations was defined as the angular distance from the location of a feature in one figure to the location of the same feature in another figure. It was hypothesized that the difficulty in discriminating mirror-reflected (or axisymmetric) pairs from disoriented identical pairs was caused by complex shifting patterns inherent in axisymmetric pairs. According to the shifts of the locations of the four structural features, five pair types were prepared. They could be ordered from completely identical to completely different in their shifts: identical 0/4 pairs, non-identical 1/4 pairs, non-identical 2/4 pairs = axisymmetric 2/4 pairs and non-identical 4/4 pairs. The latencies for non-identical pairs decreased with the increase of difference in the shifts of feature locations, indicating that serial, self-terminating comparisons of the shifts were applied to the discrimination of non-identical pairs from identical pairs. However, the longer latencies in axisymmetric 2/4 pairs than in non-identical 2/4 pairs suggested that the difficulty for axisymmetric pairs was not caused by the complex shifting patterns, and the difficulty was not satisfactorily explained by the comparisons of feature locations.Symmetry2015-01-2371Article10.3390/sym7010089891042073-89942015-01-23doi: 10.3390/sym7010089Fumio Kanbe<![CDATA[Symmetry, Vol. 7, Pages 67-88: Dihedral Reductions of Cyclic DNA Sequences]]>
http://www.mdpi.com/2073-8994/7/1/67
The data-analytic methodology of dihedral reductions for cyclic orbits of distinct-base codons is described both in terms of Fourier analysis over the dihedral groups and in (algebraically equivalent) terms of canonical projections. Numerical evaluations are presented for discrete and continuous scalar data indexed by cyclic orbits.Symmetry2015-01-1671Article10.3390/sym701006767882073-89942015-01-16doi: 10.3390/sym7010067Marlos Viana<![CDATA[Symmetry, Vol. 7, Pages 53-66: Output Effect Evaluation Based on Input Features in Neural Incremental Attribute Learning for Better Classification Performance]]>
http://www.mdpi.com/2073-8994/7/1/53
Machine learning is a very important approach to pattern classification. This paper provides a better insight into Incremental Attribute Learning (IAL) with further analysis as to why it can exhibit better performance than conventional batch training. IAL is a novel supervised machine learning strategy, which gradually trains features in one or more chunks. Previous research showed that IAL can obtain lower classification error rates than a conventional batch training approach. Yet the reason for that is still not very clear. In this study, the feasibility of IAL is verified by mathematical approaches. Moreover, experimental results derived by IAL neural networks on benchmarks also confirm the mathematical validation.Symmetry2015-01-1471Article10.3390/sym701005353662073-89942015-01-14doi: 10.3390/sym7010053Ting WangSheng-Uei GuanKa ManJong ParkHui-Huang Hsu<![CDATA[Symmetry, Vol. 7, Pages 43-52: Development of Guanidine-Bisurea Bifunctional Organocatalyst Bearing Chirality at the Inner and Outer Sides of the Urea Groups, and Application to Enantioselective α-Hydroxylation of Pyranoindolizine Intermediate for Camptothecin Synthesis]]>
http://www.mdpi.com/2073-8994/7/1/43
Pyranoindolizine is a tricyclic structure found in various biologically active compounds, such as camptothecin (CPT) and its derivatives. In the case of CPTs, the chirality at the α-position in the α-hydroxyl lactone moiety of pyranoindolizine is important for the antitumor activity. This paper deals with enantioselective oxidation of the α-position in pyranoindolizine lactone, which corresponds at C20 in CPT, with cumene hydroperoxide (CHP) in the presence of newly synthesized guanidine-bisurea bifunctional organocatalysts bearing chirality on both the inner and outer sides of the urea groups.Symmetry2015-01-1471Article10.3390/sym701004343522073-89942015-01-14doi: 10.3390/sym7010043Minami OdagiTatsuya WatanabeKazuo Nagasawa<![CDATA[Symmetry, Vol. 7, Pages 40-42: Acknowledgement to Reviewers of Symmetry in 2014]]>
http://www.mdpi.com/2073-8994/7/1/40
The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2014:[...]Symmetry2015-01-0771Editorial10.3390/sym701004040422073-89942015-01-07doi: 10.3390/sym7010040 Symmetry Editorial Office<![CDATA[Symmetry, Vol. 7, Pages 32-39: Topology and the Visualization of Space]]>
http://www.mdpi.com/2073-8994/7/1/32
Overlapping patterns provide the diagrammatics for four-dimensional space. If these patterns are three-dimensional lattices, and if one imagines them extended in three-dimensional space, then the diagram makes a model of physical space.Symmetry2014-12-3071Article10.3390/sym701003232392073-89942014-12-30doi: 10.3390/sym7010032Tony Robbin<![CDATA[Symmetry, Vol. 7, Pages 15-31: Effect of Tensor Correlations on the Density Dependence of the Nuclear Symmetry Energy]]>
http://www.mdpi.com/2073-8994/7/1/15
We analyze the effect of the tensor force and other components of the nucleon-nucleon interaction on the nuclear symmetry energy and its density dependence by using the Hellmann–Feynman theorem. The analysis is performed within the microscopic Brueckner–Hartree–Fock approach using the Argonne V18 potential plus a Urbana IX three-nucleon force. Our results show that the potential part of the nuclear Hamiltonian, and in particular its tensor component, gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy into a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that pure neutron matter is less correlated than symmetric nuclear matter.Symmetry2014-12-2971Article10.3390/sym701001515312073-89942014-12-29doi: 10.3390/sym7010015Isaac VidañaConstança ProvidênciaArtur Polls<![CDATA[Symmetry, Vol. 7, Pages 1-14: A Study on Electronic-Money Technology Using Near Field Communication]]>
http://www.mdpi.com/2073-8994/7/1/1
Recently, due to the introduction of NFC (Near Field Communication), it has become possible to make easy electronic payments. Therefore, a secure communication method is necessary in these environments. NFC can be said to be relatively safe compared to other communication methods, because it carries out communications within 10 cm. However, it has made possible the risk of impersonation attacks by a disguised reader, leaving user information on the reader. In order to solve these problems, in this paper, we propose an authentication scheme that can reduce the weight of computation by using only a hash function and XOR (eXclusive OR) operation algorithms. This paper also shows that our method is safe, since it leaves no information with the other party.Symmetry2014-12-2671Article10.3390/sym70100011142073-89942014-12-26doi: 10.3390/sym7010001Min Jung<![CDATA[Symmetry, Vol. 6, Pages 1037-1057: Coulomb Solutions from Improper Pseudo-Unitary Free Gauge Field Operator Translations]]>
http://www.mdpi.com/2073-8994/6/4/1037
Fundamental problems of quantum field theory related to the representation problem of canonical commutation relations are discussed within a gauge field version of a van Hove-type model. The Coulomb field generated by a static charge distribution is described as a formal superposition of time-like pseudo-photons in Fock space with a Krein structure. In this context, a generalization of operator gauge transformations is introduced to generate coherent states of Abelian gauge fields interacting with a charged background.Symmetry2014-12-1564Article10.3390/sym6041037103710572073-89942014-12-15doi: 10.3390/sym6041037Andreas Aste<![CDATA[Symmetry, Vol. 6, Pages 1026-1036: Benjamin–Bona–Mahony Equation with Variable Coefficients: Conservation Laws]]>
http://www.mdpi.com/2073-8994/6/4/1026
This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that the derived conserved quantities fail to satisfy the divergence criterion and so one needs to make adjustments to the derived conserved quantities in order to satisfy the divergence condition. The conservation laws are then expressed in the original variable. Finally, a conservation law is used to obtain exact solution of a special case of the Benjamin–Bona–Mahony equation.Symmetry2014-12-1564Article10.3390/sym6041026102610362073-89942014-12-15doi: 10.3390/sym6041026Ben MuatjetjejaChaudry Khalique<![CDATA[Symmetry, Vol. 6, Pages 1011-1025: Privacy-Enhancing Security Protocol in LTE Initial Attack]]>
http://www.mdpi.com/2073-8994/6/4/1011
Long-Term Evolution (LTE) is a fourth-generation mobile communication technology implemented throughout the world. It is the communication means of smartphones that send and receive all of the private date of individuals. M2M, IOT, etc., are the base technologies of mobile communication that will be used in the future cyber world. However, identification parameters, such as International Mobile Subscriber Identity (IMSI), Radio Network Temporary Identities (RNTI), etc., in the initial attach section for accessing the LTE network are presented with the vulnerability of being exposed as clear text. Such vulnerability does not end in a mere identification parameter, but can lead to a secondary attack using the identification parameter, such as replication of the smartphone, illegal use of the mobile communication network, etc. This paper proposes a security protocol to safely transmit identification parameters in different cases of the initial attach. The proposed security protocol solves the exposed vulnerability by encrypting the parameters in transmission. Using an OPNET simulator, it is shown that the average rate of delay and processing ratio are efficient in comparison to the existing process.Symmetry2014-12-1264Article10.3390/sym6041011101110252073-89942014-12-12doi: 10.3390/sym6041011Uijin JangHyungmin LimHyungjoo Kim<![CDATA[Symmetry, Vol. 6, Pages 997-1010: MLDS: Multi-Layer Defense System for Preventing Advanced Persistent Threats]]>
http://www.mdpi.com/2073-8994/6/4/997
Here we report on the issue of Advanced Persistent Threats (APT), which use malware for the purpose of leaking the data of large corporations and government agencies. APT attacks target systems continuously by utilizing intelligent and complex technologies. To overthrow the elaborate security network of target systems, it conducts an attack after undergoing a pre-reconnaissance phase. An APT attack causes financial loss, information leakage, etc. They can easily bypass the antivirus system of a target system. In this paper, we propose a Multi-Layer Defense System (MLDS) that can defend against APT. This system applies a reinforced defense system by collecting and analyzing log information and various information from devices, by installing the agent on the network appliance, server and end-user. It also discusses how to detect an APT attack when one cannot block the initial intrusion while continuing to conduct other activities. Thus, this system is able to minimize the possibility of initial intrusion and damages of the system by promptly responding through rapid detection of an attack when the target system is attacked.Symmetry2014-12-0364Article10.3390/sym604099799710102073-89942014-12-03doi: 10.3390/sym6040997Daesung MoonHyungjin ImJae LeeJong Park<![CDATA[Symmetry, Vol. 6, Pages 975-996: Brain Activity in Response to Visual Symmetry]]>
http://www.mdpi.com/2073-8994/6/4/975
A number of studies have explored visual symmetry processing by measuring event related potentials and neural oscillatory activity. There is a sustained posterior negativity (SPN) related to the presence of symmetry. There is also functional magnetic resonance imaging (MRI) activity in extrastriate visual areas and in the lateral occipital complex. We summarise the evidence by answering six questions. (1) Is there an automatic and sustained response to symmetry in visual areas? Answer: Yes, and this suggests automatic processing of symmetry. (2) Which brain areas are involved in symmetry perception? Answer: There is an extended network from extrastriate areas to higher areas. (3) Is reflection special? Answer: Reflection is the optimal stimulus for a more general regularity-sensitive network. (4) Is the response to symmetry independent of view angle? Answer: When people classify patterns as symmetrical or random, the response to symmetry is view-invariant. When people attend to other dimensions, the network responds to residual regularity in the image. (5) How are brain rhythms in the two hemispheres altered during symmetry perception? Answer: Symmetry processing (rather than presence) produces more alpha desynchronization in the right posterior regions. Finally, (6) does symmetry processing produce positive affect? Answer: Not in the strongest sense, but behavioural measures reveal implicit positive evaluation of abstract symmetry.Symmetry2014-12-0264Review10.3390/sym60409759759962073-89942014-12-02doi: 10.3390/sym6040975Marco BertaminiAlexis Makin<![CDATA[Symmetry, Vol. 6, Pages 954-974: On the Self-Mobility of Point-Symmetric Hexapods]]>
http://www.mdpi.com/2073-8994/6/4/954
In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.Symmetry2014-11-1864Article10.3390/sym60409549549742073-89942014-11-18doi: 10.3390/sym6040954Georg Nawratil<![CDATA[Symmetry, Vol. 6, Pages 938-953: Design of a Secure System Considering Quality of Service]]>
http://www.mdpi.com/2073-8994/6/4/938
Improvements in networking technologies have provided users with useful information services. Such information services may bring convenience and efficiency, but might be accompanied by vulnerabilities to a variety of attacks. Therefore, a variety of research to enhance the security of the systems and get the services at the same time has been carried out. Especially, research on intrusion-tolerant systems (ITSs) has been conducted in order to survive against every intrusion, rather than to detect and prevent them. In this paper, an ITS based on effective resource conversion (ERC) is presented to achieve the goal of intrusion-tolerance. Instead of using the fixed number of virtual machines (VMs) to process requests and recover as in conventional approaches, the ITS based on ERC can transform the assigned resources depending on the system status. This scheme is proved to maintain a certain level of quality of service (QoS) and quality of security service (QoSS) in threatening environments. The performance of ERC is compared with previous studies on ITS by CSIM 20, and it is verified that the proposed scheme is more effective in retaining a specific level of QoS and QoSS.Symmetry2014-11-1364Article10.3390/sym60409389389532073-89942014-11-13doi: 10.3390/sym6040938Seondong HeoSoojin LeeSeokjoo DooHyunsoo Yoon<![CDATA[Symmetry, Vol. 6, Pages 926-937: Keyframe Extraction from Human Motion Capture Data Based on a Multiple Population Genetic Algorithm]]>
http://www.mdpi.com/2073-8994/6/4/926
To reduce reconstruction errors during keyframe extraction and to control the optimal compression ratio, this study proposes a method for keyframe extraction from human motion capture data based on a multiple population genetic algorithm. The fitness function is defined to meet the goals of minimal reconstruction errors and the optimal compression rate, where multiple initial populations are subjected to co-evolution. The multiple population genetic algorithm considers global and local search. Experimental results showed that the algorithm can effectively extract the keyframe from motion capture data and it satisfied the desired reconstruction error.Symmetry2014-11-1264Article10.3390/sym60409269269372073-89942014-11-12doi: 10.3390/sym6040926Qiang ZhangShulu ZhangDongsheng Zhou<![CDATA[Symmetry, Vol. 6, Pages 909-925: Determining Amino Acid Chirality in the Supernova Neutrino Processing Model]]>
http://www.mdpi.com/2073-8994/6/4/909
A model is described that can be used to estimate the bulk polarization of largerotating meteoroids in the magnetic field of a neutron star. The results of this model areapplicable to the Supernova Neutrino Amino Acid Processing model, which describes onepossible way in which the amino acids, known in nearly all cases to exhibit supramolecularchirality, could have become enantiomeric.Symmetry2014-11-0364Article10.3390/sym60409099099252073-89942014-11-03doi: 10.3390/sym6040909Michael FamianoRichard BoydToshitaka KajinoTakashi OnakaKatrina KoehlerSarah Hulbert<![CDATA[Symmetry, Vol. 6, Pages 896-908: Dynamical Response of Particles in Asymmetric Ratchet Potential]]>
http://www.mdpi.com/2073-8994/6/4/896
The dynamics and response of particles in an asymmetric potential of the ratchet type is considered. An approximate asymmetric ratchet potential, which allows us to apply an analytical approach to investigate the systems’ response, is proposed based on the power series interpolation scheme. The method of multiple scales (MMS) is then employed to obtain an approximate solution at the principal resonance. Comparison between results obtained from the approximated and exact potentials show excellent agreement. The frequency response curves (FRCs) for different forcing are presented. The numerically computed FRCs were compared with the theoretical result to show the extent of agreement. Furthermore, by using perturbation methods, the stable and unstable domains of the solution were obtained.Symmetry2014-10-2764Article10.3390/sym60408968969082073-89942014-10-27doi: 10.3390/sym6040896Usman MarteUchechukwu VincentAbdulahi NjahBiodun Badmus<![CDATA[Symmetry, Vol. 6, Pages 880-895: Supramolecular Chirality in Dynamic Coordination Chemistry]]>
http://www.mdpi.com/2073-8994/6/4/880
Labile metal complexes have a useful coordination bond; which is weaker than a covalent C–C bond and is reversibly and dynamically formed and dissociated. Such labile metal complexes also can be used to construct chiral shapes and offer dynamic conversion of chiral molecular shapes in response to external stimuli. This review provides recent examples of chirality induction and describes the dynamic conversion systems produced by chiral metal complexes including labile metal centers, most of which respond to external stimuli by exhibiting sophisticated conversion phenomena.Symmetry2014-10-2464Review10.3390/sym60408808808952073-89942014-10-24doi: 10.3390/sym6040880Hiroyuki Miyake<![CDATA[Symmetry, Vol. 6, Pages 851-879: Recent Advances in Microscopic Approaches to Nuclear Matter and Symmetry Energy]]>
http://www.mdpi.com/2073-8994/6/4/851
Nuclear matter is a convenient theoretical laboratory to test many-body theories. When neutron and proton densities are different, the isospin dependence of the nuclear force gives rise to the symmetry energy term in the equation of state. This quantity is a crucial mechanism in the formation of the neutron skin in nuclei, as well as in other systems and phenomena involved in the dynamics of neutrons and protons in neutron-rich systems, such as isospin-asymmetric heavy-ion collisions. In this article, we will review phenomenological facts about the symmetry energy and recent experimental efforts to constrain its density dependence and related quantities. We will then review our microscopic approach to the equation of state of symmetric and asymmetric nuclear matter and present a corresponding set of predictions. Our calculations utilize the Dirac–Brueckner–Hartree–Fock method and realistic meson-theoretic nucleon-nucleon potentials. Chiral perturbation theory is an alternative approach, based on a well-defined scheme, which allows one to develop nuclear forces at each order of the chiral expansion. We will present and discuss predictions based on chiral perturbation theory, where we employ consistent two- and three-body chiral interactions. Throughout the article, one of the focal points is the importance of pursuing ab initio methods towards a deeper understanding of the many-body system.Symmetry2014-10-2064Review10.3390/sym60408518518792073-89942014-10-20doi: 10.3390/sym6040851Francesca Sammarruca<![CDATA[Symmetry, Vol. 6, Pages 844-850: Polar Vector Property of the Stationary State of Condensed Molecular Matter]]>
http://www.mdpi.com/2073-8994/6/4/844
Crystalline phases undergoing 180\(^{\circ}\) orientational disorder of dipolar entities in the seed or at growing (hkl) faces will show a polar vector property described by \(\infty\) /mm symmetry. Seeds and crystals develop a bi-polar state (\(\infty\)/mm), where domains related by a mirror plane m allow for a \(\infty\) m symmetry in each domain. The polarity of domains is due to energetic favorable interactions at the object-to-nutrient interface. Such interactions are well reproduced by an Ising Hamiltonian. Two-dimensional Monte Carlo simulations performed for real molecules with full long-range interactions allow us to calculate the spatial distribution of the electrical polarization Pel. The investigation has been extended to liquid droplets made of dipolar entities by molecular dynamics simulations. We demonstrate the development of an m\(\bar{\infty}\) quasi bi-polar state leading to a charged surface.Symmetry2014-10-1364Article10.3390/sym60408448448502073-89942014-10-13doi: 10.3390/sym6040844Jürg HulligerLuigi CannavacciuoloMathias Rech<![CDATA[Symmetry, Vol. 6, Pages 781-843: Chlorophylls, Symmetry, Chirality, and Photosynthesis]]>
http://www.mdpi.com/2073-8994/6/3/781
Chlorophylls are a fundamental class of tetrapyrroles and function as the central reaction center, accessory and photoprotective pigments in photosynthesis. Their unique individual photochemical properties are a consequence of the tetrapyrrole macrocycle, the structural chemistry and coordination behavior of the phytochlorin system, and specific substituent pattern. They achieve their full potential in solar energy conversion by working in concert in highly complex, supramolecular structures such as the reaction centers and light-harvesting complexes of photobiology. The biochemical function of these structures depends on the controlled interplay of structural and functional principles of the apoprotein and pigment cofactors. Chlorophylls and bacteriochlorophylls are optically active molecules with several chiral centers, which are necessary for their natural biological function and the assembly of their supramolecular complexes. However, in many cases the exact role of chromophore stereochemistry in the biological context is unknown. This review gives an overview of chlorophyll research in terms of basic function, biosynthesis and their functional and structural role in photosynthesis. It highlights aspects of chirality and symmetry of chlorophylls to elicit further interest in their role in nature.Symmetry2014-09-1063Review10.3390/sym60307817818432073-89942014-09-10doi: 10.3390/sym6030781Mathias SengeAoife RyanKristie LetchfordStuart MacGowanTamara Mielke<![CDATA[Symmetry, Vol. 6, Pages 758-780: Twinning of Polymer Crystals Suppressed by Entropy]]>
http://www.mdpi.com/2073-8994/6/3/758
We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.Symmetry2014-09-0463Article10.3390/sym60307587587802073-89942014-09-04doi: 10.3390/sym6030758Nikos KarayiannisKaterina FoteinopoulouManuel Laso<![CDATA[Symmetry, Vol. 6, Pages 722-757: Recognition of Symmetric 3D Bodies]]>
http://www.mdpi.com/2073-8994/6/3/722
The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.Symmetry2014-09-0163Article10.3390/sym60307227227572073-89942014-09-01doi: 10.3390/sym6030722Tomáš SukJan Flusser<![CDATA[Symmetry, Vol. 6, Pages 704-721: Adhesive/Repulsive Codes in Vertebrate Forebrain Morphogenesis]]>
http://www.mdpi.com/2073-8994/6/3/704
The last fifteen years have seen the identification of some of the mechanisms involved in anterior neural plate specification, patterning, and morphogenesis, which constitute the first stages in the formation of the forebrain. These studies have provided us with a glimpse into the molecular mechanisms that drive the development of an embryonic structure, and have resulted in the realization that cell segregation in the anterior neural plate is essential for the accurate progression of forebrain morphogenesis. This review summarizes the latest advances in our understanding of mechanisms of cell segregation during forebrain development, with and emphasis on the impact of this process on the morphogenesis of one of the anterior neural plate derivatives, the eyes.Symmetry2014-08-1463Review10.3390/sym60307047047212073-89942014-08-14doi: 10.3390/sym6030704Florencia Cavodeassi<![CDATA[Symmetry, Vol. 6, Pages 677-703: Supramolecular Chirality: Solvent Chirality Transfer in Molecular Chemistry and Polymer Chemistry]]>
http://www.mdpi.com/2073-8994/6/3/677
Controlled mirror symmetry breaking arising from chemical and physical origin is currently one of the hottest issues in the field of supramolecular chirality. The dynamic twisting abilities of solvent molecules are often ignored and unknown, although the targeted molecules and polymers in a fluid solution are surrounded by solvent molecules. We should pay more attention to the facts that mostly all of the chemical and physical properties of these molecules and polymers in the ground and photoexcited states are significantly influenced by the surrounding solvent molecules with much conformational freedom through non-covalent supramolecular interactions between these substances and solvent molecules. This review highlights a series of studies that include: (i) historical background, covering chiral NaClO3 crystallization in the presence of d-sugars in the late 19th century; (ii) early solvent chirality effects for optically inactive chromophores/fluorophores in the 1960s–1980s; and (iii) the recent development of mirror symmetry breaking from the corresponding achiral or optically inactive molecules and polymers with the help of molecular chirality as the solvent use quantity.Symmetry2014-08-1363Review10.3390/sym60306776777032073-89942014-08-13doi: 10.3390/sym6030677Michiya Fujiki<![CDATA[Symmetry, Vol. 6, Pages 655-676: Lubricating and Waxy Esters. VI. Effect of Symmetry about Ester on Crystallization of Linear Monoester Isomers]]>
http://www.mdpi.com/2073-8994/6/3/655
The crystal structure development of jojoba-like esters incorporating either 1-decenoic acid and/or 1-decenol, namely octadec-9-enyl dec-9-enoate (JLE-281), and its isomer dec-9-enyl oleate (JLE-282) was investigated to reveal the effect of symmetry about the ester group on crystallization of aliphatic fatty monoesters. The phase transformation path was investigated with temperature-time resolved X-ray diffraction during stepped isothermal crystallization, and while cooling from the melt at a fixed rate. Startling differences in phase behavior were uncovered between the isomers. When stepped isothermals were used, selective extinctions occurred at a transition temperature for JLE-281 but not for JLE-282. The extinctions, which are due to dramatic changes in the electronic density of certain families of planes, indicate a phase transition attributed to a brusque rearrangement of the oxygen atoms in the crystal subcell. The phase transition did not occur when the JLEs were cooled continuously. The crucial role played by the position of the alkyl chain and its orientation relative to the easy rotation site of the C–O bond in the phase trajectories of the JLEs was particularly highlighted.Symmetry2014-08-0763Article10.3390/sym60306556556762073-89942014-08-07doi: 10.3390/sym6030655Laziz BouzidiShaojun LiSuresh Narine<![CDATA[Symmetry, Vol. 6, Pages 622-654: Symmetry Breaking in NMR Spectroscopy: The Elucidation of Hidden Molecular Rearrangement Processes]]>
http://www.mdpi.com/2073-8994/6/3/622
Variable-temperature NMR spectroscopy is probably the most convenient and sensitive technique to monitor changes in molecular structure in solution. Rearrangements that are rapid on the NMR time-scale exhibit simplified spectra, whereby non-equivalent nuclear environments yield time-averaged resonances. At lower temperatures, when the rate of exchange is sufficiently reduced, these degeneracies are split and the underlying “static” molecular symmetry, as seen by X-ray crystallography, becomes apparent. Frequently, however, such rearrangement processes are hidden, even when they become slow on the NMR time-scale, because the molecular point group remains unchanged. Judicious symmetry breaking, such as by substitution of a molecular fragment by a similar, but not identical moiety, or by the incorporation of potentially diastereotopic (chemically non-equivalent) nuclei, allows the elucidation of the kinetics and energetics of such processes. Examples are chosen that include a wide range of rotations, migrations and other rearrangements in organic, inorganic and organometallic chemistry.Symmetry2014-08-0463Review10.3390/sym60306226226542073-89942014-08-04doi: 10.3390/sym6030622Michael McGlinchey<![CDATA[Symmetry, Vol. 6, Pages 589-621: Non-Crystallographic Layer Lattice Restrictions in Order-Disorder (OD) Structures]]>
http://www.mdpi.com/2073-8994/6/3/589
Symmetry operations of layers periodic in two dimensions restrict the geometry the lattice according to the five two-dimensional Bravais types of lattices. In order-disorder (OD) structures, the operations relating equivalent layers generally leave invariant only a sublattice of the layers. The thus resulting restrictions can be expressed in terms of linear relations of the a2, b2 and a · b scalar products of the lattice basis vectors with rational coefficients. To characterize OD families and to check their validity, these lattice restrictions are expressed in the bases of different layers and combined. For a more familiar notation, they can be expressed in terms of the lattice parameters a, b and . Alternatively, the description of the lattice restrictions may be simplified by using centered lattices. The representation of the lattice restrictions in terms of scalar products is dependent on the chosen basis. A basis-independent classification of the lattice restrictions is outlined.Symmetry2014-07-2163Article10.3390/sym60305895896212073-89942014-07-21doi: 10.3390/sym6030589Berthold Stöger<![CDATA[Symmetry, Vol. 6, Pages 578-588: Coset Group Construction of Multidimensional Number Systems]]>
http://www.mdpi.com/2073-8994/6/3/578
Extensions of real numbers in more than two dimensions, in particular quaternions and octonions, are finding applications in physics due to the fact that they naturally capture symmetries of physical systems. However, in the conventional mathematical construction of complex and multicomplex numbers multiplication rules are postulated instead of being derived from a general principle. A more transparent and systematic approach is proposed here based on the concept of coset product from group theory. It is shown that extensions of real numbers in two or more dimensions follow naturally from the closure property of finite coset groups adding insight into the utility of multidimensional number systems in describing symmetries in nature.Symmetry2014-07-1163Article10.3390/sym60305785785882073-89942014-07-11doi: 10.3390/sym6030578Horia Petrache<![CDATA[Symmetry, Vol. 6, Pages 566-577: Gestalt Algebra—A Proposal for the Formalization of Gestalt Perception and Rendering]]>
http://www.mdpi.com/2073-8994/6/3/566
Gestalt Algebra gives a formal structure suitable for describing complex patterns in the image plain. This can be useful for recognizing hidden structure in images. The work at hand refers to the laws of perceptual psychology. A manifold called the Gestalt Domain is defined. Next to the position in 2D it also contains an orientation and a scale component. Algebraic operations on it are given for mirror symmetry as well as organization into rows. Additionally the Gestalt Domain contains an assessment component, and all the meaning of the operations implementing the Gestalt-laws is realized in the functions giving this component. The operation for mirror symmetry is binary, combining two parts into one aggregate as usual in standard algebra. The operation for organization into rows, however, combines n parts into an aggregate, where n may well be more than two. This is algebra in its more general sense. For recognition, primitives are extracted from digital raster images by Lowe’s Scale Invariant Feature Transform (SIFT). Lowe’s key-point descriptors can also be utilized. Experiments are reported with a set of images put forth for the Computer Vision and Pattern Recognition Workshops (CVPR) 2013 symmetry contest.Symmetry2014-07-0763Article10.3390/sym60305665665772073-89942014-07-07doi: 10.3390/sym6030566Eckart Michaelsen<![CDATA[Symmetry, Vol. 6, Pages 551-565: Autosolvation: Architecture and Selection of Chiral Conformers in Alkylcobalt Carbonyl Molecular Clocks]]>
http://www.mdpi.com/2073-8994/6/3/551
Autosolvation is an important factor in stabilizing the architecture of medium complicated molecules. It is a kind of “supramolecular force” acting in intramolecular manner, consisting of orbital-orbital interactions between polar groups, separated by more than one covalent bonds within the same molecule. This effect facilitates also the development of chiral conformations. Two typical alkylcobalt carbonyl type molecules are discussed here as examples of autosolvating intramolecular interactions, leading to dramatic selection of chiral conformers and indicating also to the limits of the effect. The conformers stabilized by autosolvation and their interconversion are excellent examples of a “molecular clockwork”. Operation mode of these molecular clockworks gives some insight into the intramolecular transfer of chiral information.Symmetry2014-07-0463Review10.3390/sym60305515515652073-89942014-07-04doi: 10.3390/sym6030551Róbert KurdiAttila TáborosiClaudia ZucchiGyula Pályi<![CDATA[Symmetry, Vol. 6, Pages 516-550: Symmetry Adapted Assur Decompositions]]>
http://www.mdpi.com/2073-8994/6/3/516
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.Symmetry2014-06-2763Article10.3390/sym60305165165502073-89942014-06-27doi: 10.3390/sym6030516Anthony NixonBernd SchulzeAdnan SljokaWalter Whiteley<![CDATA[Symmetry, Vol. 6, Pages 473-515: Wigner’s Space-Time Symmetries Based on the Two-by-Two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere]]>
http://www.mdpi.com/2073-8994/6/3/473
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential features of Wigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the subgroups of the Lorentz group whose transformations leave the four-momentum of a given particle invariant. It is shown that the damping modes of the oscillator correspond to the little groups for massive and imaginary-mass particles respectively. When the system makes the transition from the oscillation to damping mode, it corresponds to the little group for massless particles. Rotations around the momentum leave the four-momentum invariant. This degree of freedom extends the Sp(2) symmetry to that of SL(2, c) corresponding to the Lorentz group applicable to the four-dimensional Minkowski space. The Poincaré sphere contains the SL(2, c) symmetry. In addition, it has a non-Lorentzian parameter allowing us to reduce the mass continuously to zero. It is thus possible to construct the little group for massless particles from that of the massive particle by reducing its mass to zero. Spin-1/2 particles and spin-1 particles are discussed in detail.Symmetry2014-06-2563Article10.3390/sym60304734735152073-89942014-06-25doi: 10.3390/sym6030473Sibel BaşkalYoung KimMarilyn Noz<![CDATA[Symmetry, Vol. 6, Pages 444-472: Chiral Liquid Crystals: Structures, Phases, Effects]]>
http://www.mdpi.com/2073-8994/6/2/444
The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of supermolecular helicity, the occurrence of novel thermodynamic phases, as well as electro-optic effects which can only be observed in chiral liquid crystalline materials. In particular, I will discuss the formation of helical superstructures in cholesteric, Twist Grain Boundary and ferroelectric phases. As examples for the occurrence of novel phases the Blue Phases and Twist Grain Boundary phases are introduced. Chirality related effects are demonstrated through the occurrence of ferroelectricity in both thermotropic as well as lyotropic liquid crystals. Lack of mirror symmetry is also discussed briefly for some biopolymers such as cellulose and DNA, together with its influence on liquid crystalline behavior.Symmetry2014-06-1662Review10.3390/sym60204444444722073-89942014-06-16doi: 10.3390/sym6020444Ingo Dierking<![CDATA[Symmetry, Vol. 6, Pages 427-443: Symmetry Detection in Visual Impairment: Behavioral Evidence and Neural Correlates]]>
http://www.mdpi.com/2073-8994/6/2/427
Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactile symmetry detection in normally sighted and visually impaired individuals. On the one hand, available evidence suggests that efficient visual symmetry detection may need normal binocular vision development. On the other hand, converging evidence suggests that symmetry can develop as a principle of haptic perceptual organization in individuals lacking visual experience. Certain features of visual symmetry detection, however, such as the higher salience of the patterns containing a vertical axis of symmetry, do not systematically apply to the haptic modality. The neural correlates (revealed with neuroimaging) associated with visual and haptic symmetry detection are also discussed.Symmetry2014-05-2662Review10.3390/sym60204274274432073-89942014-05-26doi: 10.3390/sym6020427Zaira CattaneoSilvia BonaCorinna BauerJuha SilvantoAndrew HerbertTomaso VecchiLotfi Merabet<![CDATA[Symmetry, Vol. 6, Pages 409-426: The Symmetric-Partitioning and Incremental-Relearning Classification and Back-Propagation-Network Tree Approach for Cycle Time Estimation in Wafer Fabrication]]>
http://www.mdpi.com/2073-8994/6/2/409
An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabrication factory. The CABPN tree approach is an extension from the traditional classification and regression tree (CART) approach. In CART, the cycle times of jobs of the same branch are estimated with the same value, which is far from accurate. To tackle this problem, the CABPN tree approach replaces the constant estimate with variant estimates. To this end, the cycle times of jobs of the same branch are estimated with a BPN, and may be different. In this way, the estimation accuracy can be improved. In addition, to determine the optimal location of the splitting point on a node, the symmetric partition with incremental re-learning (SP-IR) algorithm is proposed and illustrated with an example. The applicability of the CABPN tree approach is shown with a real case. The experimental results supported its effectiveness over several existing methods.Symmetry2014-05-2362Case Report10.3390/sym60204094094262073-89942014-05-23doi: 10.3390/sym6020409Toly Chen<![CDATA[Symmetry, Vol. 6, Pages 396-408: Invisibility and PT Symmetry: A Simple Geometrical Viewpoint]]>
http://www.mdpi.com/2073-8994/6/2/396
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.Symmetry2014-05-2262Article10.3390/sym60203963964082073-89942014-05-22doi: 10.3390/sym6020396Luis Sánchez-SotoJuan Monzón<![CDATA[Symmetry, Vol. 6, Pages 383-395: Hydrodynamic Helical Orientations of Nanofibers in a Vortex]]>
http://www.mdpi.com/2073-8994/6/2/383
In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically align in torsional flows of a vortex generated by mechanical rotary stirring of the sample solutions. The nanofiber, formed through bundling of linear supramolecular polymers, aligns equally in right- and left-handed vortex flows. However, in contrast, a one-handedly twisted nanofiber, formed through helical bundling of the supramolecular polymers, shows unequal helical alignments in these torsional flows. When the helical handedness of the nanofiber matches that of the vortex flow, the nanofiber aligns more efficiently in the flowing fluid. Such phenomena are observed not only with the artificial helical supramolecular nanofibers but also with biological nanofibers such as double-stranded DNA.Symmetry2014-05-2062Review10.3390/sym60203833833952073-89942014-05-20doi: 10.3390/sym6020383Akihiko Tsuda<![CDATA[Symmetry, Vol. 6, Pages 368-382: Symmetry Perspectives on Some Auxetic Body-Bar Frameworks]]>
http://www.mdpi.com/2073-8994/6/2/368
Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode.Symmetry2014-05-1562Article10.3390/sym60203683683822073-89942014-05-15doi: 10.3390/sym6020368Patrick FowlerSimon GuestTibor Tarnai