Symmetry
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Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 8, Pages 7: On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map]]>
http://www.mdpi.com/2073-8994/8/2/7
A complex map can give rise to two kinds of fractal sets: the Julia sets and the parameters sets (or the connectivity loci) which represent different connectivity properties of the corresponding Julia sets. In the significative results of (Int. J. Bifurc. Chaos, 2009, 19:2123–2129) and (Nonlinear. Dyn. 2013, 73:1155–1163), the authors presented the two kinds of fractal sets of a class of alternated complex map and left some visually observations to be proved about the boundedness and symmetry properties of these fractal sets. In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.Symmetry2016-01-2682Article10.3390/sym802000772073-89942016-01-26doi: 10.3390/sym8020007Da WangShuTang Liu<![CDATA[Symmetry, Vol. 8, Pages 6: Acknowledgement to Reviewers of Symmetry in 2015]]>
http://www.mdpi.com/2073-8994/8/1/6
The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2015. [...]Symmetry2016-01-2181Editorial10.3390/sym801000662073-89942016-01-21doi: 10.3390/sym8010006Symmetry Editorial Office<![CDATA[Symmetry, Vol. 8, Pages 5: Symmetry in Sphere-Based Assembly Configuration Spaces]]>
http://www.mdpi.com/2073-8994/8/1/5
Many remarkably robust, rapid and spontaneous self-assembly phenomena occurring in nature can be modeled geometrically, starting from a collection of rigid bunches of spheres. This paper highlights the role of symmetry in sphere-based assembly processes. Since spheres within bunches could be identical and bunches could be identical, as well, the underlying symmetry groups could be of large order that grows with the number of participating spheres and bunches. Thus, understanding symmetries and associated isomorphism classes of microstates that correspond to various types of macrostates can significantly increase efficiency and accuracy, i.e., reduce the notorious complexity of computing entropy and free energy, as well as paths and kinetics, in high dimensional configuration spaces. In addition, a precise understanding of symmetries is crucial for giving provable guarantees of algorithmic accuracy and efficiency, as well as accuracy vs. efficiency trade-offs in such computations. In particular, this may aid in predicting crucial assembly-driving interactions. This is a primarily expository paper that develops a novel, original framework for dealing with symmetries in configuration spaces of assembling spheres, with the following goals. (1) We give new, formal definitions of various concepts relevant to the sphere-based assembly setting that occur in previous work and, in turn, formal definitions of their relevant symmetry groups leading to the main theorem concerning their symmetries. These previously-developed concepts include, for example: (i) assembly configuration spaces; (ii) stratification of assembly configuration space into configurational regions defined by active constraint graphs; (iii) paths through the configurational regions; and (iv) coarse assembly pathways. (2) We then demonstrate the new symmetry concepts to compute the sizes and numbers of orbits in two example settings appearing in previous work. (3) Finally, we give formal statements of a variety of open problems and challenges using the new conceptual definitions.Symmetry2016-01-2181Article10.3390/sym801000552073-89942016-01-21doi: 10.3390/sym8010005Meera SitharamAndrew VinceMenghan WangMiklós Bóna<![CDATA[Symmetry, Vol. 8, Pages 4: Synthesis of Chiral Cyclic Carbonates via Kinetic Resolution of Racemic Epoxides and Carbon Dioxide]]>
http://www.mdpi.com/2073-8994/8/1/4
The catalytic synthesis of cyclic carbonates using carbon dioxide as a C1-building block is a highly active area of research. Here, we review the catalytic production of enantiomerically enriched cyclic carbonates via kinetic resolution of racemic epoxides catalysed by metal-containing catalyst systems.Symmetry2016-01-1481Review10.3390/sym801000442073-89942016-01-14doi: 10.3390/sym8010004Xiao WuJosé Castro-OsmaMichael North<![CDATA[Symmetry, Vol. 8, Pages 3: Organocatalytic Asymmetric α-Chlorination of 1,3-Dicarbonyl Compounds Catalyzed by 2-Aminobenzimidazole Derivatives]]>
http://www.mdpi.com/2073-8994/8/1/3
Bifunctional chiral 2-aminobenzimidazole derivatives 1 and 2 catalyze the enantioselective stereodivergent α-chlorination of β-ketoesters and 1,3-diketone derivatives with up to 50% ee using N-chlorosuccinimide (NCS) or 2,3,4,4,5,6-hexachloro-2,5-cyclohexadien-1-one as electrophilic chlorine sources.Symmetry2016-01-1381Article10.3390/sym801000332073-89942016-01-13doi: 10.3390/sym8010003Daniel SánchezAlejandro BaezaDiego Alonso<![CDATA[Symmetry, Vol. 8, Pages 2: Natural Abundance Isotopic Chirality in the Reagents of the Soai Reaction]]>
http://www.mdpi.com/2073-8994/8/1/2
Isotopic chirality influences sensitively the enantiomeric outcome of the Soai asymmetric autocatalysis. Therefore magnitude and eventual effects of isotopic chirality caused by natural abundance isotopic substitution (H, C, O, Zn) in the reagents of the Soai reaction were analyzed by combinatorics and probability calculations. Expectable enantiomeric excesses were calculated by the Pars–Mills equation. It has been found that the chiral isotopic species formed by substitution in the otherwise achiral reagents provide enantiomeric excess (e.e.) levels that are higher than the sensitivity threshold of the Soai autocatalysis towards chiral induction. Consequently, possible chiral induction exerted by these e.e. values should be taken into account in considerations regarding the molecular events and the mechanism of the chiral induction in the Soai reaction.Symmetry2016-01-0881Article10.3390/sym801000222073-89942016-01-08doi: 10.3390/sym8010002Béla BarabásRóbert KurdiGyula Pályi<![CDATA[Symmetry, Vol. 8, Pages 1: Structural Properties and Biological Prediction of ({[(1E)-3-(1H-Imidazol-1-yl)-1-phenylpropylidene] amino}oxy)(4-methylphenyl)methanone: An In Silico Approach]]>
http://www.mdpi.com/2073-8994/8/1/1
Bioactive molecules are playing essential role in the field of drug discovery and various pharmaceutical applications. Vibrational spectral investigations of the anti-Candida agent ({[(1E)-3-(1H-imidazol-1-yl)-1-phenylpropylidene]amino}oxy)(4-methylphenyl)methanone ((1E)-IPMM) have been recorded and analyzed to understand its structural geometry, inter- and intra-molecular interactions. The equilibrium geometry, harmonic vibrational wavenumber, natural bond orbital (NBO) and Frontier orbital energy analyses have been carried out with the help of density functional theory with B3LYP/6-311++G(d,p) level of theory. The detailed vibrational assignments for the title molecule were performed on the basis of potential energy distribution analysis in order to unambiguously predict its modes. The calculated wavenumbers had good agreement with the experimental values. NBO analysis has confirmed the intramolecular charge transfer interactions. The predicted docking binding energy gave insight into the possible biological activity of the title molecule.Symmetry2015-12-2881Article10.3390/sym801000112073-89942015-12-28doi: 10.3390/sym8010001Maha AlmutairiDevarasu ManimaranIssac JoeOla SalehMohamed Attia<![CDATA[Symmetry, Vol. 7, Pages 2206-2223: Petrie Duality and the Anstee–Robertson Graph]]>
http://www.mdpi.com/2073-8994/7/4/2206
We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 17, the other non-orientable of genus 52, which embed the 40-vertex cage of valency 6 and girth 5 discovered independently by Robertson and Anstee. We prove that this map (discovered by Evans) and its Petrie dual are the only regular embeddings of this graph, together with a similar result for a graph of order 40, valency 6 and girth 3 with the same automorphism group.Symmetry2015-12-2174Article10.3390/sym7042206220622232073-89942015-12-21doi: 10.3390/sym7042206Gareth JonesMatan Ziv-Av<![CDATA[Symmetry, Vol. 7, Pages 2195-2205: Estrada Index of Random Bipartite Graphs]]>
http://www.mdpi.com/2073-8994/7/4/2195
The Estrada index of a graph \(G\) of \(n\) vertices is defined by \(EE(G)=\sum_{i=1}^ne^{\lambda_i}\), where \(\lambda_1,\lambda_2,\cdots,\lambda_n\) are the eigenvalues of \(G\). In this paper, we give upper and lower bounds of \(EE(G)\) for almost all bipartite graphs by investigating the upper and lower bounds of the spectrum of random matrices. We also formulate an exact estimate of \(EE(G)\) for almost all balanced bipartite graphs.Symmetry2015-12-0774Article10.3390/sym7042195219522052073-89942015-12-07doi: 10.3390/sym7042195Yilun Shang<![CDATA[Symmetry, Vol. 7, Pages 2181-2194: When and Why Did Brains Break Symmetry?]]>
http://www.mdpi.com/2073-8994/7/4/2181
Asymmetry of brain function is known to be widespread amongst vertebrates, and it seems to have appeared very early in their evolution. In fact, recent evidence of functional asymmetry in invertebrates suggests that even small brains benefit from the allocation of different functions to the left and right sides. This paper discusses the differing functions of the left and right sides of the brain, including the roles of the left and right antennae of bees (several species) in both short- and long-term recall of olfactory memories and in social behaviour. It considers the likely advantages of functional asymmetry in small and large brains and whether functional asymmetry in vertebrates and invertebrates is analogous or homologous. Neural or cognitive capacity can be enhanced both by the evolution of a larger brain and by lateralization of brain function: a possible reason why both processes occur side-by-side is offered.Symmetry2015-12-0274Review10.3390/sym7042181218121942073-89942015-12-02doi: 10.3390/sym7042181Lesley RogersGiorgio Vallortigara<![CDATA[Symmetry, Vol. 7, Pages 2150-2180: Quaternifications and Extensions of Current Algebras on S3]]>
http://www.mdpi.com/2073-8994/7/4/2150
Let \(\mathbf{H}\) be the quaternion algebra. Let \(\mathfrak{g}\) be a complex Lie algebra and let \(U(\mathfrak{g})\) be the enveloping algebra of \(\mathfrak{g}\). The quaternification \(\mathfrak{g}^{\mathbf{H}}=\)\(\,(\,\mathbf{H}\otimes U(\mathfrak{g}),\,[\quad,\quad]_{\mathfrak{g}^{\mathbf{H}}}\,)\) of \(\mathfrak{g}\) is defined by the bracket \( \big[\,\mathbf{z}\otimes X\,,\,\mathbf{w}\otimes Y\,\big]_{\mathfrak{g}^{\mathbf{H}}}\,=\)\(\,(\mathbf{z}\cdot \mathbf{w})\otimes\,(XY)\,- \)\(\, (\mathbf{w}\cdot\mathbf{z})\otimes (YX)\,,\nonumber \) for \(\mathbf{z},\,\mathbf{w}\in \mathbf{H}\) and {the basis vectors \(X\) and \(Y\) of \(U(\mathfrak{g})\).} Let \(S^3\mathbf{H}\) be the ( non-commutative) algebra of \(\mathbf{H}\)-valued smooth mappings over \(S^3\) and let \(S^3\mathfrak{g}^{\mathbf{H}}=S^3\mathbf{H}\otimes U(\mathfrak{g})\). The Lie algebra structure on \(S^3\mathfrak{g}^{\mathbf{H}}\) is induced naturally from that of \(\mathfrak{g}^{\mathbf{H}}\). We introduce a 2-cocycle on \(S^3\mathfrak{g}^{\mathbf{H}}\) by the aid of a tangential vector field on \(S^3\subset \mathbf{C}^2\) and have the corresponding central extension \(S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)\). As a subalgebra of \(S^3\mathbf{H}\) we have the algebra of Laurent polynomial spinors \(\mathbf{C}[\phi^{\pm}]\) spanned by a complete orthogonal system of eigen spinors \(\{\phi^{\pm(m,l,k)}\}_{m,l,k}\) of the tangential Dirac operator on \(S^3\). Then \(\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})\) is a Lie subalgebra of \(S^3\mathfrak{g}^{\mathbf{H}}\). We have the central extension \(\widehat{\mathfrak{g}}(a)= (\,\mathbf{C}[\phi^{\pm}] \otimes U(\mathfrak{g}) \,) \oplus(\mathbf{C}a)\) as a Lie-subalgebra of \(S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)\). Finally we have a Lie algebra \(\widehat{\mathfrak{g}}\) which is obtained by adding to \(\widehat{\mathfrak{g}}(a)\) a derivation \(d\) which acts on \(\widehat{\mathfrak{g}}(a)\) by the Euler vector field \(d_0\). That is the \(\mathbf{C}\)-vector space \(\widehat{\mathfrak{g}}=\left(\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})\right)\oplus(\mathbf{C}a)\oplus (\mathbf{C}d)\) endowed with the bracket \( \bigl[\,\phi_1\otimes X_1+ \lambda_1 a + \mu_1d\,,\phi_2\otimes X_2 + \lambda_2 a + \mu_2d\,\,\bigr]_{\widehat{\mathfrak{g}}} \, =\)\( (\phi_1\phi_2)\otimes (X_1\,X_2) \, -\,(\phi_2\phi_1)\otimes (X_2X_1)+\mu_1d_0\phi_2\otimes X_2- \) \(\mu_2d_0\phi_1\otimes X_1 + \) \( (X_1\vert X_2)c(\phi_1,\phi_2)a\,. \) When \(\mathfrak{g}\) is a simple Lie algebra with its Cartan subalgebra \(\mathfrak{h}\) we shall investigate the weight space decomposition of \(\widehat{\mathfrak{g}}\) with respect to the subalgebra \(\widehat{\mathfrak{h}}= (\phi^{+(0,0,1)}\otimes \mathfrak{h} )\oplus(\mathbf{C}a) \oplus(\mathbf{C}d)\).Symmetry2015-11-2774Article10.3390/sym7042150215021802073-89942015-11-27doi: 10.3390/sym7042150Tosiaki KoriYuto Imai<![CDATA[Symmetry, Vol. 7, Pages 2134-2149: Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes]]>
http://www.mdpi.com/2073-8994/7/4/2134
We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed.Symmetry2015-11-1774Article10.3390/sym7042134213421492073-89942015-11-17doi: 10.3390/sym7042134David JouMichele SciaccaMaria Mongiovì<![CDATA[Symmetry, Vol. 7, Pages 2108-2133: Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions]]>
http://www.mdpi.com/2073-8994/7/4/2108
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant n-point functions. These are important for the physical identification of n-point functions as responses or correlators.Symmetry2015-11-1374Review10.3390/sym7042108210821332073-89942015-11-13doi: 10.3390/sym7042108Malte Henkel<![CDATA[Symmetry, Vol. 7, Pages 2062-2107: Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development]]>
http://www.mdpi.com/2073-8994/7/4/2062
Animal development relies on repeated symmetry breaking, e.g., during axial specification, gastrulation, nervous system lateralization, lumen formation, or organ coiling. It is crucial that asymmetry increases during these processes, since this will generate higher morphological and functional specialization. On one hand, cue-dependent symmetry breaking is used during these processes which is the consequence of developmental signaling. On the other hand, cells isolated from developing animals also undergo symmetry breaking in the absence of signaling cues. These spontaneously arising asymmetries are not well understood. However, an ever growing body of evidence suggests that these asymmetries can originate from spontaneous symmetry breaking and self-organization of molecular assemblies into polarized entities on mesoscopic scales. Recent discoveries will be highlighted and it will be discussed how actomyosin and microtubule networks serve as common biomechanical systems with inherent abilities to drive spontaneous symmetry breaking.Symmetry2015-11-1174Review10.3390/sym7042062206221072073-89942015-11-11doi: 10.3390/sym7042062Christian Pohl<![CDATA[Symmetry, Vol. 7, Pages 2047-2061: Similarity and a Duality for Fullerenes]]>
http://www.mdpi.com/2073-8994/7/4/2047
Fullerenes are molecules of carbon that are modeled by trivalent plane graphs with only pentagonal and hexagonal faces. Scaling up a fullerene gives a notion of similarity, and fullerenes are partitioned into similarity classes. In this expository article, we illustrate how the values of two important fullerene parameters can be deduced for all fullerenes in a similarity class by computing the values of these parameters for just the three smallest representatives of that class. In addition, it turns out that there is a natural duality theory for similarity classes of fullerenes based on one of the most important fullerene construction techniques: leapfrog construction. The literature on fullerenes is very extensive, and since this is a general interest journal, we will summarize and illustrate the fundamental results that we will need to develop similarity and this duality.Symmetry2015-11-0674Article10.3390/sym7042047204720612073-89942015-11-06doi: 10.3390/sym7042047Jennifer EdmondJack Graver<![CDATA[Symmetry, Vol. 7, Pages 2038-2046: Is the Hawking Quasilocal Energy “Newtonian”?]]>
http://www.mdpi.com/2073-8994/7/4/2038
The Misner–Sharp–Hernandez mass defined in general relativity and in spherical symmetry has been recognized as having a Newtonian character in previous literature. In order to better understand this feature we relax spherical symmetry and we study the generalization of the Misner–Sharp–Hernandez mass to general spacetimes, i.e., the Hawking quasilocal mass. The latter is decomposed into a matter contribution and a contribution coming solely from the Weyl tensor. The Weyl tensor is then decomposed into an electric part (which has a Newtonian counterpart) and a magnetic one (which does not), which further splits the quasilocal mass into “Newtonian” and “non-Newtonian” parts. Only the electric (Newtonian) part contributes to the quasilocal mass.Symmetry2015-11-0574Article10.3390/sym7042038203820462073-89942015-11-05doi: 10.3390/sym7042038Valerio Faraoni<![CDATA[Symmetry, Vol. 7, Pages 2025-2037: Concise Review: Asymmetric Cell Divisions in Stem Cell Biology]]>
http://www.mdpi.com/2073-8994/7/4/2025
Somatic stem cells are rare cells with unique properties residing in many organs and tissues. They are undifferentiated cells responsible for tissue regeneration and homeostasis, and contain both the capacity to self-renew in order to maintain their stem cell potential and to differentiate towards tissue-specific, specialized cells. However, the knowledge about the mechanisms controlling somatic stem cell fate decisions remains sparse. One mechanism which has been described to control daughter cell fates in selected somatic stem cell systems is the process of asymmetric cell division (ACD). ACD is a tightly regulated and evolutionary conserved process allowing a single stem or progenitor cell to produce two differently specified daughter cells. In this concise review, we will summarize and discuss current concepts about the process of ACD as well as different ACD modes. Finally, we will recapitulate the current knowledge and our recent findings about ACD in human hematopoiesis.Symmetry2015-11-0574Review10.3390/sym7042025202520372073-89942015-11-05doi: 10.3390/sym7042025Florian MurkeSymone CastroBernd GiebelAndré Görgens<![CDATA[Symmetry, Vol. 7, Pages 2009-2024: A Monge–Ampere Equation with an Unusual Boundary Condition]]>
http://www.mdpi.com/2073-8994/7/4/2009
We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.Symmetry2015-11-0574Article10.3390/sym7042009200920242073-89942015-11-05doi: 10.3390/sym7042009Marc Sedjro<![CDATA[Symmetry, Vol. 7, Pages 1989-2008: Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs]]>
http://www.mdpi.com/2073-8994/7/4/1989
We construct, for any given \( \ell = \frac{1}{2} + {\mathbb N}_0, \) second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is observed that the invariant PDEs have significant difference for \( \ell &gt; \frac{1}{3}. \)Symmetry2015-11-0374Article10.3390/sym7041989198920082073-89942015-11-03doi: 10.3390/sym7041989Naruhiko AizawaTadanori Kato<![CDATA[Symmetry, Vol. 7, Pages 1981-1988: A Hypothesis for Self-Organization and Symmetry Reduction in the Synchronization of Organ-Level Contractions in the Human Uterus during Labor]]>
http://www.mdpi.com/2073-8994/7/4/1981
We present a hypothesis for a mechanism involving self-organization of small functional units that leads to organ-level synchronization of uterine contractions in human labor. This view is in contrast to the long-held presumption that the synchronized behavior of the uterus is subject to well-defined internal organization (as is found in the heart) that exists prior to the onset of labor. The contractile units of the uterus are myocytes, which contract in response to both mechanical stretch and electrical stimulation. Throughout pregnancy progesterone maintains quiescence by suppression of “contraction-associated proteins” (CAPs). At the end of pregnancy a functional withdrawal of progesterone and an increasingly estrogenic environment leads to an increase in the production of CAPs. One CAP of particular importance is connexin 43, which creates gap junctions between the myocytes that cause them to become electrically coupled. The electrical connectivity between myocytes, combined with an increase in intrauterine pressure at the end of pregnancy shifts the uterus towards an increasingly unstable critical point, characterized by irregular, uncoordinated contractions. We propose that synchronous, coordinated contractions emerge from this critical point through a process of self-organization, and that the search for a uterine pacemaker has been unfruitful for the sole reason that it is non-existent.Symmetry2015-10-2874Article10.3390/sym7041981198119882073-89942015-10-28doi: 10.3390/sym7041981David BanneyRoger YoungJonathan PaulMohammad ImtiazRoger Smith<![CDATA[Symmetry, Vol. 7, Pages 1945-1980: New Security Development and Trends to Secure the SCADA Sensors Automated Transmission during Critical Sessions]]>
http://www.mdpi.com/2073-8994/7/4/1945
Modern technology enhancements have been used worldwide to fulfill the requirements of the industrial sector, especially in supervisory control and data acquisition (SCADA) systems as a part of industrial control systems (ICS). SCADA systems have gained popularity in industrial automations due to technology enhancements and connectivity with modern computer networks and/or protocols. The procurement of new technologies has made SCADA systems important and helpful to processing in oil lines, water treatment plants, and electricity generation and control stations. On the other hand, these systems have vulnerabilities like other traditional computer networks (or systems), especially when interconnected with open platforms. Many international organizations and researchers have proposed and deployed solutions for SCADA security enhancement, but most of these have been based on node-to-node security, without emphasizing critical sessions that are linked directly with industrial processing and automation. This study concerns SCADA security measures related to critical processing with specified sessions of automated polling, analyzing cryptography mechanisms and deploying the appropriate explicit inclusive security solution in a distributed network protocol version 3 (DNP3) stack, as part of a SCADA system. The bytes flow through the DNP3 stack with security computational bytes within specified critical intervals defined for polling. We took critical processing knowledge into account when designing a SCADA/DNP3 testbed and deploying a cryptography solution that did not affect communications.Symmetry2015-10-2374Article10.3390/sym7041945194519802073-89942015-10-23doi: 10.3390/sym7041945Aamir ShahzadMalrey LeeHyung KimSeon-mi WooNaixue Xiong<![CDATA[Symmetry, Vol. 7, Pages 1929-1944: An Application of Equivalence Transformations to Reaction Diffusion Equations]]>
http://www.mdpi.com/2073-8994/7/4/1929
In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.Symmetry2015-10-2374Article10.3390/sym7041929192919442073-89942015-10-23doi: 10.3390/sym7041929Mariano TorrisiRita Tracinà<![CDATA[Symmetry, Vol. 7, Pages 1914-1928: Generation of Supramolecular Chirality around Twofold Rotational or Helical Axes in Crystalline Assemblies of Achiral Components]]>
http://www.mdpi.com/2073-8994/7/4/1914
A multi-point approximation method clarifies supramolecular chirality of twofold rotational or helical assemblies as well as bundles of the one-dimensional (1D) assemblies. While one-point approximation of materials claims no chirality generation of such assemblies, multi-point approximations do claim possible generation in the 1D assemblies of bars and plates. Such chirality derives from deformations toward three-axial directions around the helical axes. The chiral columns are bundled in chiral ways through symmetry operations. The preferable right- or left-handed columns are bundled together to yield chiral crystals with right- or left-handedness, respectively, indicating that twofold helix symmetry operations cause chiral crystals composed of achiral components via a three-stepwise and three-directional process.Symmetry2015-10-2174Review10.3390/sym7041914191419282073-89942015-10-21doi: 10.3390/sym7041914Mikiji MiyataNorimitsu TohnaiIchiro HisakiToshiyuki Sasaki<![CDATA[Symmetry, Vol. 7, Pages 1882-1913: Age Estimation-Based Soft Biometrics Considering Optical Blurring Based on Symmetrical Sub-Blocks for MLBP]]>
http://www.mdpi.com/2073-8994/7/4/1882
Because of its many useful applications, human age estimation has been considered in many previous studies as a soft biometrics. However, most existing methods of age estimation require a clear and focused facial image as input in order to obtain a trustworthy estimation result; otherwise, the methods might produce increased estimation error when an image of poor quality is used as input. Image blurring is one of major factors that affect estimation accuracies because it can cause a face to appear younger (i.e., reduce the age feature in the face region). Therefore, we propose a new human age estimation method that is robust even with an image that has the optical blurring effect by using symmetrical focus mask and sub-blocks for multi-level local binary pattern (MLBP). Experiment results show that the proposed method can enhance age estimation accuracy compared with the conventional system, which does not consider the effects of blurring.Symmetry2015-10-1974Article10.3390/sym7041882188219132073-89942015-10-19doi: 10.3390/sym7041882Dat NguyenSo ChoKang Park<![CDATA[Symmetry, Vol. 7, Pages 1856-1881: Anonymous Multi-Receiver Identity-Based Authenticated Encryption with CCA Security]]>
http://www.mdpi.com/2073-8994/7/4/1856
In a multi-receiver encryption system, a sender chooses a set of authorized receivers and sends them a message securely and efficiently, as the message is well encrypted and only one ciphertext corresponding to the message is generated no matter how many receivers the sender has chosen. It can be applied to video conferencing systems, pay-per-view channels, remote education, and so forth. Due to privacy considerations, an authorized receiver may not expect that his identity is revealed. In 2010, anonymous multi-receiver identity-based (ID-based) encryption was first discussed, and furthermore, many works on the topic have been presented so far. Unfortunately, we find that all of those schemes fail to prove the chosen ciphertext attacks (CCA) security in either confidentiality or anonymity. In this manuscript, we propose the first anonymous multi-receiver ID-based authenticated encryption scheme with CCA security in both confidentiality and anonymity. In the proposed scheme, the identity of the sender of a ciphertext can be authenticated by the receivers after a successful decryption. In addition, the proposed scheme also is the first CCA-secure one against insider attacks. Moreover, only one pairing computation is required in decryption.Symmetry2015-10-1674Article10.3390/sym7041856185618812073-89942015-10-16doi: 10.3390/sym7041856Chun-I FanYi-Fan Tseng<![CDATA[Symmetry, Vol. 7, Pages 1841-1855: Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems]]>
http://www.mdpi.com/2073-8994/7/4/1841
A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisfying Dirichlet boundary conditions are obtained. An biological interpretation is presented in order to show that two different types of interaction between biological species can be described.Symmetry2015-10-1674Article10.3390/sym7041841184118552073-89942015-10-16doi: 10.3390/sym7041841Oleksii Pliukhin<![CDATA[Symmetry, Vol. 7, Pages 1831-1840: On the Continuity of the Hutchinson Operator]]>
http://www.mdpi.com/2073-8994/7/4/1831
We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson operator on the hyperspace of nonempty closed bounded sets need not be Hausdorff continuous is given. Infinite systems are also discussed. The work clarifies and generalizes several partial results scattered across the literature.Symmetry2015-10-1574Article10.3390/sym7041831183118402073-89942015-10-15doi: 10.3390/sym7041831Michael BarnsleyKrzysztof Leśniak<![CDATA[Symmetry, Vol. 7, Pages 1816-1830: Lie Group Method for Solving the Generalized Burgers’, Burgers’–KdV and KdV Equations with Time-Dependent Variable Coefficients]]>
http://www.mdpi.com/2073-8994/7/4/1816
In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory is applied to determine symmetry reductions which reduce the nonlinear partial differential equations to ordinary differential equations. The obtained ordinary differential equations were solved analytically and the solutions are obtained in closed form for some specific choices of parameters, while others are solved numerically. In the obtained results we studied effects of both the time t and the index of nonlinearity on the behavior of the velocity, and the solutions are graphically presented.Symmetry2015-10-1374Article10.3390/sym7041816181618302073-89942015-10-13doi: 10.3390/sym7041816Mina Abd-el-MalekAmr Amin<![CDATA[Symmetry, Vol. 7, Pages 1803-1815: Classical and Quantum Burgers Fluids: A Challenge for Group Analysis]]>
http://www.mdpi.com/2073-8994/7/4/1803
The most general second order irrotational vector field evolution equation is constructed, that can be transformed to a single equation for the Cole–Hopf potential. The exact solution to the radial Burgers equation, with constant mass influx through a spherical supply surface, is constructed. The complex linear Schrödinger equation is equivalent to an integrable system of two coupled real vector equations of Burgers type. The first velocity field is the particle current divided by particle probability density. The second vector field gives a complex valued correction to the velocity that results in the correct quantum mechanical correction to the kinetic energy density of the Madelung fluid. It is proposed how to use symmetry analysis to systematically search for other constrained potential systems that generate a closed system of vector component evolution equations with constraints other than irrotationality.Symmetry2015-10-0974Article10.3390/sym7041803180318152073-89942015-10-09doi: 10.3390/sym7041803Philip Broadbridge<![CDATA[Symmetry, Vol. 7, Pages 1788-1802: Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine]]>
http://www.mdpi.com/2073-8994/7/4/1788
This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in traditional mechanical dynamic problems and current scientific disciplines. The conditions of being quasi-filiform and nilpotent are applied carefully and in several stages, and appropriate changes of the basis are achieved in an iterative and interactive process of simplification. This has been implemented by means of the development of more than thirty Maple modules. The process has led from the first family formulation, with 64 parameters and 215 constraints, to a family of 16 parameters and 17 constraints. This structure theorem permits the exhaustive classification of the quasi-filiform nilpotent Lie algebras of dimension nine with current computational methodologies.Symmetry2015-10-0174Article10.3390/sym7041788178818022073-89942015-10-01doi: 10.3390/sym7041788Mercedes PérezFrancisco PérezEmilio Jiménez<![CDATA[Symmetry, Vol. 7, Pages 1780-1787: Physics of the Chemical Asymmetry of the Cell Membrane: Implications in Gene Regulation and Pharmacology]]>
http://www.mdpi.com/2073-8994/7/4/1780
Signalling proteins are key regulators of basic cell physiology and tissues morphogenesis. Whilst signalling proteins are paramount for the cell to function optimally, their down regulation or inhibition is also central to tune the cell and its environment. One process involved in this tuning mechanism is membrane budding, otherwise known as endocytosis. The origin of the physical force driving the budding process and endocytosis has been the subject of much controversy. After two decades the budding process is now well described and it is acknowledged that fundamental principles from soft matter physics are at play. This opens a new window for understanding gene regulations, pharmacokinetic and multi drug resistance in cancer. This review recalls the first steps that have led to a better understanding of cell biology through the use of physics and; how the use of physics has shed light in areas of cell biology, cancer and pharmacology. It is, therefore, not a review of the many enzymes involved in membrane vesiculation and membrane curvature; it is more of an historical account.Symmetry2015-09-3074Review10.3390/sym7041780178017872073-89942015-09-30doi: 10.3390/sym7041780Ziad OmranPaula WilliamsCyril Rauch<![CDATA[Symmetry, Vol. 7, Pages 1768-1779: Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata]]>
http://www.mdpi.com/2073-8994/7/4/1768
To examine the development of pattern formation from the viewpoint of symmetry, we applied a two-dimensional discrete Walsh analysis to a one-dimensional cellular automata model under two types of regular initial conditions. The amount of symmetropy of cellular automata (CA) models under regular and random initial conditions corresponds to three Wolfram’s classes of CAs, identified as Classes II, III, and IV. Regular initial conditions occur in two groups. One group that makes a broken, regular pattern formation has four types of symmetry, whereas the other group that makes a higher hierarchy pattern formation has only two types. Additionally, both final pattern formations show an increased amount of symmetropy as time passes. Moreover, the final pattern formations are affected by iterations of base rules of CA models of chaos dynamical systems. The growth design formations limit possibilities: the ratio of developing final pattern formations under a regular initial condition decreases in the order of Classes III, II, and IV. This might be related to the difference in degree in reference to surrounding conditions. These findings suggest that calculations of symmetries of the structures of one-dimensional cellular automata models are useful for revealing rules of pattern generation for animal bodies.Symmetry2015-09-2974Article10.3390/sym7041768176817792073-89942015-09-29doi: 10.3390/sym7041768Ikuko Tanaka<![CDATA[Symmetry, Vol. 7, Pages 1751-1767: New Nonlocal Symmetries of Diffusion-Convection Equations and Their Connection with Generalized Hodograph Transformation]]>
http://www.mdpi.com/2073-8994/7/4/1751
Additional nonlocal symmetries of diffusion-convection equations and the Burgers equation are obtained. It is shown that these equations are connected via a generalized hodograph transformation and appropriate nonlocal symmetries arise from additional Lie symmetries of intermediate equations. Two entirely different techniques are used to search nonlocal symmetry of a given equation: the first is based on usage of the characteristic equations generated by additional operators, another technique assumes the reconstruction of a parametrical Lie group transformation from such operator. Some of them are based on the nonlocal transformations that contain new independent variable determined by an auxiliary differential equation and allow the interpretation as a nonlocal transformation with additional variables. The formulae derived for construction of exact solutions are used.Symmetry2015-09-2974Article10.3390/sym7041751175117672073-89942015-09-29doi: 10.3390/sym7041751Valentyn Tychynin<![CDATA[Symmetry, Vol. 7, Pages 1734-1750: Fault Detection Based on Multi-Scale Local Binary Patterns Operator and Improved Teaching-Learning-Based Optimization Algorithm]]>
http://www.mdpi.com/2073-8994/7/4/1734
Aiming to effectively recognize train center plate bolt loss faults, this paper presents an improved fault detection method. A multi-scale local binary pattern operator containing the local texture information of different radii is designed to extract more efficient discrimination information. An improved teaching-learning-based optimization algorithm is established to optimize the classification results in the decision level. Two new phases including the worst recombination phase and the cuckoo search phase are incorporated to improve the diversity of the population and enhance the exploration. In the worst recombination phase, the worst solution is updated by a crossover recombination operation to prevent the premature convergence. The cuckoo search phase is adopted to escape the local optima. Experimental results indicate that the recognition accuracy is up to 98.9% which strongly demonstrates the effectiveness and reliability of the proposed detection method.Symmetry2015-09-2874Article10.3390/sym7041734173417502073-89942015-09-28doi: 10.3390/sym7041734Hongjian ZhangPing HeXudong Yang<![CDATA[Symmetry, Vol. 7, Pages 1721-1733: Symmetry Breaking and Establishment of Dorsal/Ventral Polarity in the Early Sea Urchin Embryo]]>
http://www.mdpi.com/2073-8994/7/4/1721
The mechanisms imposing the Dorsal/Ventral (DV) polarity of the early sea urchin embryo consist of a combination of inherited maternal information and inductive interactions among blastomeres. Old and recent studies suggest that a key molecular landmark of DV polarization is the expression of nodal on the future ventral side, in apparent contrast with other metazoan embryos, where nodal is expressed dorsally. A subtle maternally-inherited redox anisotropy, plus some maternal factors such as SoxB1, Univin, and p38-MAPK have been identified as inputs driving the spatially asymmetric transcription of nodal. However, all the mentioned factors are broadly distributed in the embryo as early as nodal transcription occurs, suggesting that repression of the gene in non-ventral territories depends upon negative regulators. Among these, the Hbox12 homeodomain-containing repressor is expressed by prospective dorsal cells, where it acts as a dorsal-specific negative modulator of the p38-MAPK activity. This review provides an overview of the molecular mechanisms governing the establishment of DV polarity in sea urchins, focusing on events taking place in the early embryo. Altogether, these findings provide a framework for future studies aimed to unravel the inceptive mechanisms involved in the DV symmetry breaking.Symmetry2015-09-2874Review10.3390/sym7041721172117332073-89942015-09-28doi: 10.3390/sym7041721Vincenzo CavalieriGiovanni Spinelli<![CDATA[Symmetry, Vol. 7, Pages 1699-1720: Cyclodextrins in Asymmetric and Stereospecific Synthesis]]>
http://www.mdpi.com/2073-8994/7/4/1699
Since their discovery, cyclodextrins have widely been used as green and easily available alternatives to promoters or catalysts of different chemical reactions in water. This review covers the research and application of cyclodextrins and their derivatives in asymmetric and stereospecific syntheses, with their division into three main groups: (1) cyclodextrins promoting asymmetric and stereospecific catalysis in water; (2) cyclodextrins’ complexes with transition metals as asymmetric and stereospecific catalysts; and (3) cyclodextrins’ non-metallic derivatives as asymmetric and stereospecific catalysts. The scope of this review is to systematize existing information on the contribution of cyclodextrins to asymmetric and stereospecific synthesis and, thus, to facilitate further development in this direction.Symmetry2015-09-2474Review10.3390/sym7041699169917202073-89942015-09-24doi: 10.3390/sym7041699Fliur MacaevVeaceslav Boldescu<![CDATA[Symmetry, Vol. 7, Pages 1670-1698: Application of Assistive Computer Vision Methods to Oyama Karate Techniques Recognition]]>
http://www.mdpi.com/2073-8994/7/4/1670
In this paper we propose a novel algorithm that enables online actions segmentation and classification. The algorithm enables segmentation from an incoming motion capture (MoCap) data stream, sport (or karate) movement sequences that are later processed by classification algorithm. The segmentation is based on Gesture Description Language classifier that is trained with an unsupervised learning algorithm. The classification is performed by continuous density forward-only hidden Markov models (HMM) classifier. Our methodology was evaluated on a unique dataset consisting of MoCap recordings of six Oyama karate martial artists including multiple champion of Kumite Knockdown Oyama karate. The dataset consists of 10 classes of actions and included dynamic actions of stands, kicks and blocking techniques. Total number of samples was 1236. We have examined several HMM classifiers with various number of hidden states and also Gaussian mixture model (GMM) classifier to empirically find the best setup of the proposed method in our dataset. We have used leave-one-out cross validation. The recognition rate of our methodology differs between karate techniques and is in the range of 81% ± 15% even to 100%. Our method is not limited for this class of actions but can be easily adapted to any other MoCap-based actions. The description of our approach and its evaluation are the main contributions of this paper. The results presented in this paper are effects of pioneering research on online karate action classification.Symmetry2015-09-2474Article10.3390/sym7041670167016982073-89942015-09-24doi: 10.3390/sym7041670Tomasz HachajMarek OgielaKatarzyna Koptyra<![CDATA[Symmetry, Vol. 7, Pages 1655-1669: An Elementary Derivation of the Matrix Elements of Real Irreducible Representations of so(3)]]>
http://www.mdpi.com/2073-8994/7/3/1655
Using elementary techniques, an algorithmic procedure to construct skew-symmetric matrices realizing the real irreducible representations of so(3) is developed. We further give a simple criterion that enables one to deduce the decomposition of an arbitrary real representation R of so(3) into real irreducible components from the characteristic polynomial of an arbitrary representation matrix.Symmetry2015-09-1473Article10.3390/sym7031655165516692073-89942015-09-14doi: 10.3390/sym7031655Rutwig Campoamor-Stursberg<![CDATA[Symmetry, Vol. 7, Pages 1646-1654: Uncertainty Analysis of 208Pb Neutron Skin Predictions with Chiral Interactions]]>
http://www.mdpi.com/2073-8994/7/3/1646
We report predictions for the neutron skin in 208Pb using chiral two- and three-body interactions at increasing orders of chiral effective field theory and varying resolution scales. Closely related quantities, such as the slope of the symmetry energy, are also discussed. The sensitivity of the skin to just pure neutron matter pressure when going from order 2 to order 4 of chiral effective theory is singled out in a set of calculations that employ an empirical equation of state for symmetric nuclear matter.Symmetry2015-09-1473Article10.3390/sym7031646164616542073-89942015-09-14doi: 10.3390/sym7031646Francesca Sammarruca<![CDATA[Symmetry, Vol. 7, Pages 1633-1645: Mirror Symmetry and Polar Duality of Polytopes]]>
http://www.mdpi.com/2073-8994/7/3/1633
This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a reflexive polytope.Symmetry2015-09-1073Article10.3390/sym7031633163316452073-89942015-09-10doi: 10.3390/sym7031633David Cox<![CDATA[Symmetry, Vol. 7, Pages 1613-1632: Symmetries, Lagrangians and Conservation Laws of an Easter Island Population Model]]>
http://www.mdpi.com/2073-8994/7/3/1613
Basener and Ross (2005) proposed a mathematical model that describes the dynamics of growth and sudden decrease in the population of Easter Island. We have applied Lie group analysis to this system and found that it can be integrated by quadrature if the involved parameters satisfy certain relationships. We have also discerned hidden linearity. Moreover, we have determined a Jacobi last multiplier and, consequently, a Lagrangian for the general system and have found other cases independently and dependently on symmetry considerations in order to construct a corresponding variational problem, thus enabling us to find conservation laws by means of Noether’s theorem. A comparison with the qualitative analysis given by Basener and Ross is provided.Symmetry2015-09-0873Article10.3390/sym7031613161316322073-89942015-09-08doi: 10.3390/sym7031613M.C. NucciG. Sanchini<![CDATA[Symmetry, Vol. 7, Pages 1595-1612: From Conformal Invariance towards Dynamical Symmetries of the Collisionless Boltzmann Equation]]>
http://www.mdpi.com/2073-8994/7/3/1595
Dynamical symmetries of the collisionless Boltzmann transport equation, or Vlasov equation, but under the influence of an external driving force, are derived from non-standard representations of the 2D conformal algebra. In the case without external forces, the symmetry of the conformally-invariant transport equation is first generalized by considering the particle momentum as an independent variable. This new conformal representation can be further extended to include an external force. The construction and possible physical applications are outlined.Symmetry2015-09-0773Article10.3390/sym7031595159516122073-89942015-09-07doi: 10.3390/sym7031595Stoimen StoimenovMalte Henkel<![CDATA[Symmetry, Vol. 7, Pages 1587-1594: Prevention of Exponential Equivalence in Simple Password Exponential Key Exchange (SPEKE)]]>
http://www.mdpi.com/2073-8994/7/3/1587
Simple Password Exponential Key Exchange (SPEKE) and Dragonfly are simple password-based authenticated key exchange protocols that use a value derived from a shared password as a generator for modular exponentiation, as opposed to Diffie–Hellman key exchange, which uses a fixed value. However, it has been shown that in SPEKE, an active attacker, can examine multiple passwords in a single attempt because the passwords have an exponential correlation.We show that Dragonfly can also suffer from the same problem, and we propose a simple countermeasure to prevent the exponential equivalence in SPEKE.Symmetry2015-09-0273Article10.3390/sym7031587158715942073-89942015-09-02doi: 10.3390/sym7031587Hanwook LeeDongho Won<![CDATA[Symmetry, Vol. 7, Pages 1567-1586: Design of IP Camera Access Control Protocol by Utilizing Hierarchical Group Key]]>
http://www.mdpi.com/2073-8994/7/3/1567
Unlike CCTV, security video surveillance devices, which we have generally known about, IP cameras which are connected to a network either with or without wire, provide monitoring services through a built-in web-server. Due to the fact that IP cameras can use a network such as the Internet, multiple IP cameras can be installed at a long distance and each IP camera can utilize the function of a web server individually. Even though IP cameras have this kind of advantage, it has difficulties in access control management and weakness in user certification, too. Particularly, because the market of IP cameras did not begin to be realized a long while ago, systems which are systematized from the perspective of security have not been built up yet. Additionally, it contains severe weaknesses in terms of access authority to the IP camera web server, certification of users, and certification of IP cameras which are newly installed within a network, etc. This research grouped IP cameras hierarchically to manage them systematically, and provided access control and data confidentiality between groups by utilizing group keys. In addition, IP cameras and users are certified by using PKI-based certification, and weak points of security such as confidentiality and integrity, etc., are improved by encrypting passwords. Thus, this research presents specific protocols of the entire process and proved through experiments that this method can be actually applied.Symmetry2015-08-2773Article10.3390/sym7031567156715862073-89942015-08-27doi: 10.3390/sym7031567Jungho KangJaekyung HanJong Park<![CDATA[Symmetry, Vol. 7, Pages 1536-1566: Lie Symmetry Analysis of the Hopf Functional-Differential Equation]]>
http://www.mdpi.com/2073-8994/7/3/1536
In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(x)dx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation. The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics.Symmetry2015-08-2773Article10.3390/sym7031536153615662073-89942015-08-27doi: 10.3390/sym7031536Daniel JanochaMarta WacławczykMartin Oberlack<![CDATA[Symmetry, Vol. 7, Pages 1519-1535: Enantioselective Organocatalyzed Synthesis of 2-Amino-3-cyano-4H-chromene Derivatives]]>
http://www.mdpi.com/2073-8994/7/3/1519
The structural motif that results from the fusion of a benzene ring to a heterocyclic pyran ring, known as chromene, is broadly found in nature and it has been reported to be associated with a wide range of biological activity. Moreover, asymmetric organocatalysis is a discipline in expansion that is already recognized as a well-established tool for obtaining enantiomerically enriched compounds. This review covers the particular case of the asymmetric synthesis of 2-amino-3-cyano-4H-chromenes using organocatalysis. Herein, we show the most illustrative examples of the methods developed by diverse research groups, following a classification based on these five different approaches: (1) addition of naphthol compounds to substituted α,α-dicyanoolefins; (2) addition of malononitrile to substituted o-vinylphenols; (3) addition of malononitrile to N-protected o-iminophenols; (4) Michael addition of nucleophiles to 2-iminochromene derivatives; and (5) organocatalyzed formal [4+2] cycloaddition reaction. In most cases, chiral thioureas have been found to be effective catalysts to promote the synthetic processes, and generally a bifunctional mode of action has been envisioned for them. In addition, squaramides and cinchona derivatives have been occasionally used as suitable catalysts for the substrates activation.Symmetry2015-08-2673Review10.3390/sym7031519151915352073-89942015-08-26doi: 10.3390/sym7031519Isaac SonsonaEugenia Marqués-LópezRaquel Herrera<![CDATA[Symmetry, Vol. 7, Pages 1475-1518: Performance Enhancement of Face Recognition in Smart TV Using Symmetrical Fuzzy-Based Quality Assessment]]>
http://www.mdpi.com/2073-8994/7/3/1475
With the rapid growth of smart TV, the necessity for recognizing a viewer has increased for various applications that deploy face recognition to provide intelligent services and high convenience to viewers. However, the viewers can have various postures, illumination, and expression variations on their faces while watching TV, and thereby, the performance of face recognition inevitably degrades. In order to handle these problems, video-based face recognition has been proposed, instead of a single image-based one. However, video-based processing of multiple images is prohibitive in smart TVs as the processing power is limited. Therefore, a quality measure-based (QM-based) image selection is required that considers both the processing speed and accuracy of face recognition. Therefore, we propose a performance enhancement method for face recognition through symmetrical fuzzy-based quality assessment. Our research is novel in the following three ways as compared to previous works. First, QMs are adaptively selected by comparing variance values obtained from candidate QMs within a video sequence, where the higher the variance value by a QM, the more meaningful is the QM in terms of a distinction between images. Therefore, we can adaptively select meaningful QMs that reflect the primary factors influencing the performance of face recognition. Second, a quality score of an image is calculated using a fuzzy method based on the inputs of the selected QMs, symmetrical membership functions, and rule table considering the characteristics of symmetry. A fuzzy-based combination method of image quality has the advantage of being less affected by the types of face databases because it does not perform an additional training procedure. Third, the accuracy of face recognition is enhanced by fusing the matching scores of the high-quality face images, which are selected based on the quality scores among successive face mages. Experimental results showed that the performance of face recognition using the proposed method was better than that of conventional methods in terms of accuracy.Symmetry2015-08-2573Article10.3390/sym7031475147515182073-89942015-08-25doi: 10.3390/sym7031475Yeong Kim Won LeeKi KimHyung HongKang Park<![CDATA[Symmetry, Vol. 7, Pages 1463-1474: A (1+2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions]]>
http://www.mdpi.com/2073-8994/7/3/1463
This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller–Segel system in question were found. Lie symmetry operators are used for constructing exact solutions of some boundary value problems. Moreover, it is proved that the boundary value problem for the (1+1)-dimensional Keller–Segel system with specific boundary conditions can be linearized and solved in an explicit form.Symmetry2015-08-2473Article10.3390/sym7031463146314742073-89942015-08-24doi: 10.3390/sym7031463Maksym Didovych<![CDATA[Symmetry, Vol. 7, Pages 1455-1462: Estrada and L-Estrada Indices of Edge-Independent Random Graphs]]>
http://www.mdpi.com/2073-8994/7/3/1455
Let \(G\) be a simple graph of order \(n\) with eigenvalues \(\lambda_1,\lambda_2,\cdots,\lambda_n\) and normalized Laplacian eigenvalues \(\mu_1,\mu_2,\cdots,\mu_n\). The Estrada index and normalized Laplacian Estrada index are defined as \(EE(G)=\sum_{k=1}^ne^{\lambda_k}\) and \(\mathcal{L}EE(G)=\sum_{k=1}^ne^{\mu_k-1}\), respectively. We establish upper and lower bounds to \(EE\) and \(\mathcal{L}EE\) for edge-independent random graphs, containing the classical Erdös-Rényi graphs as special cases.Symmetry2015-08-1973Technical Note10.3390/sym7031455145514622073-89942015-08-19doi: 10.3390/sym7031455Yilun Shang<![CDATA[Symmetry, Vol. 7, Pages 1436-1454: Asymmetry Assessment Using Surface Topography in Healthy Adolescents]]>
http://www.mdpi.com/2073-8994/7/3/1436
The ability to assess geometric asymmetry in the torsos of individuals is important for detecting Adolescent Idiopathic Scoliosis (AIS). A markerless technique using Surface Topography (ST) has been introduced as a non-invasive alternative to standard diagnostic radiographs. The technique has been used to identify asymmetry patterns associated with AIS. However, the presence and nature of asymmetries in the healthy population has not been properly studied. The purpose of this study is therefore to identify asymmetries and potential relationships to development factors such as age, gender, hand dominance and unilateral physical activity in healthy adolescents. Full torso scans of 83 participants were analyzed. Using Geomagic, deviation contour maps (DCMs) were created by reflecting the torso along the best plane of sagittal symmetry with each spectrum normalized. Two classes of asymmetry were observed: twist and thickness each with subgroupings. Averaged interobserver and intraobserver Kappas for twist subgroupings were 0.84 and 0.84, respectively, and for thickness subgroupings were 0.53 and 0.63 respectively. Further significant relationships were observed between specific types of asymmetry and gender such as females displaying predominately twist asymmetry, and males with thickness asymmetry. However, no relationships were found between type of asymmetry and age, hand dominance or unilateral physical activity. Understanding asymmetries in healthy subjects will continue to enhance assessment ability of the markerless ST technique.Symmetry2015-08-1773Article10.3390/sym7031436143614542073-89942015-08-17doi: 10.3390/sym7031436Connie HoEric ParentElise WatkinsMarc MoreauDouglas HeddenMarwan El-RichSamer Adeeb<![CDATA[Symmetry, Vol. 7, Pages 1410-1435: Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2)-Dimensional Boundary Value Problems]]>
http://www.mdpi.com/2073-8994/7/3/1410
A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2)-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ -2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ -2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena) to (1 + 1)-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented.Symmetry2015-08-1773Article10.3390/sym7031410141014352073-89942015-08-17doi: 10.3390/sym7031410Roman ChernihaJohn King<![CDATA[Symmetry, Vol. 7, Pages 1395-1409: Enantioselective Organocatalysis in Microreactors: Continuous Flow Synthesis of a (S)-Pregabalin Precursor and (S)-Warfarin]]>
http://www.mdpi.com/2073-8994/7/3/1395
Continuous flow processes have recently emerged as a powerful technology for performing chemical transformations since they ensure some advantages over traditional batch procedures. In this work, the use of commercially available and affordable PEEK (Polyetheretherketone) and PTFE (Polytetrafluoroethylene) HPLC (High Performance Liquid Chromatography) tubing as microreactors was exploited to perform organic reactions under continuous flow conditions, as an alternative to the commercial traditional glass microreactors. The wide availability of tubing with different sizes allowed quickly running small-scale preliminary screenings, in order to optimize the reaction parameters, and then to realize under the best experimental conditions a reaction scale up for preparative purposes. The gram production of some Active Pharmaceutical Ingredients (APIs) such as (S)-Pregabalin and (S)-Warfarin was accomplished in short reaction time with high enantioselectivity, in an experimentally very simple procedure.Symmetry2015-08-0473Article10.3390/sym7031395139514092073-89942015-08-04doi: 10.3390/sym7031395Riccardo PortaMaurizio BenagliaFrancesca CocciaSergio RossiAlessandra Puglisi<![CDATA[Symmetry, Vol. 7, Pages 1376-1394: Bäcklund Transformations for Integrable Geometric Curve Flows]]>
http://www.mdpi.com/2073-8994/7/3/1376
We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kotera flow in the affine geometry, etc. Using the fact that two different curves in a given geometry are governed by the same integrable equation, we obtain Bäcklund transformations relating to these two integrable geometric flows. Some special solutions of the integrable systems are used to obtain the explicit Bäcklund transformations.Symmetry2015-08-0373Article10.3390/sym7031376137613942073-89942015-08-03doi: 10.3390/sym7031376Changzheng QuJingwei HanJing Kang<![CDATA[Symmetry, Vol. 7, Pages 1352-1375: Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials]]>
http://www.mdpi.com/2073-8994/7/3/1352
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this paper, we identify three different integrable spin systems in (2 + 1) dimensions by introducing the interaction of the spin field with more than one scalar potential, or vector potential, or both. We also obtain the associated Lax pairs. We discuss various interesting reductions in (2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear Schrödinger family of equations, including the (2 + 1)-dimensional version of nonlinear Schrödinger–Hirota–Maxwell–Bloch equations, along with their Lax pairs.Symmetry2015-08-0373Article10.3390/sym7031352135213752073-89942015-08-03doi: 10.3390/sym7031352Ratbay MyrzakulovGalya MamyrbekovaGulgassyl NugmanovaMuthusamy Lakshmanan<![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 (νMSM) 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