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Symmetry, Volume 7, Issue 4 (December 2015) – 30 articles , Pages 1670-2223

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251 KiB  
Article
Petrie Duality and the Anstee–Robertson Graph
by Gareth A. Jones and Matan Ziv-Av
Symmetry 2015, 7(4), 2206-2223; https://doi.org/10.3390/sym7042206 - 21 Dec 2015
Cited by 3 | Viewed by 4218
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Duality)
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237 KiB  
Article
Estrada Index of Random Bipartite Graphs
by Yilun Shang
Symmetry 2015, 7(4), 2195-2205; https://doi.org/10.3390/sym7042195 - 7 Dec 2015
Cited by 8 | Viewed by 6515
Abstract
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 [...] Read more.
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. Full article
9909 KiB  
Review
When and Why Did Brains Break Symmetry?
by Lesley J. Rogers and Giorgio Vallortigara
Symmetry 2015, 7(4), 2181-2194; https://doi.org/10.3390/sym7042181 - 2 Dec 2015
Cited by 83 | Viewed by 14646
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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334 KiB  
Article
Quaternifications and Extensions of Current Algebras on S3
by Tosiaki Kori and Yuto Imai
Symmetry 2015, 7(4), 2150-2180; https://doi.org/10.3390/sym7042150 - 27 Nov 2015
Cited by 2 | Viewed by 3603
Abstract
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 [...] Read more.
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 \(\widehat{\mathfrak{h}}= (\phi^{+(0,0,1)}\otimes \mathfrak{h} )\oplus(\mathbf{C}a) \oplus(\mathbf{C}d)\). Full article
271 KiB  
Article
Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes
by David Jou, Michele Sciacca and Maria Stella Mongiovì
Symmetry 2015, 7(4), 2134-2149; https://doi.org/10.3390/sym7042134 - 17 Nov 2015
Cited by 1 | Viewed by 4349
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Duality)
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365 KiB  
Review
Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions
by Malte Henkel
Symmetry 2015, 7(4), 2108-2133; https://doi.org/10.3390/sym7042108 - 13 Nov 2015
Cited by 13 | Viewed by 4620
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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49674 KiB  
Review
Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development
by Christian Pohl
Symmetry 2015, 7(4), 2062-2107; https://doi.org/10.3390/sym7042062 - 11 Nov 2015
Cited by 18 | Viewed by 12978
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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1942 KiB  
Article
Similarity and a Duality for Fullerenes
by Jennifer J. Edmond and Jack E. Graver
Symmetry 2015, 7(4), 2047-2061; https://doi.org/10.3390/sym7042047 - 6 Nov 2015
Viewed by 4569
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Duality)
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155 KiB  
Article
Is the Hawking Quasilocal Energy “Newtonian”?
by Valerio Faraoni
Symmetry 2015, 7(4), 2038-2046; https://doi.org/10.3390/sym7042038 - 5 Nov 2015
Cited by 12 | Viewed by 3718
Abstract
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 [...] Read more.
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. Full article
7151 KiB  
Review
Concise Review: Asymmetric Cell Divisions in Stem Cell Biology
by Florian Murke, Symone Vitorianoda Conceição Castro, Bernd Giebel and André Görgens
Symmetry 2015, 7(4), 2025-2037; https://doi.org/10.3390/sym7042025 - 5 Nov 2015
Cited by 16 | Viewed by 21733
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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229 KiB  
Article
A Monge–Ampere Equation with an Unusual Boundary Condition
by Marc Sedjro
Symmetry 2015, 7(4), 2009-2024; https://doi.org/10.3390/sym7042009 - 5 Nov 2015
Cited by 1 | Viewed by 4268
Abstract
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. Full article
310 KiB  
Article
Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs
by Naruhiko Aizawa and Tadanori Kato
Symmetry 2015, 7(4), 1989-2008; https://doi.org/10.3390/sym7041989 - 3 Nov 2015
Cited by 1 | Viewed by 4833
Abstract
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 [...] Read more.
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 \( \ell > \frac{1}{3}. \) Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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2627 KiB  
Article
A Hypothesis for Self-Organization and Symmetry Reduction in the Synchronization of Organ-Level Contractions in the Human Uterus during Labor
by David Banney, Roger Young, Jonathan W. Paul, Mohammad Imtiaz and Roger Smith
Symmetry 2015, 7(4), 1981-1988; https://doi.org/10.3390/sym7041981 - 28 Oct 2015
Cited by 5 | Viewed by 5036
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Complexity and Symmetry)
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2250 KiB  
Article
New Security Development and Trends to Secure the SCADA Sensors Automated Transmission during Critical Sessions
by Aamir Shahzad, Malrey Lee, Hyung Doo Kim, Seon-mi Woo and Naixue Xiong
Symmetry 2015, 7(4), 1945-1980; https://doi.org/10.3390/sym7041945 - 23 Oct 2015
Cited by 17 | Viewed by 8290
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advanced Symmetry Modelling and Services in Future IT Environments)
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204 KiB  
Article
An Application of Equivalence Transformations to Reaction Diffusion Equations
by Mariano Torrisi and Rita Tracinà
Symmetry 2015, 7(4), 1929-1944; https://doi.org/10.3390/sym7041929 - 23 Oct 2015
Cited by 16 | Viewed by 3904
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
19664 KiB  
Review
Generation of Supramolecular Chirality around Twofold Rotational or Helical Axes in Crystalline Assemblies of Achiral Components
by Mikiji Miyata, Norimitsu Tohnai, Ichiro Hisaki and Toshiyuki Sasaki
Symmetry 2015, 7(4), 1914-1928; https://doi.org/10.3390/sym7041914 - 21 Oct 2015
Cited by 32 | Viewed by 8605
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Chiral Organic Crystal)
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29406 KiB  
Article
Age Estimation-Based Soft Biometrics Considering Optical Blurring Based on Symmetrical Sub-Blocks for MLBP
by Dat Tien Nguyen, So Ra Cho and Kang Ryoung Park
Symmetry 2015, 7(4), 1882-1913; https://doi.org/10.3390/sym7041882 - 19 Oct 2015
Cited by 10 | Viewed by 6719
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Biometric Recognition In-The-Wild)
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616 KiB  
Article
Anonymous Multi-Receiver Identity-Based Authenticated Encryption with CCA Security
by Chun-I Fan and Yi-Fan Tseng
Symmetry 2015, 7(4), 1856-1881; https://doi.org/10.3390/sym7041856 - 16 Oct 2015
Cited by 21 | Viewed by 5706
Abstract
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 [...] Read more.
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. Full article
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2151 KiB  
Article
Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems
by Oleksii Pliukhin
Symmetry 2015, 7(4), 1841-1855; https://doi.org/10.3390/sym7041841 - 16 Oct 2015
Cited by 9 | Viewed by 3952
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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209 KiB  
Article
On the Continuity of the Hutchinson Operator
by Michael F. Barnsley and Krzysztof Leśniak
Symmetry 2015, 7(4), 1831-1840; https://doi.org/10.3390/sym7041831 - 15 Oct 2015
Cited by 10 | Viewed by 4765
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Fractals)
857 KiB  
Article
Lie Group Method for Solving the Generalized Burgers’, Burgers’–KdV and KdV Equations with Time-Dependent Variable Coefficients
by Mina B. Abd-el-Malek and Amr M. Amin
Symmetry 2015, 7(4), 1816-1830; https://doi.org/10.3390/sym7041816 - 13 Oct 2015
Cited by 7 | Viewed by 4777
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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217 KiB  
Article
Classical and Quantum Burgers Fluids: A Challenge for Group Analysis
by Philip Broadbridge
Symmetry 2015, 7(4), 1803-1815; https://doi.org/10.3390/sym7041803 - 9 Oct 2015
Cited by 5 | Viewed by 4450
Abstract
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. [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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304 KiB  
Article
Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine
by Mercedes Pérez, Francisco Pérez and Emilio Jiménez
Symmetry 2015, 7(4), 1788-1802; https://doi.org/10.3390/sym7041788 - 1 Oct 2015
Viewed by 4304
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
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3127 KiB  
Review
Physics of the Chemical Asymmetry of the Cell Membrane: Implications in Gene Regulation and Pharmacology
by Ziad Omran, Paula Williams and Cyril Rauch
Symmetry 2015, 7(4), 1780-1787; https://doi.org/10.3390/sym7041780 - 30 Sep 2015
Cited by 1 | Viewed by 6065
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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9006 KiB  
Article
Effects of Initial Symmetry on the Global Symmetry of One-Dimensional Legal Cellular Automata
by Ikuko Tanaka
Symmetry 2015, 7(4), 1768-1779; https://doi.org/10.3390/sym7041768 - 29 Sep 2015
Cited by 3 | Viewed by 5053
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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228 KiB  
Article
New Nonlocal Symmetries of Diffusion-Convection Equations and Their Connection with Generalized Hodograph Transformation
by Valentyn Tychynin
Symmetry 2015, 7(4), 1751-1767; https://doi.org/10.3390/sym7041751 - 29 Sep 2015
Cited by 5 | Viewed by 3669
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Lie Theory and Its Applications)
12021 KiB  
Article
Fault Detection Based on Multi-Scale Local Binary Patterns Operator and Improved Teaching-Learning-Based Optimization Algorithm
by Hongjian Zhang, Ping He and Xudong Yang
Symmetry 2015, 7(4), 1734-1750; https://doi.org/10.3390/sym7041734 - 28 Sep 2015
Cited by 9 | Viewed by 6373
Abstract
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 [...] Read more.
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. Full article
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10554 KiB  
Review
Symmetry Breaking and Establishment of Dorsal/Ventral Polarity in the Early Sea Urchin Embryo
by Vincenzo Cavalieri and Giovanni Spinelli
Symmetry 2015, 7(4), 1721-1733; https://doi.org/10.3390/sym7041721 - 28 Sep 2015
Cited by 7 | Viewed by 11332
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Biology)
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8867 KiB  
Review
Cyclodextrins in Asymmetric and Stereospecific Synthesis
by Fliur Macaev and Veaceslav Boldescu
Symmetry 2015, 7(4), 1699-1720; https://doi.org/10.3390/sym7041699 - 24 Sep 2015
Cited by 29 | Viewed by 8726
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Asymmetric Catalysis)
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5115 KiB  
Article
Application of Assistive Computer Vision Methods to Oyama Karate Techniques Recognition
by Tomasz Hachaj, Marek R. Ogiela and Katarzyna Koptyra
Symmetry 2015, 7(4), 1670-1698; https://doi.org/10.3390/sym7041670 - 24 Sep 2015
Cited by 30 | Viewed by 9645
Abstract
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 [...] Read more.
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. Full article
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