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Symmetry, Volume 2, Issue 2 (June 2010), Pages 437-1200

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Research

Jump to: Review

Open AccessArticle Symmetry and Beauty in Plato
Symmetry 2010, 2(2), 455-465; doi:10.3390/sym2020455
Received: 22 February 2010 / Revised: 16 March 2010 / Accepted: 20 March 2010 / Published: 25 March 2010
Cited by 1 | PDF Full-text (168 KB)
Abstract
Plato writes about Beauty in many of his dialogues, particularly in the Symposium, but he has no word equivalent to our "Symmetry", and this concept was not then formalised. Nevertheless, there are indications that some aspects of the concept were understood, if
[...] Read more.
Plato writes about Beauty in many of his dialogues, particularly in the Symposium, but he has no word equivalent to our "Symmetry", and this concept was not then formalised. Nevertheless, there are indications that some aspects of the concept were understood, if only intuitively. Plato has a very abstract concept of beauty, and when he uses "beauty" to characterise the so-called "Platonic Solids" in the Timaeus, he seems to be emphasising at least their regularity. It can be argued that the way in which he specifies the detailed construction of the solids is remarkably close to a modern description in terms of (point) symmetry. For Plato, something of our symmetry is included in what he means by beauty, and the long mathematical approach to symmetry starts with the Timaeus. Full article
(This article belongs to the Special Issue Symmetry and Beauty)
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Open AccessArticle Symmetry as an Intrinsically Dynamic Feature
Symmetry 2010, 2(2), 554-581; doi:10.3390/sym2020554
Received: 4 March 2010 / Revised: 23 March 2010 / Accepted: 29 March 2010 / Published: 1 April 2010
Cited by 3 | PDF Full-text (1977 KB)
Abstract
Symmetry is one of the most prominent spatial relations perceived by humans, and has a relevant role in attentive mechanisms regarding both visual and auditory systems. The aim of this paper is to establish symmetry, among the likes of motion, depth or range,
[...] Read more.
Symmetry is one of the most prominent spatial relations perceived by humans, and has a relevant role in attentive mechanisms regarding both visual and auditory systems. The aim of this paper is to establish symmetry, among the likes of motion, depth or range, as a dynamic feature in artificial vision. This is achieved in the first instance by assessing symmetry estimation by means of algorithms, putting emphasis on erosion and multi-resolution approaches, and confronting two ensuing problems: the isolation of objects from the context, and the pertinence (or lack thereof) of some salient points, such as the centre of mass. Next a geometric model is illustrated and detailed, and the problem of measuring symmetry in a world where symmetry is not perfect nor the only attention trigger is tackled. Two algorithmic lines, based on the so-called symmetry kernel and its evolution with pattern warping, and by correlation of blocks with varying sizes and positions, are proposed and investigated. An extended illustration of the power of symmetry as a feature, based on face expression recognition, concludes the paper. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Symmetry and Asymmetry Level Measures
Symmetry 2010, 2(2), 707-721; doi:10.3390/sym2020707
Received: 23 November 2009 / Revised: 30 March 2010 / Accepted: 6 April 2010 / Published: 8 April 2010
Cited by 2 | PDF Full-text (260 KB)
Abstract
Usually, Symmetry and Asymmetry are considered as two opposite sides of a coin: an object is either totally symmetric, or totally asymmetric, relative to pattern objects. Intermediate situations of partial symmetry or partial asymmetry are not considered. But this dichotomy on the classification
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Usually, Symmetry and Asymmetry are considered as two opposite sides of a coin: an object is either totally symmetric, or totally asymmetric, relative to pattern objects. Intermediate situations of partial symmetry or partial asymmetry are not considered. But this dichotomy on the classification lacks of a necessary and realistic gradation. For this reason, it is convenient to introduce "shade regions", modulating the degree of Symmetry (a fuzzy concept). Here, we will analyze the Asymmetry problem by successive attempts of description and by the introduction of the Asymmetry Level Function, as a new Normal Fuzzy Measure. Our results (both Theorems and Corollaries) suppose to be some new and original contributions to such very active and interesting field of research. Previously, we proceed to the analysis of the state of art. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets
Symmetry 2010, 2(2), 722-766; doi:10.3390/sym2020722
Received: 24 December 2009 / Revised: 15 February 2010 / Accepted: 11 March 2010 / Published: 9 April 2010
PDF Full-text (754 KB)
Abstract
An account of symmetry is very fruitful in studies of quantum spin systems. In the present paper we demonstrate how to use the spin SU(2) and the point symmetries in optimization of the theoretical condensed matter tools: the exact diagonalization, the renormalization group
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An account of symmetry is very fruitful in studies of quantum spin systems. In the present paper we demonstrate how to use the spin SU(2) and the point symmetries in optimization of the theoretical condensed matter tools: the exact diagonalization, the renormalization group approach, the cluster perturbation theory. We apply the methods for study of Bose-Einstein condensation in dimerized antiferromagnets, for investigations of magnetization processes and magnetocaloric effect in quantum ferrimagnetic chain. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Replication and Abstraction: Symmetry in Automated Formal Verification
Symmetry 2010, 2(2), 799-847; doi:10.3390/sym2020799
Received: 27 December 2009 / Revised: 3 March 2010 / Accepted: 4 March 2010 / Published: 14 April 2010
Cited by 10 | PDF Full-text (678 KB)
Abstract
This article surveys fundamental and applied aspects of symmetry in system models, and of symmetry reduction methods used to counter state explosion in model checking, an automated formal verification technique. While covering the research field broadly, we particularly emphasize recent progress in applying
[...] Read more.
This article surveys fundamental and applied aspects of symmetry in system models, and of symmetry reduction methods used to counter state explosion in model checking, an automated formal verification technique. While covering the research field broadly, we particularly emphasize recent progress in applying the technique to realistic systems, including tools that promise to elevate the scope of symmetry reduction to large-scale program verification. The article targets researchers and engineers interested in formal verification of concurrent systems. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle The Symmetry Group of the Non-Isothermal Navier–Stokes Equations and Turbulence Modelling
Symmetry 2010, 2(2), 848-867; doi:10.3390/sym2020848
Received: 10 December 2009 / Revised: 18 March 2010 / Accepted: 12 April 2010 / Published: 16 April 2010
PDF Full-text (236 KB)
Abstract
In this work, the non-isothermal Navier–Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulence models are analyzed with the symmetries of the equations. A class of turbulence models
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In this work, the non-isothermal Navier–Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulence models are analyzed with the symmetries of the equations. A class of turbulence models which preserve the physical properties contained in the symmetry group is built. The proposed turbulence models are applied to an illustrative example of natural convection in a differentially heated cavity, and the results are presented. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation
Symmetry 2010, 2(2), 868-883; doi:10.3390/sym2020868
Received: 21 December 2009 / Revised: 30 March 2010 / Accepted: 15 April 2010 / Published: 19 April 2010
PDF Full-text (308 KB)
Abstract
Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new
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Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new algorithmic process to do this. The construction of invariant schemes consists in parametrizing the scheme with constant coefficients. These coefficients are determined in order to satisfy a fixed order of accuracy and an equivariance condition. Numerical applications with the Burgers equation illustrate the high performances of the process. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Symmetry versus Asymmetry in the Molecules of Life: Homomeric Protein Assemblies
Symmetry 2010, 2(2), 884-906; doi:10.3390/sym2020884
Received: 27 February 2010 / Revised: 7 April 2010 / Accepted: 12 April 2010 / Published: 19 April 2010
Cited by 4 | PDF Full-text (5914 KB)
Abstract
The essay is dedicated to the relation of symmetry and asymmetry-chirality in Nature. The Introduction defines symmetry and its impact on basic definitions in science and human activities. The following section Chirality of molecules reveals breifly development of notion of chirality and its
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The essay is dedicated to the relation of symmetry and asymmetry-chirality in Nature. The Introduction defines symmetry and its impact on basic definitions in science and human activities. The following section Chirality of molecules reveals breifly development of notion of chirality and its significance in living organisms and science. Homochirality is a characteristic hallmark of life and its significance is presented in the section Homochirality of Life. Proteins, important constituents of living cells performing versatile functions are chiral macromolecules composed of L-amino acids. In particular, the protein assemblies are of a great importance in functions of a cell. Therefore, they have attracted researches to examine them from different points of view. Among proteins of known three-dimensional structures about 50–80% of them exist as homomeric protein complexes. Protein monomers lack any intrinsic, underlying symmetry, i.e. enantiomorphic protein molecules involve left-handed amino acids but their asymmetry does not appear to extend to the level of quaternary structures (homomeric complexes) as observed by Chothia in 1991. In the section Homomeric assemblies we performed our analysis of very special cases of homomers revealing non-crystallographic symmetry in crystals. Homochiral proteins can crystallize only in enantiomorphic space groups. Among 230 existing space groups 65 are enantiomorphic containing limited symmetry elements that are rotation and screw-rotation axes. Any axis of rotation symmetry of a crystal lattice must be two-fold, three-fold, four-fold, or six-fold. Five-fold, seven-fold, and higher-fold rotation symmetry axes are incompatible with the symmetry under spatial displacement of the three-dimensional crystal lattice. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)
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Open AccessArticle Study of Dynamical Chiral Symmetry Breaking in (2 + 1) Dimensional Abelian Higgs Model
Symmetry 2010, 2(2), 907-915; doi:10.3390/sym2020907
Received: 5 October 2009 / Revised: 10 April 2010 / Accepted: 15 April 2010 / Published: 19 April 2010
PDF Full-text (186 KB)
Abstract
In this paper, we study the dynamical mass generation in the Abelian Higgs model in 2 + 1 dimensions. Instead of adopting the approximations in [Jiang H et al., J. Phys. A 41 2008 255402.], we numerically solve the coupled Dyson–Schwinger Equations
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In this paper, we study the dynamical mass generation in the Abelian Higgs model in 2 + 1 dimensions. Instead of adopting the approximations in [Jiang H et al., J. Phys. A 41 2008 255402.], we numerically solve the coupled Dyson–Schwinger Equations (DSEs) for the fermion and gauge boson propagators using a specific truncation for the fermion-photon vertex ansatz and compare our results with the corresponding ones in the above mentioned paper. It is found that the results quoted in the above paper remain qualitatively unaffected by refining the truncation scheme of the DSEs, although there exist large quantitative differences between the results presented in the above paper and ours. In addition, our numerical results show that the critical number of fermion flavor Nc decreases steeply with the the gauge boson mass ma (or the ratio of the Higgs mass mh to the gauge boson mass ma, r = mh/ma) increasing. It is thus easier to generate a finite fermion mass by the mechanism of DCSB for a small ratio r for a given ma. Full article
(This article belongs to the Special Issue Symmetry Breaking Phenomena)
Open AccessArticle Miscellania about Entropy, Energy, and Available Free Energy
Symmetry 2010, 2(2), 916-934; doi:10.3390/sym2020916
Received: 25 February 2010 / Revised: 12 April 2010 / Accepted: 14 April 2010 / Published: 19 April 2010
Cited by 1 | PDF Full-text (556 KB)
Abstract
While the main concepts of thermodynamics are universal, the application to specific systems is not. Thus, the universal concepts combined with specific constitutive relations permit the derivation of important results in such fields as diverse as physics, chemistry, physical chemistry, chemical engineering and
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While the main concepts of thermodynamics are universal, the application to specific systems is not. Thus, the universal concepts combined with specific constitutive relations permit the derivation of important results in such fields as diverse as physics, chemistry, physical chemistry, chemical engineering and rheology. In all of these fields equilibrium is characterized either by a maximum of entropy or by a minimum of available free energies, depending on boundary data. In the latter case there is a compromise between the entropic tendency to grow and the energetic tendency to decrease. After some historical considerations the situation is illustrated for several specific cases: planetary atmospheres, osmosis and elastic rubber molecules, pertaining to physics, chemistry and rheology respectively. Afterwards, in the later parts of the article, thermodynamics considerations are extrapolated to remote fields, to wit evolutionary genetics and sociology. Full article
(This article belongs to the Special Issue Entropy, Order and Symmetry)
Open AccessArticle Chiroptical Properties of Amino Acids: A Density Functional Theory Study
Symmetry 2010, 2(2), 935-949; doi:10.3390/sym2020934
Received: 6 March 2010 / Revised: 6 April 2010 / Accepted: 14 April 2010 / Published: 19 April 2010
Cited by 10 | PDF Full-text (3114 KB)
Abstract
Amino acids are involved in many scientific theories elucidating possible origins of life on Earth. One of the challenges when discussing the evolutionary origin of biopolymers such as proteins and oligonucleotides in living organisms is the phenomenon that these polymers implement monomers of
[...] Read more.
Amino acids are involved in many scientific theories elucidating possible origins of life on Earth. One of the challenges when discussing the evolutionary origin of biopolymers such as proteins and oligonucleotides in living organisms is the phenomenon that these polymers implement monomers of exclusively one handedness, a feature called biomolecular homochirality. Many attempts have been made to understand this process of racemic symmetry breaking. Assuming an extraterrestrial origin of the molecular building blocks of living organisms, their susceptibility to asymmetric photolysis by the absorption of circularly polarized electromagnetic radiation in interstellar space was proposed. In order to predict whether the interaction of circularly polarized light with various racemic amino acids can induce an enantiomeric excess, we investigated the electronic and chiroptical properties of the amino acids valine and isovaline by a molecular modelling approach based on quantum chemistry (Density Functional Theory). The average spectra of both L-valine and L-isovaline have been produced on the basis of Boltzmann population analysis using computed spectra for the various conformations of each amino acid. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)
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Open AccessArticle Magnetization Dynamics Symmetry in Spin Torque Induced Magnetization Switching
Symmetry 2010, 2(2), 999-1021; doi:10.3390/sym2020999
Received: 27 December 2009 / Revised: 28 April 2010 / Accepted: 30 April 2010 / Published: 7 May 2010
Cited by 1 | PDF Full-text (266 KB)
Abstract
Magnetization dynamics symmetry plays important roles in magnetization switching. Here we study magnetic field and spin torque induced magnetization switching. Spin moment transferring from polarized itinerant electrons to local magnetization provides a magnetization switching mechanism without using external magnetic field. Besides its importance
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Magnetization dynamics symmetry plays important roles in magnetization switching. Here we study magnetic field and spin torque induced magnetization switching. Spin moment transferring from polarized itinerant electrons to local magnetization provides a magnetization switching mechanism without using external magnetic field. Besides its importance in fundamental magnetization switching dynamics, spin torque magnetization switching has great application potential for future nanoscale magnetoelectronic devices. The paper explores magnetization dynamics symmetry effects on spin torque induced magnetization switching, and its interactions with random fluctuations. We will illustrate the consequences of magnetization dynamics symmetry on the critical switching current magnitude and the thermal stability energy of spin torque induced magnetization switching, which are the two most important design criteria for nanoscale spin torque magnetic devices. The concept of Logarithmic magnetization susceptibility is used to extract symmetry and damping information on spin torque induced nonlinear magnetization dynamic processes, and provides paths to control spin torque induced switching in a fluctuating environment. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Fluctuating Asymmetry in Flies, What Does It Mean?
Symmetry 2010, 2(2), 1099-1107; doi:10.3390/sym2021099
Received: 23 February 2010 / Revised: 11 May 2010 / Accepted: 27 May 2010 / Published: 4 June 2010
Cited by 1 | PDF Full-text (951 KB)
Abstract
The degree of departure from perfect symmetry in organisms, fluctuating asymmetry (FA), is seen in most populations of animals. It has particular impact on choice of mate which lies within the world of sexual selection. Here I consider a relatively little studied aspect
[...] Read more.
The degree of departure from perfect symmetry in organisms, fluctuating asymmetry (FA), is seen in most populations of animals. It has particular impact on choice of mate which lies within the world of sexual selection. Here I consider a relatively little studied aspect of sexual selection, i.e. the effect of FA on contests between males for mates, based not on display ornament but rather on agility seen in the mating systems of many insects. The model organism considered is the ubiquitous chironomid midge. In these flies, mating takes place in the air, so symmetry in the length of wings bears directly on a male’s aerobatic ability on which successful mating depends. The role of parasites and predators in creating and responding to FA in the host/prey midge is considered. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessArticle Experimental Test of L- and D-Amino Acid Binding to L- and D-Codons Suggests that Homochirality and Codon Directionality Emerged with the Genetic Code
Symmetry 2010, 2(2), 1180-1200; doi:10.3390/sym2021180
Received: 9 June 2010 / Revised: 18 June 2010 / Accepted: 22 June 2010 / Published: 23 June 2010
Cited by 2 | PDF Full-text (1010 KB)
Abstract
L-amino acids bind preferentially to their D-codons, but almost nothing is known about whether D-amino acids correspondingly prefer L-codons, or how codon directionality affects amino acid binding. To investigate these issues, two D-RNA-oligonucleotides having inverse base sequences (D-CGUA and D-AUGC) and their corresponding
[...] Read more.
L-amino acids bind preferentially to their D-codons, but almost nothing is known about whether D-amino acids correspondingly prefer L-codons, or how codon directionality affects amino acid binding. To investigate these issues, two D-RNA-oligonucleotides having inverse base sequences (D-CGUA and D-AUGC) and their corresponding L-RNA-oligonucleotides (L-CGUA and L-AUGC) were synthesized and their affinity determined for Gly and eleven pairs of L- and D-amino acids. The data support the hypothesis (Root-Bernstein, Bioessays 2007; 29: 689–698) that homochirality and codon directionality emerged as a function of the origin of the genetic code itself. Further tests involving amplification methods are proposed. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)

Review

Jump to: Research

Open AccessReview Diastereoselective Desymmetrization of Symmetric Dienes and its Synthetic Application
Symmetry 2010, 2(2), 437-454; doi:10.3390/sym2020437
Received: 30 January 2010 / Revised: 4 March 2010 / Accepted: 4 March 2010 / Published: 25 March 2010
Cited by 7 | PDF Full-text (180 KB)
Abstract
The desymmetrization of symmetric compounds is a useful approach to obtain chiral building blocks. Readily available precursors with a prochiral unit could be converted into complex molecules with multiple stereogenic centers in a single step. In this review, recent advances in the desymmetrization
[...] Read more.
The desymmetrization of symmetric compounds is a useful approach to obtain chiral building blocks. Readily available precursors with a prochiral unit could be converted into complex molecules with multiple stereogenic centers in a single step. In this review, recent advances in the desymmetrization of symmetric dienes in the diastereotopic group differentiating reaction and its synthetic application are presented. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Open AccessReview Fluctuating Asymmetry: Methods, Theory, and Applications
Symmetry 2010, 2(2), 466-540; doi:10.3390/sym2020466
Received: 22 December 2009 / Revised: 27 February 2010 / Accepted: 15 March 2010 / Published: 25 March 2010
Cited by 88 | PDF Full-text (2500 KB)
Abstract
Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though responses are often
[...] Read more.
Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though responses are often inconsistent. Researchers base studies of fluctuating asymmetry upon deviations from bilateral, radial, rotational, dihedral, translational, helical, and fractal symmetries. Here, we review old and new methods of measuring fluctuating asymmetry, including measures of dispersion, landmark methods for shape asymmetry, and continuous symmetry measures. We also review the theory, developmental origins, and applications of fluctuating asymmetry, and attempt to explain conflicting results. In the process, we present examples from the literature, and from our own research at “Evolution Canyon” and elsewhere. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Open AccessReview Fluctuating Asymmetry and Steroid Hormones: A Review
Symmetry 2010, 2(2), 541-553; doi:10.3390/sym2020541
Received: 6 January 2010 / Revised: 12 March 2010 / Accepted: 24 March 2010 / Published: 1 April 2010
Cited by 3 | PDF Full-text (63 KB)
Abstract
Fluctuating asymmetry (FA) represents random, minor deviations from perfect symmetry in paired traits. Because the development of the left and right sides of a paired trait is presumably controlled by an identical set of genetic instructions, these small imperfections are considered to reflect
[...] Read more.
Fluctuating asymmetry (FA) represents random, minor deviations from perfect symmetry in paired traits. Because the development of the left and right sides of a paired trait is presumably controlled by an identical set of genetic instructions, these small imperfections are considered to reflect genetic and environmental perturbations experienced during ontogeny. The current paper aims to identify possible neuroendocrine mechanisms, namely the actions of steroid hormones that may impact the development of asymmetrical characters as a response to various stressors. In doing so, it provides a review of the published studies on the influences of glucocorticoids, androgens, and estrogens on FA and concomitant changes in other health and fitness indicators. It follows the premise that hormonal measures may provide direct, non-invasive indicators of how individuals cope with adverse life conditions, strengthening the associations between FA and health, fitness, and behavior. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessReview Broken Time Translation Symmetry as a Model for Quantum State Reduction
Symmetry 2010, 2(2), 582-608; doi:10.3390/sym2020582
Received: 22 December 2009 / Revised: 22 March 2010 / Accepted: 22 March 2010 / Published: 1 April 2010
Cited by 4 | PDF Full-text (394 KB)
Abstract
The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry
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The symmetries that govern the laws of nature can be spontaneously broken, enabling the occurrence of ordered states. Crystals arise from the breaking of translation symmetry, magnets from broken spin rotation symmetry and massive particles break a phase rotation symmetry. Time translation symmetry can be spontaneously broken in exactly the same way. The order associated with this form of spontaneous symmetry breaking is characterised by the emergence of quantum state reduction: systems which spontaneously break time translation symmetry act as ideal measurement machines. In this review the breaking of time translation symmetry is first compared to that of other symmetries such as spatial translations and rotations. It is then discussed how broken time translation symmetry gives rise to the process of quantum state reduction and how it generates a pointer basis, Born’s rule, etc. After a comparison between this model and alternative approaches to the problem of quantum state reduction, the experimental implications and possible tests of broken time translation symmetry in realistic experimental settings are discussed. Full article
(This article belongs to the Special Issue Symmetry Breaking Phenomena)
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Open AccessReview Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems
Symmetry 2010, 2(2), 609-657; doi:10.3390/sym2020609
Received: 1 January 2010 / Revised: 31 March 2010 / Accepted: 6 April 2010 / Published: 7 April 2010
Cited by 50 | PDF Full-text (559 KB)
Abstract
Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations
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Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i) Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii) Minimization of Higgs-type potentials for higher-dimensional representations. (iii) Counting rules for Nambu–Goldstone bosons and their dispersion relations. (iv) Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail. Full article
(This article belongs to the Special Issue Symmetry Breaking Phenomena)
Open AccessReview Lie Symmetries of Differential Equations: Classical Results and Recent Contributions
Symmetry 2010, 2(2), 658-706; doi:10.3390/sym2020658
Received: 2 January 2010 / Accepted: 30 March 2010 / Published: 8 April 2010
Cited by 20 | PDF Full-text (393 KB)
Abstract
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial
[...] Read more.
Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction of links between different differential equations that turn out to be equivalent. This paper reviews some well known results of Lie group analysis, as well as some recent contributions concerned with the transformation of differential equations to equivalent forms useful to investigate applied problems. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessReview The Role of Stochastic Models in Interpreting the Origins of Biological Chirality
Symmetry 2010, 2(2), 767-798; doi:10.3390/sym2020767
Received: 1 March 2010 / Revised: 29 March 2010 / Accepted: 6 April 2010 / Published: 12 April 2010
Cited by 31 | PDF Full-text (590 KB)
Abstract
This review summarizes recent stochastic modeling efforts in the theoretical research aimed at interpreting the origins of biological chirality. Stochastic kinetic models, especially those based on the continuous time discrete state approach, have great potential in modeling absolute asymmetric reactions, experimental examples of
[...] Read more.
This review summarizes recent stochastic modeling efforts in the theoretical research aimed at interpreting the origins of biological chirality. Stochastic kinetic models, especially those based on the continuous time discrete state approach, have great potential in modeling absolute asymmetric reactions, experimental examples of which have been reported in the past decade. An overview of the relevant mathematical background is given and several examples are presented to show how the significant numerical problems characteristic of the use of stochastic models can be overcome by non-trivial, but elementary algebra. In these stochastic models, a particulate view of matter is used rather than the concentration-based view of traditional chemical kinetics using continuous functions to describe the properties system. This has the advantage of giving adequate description of single-molecule events, which were probably important in the origin of biological chirality. The presented models can interpret and predict the random distribution of enantiomeric excess among repetitive experiments, which is the most striking feature of absolute asymmetric reactions. It is argued that the use of the stochastic kinetic approach should be much more widespread in the relevant literature. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)
Open AccessReview Synthesis and Reactions of Dibenzo[a,e]pentalenes
Symmetry 2010, 2(2), 950-969; doi:10.3390/sym2020950
Received: 28 January 2010 / Revised: 11 March 2010 / Accepted: 20 April 2010 / Published: 21 April 2010
Cited by 50 | PDF Full-text (279 KB)
Abstract
Pentalene has recently received a considerable amount of attention as a ligand in sandwich-type transition metal complexes. In contrast, dibenzo[a,e]pentalene (hereafter denoted as dibenzopentalene), which is more π-extended than pentalene, has received less attention, despite its potential usefulness as a building
[...] Read more.
Pentalene has recently received a considerable amount of attention as a ligand in sandwich-type transition metal complexes. In contrast, dibenzo[a,e]pentalene (hereafter denoted as dibenzopentalene), which is more π-extended than pentalene, has received less attention, despite its potential usefulness as a building block of ladder-type π-conjugated molecules, which have recently received growing interest. However, very recently, several novel efficient methods for the synthesis of dibenzopentalenes have been reported. This review surveys recent advances in the synthesis and reactions of dibenzopentalenes and describes the aromaticity of their ionic species. Full article
Open AccessReview Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Symmetry 2010, 2(2), 970-998; doi:10.3390/sym2020970
Received: 12 January 2010 / Revised: 13 April 2010 / Accepted: 21 April 2010 / Published: 29 April 2010
Cited by 2 | PDF Full-text (211 KB)
Abstract
We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General
[...] Read more.
We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections). Full article
(This article belongs to the Special Issue Entropy, Order and Symmetry)
Open AccessReview Origin of Homochirality of Amino Acids in the Biosphere
Symmetry 2010, 2(2), 1022-1032; doi:10.3390/sym2021022
Received: 21 January 2010 / Revised: 28 April 2010 / Accepted: 10 May 2010 / Published: 13 May 2010
Cited by 9 | PDF Full-text (1045 KB) | Supplementary Files
Abstract
Discussions are made concerning realistic mechanisms for the origin of L-amino acids in the biosphere. As the most plausible mechanism, it is proposed that a mixture of racemic amino acids in the prebiotic sea caused spontaneous and effective optical resolution through self crystallization,
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Discussions are made concerning realistic mechanisms for the origin of L-amino acids in the biosphere. As the most plausible mechanism, it is proposed that a mixture of racemic amino acids in the prebiotic sea caused spontaneous and effective optical resolution through self crystallization, even if asymmetric synthesis of a single amino acid has never occurred without the aid of an optically active molecule. This hypothesis is based on recrystallization of a mixture of D,L-amino acids in the presence of excess of D,L-asparagine (Asn). The enantiomeric excess (ee) of each amino acid in the resulting crystals indicates that crystallization of co-existing amino acids with the configuration same as that of Asn took place, although it was incidental whether the enrichment occurred in L- or D-amino acids. In addition, the resulting ee was sufficiently high (up to 100%) to account for the predominance of L-amino acids on the earth. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)
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Open AccessReview Symmetry OUT, Asymmetry IN
Symmetry 2010, 2(2), 1033-1054; doi:10.3390/sym2021033
Received: 15 March 2010 / Revised: 23 April 2010 / Accepted: 18 May 2010 / Published: 25 May 2010
Cited by 2 | PDF Full-text (2461 KB)
Abstract
The formation of a perfect vertebrate body plan poses many questions that thrill developmental biologists. Special attention has been given to the symmetric segmental patterning that allows the formation of the vertebrae and skeletal muscles. These segmented structures derive from bilaterally symmetric units
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The formation of a perfect vertebrate body plan poses many questions that thrill developmental biologists. Special attention has been given to the symmetric segmental patterning that allows the formation of the vertebrae and skeletal muscles. These segmented structures derive from bilaterally symmetric units called somites, which are formed under the control of a segmentation clock. At the same time that these symmetric units are being formed, asymmetric signals are establishing laterality in nearby embryonic tissues, allowing the asymmetric placement of the internal organs. More recently, a “shield” that protects symmetric segmentation from the influence of laterality cues was uncovered. Here we review the mechanisms that control symmetric versus asymmetric development along the left-right axis among vertebrates. We also discuss the impact that these studies might have in the understanding of human congenital disorders characterized by congenital vertebral malformations and abnormal laterality phenotypes. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessReview Photochirogenesis: Photochemical Models on the Origin of Biomolecular Homochirality
Symmetry 2010, 2(2), 1055-1080; doi:10.3390/sym2021055
Received: 1 March 2010 / Revised: 26 April 2010 / Accepted: 13 May 2010 / Published: 25 May 2010
Cited by 11 | PDF Full-text (557 KB)
Abstract
Current research focuses on a better understanding of the origin of biomolecular asymmetry by the identification and detection of the possibly first chiral molecules that were involved in the appearance and evolution of life on Earth. We have reasons to assume that these
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Current research focuses on a better understanding of the origin of biomolecular asymmetry by the identification and detection of the possibly first chiral molecules that were involved in the appearance and evolution of life on Earth. We have reasons to assume that these molecules were specific chiral amino acids. Chiral amino acids have been identified in both chondritic meteorites and simulated interstellar ices. Present research reasons that circularly polarized electromagnetic radiation was identified in interstellar environments and an asymmetric interstellar photon-molecule interaction might have triggered biomolecular symmetry breaking. We review on the possible prebiotic interaction of ‘chiral photons’ in the form of circularly polarized light, with early chiral organic molecules. We will highlight recent studies on enantioselective photolysis of racemic amino acids by circularly polarized light and experiments on the asymmetric photochemical synthesis of amino acids from only one C and one N containing molecules by simulating interstellar environments. Both approaches are based on circular dichroic transitions of amino acids that will be presented as well. Full article
(This article belongs to the Special Issue Symmetry of Life and Homochirality)
Open AccessReview The Relationships between Symmetry and Attractiveness and Mating Relevant Decisions and Behavior: A Review
Symmetry 2010, 2(2), 1081-1098; doi:10.3390/sym2021081
Received: 30 April 2010 / Revised: 8 May 2010 / Accepted: 24 May 2010 / Published: 26 May 2010
Cited by 8 | PDF Full-text (199 KB)
Abstract
Evolutionary theory based research shows that attractiveness is based on biological correlates that index appropriate estrogen and testosterone levels. Symmetry affects or plays a role in the perception of many of these correlates of attractiveness. Additionally, since attractiveness affects infidelity perception and reactions,
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Evolutionary theory based research shows that attractiveness is based on biological correlates that index appropriate estrogen and testosterone levels. Symmetry affects or plays a role in the perception of many of these correlates of attractiveness. Additionally, since attractiveness affects infidelity perception and reactions, sexual satisfaction, and personality perception, symmetry also affects these areas. This paper reviews the literature on symmetry showing how symmetry affects: the correlates of attractiveness, sexual satisfaction, personality, and infidelity perceptions and reactions. Full article
(This article belongs to the Special Issue Symmetry and Beauty)
Open AccessReview Minimum Phi-Divergence Estimators and Phi-Divergence Test Statistics in Contingency Tables with Symmetry Structure: An Overview
Symmetry 2010, 2(2), 1108-1120; doi:10.3390/sym2021108
Received: 12 March 2010 / Revised: 7 May 2010 / Accepted: 10 June 2010 / Published: 11 June 2010
PDF Full-text (144 KB)
Abstract
In the last years minimum phi-divergence estimators (MϕE) and phi-divergence test statistics (ϕTS) have been introduced as a very good alternative to classical likelihood ratio test and maximum likelihood estimator for different statistical problems. The main purpose of this
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In the last years minimum phi-divergence estimators (MϕE) and phi-divergence test statistics (ϕTS) have been introduced as a very good alternative to classical likelihood ratio test and maximum likelihood estimator for different statistical problems. The main purpose of this paper is to present an overview of the main results presented until now in contingency tables with symmetry structure on the basis of (MϕE) and (ϕTS). Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
Open AccessReview Symmetry in Boolean Satisfiability
Symmetry 2010, 2(2), 1121-1134; doi:10.3390/sym2021121
Received: 31 December 2009 / Revised: 14 May 2010 / Accepted: 9 June 2010 / Published: 11 June 2010
Cited by 2 | PDF Full-text (182 KB)
Abstract
This paper reviews recent approaches on how to accelerate Boolean Satisfiability (SAT) search by exploiting symmetries in the problem space. SAT search algorithms traverse an exponentially large search space looking for an assignment that satisfies a set of constraints. The presence of symmetries
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This paper reviews recent approaches on how to accelerate Boolean Satisfiability (SAT) search by exploiting symmetries in the problem space. SAT search algorithms traverse an exponentially large search space looking for an assignment that satisfies a set of constraints. The presence of symmetries in the search space induces equivalence classes on the set of truth assignments. The goal is to use symmetries to avoid traversing all assignments by constraining the search to visit a few representative assignments in each equivalence class. This can lead to a significant reduction in search runtime without affecting the completeness of the search. Full article
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Open AccessReview A Review of New Analytic Techniques for Quantifying Symmetry in Locomotion
Symmetry 2010, 2(2), 1135-1155; doi:10.3390/sym2021135
Received: 12 May 2010 / Revised: 9 June 2010 / Accepted: 10 June 2010 / Published: 14 June 2010
Cited by 13 | PDF Full-text (656 KB)
Abstract
We present a review of novel techniques developed by our research group to improve quantitative assessment of human movement, especially assessments related to symmetric and asymmetric gait patterns. These new methods use motion capture data of the lower limb joints (e.g., joint and
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We present a review of novel techniques developed by our research group to improve quantitative assessment of human movement, especially assessments related to symmetric and asymmetric gait patterns. These new methods use motion capture data of the lower limb joints (e.g., joint and body segment angular position and/or velocity, or joint center locations) and include: (1) Regions of Deviation (ROD) analysis, (2) complexity and variability of phase portraits, and (3) multivariate shape-alignment and decomposition. We provide example demonstrations of these techniques using data from infants, typical and atypically developing children, simulated injuries of a knee or ankle, and wheelchair propulsion. Full article
(This article belongs to the Special Issue Complexity and Symmetry)
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Open AccessReview A Critical Assessment of the Performance of Magnetic and Electronic Indices of Aromaticity
Symmetry 2010, 2(2), 1156-1179; doi:10.3390/sym2021156
Received: 17 February 2010 / Revised: 7 May 2010 / Accepted: 10 June 2010 / Published: 14 June 2010
Cited by 53 | PDF Full-text (711 KB)
Abstract
The lack of reference aromatic systems in the realm of inorganic aromatic compounds makes the evaluation of aromaticity in all-metal and semimetal clusters a difficult task. To date, calculation of nucleus-independent chemical shifts (NICS) has been the most widely used method to discuss
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The lack of reference aromatic systems in the realm of inorganic aromatic compounds makes the evaluation of aromaticity in all-metal and semimetal clusters a difficult task. To date, calculation of nucleus-independent chemical shifts (NICS) has been the most widely used method to discuss aromaticity in these systems. In the first part of this work, we briefly review our previous studies, showing some pitfalls of the NICS indicator of aromaticity in organic molecules. Then, we refer to our study on the performance of some aromaticity indices in a series of 15 aromaticity tests, which can be used to analyze the advantages and drawbacks of aromaticity descriptors. It is shown that indices based on the study of electron delocalization are the most accurate among those analyzed in the series of proposed tests, while NICS(1)zz and NICS(0)πzz present the best behavior among NICS indices. In the second part, we discuss the use of NICS and electronic multicenter indices (MCI) in inorganic clusters. In particular, we evaluate the aromaticity of two series of all-metal and semimetal clusters with predictable aromaticity trends by means of NICS and MCI. Results show that the expected trends are generally better reproduced by MCI than NICS. It is concluded that NICS(0)π and NICS(0)πzz are the kind of NICS that perform the best among the different NICS indices analyzed for the studied series of inorganic compounds. Full article
(This article belongs to the Special Issue Aromaticity and Molecular Symmetry)
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