Showing papers in "Symmetry in 2010"

Fluctuating Asymmetry: Methods, Theory, and Applications

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 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.

Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

Abstract: I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of “doubly-special” relativistic (“DSR”) theories with both an observer-independent high-velocity scale and an observer-independent small-length/large-momentum scale, possibly relevant for the Planck-scale/quantum-gravity realm. I also give a true/false characterization of the structure of these theories. In particular, I discuss a DSR scenario without modification of the energy-momentum dispersion relation and without the қ-Poincare Hopf algebra, a scenario with deformed Poincare symmetries which is not a DSR scenario, some scenarios with both an invariant length scale and an invariant velocity scale which are not DSR scenarios, and a DSR scenario in which it is easy to verify that some observable relativistic (but non-special-relativistic) features are insensitive to possible nonlinear redefinitions of symmetry generators.

Behind the Looking-Glass: A Review on Human Symmetry Perception

Abstract: The human visual system is highly proficient in extracting bilateral symmetry from visual input. This paper reviews empirical and theoretical work on human symmetry perception with a focus on recent issues such as its neural underpinnings. Symmetry detection is shown to be a versatile, ongoing visual process that interacts with other visual processes. Evidence seems to converge towards the idea that symmetry detection is subserved by a preprocessing stage involving spatial filters followed by information integration across the visual field in higher-tier cortical areas.

Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems

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 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.

On the Harmonic Oscillator Model of Electron Delocalization (HOMED) Index and its Application to Heteroatomic π-Electron Systems

Abstract: The HOMA (Harmonic Oscillator Model of Aromaticity) index, reformulated in 1993, has been very often applied to describe π-electron delocalization for mono- and polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe properly various resonance effects (σ-π hyperconjugation, n-π conjugation, π-π conjugation, and aromaticity) possible for heteroatomic π-electron systems, some modifications, based on the original HOMA idea, were proposed and tested for simple DFT structures containing C, N, and O atoms. An abbreviation HOMED was used for the modified index.

Lie Symmetries of Differential Equations: Classical Results and Recent Contributions

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 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.

A Critical Assessment of the Performance of Magnetic and Electronic Indices of Aromaticity

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 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.

Recent Studies on the Aromaticity and Antiaromaticity of Planar Cyclooctatetraene

Abstract: Cyclooctatetraene (COT), the first 4nπ-electron system to be studied, adopts an inherently nonplanar tub-shaped geometry of D2d symmetry with alternating single and double bonds, and hence behaves as a nonaromatic polyene rather than an antiaromatic compound. Recently, however, considerable 8π-antiaromatic paratropicity has been shown to be generated in planar COT rings even with the bond alternated D4h structure. In this review, we highlight recent theoretical and experimental studies on the antiaromaticity of hypothetical and actual planar COT. In addition, theoretically predicted triplet aromaticity and stacked aromaticity of planar COT are also briefly described.

Synthesis and Reactions of Dibenzo[a,e]pentalenes

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 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.

Phase Diagram and Critical Properties within an Effective Model of QCD: The Nambu–Jona-Lasinio Model Coupled to the Polyakov Loop

Abstract: We investigate the phase diagram of the so-called Polyakov–Nambu–Jona-Lasinio model at finite temperature and non-zero chemical potential with three quark flavors. Chiral and deconfinement phase transitions are discussed and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. We present the phase diagram in the (T, μB) plane, paying special attention to the critical end point: as the strength of the flavor-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.

The Role of Stochastic Models in Interpreting the Origins of Biological Chirality

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 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.

Complex Networks and Symmetry I: A Review

Abstract: In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.

Structures of Annulenes and Model Annulene Systems in the Ground and Lowest Excited States

Abstract: The paper introduces general considerations on structural properties of aromatic, antiaromatic and non-aromatic conjugated systems in terms of potential energy along bond length alternation and distortion coordinates, taking as examples benzene, cyclobutadiene and cyclooctatetraene. Pentalene, formally derived from cyclooctatetraene by cross linking, is also considered as a typical antiaromatic system. The main interest is concerned with [n]annulenes and model [n]annulene molecular systems, n ranging from 10 to 18. The rich variety of conformational and configurational isomers and of dynamical processes among them is described. Specific attention is devoted to bridged [10]- and [14]annulenes in the ground and lowest excited states as well as to s-indacene and biphenylene. Experimental data obtained from vibrational and electronic spectroscopies are discussed and compared with ab initio calculation results. Finally, porphyrin, tetraoxaporphyrin dication and diprotonated porphyrin are presented as annulene structures adopting planar/non-planar geometries depending on the steric hindrance in the inner macrocycle ring. Radiative and non-radiative relaxation processes from excited state levels have been observed by means of time-resolved fluorescence and femtosecond transient absorption spectroscopy. A short account is also given of porphycene, the structural isomer of porphyrin, and of porphycene properties.

Replication and Abstraction: Symmetry in Automated Formal Verification

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 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.

On the Importance of Clar Structures of Polybenzenoid Hydrocarbons as Revealed by the π-Contribution to the Electron Localization Function

Abstract: The degree of -electron (de)localization and aromaticity of a series of polybenzenoid hydrocarbons (PBHs) has been analyzed through the π-contribution to the electron localization function (ELFπ), calculated at the B3LYP/6-311G(d,p) hybrid density functional theory level. The extent of -electron delocalization in the various hexagons of a PBH was determined through analysis of the bifurcation values of the ELF basins (BV(ELF)), the spans in the bifurcation values in each hexagon (ΔBV(ELFπ)), and the ring-closure bifurcation values of the ELFπ (RCBV(ELFπ)). These computed results were compared to the qualitative description of local aromaticities of the different hexagons in terms of Clar structures with -sextets. Benzene, (18)annulene, and thirty two PBHs were analyzed at their equilibrium geometries, and benzene and triphenylene were also analyzed at bond length distorted structures. In general, the description of PBHs in terms of Clar valence structures is supported by the ELF properties, although there are exceptions. For PBHs at their equilibrium geometries there is a clear sigmoidal relationship between the CC bond lengths and the amount of -electron (de)localization at these bonds, however, this relationship is lost for bond distorted geometries. In the latter cases, we specifically examined benzene in D3h symmetric "1,3,5-cyclohexatriene" structures and triphenylene in eight different structures. From the distorted benzenes and triphenylenes it becomes clear

Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

Abstract: We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.

Asymmetry and Symmetry in the Beauty of Human Faces

Abstract: The emphasis in the published literature has mostly been on symmetry as the critical source for beauty judgment. In fact, both symmetry and asymmetry serve as highly aesthetic sources of beauty, whether the context is perceptual or conceptual. The human brain is characterized by symbolic cognition and this type of cognition facilitates a range of aesthetic reactions. For example, both art and natural scenery contain asymmetrical elements, which nevertheless render the whole effect beautiful. A further good case in point is, in fact, human faces. Normally, faces are structurally left-right symmetrical content-wise but not size-wise or function-wise. Attractiveness has often been discussed in terms of content-wise full-face symmetry. To test whether or not attractiveness can be gleaned only from the presence of left-right full-faces we tested half faces. Three separate groups of participants viewed and rated the attractiveness of 56 full-faces (women’s and men’s), their 56 vertical left hemi-faces and 56 vertical right hemi-faces. We found no statistically significant differences in the attractiveness ratings of full- and hemi-faces (whether left or right). Instead, we found a strong and significant positive correlation between the ratings of the hemi- and full-faces. These results are consistent with the view that the underpinning of human facial beauty is complex and that bilateral symmetry does not constitute a principle factor in beauty assessment. We discuss that the highly evolved human brain, compared to other animals, as well as symbolic and abstract cognition in humans enable a wide variety of aesthetic reactions.

A Direct Road to Majorana Fields

Abstract: A concise discussion of spin-1/2 field equations with a special focus on Majorana spinors is presented. The Majorana formalism which describes massive neutral fermions by the help of two-component or four-component spinors is of fundamental importance for the understanding of mathematical aspects of supersymmetric and other extensions of the Standard Model of particle physics, which may play an increasingly important role at the beginning of the LHC era. The interplay between the two-component and the four-component formalism is highlighted in an introductory way. Majorana particles are predicted both by grand unified theories, in which these particles are neutrinos, and by supersymmetric theories, in which they are photinos, gluinos and other states.

The Relationships between Symmetry and Attractiveness and Mating Relevant Decisions and Behavior: A Review

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, 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

Symmetry and Asymmetry in Bouncing Gaits

Abstract: In running, hopping and trotting gaits, the center of mass of the body oscillates each step below and above an equilibrium position where the vertical force on the ground equals body weight. In trotting and low speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation equals that of the upper part, the duration of the lower part equals that of the upper part and the step frequency equals the resonant frequency of the bouncing system: we define this as on-offground symmetric rebound. In hopping and high speed human running, the average vertical acceleration of the center of mass during the lower part of the oscillation exceeds that of the upper part, the duration of the upper part exceeds that of the lower part and the step frequency is lower than the resonant frequency of the bouncing system: we define this as on-off-ground asymmetric rebound. Here we examine the physical and physiological constraints resulting in this on-off-ground symmetry and asymmetry of the rebound. Furthermore, the average force exerted during the brake when the body decelerates downwards and forwards is greater than that exerted during the push when the body is reaccelerated upwards and forwards. This landing-takeoff asymmetry, which would be nil in the elastic rebound of the symmetric spring-mass model for running and hopping, suggests a less efficient elastic energy storage and recovery during the bouncing step. During hopping, running and trotting the landing-takeoff asymmetry and the mass-specific vertical stiffness are smaller in larger animals than in the smaller animals suggesting a more efficient rebound in larger animals.

A Review of New Analytic Techniques for Quantifying Symmetry in Locomotion

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 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.

Photochirogenesis: Photochemical Models on the Origin of Biomolecular Homochirality

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 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.

Diagnosis of the σ-, π- and (σ+π)-Aromaticity by the Shape of the NICSzz-Scan Curves and Symmetry-Based Selection Rules

Abstract: The NICSzz-scan curves of aromatic organic, inorganic and “all-metal” molecules in conjunction with symmetry-based selection rules provide efficient diagnostic tools of the σ-, π- and/or double (σ + π)-aromaticity The NICSzz-scan curves of σ-aromatic molecules are symmetric around the z-axis, having half-band widths approximately less than 3 A with the induced diatropic ring current arising from Tx,y-allowed transitions involving exclusively σ-type molecular orbitals Broad NICSzz-scan curves (half-band width approximately higher than 3 A) characterize double (σ + π)-aromaticity, the chief contribution to the induced diatropic ring current arising from Tx,y-allowed transitions involving both σ- and π-type molecular orbitals NICSzz-scan curves exhibiting two maxima at a certain distance above and below the molecular plane are typical for (σ + π)-aromatics where the π-diatropic ring current overwhelms the σ-type one In the absence of any contribution from the σ-diatropic ring current, the NICSzz(0) value is close to zero and the molecule exhibits pure π-aromaticity

Positive Cosmological Constant and Quantum Theory

Abstract: We argue that quantum theory should proceed not from a spacetime background but from a Lie algebra, which is treated as a symmetry algebra. Then the fact that the cosmological constant is positive means not that the spacetime background is curved but that the de Sitter (dS) algebra as the symmetry algebra is more relevant than the Poincare or anti de Sitter ones. The physical interpretation of irreducible representations (IRs) of the dS algebra is considerably different from that for the other two algebras. One IR of the dS algebra splits into independent IRs for a particle and its antiparticle only when Poincare approximation works with a high accuracy. Only in this case additive quantum numbers such as electric, baryon and lepton charges are conserved, while at early stages of the Universe they could not be conserved. Another property of IRs of the dS algebra is that only fermions can be elementary and there can be no neutral elementary particles. The cosmological repulsion is a simple kinematical consequence of dS symmetry on quantum level when quasiclassical approximation is valid. Therefore the cosmological constant problem does not exist and there is no need to involve dark energy or other fields for explaining this phenomenon (in agreement with a similar conclusion by Bianchi and Rovelli).

Time-Symmetric Boundary Conditions and Quantum Foundations

Abstract: Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton’s principle would imply that both initial and final BCs are required (or more generally, a BC on a closed hypersurface in spacetime). Such a time-symmetric perspective of BCs, as applied to classical fields, leads to interesting parallels with quantum theory. This paper will map out some of the consequences of this counter-intuitive premise, as applied to covariant classical fields. The most notable result is the contextuality of fields constrained in this manner, naturally bypassing the usual arguments against so-called “realistic” interpretations of quantum phenomena.

Chiral Symmetry Breaking Phenomenon Caused by a Phase Transition

Abstract: We report the mechanism and scope of “preferential enrichment”, which is an unusual symmetry-breaking enantiomeric resolution phenomenon that is initiated by the solvent-assisted solid-to-solid transformation of a metastable polymorphic form into a thermodynamically stable one during crystallization from the supersaturated solution of certain kinds of racemic mixed crystals (ie, solid solutions or pseudoracemates) composed of two enantiomers The mechanism can well be interpreted in terms of a symmetrybreaking complexity phenomenon involving multistage processes that affect each other

Three-Dimensional Facial Asymmetry in Attractive and Normal People from Childhood to Young Adulthood

Abstract: We are currently investigating measurable esthetic characteristics in persons considered “attractive” by the media. Three-dimensional soft-tissue facial asymmetry was quantified in 380 attractive (148 males, 232 females) and 669 control (397 males, 272 females) healthy persons aged 4–30 years. The coordinates of 50 facial landmarks were collected by a computerized digitizer, and asymmetry computed. Soft-tissue facial asymmetries reduced as a function of age in all cases. Attractive children were more symmetric than control children, but the reverse was true for young adults. The effect of symmetry on attractiveness seems to change as a function of age.

Fluctuating Asymmetry and Steroid Hormones: A Review

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 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.

Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics

Abstract: A detailed analysis of deterministic (one-to-one) and stochastic (one-to-many)dynamics establishes that dS/dt> 0 is only consistent with the latter, which containsviolation of temporal symmetry and homogeneity. We observe that the former only supports dS/dt = 0 and cannot give rise to Boltzmann’s molecular chaos assumption. The ensembleaverage is more meaningful than the temporal average, especially in non-equilibriumstatistical mechanics of systems confined to disjoint phase space components, whichcommonly occurs at low temperatures. We propose that the stochasticity arises from extradegrees of freedom, which are not part of the system. We provide a simple resolution of therecurrence and irreversibility paradoxes.Keywords: deterministicandstochasticdynamics;temporalasymmetryandinhomogeneity;second law of thermodynamics; temporal and ensemble averages; phase space confinement;irreversibility and recurrence paradoxes; molecular chaos assumption; Poincar´e recurrence1. IntroductionOne of the most important developments in theoretical physics is the use of symmetry in studyingphysical phenomena. The symmetry properties of a physical system determine how it evolves intime; see for example, Noether’s theorem applicable to systems modeled by a Hamiltonian [1]. Apartfrom continuous symmetries (global or local), there are also discrete symmetries such as reflection,time-reversal invariance,

Orientational Sampling Schemes Based on Four Dimensional Polytopes

Abstract: The vertices of regular four-dimensional polytopes are used to generate sets of uniformly distributed three-dimensional rotations, which are provided as tables of Euler angles. The spherical moments of these orientational sampling schemes are treated using group theory. The orientational sampling sets may be used in the numerical computation of solid-state nuclear magnetic resonance spectra, and in spherical tensor analysis procedures.