ALBERT

Description: This paper aims to construct conservation laws for a Benjamin–Bona–Mahony equation with variable coefficients, which is a third-order partial differential equation. This equation does not have a Lagrangian and so we transform it to a fourth-order partial differential equation, which has a Lagrangian. The Noether approach is then employed to construct the conservation laws. It so happens that the derived conserved quantities fail to satisfy the divergence criterion and so one needs to make adjustments to the derived conserved quantities in order to satisfy the divergence condition. The conservation laws are then expressed in the original variable. Finally, a conservation law is used to obtain exact solution of a special case of the Benjamin–Bona–Mahony equation.

Description: A model is described that can be used to estimate the bulk polarization of largerotating meteoroids in the magnetic field of a neutron star. The results of this model areapplicable to the Supernova Neutrino Amino Acid Processing model, which describes onepossible way in which the amino acids, known in nearly all cases to exhibit supramolecularchirality, could have become enantiomeric.

Description: Long-Term Evolution (LTE) is a fourth-generation mobile communication technology implemented throughout the world. It is the communication means of smartphones that send and receive all of the private date of individuals. M2M, IOT, etc., are the base technologies of mobile communication that will be used in the future cyber world. However, identification parameters, such as International Mobile Subscriber Identity (IMSI), Radio Network Temporary Identities (RNTI), etc., in the initial attach section for accessing the LTE network are presented with the vulnerability of being exposed as clear text. Such vulnerability does not end in a mere identification parameter, but can lead to a secondary attack using the identification parameter, such as replication of the smartphone, illegal use of the mobile communication network, etc. This paper proposes a security protocol to safely transmit identification parameters in different cases of the initial attach. The proposed security protocol solves the exposed vulnerability by encrypting the parameters in transmission. Using an OPNET simulator, it is shown that the average rate of delay and processing ratio are efficient in comparison to the existing process.

Description: Mirror symmetry is often thought to be particularly salient to human observers because it engages specialized mechanisms that evolved to sense symmetrical objects in nature. Although symmetry is indeed present in many of our artifacts and markings on wildlife, studies have shown that sensitivity to mirror symmetry does not serve an alerting function and sensitivity to symmetry decreases in a rather unremarkable way when it is presented away from the centre of the visual field. Here we show that symmetrical targets are vulnerable to the same interference as other stimuli when surrounded by non-target elements. These results provide further evidence that symmetry is not special to the early visual system, and reinforce the notion that our fascination with symmetry is more likely attributable to cognitive and aesthetic factors than to specialized, low level mechanisms in the visual system.

Description: Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry. Specifically, given two arbitrary curves in a single 2D image, one can always find a 3D mirror-symmetric interpretation of these curves under quite general assumptions. The symmetric interpretation is unique under a perspective projection and there is a one parameter family of symmetric interpretations under an orthographic projection. We formally state and prove this observation for the case of one-to-one and many-to-many point correspondences. We conclude by discussing the role of degenerate views, higher-order features in determining the point correspondences, as well as the role of the planarity constraint. When the correspondence of features is known and/or curves can be assumed to be planar, 3D symmetry becomes non-accidental in the sense that a 2D image of a 3D asymmetric shape obtained from a random viewing direction will not allow for 3D symmetric interpretations.

Description: A large number of interesting organocatalytic enantioselective protocols have been explored and successfully applied in the last decade. Among them, the Henry (nitroaldol) reaction represents a powerful carbon-carbon bond-forming procedure for the preparation of valuable synthetic intermediates, such as enantioenriched nitro alcohols, which can be further transformed in a number of important nitrogen and oxygen-containing compounds. This area of research is still in expansion and a more complex version of this useful process has recently emerged, the domino Michael/Henry protocol, affording highly functionalized cycles with multiple stereogenic centers.

Description: Much is already known about single mirror symmetry, but multiple mirror symmetry is still understood poorly. In particular, perceptually, multiple symmetry does not seem to behave as suggested by the number of symmetry axes alone. Here, theoretical ideas on single symmetry perception and their extensions to multiple symmetry are discussed alongside empirical findings on multiple symmetry perception. The evidence suggests that, apart from the number of axes, also their relative orientation is perceptually relevant. This, in turn, suggests that perception is responsible for the preponderance of 3-fold and 5-fold symmetries in flowers as well as for their absence in decorative art.

Description: 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.

Description: From elemental particles to human beings, matter is dissymmetric with respect to mirror symmetry. In 1860, Pasteur conjectured that biomolecular handedness— homochirality—may originate from certain inherent dissymmetric forces existing in the universe. Kipping, a pioneer of organosilicon chemistry, was interested in the handedness of sodium chlorate during his early research life. Since Kipping first synthesized several Si-Si bonded oligomers bearing phenyl groups, Si-Si bonded high polymers carrying various organic groups—polysilanes—can be prepared by sodium-mediated condensation of the corresponding organodichlorosilanes. Among these polysilanes, optically active helical polysilanes with enantiomeric pairs of organic side groups may be used for testing the mirror symmetry-breaking hypothesis by weak neutral current (WNC) origin in the realm of chemistry and material science. Several theoretical studies have predicted that WNC-existing chiral molecules with stereogenic centers and/or stereogenic bonds allow for distinguishing between image and mirror image molecules. Based on several amplification mechanisms, theorists claimed that minute differences, though still very subtle, may be detectable by precise spectroscopic and physicochemical measurements if proper chiral molecular pairs were employed. The present paper reports comprehensively an inequality between six pairs of helical polysilane high polymers, presumably, detectable by (chir)optical and achiral 29Si-/13C- NMR spectra, and viscometric measurements.

Description: Intrinsic dynamics of the central vestibular system (CVS) appear to be at least partly determined by the symmetries of its connections. The CVS contributes to whole-body functions such as upright balance and maintenance of gaze direction. These functions coordinate disparate senses (visual, inertial, somatosensory, auditory) and body movements (leg, trunk, head/neck, eye). They are also unified by geometric conditions. Symmetry groups have been found to structure experimentally-recorded pathways of the central vestibular system. When related to geometric conditions in three-dimensional physical space, these symmetry groups make sense as a logical foundation for sensorimotor coordination.

Description: 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.

Description: An efficient algorithm leading to the Fries canonical structure is presented for benzenoid hydrocarbons. This is a purely topological approach, which is based on adjacency matrices and the Hadamard procedure of matrix multiplication. The idea is presented for naphthalene, as an example. The Fries canonical-structures are also derived for anthracene, coronene, triphenylene, phenanthrene, benz[a]pyrene, and one large benzenoid system. The Fries concept can be convenient for obtaining Clar structures with the maximum number of sextets, which in turn effectively represent π-electron (de)localization in benzenoid hydrocarbons.

Description: 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.

Description: 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 contains violation 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 ensemble average is more meaningful than the temporal average, especially in non-equilibrium statistical mechanics of systems confined to disjoint phase space components, which commonly occurs at low temperatures. We propose that the stochasticity arises from extra degrees of freedom, which are not part of the system. We provide a simple resolution of the recurrence and irreversibility paradoxes.

Description: The paper reviews the polyanionic hexagons of silicon and germanium, focusing on aromaticity. The chair-like structures of hexasila- and hexagermabenzene are similar to a nonaromatic cyclohexane (CH2)6 and dissimilar to aromatic D6h-symmetric benzene (CH)6, although silicon and germanium are in the same group of the periodic table as carbon. Recently, six-membered silicon and germanium rings with extra electrons instead of conventional substituents, such as alkyl, aryl, etc., were calculated by us to have D6h symmetry and to be aromatic. We summarize here our main findings and the background needed to reach them, and propose a synthetically accessible molecule.

Description: 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.

Description: We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the Pöschl-Teller systems) while the case κ 〈 0 is described by the compact group SU(2) (as for the Morse system). We construct the phase operators and the corresponding temporally stable phase eigenstates for Aκ in this group-theoretical context. The SU(2) case is exploited for deriving families of mutually unbiased bases used in quantum information. Along this vein, we examine some characteristics of a quadratic discrete Fourier transform in connection with generalized quadratic Gauss sums and generalized Hadamard matrices.

Description: 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.

Description: We consider a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise, and one irreducible representation (IR) of the symmetry algebra splits into independent IRs describing a particle an its antiparticle only in the approximation when de Sitter energies are much less than the characteristic of the field. As a consequence, the very notions of particles and antiparticles are only approximate and such additive quantum numbers as the electric, baryon and lepton charges are conserved only in this approximation. There can be no neutral elementary particles and the spin-statistics theorem can be treated simply as a requirement that standard quantum theory should be based on complex numbers.

Description: Although symmetry may be important for understanding the selection of form in art over the historical period, this preference may have originally stemmed from certain basic perceptual mechanism that initially arose during prehistory. The first signs of an awareness to symmetry can be found in the archaeological record with the arrival of Acheulean handaxes, especially those dating from 500,000 years ago onwards, which are typified by a prodigious bilateral symmetry. As handaxes represent the earliest material record of an interest in symmetry by the human lineage, they provide a privileged means of understanding why this kind of form came to be valued by later human groups, particularly in relation to “art”. Although still controversial, the preference for symmetry at such an early date has been linked to various aspects of perception relating to enduring evolutionary factors. In this regard, it will be demonstrated how the preference for symmetrical Acheulean tools arose out of long standing perceptual correlates relating to ecological factors that predated the arrival of hominins.

Description: 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.

Description: The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite  it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of the pricing equation can keep invariant under all the local num´eraire transformations, this symmetry behind the pricing equation of derivatives is revealed. In addition a  corresponding relationship between the curvature of the fiber bundle and the arbitrage in finance arises.

Description: 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.

Description: Information optimization is a centerpiece phenomenon in the universe. It develops from simplicity, then continuously breaks symmetry and cycles through instability to progress to increasingly dense nodes of complexity and diversity. Intelligence has arisen as the information optimization node with the greatest complexity. A contemporary imbalance is presented in that exponentially growing technology could be poised as a potential sole successor to human intelligence. A complex dynamical system is emerging in response, the engineering of life into technology. Numerous network elements are developing which could self-organize into the next node of symmetry, a phase transition in intelligence.

Description: Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.

Description: 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.

Description: Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant) notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.

Description: Asymmetry and symmetry coexist in natural and human processes.  The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion) and symmetric opposition (sinusoidal waves) are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition). These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series). The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.

Description: 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).

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: This work expands the results and derivations presented in a recent letter. It is argued that symmetry breaking Hartree-Fock (HF) solutions of a simple model of the Cu-O planes in La2CuO4, are able to describe the insulator and antiferromagnetic characters of this material. Then, this classical primer of a Mott insulator is alternatively obtained here as an exact Slater insulator within the simplest of the first principles schemes. Moreover, pseudogap HF states are also predicted. The maximal energy gap of 100 meV over the Fermi surface of this wavefunction, reasonably well matches the ARPES upper pseudogap measurements for La2CuO4 in the zero doping limit. These surprising results followed after eliminating spin and crystal symmetry constraints usually imposed on the HF orbitals. The discussion helps to clarify the role of the antiferromagnetism and pseudogaps in the physics of the HTSC materials and indicates a promising way to start conciliating the Mott and Slater pictures for the description of the transition metal oxides.

Description: 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.

Description: 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.

Description: The origin of homochirality in life remains a mystery that some believe is essential for life, and which may result from chiral symmetry breaking interactions with galactic organic material.

Description: 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.

Description: 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.

Description: 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).

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Through-space isotropic NMR shielding values of a perpendicular diatomic hydrogen probe moved in a 0.5 Å grid 2.5 Å above several polycyclic aromatic/antiaromatic ring and aromatic/aromatic hydrocarbons were computed with Gaussian 03 at the GIAO HF/6-31G(d,p) level. Combinations of benzene fused with cyclobutadiene, with the tropylium ion, and with the cyclopentadienyl anion were investigated. Subtraction of the isolated H2 isotropic value gave shielding increments(Δσ), which, when plotted against Cartesian coordinates of the probe over each hydrocarbon, gave representations of three-dimensional isotropic shielding increment surfaces. The results are related to the degree of bond length alternation, the extent of electron delocalization, and (for the ions) the NPA charge distribution. The shielding increment data are compared to NICS(1) values computed at the same level; both indicate the degree of aromaticity or antiaromaticity of the component rings.

Description: 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 Å 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 Å) 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.

Description: We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the quaternion group.

Description: Quantum theory is a probabilistic calculus that enables the calculation of the probabilities of the possible outcomes of a measurement performed on a physical system. But what is the relationship between this probabilistic calculus and probability theory itself? Is quantum theory compatible with probability theory? If so, does it extend or generalize probability theory? In this paper, we answer these questions, and precisely determine the relationship between quantum theory and probability theory, by explicitly deriving both theories from first principles. In both cases, the derivation depends upon identifying and harnessing the appropriate symmetries that are operative in each domain. We prove, for example, that quantum theory is compatible with probability theory by explicitly deriving quantum theory on the assumption that probability theory is generally valid.

Description: Asymmetric Michael addition of carbon nucleophiles, nitroalkanes and a β-ketoester, to enones was investigated by using a primary amino acid lithium salt as a catalyst.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.

Description: The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.

Description: The consequences for five-colour QCD of a novel symmetry-breaking mechanism, published in an earlier paper, are further explored. In addition to the emergence of QED and three-colour QCD, there is also a candidate for the Z0μ. The representation theory of SU (N) is applied to the matter sector and yields the quark and electron charge ratios, and a mechanism for generating fermion particle masses.

Description: 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.

Description: Within recent discussions in the Philosophy of Mind, the nature of conscious phenomenal states or qualia (also called ‘raw feels’ or the feel of ‘what it is like to be’) has been an important focus of interest. Proponents of Mind-Body Type-Identity theories have claimed that mental states can be reduced to neurophysiological states of the brain. Others have denied that such a reduction is possible; for them, there remains an explanatory gap. In this paper, functionalist, physicalist, epiphenomenalist, and biological models of the mind are discussed and compared. Donald Davidson’s Anomalous Monism is proposed as a unifying framework for a non-reductive theory of qualia and consciousness. Downward Causation, Emergence through Symmetry-breaking, and Dynamical Systems Theory are used to show how consciousness and qualia emerge from their neural substrate and can also be causally efficacious.

Description: From the physics point of view, time is now best described through General Relativity as part of space-time, which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics and quantum mechanical effects. This irreversibility can look puzzling since time-like loops (and hence time machines) can appear in General Relativity (for example in the Gödel universe, a solution of Einstein’s equations). We take this apparent discrepancy as a warning bell, pointing out that time as we understand it might not be fundamental and that whatever theory lying beyond General Relativity may not include time as we know it as a fundamental structure. We propose therefore, following the philosophy of analog models of gravity, that time and gravity might not be fundamental per se, but only emergent features. We illustrate our proposal using a toy-model where we show how the Lorentzian signature and Nordström gravity (a diffeomorphisms invariant scalar gravity theory) can emerge from a timeless non-dynamical space. This article received the fourth prize at the essay competition of the Foundational Questions Institute on the nature of time.

Description: Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that “quantisation commutes with reduction” and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.

Description: The 1,4-conjugate addition of nucleophiles to α,β-unsaturated carbonyl compounds represents one fundamental bond-forming reaction in organic synthesis. The development of effective organocatalysts for the enantioselective conjugate addition of malonate, nitroalkane and other carbon and heteroatom nucleophiles to cycloenones constitutes an important research field and has been explored in recent years. At the same time, asymmetric Diels-Alder reactions have been developed and often a mechanism has been demonstrated to be a double addition rather than synchronous. This review aims to cover literature up to the end of 2010, describing all the different organocatalytic asymmetric 1,4-conjugate additions even if they are listed as transfer hydrogenation, cycloadditions or desymmetrization of aromatic compounds.

Description: The paper presents an application of the asymmetry approach to spirooxindoles via Brevicolline, Cinchonidine or Cinchonine catalyzed one-pot multicomponent synthesis. Brevicolline, in comparison with Cinchonidine or Cinchonine, catalyzes the reaction of isatins, acetylacetone/ethyl 3-oxobutanoate and malononitrile, with the formation of spiro[oxindole-3,4'-4'H-pirane] derivatives in an optically active form in very good to excellent yields.

Description: A subset S of a group G is symmetric if there is an element g є G such that gS-1g = S. We study some Ramsey type functions for symmetric subsets in finite Abelian groups.

Description: 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.

Description: 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.

Description: The degree of p-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 p-electron delocalization in the various hexagons of a PBH was determined through analysis of the bifurcation values of the ELFp basins (BV(ELFp)), 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 p-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 ELFp 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 p-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 that there is a distinct tendency for the p-electron network to retain delocalization (aromaticity). The ELFp analysis thus reveals an antidistortive rather than a distortive behavior of the p-electrons in these investigated compounds.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: When liquid molecules are confined in a narrow gap between smooth surfaces, their dynamic properties are completely different from those of the bulk. The molecular motions are highly restricted and the system exhibits solid-like responses when sheared slowly. This solidification behavior is very dependent on the molecular geometry (shape) of liquids because the solidification is induced by the packing of molecules into ordered structures in confinement. This paper reviews the measurements of confined structures and friction of symmetric and asymmetric liquid lubricants using the surface forces apparatus. The results show subtle and complex friction mechanisms at the molecular scale.

Description: In this paper, we study the influence of hard supersymmetry breaking terms in a N = 1, d = 4 supersymmetric model, in S1 × R3 spacetime topology. It is shown that when the radius of the compact dimension is large supersymmetry is unbroken, and dynamically breaks as the radius decreases. We point out that this resembles the inverse symmetry breaking of continuous symmetries at finite temperature (however, in the case of supersymmetry, the role of the temperature is played by the compact dimension’s radius). Furthermore, we also find a universality in the dependence of the critical length Lc as a function of a coupling g3, after comparing all cases.

Description: 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-Poincaré Hopf algebra, a scenario with deformed Poincaré 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.

Description: This feature article gives a general introduction to the phenomenon of supramolecular chirogenesis using the most representative examples of different chirogenic assemblies on the basis of ethane-bridged bis-porphyrinoids. Supramolecular chirogenesis is based upon a smart combination of supramolecular chemistry and chirality sciences and deals with various aspects of asymmetry induction, transfer, amplification, and modulation. These chiral processes are governed by numerous noncovalent supramolecular forces thus allowing a judicious, mechanistic, and dynamic control by applying a variety of internal and external influencing factors. Currently, supramolecular chirogenesis is widely used in different fields of fundamental and applied branches of science and modern technology, touching on such important issues as origin of chirality on the Earth, asymmetry sensing, enantioselective catalysis, nonlinear optics, polymer and materials science, pharmacy and medicine, nanotechnology, molecular and supramolecular devices, chiral memory, absolute configuration determination, etc.

Description: As a contribution to the mysteries of human symmetry perception, reaction time data were collected on the detection of symmetry or repetition violations, in the context of short term visual memory studies. The histograms for reaction time distributions are rather narrow in the case of symmetry judgments. Their analysis was performed in terms of a simple kinetic model of a mental process in two steps, a slow one for the construction of the representation of the images to be compared, and a fast one, in the 50 ms range, for the decision. There was no need for an additional ‘mental rotation’ step. Symmetry seems to facilitate the construction step. I also present here original stimuli showing a color equalization effect across a symmetry axis, and its counterpart in periodic patterns. According to a “folded sheet model”, when a shape is perceived, the brain automatically constructs a mirror-image representation of the shape. Based in part on the reaction time analysis, I present here an alternative “transparent sheet” model in which the brain constructs a single representation, which can be accessed from two sides, thus generating simultaneously a pattern and its mirror-symmetric partner. Filtering processes, implied by current models of symmetry perception could intervene at an early stage, by nucleating the propagation of similar perceptual groupings in the two symmetric images.

Description: We show that in long-time the heat semi-group on a path group associated to a Bilaplacian on the group tends to the Haar distribution on a path group.

Description: In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.

Description: The author used the automatic proof procedure introduced in [1] and verified that the 4096 homomorphic recurrent double sequences with constant borders defined over Klein’s Vierergruppe K and the 4096 linear recurrent double sequences with constant border defined over the matrix ring M2(F2) can be also produced by systems of substitutions with finitely many rules. This permits the definition of a sound notion of geometric content for most of these sequences, more exactly for those which are not primitive. We group the 4096 many linear recurrent double sequences with constant border I over the ring M2(F2) in 90 geometric types. The classification over Klein’s Vierergruppe Kis not explicitly displayed and consists of the same geometric types like for M2(F2), but contains more exceptions. There are a lot of cases of unsymmetric double sequences converging to symmetric geometric contents. We display also geometric types occurring both in a monochromatic and in a dichromatic version.

Description: We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have pmm, pmg, pgg or cmm symmetry [1]. These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups [2]. We display the algorithms’ output and give enumeration tables for small values of n. This work is a continuation of our earlier works for the symmetry groups p3, p31m, p3m1, p4, p4g, p4m, p6, and p6m [3–5].

Description: The major issue regarding magnetic response in nature—“negative values for the permeability μ of material parameters, especially in terahertz or optical region” makes the electromagnetic properties of natural materials asymmetric. Recently, research in metamaterials has grown in significance because these artificial materials can demonstrate special and, indeed, extraordinary electromagnetic phenomena such as the inverse of Snell’s law and novel applications. A critical topic in metamaterials is the artificial negative magnetic response, which can be designed in the higher frequency regime (from microwave to optical range). Artificial magnetism illustrates new physics and new applications, which have been demonstrated over the past few years. In this review, we present recent developments in research on artificial magnetic metamaterials including split-ring resonator structures, sandwich structures, and high permittivity-based dielectric composites. Engineering applications such as invisibility cloaking, negative refractive index medium, and slowing light fall into this category. We also discuss the possibility that metamaterials can be suitable for realizing new and exotic electromagnetic properties.

Description: Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qu)bit, the transformation being controlled by the other w−1 (qu)bits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.

Description: Various organocatalysts have been developed for the aldol reaction but particular attention has been paid to prolinamide derivatives. They are easy to prepare and their catalytic activity can be readily tuned through structural modification. In this review, the comparison of catalytic activities between prolinethioamides and their respective amides in direct asymmetric aldol reactions is presented.

Description: Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of experiments and the discussion of methodological problems is preceded by a brief overview of the role which symmetry has played in the visual arts.

Description: Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac’s light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein’s Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics. It is thus possible to transmit physics from one branch of physics to the other branch using the mathematical basis common to them.

Description: 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).

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Chemists use one set of orbitals when comparing to a structural formula, hybridized AOs or NBOs for example, and another for reasoning in terms of frontier orbitals, MOs usually. Chemical arguments can frequently be made in terms of energy and/or electron density without the consideration of orbitals at all. All orbital representations, orthogonal or not, within a given function space are related by linear transformation. Chemical arguments based on orbitals are really energy or electron density arguments; orbitals are linked to these observables through the use of operators. The Valency Interaction Formula, VIF, offers a system of chemical reasoning based on the invariance of observables from one orbital representation to another. VIF pictures have been defined as one-electron density and Hamiltonian operators. These pictures are classified in a chemically meaningful way by use of linear transformations applied to them in the form of two pictorial rules and the invariance of the number of doubly, singly, and unoccupied orbitals or bonding, nonbonding, and antibonding orbitals under these transformations. The compatibility of the VIF method with the bond pair – lone pair language of Lewis is demonstrated. Different electron lone pair representations are related by the pictorial rules and have stability understood in terms of Walsh’s rules. Symmetries of conjugated ring systems are related to their electronic state by simple mathematical formulas. Description of lone pairs in conjugated systems is based on the strength and sign of orbital interactions around the ring. Simple models for bonding in copper clusters are tested, and the bonding of O2 to Fe(II) in hemoglobin is described. Arguments made are supported by HF, B3LYP, and MP2 computations.

Description: 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.

Description: Our paper analyzes some aspects of Uncertainty Measures. We need to obtain new ways to model adequate conditions or restrictions, constructed from vague pieces of information. The classical entropy measure originates from scientific fields; more specifically, from Statistical Physics and Thermodynamics. With time it was adapted by Claude Shannon, creating the current expanding Information Theory. However, the Hungarian mathematician, Alfred Rényi, proves that different and valid entropy measures exist in accordance with the purpose and/or need of application. Accordingly, it is essential to clarify the different types of measures and their mutual relationships. For these reasons, we attempt here to obtain an adequate revision of such fuzzy entropy measures from a mathematical point of view.

Description: An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while μ(G) is the cardinality of a maximum matching. If sk is the number of independent sets of size k in G, then I(G; x) = s0 + s1x + s2x2 + ... + sαxα, α = α (G), is called the independence polynomial of G (Gutman and Harary, 1986). If sj = sαj for all 0 ≤ j ≤ [α/2], then I(G; x) is called symmetric (or palindromic). It is known that the graph G ° 2K1, obtained by joining each vertex of G to two new vertices, has a symmetric independence polynomial (Stevanović, 1998). In this paper we develop a new algebraic technique in order to take care of symmetric independence polynomials. On the one hand, it provides us with alternative proofs for some previously known results. On the other hand, this technique allows to show that for every graph G and for each non-negative integer k ≤ μ (G), one can build a graph H, such that: G is a subgraph of H, I (H; x) is symmetric, and I (G ° 2K1; x) = (1 + x)k · I (H; x).

Description: Symmetric patterns are more appealing to human observers than asymmetric ones. Here, we investigate the visual information processing mechanisms underlying this aesthetic preference. All stimuli were derived from phase scrambled versions of forty face or nature images. In addition to the scrambled images, there were four other types of test image: symmetric, in which one part of the image was a reflection of another around an axis; repetitive, in which one part of the image was a copy of the other; anti-symmetric, similar to symmetric but with the contrast of one side reversed; and interleaved patterns, in which half of the symmetric pattern was replaced by a scrambled image. The number of axes ranged from 1 to 16 for all image types. The task of our 20 observers was to give a preference rating to each image on a 6-point Lickert scale. The preference rating increased with the number of axes for all stimulus types. The observers showed a similar preference for symmetric and repetitive patterns and slightly less preference for anti-symmetric patterns. The preference for interleaved patterns was much less than for other types of stimuli. Preference for an image cannot be explained by either the ecological significance of its content or the slope of its amplitude spectrum. Instead, preference can be accounted for by the complexity of the image.

Description: Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one of 17 different Wallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns. This study presents the results from a grouping experiment using stimuli from the different wallpaper groups. We find that while different images from the same wallpaper group are perceived as similar to one another, not all groups have the same degree of self-similarity. The similarity relationships between wallpaper groups appear to be dominated by rotations.