Exact Symmetry Research Articles

The physiological linkage between molar inclination and dental macrowear pattern.

ObjectivesExact symmetry and perfect balance between opposite jaw halves, as well as between antagonistic teeth, is not frequently observed in natural masticatory systems. Research results show that asymmetry in our body, skull, and jaws is often related to genetic, epigenetic, environmental and individual ontogenetic factors. Our study aims to provide evidence for a significant link between masticatory asymmetry and occlusal contact between antagonist teeth by testing the hypothesis that tooth inclination is one of the mechanisms driving distribution of wear in masticatory phases in addition to dietary and cultural habits.Materials and MethodsThe present work investigates the relationship between dental macrowear patterns and tooth inclinations on a sample of complete maxillary and mandibular 3D models of dental arches from 19 young and adult Yuendumu Aboriginal individuals. The analysis was carried out on first molars (M1) from all quadrants. Occlusal Fingerprint Analysis was used for the quantification of macrowear patterns, and 2D cross‐sectional geometric analysis was carried out to investigate asymmetry in dental arches.ResultsThe asymmetry is highly variable on both arches, and it is associated with differences in the inclination of upper M1 crowns. Each molar has variable inclination (buccal/lingual) which influence tooth to tooth contact, producing greater or lesser variation in wear pattern. Interindividual variability of morphological variation of the occlusal relationship has to be considered in macrowear analysis.DiscussionOur results suggest that overall asymmetry in the masticatory apparatus in modern humans affects occlusal contact areas between antagonist teeth influencing macrowear and chewing efficiency during ontogeny.

Enantiomorphism and rule similarity in the astigmatism axes of fellow eyes: A population-based study

PurposeTo evaluate the relationship patterns between astigmatism axes of fellow eyes (rule similarity and symmetry) and to determine the prevalence of each pattern in the studied population. MethodsThis population-based study was conducted in 2015 in Iran. All participants had tests for visual acuity, objective refraction, subjective refraction (if cooperative), and assessment of eye health at the slit-lamp. Axis symmetry was based on two different patterns: direct (equal axes) and mirror (mirror image symmetry) or enantiomorphism. Bilateral astigmatism was classified as isorule if fellow eyes had the same orientation (e.g. both eyes were with-the-rule) and as anisorule if otherwise. ResultsOf the total cases of bilateral astigmatism, 80% were isorule, and in the studied population, the prevalence of isorule and anisorule astigmatism was 14.89% and 3.53%, respectively. The prevalence of isorule increased with age (p<0.001). The prevalence of both isorule and anisorule increased at higher degrees of spherical ametropia (p<0.001). Median inter-ocular axis difference was 10° in mirror symmetry and 20° in direct symmetry with no significant difference between two genders (p>0.288). Both symmetry patterns reduced with age (p<0.001). Among cases of bilateral astigmatism, 15.5% and 19.8% had exact direct and mirror symmetry, respectively. ConclusionBilateral astigmatism is mainly isorule in the population and anisorule astigmatism is rare. The enantiomorphism is the most common pattern in the population of bilateral astigmatism.

X-ray structure of an asymmetrical trimeric ferredoxin-photosystem I complex.

Photosystem I (PSI), a large protein complex located in the thylakoid membrane, mediates the final step in light-driven electron transfer to the stromal electron carrier protein ferredoxin (Fd). Here, we report the first structural description of the PSI-Fd complex from Thermosynechococcus elongatus. The trimeric PSI complex binds three Fds in a non-equivalent manner. While each is recognized by a PSI protomer in a similar orientation, the distances between Fds and the PSI redox centres differ. Fd binding thus entails loss of the exact three-fold symmetry of the PSI's soluble subunits, inducing structural perturbations which are transferred to the lumen through PsaF. Affinity chromatography and nuclear magnetic resonance analyses of PSI-Fd complexes support the existence of two different Fd-binding states, with one Fd being more tightly bound than the others. We propose a dynamic structural basis for productive complex formation, which supports fast electron transfer between PSI and Fd.

SENR/NRPy+ : Numerical relativity in singular curvilinear coordinate systems

We report on a new open-source, user-friendly numerical relativity code package called SENR/NRPy+. Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally-suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy+ provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy+ into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time we demonstrate--in the context of puncture, trumpet, and dual black hole evolutions--nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while holding the spherical-like coordinate grids fixed at moderate resolution. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero inside horizons, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.

Symmetries of a reduced fluid-gyrokinetic system

Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically, the nonlinear system constructed by Zocco &amp; Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary $k_{\bot }\unicode[STIX]{x1D70C}_{i}$, where $k_{\bot }$ is the perpendicular wave vector of the fluctuations and $\unicode[STIX]{x1D70C}_{i}$ the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman–Kendall solution for a collapsing current sheet.

Interplay of Coulomb interactions and disorder in three-dimensional quadratic band crossings without time-reversal symmetry and with unequal masses for conduction and valence bands

Coulomb interactions famously drive three dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work, Phys. Rev. B 95, 205106 (2017), the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the bandstructure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder, and that a runaway flow to strong disorder occurs. In this work, we extend that analysis by relaxing the assumption of time-reversal symmetry and allowing the electron and hole masses to differ (but continuing to assume isotropy of the low energy bandstructure). We first incorporate time-reversal symmetry breaking disorder, and demonstrate that there do not appear any new fixed points. Moreover, while the system continues to flow to strong disorder, time-reversal-symmetry-breaking disorder grows asymptotically more slowly than time-reversal-symmetry-preserving disorder, which we therefore expect should dominate the strong-coupling phase. We then allow for unequal electron and hole masses. We show that whereas asymmetry in the two masses is irrelevant in the clean system, it is relevant in the presence of disorder, such that the 'effective masses' of the conduction and valence bands should become sharply distinct in the low-energy limit. We calculate the RG flow equations for the disordered interacting system with unequal band masses, and demonstrate that the problem exhibits a runaway flow to strong disorder. Along the runaway flow, time-reversal-symmetry-preserving disorder grows asymptotically more rapidly than both time-reversal-symmetry-breaking disorder and the Coulomb interaction.

Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type

A one-dimensional nonlinear fractional filtration equation with the Riemann–Liouville time-fractional derivative is proposed for modeling fluid flow through a porous medium. This equation is derived under an assumption that the fluid has a fractional equation of state in which the fluid density depends on the time-fractional derivative of pressure. The obtained equation belongs to the diffusion-wave type of equations. A case when the order of fractional differentiation is close to an integer number is considered, and a small parameter is introduced into the fractional filtration equation under consideration. An expansion of the Riemann–Liouville time-fractional derivative into the series with respect to this small parameter is obtained. Using this expansion, a first-order approximation of the derived fractional filtration equation is performed. Next, the problem of approximate Lie point symmetry group classification for this approximate nonlinear filtration equation with a small parameter is studied. It is shown that approximate symmetry groups admitted by different realizations of the approximate filtration equation have much more dimensions than the corresponding exact Lie point symmetry groups admitted by unperturbed fractional diffusion-wave equations. Obtained classification results permit to construct approximate invariant solutions for the considered nonlinear time-fractional filtration equations.

The observation of resistivity change on the ultrasonic treated Fe-Cr ODS sinter alloy under magnetic field influence

About the observation of resistivity change on the ultrasonic treated Fe-Cr ODS sinter alloy under magnetic field influence. This paper reported about the observation of the resistivity change in the ultrasonic pre-treated Fe-Cr ODS sinter alloy under the influence of magnetic field at the Center for Science and Technology of Advanced Material, Nuclear Energy Agency of Indonesia. Fe-Cr ODS alloy were sinthesized by vacuum sintering of Fe- and Cr-powder dispersed Y2O3. However, before sintering the powder mixture was subjected to the irradiation process by ultrasonic for 50 hours at 20 kHz and then isostatic pressed up to 50.91 MPa to form a coin of 10 mm in diameter. LCR meassurement revealed the decreasing of resistivity about 3 times by increasing of applied magnetic field from 0 to 70 mT. In addition, VSM meassurement was performed on both as powder material and as sintered sample. The results showed increasing the magnetization with increasing magnetic field and the curve exhibits almost exact symmetry S-form with small hysterese indicating fast changing magnetization and demagnetization capability without energy loss. This opens strong speculations about the existence of magnetoresistant property of the material which is important for many application in field of sensors or electro magnetic valves.

Leptogenesis as an origin of hot dark matter and baryon asymmetry in the E6 inspired SUSY models

We explore leptogenesis within the E6 inspired U(1) extension of the MSSM in which exact custodial symmetry forbids tree-level flavour-changing transitions and the most dangerous baryon and lepton number violating operators. This supersymmetric (SUSY) model involves extra exotic matter beyond the MSSM. In the simplest phenomenologically viable scenarios the lightest exotic fermions are neutral and stable. These states should be substantially lighter than 1eV forming hot dark matter in the Universe. The low-energy effective Lagrangian of the SUSY model under consideration possesses an approximate global U(1)E symmetry associated with the exotic states. The U(1)E symmetry is explicitly broken because of the interactions between the right-handed neutrino superfields and exotic matter supermultiplets. As a consequence the decays of the lightest right-handed neutrino/sneutrino give rise to both U(1)E and U(1)B−L asymmetries. When all right-handed neutrino/sneutrino are relatively light ∼106–107GeV the appropriate amount of the baryon asymmetry can be induced via these decays if the Yukawa couplings of the lightest right-handed neutrino superfields to the exotic matter supermultiplets vary between ∼10−4–10−3.

Automatic and Exact Symmetry Recognition of Structures Exhibiting High-Order Symmetries

AbstractSymmetry analysis is common and important, and the involved symmetry is in general self evident or manually recognized. However, for a structure with high-order symmetry or complex geometry...

Filovirus Filament Proteins.

Filoviruses are highly filamentous enveloped animal viruses that can cause severe haemorrhagic fevers. The filovirus ribonucleoprotein forms a highly organized double-layered helical nucleocapsid (NC) containing five different virally encoded proteins. The inner layer consists of NP, the RNA binding protein, complexed with the monopartite linear genome. A distinctive outer layer links individual NP subunits with bridges composed of VP24-VP35 heterodimers, which achieves condensation of the NP-RNA into tight helical coils. There are no vertical connections between the outer helical layers, explaining the flexibility of the NC and its ability to bend into tight curves without breaking the genomic RNA. These properties allow the formation of enveloped virions with varying polymorphisms, including single, linear, continuous, linked, comma-shaped and torroidal forms. Virion length is modular so that just one, or two or more genome copies may be present in each virion, producing polyploid particles. The matrix protein VP40, which drives budding and envelopment, is found in a layer adjacent to the inner cytoplasmic side of viral envelope and is arranged in a 5 nm lattice structure, but its exact symmetry is unclear. There is a constant low density gap between VP40 and the nucleocapsid, so that the latter is held rigidly centred on the long axis of the viral filament. This gap likely contains a region of flexible contacts between VP40 and the NC. The unique morphology of filoviruses may be related to high titre replication, their ease of transmission, and abilities to invade a wide range of host cells and tissues.

Superconducting gap of quasi-one-dimensional Cr-based superconductor RbCr3As3

Since the discovery of high-temperature superconductivity in cuprates, finding more unconventional superconductors and understanding their superconducting pairing mechanism has been an important theme in condensed matter physics. Recently, ternary Cr-based superconductors A2Cr3As3 (A=K, Rb, Cs) and ACr3As3 (A=K, Rb) were reported, which own quasi-one-dimensional crystal structure, containing[(Cr3As3)-] linear chains. A2Cr3As3 belongs to P6m2 space group, and ACr3As3 crystallizes in a centrosymmetric structure with the space group P63/m. Many experiments, such as nuclear magnetic resonance, London penetration depth, show that A2Cr3As3 is an unconventional superconductor. However, these A2Cr3As3 compounds are extremely unstable in air. Here, we study the superconducting gap of the air-stable RbCr3As3 single crystal, using ultralow-temperature thermal conductivity measurement. The resistivity of RbCr3As3 single crystal shows a superconducting transition temperature Tczero at 6.6 K. The normal-state resistivity data from 20 K to 8 K are fitted to (T)=0 + AT2, which gives a residual resistivity of 0=781 cm. Then, the thermal conductivity of RbCr3As3 single crystal is measured at temperature down to 80 mK and in magnetic fields up to 9 T. In zero field, residual linear term 0/T=7.5 WK-2cm-1 is observed, which is about 24% of its normal-state value, suggesting nodes in the superconducting gap. At low field, the 0/T of RbCr3As3 shows a relatively faster field dependence than single-gap s-wave superconductors. These results reveal that RbCr3As3 is likely an unconventional superconductor with superconducting gap nodes, although the exact superconducting gap symmetry and structure for this quasi-one-dimensional superconductor needs further investigation.

Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect

The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This article investigates an emergent symmetry in the fractional quantum Hall effect, namely the PH symmetry of {\em composite fermions}, which relates states at composite fermion filling factors $\nu^*=n+\bar{\nu}$ and $\nu^*=n+1-\bar{\nu}$, where the integer $n$ is the $\Lambda$ level index and $0\leq \bar{\nu}\leq 1$. Detailed calculations using the microscopic theory of composite fermions demonstrate that for low lying $\Lambda$ levels (small $n$): (i) the 2-body interaction between composite-fermion particles is very similar, apart from a constant additive term and an overall scale factor, to that between composite-fermion holes in the same $\Lambda$ level; and (ii) the 3-body interaction for composite fermions is an order of magnitude smaller than the 2-body interaction. Taken together, these results imply an approximate PH symmetry for composite fermions in low $\Lambda$ levels, which is also supported by exact diagonalization studies and available experiments. This symmetry, which relates states at electron filling factors $\nu={n+\bar{\nu}\over 2(n+\bar{\nu})\pm 1}$ and $\nu={n+1-\bar{\nu}\over 2(n+1-\bar{\nu})\pm 1}$, is not present in the original Hamiltonian and owes its existence entirely to the formation of composite fermions. With increasing $\Lambda$ level index, the 2-body and 3-body pseudopotentials become comparable, but at the same time they both diminish in magnitude, indicating that the interaction between composite fermions becomes weak as we approach $\nu=1/2$.

Multiple testing with close to equally correlated structure

In clinical trials with multiple primary endpoints or with multiple observations on the same sampling unit, the maximum of all observations is a convenient statistic that controls the familywise error rate. The quantile of this statistic depends on the correlation among multiple observations. To simplify modeling, the compound symmetry (CS) covariance structure is frequently used. The assumption of exact compound symmetry cannot usually be justified, and further sensitivity studies under more varied correlations are recommended. The need for multiple simulations may impose an increased demand on computer and time resources. To evaluate the sensitivity of simulation results restricted to CS structure, we calculated the linear part of the Taylor expansion of the cumulative distribution function (CDF) for the maximum statistic. Furthermore, we derived the Taylor expansion for quantiles of the maximum statistic. Our simulation studies on the linear approximation of quantiles confirmed good performance of the linearization formula.

Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems.

We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin-valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies.

Approximate Noether symmetries and collineations for regular perturbative Lagrangians

Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.

Implication of quadratic divergences cancellation in the two Higgs doublet model

With the aim of exploring the Higgs sector of the Two Higgs Doublet Model (2HDM), we have chosen the exact and soft Z2 symmetry breaking versions of the 2HDM with non-zero vacuum expectation values for both Higgs doublets (Mixed Model). We consider two SM-like scenarios: with 125 GeV h and 125 GeV H. We have applied the condition for cancellation of quadratic divergences in the type II 2HDM in order to derive masses of the heavy scalars. Solutions of two relevant conditions were found in the considered SM-like scenarios. After applying the current LHC data for the observed 125 GeV Higgs boson, the precision electroweak data test and lower limits on the mass of H+, the allowed region of parameters shrink strongly.

Hard-core bosons in flat band systems above the critical density

We investigate the behaviour of hard-core bosons in one- and two-dimensional flat band systems, the chequerboard and the kagomé lattice and one-dimensional analogues thereof. The one-dimensional systems have an exact local reflection symmetry which allows for exact results. We show that above the critical density an additional particle forms a pair with one of the other bosons and that the pair is localised. In the two-dimensional systems exact results are not available but variational results indicate a similar physical behaviour.

The Role of Templating in the Emergence of RNA from the Prebiotic Chemical Mixture.

Biological RNA is a uniform polymer in three senses: it uses nucleotides of a single chirality; it uses only ribose sugars and four nucleobases rather than a mixture of other sugars and bases; and it uses only 3′-5′ bonds rather than a mixture of different bond types. We suppose that prebiotic chemistry would generate a diverse mixture of potential monomers, and that random polymerization would generate non-uniform strands of mixed chirality, monomer composition, and bond type. We ask what factors lead to the emergence of RNA from this mixture. We show that template-directed replication can lead to the emergence of all the uniform properties of RNA by the same mechanism. We study a computational model in which nucleotides react via polymerization, hydrolysis, and template-directed ligation. Uniform strands act as templates for ligation of shorter oligomers of the same type, whereas mixed strands do not act as templates. The three uniform properties emerge naturally when the ligation rate is high. If there is an exact symmetry, as with the chase of chirality, the uniform property arises via a symmetry-breaking phase transition. If there is no exact symmetry, as with monomer selection and backbone regioselectivity, the uniform property emerges gradually as the rate of template-directed ligation is increased.

Comment on “Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics”

Li and Miao [Phys. Rev. A 85, 042110 (2012)] proposed a non-Hermitian Hamiltonian that is neither Hermitian nor $PT$ symmetric but exhibits real eigenvalues for some values of the model parameters. In order to explain this fact, they resorted to $PT$-pseudo Hermiticity and to a so-called permutation symmetry. Here we show that the spectrum of this Hamiltonian can be easily analyzed in the usual way in terms of exact or broken antiunitary symmetries that appear to be more relevant than the permutation symmetry. In addition, we show why the authors' Hamiltonian and the well-known Pais-Uhlenbeck oscillator lead to the same fourth-order differential equation for the coordinates.