Symmetric Ones Research Articles

Deep functional maps for simultaneously computing direct and symmetric correspondences of 3D shapes

We introduce a novel method of isometric correspondences for 3D shapes, designed to address the problem of multiple solutions associated with deep functional maps when matching shapes with left-to-right reflectional intrinsic symmetries. Unlike the existing methods that only find the direct correspondences using single Siamese network, our proposed method is able to detect both the direct and symmetric correspondences among shapes simultaneously. Furthermore, our method detects the reflectional intrinsic symmetry of each shape. Key to our method is the using of two Siamese networks that learn consistent direct descriptors and their symmetric ones, combined with carefully designed regularized functional maps and supervised loss. This leads to the first deep functional map capable of both producing two high-quality correspondences of shapes and detecting the left-to-right reflectional intrinsic symmetry of each shape. Extensive experiments demonstrate that the proposed method obtains more accurate results than state-of-the-art methods for shape correspondences and reflectional intrinsic symmetries detection.

(Keynote) Molecular Engineering Strategies for Symmetric Aqueous Organic Redox Flow Batteries

In this contribution we use electronic structure calculations to reveal structure-property relationships for symmetric aqueous organic redox flow battery (RFB) materials. Unlike normal asymmetric RFBs, the symmetric ones are based on bipolar electrolytes that exist in at least three oxidation states and can undergo a minimum of two distinct redox processes. We compute from first principles the redox potentials of selected electrolytes based on quinone, pyrazine, and pyridazine redox-active moieties.[1] The objective is to understand how the interaction between the redox units affects the potentials and solvation energies. We find that electronic interaction between redox units and intramolecular hydrogen bonding can be exploited to tune the difference between the redox potentials, i.e., the theoretical voltage of the battery. The redox potentials can be further fine-tuned in either direction by adding substituents. Starting from these observations, we formulate a set of rules that will help in finding improved electrolytes for symmetric RFBs.[1] R. P. Fornari, M. Mesta, J. Hjelm, T. Vegge, P. de Silva, “Molecular Engineering Strategies for Symmetric Aqueous Organic Redox Flow Batteries”, ACS Materials Lett. 2020, 2, 3, 239–246.

Block symmetric-triangular preconditioners for generalized saddle point linear systems from piezoelectric equations

Based on the symmetric-triangular (ST) decomposition technique, a class of block ST (BST) preconditioners are proposed for generalized saddle point linear systems arising from the meshfree discretization of piezoelectric equations. By applying the BST preconditioners, we first transform the generalized saddle point linear systems into symmetric positive definite ones, which then can be solved in a fast and efficient way by the classical conjugate gradient (CG) or the preconditioned CG (PCG) iteration methods. Two practical BST preconditioners are presented and analyzed in detail. Eigen-properties and upper bounds of the condition numbers of the preconditioned matrices are proved. Implementation aspects are discussed. Finally, two numerical experiments arising from the piezoelectric strip shear deformation problem and the piezoelectric strip bending problem are presented. Numerical results show that the iteration steps of the PCG methods are independent of the number of degrees of freedom and the proposed BST preconditioners perform much better than some existing preconditioning techniques.

The canine T wave: a retrospective analysis on qualitative and quantitative T wave variables obtained in 129 healthy dogs and proposed reference intervals

Introduction/objectiveThe T wave is a poorly characterized electrocardiographic variable in small animals. Therefore, this study aimed to describe T wave features in a large population of healthy dogs. Animals, materials, and methodsMedical records were reviewed to identify healthy dogs ≥one-year-olds that underwent an electrocardiogram. T wave qualitative (morphology, polarity, and concordance between R and T waves) and quantitative (duration, amplitude, mean electrical axis, ratio between T and R waves amplitudes, interval from the peak to the end of the T wave, and ratio between the duration of the latter interval and that of the QT) variables were evaluated. Continuous and categorical variables were compared between dogs of distinct sex, body weight (BW), age and somatotype using the Mann–Whitney U test and χ2 test, respectively. Spearman's correlation coefficients between quantitative variables and age and BW were calculated. Reference intervals of quantitative variables were determined in the overall population. ResultsOne hundred and twenty-nine dogs were enrolled. Concerning morphology, the asymmetrical (slow/fast) pattern occurred more frequently than the symmetrical and biphasic ones. Concerning polarity, positive T waves occurred more frequently than negative and neutral ones. T and R waves were predominantly concordant. No meaningful differences were found when comparing qualitative and quantitative variables between dogs of distinct sex, BW, age and somatotype. No significant correlations were found between quantitative variables and age and BW. Reference intervals of quantitative variables are provided. ConclusionsCanine T wave features were addressed and statistically reliable reference intervals made available for clinical use.

Statistical–mechanical theory of topological indices

Topological indices (TI) are algebraic invariants of molecular graphs representing the topology of a molecule, which are very valuable in quantitative structure–property relations (QSPR). Here we prove that TI are the partition functions of such molecules when the temperature of the thermal bath at which they are submerged is very high. These partition functions are obtained by describing molecular electronic properties through tight-binding Hamiltonians (TBH), where the hopping parameters are topological properties describing atom–atom interactions. We prove that the TBH proposed here are non-Hermitian diagonalizable Hamiltonians which can be replaced by symmetric ones. In this way we propose a statistical–mechanical theory for TI, which is exemplified by deriving the Randić, Zagreb, Balaban, Wiener and ABC indices. The work also illuminates how to improve QSPR models using the current theoretical framework as well as how to derive statistical–mechanical parameters of molecular graphs.

Möbius mirrors

An accelerating boundary (mirror) acts as a horizon and black hole analog, radiating energy with some particle spectrum. We demonstrate that a Möbius transformation on the null coordinate advanced time mirror trajectory uniquely keeps invariant not only the energy flux but the particle spectrum. We clarify how the geometric entanglement entropy is also invariant. The transform allows generation of families of dynamically distinct trajectories, including -symmetric ones, mapping from the eternally thermal mirror to the de Sitter horizon, and different boundary motions corresponding to Kerr or Schwarzschild black holes.

Mass independent isotopic fractionation: A key to plasma chemistry

We propose a numerical model allowing to calculate the relative variations of isotopic ratios involved in a mass-independent isotopic fractionation (MIF) effect. This model is derived from classical trajectory simulation performed to reproduce the reactions yielding the isotopomers of ozone. In the ozone simulation, we did not introduce quantum mechanical selection rules for trajectories or the potential surface, but we separated instead exchange and non-exchange collisions, in order to introduce the fundamental quantum mechanical requirement according to which, for indistinguishable isotopes, the two possible reaction channels (elastic scattering or particle exchange) have to be superposed. The MIF effect is related to the molecular symmetry of the complex by the result that a different fraction of isotopically asymmetric complexes (formed by distinguishable isotopes) is stabilized than for symmetric ones (formed by indistinguishable isotopes).The model is applied on the results obtained experimentally for Mg and Ti isotopes in plasma. In plasma, Mg and Ti radicals resulting from the molecular dissociation of chlorides react with their parent molecules. In presence of hydrocarbons, isotope exchange rates are greatly enhanced when the intermediate activated complexes are adsorbed at the surface of the carbonaceous grains growing in the plasma. If a chemical reaction with the grain stabilizes the complex faster than its dissociation, MIF effects are observed. In such a chemical situation, the isotopic fractionation greatly exceed the usual theoretical predictions. Several characteristics of the MIF isotopic patterns are reproduced by the model.

The vibration study of a sandwich conical shell with a saturated FGP core

This paper is provided to analyze the free vibration of a sandwich truncated conical shell with a saturated functionally graded porous (FGP) core and two same homogenous isotropic face sheets. The mechanical behavior of the saturated FGP is assumed based on Biot’s theory, the shell is modeled via the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. Three different porosity distribution patterns are studied including one homogenous uniform distribution pattern and two non-homogenous symmetric ones. The porosity parameters in mentioned distribution patterns are regulated to make them the same in the shell’s mass. The equations of motion are solved exactly in the circumferential direction via proper sinusoidal and cosinusoidal functions, and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). The precision of the model is approved and the influences of several parameters such as circumferential wave number, the thickness of the FGP core, porosity parameter, porosity distribution pattern, the compressibility of the pore fluid, and boundary conditions on the shell’s natural frequencies are investigated. It is shown that the highest natural frequencies usually can be achieved when the larger pores are located close to the shell’s middle surface and in each vibrational mode, there is a special value of the porosity parameter which leads to the lowest natural frequencies. It is deduced that in most cases, natural frequencies decrease by increasing the thickness of the FGP core. In addition, reducing the compressibility of the porefluid a small growth in the natural frequencies can be seen.

An eye-tracking based investigation into reading behavior during Chinese-English sight translation: The effect of word order asymmetry

The focus of this study is the reading behavior of student interpreters during the process of Chinese-English sight translation. Eye-tracking was adopted to examine whether and how student interpreters’ real-time reading is affected by the degree of word order asymmetry and modulated by the amount of contextual information available. A group of interpreter trainees sight translated asymmetric sentences (sentences that are structurally asymmetric to the target language) and symmetric sentences (sentences that are similar to the structure of the target language). These sentences were presented in isolation and embedded in discourse. Their eye movements were recorded for an analysis of their rereading rate and reading ahead frequency. The results show that the rereading rate for the asymmetric sentences was significantly higher than that for the symmetric ones. There were no notable differences in the reading ahead frequency between the two types of sentences. The role of context was limited in modulating the asymmetry-induced effect. This study addresses real-time reading behavior at the word level during sight translation and deepens our understanding of the cognitive processing involved in interpretation, as well as the potential influencing factors.

Toward Compilation of Balanced Protein Stability Data Sets: Flattening the ΔΔG Curve through Systematic Enrichment.

Often studies analyzing stability data sets and/or predictors ignore neutral mutations and use a binary classification scheme labeling only destabilizing and stabilizing mutations. Recognizing that highly concentrated neutral mutations interfere with data set quality, we have explored three protein stability data sets: S2648, PON-tstab, and the symmetric Ssym that differ in size and quality. A characteristic leptokurtic shape in the ΔΔG distributions of all three data sets including the curated and symmetric ones was reported due to concentrated neutral mutations. To further investigate the impact of neutral mutations on ΔΔG predictions, we have comprehensively assessed the performance of 11 predictors on the PON-tstab data set. Correlation and error analyses showed that all of the predictors performed the best on the neutral mutations, while their performance became gradually worse as the ΔΔG of the mutations departed further from the neutral zone regardless of the direction, implying a bias toward dense mutations. To this end, after unraveling the role of concentrated neutral mutations in biases of stability data sets, we described a systematic enrichment approach to balance the ΔΔG distributions. Before enrichment, mutations were clustered based on their biochemical and/or structural features, and then three mutations were selected from every 2 kcal/mol of each cluster. Upon implementation of this approach by distinct clustering schemes, we generated five subsets varying in size and ΔΔG distributions. All subsets showed improved ΔΔG and frequency distributions. We ultimately reported that the errors toward enriched subsets were higher than those toward the parent data sets, confirming the enrichment of difficult-to-predict mutations in the subsets. In summary, we elaborated the prediction bias toward a concentrated neutral zone and also implemented a rational strategy to tackle this and other forms of biases. Ultimately, this study equipping us with an extended view of shortcomings of stability data sets is a step taken toward development of an unbiased predictor.

An Optimal Procedure for the Design of Discrete Constrained Lens Antennas with Minimized Optical Aberrations. Part III: Three-Dimensional Architectures with an Extended Field of View

In this paper, an innovative procedure is proposed for the design of three-dimensional discrete lens antennas characterized by an extended field of view. While in a companion paper the design procedure was based on the definition of multifocal constrained lenses and on their evolution in rotationally symmetric ones, in this paper, lenses are assumed from the beginning to be rotationally symmetric and are derived by enforcing minimized optical aberrations specifically for the largest scanning directions. It is shown that, for discrete lenses exhibiting a feeding array with a cross section, projected in a plane perpendicular to the main lens axis, larger as compared to the back lens cross section, there are significant improvements (15–20%) in terms of maximum aberrations and, at the same time, similar or slightly improved accommodation in terms of volume can be obtained as compared to the architectures considered in the companion paper. Because of this property, the proposed lens antennas may be particularly useful in emerging applications requiring an extended field of view.

Compromising Charge Generation and Recombination with Asymmetric Molecule for High‐Performance Binary Organic Photovoltaics with Over 18% Certified Efficiency

AbstractBalancing the charge generation and recombination constitutes a major challenge to break the current limit of organic photovoltaics (OPVs). To address this issue, an asymmetric non‐fullerene acceptor, namely the AC9, is developed and high‐performance OPV with a champion efficiency of 18.43% (18.1% certified) is demonstrated. This represents the record value among binary OPVs. Comprehensive analysis on exciton dissociation, charge collection, carrier transport, and recombination has been carried out, unveiling that the improved device performance of asymmetric AC9‐based OPVs is originated from a better compromise between charge generation and non‐radiative charge recombination, compared with the corresponding symmetric ones. This work provides a high‐performing molecule and paves the way for high‐performance OPVs through asymmetric molecular design.

Potential energy surfaces of a stacked dimer of benzene and its radical cation: what remains and what appears.

A stepwise qualitative consideration of the reduction in symmetry for the highly symmetrical "right sandwich" and "twisted sandwich" structures of the stacked benzene dimer caused by the pseudo-Jahn-Teller effect made it possible to construct a scheme of the potential energy surface (PES) of this dimer. Thirty-six equivalent structures of minimum energy are ordered on this extremely flat surface, transforming into each other in an almost barrier-free manner. There are two kinds of these transformations, both of which are pseudorotation. The transformation pathways inherent in this neutral dimer are also characteristic of its radical cation (RC). Structural transformations of the RC are inextricably linked with changes in its electronic state since its stationary structures relate to different electronic states. (C6H6)2+˙ exists in the form of two orbital isomers, each of which "pseudorotates" on its own area of the PES. During the pseudorotation, the SOMO distribution on the fragments of (C6H6)2+˙ changes, which is identical to what occurs during the pseudorotation of the Jahn-Teller benzene RC. These areas are connected by pairwise interconversions of their minimum energy structures. The interconversion of the orbital isomers is a bypassing of conical intersections between corresponding electronic states, which occurs through a synchronized pseudorotation of the fragments. The conclusions of the qualitative consideration and the results of quantum chemical calculations of various levels performed for (C6H6)2+˙ are in full agreement with each other. The revealed features of the structure of the PES of the two reference systems in studying the intermolecular and ion-molecule interactions are the basis for considering their more complex analogs, primarily their less symmetrical ones.

Plotting Lamb waves dispersion curves of an aluminum plate by the Semi-Analytical Finite Element (SAFE) method and comparison with analytical curves

It is well known that the propagation of Lamb waves in elastic solid medias depends on the frequency and on the material properties, but it does not depend on the propagation direction in isotropic medias and gives rise to two basic types of modes, symmetric and antisymmetric ones. This paper presents an application of the semi-analytical finite element (SAFE) method on an isotropic aluminum plate of thickness e = 2mm. The main goal of this paper is to make a quantitative evaluation of the SAFE method by carrying out the following tasks: a) calculation of the dispersion curves (wavenumber, phase velocity, group velocity, b) calculation of the relative error and validation of the proposed algorithm, c) comparison between the curves obtained by SAFE method on those obtained by Bisection method. It should be noted here that our study is restricted on the propagative modes.

Chemical bonding theories as guides for self-interaction corrected solutions: Multiple local minima and symmetry breaking.

Fermi-Löwdin orbitals (FLOs) are a special set of localized orbitals, which have become commonly used in combination with the Perdew-Zunger self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained for a set of occupied orbitals by specifying a classical position for each electron. These positions are known as Fermi-orbital descriptors (FODs), and they have a clear relation to chemical bonding. In this study, we show how FLOs and FODs can be used to initialize, interpret, and justify SIC solutions in a common chemical picture, both within FLO-SIC and in traditional variational SIC, and to locate distinct local minima in either of these approaches. We demonstrate that FLOs based on Lewis theory lead to symmetry breaking for benzene-the electron density is found to break symmetry already at the symmetric molecular structure-while ones from Linnett's double-quartet theory reproduce symmetric electron densities and molecular geometries. Introducing a benchmark set of 16 planar cyclic molecules, we show that using Lewis theory as the starting pointcan lead to artifactual dipole moments of up to 1D, while Linnett SIC dipole moments are in better agreement with experimental values. We suggest using the dipole moment as a diagnostic of symmetry breaking in SIC and monitoring it in all SIC calculations. We show that Linnett structures can often be seen as superpositions of Lewis structures and propose Linnett structures as a simple way to describe aromatic systems in SIC with reduced symmetry breaking. The role of hovering FODs is also briefly discussed.

Investigation of Postdemagnetization Unbalanced Magnetic Force in PM Machines Considering Short-Circuit Faults

This article investigates postdemagnetization unbalanced magnetic force (UMF) in single-three-phase permanent magnet (STPPM) and dual-three-phase PM (DTPPM) machines considering three-phase short circuit (3PSC). First, when eccentricities are not considered, for rotationally symmetrical STPPM machines and DTPPM machines with each winding group being rotationally symmetrical, demagnetization distribution is symmetrical. Therefore, there is still no UMF after demagnetization. For rotationally asymmetric STPPM machines and DTPPM machines with each winding group being rotationally asymmetric, the first-order harmonic is added to the UMF $x$ and $y$ components. Then, the influence of eccentricity on 3PSC current and demagnetization is analyzed, and postdemagnetization UMF for STPPM machines with eccentricities is investigated. It shows that eccentricities almost have no influence on 3PSC currents but gather demagnetization around PMs facing larger airgap length. As a result, under static eccentricity, the original UMF components decrease, while the first-order harmonic is added after demagnetization. Under rotating eccentricity, the original UMF components decrease in asymmetric STPPM machines, whereas they increase in symmetrical ones. The postdemagnetization UMF for DTPPM machines considering eccentricities is similar to that for symmetrical STPPM machines. In addition, the variations of UMF harmonics increase with the eccentricity ratio. Finally, experiments are conducted to validate the theoretical analysis.

Symmetric and asymmetric separation of variables for an integrable case of the complex Kirchhoff's problem

In the present paper we develop a method of the vector fields Zi[9] in the theory of separation of variables. For an integrable case of the complex Kirchhoff's problem on e⁎(3), which has been never considered before, we construct—with the help of this method—two types of separation of variables (SoV): symmetric and asymmetric ones. Our asymmetric SoV is unusual: it is characterized by the quadratures containing differentials defined on two different curves of separation. It is a direct analogue of asymmetric SoV for the Clebsch model [17]. In the case of symmetric SoV both curves of separation are the same. This case has an additional bonus: on zero level set of one of the Casimir functions it yields a direct analogue of the famous Weber-Neumann separated coordinates. They are also considered in the present paper in some details.

Modeling and simulation of car accidents at a signalized intersection using cellular automata

In this paper, we propose a two-lane cellular automata model that explains the relationship between traffic-related parameters and likelihood of accidents Pac at a signalized intersection. It is found that, the risk of collision rises as well as the lane-changing probability Pchg augments, besides, the accidents and inflow α show a nonlinear relationship. Moreover, Pac exhibits three different phases (I, II and III) depending on α. Likewise, the system exhibits a second (first) order transition from phase I to phase II when Pchg>0 (Pchg=0). Nevertheless, the transition from phase II to phase III is of first (second) order when Pchg>0 (Pchg=0). In addition, the result analysis shows that the distribution of accidents according to the intersection sites is not equiprobable. Furthermore, when the traffic arriving strength is not very high, the green light length of one road should be increased to restrain Pac and enhance the road safety. Finally, the model results illustrated that the traffic at the intersection is more dangerous adopting asymmetric lane-changing rules than symmetric ones.

Studies of a new-style resonator to control electro-mechanical coupling bandgap of a locally resonant piezoelectric/elastic phononic crystal double-layer nonlocal nanobeam

The paper proposed a model of a locally resonant (LR) piezoelectric/elastic phononic crystal (PC) nanobeam with periodically attached “spring-mass” resonator and additional spring between upper and lower nanobeams, as well as horizontal spring between mass and foundation. Euler beam theory and nonlocal piezoelectricity theory are coupled and introduced to plane wave expansion (PWE) method to calculate the band structures of such a model with different parameters. Numerical results and further analysis demonstrate that all the bands of double-layer nanobeam can be divided into symmetric and antisymmetric ones. Adding additional and horizontal springs play a role in control the symmetric and antisymmetric bands respectively, which make wider band gaps be opened than corresponding single-layer nanobeam. Moreover, the change of parameters of electro-mechanical coupling fields and resonator can be applied to effectively control the starting frequencies and widths of band gaps, which can provide a theoretical basis for active control of vibration. Effects of geometric and non-dimensional nonlocal parameters on band gaps are also discussed. All the studies are expected to be applied to actively control vibration propagation in the field of nano electro-mechanical system (NEMS).

Symmetry properties and widths of the filamentary structures in the Orion A giant molecular cloud

We identify 225 filaments from an H2 column density map constructed using simultaneous 12CO, 13CO and C18O (J = 1–0) observations carried out as a part of the Milky Way Imaging Scroll Painting (MWISP) project.We select 46 long filaments with lengths above 1.2 pc to analyze the filament column density profiles. We divide the selected filaments into 397 segments and calculate the column density profiles for each segment. The symmetries of the profiles are investigated. The proportion of intrinsically asymmetrical segments is 65.3%, and that of intrinsically symmetrical ones is 21.4%. The typical full width at half maximum (FWHM) of the intrinsically symmetrical filament segments is ∼ 0.67 pc with the Plummer-like fitting, and ∼ 0.50 pc with the Gaussian fitting, respectively. The median FWHMs derived from the second-moment method for intrinsically symmetrical and asymmetrical profiles are ∼ 0.44 and 0.46 pc, respectively. Close association exists between the filamentary structures and the YSOs in the region.