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Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the "Swampland" program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not. [ABSTRACT FROM AUTHOR]

Until now, research has not taken into consideration the physicochemical purine–pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. Its basic structure is a purine–pyrimidine symmetry net with double mirror symmetry. Accordingly, the symmetry of the genetic code directly shows its organisation based on the principle of nucleotide Watson–Crick and codon–anticodon pairing. The maximal purine–pyrimidine symmetries of codons show that each codon has a strictly defined and unchangeable position within the genetic code. We discovered that the physicochemical symmetries of the genetic code play a fundamental role in recognising and differentiating codons from mRNA and the anticodon tRNA and aminoacyl-tRNA synthetases in the transcription and translation processes. These symmetries also support the wobble hypothesis with non-Watson–Crick pairing interactions between the translation process from mRNA to tRNA. The Supersymmetry Genetic Code table shows a specific arrangement of the second base of codons, according to which it is possible that an anticodon from tRNA recognises whether a codon from mRNA belongs to an amino acid with two or four codons, which is very important in the purposeful use of the wobble pairing process. Therefore, we show that canonical and wobble pairings essentially do not lead to misreading and errors during translation, and we point out the role of physicochemical purine–pyrimidine symmetries in decreasing disorder according to error minimisation and preserving the integrity of biological processes during proteinogenesis. [ABSTRACT FROM AUTHOR]

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism. [ABSTRACT FROM AUTHOR]

In this study, we focused on assessing the symmetry of shapes and quantifying an index of 'order' in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was calculated for the distribution of the Casorati curvatures in both segments to determine the similarity between them. This was proposed as an indicator of the 'order' exhibited by the shape. To validate the effectiveness of the proposed index, sensory evaluation experiments were conducted on three shapes: extruded, rotated, and vase. For the rotated shape, the coefficient of determination between the proposed index and the sensory evaluation value of 'order' on a 5-point Likert scale was found to be less than 0.1. The reason for the poor correlation coefficient of determination may be attributed to the bias in human perception, where individuals tend to perceive mirror symmetry with respect to the plane that includes the vertical axis when recognizing the mirror symmetry of an object. In contrast, for the extruded and vase shapes, the coefficients of determination were 0.36 and 0.66, respectively, supporting the validity of the proposed index. Nonetheless, the coefficient of determination decreased slightly for familiar extruded shapes and asymmetric vase shapes. In future research, our aim is to quantify 'aesthetic preference' by combining the 'order' and 'complexity' indexes. [ABSTRACT FROM AUTHOR]

Overwhelming astronomical evidence for dark matter and absence of any laboratory evidence for it despite many dedicated searches have fueled speculation that dark matter may reside in a parallel universe interacting with the familiar universe only via gravitational interactions as well as possibly via some ultra-weak forces. In this scenario, we postulate that the visible universe co-exists with a mirror world consisting of an identical duplicate of forces and matter of our world, obeying a mirror symmetry. This picture, motivated by particle physics considerations, not only provides a natural candidate for dark matter but also has the potential to explain the matter dark matter coincidence problem, i.e., why the dark matter content of the universe is only a few times the visible matter content. One requirement for mirror models is that the mirror world must be colder than our world to maintain the success of big bang nucleosynthesis. After a review of the basic features of the model, we present several new results: first is that the consistency between the coldness of the mirror world and the explanation of the matter dark matter coincidence implies an upper bound on the inflation reheat temperature of the universe to be around 10 6.5 GeV. We also argue that the coldness implies the mirror world consists mainly of mirror Helium and very little mirror hydrogen, which is the exact opposite of what we see in the visible world. [ABSTRACT FROM AUTHOR]

A theoretical account of development in mesocortical anatomy is derived from the free energy principle, operating in a neural field with both Hebbian and anti-Hebbian neural plasticity. An elementary structural unit is proposed, in which synaptic connections at mesoscale are arranged in paired patterns with mirror symmetry. Exchanges of synaptic flux in each pattern form coupled spatial eigenmodes, and the line of mirror reflection between the paired patterns operates as a Markov blanket, so that prediction errors in exchanges between the pairs are minimized. The theoretical analysis is then compared to the outcomes from a biological model of neocortical development, in which neuron precursors are selected by apoptosis for cell body and synaptic connections maximizing synchrony and also minimizing axonal length. It is shown that this model results in patterns of connection with the anticipated mirror symmetries, at micro-, meso- and inter-arial scales, among lateral connections, and in cortical depth. This explains the spatial organization and functional significance of neuron response preferences, and is compatible with the structural form of both columnar and noncolumnar cortex. Multi-way interactions of mirrored representations can provide a preliminary anatomically realistic model of cortical information processing. [ABSTRACT FROM AUTHOR]

In order to improve the mechanical properties and durability of lightweight aggregate concrete in extreme environments, this study utilized Inner Mongolia pumice as the coarse aggregate to formulate pumice lightweight aggregate concrete (P-LWAC) with a silica powder content of 0%, 2%, 4%, 6%, 8%, and 10%. Under sulfate dry–wet cycling conditions, this study mainly conducted a mass loss rate test, compressive strength test, NMR test, and SEM test to investigate the improvement effect of silica powder content on the corrosion resistance performance of P-LWAC. In addition, using grey prediction theory, the relationship between pore characteristic parameters and compressive strength was elucidated, and a grey prediction model GM (1,3) was established to predict the compressive strength of P-LWAC after cycling. Research indicates that under sulfate corrosion conditions, as the cycle times and silica powder content increased, the corrosion resistance of P-LWAC showed a trend of first increasing and then decreasing. At 60 cycles, P-LWAC with a content of 6% exhibited the lowest mass loss rate and the highest relative dynamic elastic modulus, compressive strength, and corrosion resistance coefficient. From the perspective of data distribution, various durability indicators showed a clear mirror symmetry towards both sides with a silica powder content of 6% as the symmetrical center. The addition of silica fume reduced the porosity and permeability of P-LWAC, enhanced the saturation degree of bound fluid, and facilitated internal structural development from harmful pores towards less harmful and harmless pores, a feature most prominent at the 6% silica fume mixing ratio. In addition, a bound fluid saturation and pore size of 0.02~0.05 μm/% exerted the most significant influence on the compressive strength of P-LWAC subjected to 90 dry–wet cycles. Based on these two factors, grey prediction model GM (1,3) was established. This model can accurately evaluate the durability of P-LWAC, improving the efficiency of curing decision-making and construction of concrete materials. [ABSTRACT FROM AUTHOR]

Mimicking the photosynthesis of green plants to combine water oxidation with CO2 reduction is of great significance for solving energy and environmental crises. In this context, a trinuclear nickel complex, [NiII3(paoH)6(PhPO3)2]·2ClO4 (1), with a novel structure has been constructed with PhPO32− (phenylphosphonate) and paoH (2-pyridine formaldehyde oxime) ligands and possesses a reflection symmetry with a mirror plane revealed by single-crystal X-ray diffraction. Bulk electrocatalysis demonstrates that complex 1 can homogeneously catalyze water oxidation and CO2 reduction simultaneously. It can catalyze water oxidation at a near-neutral condition of pH = 7.45 with a high TOF of 12.2 s−1, and the Faraday efficiency is as high as 95%. Meanwhile, it also exhibits high electrocatalytic activity for CO2 reduction towards CO with a TOF of 7.84 s−1 in DMF solution. The excellent electrocatalytic performance of the water oxidation and CO2 reduction of complex 1 could be attributed to the two unique µ3-PhPO32− bridges as the crucial factor for stabilizing the trinuclear molecule as well as the proton transformation during the catalytic process, while the oxime groups modulate the electronic structure of the metal centers via π back-bonding. Therefore, apart from the cooperation effect of the three Ni centers for catalysis, simultaneously, the two kinds of ligands in complex 1 can also synergistically coordinate the central metal, thereby significantly promoting its catalytic performance. Complex 1 represents the first nickel molecular electrocatalyst for both water oxidation and CO2 reduction. The findings in this work open an avenue for designing efficient molecular electrocatalysts with peculiar ligands. [ABSTRACT FROM AUTHOR]

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes. [ABSTRACT FROM AUTHOR]

Recently, the formation of chiral materials by the self-organization of achiral small molecules has attracted much attention. How can we obtain chirality without a chiral source? Interesting approaches, such as mechanical rotation, circularly polarized light, and asymmetric reaction fields, have been used. We describe recent research developments in supramolecular chirality in liquid crystals, focusing primarily on our group's experimental results. We present the following concepts in this review. Spontaneous mirror symmetry breaking in self-assembled achiral trimers induces supramolecular chirality in the soft crystalline phase. Two kinds of domains with opposite handedness exist in non-equal populations. The dominant domain is amplified to produce a homochiral state. Chirality is transferred to a polymer film during the polymerization of achiral monomers by using the homochiral state as a template. Finally, we discuss how the concepts obtained from this liquid crystal research relate to the origin of homochirality in life. [ABSTRACT FROM AUTHOR]

The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the form of codons; (3) direct–complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns; (4) A + T-rich and C + G-rich alternate codons in the same row between both columns of the genetic code; (5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axis. The SSyGC table has a unique physicochemical purine–pyrimidine symmetry net which is as the core symmetry common for all, with more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries are present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here, we show that the free energy value of each codon incorporated as fundamentally mapping the "energy code" in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table, the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time, the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine–pyrimidine symmetry net, the quadruplet symmetry of DNA molecule, and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecules, and the energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the "energy code" are unique, unchangeable, and have the power of natural laws. [ABSTRACT FROM AUTHOR]

Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code and the Extended Genetic RNA code type II, which includes codons of the types YNY, YNR, and RNR. Each of the four subsets of codons can be represented in a 4-dimensional hypercube. Altogether, these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group of order 4; YNY: binary group; YNR: amplified octahedral group; and RNR: binary group. We demonstrate that for each hypercube, the group of symmetries in Class 1 is the same as the group of symmetries in Class 2. The biological implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

Chirality, the absence of mirror symmetry, is predominant in nature. The chiral nature of the electromagnetic field behaves differently with chiral matter for left circularly polarized and right circularly polarized light. The chiroptical behavior in the sensing of naturally occurring chiral objects is weak, and improving the chiroptical response enhances the chiral sensing platform. This review covers the fundamental concepts of chiral metasurfaces and various types of single- and multi-layered chiral metasurfaces. In addition, we discuss tunable and deep-learning-based chiral metasurfaces. Tunability is achieved by manipulating the meta-atom's property in response to external stimuli for applications such as optical modulation, chiral photonics, advanced sensing, and adaptive optics. Deep-learning modeling techniques, such as CNNs and GANs, offer efficient learning of the complex relationships in data, enabling the optimization and accurate prediction of chiral metasurface properties. The challenges in the design and fabrication of chiral metasurface include achieving broadband performance and scalability and addressing material limitations. Chiral metasurface performance is evaluated by optical rotation, circular dichroism enhancement, and tunability, which are quantified through the spectroscopic measurement of circular dichroism and optical rotation. Chiral metasurface progress enables applications, including metaholography, metalenses, and chiral sensing. Chiral sensing improves the detection of pharmaceuticals and biomolecules, increasing the sensitivity and accuracy of analytical diagnostics. [ABSTRACT FROM AUTHOR]

Chiral BIC can reach ultrahigh quality factors (Q-factor) based on its asymmetry, with broken mirror symmetries and in-plane inversion. Only by in-plane structural perturbation can chiral quasi-BIC (q-BIC) appear, so it is much more realizable and reasonable for the manufacturers in practical productions and fabrications considering the technology and means that are available. In this paper, we design a new dielectric metasurface employing H-shaped silica meta-atoms in the lattice, which is symmetrical in structure, obtaining chiral BIC with ultrahigh Q-factor (exceeding 105). In this process, we change the length of the limbs of the structure to observe the specific BICs. Previous scholars have focused on near-infrared-wavelength bands, while we concentrate on the terahertz wavelength band (0.8–1 THz). We found that there is more than one BIC, thus realizing multiple BICs in the same structure; all of them exhibit excellent circular dichroism (CD) (the maximum value of CD is up to 0.8127) for reflectance and transmittance, which provides significant and unique guidance for the design of multi-sensors. Meanwhile, we performed temperature sensing with chiral BIC; the sensitivity for temperature sensing can reach 13.5 nm/°C, which exhibits high accuracy in measuring temperature. As a consequence, the result proposed in this study will make some contributions to advanced optical imaging, chiral sensors with high frequency and spectral resolution, optical monitoring of environmental water quality, multiple sensors, temperature sensing, biosensing, substance inspection and ambient monitoring and other relevant optical applications. [ABSTRACT FROM AUTHOR]

Symmetries have not been completely determined and explained from the discovery of the DNA structure in 1953 and the genetic code in 1961. We show, during 10 years of investigation and research, our discovery of the Supersymmetry Genetic Code table in the form of 2 × 8 codon boxes, quadruplet DNA symmetries, and the classification of trinucleotides/codons, all built with the same physiochemical double mirror symmetry and Watson–Crick pairing. We also show that single-stranded RNA had the complete code of life in the form of the Supersymmetry Genetic Code table simultaneously with instructions of codons' relationship as to how to develop the DNA molecule on the principle of Watson–Crick pairing. We show that the same symmetries between the genetic code and DNA quadruplet are highly conserved during the whole evolution even between phylogenetically distant organisms. In this way, decreasing disorder and entropy enabled the evolution of living beings up to sophisticated species with cognitive features. Our hypothesis that all twenty amino acids are necessary for the origin of life on the Earth, which entirely changes our view on evolution, confirms the evidence of organic natural amino acids from the extra-terrestrial asteroid Ryugu, which is nearly as old as our solar system. [ABSTRACT FROM AUTHOR]

Two-dimensional Janus materials have unique structural characteristics due to their lack of out-of-plane mirror symmetry, resulting in many excellent physical and chemical properties. Using first-principle calculations, we performed a detailed investigation of the possible stable structures and properties of two-dimensional Janus NbSH. We found that both Janus 1T and 2H structures are semiconductors, unlike their metallic counterparts MoSH. Furthermore, we predicted a new stable NbSH monolayer using a particle swarm optimization method combined with first-principle calculations. Interestingly, the out-of-plane mirror symmetry is preserved in this newly found 2D structure. Furthermore, the newly found NbSH is metallic and exhibits intrinsic superconducting behavior. The superconducting critical temperature is about 6.1 K under normal conditions, which is found to be very sensitive to stress. Even under a small compressive strain of 1.08%, the superconducting critical temperature increases to 9.3 K. In addition, the superconductivity was found to mainly originate from Nb atomic vibrations. Our results show the diversity of structures and properties of the two-dimensional Janus transition metal sulfhydrate materials and provide some guidelines for further investigations. [ABSTRACT FROM AUTHOR]

The two discrete generators of the full Lorentz group O (1 , 3) in 4 D spacetime are typically chosen to be parity inversion symmetry P and time reversal symmetry T, which are responsible for the four topologically separate components of O (1 , 3) . Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of P, while C P symmetry resembles T in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi–Yau mirror symmetry in string theory is clarified. Extension beyond the Standard Model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy are discussed. [ABSTRACT FROM AUTHOR]

Biomolecules are frequently chiral compounds, existing in enantiomeric forms. Amino acids represent a meaningful example of chiral biological molecules. Both L- and D-amino acids play key roles in the biochemical structure and metabolic processes of living organisms, from bacteria to mammals. In this review, we explore the enantiospecific interaction between proteins and chiral amino acids, introducing theoretical models and describing the molecular basis of the ability of some of the most important enzymes involved in the metabolism of amino acids (i.e., amino acid oxidases, dehydrogenases, and aminotransferases) to discriminate the opposite enantiomers. Our analysis showcases the power of natural evolution in shaping biological processes. Accordingly, the importance of amino acids spurred nature to evolve strictly enantioselective enzymes both through divergent evolution, starting from a common ancestral protein, or through convergent evolution, starting from different scaffolds: intriguingly, the active sites of these enzymes are frequently related by a mirror symmetry. [ABSTRACT FROM AUTHOR]

Rectangular billiards have two mirror symmetries with respect to perpendicular axes and a twofold (fourfold) rotational symmetry for differing (equal) side lengths. The eigenstates of rectangular neutrino billiards (NBs), which consist of a spin-1/2 particle confined through boundary conditions to a planar domain, can be classified according to their transformation properties under rotation by π ( π / 2 ) but not under reflection at mirror-symmetry axes. We analyze the properties of these symmetry-projected eigenstates and of the corresponding symmetry-reduced NBs which are obtained by cutting them along their diagonal, yielding right-triangle NBs. Independently of the ratio of their side lengths, the spectral properties of the symmetry-projected eigenstates of the rectangular NBs follow semi-Poisson statistics, whereas those of the complete eigenvalue sequence exhibit Poissonian statistics. Thus, in distinction to their nonrelativistic counterpart, they behave like typical quantum systems with an integrable classical limit whose eigenstates are non-degenerate and have alternating symmetry properties with increasing state number. In addition, we found out that for right triangles which exhibit semi-Poisson statistics in the nonrelativistic limit, the spectral properties of the corresponding ultrarelativistic NB follow quarter-Poisson statistics. Furthermore, we analyzed wave-function properties and discovered for the right-triangle NBs the same scarred wave functions as for the nonrelativistic ones. [ABSTRACT FROM AUTHOR]

This paper reviews the puzzles in modern neutron lifetime measurements and related unitarity issues in the CKM matrix. It is not a comprehensive and unbiased compilation of all historic data and studies, but rather a focus on compelling evidence leading to new physics. In particular, the largely overlooked nuances of different techniques applied in material and magnetic trap experiments are clarified. Further detailed analysis shows that the "beam" approach of neutron lifetime measurements is likely to give the "true" β -decay lifetime, while discrepancies in "bottle" measurements indicate new physics at play. The most feasible solution to these puzzles is a newly proposed ordinary-mirror neutron ( n − n ′ ) oscillation model under the framework of mirror matter theory. This phenomenological model is reviewed and introduced, and its explanations of the neutron lifetime anomaly and possible non-unitarity of the CKM matrix are presented. Most importantly, various new experimental proposals, especially lifetime measurements with small/narrow magnetic traps or under super-strong magnetic fields, are discussed in order to test the surprisingly large anomalous signals that are uniquely predicted by this new n − n ′ oscillation model. [ABSTRACT FROM AUTHOR]

Positioning error components related to tropospheric and ionospheric delays are caused by the atmosphere in positioning determined by global navigation satellite systems (GNSS). Depending on the user's requirements, the position error caused by tropospheric influences, which is commonly referred to as zenith tropospheric delay (ZTD), must be estimated during position determination or determined later by external tropospheric corrections. In this study, a new approach was adopted based on the reduction of residual tropospheric error (RTE), i.e., the unmodeled part of the tropospheric error that remains included in the total geodetic position error, along with other unmodeled systematic and random errors. The study was performed based on Global Navigation Satellite System (GLONASS) positioning solutions and accompanying meteorological parameters in a defined and harmonized temporal-spatial frame of three locations in the Republic of Croatia. A multidisciplinary approach-based analysis from a navigational science aspect was applied. The residual amount of satellite positioning signal tropospheric delay was quantitatively reduced by employing statistical analysis methods. The result of statistical regression is a model which correlates surface meteorological parameters with RTE. Considering the input data, the model has a regional character, and it is based on the Saastamoinen model of zenith tropospheric delay. The verification results show that the model reduces the RTE and thus increases the geodetic accuracy of the observed GNSS stations (with horizontal components of position accuracy of up to 3.8% and vertical components of position of up to 4.37%, respectively). To obtain these results, the Root Mean Square Error (RMSE) was used as the fundamental parameter for position accuracy evaluation. Although developed based on GLONASS data, the proposed model also shows a considerable degree of success in the verification of geodetic positions based on Global Positioning System (GPS). The purpose of the research, and one of its scientific contributions, is that the proposed method can be used to quantitatively monitor the dynamics of changes in deviations of X, Y, and Z coordinate values along coordinate axes. The results show that there is a distinct interdependence of the dynamics of Y and Z coordinate changes (with almost mirror symmetry), which has not been investigated and published so far. The resultant position of the coordinates is created by deviations of the coordinates along the Y and Z axes—in the vertical plane of space, the deviations of the coordinate X (horizontal plane) are mostly uniform and independent of deviations along the Y and Z axes. The proposed model shows the realized state of the statistical position equilibrium of the selected GNSS stations which were observed using RTE values. Although of regional character, the model is suitable for application in larger areas with similar climatological profiles and for users who do not require a maximum level of geodetic accuracy achieved by using Satellite-Based Augmentation Systems (SBAS) or other more advanced, time-consuming, and equipment-consuming positioning techniques. [ABSTRACT FROM AUTHOR]

This paper presents the results of numerical simulations of a nonlinear bistable system for harvesting energy from ambient vibrating mechanical sources. Detailed model tests were carried out on an inertial energy harvesting system consisting of a piezoelectric beam with additional springs attached. The mathematical model was derived using the bond graph approach. Depending on the spring selection, the shape of the bistable potential wells was modified including the removal of wells' degeneration. Consequently, the broken mirror symmetry between the potential wells led to additional solutions with corresponding voltage responses. The probability of occurrence for different high voltage/large orbit solutions with changes in potential symmetry was investigated. In particular, the periodicity of different solutions with respect to the harmonic excitation period were studied and compared in terms of the voltage output. The results showed that a large orbit period-6 subharmonic solution could be stabilized while some higher subharmonic solutions disappeared with the increasing asymmetry of potential wells. Changes in frequency ranges were also observed for chaotic solutions. [ABSTRACT FROM AUTHOR]

Fano resonances that feature strong field enhancement in the narrowband range have motivated extensive studies of light–matter interactions in plasmonic nanomaterials. Optical metasurfaces that are subject to different mirror symmetries have been dedicated to achieving nanoscale light manipulation via plasmonic Fano resonances, thus enabling advantages for high-sensitivity optical sensing and optical switches. Here, we investigate the plasmonic sensing and switches enriched by tailorable multiple Fano resonances that undergo in-plane mirror symmetry or asymmetry in a hybrid rotational misalignment metasurface, which consists of periodic metallic arrays with concentric C-shaped- and circular-ring-aperture unit cells. We found that the plasmonic double Fano resonances can be realized by undergoing mirror symmetry along the X-axis. The plasmonic multiple Fano resonances can be tailored by adjusting the level of the mirror asymmetry along the Z-axis. Moreover, the Fano-resonance-based plasmonic sensing that suffer from mirror symmetry or asymmetry can be implemented by changing the related structural parameters of the unit cells. The passive dual-wavelength plasmonic switches of specific polarization can be achieved within mirror symmetry and asymmetry. These results could entail benefits for metasurface-based devices, which are also used in sensing, beam-splitter, and optical communication systems. [ABSTRACT FROM AUTHOR]

Symmetries play an essential role in the field of physics. In this paper, we examine the relationship between the eigen-amplitudes of four (2 × 2) symmetrical antennas and the symmetry of the amplitudes of their sources (excitations) using mirroring effects. In our case, we find that changing mirrors using symmetry is identical to the point group theory. By exploiting the symmetry problem, we can show the advantage of reducing the size of the analysis domain, at least by a factor of two or more (2, 4, and 8...etc.) (depending on the problem). Several simulation examples have been developed by the MoM-GEC and HFSS to validate this approach. [ABSTRACT FROM AUTHOR]

In this article, we show that mono/oligonucleotide quadruplets, as basic structures of DNA, along with our classification of trinucleotides, disclose an organization of genomes based on purine–pyrimidine symmetry. Moreover, the structure and stability of DNA are influenced by the Watson–Crick pairing and the natural law of DNA creation and conservation, according to which the same mono- or oligonucleotide insertion must be inserted simultaneously into both strands of DNA. Taken together, they lead to quadruplets with central mirror symmetry and bidirectional DNA strand orientation and are incorporated into Chargaff's second parity rule (CSPR). Performing our quadruplet frequency analysis of all human chromosomes and of Neuroblastoma BreakPoint Family (NBPF) genes, which code Olduvai protein domains in the human genome, we show that the coding part of DNA violates CSPR. This may shed new light and give rise to a novel hypothesis on DNA creation and its evolution. In this framework, the logarithmic relationship between oligonucleotide order and minimal DNA sequence length, to establish the validity of CSPR, automatically follows from the quadruplet structure of the genomic sequence. The problem of the violation of CSPR in rare symbionts is discussed. [ABSTRACT FROM AUTHOR]

Robust edge states of periodic crystals with Dirac points fixed at the corners or centers of the Brillouin zones have drawn extensive attention. Recently, researchers have observed a special edge state associated with Dirac cones degenerated at the high symmetric boundaries of the first irreducible Brillouin zone. These nodal points, characterized by vortex structures in the momentum space, are attributed to the unavailable band crossing protected by mirror symmetry. By breaking the time reversal symmetry with intuitive rotations, valley-like states can be observed in a pair of inequivalent insulators. In this paper, an improved direct inverse design method is first applied to realize the valley-like states. Compared with the conventional strategy, the preparation of transition structures with degeneracy points is skipped. By introducing the quantitative gauge of mode inversion error, insulator pairs are directly obtained without manually tuning the structure with Dirac cone features. [ABSTRACT FROM AUTHOR]

The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach for investigations of quantum gravity. An alternative top-down approach aims to explore the imprints and the constraints imposed by string-theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli and provide a probe to constrain and explore the moduli spaces of (2, 0) string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications have yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. T-duality is another important property of string theory and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality and the related equivalence postulate of quantum mechanics provide the background independent overarching principles underlying quantum gravity. [ABSTRACT FROM AUTHOR]

The Planck mission detected a positive correlation between the intensity (T) and B-mode polarization of the Galactic thermal dust emission. The T B correlation is a parity-odd signal, whose statistical mean vanishes in models with mirror symmetry. Recent work has shown, with strong evidence, that local handedness of the misalignment between the dust filaments and the sky-projected magnetic field produces T B signals. However, it remains unclear whether the observed global T B signal is caused by statistical fluctuations of magnetic misalignment angles or whether some parity-violating physics in the interstellar medium sets a preferred misalignment handedness. The present work aims to make a quantitative statement about how confidently the statistical fluctuation interpretation is ruled out by filament-based simulations of polarized dust emission. We use the publicly available DUSTFILAMENTS code to simulate the dust emission from filaments whose magnetic misalignment angles are symmetrically randomized and construct the probability density function of ξ p , a weighted sum of the T B power spectrum. We find that the Planck data have a ≳ 10 σ tension with the simulated ξ p distribution. Our results strongly support the idea that the Galactic filament misalignment has a preferred handedness, whose physical origin is yet to be identified. [ABSTRACT FROM AUTHOR]

Two polytypic modifications of new non-centrosymmetric iodate Rb3Sc(IO3)6 are synthesized hydrothermally. Their structures demonstrate different degrees of ordering and are solved in the same space group, Pc, with differing choice of b-axis: either 20 or 40 Å is selected from the same diffraction data, measured on crystals with better ordering. The difference in NLO properties of two polytypes is disclosed. Topology–symmetry analysis of separated blocks and layers allowed determination of local symmetry corresponding to mirror plane m, which defines strong optical nonlinearity. Layer alternation indicates a polytypic nature of Rb, Sc-iodate and its similarity to K, In- and K, Sc-nonlinear-optical iodate crystals, space group Fdd2, belonging to the proposed common family A3M(IO3)6 (A = K, Rb; M = Sc, In), whose properties are explained on a symmetry basis for every known member. Hypothetical structural variant is predicted; structural disorder and crystal growth conditions are discussed as factors affecting properties. [ABSTRACT FROM AUTHOR]

Two-dimensional transition metal dichalcogenides (TMDs) with Janus structures are attracting increasing attention due to their emerging superior properties in breaking vertical mirror symmetry when compared to conventional TMDs, which can be beneficial in fields such as piezoelectricity and photocatalysis. The structural investigations of such materials, along with other 2D materials, can be successfully carried out using the Raman spectroscopy method. One of the key elements in such research is the theoretical spectrum, which may assist in the interpretation of experimental data. In this work, the simulated Raman spectrum of 1H-MoSSe and the predicted Raman spectra for 1T, 1T', and 1H' polymorph modifications of MoSSe monolayers were characterized in detail with DFT calculations. The interpretation of spectral profiles was made based on the analysis of the lattice dynamics and partial phonon density of states. The presented theoretical data open the possibility of an accurate study of MoSSe polymorphs, including the control of the synthesized material quality and the characterization of samples containing a mixture of polymorphs. [ABSTRACT FROM AUTHOR]

Due to the chiral uniformity of proteins and carbohydrates, the basic building blocks of living matter, the mirror symmetry characteristics of drugs are of exceptional importance for medicinal chemistry. In this work, we present a new synthesis of the mono-enantiomeric chiral drug prenalterol 1 based on the symmetry-breaking phenomenon, namely, the spontaneous resolution of 4-hydroxyphenyl glycerol ether 2. The single crystal X-ray diffraction method was used to investigate both rac- and (S)-1 as well as (R)-2. A feature of the main crystal-forming supramolecular motif (SMM) for diol 2 is the participation of three different molecules representing different types of hydroxyl groups in the formation of its repeating unit. The type of prenalterol SMM, as in the case of the related drugs propranolol 3 and pindolol 4, appears to be a chirality driven property, and is dictated by the enantiomeric composition of the crystals. In single-enantiomeric forms, infinite one-dimensional chains are realized, organized around helical axes, while in racemates, zero-dimensional cycles are realized, organized around inversion symmetry elements. The results obtained again demonstrate the influence of the chiral polarization of a substance not only on the general (selection of a space group), but also on particular characteristics of matter crystal organization, namely selection of a specific SMM. [ABSTRACT FROM AUTHOR]

The spin–orbit torques (SOTs) in the heavy metal (HM)/ferromagnetic metal (FM) structure hold promise for next-generation low-power and high-density spintronic memory and logic applications. For the SOT switching of a perpendicular magnetization, an external magnetic field is inevitable for breaking the mirror symmetry, which is not practical for high-density nanoelectronics applications. In this work, we study the current-induced field-free SOT switching and SOT perpendicular effective field ( H z e f f ) in a variety of laterally asymmetric multilayers, where the asymmetry is introduced by growing the FM layer in a wedge shape. We show that the design of structural asymmetry by wedging the FM layer is a universal scheme for realizing field-free SOT switching. Moreover, by comparing the FM layer thickness dependence of ( H z e f f ) in different samples, we show that the efficiency (β = H z e f f /J, J is the current density) is sensitive to the HM/FM interface and the FM layer thickness. The sign of β for thin FM thicknesses is related to the spin Hall angle (θSH) of the HM layer attached to the FM layer. β changes its sign with the thickness of the FM layer increasing, which may be caused by the thickness dependence of the work function of FM. These results show the possibility of engineering the deterministic field-free switching by combining the symmetry breaking and the materials design of the HM/FM interface. [ABSTRACT FROM AUTHOR]

Symmetry in nature is a result of biological self-organization, driven by evolutionary processes. Detected by the visual systems of various species, from invertebrates to primates, symmetry determines survival relevant choice behaviors and supports adaptive function by reducing stimulus uncertainty. Symmetry also provides a major structural key to bio-inspired artificial vision and shape or movement simulations. In this psychophysical study, local variations in color covering the whole spectrum of visible wavelengths are compared to local variations in luminance contrast across an axis of geometrically perfect vertical mirror symmetry. The chromatic variations are found to delay response time to shape symmetry to a significantly larger extent than achromatic variations. This effect depends on the degree of variability, i.e., stimulus complexity. In both cases, we observe linear increase in response time as a function of local color variations across the vertical axis of symmetry. These results are directly explained by the difference in computational complexity between the two major (magnocellular vs. parvocellular) visual pathways involved in filtering the contrast (luminance vs. luminance and color) of the shapes. It is concluded that color variability across an axis of symmetry proves detrimental to the rapid detection of symmetry, and, presumably, other structural shape regularities. The results have implications for vision-inspired artificial intelligence and robotics exploiting functional principles of human vision for gesture and movement detection, or geometric shape simulation for recognition systems, where symmetry is often a critical property. [ABSTRACT FROM AUTHOR]

EEG, fMRI and TMS studies have implicated the extra-striate cortex, including the Lateral Occipital Cortex (LOC), in the processing of visual mirror symmetries. Recent research has found that the sustained posterior negativity (SPN), a symmetry specific electrophysiological response identified in the region of the LOC, is generated when temporally displaced asymmetric components are integrated into a symmetric whole. We aim to expand on this finding using dynamic dot-patterns with systematically increased intra-pair temporal delay to map the limits of temporal integration of visual mirror symmetry. To achieve this, we used functional near-infrared spectroscopy (fNIRS) which measures the changes in the haemodynamic response to stimulation using near infrared light. We show that a symmetry specific haemodynamic response can be identified following temporal integration of otherwise meaningless dot-patterns, and the magnitude of this response scales with the duration of temporal delay. These results contribute to our understanding of when and where mirror symmetry is processed in the visual system. Furthermore, we highlight fNIRS as a promising but so far underutilised method of studying the haemodynamics of mid-level visual processes in the brain. [ABSTRACT FROM AUTHOR]

Legendre's equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of the first and second kind. In physics, however, commonly the only acceptable members of this set are Legendre polynomials. The quantization of the eigenvalues of Legendre's operator is a consequence of this. We present and explain a stand-alone and in-depth argument for rejecting all solutions of Legendre's equation in physics apart from the polynomial ones. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre's equation are quintessential to the argument. We demonstrate that the evenness or oddness of Legendre polynomials is a consequence of the same premises. [ABSTRACT FROM AUTHOR]

Featured Application: Photothermal characterization of chiro-optical phenomena in metasurfaces. Chirality, a lack of mirror symmetry, is present in nature at all scales; at the nanoscale, it governs the biochemical reactions of many molecules, influencing their pharmacology and toxicity. Chiral substances interact with left and right circularly polarized light differently, but this difference is very minor in natural materials. Specially engineered, nanostructured, periodic materials can enhance the chiro-optical effects if the symmetry in their interactions with circular polarization is broken. In the diffraction range of such metasurfaces, the intensity of diffracted orders depends on the chirality of the input beam. In this work, we combine a photothermal deflection experiment with a novel theoretical framework to reconstruct both the thermal and optical behavior of chiro-optical behavior in diffracted beams. [ABSTRACT FROM AUTHOR]

This paper studies wave propagation in a periodic parallel-plate waveguide with equilateral triangular holes. A mode-matching method is implemented to analyze the dispersion diagram of the structure possessing glide and mirror symmetries. Both structures present an unexpected high degree of isotropy, despite the triangle not being symmetric with respect to rotations of 90°. We give some physical insight on the matter by carrying out a modal decomposition of the total field on the hole and identifying the most significant modes. Additionally, we demonstrate that the electrical size of the triangular hole plays a fundamental role in the physical mechanism that causes that isotropic behavior. Finally, we characterize the influence of the different geometrical parameters that conform the unit cell (period, triangle size, hole depth, separation between metallic plates). The glide-symmetric configuration offers higher equivalent refractive indexes and widens the stopband compared to the mirror-symmetric configuration. We show that the stopband is wider as the triangle size is bigger, unlike holey structures composed of circular and elliptical holes where an optimal hole size exists. [ABSTRACT FROM AUTHOR]

The complex dispersion relations along the main symmetry directions of two-dimensional finite size periodic arrangements of resonant or non-resonant scatterers are recovered by using an extension of the SLaTCoW (Spatial LAplace Transform for COmplex Wavenumber) method. This method relies on the analysis of the spatial Laplace transform instead of the usual spatial Fourier transform of the measured wavefield in the frequency domain. We apply this method to finite dimension square periodic arrangements of both rigid and resonant scatterers embedded in air, i.e., to finite size sonic crystals and finite size acoustic metamaterials, respectively. The main hypothesis considered in this work is the mirror symmetry of the finite structure with respect to its median axis along the analyzed direction. However, we show that the method is robust enough to provide excellent results even if this hypothesis is not fully satisfied. Effectively, a minor asymmetry could be considered as a side effect when the structure is large enough because Laplace transforming the field along the main symmetry directions also implies averaging the field in the perpendicular one. The calculated complex dispersion relations are in excellent agreement with those obtained by an already validated technique, like the Extended Plane Wave Expansion (EPWE). The methodology employed in this work is intended to be directly used for the experimental characterization of real 2D periodic and resonant systems. [ABSTRACT FROM AUTHOR]

A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of X = OP1 ( 1, 1) to the augmentation polynomial of Legendrian contact homology. We describe how to use this conjecture to compute genus zero, one boundary component open Gromov-Witten invariants for Lagrangian submanifolds LK ⊂ X obtained from the conormal bundles of knots K ⊂ S³. This computation is then performed for two non-toric examples (the figure-eight and three-twist knots). For (r, s) torus knots, the open Gromov-Witten invariants can also be computed using Atiyah-Bott localization. Using this result for the unknot and the (3, 2) torus knot, we show that the augmentation polynomial can be derived from these open Gromov-Witten invariants. [ABSTRACT FROM AUTHOR]

We present a new algorithm for 3D shape reconstruction from stereo image pairs that uses mirror symmetry as a biologically inspired prior. 3D reconstruction requires some form of prior because it is an ill-posed inverse problem. Psychophysical research shows that mirror-symmetry is a key prior for 3D shape perception in humans, suggesting that a general purpose solution to this problem will have many applications. An approach is developed for finding objects that fit a given shape definition. The algorithm is developed for shapes with two orthogonal planes of symmetry, thus allowing for straightforward recovery of occluded portions of the objects. Two simulations were run to test: (1) the accuracy of 3D recovery, and (2) the ability of the algorithm to find the object in the presence of noise. We then tested the algorithm on the Children's Furniture Corpus, a corpus of stereo image pairs of mirror symmetric furniture objects. Runtimes and 3D reconstruction errors are reported and failure modes described. [ABSTRACT FROM AUTHOR]

This paper introduces a new concept of mirror symmetry, called "anomalous mirror symmetry", which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown. [ABSTRACT FROM AUTHOR]

This expository article explores the connection between the polar duality from polyhedral geometry and mirror symmetry from mathematical physics and algebraic geometry. Topics discussed include duality of polytopes and cones as well as the famous quintic threefold and the toric variety of a reflexive polytope. [ABSTRACT FROM AUTHOR]

The Necker cube is a striking example for perceptual dominance of 3D over 2D. Object symmetry and obliqueness of angles are co-varying cues that may underlie the perceived slant of Necker cubes. To investigate the power of the oblique-angle cue, slants were judged of extremely simple symmetrical shapes. Slant computations based on an assumption of orthogonality were made for two abutting lines as a function of vertex angle and the slant of the screen. Computed slants were compared with slants judged by six subjects under binocular viewing conditions. Judged slant was highly correlated with slant specified by the oblique angles under an assumption of orthogonality. The contributions of screen cues, including binocular disparity, were negligible. The consistency of the judgments across subjects indicates the assumption of orthogonality as one of the principles underlying slant perception. Necker cubes illustrate that the visual system can disengage unambiguous cues in favor of ambiguous object-symmetry and oblique-angle cues, if the latter indicate very different slants. Selective disengagement of cues may be the mechanism that underlies the success of 2D images in ancient, as well as modern civilizations. [ABSTRACT FROM AUTHOR]

The present experiment investigates whether patterns of shifts of feature locations could affect the same/different decisions of simultaneously presented pairs of geometrical figures. A shift of locations was defined as the angular distance from the location of a feature in one figure to the location of the same feature in another figure. It was hypothesized that the difficulty in discriminating mirror-reflected (or axisymmetric) pairs from disoriented identical pairs was caused by complex shifting patterns inherent in axisymmetric pairs. According to the shifts of the locations of the four structural features, five pair types were prepared. They could be ordered from completely identical to completely different in their shifts: identical 0/4 pairs, non-identical 1/4 pairs, non-identical 2/4 pairs = axisymmetric 2/4 pairs and non-identical 4/4 pairs. The latencies for non-identical pairs decreased with the increase of difference in the shifts of feature locations, indicating that serial, self-terminating comparisons of the shifts were applied to the discrimination of non-identical pairs from identical pairs. However, the longer latencies in axisymmetric 2/4 pairs than in non-identical 2/4 pairs suggested that the difficulty for axisymmetric pairs was not caused by the complex shifting patterns, and the difficulty was not satisfactorily explained by the comparisons of feature locations. [ABSTRACT FROM AUTHOR]

Gestalt Algebra gives a formal structure suitable for describing complex patterns in the image plain. This can be useful for recognizing hidden structure in images. The work at hand refers to the laws of perceptual psychology. A manifold called the Gestalt omain is defined. Next to the position in 2D it also contains an orientation and a scale component.Algebraic operations on it are given for mirror symmetry as well as organization into rows.Additionally the Gestalt Domain contains an assessment component, and all the meaning of the operations implementing the Gestalt-laws is realized in the functions giving this component. The operation for mirror symmetry is binary, combining two parts into one aggregate as usual in standard algebra. The operation for organization into rows, however, combines n parts into an aggregate, where n may well be more than two. This is algebra in its more general sense. For recognition, primitives are extracted from digital raster images by Lowe's Scale Invariant Feature Transform (SIFT). Lowe's key-point descriptors can also be utilized. Experiments are reported with a set of images put forth for the Computer Vision and Pattern Recognition Workshops (CVPR) 2013 symmetry contest. [ABSTRACT FROM AUTHOR]

The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of supermolecular helicity, the occurrence of novel thermodynamic phases, as well as electro-optic effects which can only be observed in chiral liquid crystalline materials. In particular, I will discuss the formation of helical superstructures in cholesteric, Twist Grain Boundary and ferroelectric phases. As examples for the occurrence of novel phases the Blue Phases and Twist Grain Boundary phases are introduced. Chirality related effects are demonstrated through the occurrence of ferroelectricity in both thermotropic as well as lyotropic liquid crystals. Lack of mirror symmetry is also discussed briefly for some biopolymers such as cellulose and DNA, together with its influence on liquid crystalline behavior. [ABSTRACT FROM AUTHOR]

Integrating shape contours in the visual periphery is vital to our ability to locate objects and thus make targeted saccadic eye movements to efficiently explore our surroundings. We tested whether global shape symmetry facilitates peripheral contour integration and saccade targeting in three experiments, in which observers responded to a successful peripheral contour detection by making a saccade towards the target shape. The target contours were horizontally (Experiment 1) or vertically (Experiments 2 and 3) mirror symmetric. Observers responded by making a horizontal (Experiments 1 and 2) or vertical (Experiment 3) eye movement. Based on an analysis of the saccadic latency and accuracy, we conclude that the figure-ground cue of global mirror symmetry in the periphery has little effect on contour integration or on the speed and precision with which saccades are targeted towards objects. The role of mirror symmetry may be more apparent under natural viewing conditions with multiple objects competing for attention, where symmetric regions in the visual field can pre-attentively signal the presence of objects, and thus attract eye movements. [ABSTRACT FROM AUTHOR]

Solvent chirality transfer of (S)-/(R)-limonenes allows the instant generation of optically active PF8P2 aggregates with distinct circular dichroism (CD)/circularly polarized luminescence (CPL) amplitudes with a high quantum yield of 16-20%. The present paper also reports subtle mirror-symmetry-breaking effects in CD-/CPL-amplitude and sign, CD/UV-vis spectral wavelengths, and photodynamics of the aggregates, though the reasons for the anomaly are unsolved. However, these photophysical properties depend on (i) the chemical natures of chiral and achiral molecules when used in solvent quantity, (ii) clockwise and counterclockwise stirring operations, and (iii) the order of addition of limonene and methanol to the chloroform solution. [ABSTRACT FROM AUTHOR]