Complex Symmetry Research Articles

Stabilizing lattice gauge theories through simplified local pseudogenerators

The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the ${\mathbb{Z}}_{2}$ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.

Topological superfluid defects with discrete point group symmetries

Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose–Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry.

A new class of biological ion-driven rotary molecular motors with 5:2 symmetry.

Several new structures of three types of protein complexes, obtained by cryo-electron microscopy (cryo-EM) and published between 2019 and 2021, identify a new family of natural molecular wheels, the “5:2 rotary motors.” These span the cytoplasmic membranes of bacteria, and their rotation is driven by ion flow into the cell. They consist of a pentameric wheel encircling a dimeric axle within the cytoplasmic membrane of both Gram-positive and gram-negative bacteria. The axles extend into the periplasm, and the wheels extend into the cytoplasm. Rotation of these wheels has never been observed directly; it is inferred from the symmetry of the complexes and from the roles they play within the larger systems that they are known to power. In particular, the new structure of the stator complex of the Bacterial Flagellar Motor, MotA5B2, is consistent with a “wheels within wheels” model of the motor. Other 5:2 rotary motors are believed to share the core rotary function and mechanism, driven by ion-motive force at the cytoplasmic membrane. Their structures diverge in their periplasmic and cytoplasmic parts, reflecting the variety of roles that they perform. This review focuses on the structures of 5:2 rotary motors and their proposed mechanisms and functions. We also discuss molecular rotation in general and its relation to the rotational symmetry of molecular complexes.

Complex symmetry of linear combinations of composition operators on the Fock space

Complex symmetry of linear combinations of composition operators on the Fock space

Permutation invariant polynomial neural network based diabatic ansatz for the (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller systems.

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of H3 + is studied, which is an (E + A) × (e + a) Jahn-Teller and Pseudo-Jahn-Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. The adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

Strong cladding mode excitation in ultrathin fiber inscribed Bragg grating with ultraviolet photosensitivity.

Strong UV-written Bragg gratings written in 50 µm-diameter cladding single mode fibers compatible with conventional fiber couple core guided light to dozens of cladding modes distributed across 140 nm in the 1400-1600 nm region, without the need for complex symmetry breaking mechanisms such as tilted, laterally offset, or localized gratings. The extent of the coupling to high order modes and the smaller cladding diameter both contribute to increasing the sensitivity to surrounding refractive index changes by more than one order of magnitude, and to an increased spacing between mode resonances to facilitate unambiguous measurements of larger index changes between 1.3 and 1.44. These improvements are confirmed by theoretical and experimental studies that also cover the temperature and strain differential sensitivities of the cladding mode resonances for complete multiparameter sensing capability.

Shape asymmetry - what's new?

Studies of shape asymmetry have become increasingly abundant as the methods of geometric morphometrics have gained widespread use. Most of these studies have focussed on fluctuating asymmetry and have largely obtained similar results as more traditional analyses of asymmetry in distance measurements, but several notable differences have also emerged. A key difference is that shape analyses provide information on the patterns, not just the amount of variation, and therefore tend to be more sensitive. Such analyses have shown that apparently symmetric structures in animals consistently show directional asymmetry for shape, but not for size. Furthermore, the long-standing prediction that phenotypic plasticity in response to environmental heterogeneity can contribute to fluctuating asymmetry has been confirmed for the first time for the shape of flower parts (but not for size). Finally, shape analyses in structures with complex symmetry, such as many flowers, can distinguish multiple types of directional asymmetry, generated by distinct direction-giving factors, which combine to the single component observable in bilaterally symmetric structures. While analyses of shape asymmetry are broadly compatible with traditional analyses of asymmetry, they incorporate more detailed morphological information, particularly for structures with complex symmetry, and therefore can reveal subtle biological effects that would otherwise not be apparent. This makes them a promising tool for a wide range of studies in the basic and applied life sciences.

Directional asymmetry and direction‐giving factors: Lessons from flowers with complex symmetry

Directional asymmetry is a systematic difference between the left and right sides for structures with bilateral symmetry or a systematic differentiation among repeated parts for complex symmetry. This study explores factors that produce directional asymmetry in the flower of Iris pumila, a structure with complex symmetry that makes it possible to investigate multiple such factors simultaneously. The shapes and sizes of three types of floral organs, the falls, standards, and style branches, were quantified using the methods of geometric morphometrics. For each flower, this study recorded the compass orientations of floral organs as well as their anatomical orientations relative to the two spathes subtending each flower. To characterize directional asymmetry at the whole‐flower level, differences in the average sizes and shapes according to compass orientation and relative orientation were computed, and the left–right asymmetry was also evaluated for each individual organ. No size or shape differences within flowers were found in relation to anatomical position; this may relate to the terminal position of flowers in Iris pumila, suggesting that there may be no adaxial–abaxial polarity, which is very prominent in many other taxa. There was clear directional asymmetry of shape in relation to compass orientation, presumably driven by a consistent environmental gradient such as solar irradiance. There was also clear directional asymmetry between left and right halves of every floral organ, most likely related to the arrangement of organs in the bud. These findings indicate that different factors are acting to produce directional asymmetry at different levels. In conventional analyses not recording flower orientations, these effects would be impossible to disentangle from each other and would probably be included as part of fluctuating asymmetry.

Urbach and Judd-Ofelt analysis of crystalline samarium (III) complexes with β-ketocarboxylate and nitrogen donor secondary ligands

The scarlet Sm (III) complexes with eight coordination number, as favoured by EDAX and elemental analytical data, were synthesized with fluorinated β-keto carboxylic acid as primary ligand and neo, batho, phen, dmph, and bypy as secondary ligand. Binary and ternary complexes of Sm(III) ion [Sm(ligand)32H2O], [Sm(ligand)3secondary ligand] respectively were prepared by one-step grinding method. The complexes exhibit crystalline character, nanoparticle size and outstanding thermal stability, they also have high color purity and as warm orange light sources. In UV visible light, complexes display several characteristic emission transitions such as (4G5/2 → 6H5/2, 4G5/2 → 6H7/2 and 4G5/2 → 6H9/2) under the excitation of Sm (III) ion. The scarlet luminescence in UV domain is accredited to the 4G5/2 → 6H7/2 transition at 605 nm wavelength. The proton NMR and FT-IR data are reliable with coordination behavior of organic ligand and secondary ligand with Sm(III) ion. To understand the semiconducting nature, materiality in solar cell and photovoltaic devices with the help of HOMO- LUMO bandgap analysis and Urbach energy were examined. The calculated Judd-Ofelt parameter is a crucial aspect to describe the rigidity and symmetry of complexes. The anti-microbial investigation demonstrated that all complexes are practically applicable in bioassays.

Analysis of the phase transition of patch colloidal particles and the molecular dynamics simulation

Anisotropic particle system means that the interaction between particles in the system depends not only on their spatial coordinates, but also on the orientation of each particle due to the influence of many factors such as structure, shape, electronic properties and environment. The introduction of orientation coordinates makes the phase space describing this kind of system have higher degrees of freedom and more complex symmetry. Therefore, the study of its general properties has more basic significance in physics. Patch colloidal particles, which have become one of the research hotspots in the field of soft matter physics in recent years, are a typical mesoscopic physical system with anisotropic interaction. In this paper, the two-dimensional patch colloidal particle system is studied as follows: (1) the phase structure of the system is preliminarily studied and analysed. It is found that the phase behaviour of the system at high temperature is similar to that of isotropic Lennard - Jones system is similar. Under low temperature, the system with low patch coverage has strip structure in the condensed phase and complex self-assembly structure in the gas phase; (2) It is found that the long-term diffusion belongs to isotropic normal diffusion, while the short-term diffusion is anisotropic ballistic diffusion, and the particle motion direction is always perpendicular to the patch orientation; (3) The melting behavior of the system is studied. It is found that the melting is a two-step phase transition, which is the same as that of the two-dimensional isotropic colloidal system;

Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.

Complex symmetry and normality of Toeplitz composition operators on the hardy space

In this paper, we investigate the conditions under which the Toeplitz composition operator on the Hardy space H2 becomes complex symmetric with respect to a certain conjugation. We also study various normality conditions for the Toeplitz composition operator on H2.

THERMO CAPILLARY CONVECTION WITH DIFFUSIVE-TYPE EVAPORATION IN A THREE-DIMENSIONAL CHANNEL UNDER THE CONDITIONS OF COMBINED THERMAL LOAD

Three-dimensional generalization of the Ostroumov-Birikh solution of the classical convection equations has been obtained in order to model two-layer flows under the conditions of liquid-vapor phase transition of the diffusive type at the interface. A liquid and gas-vapor mixture fills an endless rectangular duct subjected to the action of a longitudinal temperature gradient and a transversely directed gravity field. The exact solution is interpreted as a solution describing the flows on the working section in a sufficiently long cuvette. The distinguishing characteristics of evaporative convection in the working systems like the ethanol-nitrogen and HFE7100-nitrogen are investigated in the case of different types of the boundary temperature regimes imposed on channel walls. Here, the thermal load is applied on a substrate, according to the linear law with respect to the longitudinal coordinate, whereas the upper and lateral walls are thermally insulated. The longitudinal temperature gradients and transverse temperature drops in the fluid systems, caused both by external thermal load and evaporation processes at the interface, lead to the formation of vortex structures with a complex symmetry and a peculiar vapor concentration field. The flow topology essentially differs with respect to the intensity of the thermal load and type of the liquid coolant. The characteristics of evaporative convection modes, including the evaporative mass flow rate and maximum interfacial temperature and velocity, are analyzed. The study of the characteristic features appearing upon boundary heating allows one to determine flow control mechanisms and to forecast possible forms of instability.

Three-dimensional Measuring of Zygomaticomaxillary Complex Symmetry after Fixation of Unilateral Zygomaticomaxillary Complex Fracture

Three-dimensional Measuring of Zygomaticomaxillary Complex Symmetry after Fixation of Unilateral Zygomaticomaxillary Complex Fracture

Complex symmetry of Toeplitz operators

We introduce a new class of conjugations and characterize complex symmetric Toeplitz operators on the Hardy space with respect to those conjugations. Also, we prove that complex symmetricity and uet property are the same for a certain class of Toeplitz operators. We also discuss the analytic symmetricity for Toeplitz operators. Our results extend several known results by providing unified ways of treating them

FINITE SUM OF COMPOSITION OPERATORS ON FOCK SPACE

AbstractWe investigate unbounded, linear operators arising from a finite sum of composition operators on Fock space. Real symmetry and complex symmetry of these operators are characterised.

A Novel Method for Quantitative Three-Dimensional Analysis of Zygomatico-Maxillary Complex Symmetry.

Objective:To develop a reliable and accurate method to quantify the symmetry of the zygomaticomaxillary complex (ZMC).Methods:Virtual three-dimensional models were created from 53 computed-tomography scans: 15 healthy cases without maxillofacial disorders and 38 patients with ZMC fractures requiring surgical treatment.Asymmetry of the ZMC was measured using a mirroring and surface-based matching technique that uses the anterior cranial fossa as reference to determine the symmetrical position of the ZMC. The measure for ZMC asymmetry was defined as mean surface distance (MSD) between the ZMC-surface and the symmetrical position.Reliability of the method was tested in the 15 healthy cases. Inter-and intra-observer correlation coefficients (Ce) and variabilities were assessed. Accuracy was assessed by comparing ZMC asymmetry between healthy and ZMC fracture cases, and by assessing correlation of ZMC fracture severity with ZMC asymmetry.Results:The average MSD of the 15 healthy cases was 1.40 ± 0.54 mm and the average MSD of the 38 ZMC fracture cases was 2.69 ± 0.95 mm (P < 0.01). Zygomaticomaxillary complex asymmetry correlated with fracture severity (P = 0.01). Intra-rater CC was 0.97 with an intra-rater variability of 0.09 ± 0.11 mm. Inter-rater Ce was 0.95 with an inter-rater variability of 0.12 ± 0.13 mm.Conclusions:Our method is reliable and accurate for quantitative three-dimensional analysis of ZMC-symmetry. It takes into account asymmetry caused by the shape of the ZMC as well as asymmetry caused by the position of the ZMC.Clinical relevance:This method is useful for the evaluation of ZMC asymmetry associated with congenital and acquired disorders of craniofacial skeleton, for surgical planning and for evaluation of postoperative results.

IPVP-MCV: A Multi-Classifier Voting Model for the Accurate Identification of Phage Virion Proteins

The classic structure of a bacteriophage is commonly characterized by complex symmetry. The head of the structure features icosahedral symmetry, whereas the tail features helical symmetry. The phage virion protein (PVP), a type of bacteriophage structural protein, is an essential material of the infectious viral particles and is responsible for multiple biological functions. Accurate identification of PVPs is of great significance for comprehending the interaction between phages and host bacteria and developing new antimicrobial drugs or antibiotics. However, traditional experimental approaches for identifying PVPs are often time-consuming and laborious. Therefore, the development of computational methods that can efficiently and accurately identify PVPs is desired. In this study, we proposed a multi-classifier voting model called iPVP-MCV to enhance the predictive performance of PVPs based on their amino acid sequences. First, three types of evolutionary features were extracted from the position-specific scoring matrix (PSSM) profiles to represent PVPs and non-PVPs. Then, a set of baseline models were trained based on the support vector machine (SVM) algorithm combined with each type of feature descriptors. Finally, the outputs of these baseline models were integrated to construct the proposed method iPVP-MCV by using the majority voting strategy. Our results demonstrated that the proposed iPVP-MCV model was superior to existing methods when performing the rigorous independent dataset test.

Bottom-up coarse-grain modeling of plasticity and nanoscale shear bands in α-RDX.

Computationally inexpensive particle-based coarse-grained (CG) models are essential for use in molecular dynamics (MD) simulations of mesoscopically slow cooperative phenomena, such as plastic deformations in solids. Molecular crystals possessing complex symmetry present enormous practical challenges for particle-based coarse-graining at molecularly resolved scales, when each molecule is in a single-site representation, and beyond. Presently, there is no published pairwise non-bonded single-site CG potential that is able to predict the space group and structure of a molecular crystal. In this paper, we present a successful coarse-graining at a molecular level from first principles of an energetic crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX) in the alpha phase, using the force-matching-based multiscale coarse-graining (MSCG/FM) approach. The new MSCG/FM model, which implements an optimal pair decomposition of the crystal Helmholtz free energy potential in molecular center-of-mass coordinates, was obtained by force-matching atomistic MD simulations of liquid, amorphous, and crystalline states and in a wide range of pressures (up to 20GPa). The MSCG/FM potentials for different pressures underwent top-down optimization to fine-tune the mechanical and thermodynamic properties, followed by consolidation into a transferable density-dependent model referred to as RDX-TC-DD (RDX True-Crystal Density-Dependent). The RDX-TC-DD model predicts accurately the crystal structure of α-RDX at room conditions and reproduces the atomistic reference system under isothermal (300K) hydrostatic compression up to 20GPa, in particular, the Pbca symmetry of α-RDX in the elastic regime. The RDX-TC-DD model was then used to simulate the plastic response of uniaxially ([100]) compressed α-RDX resulting in nanoscale shear banding, a key mechanism for plastic deformation and defect-free detonation initiation proposed for many molecular crystalline explosives. Additionally, a comparative analysis of the effect of core-softening of the RDX-TC-DD potential and the degree of molecular rigidity in the all-atom treatment suggests a stress-induced short-range softening of the effective intermolecular interaction as a fundamental cause of plastic instability in α-RDX. The reported RDX-TC-DD model and overall workflow to develop it open up possibilities to perform high quality simulation studies of molecular energetic materials under thermal and mechanical stimuli, including extreme conditions.

Bateson and Wright on Number and Quantity: How to Not Separate Thinking from Its Relational Context

As part of his explication of the epistemological error made in separating thinking from its ecological context, Bateson distinguished counts from measurements. With no reference to Bateson, the measurement theory and practice of Benjamin Wright also recognizes that number and quantity are different logical types. Describing the confusion of counts and measures as schizophrenic, like Bateson, Wright, a physicist and certified psychoanalyst, showed mathematically that convergent stochastic processes informing counts are predictable in ways that facilitate methodical measurements. Wright’s methods experimentally evaluate the complex symmetries of nonlinear and stochastic numeric patterns as a basis for estimating interval quantities. These methods also retain connections with locally situated concrete expressions, mediating the data display by contextualizing it in relation to the abstractly communicable and navigable quantitative unit and its uncertainty. Decades of successful use of Wright’s methods in research and practice are augmented in recent collaborations of metrology engineers and psychometricians who are systematically distinguishing numeric counts from measured quantities in new classes of knowledge infrastructure. Situating Wright’s work in the context of Bateson’s ideas may be useful for infrastructuring new political, economic, and scientific outcomes.