Complete Symmetry Research Articles

Modeling Pollutant Diffusion in the Ground Using Conformable Fractional Derivative in Spherical Coordinates with Complete Symmetry

The conformal fractional derivative (CFD) has become a hot research topic since it has a physical interpretation and is easier to grasp and apply to problems compared with other fractional derivatives. Its application to heat transfer, diffusion, diffusion-advection, and wave propagation problems can be found in the literature. Fractional diffusion equations have received great attention recently due to their applicability in physical, chemical, and biological processes and engineering. The diffusion of the pollutants within the ground, which is an important environmental problem, can be modeled with a diffusion equation. Diffusion in some porous materials or soil can be modeled more accurately with fractional derivatives or the conformal fractional derivative. In this study, the diffusion problem of a spilled pollutant leaking into the ground modeled with the conformal fractional time derivative in spherical coordinates has been solved analytically using the Fourier series for a constant mass flow rate and complete symmetry under the assumptions of homogeneous and isotropic soil, constant soil temperature, and constant permeability. The solutions have been simulated spatially and in time. A parametric analysis of the problem has been performed for several values of the CFD order. The simulation results are interpreted. It has also been suggested how to find the parameters of the soil to see whether the CFD can be used to model the soil or not. The approach described here can also be used for modeling pollution problems involving different boundary conditions.

The Upper Extremity Lymphatic System Is Not Symmetrical in Individuals: An Anatomic Study Utilizing ICG Lymphography and SPECT/CT Lymphoscintigraphy.

We evaluated whether superficial lymphatic anatomy and functional lymph node drainage are symmetric between the right and left upper extremities of healthy female volunteers, and if handedness is associated with symmetry of superficial lymphatic anatomy. Symmetry of lymphatic anatomy has been assumed historically. This assumption of individual anatomic symmetry is being utilized clinically and in research without validation. 36 normal female volunteers underwent bilateral indocyanine green (ICG) lymphography and lymphoscintigraphy of the upper extremities. Eight collecting vessel pathways of each upper extremity were mapped on ICG lymphography. 13 lymph node groups were visualized on lymphoscintigraphy. Symmetry of lymphatic anatomy and functional drainage were established by comparing the right and left extremities of each participant. Hand dominance was assessed by hand grip strength on a hand dynamometer. Among the 36 participants, 10 (28%) showed symmetry of all eight upper extremity lymphatic pathways with ICG. However, only 1 (3%) participant demonstrated complete symmetry amongst the 13 lymph node groups. Total symmetry of lymphatic channels was observed on ICG in seven (39%) participants with hand dominance and three (17%) participants without hand dominance (X2 = 2.215, P = 0.137). Lymphatic anatomy and functional drainage of the upper extremities are not consistently symmetric. Functional nodal drainage as demonstrated by lymphoscintigraphy shows less symmetry than anatomic studies of lymphatic channels using ICG. Symmetric lymphatic anatomy does not appear to correlate with hand dominance. These findings challenge the prevailing assumption of left-right lymphatic symmetry.

A zero precision loss framework for EEG channel selection: enhancing efficiency and maintaining interpretability

The brain-computer interface (BCI) systems based on motor imagery typically rely on a large number of electrode channels to acquire information. The rational selection of electroencephalography (EEG) channel combinations is crucial for optimizing computational efficiency and enhancing practical applicability. However, evaluating all potential channel combinations individually is impractical. This study aims to explore a strategy for quickly achieving a balance between maximizing channel reduction and minimizing precision loss. To this end, we developed a spatio-temporal attention perception network named STAPNet. Based on the channel contributions adaptively generated by its subnetwork, we propose an extended step bi-directional search strategy that includes variable ratio channel selection (VRCS) and strided greedy channel selection (SGCS), designed to enhance global search capabilities and accelerate the optimization process. Experimental results show that on the High Gamma and BCI Competition IV 2a public datasets, the framework respectively achieved average maximum accuracies of 91.47% and 84.17%. Under conditions of zero precision loss, the average number of channels was reduced by a maximum of 87.5%. Additionally, to investigate the impact of neural information loss due to channel reduction on the interpretation of complex brain functions, we employed a heatmap visualization algorithm to verify the universal importance and complete symmetry of the selected optimal channel combination across multiple datasets. This is consistent with the brain’s cooperative mechanism when processing tasks involving both the left and right hands.

FRET calibration by symmetrization on the cell surface

Maximum position of Shannon-information of FRET frequency distribution represented as a function of the α (or G) calibrating factor as calculated in the framework of dual-laser flow cytometric FRET method – also called 3-cube FRET – gives a fairly good approximation of the real α, using only a single FRET sample. The estimation is accurate for completely symmetric FRET distributions like Gaussian and uniform. For non-symmetric distributions, the committed error has been found to depend on the direction and degree of deviation from the complete symmetry. The maximum information is characterized also by zero skewness, and minima in kurtosis and in the χ-value, defined as the “absolute deviation from the Gaussian”, as other α- functions characterizing shape. As to practice, information maximum of FRET distribution can be used to determine α, whenever symmetry can be assumed. In other cases, the goodness of estimation can be inferred from the information content and shape parameters (skewness, kurtosis and “χ-value”) of the primarily measured FRET parameter A′, based on their inverse correlations with their counterparts computed with the target FRET distribution. Above a threshold in FRET efficiency or its coefficient of variation, resonant peaks (“Ω-curves”) in FRET information appear on the α-scale, with their positions stabilized around α values with reduced fluctuations dictated by symmetry of the target FRET distribution. The phenomenon is explained by a FRET-induced broadening of the A′ distribution reaching the domain containing A′ = −α.

Enumeration of Spin-Space Groups: Toward a Complete Description of Symmetries of Magnetic Orders

Symmetries of three-dimensional periodic scalar fields are described by 230 space groups (SGs). Symmetries of three-dimensional periodic (pseudo)vector fields, however, are described by the spin-space groups (SSGs), which were initially used to describe the symmetries of magnetic orders. In SSGs, the real-space and spin degrees of freedom are unlocked in the sense that an operation could have different spatial and spin rotations. SSGs give a complete symmetry description of magnetic structures and have natural applications in the band theory of itinerary electrons in magnetically ordered systems with weak spin-orbit coupling. , a concept raised recently that belongs to the symmetry-compensated collinear magnetic orders but has nonrelativistic spin plitting, is well described by SSGs. Because of the vast number and complicated group structures, SSGs have not yet been systematically enumerated. In this work, we exhaust SSGs based on the invariant subgroups of SGs, with spin operations constructed from three-dimensional (3D) real representations of the quotient groups for the invariant subgroups. For collinear and coplanar magnetic orders, the spin operations can be reduced into lower-dimensional real representations. As the number of SSGs is infinite, we consider only SSGs that describe magnetic unit cells up to 12 times crystal unit cells. We obtain 157 289 noncoplanar, 24 788 coplanar-noncollinear, and 1421 collinear SSGs. The enumerated SSGs are stored in an online database with a user-friendly interface. We develop an algorithm to identify SSGs for realistic materials and find SSGs for 1626 magnetic materials. We also discuss several potential applications of SSGs, including the representation theory, topological states protected by SSGs, structures of spin textures, and refinement of magnetic neutron diffraction patterns using SSGs. Our results serve as a solid starting point for further studies of symmetry and topology in magnetically ordered materials. Published by the American Physical Society 2024

SAT Modulo Symmetries for Graph Generation and Enumeration

We propose a novel SAT-based approach to graph generation. Our approach utilizes the interaction between a CDCL SAT solver and a special symmetry propagator where the SAT solver runs on an encoding of the desired graph property. The symmetry propagator checks partially generated graphs for minimality with respect to a lexicographic ordering during the solving process. This approach has several advantages over a static symmetry breaking: (i) symmetries are detected early in the generation process, (ii) symmetry breaking is seamlessly integrated into the CDCL procedure, and (iii) the propagator performs a complete symmetry breaking without causing a prohibitively large initial encoding. We instantiate our approach by generating extremal graphs with certain restrictions in terms of forbidden subgraphs and diameter. In particular, we could confirm the Murty-Simon Conjecture (1979) on diameter-2-critical graphs for graphs up to 19 vertices and prove the exact number of Ramsey graphs \(\mathcal{R}(3,5,n)\) and \(\mathcal{R}(4,4,n)\) .

Numerical study on solar photovoltaic/thermal system with tesla valve

In recent years, photovoltaic/thermal (PV/T) systems have played a crucial role in reducing energy consumption and environmental degradation, nonetheless, the low energy conversion efficiency presents a considerable obstacle for PV/T systems. Therefore, improving heat conversion efficiency is essential to enhance energy efficiency. In this paper, the PV/T system with the Tesla valve is proposed to solve this problem. Firstly, the cooling effect is simulated and analyzed in the system with four different flow channel structures: semicircle, rectangle, triangle and Tesla valve. The results indicate that the system with the Tesla valve exhibits superior cooling performance. Subsequently, several factors including angle, valve number, valve type, and pipe diameter ratio for the Tesla valve are further studied through numerical and simulation analysis. The results reveal that Tesla valves demonstrate optimal cooling performance when possessing the following structural parameters: complete symmetry, more valves, a 30-degree angle and a pipe diameter ratio of 1. Finally, four different types of fluid are selected to explore the Tesla valve. The conclusion shows that nanofluids with high density, low specific heat, and high thermal conductivity also improve the cooling performance. Thus, the PV/T system with the Tesla valve exhibits good heat dissipation and energy storage efficiency, electrical efficiency can reach 16.32% and thermal efficiency reach 59.65%.

Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D \mathbb{Z}_2ℤ2 gauge theory with an emergent fermion, and point out that pumping chiral p+ipp+ip topological states gives rise to a \mathbb{Z}_{8}ℤ8 0-form symmetry with mixed gravitational anomaly. This ordinary symmetry mixes with the other higher symmetries to form a 3-group structure, which we examine in detail. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization of T^3T3 (3-torus) and T^2 \rtimes_{C_2} S^1T2⋊C2S1 (2-torus bundle over the circle) respectively, and pumping p+ipp+ip states. Our considerations also imply the possibility of a logical TT gate by placing the code on \mathbb{RP}^3ℝℙ3 and pumping a p+ipp+ip topological state.

Locally adaptive inversions in structured populations.

Inversions have been proposed to facilitate local adaptation, by linking together locally coadapted alleles at different loci. Prior work addressing this question theoretically has considered the spread of inversions in "continent-island" scenarios in which there is a unidirectional flow of maladapted migrants into the island population. In this setting, inversions capturing locally adaptive haplotypes are most likely to invade when selection is weak, because stronger local selection (i) more effectively purges maladaptive alleles and (ii) generates linkage disequilibrium between adaptive alleles, thus lessening the advantage of inversions. We show this finding only holds under limited conditions by studying the establishment of inversions in a more general two-deme model, which explicitly considers the dynamics of allele frequencies in both populations linked by bidirectional migration. In this model, the level of symmetry between demes can be varied from complete asymmetry (continent-island) to complete symmetry. For symmetric selection and migration, strong selection increases the allele frequency divergence between demes thereby increasing the frequency of maladaptive alleles in migrants, favoring inversions-the opposite of the pattern seen in the asymmetric continent-island scenario. We also account for the likelihood that a new inversion captures an adaptive haplotype in the first instance. When considering the combined process of capture and invasion in "continent island" and symmetric scenarios, relatively strong selection increases inversion establishment probability. Migration must also be low enough that the inversion is likely to capture an adaptive allele combination, but not so low as to eliminate the inversion's advantage. Overall, our analysis suggests that inversions are likely to harbor larger effect alleles that experience relatively strong selection.

Symmetric U-Net Model Tuned by FOX Metaheuristic Algorithm for Global Prediction of High Aerosol Concentrations

In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented images to make the prediction. For this, the classic U-Net model was modified to use ConvLSTM2D layers with MaxPooling3D and UpSampling3D layers. In order to achieve complete symmetry, the output data are given in the form of a series of eight segmented images shifted by one image in the time sequence so that the last image actually represents the forecast of the next image of high aerosol concentrations. The proposed model structure was tuned by the new FOX metaheuristic algorithm. Based on our analysis, we found that this algorithm is suitable for tuning deep learning models considering their stochastic nature. It was also found that this algorithm spends the most time in areas close to the optimal value where there is a weaker linear correlation with the required metric and vice versa. Taking into account the characteristics of the used database, we concluded that the model is capable of generating adequate data and finding patterns in the time domain based on the ddc and dtc criteria. By comparing the achieved results of this model using the AUC-PR metric with the previous results of the ResNet3D-101 model with transfer learning, we concluded that the proposed symmetric U-Net model generates data better and is more capable of finding patterns in the time domain.

Accurate diabatization based on combined-hyperbolic-inverse-power-representation: 1,2 2A' states of BeH2.

A diabatic potential energy matrix (DPEM) for the two lowest states of BeH2+ has been constructed using the combined-hyperbolic-inverse-power-representation (CHIPR) method. By imposing symmetry constraints on the coefficients of polynomials, the complete nuclear permutation inversion symmetry is correctly preserved in the CHIPR functional form. The symmetrized CHIPR functional form is then used in the diabatization by ansatz procedure. The abinitio energies are reproduced with satisfactory accuracy. In addition, the CHIPR-based DPEM also reproduces the local topology of a conical intersection. Future work will focus on a complete four-state diabatic representation with emphasis on the long-range interactions and spin-orbit couplings, which will enable accurate quantum scattering calculations for the Be+(2P) + H2 → BeH+(X1Σ+) + H(2S) reaction.

The use of derma-fat grafts to eliminate defects during operations on the parotid glands

Introduction. The effectiveness of surgical treatment of parotid gland tumors is determined by the frequency of local relapse and functional and aesthetic results, which are determined not only by the anatomical and functional safety of the facial nerve. It is also very important to level aesthetic deformities of the parotid region and reduce the severity of frey’s syndrome. Aim. To retrospectively analyze the use of dermal fat grafts to correct defects during operations on the parotid glands. Materials and methods. Our study included 7 patients (2 men and 5 women) who were treated at the Leningrad Regional Clinical Oncology Dispensary named after L. D. Roman from 2021 to 2022. The average age of the patients was 49.7 years (42–64 years), the average follow-up period was 20.4 months (19–22 months). All patients underwent total / subtotal resection of the parotid gland; we used an abdominal dermal fat graft to close the defect. Histological examination of the surgical material revealed a pleomorphic adenoma of the parotid gland in 5 cases; in 2 cases, a ma-lignant tumor (adenocystic carcinoma and basal cell carcinoma of the salivary glands), which required adjuvant radiation therapy in radical doses. To assess aesthetic and functional results in the recipient and donor areas, we developed and used a questionnaire. Results. 6–8 months after the end of treatment, 5 patients completed questionnaires. 4 people indicated complete symmetry of the face, one patient indicated an average depression. 3 patients did not note any pain in the parotid area, 2 patients had minor discomfort that did not cause any problems. Only one respondent noted redness of the face when eating, which did not cause him any problems; the rest of the survey participants did not find these changes. None of the survey participants noted the appearance of sweat on their face when eating. Conclusion. The use of dermal fat grafts can improve the aesthetic and functional results of treatment in patients undergoing operations on the parotid glands. This technique is quite easy to use and does not significantly increase the time of surgical intervention. A derma-fat graft does not make it difficult to monitor disease relapses.

Морфометрические особенности разного типа структурных компонентов внутриорганного венозного русла селезенки

Objective: to establish morphometric characteristics of different types of splenic venous vasculature’s structural components - bi-units (BUs) in males and females, of the 1st and 2nd periods of adulthood. Materials and methods. The study is based on the results of a morphometric study of corrosion casts of the splenic venous system of 64 people (32 men, 32 women; 32 first period of adulthood, 32 second period of adulthood) who died of sudden death and accidental causes between the ages of 21 and 60. The diameters (D) and lengths (L) of the venous segments forming the BU were measured. The splenic venous vasculature was represented as a system consisting of four types of BU: 1 - complete asymmetry, the values of the internal diameters of the proximal segment (D), the distal segments with larger diameter (dmax) and the distal segment with smaller diameter (dmin) are not equal- D≠dmax≠dmin; 2 - lateral asymmetry, D=dmax and dmax≠dmin; 3 - unilateral symmetry - D≠dmax≠dmin and dmax=dmin; 4 - complete symmetry, D=dmax=dmin. Results. All four types of BUs are present in the composition of splenic venous vasculature; the relative number, of the total number of BUs of splenic venous vasculature type 1 is 55.2%; type 2 - 4.7%, type 3 - 38.0%, type 4 - 2.1%; the presence of a reliable relationship between the relative number of BUs of different types, sex and age group; the sizes of all four types of BUs were determined; the largest size is BU of type 1, and the smallest - BU of type 4; the most symmetrical bi-unites are of types 3 and 4, the most asymmetrical - of types 1 and 2; the relative number of BU of type 1 decreases, BU of type 3 increases, and types 2 and 4 practically do not change in the direction from proximal to distal parts of the vasculature. Conclusion. The results obtained can serve as a foundation for the creation of a morphometric reference standard of splenic venous vasculature and should be taken into account in its numerical modelling.

Cournot meets Bayes-Nash: A discontinuity in behavior in finitely repeated duopoly games

We conduct a series of Cournot duopoly market experiments with a high number of repetitions and fixed matching. Our treatments include markets with (a) complete cost symmetry and complete information, (b) slight cost asymmetry and complete information, and (c) varying cost asymmetries and incomplete information. For the case of complete cost symmetry and complete information, our data confirm the well-known result that duopoly players achieve, on average, partial collusion. However, as soon as any level of cost asymmetry or incomplete information is introduced, observed average individual quantities are remarkably close to the static Bayes-Nash equilibrium predictions.

Path-dependent selection—a bridge between natural selection and neutral selection

Path-dependent selection follows the premise of complete symmetry in the neutral theory of selection; mutations in the natural world are entirely based on statistical randomness, lack directionality, and thus do not exhibit differences in fitness. Under specific spatiotemporal conditions, however, evolutionary positive feedback effects resulting from the specific environment will result in the breakdown of symmetry pre-assumed in neutral selection. This evolutionary positive feedback, a recursive effect, is of Lamarckian active selection or inheritance of acquired characteristics. The mutual antagonistic interactions between the positive selection of recursive effect and the passive selection under natural selection pressure of the environment in multidimensional conditions will result in evolutionary paths. Path-dependent selection proposes that the evolutionary process of organisms is a selection process based on path frequencies rather than an increase in fitness, with a strong reliance on the paths that it has taken in the past. Because of the existence of transition probabilities between different paths or within the same path (such as plasmid transfer, transposons, and function transfer in ecological interactions), path formation will exhibit acceleration or deceleration effects, explaining Gould’s principles such as punctuated equilibrium. When environmental selection pressure is weak or zero, most or all paths (like neutral selection outcomes) may be possible. The frequencies of different paths will differentiate as environmental selection increases, and the paths with higher frequencies will be more easily selected. When the evolutionary process or history has no impact on the evolution of the paths themselves (a static, equilibrium state), the path with the highest frequency is the shortest or optimal path used by evolution—a result consistent with Darwin’s theory of natural selection. Path-dependent selection, which draws inspiration from modern physics, particularly path integral methods in quantum mechanics, may provide us with a new perspective and approach to explaining the evolution of life.

Shift Current with Gaussian Basis Sets and General Prescription for Maximally Symmetric Summations in the Irreducible Brillouin Zone.

The bulk photovoltaic effect is an experimentally verified phenomenon by which a direct charge current is induced within a non-centrosymmetric material by light illumination. Calculations of its intrinsic contribution, the shift current, are nowadays amenable from first-principles employing plane-wave bases. In this work, we present a general method for evaluating the shift conductivity in the framework of localized Gaussian basis sets that can be employed in both the length and velocity gauges, carrying the idiosyncrasies of the quantum-chemistry approach. The (possibly magnetic) symmetry of the system is exploited in order to fold the reciprocal space summations to the representation domain, allowing us to reduce computation time and unveiling the complete symmetry properties of the conductivity tensor under general light polarization.

Non-invertible symmetry webs

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with GG 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [SciPost Phys. 15, 122 (2023)]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups GG, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.

Lie Symmetry Classification, Optimal System, and Conservation Laws of Damped Klein–Gordon Equation with Power Law Non-Linearity

We used the classical Lie symmetry method to study the damped Klein–Gordon equation (Kge) with power law non-linearity utt+α(u)ut=(uβux)x+f(u). We carried out a complete Lie symmetry classification by finding forms for α(u) and f(u). This led to various cases. Corresponding to each case, we obtained one-dimensional optimal systems of subalgebras. Using the subalgebras, we reduced the Kge to ordinary differential equations and determined some invariant solutions. Furthermore, we obtained conservation laws using the partial Lagrangian approach.

Design of an Ultra-Wideband Transparent Wave Absorber.

In this paper, a multilayer ultra-wideband transparent metamaterial wave absorber is proposed, which has the characteristics of ultra-wideband wave absorption, light transmission and flexible bending; in addition, due to the complete symmetry of the structure, the absorber has polarization insensitivity to incident electromagnetic waves. Both simulation and experimental results show that the frequency range of the microwave absorption rate is higher than 90% between 8.7 GHz and 38.9 GHz (between which most of the absorption rate can reach more than 95%), the total bandwidth is 30.2 GHz, and the relative bandwidth is 126.9%, realizing microwave broadband absorption and covering commonly used communication frequency bands such as X-band, Ku-band, and K-band. A sample was processed and tested. The test results are in good agreement with the results of the theoretical analysis, which proves the correctness of the theoretical analysis. In addition, through the selection and oxidation of indium tin (ITO) materials, the metamaterial also has the characteristics of optical transparency and flexibility, so it has potential application value in the window radar stealth and conformal radar stealth of weapons and equipment.

Green chiral separation of racemic mixture via crystallization induced deracemization process synergistically intensified by ultrasound and temperature cycling

Deracemization is a promising chiral resolution technique that combines racemization reaction with stereoselective crystallization for complete chiral symmetry breaking and has attracted much attention. However, the integration process of reaction-crystallization is rather complex and often requires long operation time with high initial solid enantiomer excess which greatly limits its wide application. Herein, we proposed a novel strategy that combines the use of both ultrasound and temperature cycles to accelerate the process of deracemization and thereby chiral separation. A chiral compound, N-acetyl-dl-leucine, was selected as a model drug for experimental validation. We found that either ultrasound or temperature cycle process was capable of accelerating the deracemization efficiency, nonetheless, the combination of the two methods leads to the antagonistic action, decreasing process efficiency and product chiral purity. Through the time-elapsed characterizations on enantiomeric purity of N-acetyl-l-leucine over the course of deracemization, we revealed that the ultrasound negatively impacted the process efficiency of chiral separation via promotion of primary heterogeneous nucleation during the cooling stage. Finally, we strategically designed a synergistic process intensification of crystallization-induced deracemization between temperature cycling and the periodic ultrasound that switches on only during the heating stage to achieve highly efficient separation of pure N-acetyl-l-leucine with theoretical 100% yield at extremely low initial solid ee%.