Symmetry Aspects Research Articles

Adapting spatiotemporal gait symmetry to functional electrical stimulation during treadmill walking.

Individuals with neurological impairments often exhibit asymmetrical gait patterns. This study explored the potential of using functional electrical stimulation (FES) as a perturbation method during treadmill walking to promote gait symmetry adaptation by investigating whether the FES perturbation could induce gait adaptation concerning spatial and temporal gait symmetry in healthy subjects. In the FES perturbation, both legs received electrical pulses at the same period as the subjects' initial stride duration, and the temporal gap between the two pulses for each leg was manipulated over a 7-min period. Following this, subjects continued to walk for another 5 minutes without FES. Subjects participated in two trials: implicit and explicit. In the implicit trial, they walked comfortably during FES perturbation without consciously adjusting their gait. In the explicit trial, they voluntarily synchronized their toe-off phase to the stimulation timing. To examine the effects of the FES perturbation, we measured step length and stance time and then analyzed changes in step length and stance time symmetries alongside their subsequent aftereffects. During the explicit trial, subjects adapted their gait patterns to the electrical pulses, resulting in a directional change in stance time (temporal) symmetry, with the left stance becoming shorter than the right. The stance time asymmetry induced by FES perturbation showed a slight residual effect. In the implicit trial, the directional change trend was slightly observed but not statistically significant. No consistent trend in step length (spatial) symmetry changes was observed in either condition, indicating that subjects may adapt their spatial gait patterns independently of their temporal patterns. Our findings suggest that the applied FES perturbation strategy under explicit condition can induce adaptations in subjects' temporal gait asymmetry, particularly in stance. The implicit condition showed a similar slight trend but was not statistically significant. Further experiments would provide deeper understanding into the mechanism behind subjects' response to FES perturbations, as well as the long-term effects of these perturbations on the spatial and temporal aspects of gait symmetry.

Symmetries and symmetry-generated averages of elastic constants up to the sixth order of nonlinearity for all crystal classes, isotropy and transverse isotropy.

Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.

Comments on Global Symmetries and Anomalies of 5d SCFTs

We study various aspects of global symmetries in five-dimensional superconformal field theories. Whenever a supersymmetry-preserving relevant deformation is available, the infrared gauge theory description might exhibit a finite order mixed ’t Hooft anomaly between a 1-form symmetry and the instantonic symmetry. This anomaly constrains the flavor symmetry group acting faithfully on the SCFT and the consistency of certain RG flows. As an additional example, we consider the instructive case of three-dimensional N=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=4$$\\end{document} SQED. Finally, we discuss the compatibility between conformal invariance and the presence of 1-form and 2-group global symmetries.

Fractal Biology — Evolution from Molecular to Cognitive, and Psychological Dimensions

Biological and artificial intelligence (BI and AI) share the fundamental principles of space-time information processing based on symmetry transformation. Therefore, cognitive-science-inspired AI represents a promising area of exploration. A convincing example are the fractal structure of human languages and protein assembly. Biological processes’ temporal and spatial plasticity links them to basic laws of physics. Continuous advances in fundamental physical theories allow understanding of all aspects of space-time symmetry (STS) natively intertwined with the principle of relativity and causality. Spatial aspects of symmetry represented by three sub-domains such as chirality, fractality, and topology, are widely studied in biology. The role of chirality in biology has been analyzed in several recent reviews. However, the fractals and topological states of biological structures is a relatively new and fast-developing branch of science. Here, we trace publications exploring the role of fractal symmetry in all hierarchical states of biological organization, including at the molecular, cellular, morphological, physiological, perceptual, cognitive, and psychological levels. The coverage of the above-listed areas in current studies is sharply unequal and unsystematic. A broad view of biological fractality opens a unique opportunity to discriminate between a healthy state and a wide range of disease conditions. Psychiatric, neurological, and immune disorders are associated with aberrant molecular assembly and morphological changes in neural circuits, suggesting that the chain of chirality/fractality transfer through all levels of physiological organization deserves persistent attention.

Aspects of categorical symmetries from branes: SymTFTs and generalized charges

Aspects of categorical symmetries from branes: SymTFTs and generalized charges

Aspects of Symmetry in Petri Nets

Symmetry is a fundamental mathematical property applicable to the description of various shapes both geometrical and representational. Symmetry is central to understanding the nature of various objects. It can be used as a simplifying principle when structures are created. Petri nets are widely covered formalisms, useful for modeling different types of computer systems or computer configurations. Different forms of Petri nets exist along with several forms of representation. Petri nets are useful for i) deterministic and ii) non-deterministic modeling. The aspect of symmetry in Petri nets requires in-depth treatment that is often overlooked. Symmetry is a fundamental property found in Petri nets. This work tries to briefly touch on these properties and explain them with simple examples. Hopefully, readers will be inspired to carry out more work in this direction.

The wrapped Fukaya category for semi-toric Calabi–Yau

We introduce the wrapped Donaldson–Fukaya category of a (generalized) semi-toric SYZ fibration with Lagrangian section satisfying a tameness condition at infinity. Examples include the Gross fibration on the complement of an anti-canonical divisor in a toric Calabi–Yau 3-fold. We compute the wrapped Floer cohomology of a Lagrangian section and find that it is the algebra of functions on the Hori–Vafa mirror. The latter result is the key step in proving homological mirror symmetry for this case. The techniques developed here allow the construction in general of the wrapped Fukaya category on an open Calabi–Yau manifold carrying an SYZ fibration with nice behavior at infinity. We discuss the relation of this to the algebraic vs analytic aspects of mirror symmetry.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics.

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Non-Hermitian extended midgap states and bound states in the continuum

We investigate anomalous localization phenomena in non-Hermitian systems by solving a class of generalized Su–Schrieffer–Heeger/Rice–Mele models and by relating their provenance to fundamental notions of topology, symmetry-breaking, and biorthogonality. We find two types of bound states in the continuum, both stable even in the absence of chiral symmetry: the first being skin bulk states, which are protected by the spectral winding number. The second type is constituted by boundary modes associated with a quantized biorthogonal polarization. Furthermore, we find an extended state stemming from the boundary state that delocalizes while remaining in the gap at bulk critical points. This state may also delocalize within a continuum of localized (skin) states. These results clarify fundamental aspects of topology and symmetry in light of different approaches to the anomalous non-Hermitian bulk-boundary correspondence and are of direct experimental relevance for mechanical, electrical, and photonic systems.

Aspects of higher spin symmetry in flat space

Aspects of higher spin symmetry in flat space

The Iranian enigmatic endemic Salvia majdae (Lamiaceae): its taxonomic status based on floral ontogeny

Since the first description of Salvia majdae (syn. Zhumeria majdae) in 1967, its taxonomic status has remained an enigma within Salvia senso lato due to its unusual characters, in particular the floral structure. Based on recent molecular phylogenetic data, two defensible opinions on its status have been proposed. Here, we studied the floral development of this species using scanning electron microscopy to resolve this ambiguity. The aspects of floral symmetry were also studied. Like species of Salvia and representative genera of Lamiaceae, the initiation sequence of sepals and stamens in S. majdae is unidirectional from adaxial to abaxial and reverse, respectively. The flowers show temporal overlaps in initiation of petals and stamens. However, in contrast, the bidirectional initiation of the petals in S. majdae is reversed, starting with the abaxial middle petal, followed by the two adaxial ones, and then finally ending with the two lateral ones. The filaments of the sterile stamens are elongated and exposed as staminodes thorough development. We conclude that subequal growth of the calyx lips, weak cochlear aestivation and bidirectional initiation of the petals and well‐developed sterile stamen primordia are responsible for the weak floral asymmetry in S. majdae. Based on these data, S. majdae shows significant differences from Salvia.

The Effect Of Local Flour Based Yudane On The Quality Of Shokupan Bread

This research aims to analyze the quality of shokupan bread using yudane with local ingredients including rice flour, glutinous rice flour, and mocaf flour. The research was conducted at the Pastry & Bakery Laboratory, Department of Culinary Education, Faculty of Engineering, Jakarta State University. The method used in this research was an experiment, analyzing the quality of shokupan bread with a 20% local yudane. The quality testing was performed by 5 trained panelists using a hedonic quality scale, including external factors such as volume, shape symmetry, uniformity of baking, and crust characteristics, as well as internal factors such as pores, crumb color, texture, aroma, taste, and chewing quality. The research results showed that among the external factors, the shokupan bread variant with mocaf-based yudane obtained the highest score in terms of volume with a value of 3.8. Meanwhile, in terms of crust color, the shokupan bread variant with glutinous rice flour-based yudane received the highest rating with a value of 3.8. On the aspect of shape symmetry, the shokupan bread variant with rice flour-based yudane obtained the highest score of 3.2. In terms of internal factors, the shokupan bread variant with glutinous rice flour-based yudane showed the highest ratings in terms of pores (3.4), crumb color (3.4), texture (3.4), taste (3.4), and chewing quality (4.0). However, the aspect of aroma received the highest rating in the shokupan bread variant with mocaf-based yudane with an average value of 3.2. In conclusion, based on the research results, shokupan bread made with glutinous rice flour-based yudane produced the best quality bread.

DUO-GAIT: A gait dataset for walking under dual-task and fatigue conditions with inertial measurement units

In recent years, there has been a growing interest in developing and evaluating gait analysis algorithms based on inertial measurement unit (IMU) data, which has important implications, including sports, assessment of diseases, and rehabilitation. Multi-tasking and physical fatigue are two relevant aspects of daily life gait monitoring, but there is a lack of publicly available datasets to support the development and testing of methods using a mobile IMU setup. We present a dataset consisting of 6-minute walks under single- (only walking) and dual-task (walking while performing a cognitive task) conditions in unfatigued and fatigued states from sixteen healthy adults. Especially, nine IMUs were placed on the head, chest, lower back, wrists, legs, and feet to record under each of the above-mentioned conditions. The dataset also includes a rich set of spatio-temporal gait parameters that capture the aspects of pace, symmetry, and variability, as well as additional study-related information to support further analysis. This dataset can serve as a foundation for future research on gait monitoring in free-living environments.

Parameterized transformations and truncation: When is the result a copula?

Our starting point are several general classes of real functions defined on the unit square satisfying some basic properties such as a boundary condition or several types of monotonicity and continuity. Applying to these functions some parameterized transformations and other constructions such as the transpose and flipping (which describe different aspects of symmetry) and truncation, we ask for conditions yielding (again) a bivariate copula. Some of these transformations are involutive (on one or more classes of functions), others are not even injective, and occasionally they induce additional properties, yielding, e.g., a (quasi-)copula. For several typical scenarios we identify the (not necessarily convex) sets of parameters leading to a copula and conditions imposing a minimal set of parameters.

Flat band separation and robust spin Berry curvature in bilayer kagome metals

AbstractKagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV6Sn6 kagome family (where X is a rare-earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin–orbit coupling gaps. These states would carry a finite spin Berry curvature, and topological surface states. Here we investigate the spin and electronic structure of the XV6Sn6 kagome family. We obtain evidence for a finite spin Berry curvature contribution at the centre of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin–orbit coupling. In addition, the spin Berry curvature is further investigated in the charge density wave regime of ScV6Sn6 and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle-resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin Berry curvature of topological kagome metals and helps to define its spectroscopic fingerprint.

Design of Unilateral Complete Presurgical Nasoalveolar Molding (PNAM) Corrector Based on Feature Points Extraction of Complex 3D Surface

Cleft lip and palate is a congenital maxillofacial deformity. Unilateral complete cleft lip and palate is one of the most common clinical types. Nasal alveolar molding (PNAM) is a recognized strategy for the treatment of cleft lip and palate. However, the current design of PNAM devices mainly relies on the subjective experience of doctors. The purpose of this paper is to describe the design and manufacture of a new computer-aided design appliance, which can be applied to the presurgical nasoalveolar molding of unilateral complete cleft lip and palate, eliminate individual differences, and improve production efficiency. In this paper, seven feature points on the healthy side and the affected side are extracted by the method of Gaussian curvature and ridge line extraction, and the healthy side rotation and built-in model are designed by using these seven feature points, which can quickly generate eight treatment stages of PNAM. The correction effects of the PNAM appliance designed in this paper were compared with the original maxillary model and the clinical PNAM appliance (hand-made by subjective experience) from the aspects of alveolar fissure width and symmetry. The PNAM appliance designed in this paper can effectively improve the symmetry of patients with unilateral complete cleft lip and palate (morphological similarity: t = 3.250, p ≤ 0.01; length similarity: t = 1.559, p = 0.150) and reduce the width of alveolar cleft (t = 8.330, p < 0.01). This can fully achieve the therapeutic effect of PNAM appliances prepared by experienced doctors and is more efficient. The method based on complex 3D surface feature point extraction can provide the basis for the design and evaluation of a unilateral complete PNAM correction model, improve the design and production efficiency of unilateral complete cleft lip and palate appliance, eliminate the design problems caused by individual differences, and reduce the burden of doctors.

Aspects of chiral symmetry in QCD at T=128 MeV

We investigate several aspects of chiral symmetry in QCD at a temperature of $T=128\text{ }\text{ }\mathrm{MeV}$. The study is based on a $24\ifmmode\times\else\texttimes\fi{}9{6}^{3}$ lattice-QCD ensemble with $\mathrm{O}(a)$-improved Wilson quarks and physical up, down and strange quark masses. The pion quasiparticle turns out to be significantly lighter than the zero-temperature pion mass, even though the corresponding static correlation length is shorter. We perform a quantitative comparison of our findings to predictions of chiral perturbation theory. Among several order parameters for chiral symmetry restoration, we compute the difference of the vector- and axial-vector time-dependent correlators and find it to be reduced by a factor $\ensuremath{\sim}2/3$ as compared to its vacuum counterpart.

Pole-skipping of holographic correlators: aspects of gauge symmetry and generalizations

In the framework of anti-de Sitter space/conformal field theory (AdS/CFT), we study the pole-skipping phenomenon of the holographic correlators of boundary operators. We explore the locations of the pole-skipping points case by case with the U(1)-gauged form models in the asymptotic AdS bulk of finite temperature. In general, in different cases all the points are located at the Matsubara frequencies with corresponding wave vectors dispersed in the momentum space, displaying different types of patterns. Specifically, in the massless cases with U(1) symmetry, the wave vectors of the pole-skipping points have a form-number dependence, and a trans-mode equivalence in the dual fields is found in correspondence with electromagnetic duality. In the massive cases with explicit symmetry breaking, the points degenerate to be independent of the form number. We expect in such kind of pole-skipping properties implications of distinctive physics in the chaotic systems. These properties are further examined by higher-order computation, which provides a more complete pole-skipping picture. Our near-horizon computation is verified with the double-trace method especially in the example of 2-form where there is dimension-dependent boundary divergence. We illustrate in these cases that the pole-skipping properties of the holographic correlators are determined by the IR physics, consistent with the ordinary cases in previous studies.

Extinction and Ergodic Stationary Distribution of COVID-19 Epidemic Model with Vaccination Effects

Human society always wants a safe environment from pollution and infectious diseases, such as COVID-19, etc. To control COVID-19, we have started the big effort for the discovery of a vaccination of COVID-19. Several biological problems have the aspects of symmetry, and this theory has many applications in explaining the dynamics of biological models. In this research article, we developed the stochastic COVID-19 mathematical model, along with the inclusion of a vaccination term, and studied the dynamics of the disease through the theory of symmetric dynamics and ergodic stationary distribution. The basic reproduction number is evaluated using the equilibrium points of the proposed model. For well-posedness, we also test the given problem for the existence and uniqueness of a non-negative solution. The necessary conditions for eradicating the disease are also analyzed along with the stationary distribution of the proposed model. For the verification of the obtained result, simulations of the model are performed.

Dibaryon resonances and short-range NN interaction* *The work has been partially supported by RFBR, grants Nos. 19-02-00011 and 19-02-00014. M.N.P. also appreciates support from the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”

The dibaryon concept for nuclear force is presented, assuming that the attraction between nucleons at medium distances is mainly due to the s-channel exchange of an intermediate six-quark (dibaryon) state. To construct the respective NN interaction model, a microscopic six-quark description of the NN system is used, in which symmetry aspects play a special role. It is shown that the NN interaction in all important partial waves can be described by the superposition of long-range t-channel one-pion exchange and s-channel exchange by an intermediate dibaryon. The model developed in this study provides a good description of both elastic phase shifts and inelasticities of NN scattering in all S, P, D, and F partial waves at energies from zero to 600–800 MeV and even higher. The parameters of the intermediate six-quark states, corresponding to the best fit of NN scattering data, are found to be consistent with the parameters of the known dibaryon resonances in those NN partial configurations, where their existence has been experimentally confirmed. Predictions for new dibaryon states are given as well.