Search Results (1,380)

An important goal in cardiology and other fields is to identify and control dynamic spiral wave patterns in reaction–diffusion partial differential equations. This research focuses on the Barkley model. The spiral wave motion is controlled and suppressed within the Euclidean group rather than through Euclidean symmetry by applying a controller equation. The eigenfunctions associated with the left eigenspace of the adjoint linear equation can be used to characterize the drift or movement of the spiral wave tip trajectory when the system is perturbed. These eigenfunctions provide details regarding how the spiral wave reacts to disruptions. Perturbations to the Barkley system are examined by applying control functions and calculating the principle eigenvalue numerically. The left eigenfunctions of the Barkley equation are determined by solving the left problem associated with the $2\mathrm{D}$ Barkley equation and a $1\mathrm{D}$ dynamical controller. In addition, the control function can be used to suppress the periodic and meandering regimes of the system. In this work, the focus is on the periodic regime. Full article

In this work, it is shown that, based on the linear analysis, as long as a theory of gravity is diffeomorphism invariant and possesses the tensor degrees of freedom propagating at a constant, isotropic speed without dispersion, its asymptotic symmetry group of an isolated system contains the (extended/generalized) Bondi–Metzner–Sachs group. These asymptotic symmetries preserve the causal structure of the tensor degrees of freedom. They possess the displacement, spin and center-of-mass memory effects. These effects depend on the asymptotic shear tensor. The displacement memory effect is the vacuum transition and parameterized by a supertranslation transformation. All of these hold even when the Lorentz symmetry is broken by a special timelike direction. Full article

Dynamic mobilization exercises (DME) are an effective strategy to prevent musculoskeletal injuries and promote back health in sport horses. Previous studies focused mainly on multifidus muscle cross-sectional area, with limited data on locomotion and adaptation timing. This study evaluated locomotor changes using accelerometry, over 8 weeks of DME application in 14 sedentary horses: a DME group (n = 8) performing 10 different DME (3 neck flexions, 1 neck extension and 3 lateral bending exercises to each side), 5 repetitions of each DME per session, 3 sessions/week, and a control group (n = 6), that continued with their daily routine activities without any other training. During the study period, all horses were housed in medium-sized paddocks. Accelerometric measurements were performed at walk and trot before intervention, 2 h and 24 h after a DME session, and at 2, 4, 6, and 8 weeks. The DME group showed significant increases in dorsoventral displacement and dorsoventral and mediolateral activities from week 4, at both walk and trot, which then stabilized. Longitudinal activity increased from week 2 on trot and from week 4 at walk. Locomotor symmetry and stride length improved at week 6, while stride frequency decreased at week 8; velocity remained unchanged. These findings indicate that DME enhances dorsoventral, mediolateral and longitudinal activities, producing longer, more symmetrical strides. Overall, DME appears to promote more symmetrical movement patterns. Full article

Practical problems often drive the development of new statistical methods by presenting real-world challenges. Testing the homogeneity of n independent Poisson means when only one observation per population is available is considered in this paper. This scenario is common in fields where limited data from multiple sources must be analyzed to determine whether different groups share the same underlying event rate or mean. These settings often exhibit underlying structural or spatial symmetries that influence statistical behavior. Traditional methods that rely on large sample sizes are not applicable. Hence, it is crucial to develop techniques tailored to the constraints of single observations. Under the null hypothesis, with large n and a fixed common mean $\lambda$, the likelihood ratio test statistic (LRTS) is shown to be asymptotically normally distributed, with the mean and variance being approximated by a truncation method and a parametric bootstrap method. Moreover, with fixed n and large $\lambda$, under the null hypothesis, the LRTS is shown to be asymptotically distributed as a chi-square with $n-1$ degrees of freedom. The Bartlett correction method is applied to improve the accuracy of the asymptotic distribution of the LRTS. We highlight the practical relevance of the proposed method through applications to wildfire and radioactive event data, where correlated observations and sparse sampling are common. Simulation studies further demonstrate the accuracy and robustness of the test under various scenarios, making it well-suited for modern applications in environmental science and risk assessment. Full article

Symmetry is a fundamental principle in mathematics, physics, and biology, where it governs structure and invariance. Classical symmetry analysis focuses on exact group-theoretic descriptions, but rarely addresses how robust a symmetric configuration is to perturbations. In this work, we introduce a probabilistic framework for quantifying the stability of finite point-set symmetries under random deletions. Specifically, given a finite set of points with a prescribed nontrivial symmetry group, we define the probability $P_N$ that removing N points reduces the symmetry to the trivial group $C_1$. The complementary quantity $S_N=1-P_N$ serves as a measure of symmetry stability, providing a robustness profile of the configuration. We calculate $S_N$ explicitly for representative families of symmetric point sets, including linear arrays, polygons, polyhedra, directed necklace of points, and crystallographic unit cells. Our results demonstrate unexpected behaviors: the regular hexagon loses symmetry with a probability of 0.6 under the removal of three vertices, while cubes and tetrahedra exhibit the maximal robustness ($S_N=1$) for all admissible N. We further introduce a Shannon entropy of symmetry stability, which quantifies the overall uncertainty of symmetry breaking across all deletion sizes. This framework extends classical symmetry studies by incorporating randomness, linking group theory with probabilistic combinatorics, and suggesting applications ranging from crystallography to defect tolerance in physical systems. Full article

Multiple-Q magnetic states encompass a broad class of noncollinear and noncoplanar spin textures generated by the superposition of spin density waves. In this study, we theoretically explore the emergence of vortex crystals formed by multiple-Q spin density waves on a two-dimensional triangular lattice with $D_{3\mathrm{h}}$ point group symmetry. Using simulated annealing applied to an effective spin model, we demonstrate that the synergy among the easy-plane single-ion anisotropy, the biquadratic interaction, and the out-of-plane Dzyaloshinsky–Moriya interaction defined in momentum space can give rise to a variety of double-Q and triple-Q vortex crystals. We further examine the role of easy-plane single-ion anisotropy in triple-Q vortex crystals and show that weakening the anisotropy drives topological transitions into skyrmion crystals with skyrmion numbers $\pm 1$ and $\pm 2$. The influence of an external magnetic field is also analyzed, revealing a field-induced phase transition from vortex crystals to single-Q conical spirals. These findings highlight the crucial role of out-of-plane Dzyaloshinskii–Moriya interactions in stabilizing unconventional vortex crystals, which cannot be realized in systems with purely polar or chiral symmetries. Full article

We study unconventional multipole moments arising from noncollinear magnetic structures within an augmented framework encompassing electric, magnetic, magnetic toroidal, and electric toroidal multipoles. Employing a tight-binding model for an s-p hybridized orbital system, we analyze two spiral magnetic textures and classify the resulting multipoles according to magnetic point group symmetry. Different spiral wave types, such as cycloidal and proper-screw forms, activate distinct multipole components, with odd-parity multipoles emerging from local s-p parity mixing induced by magnetically driven inversion-symmetry breaking. Calculated multipole structure factors reveal finite-q peaks originating from higher-order magnetic-dipole-scattering processes and their characteristic couplings between Fourier components of the magnetic dipole texture. Our results demonstrate that magnetic ordering can generate parity-mixed states without intrinsic structural inversion asymmetry, offering new pathways to realize cross-correlation phenomena in functional magnetic materials. Full article

This cross-sectional study analyzed the lower limb (LL) behavior in terms of gait asymmetry and joints’ kinematic parameters, comparing people with multiple sclerosis (pwMS) and unaffected individuals. Methods: Data from 15 patients, EDSS ≤ 4.5, and 15 healthy control volunteers were gathered. The VICON Motion Capture System (14 infrared cameras), NEXUS software, Plug-in–Gait skeleton model and reflective markers were used to collect data for each subject during five gait cycles on a plane surface. Biomechanical analysis included evaluation of LL joints’ range of motion (ROM) bilaterally, as well as movement symmetry. Results: Comparative biomechanical analysis revealed a hierarchy of vulnerability between the groups: the ankle is the most affected joint in pwMS (p = 0.008–0.014), the knee is moderately affected (p = 0.015 in swing phase), and the hip is the least affected (p > 0.05 in all phases). The swing phase showed the most significant left–right asymmetry impairment, as reflected by root mean square error (RMSE) values: swing-phase RMSE = 9.306 ± 4.635 (higher and more variable) versus stance-phase RMSE = 6.363 ± 2.306 (lower and more consistent). Conclusions: MS does not affect the joints structurally; rather, it eliminates the ability to differentiate the fine-tuning control between them. The absence of significant left–right joint asymmetry differences during complete gait cycle indicates dysfunction in the global motor control. Full article

Cellular organisms store heritable information in two forms, genetic and epigenetic, the latter being largely dependent on cytosine methylation (5mC). Chargaff’s Second Parity Rule (CSPR) describes the nucleotide composition of cellular genomes in terms of intra-strand DNA symmetry. However, it remains unknown whether DNA methylation patterns display intra-strand DNA symmetry. Computational analysis was conducted of the DNA methylation patterns observed in human cell lines and in tissue samples from healthy donors. Analysis of 5mC marks in mutually reverse-complementary pairs of short oligomers, containing CpG dinucleotide in the middle, revealed deviations from CSPR and methylation asymmetry that can be observed for two non-overlapping mirror groups defined by CpG methylation values. Deviations from CSPR, together with combinatorial probabilities of pattern distributions and computer simulations, highlight the non-random nature of methylation processes and enabled us to identify specific cell types as outliers. Further analysis revealed a compensatory methylation asymmetry that reduces deviations from intra-strand symmetry and implies the existence of strand-specific methylation during cell differentiation. Among six pairs of reverse-complementary tetranucleotides, four pairs with specific sequence motifs display pronounced methylation asymmetry. This mirror asymmetry may be associated with chromosome folding and the formation of a complex three-dimensional landscape. Full article

In this paper we analyze complex systems dynamics using a multifractal framework derived from Scale Relativity Theory (SRT). By extending classical differential geometry to accommodate non-differentiable, scale-dependent behaviors, we formulate Schrödinger-type equations that describe multifractal geodesics. These equations reveal deep analogies between quantum mechanics and macroscopic complex dynamics. A key feature of this approach is the identification of hidden symmetries governed by multifractal analogs of classical groups, particularly the SL(2ℝ) group. These symmetries help explain universal dynamic behaviors such as double period dynamics, damped dynamics, modulated dynamics, or chaotic dynamics. The resulting framework offers a unified geometric and algebraic perspective on the emergence of order within complex systems, highlighting the fundamental role of fractality and scale covariance in nature. Full article

The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces in Petrov) in the presence of electromagnetic fields invariant with respect to the action of the group of space motions is summarized. A new classification method is used, common to all homogeneous zero spaces of Petrov. The method is based on the use of canonical reper vectors and on the use of a new approach to the systematization of solutions. The classification results are presented in a form more convenient for further use. Using the previously made refinement of the classification of Petrov spaces, the classification of exact solutions of Maxwell vacuum equations for spaces with the group of motions $G_3\left(VIII\right)$ is completed. Full article

This study investigates Weibull distribution modeling for data under grouped observations. Two data grouping methods (equal-width and optimal) were compared for estimating parameters of the Weibull distribution using maximum likelihood estimation (MLE) in each case. Methodologically, our contribution is twofold: First, we derive the correct Fisher information matrix for grouped data in the two-parameter Weibull and use it to compute optimal interval boundaries. Second, we derive maximum likelihood estimators for data grouped under these optimal intervals. The fit of the assumed distributions was evaluated using chi-squared goodness-of-fit tests. We also calculated Asymptotic Relative Efficiency (ARE) to compare the precision of parameter estimates across different grouping approaches. Optimal boundaries yielded systematically higher ARE than equal-width grouping in 100% of comparisons for the shape parameter $c$. Gains for the scale parameter $b$ were smaller and occurred in about 62% of cases. Optimal grouping also produced generally higher chi-squared $\left({\chi }^2\right)$ goodness-of-fit p-values than equal-width grouping, indicating a better fit. From a symmetry standpoint, the Weibull distribution is inherently asymmetric, with the degree of asymmetry governed by the shape parameter $c$. We show that the choice of grouping affects the estimate of $c$ and, thus, the inferred skewness, further explaining why optimally designed intervals yield both higher precision and a more faithful representation of failure behavior. Full article

The citrate–nitrate method was employed to synthesize the magnesium chromite (MgCr₂O₄) spinel, followed by calcination at 700 °C for 3 h. The synthesized compound was analyzed using techniques including powder XRD, SEM-EDAX, FTIR, UV-DRS, and LCR Meter. The structural analysis was conducted using an X-ray diffractometer, which revealed the formation of the cubic crystal symmetry of the sample with the corresponding Fd-3 m space group. The average crystallite size of the sample was calculated around 15.38 nm. Using tetrahedral and octahedral positions, the lattice vibrations of the associated chemical bonds were identified using Fourier transform infrared (FTIR) spectroscopy. SEM (scanning electron microscopy) micrographs showed that the spherical nature of the particles and the constituent particles were between 10 and 40 nm in size. The optical bandgap value was evaluated using Tauc’s plot. Pellets of the powdered sample were prepared for determining the dielectric aspects, such as the dielectric constant (ε′) and tangent loss (tanδ), in the frequency range of 10 Hz–8 MHz at room temperature. The charge transport mechanism was explored from the complex impedance spectroscopy study. The obtained results indicate that magnesium chromite may be a potential candidate in the fabrication of sensors, micro-electronic devices, etc. Full article

Crawling is an almost universal stage of locomotor development in infants; however, it is difficult to quantify using typical motion analysis techniques. The crawling stage therefore has underutilized potential to assess development and detect deviations or abnormalities. This study measured longitudinal weightbearing asymmetries in typically developing (TD) crawling children and compared this population to children with limb loss or limb differences (LLD) using a pressure-sensing mat. The LLD group bore significantly more weight using their arms vs. their legs than the TD group (p < 0.001), but even in cases of unilateral limb loss, bilateral weightbearing symmetry was similar to TD, controlling for body mass and age (p = 0.570). As children in the TD group developed and gained body mass, their weight shifted significantly to their left side (η² = 0.050) and away from their arms and toward their legs (η² = 0.255). The results provide insight into the biomechanical development of TD infant crawling, and the ways in which an atypically developing population manages weightbearing during crawling. The establishment of symmetry data will be useful, as crawling can serve as an opportunity for earlier detection of neuromotor conditions such as cerebral palsy. Furthermore, insight into the crawling patterns of children with limb loss and limb difference can inform prosthetic prescription and the need to consider a missing weight shift toward the legs as children develop. Full article

Collective intelligence systems have demonstrated considerable potential in dynamic adversarial environments due to their distributed, self-organizing, and highly robust characteristics. The crux of an efficacious defense lies in establishing a dynamically adjustable, non-uniform defense structure through the differentiation of internal member roles. The proposed model is a heterogeneous-swarm adaptive-defense model based on symmetry breaking and skin effect. The model draws from symmetry theory, incorporating the skin effect of conductor currents and the hierarchical structural characteristics of biological groups, such as starlings. The construction of a radially symmetric dynamic hierarchical swarm structure is achieved by assigning different types of individuals with distinct safety radius preferences. Secondly, the principle of symmetry breaking is employed to establish a phase transition mechanism from radial symmetry to directed defense, thereby achieving an adaptive barrier formation algorithm. This algorithm enables the defensive group to assess threat characteristics and dynamically adjust defense resource deployment. The simulation results obtained from this study validate the phase transition process from continuous rotational symmetry to directed defense. This process demonstrates the barrier formation mechanism and ensures the safety and integrity of the core units within the group. Full article