Search Results (102)

I address the challenge of extracting reliable insights from large datasets using a simplified model that illustrates how hierarchical classification can distort outcomes. The model consists of discrete pixels labeled red, blue, or white. Red and blue indicate distinct properties, while white represents unclassified or ambiguous data. A macro-color is assigned only if one color holds a strict majority among the pixels. Otherwise, the aggregate is labeled white, reflecting uncertainty. This setup mimics a percolation threshold at fifty percent. Assuming that directly accessing the various proportions from the data of colors is infeasible, I implement a hierarchical coarse-graining procedure. Elements (first pixels, then aggregates) are recursively grouped and reclassified via local majority rules, ultimately producing a single super-aggregate for which the color represents the inferred macro-property of the collection of pixels as a whole. Analytical results supported by simulations show that the process introduces additional white aggregates beyond white pixels, which could be present initially; these arise from groups lacking a clear majority, requiring arbitrary symmetry-breaking decisions to attribute a color to them. While each local resolution may appear minor and inconsequential, their repetitions introduce a growing systematic bias. Even with complete data, unavoidable asymmetries in local rules are shown to skew outcomes. This study highlights a critical limitation of recursive data reduction. Insight extraction is shaped not only by data quality but also by how local ambiguity is handled, resulting in built-in biases. Thus, the related flaws are not due to the data but to structural choices made during local aggregations. Although based on a simple model, these findings expose a high likelihood of inherent flaws in widely used hierarchical classification techniques. Full article

This paper addresses the problem of optimizing obesity, which has been a challenging issue in the last decade based on recent data revealed in 2024 by the World Health Organization (WHO). The current work introduces a new mathematical model of the dynamics of weight over time with embedded control parameters to optimize the number of obese, overweight, and comorbidity populations. The mathematical formulation of the model is developed under certain sufficient conditions that guarantee the positivity and boundedness of solutions over time. The model structure exhibits inherent symmetry in population group transitions, particularly around the equilibrium state, which allows the application of analytical tools such as the Routh–Hurwitz and Metzler criteria. Then, the analysis of local and global stability of the obesity-free equilibrium state is discussed based on these criteria. Based on the Pontryagin maximum principle (PMP), the deviation from the obesity-free equilibrium state is controlled. The model’s effectiveness is demonstrated through simulation using the Forward–Backward Sweeping algorithm with parameters derived from recent research in human health. Incorporating symmetry considerations in the model enhances the understanding of system behavior and supports balanced intervention strategies. Results suggest that the model can effectively inform strategies to mitigate obesity prevalence and associated health risks. Full article

Vanillin photoinduced deprotonation was evaluated and analyzed. Vibronic states and transitions were computationally investigated. Optimizations and vertical electron transitions in the gas phase and with the continuum solvation model were computed using the time-dependent density functional theory. Static absorption and emission (photostatic optical) spectra were statistically averaged over the excited instantaneous molecular conformers fluctuating on quantum–classical molecular dynamic trajectories. Photostatic optical spectra were generated using the hybrid quantum–classical molecular dynamics for explicit solvent models. Conical intersection searching and nonadiabatic molecular dynamics simulations defined potential energy surface propagations, intersections, dissipations, and dissociations. The procedure included mixed-reference spin–flip excitations for both procedures and trajectory surface hopping for photodynamics. Insignificant structural deformations vs. hydroxyl bond cleavage followed by deprotonation were demonstrated starting from different initial structural conditions, which included optimized, transition state, and several other important fluctuating configurations in various environments. Vanillin electronic structure changes were illustrated and analyzed at the key points on conical intersection and nonadiabatic molecular dynamics trajectories by investigating molecular orbital symmetry and electron density difference. The hydroxyl group decomposed on transition to a σ-molecular orbital localized on the elongated O–H bond. Full article

Reliable and accurate docking remains a fundamental challenge for autonomous mobile robots (AMRs) operating in complex industrial environments with dynamic lighting, motion blur, and occlusion. This study proposes a novel multi-sensor fusion-based docking framework that significantly enhances robustness and precision by integrating YOLOv8-based AprilTag detection, depth-aided 3D localization, and LiDAR-based orientation correction. A key contribution of this work is the construction of a custom AprilTag dataset featuring real-world visual disturbances, enabling the YOLOv8 model to achieve high-accuracy detection and ID classification under challenging conditions. To ensure precise spatial localization, 2D visual tag coordinates are fused with depth data to compute 3D positions in the robot’s frame. A LiDAR group-symmetry mechanism estimates heading deviation, which is combined with visual feedback in a hybrid PID controller to correct angular errors. A finite-state machine governs the docking sequence, including detection, approach, yaw alignment, and final engagement. Simulation and experimental results demonstrate that the proposed system achieves higher docking success rates and improved pose accuracy under various challenging conditions compared to traditional vision- or LiDAR-only approaches. Full article

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involution $\tau$ on X and a Cartan involution $\theta$ of G, producing an involution $\sigma ={\theta }_{\ast }\circ {\tau }_{\ast }$. These fixed points are shown to correspond to stable $G_{\mathbb{R}}$-bundles over the real curve $(X_{\tau },\tau )$, where $G_{\mathbb{R}}$ is the real form associated with $\theta$. The fixed point set ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ consists of exactly $2^r$ connected components, each a smooth complex manifold of dimension ${\displaystyle \frac{(g-1)\dim G}{2}}$, where r is the rank of the fundamental group of the compact form of G. A cohomological obstruction in $H^2(X_{\tau },{\pi }_1\left(G_{\mathbb{R}}\right))$ characterizes which bundles are fixed. A key result establishes a derived equivalence between coherent sheaves on ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ and on the fixed point set of the dual involution on the moduli space of $G^{\vee }$-local systems, where $G^{\vee }$ denotes the Langlands dual of G. This provides an extension of the Geometric Langlands Correspondence to settings with involutions. An application to the Chern–Simons theory on real curves interprets ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ as a $(B,B,B)$-brane, mirror to an $(A,A,A)$-brane in the Hitchin system, revealing new links between real structures, quantization, and mirror symmetry. Full article

In transducer arrays, symmetric grouping of identical elements is often employed to achieve uniform array performance. Such arrays can possess high coupling, preventing localized operation of individual transducers. This paper provides insight into how forced vibration localizes in a symmetric system of coupled oscillators. We use a simple lumped-parameter model of highly coupled oscillators derived from ultrasound transducer arrays. Forced vibration localization can be shown to be inversely related to the coupling strength between the oscillators. The results demonstrate how forced vibration in a coupled symmetric system may localize through modal superposition and how it may be tuned via the spacing of natural frequencies. Breaking the system’s symmetry leads to normal mode localization, which can be shown to affect the forced vibration response. The results reveal a variation in the system’s resonance frequency, attributed to curve veering effects. Full article

A mononuclear complex [Dy(phenN₆)(HL′)₂]PF₆·CH₂Cl₂ (H₂L′ = R/S-1,1′-binaphthyl-2,2′-diphenol) with local D_6h symmetry was synthesized. Structural determination shows that Dy³⁺ was encapsulated within the coordination cavity of the neutral hexaaza macrocyclic ligand phenN₆, forming a non-planar coordination environment. The axial positions are occupied by two phenoxy groups of binaphthol in the trans form. The local geometry of Dy³⁺ closely resembles a regular hexagonal bipyramid D_6h configuration. The axial Dy-O_phenoxy distances are 2.189(5) and 2.145(5) Å, respectively, while the Dy-N bond lengths in the equatorial plane are in the range of 2.524(7)–2.717(5) Å. The axial O_phthalmoxy-Dy-O_phthalmoxy bond angle is 162.91(17)°, which deviates from the ideal linearity. Under the excitation at 320 nm, the complex exhibits a characteristic emission peak at 360 nm, corresponding to the naphthalene ring. The AC susceptibility measurements under an applied DC field of 1800 Oe show distinct temperature-dependent and frequency-dependent AC magnetic susceptibility, typical of single-molecule magnetic behavior. The Cole–Cole plot in the temperature range of 6.0–28.0 K was fitted using a model incorporating Orbach and Raman relaxation mechanisms, giving an effective energy barrier of U_eff = 300.2 K. Theoretical calculations on complex 1 reveal that the magnetization relaxation proceeds through the first excited Kramers doublets with a calculated magnetization blocking barrier of 404.1 cm⁻¹ (581.4 K). Full article

The particle swarm optimization algorithm, known for its swift convergence and minimal parameters, is widely used to solve various complex optimization problems. Despite its merits, it encounters challenges such as susceptibility to premature convergence and reduced search capability in later stages. To improve the optimization performance of the algorithm, this study designs an advanced adaptive Group Learning Particle Swarm Optimization (GLPSO) algorithm based on the concept of symmetry. Firstly, a new coefficient is proposed to enable rapid convergence of the algorithm, allowing the population to quickly converge to the optimal position. By adopting a group learning mechanism, the optimal particles in each group are learned during particle updates; this enhances the diversity of particle learning in the algorithm, improving its global search capability. A novel adaptive perturbation rule is proposed, enabling particles to perform perturbations in a more suitable manner, thereby enhancing the population’s ability to escape local optima. GLPSO is compared with several advanced algorithms on internationally recognized high-dimensional benchmark functions and is also applied to some constrained engineering problems. The results indicate that GLPSO outperforms other improved algorithms on most test problems and provides competitive and high-quality solutions for engineering problems. Overall, GLPSO enhances its optimization capability while maintaining robustness. Full article

We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the hidden symmetry into an explicit one. The method is able to learn the pixel translation operator from a dataset with only an approximate translation symmetry and can learn quite different types of symmetries that are not apparent to the naked eye. The method is based on the formulation of an information-theoretic loss function that measures both the degree of symmetry of a dataset under a candidate symmetry generator and a proposed notion of locality of the samples, which is coupled to symmetry. We demonstrate that this coupling between symmetry and locality, together with an optimization technique developed for entropy estimation, results in a stable system that provides reproducible results. Full article

This study explores the integration of a custom-designed pneumatic spring into a car-seat cushion and its interaction with a simplified human body model using the Finite Element Method (FEM). A 3D half-symmetry FEM framework, developed from experimental data, ensured computational efficiency and convergence. This research bridged experimental and numerical approaches by analyzing the contact pressure distributions between a seat cushion and a volunteer with representative biometric characteristics. The model incorporated two material groups: (1) human body components (bones and muscles) and (2) seat cushion materials (polyurethane foam, latex, and fabric tape). Mechanical properties were obtained from both the literature and experiments, and simulations were conducted using MSC.Marc software under realistic boundary and initial conditions. The simulation results exhibited strong agreement with experimental data, validating the model’s reliability in predicting contact pressure distribution and optimizing seat cushion designs. Contrary to the conventional notion that uniformly distributed contact pressure inherently enhances comfort, this study emphasizes that the precise localization of pressure plays a crucial role in static and long-term seating ergonomics. Both experimental and simulation results demonstrated that modulating the pneumatic spring’s internal pressure from 0 kPa to 25 kPa altered peak contact pressure by approximately 3.5 kPa (around 20%), significantly influencing pressure redistribution and mitigating high-pressure zones. By validating this FEM-based approach, this study reduces dependence on physical prototyping, lowering design costs, and accelerating the development of ergonomically optimized seating solutions. The findings contribute to a deeper understanding of human–seat interactions, offering a foundation for next-generation automotive seating innovations that enhance comfort, fatigue reduction, and adaptive pressure control. Full article

We herein present a comprehensive investigation of the eudialyte group minerals from the nepheline syenites of Rouma Island in the Los Archipelago, Conakry region, Guinea. Two distinct mineral phases were identified: an oneillite-like phase, associated with the agpaitic rock suite, and, for the first time in this locality, kentbrooksite, occurring in pegmatites. The oneillite-like phase crystallizes in the trigonal system (space group R3), with unit cell parameters a = 14.1489(2) Å, c = 30.1283(5) Å and an idealized crystal chemical formula of Na₁₅(Mn,REE)₃(Ca,Mn)₃(Fe,Mn)₃Zr₃(Zr,Si,Al,Nb,Ti)₁ (Si₂₅O₇₃)(O,OH,H₂O)₃(OH,Cl,F)₂. Kentbrooksite also exhibits trigonal symmetry (space group R3m), with unit cell parameters a = 14.2037(3) Å c = 30.1507(9) Å and an idealized formula of (Na,REE)₁₅(Ca,Mn)₆(Mn,Fe)₃Zr₃(Nb,Si)₁(Si₂₅O₇₃)(O,OH,H₂O)₃(F,Cl,OH)₂. Compared to the oneillite-like phase, kentbrooksite is markedly enriched in Mn and rare earth elements (REE). This geochemical distinction aligns with the progressive mineralogical evolution of the system, transitioning from the miaskitic to agpaitic suite (oneillite-like phase) and subsequently to pegmatites (kentbrooksite). These findings are consistent with the broader-scale observations regarding the syenite ring structure of the Los Archipelago. Full article

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory. Full article

The computational complexity of existing multi-symbol detection (MSD) algorithms grows exponentially as the observation intervals increase, resulting in difficulties in algorithm implementation for detecting pulse code modulation/frequency modulation (PCM/FM) signals, especially for multi-channel signals. To address the challenges, we proposed a low-complexity MSD algorithm based on the averaged matched filtering. The proposed algorithm groups the local reference signals based on the different importance levels of the middle and edge bits in the correlation operations and averages the edge bits, leading to a considerable decrease in matching branches. Furthermore, it leverages the phase symmetry, and the proposed algorithm retains half of the averaged local reference signals for the matching operation, thus further reducing the matching branches. The proposed algorithm reduces the storage of the local signals and correlation operations to one-eighth compared to the traditional MSD algorithm under different observation lengths. Additionally, based on the structure of multiplexed FIR filters, the proposed algorithm optimizes single-channel single-coefficient FIR filters into four-channel double-coefficient FIR filters, further reducing the hardware resource consumption by approximately 25%. The simulation results showed that the proposed algorithm achieved demodulation performance comparable to the traditional MSD algorithms while reducing the computational complexity by 87.5%. Compared to the decision-feedback MSD algorithm, it achieves higher demodulation gain with a 75% complexity reduction. The Field Programmable Gate Array (FPGA) platform implementation results showed that the proposed algorithm reduces hardware resource consumption by nearly 90% compared with the traditional algorithm, and the hardware demodulation performance loss is less than 1 dB compared with the simulation results. Full article

Spatial cognition, a critical component of human cognitive function, can be enhanced through targeted training, such as virtual reality (VR)-based interventions. Recent advances in electroencephalography (EEG)-based functional connectivity analysis have highlighted the importance of network topology features for understanding cognitive processes. In this paper, a framework based on a cross fuzzy entropy network graph (CFENG) is proposed to extract spatial cognitive EEG network topological features. This framework involves calculating the similarity and symmetry between EEG channels using cross fuzzy entropy, constructing weighted directed network graphs, transforming one-dimensional EEG signals into two-dimensional brain functional connectivity networks, and extracting both local and global topological features. The model’s performance is evaluated and interpreted using an XGBoost classifier. Experiments on an EEG dataset from group spatial cognitive training validated the CFENG model. In the Gamma band, the CFENG achieved 97.82% classification accuracy, outperforming existing methods. Notably, the asymmetrically distributed EEG channels Fp1, P8, and Cz contributed most to spatial cognitive signal classification. An analysis after 28 days of training revealed that specific VR games enhanced functional centrality in spatial cognition-related brain regions, reduced information flow path length, and altered information flow symmetry. These findings support the feasibility of VR-based spatial cognitive training from a brain functional connectivity perspective. Full article

Direct methods based on iterative projection algorithms can determine protein crystal structures directly from X-ray diffraction data without prior structural information. However, traditional direct methods often converge to local minima during electron density iteration, leading to reconstruction failure. Here, we present an enhanced direct method incorporating genetic algorithms for electron density modification in real space. The method features customized selection, crossover, and mutation strategies; premature convergence prevention; and efficient message passing interface (MPI) parallelization. We systematically tested the method on 15 protein structures from different space groups with diffraction resolutions of 1.35∼2.5 Å. The test cases included high-solvent-content structures, high-resolution structures with medium solvent content, and structures with low solvent content and non-crystallographic symmetry (NCS). Results showed that the enhanced method significantly improved success rates from below 30% to nearly 100%, with average phase errors reduced below 40°. The reconstructed electron density maps were of sufficient quality for automated model building. This method provides an effective alternative for solving structures that are difficult to predict accurately by AlphaFold3 or challenging to solve by molecular replacement and experimental phasing methods. The implementation is available on Github. Full article