Search Results (370)

Flat bands exhibit vanishing group velocity and marked sensitivity to lattice geometry, making them a useful setting for studying localization driven by destructive interference. In this work, electrical-circuit simulations are employed to investigate flat-band systems in one, two, and three dimensions. A one-dimensional two-band circuit is first considered, and its flat-band response is characterized through node-to-ground impedance spectra and steady-state voltage distributions. The analysis is then extended to two- and three-dimensional Lieb lattice circuits characterized by sublattice imbalance. In the two-dimensional Lieb circuit, the flat band touches the dispersive bands at a Dirac point, so hybridization with dispersive modes affects the observed localization. Under periodic boundary conditions, wave vector quantization also produces responses that depend on whether the number of unit cells is even or odd. By contrast, in the three-dimensional Lieb circuit, the flat band is spectrally isolated from the dispersive bands, allowing stronger spatial confinement and clearer sublattice selectivity. The one-dimensional, two-dimensional, and three-dimensional models therefore represent three different situations: a singular flat band, a flat band that touches dispersive bands, and a spectrally isolated flat band. Comparing these cases shows how different degeneracy conditions shape impedance responses and localization patterns in electrical circuit systems. At the flat band frequency, the localized voltage response can also be used to generate spatial patterns in both two-dimensional and three-dimensional circuits, pointing to a possible route for spatial mode control of compact localized states in electrical systems. Full article

Traditional visual Simultaneous Localization and Mapping (SLAM) systems achieve high accuracy in static environments. However, in indoor dynamic scenes with frequent object motions, the presence of moving objects severely violates the scene rigidity assumption, often leading to significant performance degradation and tracking instability. To explicitly address this challenge, this paper introduces LIG-SLAM, a resource-efficient visual SLAM solution that extends the ORB-SLAM3 architecture. By incorporating dynamic object perception and geometric constraints, the system achieves robust localization in dynamic indoor environments, while its inference efficiency is significantly enhanced through targeted optimization. Specifically, a YOLOv5-based instance segmentation network is employed to obtain pixel-level segmentation of dynamic regions. To mitigate the erroneous rejection of static feature points, epipolar geometric constraints are incorporated to improve the accuracy of dynamic feature selection. Furthermore, a RANSAC-based depth consistency check is adopted to further enhance accuracy and alleviate the effects of epipolar degeneracy. Unlike conventional semantic SLAM frameworks, the proposed system incorporates ONNX-based optimization, thereby accelerating inference and improving real-time performance. Empirical evaluations conducted on TUM dynamic datasets indicate that the developed approach surpasses ORB-SLAM3 by a substantial margin, achieving a reduction of over 90% in terms of the Absolute Trajectory Error (ATE). Compared with existing semantic SLAM approaches, it achieves improvements in both accuracy and real-time performance, particularly in challenging indoor dynamic scenarios. Full article

Adversarial perturbations measured by ${\mathsf{\ell }}_p$ norms do not reflect key structural constraints in tabular security data, including anisotropic geometry, feature dependence, and distributional plausibility. We introduce a composite attacker cost functional $C_{\mathrm{atk}}(\mathit{x},{\mathit{x}}^{\prime })=\tau max\{0,m\left({\mathit{x}}^{\prime }\right)\}+{\lambda }_1{\mathit{\delta }}^{\top }{\mathit{G}}_{\perp }^{\left(\gamma \right)}\left(\mathit{x}\right)\mathit{\delta }+\lambda {\displaystyle \sum _j}{\omega }_j|{\delta }_j|+{\lambda }_2{\mathit{\delta }}^{\top }{\mathit{L}}_H\mathit{\delta }+{\lambda }_3\left[log{\widehat{f}}_1^{\left(ϵ\right)}\left(\mathit{x}\right)-log{\widehat{f}}_1^{\left(ϵ\right)}\left({\mathit{x}}^{\prime }\right)\right]+{\displaystyle \sum _{j\in supp\left(\mathit{\delta }\right)}}{c}_j+\beta {\left|\mathcal{M}(supp\left(\mathit{\delta }\right))\right|}^{\nu },$ which integrates a spectrally truncated geometric term, a graph-based coherence penalty, a smooth copula density barrier, and a superlinear module-spread term. Under spectral degeneracy of the legitimate-class covariance, we establish nonnegativity under density dominance, exact zero self-cost, lower semicontinuity, and ${\lambda }_3{\kappa }_K$-weak convexity of the continuous component on compact convex sets, for both affine and ${\rho }_m$-weakly convex scoring functions. These properties yield existence of constrained minimizers. The continuous component is locally Lipschitz, whereas the full functional is not due to the support-counting term. A component feasibility result shows that each term eliminates a distinct class of degenerate perturbations. Limiting regimes and refined evasion cost bounds are derived. An empirical instantiation on PHIUSIIL indicates that perturbations with identical ${\mathsf{\ell }}_2$ norm can incur costs differing by an order of magnitude. Full article

Molecular diagnosis has advanced rapidly in neurogenetic disorders, yet translating genotype into patient-specific predictions of brain network dysfunction and progression remains limited. Virtual brain models provide a structured solution by embedding individual anatomy and connectomics into biophysical whole-brain simulations. The critical step is to position genetics not as a diagnostic label, but as a constructive input to model design. This review outlines a genetics-centered framework for virtual brain modeling. First, atlas-derived transcriptomic and cell-type maps can define region-specific molecular priors, constraining vulnerability or excitability parameters and reducing model degeneracy. Second, when reproducible genotype-linked network phenotypes exist, mutation groups can inform stratified initialization and progression regimes. Third, at the patient level, exome and CNV data—summarized as pathway burdens and, where appropriate, calibrated polygenic modifiers—can be translated into individualized priors or regularizers, provided that mapping rules are explicit and externally validated. By integrating genetics at multiple levels of evidence, virtual brain models gain mechanistic plausibility, improved calibration, and explicit uncertainty quantification. The most realistic impact over the next few years is likely to be improved stratification, progression-aware forecasting, and scenario-based decision support in rare neurogenetic diseases, especially where longitudinal cohort infrastructure and validated biomarker inputs are already available, rather than deterministic individual prediction. Full article

The dielectric response provides an integral description of polarization mechanisms across frequency ranges and constitutes a key physical basis for understanding ferroelectric behavior. Here, we systematically investigate the broadband dielectric response of Group-II metal oxide (BeO, MgO, CaO, ZnO, and CdO) monolayers using first-principles calculation. In the low-frequency regime, ionic polarization governs the dielectric response. A distinctive feature is the LO–TO degeneracy at the Γ point accompanied by a V-shaped nonanalytic LO phonon dispersion. d-state hybridization increases with the metal atomic number, resulting in higher Born effective charge, which works together with phonon softening, reduced mass and unit cell area to significantly strengthen the ionic dielectric contribution. The quasiparticle band gap decreases with the metal atomic number, driving redshifts of the dielectric function and wide band optical response from the deep-ultraviolet to the near-infrared. Particularly, CdO exhibits the strongest electronic polarization, with an optical dielectric constant of 2.68 and a static refractive index of 1.64. This work establishes a complete dielectric spectrum from ionic to electronic polarization, providing theoretical guidance for polarization engineering and design of two-dimensional ferroelectric devices. Full article

The Gielis superformula is a powerful parametric tool that generates an infinite variety of natural and organic curves and surfaces through a compact set of parameters. However, classical differential geometry has lacked a unified framework for analyzing their curvature, torsion, and intrinsic geometric properties. This study addresses this gap by developing a novel superelliptic geometric framework that integrates the superformula with the differential geometry of curves and surfaces. We define the superelliptic inner and cross products, the star derivative, and the superelliptic Frenet frame to extend Euclidean and Riemannian interpretations of curvature and torsion to a more flexible parametric structure. The framework provides a uniform geometric characterization of all Gielis curves and surfaces in an intrinsic sense with respect to the proposed superelliptic metric, rather than relying on their classical Euclidean parametric representations; singular cases (e.g., $n_1<2$), which correspond to non-smooth or corner-like behavior in the Euclidean setting due to degeneracies in the radial function $r\left(t\right)$, are regularized within this framework, since the induced metric maps such Gielis-type curves to intrinsically circular geometries with constant superelliptic curvature. This unifies the entire family under a common, robust foundation while preserving orthonormality and differentiability. This superelliptic approach offers a consistent and computationally tractable model that bridges mathematical abstraction with real-world morphology, with the superformula serving as a representative example of the framework’s broad generality for diverse geometric structures. The proposed theoretical framework is further supported by computational visualization, and all figures and numerical illustrations presented in this study were generated using MATLAB R2024a, ensuring a consistent implementation of the proposed superelliptic model. Full article

Multi-omics technologies enable parallel quantification of proteomic and metabolomic layers, yet enzyme abundance often shows weak or nonlinear correspondence under diverse biological conditions. This apparent discordance has been attributed to both technical limitations—such as dynamic range compression in LC-MS/MS, metabolite derivatization artifacts, and missing values in proteomic measurements—as well as intrinsic biological properties of metabolic network architecture. While technical factors contribute to cross-omic mismatch, accumulating evidence suggests that constraint-driven network behavior plays a major role in shaping this decoupling. Enzyme abundance constrains catalytic capacity; however, realized flux is selected within this capacity under distributed flux control, as formalized by flux control coefficients in metabolic control analysis, and is further modulated by enzyme kinetics (e.g., km and Vmax), post-translational modifications, substrate availability, and thermodynamic constraints. Metabolite pools, in turn, reflect the physicochemical state of the system, while specific metabolites can also act as regulatory effectors that modulate enzymatic activity and cellular signaling. Because metabolic networks are underdetermined, multiple flux configurations can satisfy identical protein abundance and metabolite concentration data. Static cross-layer correlation is therefore insufficient for mechanistic inference. We synthesize biological mechanisms—including post-translational regulation, allostery, thermodynamic buffering, spatial compartmentalization, feedback amplification, and redox gating—that weaken linear abundance–metabolite expectations. We further outline a constraint-based interpretation framework in which proteomics imposes capacity bounds, metabolomics informs reaction directionality and metabolite pool constraints, and flux-informed approaches reduce solution degeneracy by providing additional information on pathway activity. Moving beyond correlation requires integrating perturbation, temporal resolution, and constraint-aware modeling. Proteome–metabolome discordance should therefore be interpreted not as inconsistency, but as indicative of constraint-driven state selection within high-dimensional biochemical systems. Full article

The temporal effects associated with surface plasmon polaritons (SPP) in a slab of conductive quantum material (metal, graphene, or semiconductor) are described as a quantum plasma. Exchange potentials associated with quantum degeneracy are included. We derive a new dispersion relation of SPP modes in a quantum plasma slab with finite size, which reduces to the previously known cases of a single plasma boundary and of a two-dimensional slab in the appropriate limits. A new SPP instability regime due to exchange quantum effects is demonstrated. The phenomenology of time refraction and time reflection is extended to SPP, and the frequency shifts and amplitude transformations due to a time boundary are derived. Finite time boundary effects and arbitrary temporal changes of the medium are also considered. Full article

The Janus monolayers have recently attracted substantial interest due to their unique asymmetric structures and intriguing physical properties. In this work, we explore the thermoelectric properties of the Janus monolayer ZrBrI, using first-principles calculations and Boltzmann transport theory. We demonstrate that the system maintains good dynamic and thermal stability, as evidenced by the absence of imaginary phonon modes and small lattice fluctuation at a higher temperature of 600 K. The hybrid functional calculations reveal that the monolayer exhibits a relatively small indirect gap of 1.22 eV, and the energy bands near the conduction band minimum exhibit double degeneracy with weak dispersions, which is very beneficial for enhancing the n-type power factor. Meanwhile, a relatively lower lattice thermal conductivity is found due to strong lattice anharmonicity caused by the antibonding state and the symmetry breaking of the structure. Collectively, a larger ZT value of 3.9 at 600 K can be realized for the n-type Janus monolayer ZrBrI at an optimal concentration of $1.89\times {10}^{13} {\mathrm{cm}}^{-2}$, highlighting its promising thermoelectric application in the intermediate temperature region. Full article

Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article

Variational models describe deformation and stability through the first and second variations in an underlying functional, but the relationship between these responses is seldom expressed as an intrinsic equilibrium quantity of the model itself. A canonical curvature–strain representation for equilibrium ratios arising in variational field settings is developed. For a twice Fréchet differentiable functional and an admissible perturbation generator, strain is defined as normalized first-order response and curvature as normalized second-order response along the generator direction. Their quotient defines a curvature–strain ratio that measures proportional balance between deformation and curvature within the model. The main result shows that this curvature–strain ratio is a canonical representative of a response ratio already implicit in the variational data. Under canonical normalization, the curvature–strain ratio coincides with the quotient of second- and first-order response, and stationarity of the curvature–strain ratio is equivalent to proportional stationarity of that response quotient along the admissible flow. A further theorem establishes transfer of local isolation: when the second-variation operator satisfies standard hypotheses such as compact resolvent and non-degeneracy of the constrained extremum, isolated equilibrium ratios persist in the curvature–strain representation for the same operator-theoretic reasons. Quadratic scalar and Maxwell-type models illustrate the construction. The paper establishes a mathematically controlled curvature–strain representation of equilibrium ratios within ordinary variational theory, with emphasis on the analysis of variational response and equilibrium balance. Full article

The theory of physical degrees of freedom (DoF) developed by Franceschetti–Migliore–Minero (FMM) establishes a fundamental phase transition in the singular-value spectrum of electromagnetic radiation operators under maximal rotational symmetry. In this work, we revisit this result from a symmetry-explicit operator-theoretic perspective and extend it to scenarios with reduced and controllable symmetries, with particular emphasis on reconfigurable intelligent surfaces (RISs). We model the radiation process as a compact operator acting between admissible source and observation spaces and characterize its symmetry through group equivariance. This formulation enables a systematic decomposition of the operator into irreducible representation sectors associated with the effective symmetry group, defined as the intersection of symmetries supported jointly by the source architecture, RIS geometry and programmability, receiver configuration, and propagation environment. We show that the FMM phase transition persists within each symmetry sector and that the total DoF budget is redistributed across sectors according to symmetry constraints. A key outcome of this analysis is the distinction between physical and effective degrees of freedom. While breaking the maximal $\mathrm{SO}\left(2\right)$ symmetry does not increase the total number of electromagnetic DoF dictated by physics, symmetry reduction modifies their allocation across sectors, potentially lifting degeneracies and increasing the number of degrees of freedom that can be effectively addressed by a given excitation, RIS control, and measurement architecture, even when the total number of physical DoF remains fixed by fundamental limits. This clarifies the role of controlled symmetry breaking as a design mechanism rather than a means to surpass fundamental limits. The proposed framework bridges electromagnetic operator theory, representation theory, and RIS-enabled system design, providing both rigorous symmetry-resolved DoF accounting and actionable insights for excitation, surface programmability, and measurement strategies under practical architectural constraints. Full article

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex $SU\left(2\right)$ scalar doublet $\varphi$, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the $\lambda$ corresponding to the Standard Model (SM) fourth-order coupling is instead derived as $\frac{\lambda }{5}$. The factor of $\frac{1}{5}$ is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in $\varphi$ dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves $\lambda$ in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

Quasi-brittle structures modeled with softening constitutive laws may lose the uniqueness of equilibrium, producing bifurcation and multiple admissible crack evolutions even under symmetric loading. This paper develops a stability test and a constructive multiplicity procedure for finite element cracking analyses formulated as a Parametric Linear Complementarity Problem (PLCP) solved in tableau form. The approach exploits the pivot sequence of a complementary tableau to monitor stability by tracking the positive definiteness of the reduced active-mode Hessian $\widehat{\mathbf{A}}$ through a complement condition, without eigenvalue computations. A direct relationship between loss of positive definiteness and the sign of the incremental load factor $\Delta \dot{\mathsf{\alpha }}$ is established, providing an intrinsic indicator of transition to descending response. When degeneracy occurs, a “void pivot” mechanism is introduced to generate an alternative admissible tableau, enabling a systematic construction of multiple isolated solutions associated with competing crack patterns. The method is demonstrated on a two-notched direct tension specimen with cohesive softening, where symmetric and antisymmetric paths emerge at a critical step. The implementation is compatible with parallelized matrix operations and remains effective in the presence of non-holonomic constraints. Full article

Motivated by the persistent short-baseline anomalies that hint at the possible existence of physics beyond the standard three-flavor paradigm, we study the phenomenology of light sterile neutrinos in the minimal (3 + 1) framework using two future experiments: the MuOn-decay MEdium-baseline NeuTrino beam experiment (MOMENT) and the Deep Underground Neutrino Experiment (DUNE). We place constraints on active–sterile mixing parameters, probe CP-violation discovery potential, and examine correlations between the standard Dirac CP phase and the additional CP phases arising from active–sterile mixing to quantify phase degeneracies. We present exclusion limits and demonstrate the crucial role of the near detector in improving sensitivities by one or two orders of magnitude compared to a configuration with only the far detector. We find that the presence of sterile neutrinos can reduce the CP-violation sensitivity in long-baseline neutrino oscillation experiments. For large sterile mass splittings, the rapid oscillations average out, leading to strong parameter degeneracies in DUNE. In contrast, MOMENT retains strong sensitivity to CP violation and efficiently disentangles the standard and sterile CP phases. Our results highlight the strong complementarity between DUNE and MOMENT and show that their combined capabilities provide a powerful test of the light sterile neutrino hypothesis in regions of the parameter space that remain weakly constrained by current data. Full article