Search Results (188)

We propose an exploratory framework for a Bohmian model of quantum matter propagating on a classical curved spacetime background. The gravitational sector is governed by classical Einstein field equations throughout; no quantisation of spacetime is attempted. The wave function emerges as the scalar contraction $\mathrm{\Psi }={\psi }_{\nu }{\psi }^{\nu }\in \mathbb{C}$ of a complex-valued tensorial field ${\psi }^{\mu }$, encoding quantum dynamics in a geometric object. The wave tensor interacts with spacetime via the stress–energy tensor $T_{\mu \nu }$, mediated by a real scalar field a of dimension volume, so that $a{T}_{\mu \nu }{\psi }^{\mu }{\psi }^{\nu }$ yields the correct potential energy. We derive a covariant Adapted Schrödinger Equation as the unique minimal covariant lift of the standard equation, justify it from four guiding principles, and verify three internal consistency checks. Under seven explicit approximations the framework reproduces the Schrödinger equation with Coulomb potential for the hydrogen atom. We also derive a dynamical equation for ${\psi }^{\mu }$ that entails the Adapted Schrödinger Equation by contraction. Two open problems are then resolved. First, a complete Lagrangian formulation is provided: a real-valued action for $\mathrm{\Psi }$ yields the Adapted Schrödinger Equation via the Euler–Lagrange equations; a separate action for ${\psi }^{\mu }$, extended by a non-polynomial term, yields the full dynamical equation variationally. Second, two experimental predictions are derived. Expanding to first post-Newtonian order, the perturbation Hamiltonian has coefficients $(3, 1)$ on the kinetic and potential operators; via the virial theorem these produce a coordinate-time blueshift, which after photon propagation yields the universal Einstein gravitational redshift $\delta \nu /\nu =\mathrm{\Phi }/c^2$, confirming consistency with the equivalence principle. The same kinetic coefficient independently predicts that free quantum wave packets spread more slowly by the fractional amount $3\left|\mathrm{\Phi }\right|/c^2$, a correction absent in standard non-relativistic quantum mechanics. Full article

We investigatewhether a finite local information capacity of spacetime can account for the gravitational phenomena commonly attributed to cold dark matter. Starting from a covariant effective-field-theory description, we modelcoarse-grained entropy deposition as a dynamical scalar field $S\left(x\right)$ whose stress–energy tensor contributes to structure formation. The macroscopic action contains a single dimensionless coupling λ multiplying the canonical kinetic term, ensuring ghost-free dynamics and conservation of the associated stress–energy tensor. In a slow-roll regime, defined by a covariant source term $\Gamma \equiv \ddot{S}+3H\dot{S}=0$, where H is the Hubble parameter and overdot denotes derivative with respect to cosmic time, and $|\ddot{S}|\ll H|\dot{S}|$, the entropy sector behaves as pressureless dust at background and in linear order. Implemented in a modified Cosmic Linear Anisotropy Solving System (CLASS) Boltzmann solver, the entropy component fits Planck satellite 2018 cosmic microwave background (CMB) data, baryon acoustic oscillation (BAO) measurements, and the Pantheon + Type Ia supernova sample for $0.5\lesssim \lambda \lesssim 2$, while preserving the linear growth factor to within 0.2% over Euclid space telescope scales. To regulate ultraviolet contributions, we introduce a holographically motivated prescription in which gravitationally active entropy deposition is confined to causal two-surfaces, yielding a $\rho \propto r^{-2}$ halo envelope with a finite-density core determined by local entropy saturation. Fixing the flux scale $\mathcal{A}$ from astrophysical entropy budgets reproduces Milky-Way-mass halos without introducing fine-tuned length scales. Pilot N-body simulations that evolve the entropy field on a staggered grid reproduce the halo mass function down to ${10}^{10.5}{M}_{\odot }$, mitigate the cusp–core and missing-satellite tensions, and remain consistent with cluster lensing constraints. On linear scales, the model predicts percent-level, scale-dependent deviations in the lensing convergence and matter power spectra, testable by Euclid space telescope, the Roman Space Telescope High Latitude Survey, and the CMB-S4 experiment. Full article

Background/Objectives: White matter (WM) tract detection is critical in the presurgical planning of tumor resection. However, standard-of-care imaging techniques including T₁-weighted, T₂-weighted, and Diffusion Tensor Imaging (DTI) often fail to identify WM tracts within edematous regions. In T₁/T₂-weighted imaging, edema increases extracellular water and reduces tissue contrast, and in diffusion-weighted imaging, edema elevates isotropic diffusion, reducing sensitivity to anisotropic diffusion along WM tracts. Advanced biophysical diffusion modeling techniques such as Neurite Orientation Dispersion and Density Imaging (NODDI) and the Standard Model (SM) address this limitation by compartmentalizing the diffusion signal into free-water, intra-neurite, and extra-neurite contributions. Here, we test if biophysical multi-compartment models can robustly identify WM tracts and recover tractography streamlines within edematous regions. Methods: In this study, we use multi-shell diffusion-weighted MRI data obtained from patients with meningiomas—a pathology allowing for isolation of the effects of edema without the confounding effects of tumor cell invasion. We compared FA from standard and free-water-corrected DTI, the orientation dispersion index (ODI) from NODDI, and P₂ (a scalar descriptor of fiber orientation coherence) from the SM fODF in edematous and unaffected contralateral WM regions. As a proof of concept, we visually evaluated the tractography performance across models. Results: Our results show that (1 − ODI) and P₂ values in edema remained close to within-subject contralateral measurements, contrasting with substantial reductions in FA and FW-FA. (1 − ODI) showed a small but statistically significant increase in edema (~8%, p = 0.02), while P₂ was unchanged. Conclusions: These results highlight the potential of biophysical diffusion models for preoperative mapping in edema. Full article

This manuscript investigates conformal $\eta$-Ricci–Yamabe solitons of type $(\kappa ,l)$ on Kählerian Norden space-time admitting a Kählerian Norden torse-forming vector field. Necessary conditions are obtained under which the soliton exhibits expanding, steady, or shrinking behavior. The analysis is further extended to several physically relevant fluid models, including dark fluid, dust fluid, stiff matter, and radiational fluid, and the corresponding geometric constraints are derived. In addition, structural results are established for Kählerian Norden space-times with a vanishing space–matter tensor and with a divergence-free matter tensor, highlighting their influence on the curvature geometry. The study also addresses several intrinsic curvature conditions of the space-time, such as conformal flatness, Ricci semi-symmetry, Ricci recurrence, and pseudo-Ricci symmetry, leading to a collection of geometric and physical characterizations. The results obtained provide a unified geometric framework linking Ricci–Yamabe soliton structures, fluid dynamics, and curvature properties within the setting of Kählerian Norden geometry. Full article

Accurate calibration is essential for ensuring the performance of magnetic gradient tensor (MGT) arrays. Existing calibration methods generally rely on mechanical rotation to obtain magnetic responses under multiple orientations. However, for large-scale cubic MGT arrays, rotating the entire array using a high-precision non-magnetic turntable is often costly and impractical, while manual rotation is difficult to control and may introduce array-center offsets. To address these limitations, this paper proposes a rotation-free scalar calibration framework for cubic MGT arrays, in which a tri-axial Helmholtz coil system generates constant-magnitude magnetic fields with randomized orientations while compensating for ambient magnetic drifts. Based on the acquired data, a hierarchical calibration algorithm is developed to estimate sensor-level intrinsic errors and array-level misalignment errors. Experimental results show that the proposed method reduces the joint tensor invariant $C_T$ from $9.07\times {10}^3$ nT/m to 11.51 nT/m, corresponding to a 99.87% reduction. In addition, compared with a conventional rotation-based fast calibration method, the proposed framework further decreases the mean and RMS of the joint $C_T$ by 62.7% and 63.1%, respectively. These results demonstrate that the proposed framework improves the spatial consistency of the MGT array and provides a practical calibration solution for large-scale MGT array systems. Full article

Background: The aim of the present study was to identify the discipline with the greatest predictive value for overall performance in Olympic-distance triathlon. Methods: Data were extracted from the API (Application Programming Interface) service on the World Triathlon website by signing up for the free service. A custom Python code was written to perform different data collection operations. General statistical analyses and machine learning analyses were performed by creating a Jupyter Notebook file. TensorFlow and PyTorch libraries were used for machine learning analysis. Results: Fifty percent of the employed models identified cycling as the most predictive discipline for race success for both sexes, whereas 33% selected running as the determining discipline. To achieve a podium finish, approximately 78% of the models classified running as the most predictive discipline for males, and approximately 56% of the models did so for females. For finishes between fourth and tenth place, approximately 78% of the models proposed running as the most predictive discipline for both sexes. Swimming was never identified as the most predictive discipline by the majority of models for any group or sex. Conclusion: The most predictive discipline in Olympic triathlon depends on the athlete’s sex and competitive level. Nonetheless, running remains the most consistently predictive discipline, whereas swimming rarely acts as a performance differentiator. Full article

While the standard Schwarzschild metric is overwhelmingly employed in general relativity (GR) as the starting point for various spherical spacetime metric calculations, its isotropic (ISO) form is mentioned in more specialized contexts and its derivation is barely discussed in published GR literature. In this work, we review the isotropic metric, stressing that it stands out as a useful spherically symmetric metric to be employed also in traditional GR problems. We start by deriving the ISO metric through solving the vacuum field equations in Cartesian coordinates, thereby obtaining the Ricci tensor also in spherical coordinates. We then analytically calculate the Riemann tensor in Cartesian coordinates, proving its consistency with the Ricci tensor calculation for pedagogical reasons. Finally, from the Riemann tensor we exactly evaluate the Kretschmann scalar, which lacks metric singularities, a result consistent with the known singular behavior of the standard Schwarzschild metric. We conclude that the isotropic metric naturally emerges as a suitable candidate for modeling static neutron stars and regular black holes, thereby complementing the present attempts to understand these rapidly evolving research fields. Full article

Unmanned aerial vehicle (UAV) small object detection faces critical challenges including irreversible geometric detail loss during multi-level downsampling, cross-scale feature distortion from interpolation blur and aliasing, and limited long-range dependency modeling due to constrained receptive fields. To address these limitations, we propose HMF-DEIM (High-Fidelity Multi-Domain Fusion Transformer for UAV Small Object Detection), an end-to-end architecture tailored for UAV small object detection. First, we design a lightweight hierarchical differentiation backbone that removes redundant deepest-layer features (P5) to prevent tiny object information loss, employing Multi-Domain Feature Blending (MDFB) in shallow layers for geometric detail preservation and a Hierarchical Attention-guided Feature Modulation Block (HAFMB) in deep layers for global semantic modeling. Second, we develop a full-chain high-fidelity feature transformation framework comprising Channel-Adaptive Shift Upsampling (CASU) for interpolation-free resolution recovery, Multi-scale Context Alignment Fusion (MCAF) for bridging deep–shallow semantic gaps via bidirectional gating, and Diversified Residual Frequency-aware Downsampling (DRFD) for aliasing suppression through a three-branch parallel architecture. Finally, we devise the FocusFeature module that aligns multi-scale features to a unified scale and employs parallel multi-scale large-kernel depthwise convolutions to capture cross-scale long-range dependencies, generating dual-scale (P3/P4) features balancing details and semantics. Experiments demonstrate that HMF-DEIM outperforms DEIM on VisDrone2019 test by 0.405 mAP⁵⁰ (+2.1%) and 0.235 mAP^50–95 (+1.6%), with a remarkable 21.3% relative improvement in AP_s for tiny objects, while maintaining real-time inference (465 FPS with TensorRT FP16) on an NVIDIA A100 GPU with only 11.87M parameters and 34.1 GFLOPs. Further validation on AI-TOD v2 and DOTA v1.5 datasets confirms robust generalization across diverse aerial scenarios, making it a practical solution for resource-constrained UAV applications. Full article

This work places the invariant $d{s}^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension of Fermat’s principle to massive particles—namely, the requirement that freely falling bodies follow trajectories that extremize proper time, which for timelike motion corresponds to a local maximum—and invoking the universality of Galilean free fall, we derive the form of $d{s}^2$ in a static gravitational field. Lorentz invariance then provides the natural framework to extend this result to systems involving moving matter. The invariant derived through this procedure matches the weak-field limit of General Relativity formulated in the harmonic gauge. Within this linearized regime, we show that the structure of the theory already contains the seeds of its nonlinear completion: any dynamically consistent extension to strong gravitational fields necessarily involves the Ricci tensor. From this viewpoint, Einstein’s field equations appear not as a postulated geometric law but as the unique covariant closure required to ensure energy–momentum conservation and the self-consistency of the gravitational interaction. Full article

A two-fluid model can be described by an anisotropic fluid matter, and we introduced the notion of an anisotropic fluid spacetime. The algebraic and differential properties of an anisotropic fluid spacetime equipped with several forms of the stress–energy tensor is the focus of this research. We show that an anisotropic fluid spacetime with a radial pressure $p^{\Vert }$, transverse pressure $p^{\perp }$, and the energy density $\rho$ is a generalized quasi-Einstein spacetime. We prove that a dark matter era or an anisotropic fluid spacetime with vanishing vorticity is represented by an anisotropic fluid spacetime endowed with a covariant constant stress–energy tensor; on the contrary, a dark matter era or the expansion scalar vanishes is represented by an anisotropic fluid spacetime endowed with a Codazzi type of stress–energy tensor, as long as $\mathcal{A}$ stays invariant under the velocity vector field $\zeta$. Furthermore, we use the Killing velocity vector field, parallel vector fields to characterize Ricci Semi-Symmetric, $\mathcal{T}$-recurrent, Pseudo-Ricci symmetric, and $\widehat{\mathbb{R}}$-harmonic anisotropic fluid spacetime. We find that the anisotropic fluid spacetime reflect a stiff matter and a radiation era with these geometric symmetries. Finally, we provide findings for an anisotropic fluid spacetime with a divergence-free matter tensor and the vanishing space-matter tensor and explore the dynamical aspects of cosmological epoch of an anisotropic fluid spacetime coupled with $f\left(\mathcal{R}\right)$-gravity. Full article

We propose and develop a unified framework for Weyl-type symmetry in von Neumann algebras. Motivated by recent automorphism-rigidity phenomena that identify finite Weyl groups inside automorphism groups of crossed products arising from lattice actions on homogeneous spaces, we introduce the Weyl group of an inclusion $W(M;B):={\mathrm{Aut}}_B\left(M\right)/{\mathrm{Inn}}_B\left(M\right)$, for a unital inclusion $B\subset M$ of von Neumann algebras, and investigate its structure across several rigidity regimes. Our main results (1) prove finiteness or triviality of $W(M;B)$ for large classes of nonamenable crossed products, including hyperbolic and product-type actions with spectral gap and malleability; (2) establish a subgroup-normalizer rigidity principle for inclusions $L(\Lambda )\subset L(\Gamma )$ that identifies ${\mathrm{Aut}}_{L(\Lambda )}\left(L(\Gamma )\right)$ with a discrete group controlled by $N_{\Gamma }(\Lambda )$; (3) show that permutation-type symmetry for product/tensor decompositions is the only possible nontrivial symmetry of the underlying group subalgebras; and (4) extend the analysis to type III factors via Maharam extensions and unique-Cartan phenomena, proving that $W(M;B)$ is discrete and often trivial, leaving only modular flows as outer symmetries. Consequences include new computations of outer automorphism groups, constraints on intermediate subalgebras, and classification consequences for crossed products and amalgamated free products. The methods combine Popa’s intertwining-by-bimodules, spectral-gap and s-malleable deformations, boundary/ucp-map rigidity, and groupoid/Cartan techniques. Full article

In this paper, an anisotropic object electromagnetic image reconstruction system based on a two-stage multi-frequency extended network is developed by deep learning techniques. We obtain the scattered field information by irradiating the TM different polarization waves to uniaxial objects located in free space. We input the measured single-frequency scattered field into the Deep Residual Convolutional Neural Network (DRCNN) for training and to be further extended to multi-frequency data by the trained model. In the second stage, we feed the multi-frequency data into the Deep Convolutional Encoder–Decoder (DCED) architecture to reconstruct an accurate distribution of the dielectric constants. We focus on EMIS applications using Transverse Magnetic (TM) and Transverse Electric (TE) waves in 2D scenes. Numerical findings confirm that our method can effectively reconstruct high-contrast uniaxial objects under limited information. In addition, the TM/TE scattering from uniaxial anisotropic objects is governed by polarization-dependent Lippmann–Schwinger integral equations, yielding a nonlinear and severely ill-posed inverse operator that couples the dielectric tensor components with multi-frequency field responses. Within this mathematical framework, the proposed two-stage DRCNN–DCED architecture serves as a data-driven approximation to the anisotropic inverse scattering operator, providing improved stability and representational fidelity under limited-aperture measurement constraints. Full article

In this contribution, we propose and study long-time behaviors of a new class of N-dimensional delayed Kirchhoff–Carrier-type problems with variable transfer coefficients involving a logarithmic nonlinearity. We take into account the dependence of diffusion and damping coefficients on the position and direction, as well as the presence of different types of delays. This class of nonlocal anisotropic and nonlinear wave-type equations with multiple time-varying mixed delays and dampings, of a fairly general form, containing several arbitrary functions and free parameters, is of the following form: ${\displaystyle \frac{{\partial }^{2}u}{\partial t^2}-{div(\mathcal{K}(\Vert \sigma \nabla u\Vert }_{L^2(\Omega )}^2)A_{\sigma }{(\mathbf{x})\nabla u)+\mathcal{M}(\Vert u\Vert }_{L^2(\Omega )}^2)u-div(\zeta (t)A_{\sigma }(\mathbf{x})\nabla \frac{\partial u}{\partial t})+d_0(t)\frac{\partial u}{\partial t}+{\mathbb{D}}_r(\mathbf{x},t;\frac{\partial u}{\partial t})=\mathbb{G}(u),}$ where $u(\mathbf{x},t)$ is the state function, $\mathcal{M}$ and $\mathcal{K}$ are the nonlocal Kirchhoff operators and the nonlinear operator $\mathbb{G}(u)$ corresponds to a logarithmic source term. The symmetric tensor $A_{\sigma }$ describes the anisotropic behavior and processes of the system, and the operator ${\mathbb{D}}_r$ represents the multiple time-varying mixed delays related to velocity ${\displaystyle \frac{\partial u}{\partial t}}$. Our problem, which encompasses numerous equations already studied in the literature, is relevant to a wide range of practical and concrete applications. It not only considers anisotropy in diffusion, but it also assumes that the strong damping can be totally anisotropic (a phenomenon that has received very little mathematical attention in the literature). We begin with the reformulation of the problem into a nonlinear system coupling a nonlocal wave-type equation with ordinary differential equations, with the help of auxiliary functions. Afterward, we study the local existence and some necessary regularity results of the solutions by using the Faedo–Galerkin approximation, combining some energy estimates and the logarithmic Sobolev inequality. Next, by virtue of the potential well method combined with the Nehari manifold, conditions for global in-time existence are given. Finally, subject to certain conditions, the exponential decay of global solutions is established by applying a perturbed energy method. Many of the obtained results can be extended to the case of other nonlinear source terms. Full article

The inherent diffraction of electromagnetic waves, such as shortwaves and microwaves, severely limits the effective signal transmission distance, thereby constraining the development of related applications like radar and communications. This work experimentally demonstrates the use of a virtual hyperbolic metamaterial (VHMM) realized via a plasma filament array induced in air by a femtosecond laser. We characterize the ability of this VHMM to control electromagnetic waves in the shortwave and microwave bands, particularly its guiding and collimating effects. By combining experimental measurements with effective medium theory, we confirm that under specific parameters, the principal diagonal components of the permittivity tensor for the plasma array exhibit opposite signs, manifesting typical hyperbolic dispersion characteristics which enable the guiding of electromagnetic waves. This research provides a feasible approach for utilizing lasers to create dynamically reconfigurable and non-physical structures in free space for manipulating long-wavelength electromagnetic radiation, demonstrating potential for applications in areas such as radar, communications, and remote sensing. Full article