Search Results (237)

With the continuous advancement of polarization spectral sensing technology, multi-band polarization image fusion has emerged as a novel approach to image fusion. By integrating spectral and polarization information, this method overcomes the limitations of relying on a single information source and significantly improves overall image quality. To address this, this paper proposes a new polarization spectral fusion algorithm. First, feature matching is employed to achieve pixel-level spatial alignment of multi-band polarization images. Then, a fusion strategy based on multi-scale decomposition and singular value decomposition is adopted to preserve structural information and fine details. Subsequently, fractional-order processing and guided filtering are applied to enhance details and suppress noise. Finally, a progressive reconstruction from low to high scales is performed to ensure hierarchical consistency and information integrity throughout the fusion process. In addition, spectral information is utilized for color restoration, enabling the final image to achieve high spatial resolution while maintaining natural and rich color representation.Experimental results demonstrate that the proposed method effectively integrates features from different spectral bands and polarization information while preserving maximum similarity, leading to significant improvements in both image quality and detail representation. Full article

This paper explores the relationship between random matrix theory (RMT) and the use of weight conditioning for training deep neural networks by employing an integrated framework. It has been shown that trained neural networks produce singular value distributions that follow universal distributions prescribed by RMT; however, the presence of non-universal outliers in the distribution can contain significant information particular to the task being performed. In addition, this research investigates how the application of diagonal row equilibration as a form of conditioning affects spectral behavior and optimization stability within deep neural networks. The results show that through conditioning, the random bulk of the singular value decomposition (SVD) spectrum is effectively compressed into a narrow band about the value 1, significantly reducing the Marchenko–Pastur bounds. The results also support the claim that weight conditioning retains the informative nature of the spectral outliers. The experimental results show that weight condition numbers (κ(W)) decreased from extremely ill-conditioned regimes of approximately 10³ to 10⁴ to almost 1.0, producing smoother training landscapes, a quicker convergence rate, and an improved ability for gradients to propagate. These results suggest that conditioning weights can be thought of as an implicit spectral regularize linking RMT evidence and concepts to the practical optimization of deep learning methods. Full article

The dominant pores governing methane adsorption in coal are micropores (pore size < 2 nm). Their spatial heterogeneity can be quantitatively characterized using multifractal theory; however, the evolution patterns and mechanisms of microporous structures across different coalification degrees remain unclear. This research selected a series of coal samples from different ranks and identified the coalification degree using the maximum vitrinite reflectance (Rₒ_,max). By comprehensively employing low-temperature CO₂ adsorption experiments and multifractal analysis, the evolution patterns of the microporous structures and their multifractal spectral parameters were systematically revealed, and the underlying control mechanisms were explored. Results indicate that micropore volume (PV) and specific surface area (SSA) first exhibit a decrease and then increase as Rₒ_,max increases, with the trough occurring during the second coalification jump at Rₒ_,max = 1.2–1.4%. The pore sizes exhibit bimodal distributions, with the primary peak occurring in the range of 0.45–0.65 nm and the secondary peak occurring in the range of 0.8–0.9 nm. All microporous structures possess pronounced multifractal characteristics. The generalized dimension spectrum width (ΔD) and singularity spectrum width (Δα) exhibit an increasing–decreasing–increasing trend with Rₒ_,max, whereas the Hurst exponent (H) follows an inverted parabolic curve, first increases then decreases. This contrasts with the trends in PV and SSA, indicating that the evolution of pore-space heterogeneity and connectivity is independent of and lags the changes in micropore quantity. These patterns are governed by a structural phase transition within the coal macromolecular network. Marked by the second coalification jump, the microporous system shifts from a flexible degradation–polycondensation paradigm to a rigid ordering–construction paradigm. This transition drives the asynchronous, synergistic evolutions of pore quantity, spatial heterogeneity (ΔD and Δα), and topological connectivity (H). This research provides a theoretical basis for quantitatively evaluating pore heterogeneity in coal reservoirs. Full article

We develop a fast numerical method for solving nonlinear diffusion equations with memory phenomena, a class of problems arising within viscoelastic materials, anomalous transport, and hereditary systems. The primary computational problem is the nonlocal temporal dependence captured by Volterra-type memory operators, which makes direct evaluation scale quadratically with the number of time steps ($O\left(N_t^2\right)$), rendering prolonged simulations prohibitively expensive. To address this bottleneck, we develop a novel synthesis that combines a high-order spectral method for spatial discretization with a fast memory algorithm based on a sum-of-exponentials approximation. The spectral method obtains exponential spatial convergence for smooth solutions. At the same time, the fast memory algorithm reduces memory usage and computational complexity to $O\left(N_t\right)$, yielding computational speedups exceeding 414x for prolonged simulations. We rigorously prove that the proposed scheme preserves the discrete energy dissipation law of the continuous system under mild assumptions on the memory kernel, thereby ensuring unconditional stability. Error analysis verifies spectral accuracy in space and first-order temporal convergence. Extensive numerical experiments using exponentially decaying and weakly singular kernels validate the theoretical results and illustrate the method’s effectiveness for modeling viscoelastic transport phenomena and irregular diffusion in complex systems. Full article

This study presents a structured methodology for optimizing the placement and selection of accelerometer sensors for structural health monitoring in civil infrastructures. The approach integrates both ambient and forced vibration testing data, followed by a unified analysis of sensor energy distribution through singular value decomposition of the cross power spectral density. The energy associated with each sensor is normalized and decomposed into its vertical, longitudinal, and transversal components, allowing for detailed ranking and visualization across different structural elements such as the deck and supporting piers. A comparative analysis between the energy distributions obtained from ambient and forced vibrations is conducted to identify consistent sensor locations. The sensor configuration is then iteratively refined using a combination of global dynamic criteria and local spatial constraints to ensure both stability and optimal spatial distribution. The resulting framework enables the systematic design of sensor layouts that combine energy-based robustness with optimal spatial distribution across all three spatial components, while significantly reducing the number of required sensors, ensuring the preservation of damage detection capability and long-term structural health monitoring. Full article

Weak measurement enables the amplification of weak physical effects via post-selection and has become an important tool in precision optical metrology; however, conventional schemes based on mean-pointer shifts suffer from response saturation, limited linear range, and stringent stability requirements. Here, we propose and experimentally demonstrate a weak-measurement scheme based on spectral-interference trough shifts, where the zero-intensity points of the post-selected spectrum act as the measurement pointer, establishing an analytical mapping between the trough displacement and the target phase or time delay. Theoretical analysis shows that, under detector resolution limits, the measurement resolution depends solely on the frequency of extinction point and is independent of weak-value singular amplification or bias-phase modulation, thereby maintaining high sensitivity while avoiding pointer saturation. Experiments demonstrate that the trough-shift scheme achieves significantly better agreement between measured and theoretical sensitivities than biased weak measurement and provides a stable linear response without additional bias-compensation structures, reaching a minimum resolvable phase variation at the ${10}^{-7}$ level. Moreover, the approach intrinsically supports multi-period traceable measurements and exhibits strong robustness against intensity fluctuations and spectral distortions, offering a promising route toward high-sensitivity, large-dynamic-range, and stable weak measurement-based optical sensing. Full article

This work constructs an orthogonal function system on bounded intervals $[0,R]$ associated with the Atangana–Baleanu–Caputo (ABC) fractional derivative for $\alpha \in (1/2,1)$. Starting from a fractional Laguerre-type equation involving the ABC operator, solutions are obtained via a generalized Frobenius method, yielding series representations with characteristic exponent $\alpha -1$. Rather than postulating a weight function by analogy with classical or Caputo settings, the weight is derived directly from the requirement that the underlying fractional operator be formally self-adjoint on a suitable admissible domain. This operator-theoretic approach leads to the explicit Mittag–Leffler weight $w_{\alpha }\left(x\right)=x^{-(2\alpha -1)}{E}_{\alpha }(-x^{\alpha })$, which intrinsically reflects the nonlocal memory structure of the ABC kernel. A similarity transformation removes the universal singular factor and produces regularized eigenfunctions that are continuous on $[0,R]$ and orthogonal in the weighted $L^2$ space. The weight identity and formal self-adjointness are rigorously verified through a right-Volterra uniqueness argument. Numerical experiments confirm orthogonality up to machine precision, demonstrate spectral convergence for a model ABC differential equation, and illustrate consistency with classical Laguerre polynomials in the limit $\alpha \to 1^{-}$. The resulting framework provides a self-consistent orthogonal system suitable for spectral approximations of problems governed by the ABC operator on bounded domains. Full article

Motivated by the fact that the Fibonacci sequence is the simplest nontrivial second-order recurrence with a rational generating function, we develop a Fibonacci-weighted Hardy theory for bicomplex holomorphic functions. Starting from the coefficient norm ${\sum }_{n\ge 0}{\left|a_n\right|}^2/F_{n+1}$, we obtain a bicomplex Hilbert module whose reproducing kernel is governed by ${(1-t-t^2)}^{-1}$ and whose maximal disk of holomorphy is determined sharply by the nearest kernel singularity, giving the radius ${\rho }_F={\phi }^{-1/2}$ (the square-root inverse of the golden ratio $\phi$). The arithmetic recurrence makes several objects fully explicit: we derive closed formulas for the kernels through the idempotent decomposition of $\mathbb{BC}$, compute exact norms of the shift powers and a golden-ratio spectral radius, and package the local theory into a sheaf of Fibonacci-holomorphic germs that are compatible with the bicomplex idempotent splitting. We also treat $(p,q)$-Fibonacci weights, obtaining a one-parameter family of rational kernels ${(1-pt-q{t}^2)}^{-1}$ and corresponding operator bounds. In addition to providing a concrete bicomplex model within weighted Hardy theory, the resulting explicit kernels furnish benchmark examples for kernel-based interpolation and for the operator theory of unilateral weighted shifts. Full article

We present an analytical solution for the complex spectrum of a Creutz ladder subject to an imaginary Stark potential. By mapping the system to a momentum-space differential equation, we derive the closed-form solution for the momentum-space wavefunctions. We identify a distinct cross-shaped spectrum consisting of discrete localized sectors and a continuous branch of asymptotically real states. Our derivation reveals that the discrete sectors arise from a global phase winding condition, whereas the asymptotically real branch emerges when the energy magnitude is smaller than the inter-cell hopping strength, a regime in which the momentum-space wavefunction develops singularities. We demonstrate that these singularities prevent standard quantization; instead, the open boundary conditions are satisfied via a size-dependent imaginary energy component that regulates the wavefunction decay. To investigate the properties of this branch in the thermodynamic limit, we perform large-scale finite-size scaling analysis up to system sizes $L\sim {10}^9$. The numerical results confirm the power-law decay of the residual imaginary energy, supporting the asymptotic reality of these states. Furthermore, scaling of the inverse participation ratio and fractal dimension indicates that these states, while exhibiting size-dependent localization in finite systems, evolve into an extended phase in the thermodynamic limit. Our results establish a theoretical framework for understanding spectral transitions in systems with imaginary Stark potentials, with potential realizations in photonic frequency synthetic dimensions. Full article

(1) Background: Electroencephalography (EEG) is widely used to monitor the depth of anesthesia; however, conventional Fourier-based analyses are limited in their ability to characterize non-stationary anesthetic-induced EEG dynamics. In this study, we investigated the utility of singular spectrum analysis (SSA) combined with the Hilbert transform for extracting physiologically meaningful EEG features under sevoflurane general anesthesia. (2) Methods: Frontal EEG data from ten patients undergoing sevoflurane anesthesia were analyzed from the maintenance phase through emergence. Using SSA, short EEG segments were decomposed into six intrinsic mode functions (IMFs) without pre-specified basis functions or frequency bands. Hilbert spectral analysis was applied to each IMF to obtain instantaneous frequency and amplitude characteristics. (3) Results: The SSA-based decomposition clearly captured phase-dependent EEG changes, including α spindle activity during maintenance and increasing high-frequency components preceding emergence. Multiple linear regression models incorporating IMF center frequencies and total power demonstrated strong correlations with the bispectral index (BIS), achieving high predictive accuracy (R² = 0.88, MAE < 4). Compared with conventional spectral approaches, SSA provided superior temporal resolution and stable feature extraction for non-stationary EEG signals. (4) Conclusions: These findings indicate that SSA combined with Hilbert analysis is a robust framework for quantitative EEG analysis during general anesthesia and may enhance real-time, individualized assessments of anesthetic depth. Full article

Theenergy of a graph is a classical spectral invariant defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. Recently, the notion of local energy was introduced to measure the contribution of vertices to the total energy via vertex deletion. In this paper, we first study the variation of graph energy under the deletion of a set of vertices and obtain general upper bounds in terms of vertex degrees, together with a characterization of the equality cases under natural structural conditions. These results provide the foundation for extending the concept of local energy to digraphs. Using the singular values of the adjacency matrix, we define the local energy of a digraph and derive sharp upper bounds in terms of the in-degree and out-degree of a vertex. The equality cases are characterized by introducing a special class of vertices, called star-vertices. Finally, we obtain sharp bounds for the total local energy of a digraph in terms of its energy and of the Randić index. Full article

We propose a low-complexity hybrid beamforming method for massive Multiple-Input Multiple-Output (MIMO) systems that is robust to Channel State Information (CSI) estimation errors. These errors stem from hardware impairments, pilot contamination, limited training, and fast fading, causing spectral-efficiency loss. However, existing hybrid beamforming solutions typically either assume near-perfect CSI or rely on greedy/black-box designs without an explicit mechanism to regularize the error-distorted singular modes, leaving a gap in unified, low-complexity, and theoretically grounded robustness. We unfold the Alternating Direction Method of Multipliers (ADMM) into a trainable Deep Learning (DL) network, termed DL-ADMM, to jointly optimize Radio-Frequency (RF) and baseband precoders and combiners. In DL-ADMM, the ADMM update mappings are learned (layer-wise parameters and projections) to amortize the joint RF/baseband optimization, whereas Regularized Singular Value Decomposition (RSVD) acts as an analytical regularizer that reshapes the observed channel’s singular values to suppress noise amplification under imperfect CSI. RSVD is integrated to stabilize singular modes and curb noise amplification, yielding a unified and scalable design. For ${\sigma }_e^2=0.1$, the proposed DL-ADMM-Reg achieves approximately 8–11 bits/s/Hz higher spectral efficiency than Orthogonal Matching Pursuit (OMP) at Signal-to-Noise Ratio (SNR) $=20$–40 dB, while remaining within <1 bit/s/Hz of the digital-optimal benchmark across both $(N_t,N_r)=(32,32)$ and $(64,64)$ settings. Simulations confirm higher spectral efficiency and robustness than OMP and Adaptive Phase Shifters (APSs). Full article

The morphology of solid surfaces encodes fundamental information about the physical mechanisms that govern their formation. Here, we reinterpret scanning electron microscopy (SEM) micrographs of oxide thin films as two-dimensional self-affine morphology fields (not height-metrology) and analyze them using a multiscale statistical-physics framework that integrates spectral, multifractal, geometric, and topological descriptors. Fourier-based power spectral density (PSD) provides the spectral slope $\beta$ and apparent Hurst exponent $H$, while multifractal scaling yields the information dimensions $D_q$, the singularity spectrum $f\left(\alpha \right)$, and its width $\mathsf{\Delta }\alpha$, which quantify scale hierarchy and intermittency. Lacunarity captures intermediate-scale heterogeneity, and Minkowski functionals—especially the Euler characteristic $\chi \left(\theta \right)$—probe connectivity and identify the onset of a percolation-like network structure. Two representative surfaces with contrasting morphologies are used as model systems: one exhibiting an anisotropic, porous, strongly multifractal structure with fragmented domains; the other showing a compact, nearly isotropic, and nearly monofractal organization. The porous surface/topography displays steep PSD decay, broad multifractal spectra, and positive $\chi$, consistent with a sub-percolated, diffusion-limited, Edwards–Wilkinson-like (EW-like) growth regime. Conversely, the compact surface/topography exhibits gentler spectral slopes, narrower $f\left(\alpha \right)$, enhanced lacunarity at intermediate scales, and a $\chi \left(\theta \right)$ zero-crossing indicative of a connectivity transition where a surface becomes a percolating network, consistent with a Kardar–Parisi–Zhang-like (KPZ-like) correlated growth regime. These results demonstrate that individual SEM micrographs encode quantitative fingerprints of nonequilibrium universality classes and topology-driven transitions from fragmented surfaces to connected networks, showing that SEM intensity maps can serve as a quantitative probe for testing theories of rough surfaces and kinetic growth in experimental thin-film systems. Full article

At present, most of the switchgear partial discharge detection means are offline detection and cannot monitor multiple partial discharge sources online at the same time. Based on this, this paper investigates the application of ultrasonic technology in localized discharge fault localization in high-voltage switchgear, removes the background noise of localized discharge in switchgear by using soft and hard filtering; proposes a generalized cubic correlation algorithm on the basis of TODA, improves the accuracy of the time difference acquisition in the case of low signal-to-noise ratio; determines the number of multiple localized discharging power sources by using the single-channel signal blind source separation technique and singularity spectral analysis; and determines the number of multiple localized discharging power sources by using independent component analysis to separate them. As well as for the problem that TDOA cannot be directly applied to the localization of multiple partial discharge sources, independent component analysis is used to separate the mixed signals, and the disordered coordinate selection method is proposed to determine the coordinates of multiple partial discharge sources. The experimental results show that (1) the noise reduction method is able to remove the excess interference while preserving the localized discharge signals; (2) the improved generalized cubic inter-correlation algorithm is more resistant to interference and has less error than other time delay estimation algorithms. The localization error is reduced by 60 mm~68 mm compared to the basic correlation algorithm, 41 mm~47 mm compared to the twice correlation algorithm, and 17 mm~20 mm compared to the three times correlation algorithm, which is a big improvement compared to the pre-improved algorithm. (3) It is able to locate the multiple localized power sources, and the accuracy of the number of localized power sources reaches 88%. Full article

This study applies spectral analysis and singular spectrum analysis (SSA) to mean annual runoff of the Dniester River for 1950–2024 to identify dominant periodic components governing the hydrological regime of this transboundary basin shared by Ukraine and Moldova. The novelty lies in a basin-specific integration in the first systematic application of a combined spectral–SSA framework to the Dniester River, enabling consistent characterization of runoff variability and assessment of large-scale natural drivers. Time series from three gauging stations are analysed to develop data-driven runoff models and medium-term forecasts. Four stable groups of periodic variability are identified, with characteristic timescales of approximately 30, 11, 3–5.8, and 2 years, corresponding to major atmospheric–oceanic oscillations (AMO, NAO, PDO, ENSO, QBO) and the 11-year solar cycle. Cross-spectral and coherence analyses reveal a statistically significant relationship between solar activity and river discharge, with an estimated lag of about 2 years. SSA reconstructions explain more than 80% of discharge variance, indicating high model reliability. Forecast comparisons show that spectral methods tend to amplify long-term trends, CNN–LSTM models produce conservative trajectories, while a hybrid ensemble approach provides the most balanced and physically interpretable projections. Ensemble forecasts indicate reduced runoff during 2025–2028, followed by recovery in 2029–2034, supporting long-term water-resources planning and climate adaptation. Full article