If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. In an earlier work we provided a comprehensive treatment of orientable Euclidean three-manifolds; but a thorough exploration of cosmic topology must include non-orientable three-manifolds as candidates for the geometry of space. In this paper we consider the non-orientable Euclidean topologies E 7–E 10, E 13–E 15, and E 17, encompassing the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the CMB sky. As for orientable three-manifolds, we find that in manifolds where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB, we expect a correlation signal that is larger than cosmic variance noise in the CMB. The parameter space of the non-orientable Euclidean manifolds is quite rich, supporting, for example, complex dependencies of clone distances on those parameters. Our limited selection of manifold parameters — both the values of those we fix, and the choices of which to vary — are therefore exemplary of interesting behaviors (e.g., of how well the manifold can be distinguished from the covering space), but not necessarily representative. Future searches for topology will certainly require a much more thorough exploration of the parameter space to determine what values of the parameters predict statistical correlations that are convincingly attributable to topology.

CATpie: A Python tool for quantifying membrane curvature, area, and geometrically faithful normal-line thickness from molecular dynamics simulations.

Abstract. Fast response calculations in the frequency domain are valuable during the initial design of floating wind turbines, where many design variants must be evaluated. A direct frequency-domain treatment of aero-elastic rotor loads is typically infeasible due to the azimuthal time dependence of the system matrices. To overcome this limitation, we introduce a perturbation-based formulation inspired by Hill's method, which reformulates the response equations into separate orders involving constant system matrices derived via Fourier decomposition. This enables accurate and efficient response computation using the fast Fourier transform (FFT). For comparison, a Laplace-based perturbation method is also developed using the Laplace transform instead of the Fourier transform. To evaluate the novel fast response methods, we develop an azimuthally periodic and fully linearized model of a floating wind turbine. The response to various load cases is computed under different inflow and floater motion conditions. The proposed Fourier-based fast response method achieves high accuracy, with peak and standard deviation errors of 2 % and 3.5 %, respectively, while reducing computation time to 2.5 s for a 4096 s simulation – significantly faster than linear (45 s) and time-domain (90 s) models. Through detailed comparison, we find that one of our approaches, the so-called single perturbation method, offers an effective trade-off between accuracy and speed, making it suitable for design and optimization studies.

The placement of the stops for refueling is an important challenge for the economic aspect in nuclear energy production industry. In this paper, we intend to study, in the context of the so-called PWR1300—a pressurized water reactor of 1300 MW, how economical criteria, including the mean core burnup, and safety criteria, such as hot power factor (which are often not correlated) are sensitive to repositioning. Given the huge number of possible combinations and the very expensive CPU cost of a steady-cycle simulation, we have set a methodology based on a surrogate model using Fourier expansion of the criterion function on the symmetric group S n . We address this problem in an efficient way, taking into account the limited computational resources; thus, we restrict our analysis to the permutation operating only on the Uox gadolinium assemblies as UGd. The criteria functions are evaluated by using the Minos Solver of APOLLO3® neutronics simulation code along the last converged depletion cycle. As a result, we establish a design of experiments from which is derived an expansion Fourier surrogate model of the first and second degree, with very good accuracy. In fact, for most of the criteria, the surrogate model of the second degree has a coefficient of determination greater than 0.8. We then study the sensitivity of the criteria from the substitution model and present, as a result, an intensity map that attests to the importance of specific repositioning of the UGd. These first results show that the criteria are repositioning-sensitive and call for further investigation into the application of more complex permutation, including Uox and UGd simultaneously.

ABSTRACT A fractional two-temperature dual-phase-lag (TTDPL) bioheat model is developed to investigate thermoelastic heat transfer in human skin tissue subjected to electromagnetic radiation. The proposed formulation incorporates Caputo fractional derivatives, two-temperature theory, blood perfusion, temperature-dependent metabolic heat generation, and electromagnetic heating within the modified Pennes bioheat framework. To describe the coupled interactions among thermal, mechanical, and electromagnetic fields, the heat transfer equation is integrated with Maxwell’s equations and the thermoelastic equation of motion. The governing equations are transformed into a dimensionless form and solved analytically using the Laplace transform technique, while the corresponding physical-domain solutions are obtained through numerical inversion based on the Fourier series expansion method. The effects of the fractional-order parameter, phase-lag times, electromagnetic intensity, and metabolic heat source on the thermal response and tissue behavior are examined in detail. The results reveal a distinct difference between conductive and thermodynamic temperatures, highlighting the importance of the two-temperature concept in characterizing non-equilibrium heat transfer. Furthermore, the fractional-order parameter significantly influences memory-dependent heat conduction, whereas phase-lag parameters and electromagnetic loading strongly affect temperature evolution. Thermal damage analysis is also performed to identify safe and critical exposure conditions. The developed model provides a useful framework for evaluating thermal responses during electromagnetic and thermal therapeutic applications.

Accurate phase response curve (PRC) models are essential for closed-loop neuromodulation, yet biological non-stationarity-driven by medication, sleep cycles, or plasticity-limits the efficacy of traditional offline identification. An adaptive, computationally efficient PRC estimation algorithm is proposed for real-time, online identification in embedded devices.

Approach: A parametric Fourier series model approximates the PRC, and coefficients are updated after each stimulus using a recursive Least Mean Squares (LMS) rule driven by prediction error. Spectral weighting enforces smoothness, while a power-law adaptive learning-rate schedule balances rapid initial acquisition with high-precision refinement. The framework was evaluated in a stochastic theta neuron model and a reduced Hodgkin Huxely model.

Main results: Robust convergence was achieved in a stochastic setting. Analysis of the speed-precision trade-off identified an adaptive learning-rate schedule that is near-optimal for a given sample size. The Fourier representation also yields an instantaneous smooth derivative, enabling real-time selection of stimulation phases for synchronization or desynchronization without numerical smoothing or historical buffering.
Significance: The algorithm requires only basic arithmetic, making it well suited to resource-constrained implantable pulse generators. Continuous adaptation allows tracking of non-stationary dynamics and supports personalized closed-loop neuromodulation without repeated offline recalibration.&#xD.

Cardiovascular diseases are a primary global health concern, requiring continuous monitoring and accurate diagnostic mechanisms for early detection and prevention. The integration of the Internet of Medical Things (IoMT), deep learning, and blockchain technologies has enabled intelligent healthcare systems capable of real-time cardiac assessment and enhanced security in the management of medical information. However, existing heart disease monitoring systems are affected by noisy physiological signals, inefficient feature extraction, limited classification accuracy, and insufficient security in distributed environments, motivating the development of a robust and reliable diagnostic framework with improved security. To address these challenges, this research proposes an IoMT and Blockchain-Based Heart Disease Monitoring System Using Hybrid Black-Winged Spherical Structural Graph Convolution Neural Network (HBW-SSG-CNN). The proposed workflow begins with IoMT-based acquisition of ECG and PCG signals, followed by preprocessing using quasi-cross bilateral filtering (QCBF) to suppress noise while preserving critical cardiac structures. Signal decomposition is performed using Spectral Envelope-Based Adaptive Empirical Fourier Decomposition (SE-AEFD), followed by feature extraction using the Short-Time Quaternion Quadratic Phase Fourier Transform (ST-QQPFT). Feature dimensionality is optimized using the Success-Based Optimization Algorithm (SBOA), and heart disease classification is performed using a Hybrid Structural Graph Attention Network with Spherical Convolutional Neural Network (HS-GAT-SCNN), further enhanced by the Black-Winged Kite Algorithm (BWKA). To enhance data integrity and improve security, an Adaptive Hash Algorithm with Weighted Probability Model (AHA-WPM) is integrated with a Fair Consensus Blockchain for Heterogeneous Miners (FCB-HM). The proposed model is evaluated using publicly available benchmark datasets, including PhysioNet cardiac signal datasets and the Cleveland heart disease dataset. Experimental evaluation demonstrates superior performance with an accuracy of 99.21%, sensitivity of 98.94%, specificity of 99.08%, and F1-score of 99.02%. The results confirm that the proposed framework provides a highly accurate, scalable, and security-enhanced solution for near real-time heart disease monitoring in IoMT-enabled healthcare systems.

Physical entropy sources that remain stable under extreme temperatures are essential for cryptography in emerging technological frontiers in deep space exploration, geothermal energy harvesting, and nuclear energy. However, conventional semiconductor platforms fail to generate stable and reliable cryptographic keys above 200 °C due to performance degradation. Here, we report a diamond-based cryptographic primitive that exploits the defect-rich sp2-bonded grain boundary network in nitrogen-incorporated ultrananocrystalline diamond (n-UNCD) film as a robust entropy source to generate cryptographic keys that remain operationally stable even after enduring extreme temperatures of 700 °C for 54 h while also surviving thermal cycling between room temperature and 700 °C for 48 h. The strength of the generated keys is assessed through several cryptographic metrics such as bit uniformity, entropy, hamming distances, and correlation coefficients, all of which are found to be near their respective ideal values. Moreover, the generated keys pass the NIST SP 800 and SP 800-90B tests and are also resilient to supply bias variations and a regression-based machine learning attack model based on the Fourier series. The robustness of the keys is attributed to the better thermal stability and chemical inertness of the n-UNCD film. This is supported by high-resolution energy-dispersive X-ray spectroscopy (EDS), which shows no significant lateral diffusion of metal atoms into the n-UNCD layer, and by Raman spectroscopy, which reveals no significant changes in the bonding configuration of the n-UNCD structure. Our findings highlight the remarkable potential of n-UNCD film for extreme environment cryptography by expanding the operational limits of conventional hardware security platforms.

The rapid evolution of high-speed optical communication networks has intensified the demand for ultra-high-capacity links, positioning electro-optic modulators (EOMs) and Mach-Zehnder interferometers (MZIs) as pivotal components in microwave photonic systems. However, the performance of these devices is fundamentally limited by nonlinear effects, which induce harmonic distortions and intermodulation products. In this paper, we propose a generalized analytical framework to characterize the output frequency spectrum and temporal waveform of an EOM-MZI modulator. Our model incorporates a quadratic refractive index profile and utilizes a Fourier series representation of the driving signal in conjunction with a multi-harmonic Jacobi-Anger expansion to provide closed-form solutions for the modulated optical field. The proposed framework is rigorously validated against numerical simulations for bit rates ranging from 5 to 50Gbps. Results demonstrate high precision, with the model accurately capturing complex nonlinear behaviors and intermodulation products. Furthermore, we investigate the impact of pulse duty cycle optimization, revealing that for ultra-high-speed operations (above 35Gbps), reducing the duty cycle to 30% significantly enhances the extinction ratio and Q-factor by mitigating nonlinear distortions. This analytical approach offers a computationally efficient alternative to intensive numerical solvers, providing a robust tool for the design and optimization of next-generation high-speed optical communication links. The proposed framework enables simultaneous analysis of spectral broadening, harmonic generation, intermodulation effects, and waveform distortion in both frequency and time domains.

Semi-analytical method and vibration isolation analysis of dynamic response of multi-layer gradient BCC lattice structures

Echo state networks are well-known for their ability to learn temporal patterns through simple feedback to a large recurrent network with random connections. However, the learning process itself remains poorly understood. We develop a quantitative theory that explains learning in a regime where the network dynamics is stable and the feedback is weak. We show that the dynamics is governed by a finite number of master modes whose nonlinear interactions can be described by a normal form. This formulation provides a simple picture of learning as a Fourier decomposition of the target pattern with amplitudes determined by nonlinear interactions that, remarkably, become independent of the network randomness in the limit of large network size. We further show that the description extends to moderate feedback and recurrent networks with multiple unstable modes.

The trend term and noise in blasting vibration signals severely affect the accuracy of analysis. However, existing adaptive decomposition methods still have limitations in removing these trend and noise components. This study develops a Fourier decomposition-based (FDM) preprocessing approach for blasting vibration signals by optimizing key parameters, including the cross-correlation threshold, the ultra-low-frequency energy threshold, and the decomposition search path. A comparison between the High-to-Low Frequency Searching (HTL-FS) and Low-to-High Frequency Searching (LTH-FS) search paths indicates that LTH-FS achieves superior decomposition performance when applied to blasting vibration signals. The sensitivity of FDM to different ultra-low-frequency energy thresholds is systematically examined, and a criterion for identifying valid components is established. The results demonstrate that FDM can effectively separate low-frequency trend components, high-frequency noise, and meaningful signal information in blasting vibration records. Compared with Empirical Mode Decomposition (EMD), Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and Variational Mode Decomposition (VMD), the pure signal obtained via FDM exhibits the smoothest time-history curve, the highest signal-to-noise ratio (23.2406), and the lowest root-mean-square error (0.0246). At the same time, this paper further confirms the effectiveness of FDM as a high-precision preprocessing method for blasting signals by analyzing the blasting vibration signals in two actual cases: the Chongli Tunnel blasting project and the Caomao Mountain Tunnel blasting project.

Microseismic monitoring data are characterized by strong background noise and low signal-to-noise ratio (SNR), posing challenges for effective signal identification and real-time processing. Existing methods generally suffer from poor adaptability, low processing accuracy, and insufficient computational efficiency. To address these issues, this study proposes an adaptive spectral segmentation method for microseismic signal extraction. First, the Ramanujan subspace method is employed to suppress periodic noise and eliminate spectral peak interference. Subsequently, an adaptive band number determination criterion based on the sampling rate is established, and adaptive empirical Fourier decomposition is adopted to achieve optimized spectral segmentation. Finally, the Gini coefficient is introduced to establish an adaptive threshold screening mechanism for automatic reconstruction of effective signals. For real-time processing of multi-channel data, a unified filtering strategy based on statistical overlapping bands is proposed, enabling rapid processing of subsequent data using common bands. Experiments on synthetic and field data demonstrate that the proposed adaptive spectral segmentation method yields significant advantages: on synthetic data, SNR improvements of up to 4.65 dB over modal decomposition methods (e.g., empirical mode decomposition, ensemble empirical mode decomposition, and variational mode decomposition) and wavelet packet decomposition, along with a 72% reduction in multi-channel processing time using the unified filtering strategy. These results highlight its high adaptability and practicality for low-SNR microseismic signal processing.

Abstract The one-dimensional dynamic contact problem describing a rigid obstacle collided by an elastic bar is considered in gravitational field. The collision problem is non-smooth with respect to velocity and axial strain, and formulated as a variational inequality. For the corresponding wave equation subject to complementary conditions which are imposed at the contact boundary, its nonlinear solution is expressed with the help of Fourier Series representing longitudinal vibrations. Moreover, before the bar rebound, an analytical solution comprising piece-wise quadratic function is constructed on a partition of the rectangular space-time domain along characteristics. The analytical benchmark is implemented for low initial speeds in numerical experiments solving the variational inequality over uniform space-time triangulation with the Space-Time Primal-Dual Active Set method of semi-smooth Newton type.

This paper develops a nodal finite element Crank-Nicolson method of lines to solve the time-dependent Maxwell's equations on polygonal domains with reentrant corners. Nodal Finite Element methods are used to solve Maxwell's equations with an optimal convergence rate when the domain is convex or has a smooth boundary, but may fail to converge if the domain has a reentrant corner. The Defect-Correction method presented is based on a decomposition of the solution in terms of Fourier and Bessel's series, an extraction of the singular function and an approximation of the regular part of the solution. Optimal convergence results are recovered using the method in both the energy norm or the $L^2$-norm.

Co-circulation of multiple influenza subtypes poses a major challenge to global public health. However, its specific impact on non-stationary epidemic sequences and coupling relationships with environmental drivers remains poorly understood. By integrating STL, Adaptive Fourier Decomposition, Continuous Wavelet Transform, and Wavelet Coherence, we analyzed 323 weekly influenza surveillance time series from China (2011-2025). The study identifies a fundamental regime shift during co-circulation periods, transitioning from ordered single-dominant transmission to a chaotic state. This instability is characterized by significant dominant periodicity dispersion, amplified seasonality shifts, and high-intensity anomalies in residual components, with overall seasonal strength dropping by 28%. Crucially, we uncover a marked north-south mechanistic divergence: northern regions exhibited "Environmental Locking," remaining strongly constrained by climates during co-circulation; conversely, southern regions demonstrated "Environmental Decoupling" (H3N2 phase consistency with soil moisture plummeted from R=0.45 to 0.07), where viral ecological competition overshadowed environmental drivers. Influenza co-circulation acts as a systemic perturbation reshaping transmission dynamics. Our findings highlight the necessity for context-adaptive strategies: northern regions can maintain reliance on meteorological warnings, while southern regions must dynamically shift focus toward real-time virological surveillance during co-circulation to capture rapid ecological shifts.

Averaged spin state catalog framework for uncontrolled space objects

We investigate the imaging and polarization properties of Kerr-MOG black holes surrounded by geometrically thick accretion flows. The MOG parameter α introduces deviations from the Kerr metric, providing a means to test modified gravity in the strong field regime. Two representative accretion models are considered: the phenomenological radiatively inefficient accretion flow (RIAF) and the analytical ballistic approximation accretion flow (BAAF). Using general relativistic radiative transfer, we compute synchrotron emission and polarization maps under different spins, MOG parameters, inclinations, and observing frequencies. In both models, the photon ring and central dark region expand with increasing α, whereas frame dragging produces pronounced brightness asymmetry. The BAAF model predicts a narrower bright ring and distinct polarization morphology near the event horizon. By introducing the net polarization angle χ net and the second Fourier mode ∠β 2, we quantify inclination- and frame-dragging-induced polarization features. Our results reveal that both α and spin significantly influence the near-horizon polarization patterns, suggesting that high-resolution polarimetric imaging could serve as a promising probe of modified gravity in the strong field regime.

A law of large numbers concerning the distribution of critical points of random Fourier series

• New analytical formulas are derived for drain spacing under non-steady flow conditions. • Asymptotic analysis is employed to enhance the accuracy of Glover’s classical equation. • Drain spacing is accurately computed while accounting for higher-order terms in the Fourier series solution. • Highly accurate solutions are achieved at t = 3 days, with relative errors consistently below 3.4%. Glover’s equation is used to describe the drawdown of the maximum height of the groundwater table to a desired depth within a specified time interval between two drainage pipes, following a sudden rise of the groundwater table, in the case where the drains are installed in a homogeneous soil over an impermeable layer. The determination of the appropriate drain spacing ( L ) under non-steady-state drainage conditions, assuming that the groundwater table is initially horizontal and parallel to the plane of the drains, is obtained from the solution of the linearized Boussinesq equation when all terms of the exponential series except the first are neglected for all times except very small ones. In the present study, a methodology is proposed in which additional terms of the exponential series are incorporated in a simple manner for the calculation of the drain spacing. This improvement enables the determination of drain spacing independently of time t. Results from a numerical example indicate that solutions obtained using three to six terms of the series provide highly accurate and reliable results for t = 3 days, with relative errors below 3.4%, in contrast to the classical Glover equation, which exhibits significant prediction errors for drain spacing over the same time period.