The phenomenon of underscreening, where the screening of the electrostatic potential in the bulk electrolyte is weaker than it should be according to the canonical Debye-Hückel theory, has significant implications for colloidal stability in highly concentrated electrolytes. Current experimental and computational investigations of this phenomenon have been limited to single mode analyses, despite statistical mechanics predicting that many modes are present simultaneously. We hypothesise that using a multi-modal approach will provide insights not yet observed. Here we apply Fourier analysis to radial charge densities, derived from polarisable molecular dynamic simulations of aqueous alkali chloride electrolytes, to determine if multiple modes are present. Prony's method is then applied to a multi-modal ansatz to estimate screening lengths associated with each mode. Fourier analysis revealed that there are many modes present in the radial charge density. For all electrolytes considered at low concentrations the dominant mode was a non-oscillatory Yukawa decay mode, while at higher concentrations modes with non-zero spatial frequencies dominated. Resulting screening modes with oscillatory wavelengths ∼5-15Å from Prony's method agree with the largest experimental screening lengths from surface force apparatus and fluorescence experiments. Concurrently, screening lengths with shorter oscillatory wavelengths, 3-5Å, have smaller magnitudes and agree with other experiments such as atomic force microscopy and optical second harmonic scattering experiments.

The limitations of traditional methods for identifying resonance frequencies have driven the development of Resonance Mode Analysis (RMA) as a more effective alternative. Despite its potential, RMA faces challenges in computational efficiency, particularly in multi-terminal transmission grids. To address this, Rapid RMA, a power iteration (PI)-based approach for determining the dominant eigenvalue of the nodal impedance matrix, was introduced. However, the PI-based approach can exhibit slow convergence or fail under certain conditions. To overcome these limitations, recent advancements have proposed two new methodologies: Faster RMA, a modified shifted-inverse PI-based method, and Lanczos-based RMA, a non-Hermitian Lanczos method. This paper evaluates the computational performance of RMA-based methods using various software tools (including normal computation, parallel computation and sparse techniques) across three distinct hardware-computing systems. The study highlights practical differences in computational speed and efficiency for RMA applications under diverse scenarios. By emphasising the critical role of optimising computational tools, the paper examines how hardware and software configurations influence RMA performance, particularly in transmission grids and microgrid clusters, using MATLAB/Simulink simulations. Finally, the paper proposes an efficient RMA-based methodology that is adaptable to a wide range of grid configurations and computational environments. This approach is applied to stability studies using the positive-mode-damping stability criterion, thereby offering a robust framework for advancing harmonic resonance analysis in power systems.

The room-temperature shimming coils are installed within the bore of the superconducting magnet. By applying different excitation currents to each set of coils, different compensating magnetic fields are generated to modify specific components of the main magnetic field, thereby improving its uniformity. For a nuclear magnetic resonance spectrometer operating at 400 MHz, the initial magnetic field uniformity must be better than 1 ppm in a 10 mm DSV (Diameter Spherical Volume). After active shimming using the room-temperature shimming coils, the uniformity should be improved to within 10 ppb in the same DSV. This paper focuses on the design of a room-temperature shimming system for a 400 MHz NMR spectrometer. The coil design for each shimming order is based on spherical harmonic function analysis and the target field method, implemented via the finite difference stream function approach. Additionally, the measurement system and power supply system for the shimming coils are described.

Convolutional Fourier Analysis Network (CONV-FAN-POX): A novel Time–Frequency approach for medical image analysis

Quantifying gradual forest change from a harmonic analysis of dense Landsat time series stacks - a case study of Dali Bai Autonomous Prefecture

The detection and analysis of faults in the ball bearings of induction motors are crucial for ensuring the reliable operation of motors. This paper deals with the use of Motor Current Signature Analysis (MCSA) together with Harmonics Fast Fourier Transform (FFT) to identify bearing defects. During operation, the bearings of induction motors are subjected to dynamic forces, which account for their deterioration is one of the leading causes of motor breakdowns in industrial systems. This study used a three-phase, 440V, four-pole, 1500 RPM induction motor for experimental testing.; three different bearing fault conditions of dry bearing, insufficient lubrication, and ball-damaged bearing were introduced in the setup. The performance analysis of the motor is carried out under no-load and rated-load conditions, and comparisons are drawn between the healthy and faulty states. From the results, it can be observed that due to the development of bearing faults, certain important parameters like torque, mechanical power, electrical power, power factor, three-phase voltage and current are increased; whereas the motor speed and efficiency decreased. Further, harmonic analysis indicates an increased harmonic content, with significant harmonics up to the 21st order. Hence, from the obtained results, it is concluded that MCSA and harmonic analysis are powerful tools that can be employed for early diagnosis and detection of induction motor bearing failures.

With the increasing demand for sleep health monitoring, automatic sleep staging using single-channel electroencephalogram (EEG) signals has become increasingly prominent due to its clinical practicality. Existing methods have achieved notable progress, but they often fail to adequately capture long-term temporal dependencies and struggle to characterize transition phases. We propose SleepLT, an automated sleep staging framework that integrates multi-scale wavelet decomposition (MWD) and multi-head latent Fourier attention (MLFA). The MLFA module incorporates Fourier analysis into self-attention mechanisms and employs a partially weight-sharing bottleneck to optimize Key/Value generation, effectively capturing sleep rhythms. Extensive experiments on SleepEDF-78 and SHHS datasets demonstrate strong and consistent performance, with Macro F1 improvements of 2.1–3.2% over the compared baselines. Visualizations confirm that SleepLT enhances inter-class discriminability between sleep stages, robustly detects salient waveforms, and effectively captures transitions through long-sequence modeling. These results indicate that SleepLT is effective for automatic sleep staging from single-channel EEG, particularly in improving the recognition of ambiguous transitional stages such as N1 and REM.

In this paper, we consider a class of multi-term time-fractional nonlinear diffusion equations (MTFNDEs) with initial boundary value conditions. Due to the initial singularity of the solutions of MTFNDEs, many existing numerical methods suffer from order reduction. To overcome this challenge, we derive a new scheme with $\min\{(\delta + \alpha_m - \alpha_{m-1})/\beta, 2\}$-order accuracy in time for $0 < \alpha_{m-1} < \alpha_m \leq 1$ and $0 < \delta < 1$ by combining the technique of variable transformation $t = s^{1/\beta}$ ($0 < \beta \leq 1$) and the linear interpolation. Meanwhile, the unconditional stability and convergence of the scheme are proved through the Fourier analysis method. Finally, numerical experiments have been given to support the theoretical results and efficiency of our proposed scheme.

Slide-based lectures remain the primary means by which undergraduate students learn about the mathematical, physical, and systems-level foundations of medical imaging. However, despite their central educational role, no openly available dataset pairs imaging lecture slides with clean, well-aligned explanatory narration suitable for scientific and educational research. The authors introduced MEDI-SLATE: medical imaging slide-lecture aligned teaching ensemble, constructed from a complete undergraduate biomedical engineering medical imaging course. The dataset contains 1117 high-resolution slides paired with refined narration derived from classroom audio through automatic speech recognition, followed by careful manual cleanup. MEDI-SLATE encompasses linear systems, Fourier analysis, signal processing, X-ray physics, computed tomography, positron emission tomography/single photon emission computed tomography, magnetic resonance imaging , ultrasound, and optical imaging. In addition to the slide-text pairs, the dataset includes lecture-level difficulty tags, key ideas, common student misunderstandings, and practice questions sourced directly from the instructor's materials. A fully reproducible preprocessing pipeline covering slide extraction, narration refinement, alignment, and corpus-level analyses is provided. MEDI-SLATE offersa high-fidelity, openly available resource for medical imaging education, curriculum development, multimodal learning research, and creation of artificial intelligence-assisted instructional tools, with all data and codes released for transparent use and future extension.

Geogrids have emerged as a widely adopted reinforcement solution for asphalt concrete mixes to enhance fatigue resistance and mitigate reflection cracking. However, precisely quantifying the fatigue life improvement provided by geogrid reinforcement remains a challenge. In this study, a novel method is developed to assess the effectiveness of geogrid reinforcement in asphalt concrete beams using the harmonics of the stress response. Four types of beam specimens were fabricated for four-point bending beam (4PB) testing – plain and notched beams, with and without geogrid reinforcement. The stress response obtained from the 4PB test was subjected to Fast Fourier Transform (FFT) analysis to determine the evolution of the fundamental and the third harmonic. While the conventional methods of identifying fatigue life were found to be ineffective in capturing the fatigue life of reinforced asphalt concrete beams accurately, the ratio of the third harmonic to the fundamental harmonic, an indicator of fatigue damage, increases sharply for plain beams and at a slower rate for reinforced beams. Fatigue life determined from the evolution of the harmonic ratio revealed significant improvements in fatigue performance, with improvement factors reaching up to 2.5 and 10 for unnotched and notched beam specimens, respectively. These findings provide a more precise methodology to quantify the fatigue life of reinforced asphalt mixtures.

In this article, we propose a non-archimedean framework for information processing based on the arithmetic and geometry of p-adic numbers. Exploiting the ultrametric structure of Qp, we introduce norm-based p-adic operations inspired by classical logical connectives that exhibit strong stability under perturbations. The non-archimedean nature of the p-adic norm induces natural scale separation and clustering properties, leading to robust information encoding and spectral localization. Using p-adic Fourier analysis, we show that hierarchical signals decompose into disjoint frequency bands, enabling multiscale information processing with reduced interference. These results provide a mathematical foundation for robust and hierarchical information architectures, with potential applications in signal processing, error-tolerant computation, and non-classical information systems.

Abstract We propose a family of quantum algorithms for estimating Gowers uniformity norms $$ U^k $$ U k over finite abelian groups, extending earlier quantum methods for the $$ U^2 $$ U 2 -norm to arbitrary prime fields and higher-order uniformity norms. Our algorithms prepare quantum states encoding higher-order finite differences and apply Fourier sampling together with amplitude estimation to obtain estimates of Gowers norms. As a central application, we study algebraic property testing problems of distinguishing whether a bounded function $$ f: \mathbb {F}_p^n \rightarrow \mathbb {C} $$ f : F p n → C is a low-degree phase polynomial or is far from any such structure. We show that whenever an inverse theorem for the $$ U^{d+1} $$ U d + 1 -norm is available, our quantum framework yields a corresponding structure-testing algorithm whose query and measurement complexity depends explicitly on the quantitative bounds of that inverse theorem. In particular, using the recent quasipolynomial inverse theorem for the $$ U^4 $$ U 4 -norm over $$ \mathbb {F}_p^n $$ F p n , we obtain quasipolynomial-time quantum algorithms for detecting cubic phase polynomials. For higher-order norms such as $$ U^5 $$ U 5 and $$ U^6 $$ U 6 over $$ \mathbb {F}_2^n $$ F 2 n , the best known inverse theorems provide only tower-type quantitative bounds; accordingly, our detection algorithms remain correct but inherit complexity corresponding to tower-type quantitative bounds. We also present a quantum method for estimating the number of 3-term arithmetic progressions in Boolean functions via the $$ U^2 $$ U 2 -norm. Although not query-optimal compared to Grover-style counting, this approach is sensitive to additive structure and naturally aligned with tools from higher-order Fourier analysis. Finally, we observe that Gowers norms are invariant under certain classes of shift-type noise, implying that our algorithms retain robustness under natural quantum noise models. This suggests that Gowers norm-based quantum procedures may serve as stable primitives for quantum property testing, learning theory, and the analysis of pseudorandomness in the NISQ regime.

By employing the harmonic analysis associated with the Bessel function on $[0, +\infty[$, we study two classes of generalized wavelet packets and their related generalized wavelet transformations, along with the Plancherel, Calderon, and reconstruction formulas for these transforms.

Moiré fringes contain critical phase information whose precise extraction is of paramount importance. In this paper, a method for moiré fringe phase information extraction based on transfer learning (TL-MFPE) was proposed, with the main purpose of improving training efficiency. The phase unwrapping process is pre-trained, after which the pre-trained model is incorporated into the phase extraction process. Compared with two traditional methods: (1) Fourier analysis and multigrid method (FA+MG), (2) Fourier analysis and quality-guided method (FA+QG), as well as end-to-end deep learning method, our proposed method achieves significantly superior performances in terms of accuracy and noise resistance for moiré fringe phase extraction. Furthermore, constraining the training process with the phase unwrapping procedure compensates for the limited sample size in the dataset, enhancing the model's ability to extract phase information, it is crucial in the training process of real moiré fringes. In a word, this approach is expected to improve the reliability and efficiency of moiré deflectometry, providing more robust technical support for its application.

Semi-automated forensic examination of handwritten character loops.

Characterization and prediction of low earth orbit satellite clock offsets based on Fourier analysis network

Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulence

Extreme sea levels along the Mexican coasts pose an increasing risk to coastal infrastructure and communities, particularly under the combined influence of tropical cyclones and ongoing sea-level rise. This study analyzes tide-gauge records from the Mexican Pacific and Gulf of Mexico–Caribbean coasts to characterize the statistical behavior and seasonal modulation of extreme sea-level residuals. Astronomical tides were removed through harmonic analysis to isolate the meteorological residual associated with storm-driven processes. Extreme events were evaluated using complementary extreme-value frameworks, including Generalized Extreme Value (GEV) distributions applied to monthly maxima and a Peaks-Over-Threshold (POT) approach applied to the continuous residual series with temporal declustering and Generalized Pareto Distribution (GPD) fitting. While both approaches consistently capture regional patterns, the POT–GPD framework is adopted as the primary basis for return-level estimation due to its explicit representation of event-scale extremes. The results reveal marked regional variability. Pacific stations exhibit bounded or near-Gumbel behavior (ξ ≈ −0.30 to −0.02) and a strong seasonal concentration of extremes during the tropical cyclone season. In contrast, Gulf of Mexico–Caribbean stations display higher absolute extremes and a broader seasonal footprint, with Veracruz showing a tendency toward heavier-tailed behavior (ξ ≈ 0.13). Return levels for a 25-year return period range from approximately 0.85–0.95 m in the Pacific to about 1.7 m in Veracruz. Longer return periods (e.g., 100 years) exceed 2.2 m in Veracruz but are associated with substantial uncertainty due to record-length limitations. The analysis of ENSO variability indicates that ENSO acts primarily as a secondary modulator of background sea-level variability rather than a deterministic driver of extreme events, with the largest anomalies typically associated with tropical cyclone activity. Overall, the results demonstrate that extreme sea levels along the Mexican coasts are governed by region-specific forcing and tail behavior requiring localized extreme-value modeling strategies. The proposed framework provides a robust and reproducible baseline for coastal hazard assessment and supports the integration of sea-level rise into future risk and design analyses.

Alluvial rivers have long been described by hydraulic geometry theory, which links equilibrium channel dimensions to flow discharge. Yet natural rivers are inherently dynamic, with planforms evolving over time and widths fluctuating around an equilibrium state. Despite increasingly refined datasets, the mechanisms underlying river width variability remain poorly understood. Here, we analyze a globally distributed set of alluvial rivers using high-resolution satellite imagery to examine spatial patterns of width variability. When normalized by mean channel width, we identify three characteristic wavelengths of width variability, each associated with a distinct geomorphic feature: meander bends, mid-channel bars, and localized bank-line incisions linked to intermittent bank collapse. Fourier analysis reveals a strong inverse relation between intermittent collapse-driven width variability and bend-average curvature, suggesting that intermittent bank collapse plays a prominent geomorphic role in mildly curved rivers. Numerical modeling further demonstrates that intermittent bank collapse affects the overall river morphodynamics, accelerating lateral migration and enhancing floodplain reworking. By illustrating intermittent bank collapse as a significant mechanism of river width adjustment, our findings refine classical fluvial geomorphology theory and hold implications for river restoration and organic carbon flux estimation in a warming era.

We make progress on two interrelated problems at the intersection of geometric measure theory, additive combinatorics and harmonic analysis: the discretised sum-product problem, and the dimension of Furstenberg sets. Along the way, we obtain new information on the dimension of exceptional sets of orthogonal projections. First, we give a new proof of the following asymmetric sum-product theorem: Let A , B , C ⊂ R A,B,C \subset \mathbb {R} be Borel sets with 0 > dim H B ≤ dim H A > 1 0 > {\dim _{\mathrm {H}}} B \leq {\dim _{\mathrm {H}}} A > 1 and dim H B + dim H C > dim H A {\dim _{\mathrm {H}}} B + {\dim _{\mathrm {H}}} C > {\dim _{\mathrm {H}}} A . Then, there exists c ∈ C c \in C such that dim H ( A + c B ) > dim H A . \begin{equation*} {\dim _{\mathrm {H}}} (A + cB) > {\dim _{\mathrm {H}}} A. \end{equation*} We use this to show that every ( s , t ) (s,t) -Furstenberg set F ⊂ R 2 F \subset \mathbb {R}^{2} associated with a line set of equal Hausdorff and packing dimension t t satisfies dim H F ≥ min { s + t , 3 s + t 2 , s + 1 } . \begin{equation*} {\dim _{\mathrm {H}}} F \geq \min \left \{s + t,\tfrac {3s + t}{2},s + 1\right \}. \end{equation*}