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Image watermarking often involves the use of handheld devices under non-structured conditions for authentication purposes, particularly in the print-cam process where smartphone cameras are used to capture watermarked printed images. However, these images frequently suffer from perspective distortions, making them unsuitable for automated information detection. To address this issue, Cam-Unet, an end-to-end neural network architecture, is presented to predict the mapping from distorted images to rectified ones, specifically tailored for print-cam challenges applied to ID images. Given the limited availability of large-scale real datasets containing ground truth distortions, we created an extensive synthetic dataset by subjecting undistorted images to print-cam attacks. The proposed network is trained on this dataset, using various data augmentation techniques to improve its generalization capabilities. Accordingly, this paper presents an image watermarking system for the print-cam process. The approach combines Fourier transform-based watermarking with Cam-Unet as perspective distortion correction. Results show that the proposed method outperforms existing watermarking approaches typically employed to counter print-cam attacks and achieves an optimal balance between efficiency and cost-effectiveness. [ABSTRACT FROM AUTHOR]

Using the data from weather observation stations, an assessment of statistical significance of the first harmonic amplitude of the long-term average daily precipitation series in Russia in 1961‒2020 and their changes in 1991‒2020 compared to 1961‒1990 is made. It is shown that at most stations the first harmonic has a reliable value different from the noise, except for eleven stations in the southern regions of the European part of Russia. It is revealed that on average there is a significant decrease in the first harmonic amplitudes of the daily precipitation series across Russia. An analysis of the spatial distribution of the studied quantities is performed and the presence of large areas with their homogeneous character is demonstrated. [ABSTRACT FROM AUTHOR]

As the number of electronic gadgets in our daily lives is increasing and most of them require some kind of human interaction, this demands innovative, convenient input methods. There are limitations to state-of-the-art (SotA) ultrasound-based hand gesture recognition (HGR) systems in terms of robustness and accuracy. This research presents a novel machine learning (ML)-based end-to-end solution for hand gesture recognition with low-cost micro-electromechanical (MEMS) system ultrasonic transducers. In contrast to prior methods, our ML model processes the raw echo samples directly instead of using pre-processed data. Consequently, the processing flow presented in this work leaves it to the ML model to extract the important information from the echo data. The success of this approach is demonstrated as follows. Four MEMS ultrasonic transducers are placed in three different geometrical arrangements. For each arrangement, different types of ML models are optimized and benchmarked on datasets acquired with the presented custom hardware (HW): convolutional neural networks (CNNs), gated recurrent units (GRUs), long short-term memory (LSTM), vision transformer (ViT), and cross-attention multi-scale vision transformer (CrossViT). The three last-mentioned ML models reached more than 88% accuracy. The most important innovation described in this research paper is that we were able to demonstrate that little pre-processing is necessary to obtain high accuracy in ultrasonic HGR for several arrangements of cost-effective and low-power MEMS ultrasonic transducer arrays. Even the computationally intensive Fourier transform can be omitted. The presented approach is further compared to HGR systems using other sensor types such as vision, WiFi, radar, and state-of-the-art ultrasound-based HGR systems. Direct processing of the sensor signals by a compact model makes ultrasonic hand gesture recognition a true low-cost and power-efficient input method. [ABSTRACT FROM AUTHOR]

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays. [ABSTRACT FROM AUTHOR]

The main aim of this article is to derive certain continuity and boundedness properties of the coupled fractional Fourier transform on Schwartz-like spaces. We extend the domain of the coupled fractional Fourier transform to the space of tempered distributions and then study the mapping properties of pseudo-differential operators associated with the coupled fractional Fourier transform on a Schwartz-like space. We conclude the article by applying some of the results to obtain an analytical solution of a generalized heat equation. [ABSTRACT FROM AUTHOR]

In order to realize the real-time processing and analysis of astronomical ultrawide bandwidth signals, this study proposes a sub-band division algorithm based on RFSoC. The algorithm uses Kaiser window to design FIR prototype low-pass filter, adopts critical sampling polyphase filter bank to decompose ultra-wide bandwidth signal into several sub-bands, and encapsulates each sub-band into VDIF data frame and sends it to GPU server. The algorithm is implemented on RFSoC platform, and its effectiveness is verified by simulation and actual observation. The experimental results show that the algorithm can divide the astronomical ultra-wide bandwidth signal into multiple sub-bands in real time, packetize and transmit them to GPU. This research provides reproducible design and project for ultra-wide bandwidth signal sub-band division with low spectrum leakage and aliasing, high data accuracy, and fast processing speed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a problem of estimating a large loss probability of financial derivatives portfolio, which are commonly modeled as nested expectations. However, the cost of nested simulation may be too expensive and thus multilevel Monte Carlo (MLMC) method is recently used to reduce the nested simulation complexity. When using antithetic MLMC to solve the indicator function, we get the complexity of O(ϵ -5/2). To decrease the computational burden, we use a Fourier transform method to modify the form of indicator function. The new estimator is sufficiently smooth and enables the antithetic MLMC method to achieve a better complexity. In addtion, we combine quasi-Monte Carlo (QMC) with MLMC to reduce the variance of inner estimator. Numerical results show that using the Fourier transform method in both MLMC and MLQMC can attain the optimal complexity O(ϵ -2). [ABSTRACT FROM AUTHOR]

Research on knocking combustion is vitally essential since it impacts engine performance regarding noise and emissions, fuel consumption, power density, and durability. Because of end-gas auto-ignition, current SI engines may experience conventional knock, which restricts increasing the compression ratio to increase thermal efficiency. Therefore, this paper examined the in-cylinder pressure and vibration of a port fuel-injected gasoline engine under knocking and non-knocking conditions. The heat release rate was calculated from pressure traces where the crank angle resolutions were not constant, and the conversion from the time domain to the frequency domain of knock sensor signals by using the Fourier Transform was performed. The result reveals that more heat is released during knocking combustion than during non-knocking combustion. When there is a knock, the temperature variation increases. This would facilitate the use of heat transfer studies to detect knock occurrences. Moreover, knocking is caused by an ignition timing that is too advanced, 22°BTC, compared to the non-knocking spark case, 14°BTC. In the frequency domain, the amplitude of the knocking combustion is higher than the amplitude of the non-knocking combustion, indicating the engine’s noise and vibration. [ABSTRACT FROM AUTHOR]

Background: Alterations in sleep have been described in multiple health conditions and as a function of several medication effects. However, evidence generally stems from small univariate studies. Here, we apply a large-sample, data-driven approach to investigate patterns between in sleep macrostructure, quantitative sleep EEG, and health. Methods: We use data from the MrOS Sleep Study, containing polysomnography and health data from a large sample (N = 3086) of elderly American men to establish associations between sleep macrostructure, the spectral composition of the electroencephalogram, 38 medical disorders, 2 health behaviors, and the use of 48 medications. Results: Of sleep macrostructure variables, increased REM latency and reduced REM duration were the most common findings across health indicators, along with increased sleep latency and reduced sleep efficiency. We found that the majority of health indicators were not associated with objective EEG power spectral density (PSD) alterations. Associations with the rest were highly stereotypical, with two principal components accounting for 85–95% of the PSD-health association. PC1 consists of a decrease of slow and an increase of fast PSD components, mainly in NREM. This pattern was most strongly associated with depression/SSRI medication use and age-related disorders. PC2 consists of changes in mid-frequency activity. Increased mid-frequency activity was associated with benzodiazepine use, while decreases were associated with cardiovascular problems and associated medications, in line with a recently proposed hypothesis of immune-mediated circadian demodulation in these disorders. Specific increases in sleep spindle frequency activity were associated with taking benzodiazepines and zolpidem. Sensitivity analyses supported the presence of both disorder and medication effects. Conclusions: Sleep alterations are present in various health conditions. [ABSTRACT FROM AUTHOR]

To further enhance the security of image encryption, a new chaos-based image encryption algorithm (IEA) based on discrete Fourier transform and Joseph traversal is proposed to encrypt the plain image in both the frequency domain and space domain simultaneously. In the proposed IEA, the logistic map is used to generate the appropriate chaotic sequence, and the improved Joseph traversal is used to scramble the image in different starting positions and variable step sizes. Then, block diffusion is performed at the end. The main finding concerning the proposed IEA is that the combination of discrete Fourier transform and Joseph traversal can enhance the security of the image information, which has been validated by measuring the performance in resisting the common types of attacks. [ABSTRACT FROM AUTHOR]

In the realm of neural network-based noise reduction, conventional models predominantly address Gaussian and blur artifacts across entire images. However, they encounter notable challenges when directly applied to periodic noise characteristics of high-resolution infrared sequential imagery. The high resolution also complicates the construction of suitable datasets. Our study introduces an innovative strategy that transforms two-dimensional images into one-dimensional signals, eliminating the need for processing the full image. We have developed a simulated dataset that closely mirrors natural infrared line scanning images derived from the FLIR dataset. To address low-frequency periodic noise, we propose two neural-network-based denoising approaches. The first employs a neural network to deduce noise from the one-dimensional signal, while the second utilizes discrete Fourier transforms for noise prediction within the frequency domain. Our experimental results highlight the Restormer model's exemplary performance in direct noise prediction, where denoised images attain a PSNR of around 41 and an SSIM close to 0.9 on simulated data, leaving minimal residual noise in the actual denoised images. Further, we investigate the influence of Fourier coefficients, as predicted by neural networks, on the denoising process in the second approach. Employing 12 frequency coefficients, the Restormer and NAFNet models both reach a PSNR near 34 and an SSIM of approximately 0.842. [ABSTRACT FROM AUTHOR]

For the fourth-order partial differential equation proposed by Fushchich for mathematical description of heat and mass transfer processes, the class of uniqueness and the class of correctness of the Cauchy problem have been established. Using the Fourier transform, a solution to the Cauchy problem is found in an explicit analytical form. It is shown that the new equation does not improve the properties of the classical heat conduction equation, but it allows one to describe heat transfer processes taking into account relaxation effects within the framework of the Galileo-invariant mathematical theory of transfer. [ABSTRACT FROM AUTHOR]

New classes of evolution differential equations with the Liouville derivative in Banach spaces are studied. Equations are considered on the whole real line and are not endowed by the initial conditions. Using the methods of the Fourier transform theory, we prove the unique solvability in the sense of classical solutions for the equation solved with respect to the Liouville fractional derivative with a bounded operator at the unknown function. This allows us to obtain the analogous result for the equation with a linear degenerate operator at the fractional derivative and with a spectrally bounded pair of operators. Abstract results are applied to obtain new results on the unique solvability of systems of ordinary differential equations, boundary problems to partial differential equations, and systems of equations. [ABSTRACT FROM AUTHOR]

This paper introduces a method for high-resolution lattice image reconstruction and dislocation analysis based on diffraction extinction. The approach primarily involves locating extinction spots in the Fourier transform spectrum (reciprocal space) and constructing corresponding diffraction wave functions. By the coherent combination of diffraction and transmission waves, the lattice image of the extinction planes is reconstructed. This lattice image is then used for dislocation localization, enabling the observation and analysis of crystal planes that exhibit electron diffraction extinction effects and atomic jump arrangements during high-resolution transmission electron microscopy (HRTEM) characterization. Furthermore, due to the method's effectiveness in localizing dislocations, it offers a unique advantage when analyzing high-resolution images with relatively poor quality. The feasibility of this method is theoretically demonstrated in this paper. Additionally, the method was successfully applied to observed edge dislocations, such as 1 / 6 [ 21 1 − ] , 1 / 6 [ 2 − 1 1 − ] , and 1 / 2 [ 0 1 − 1 ] , which are not easily observable in conventional HRTEM characterization processes, in electro-deposited Cu thin films. The Burgers vectors were determined. Moreover, this paper also attempted to observe screw dislocations that are challenging to observe in high-resolution transmission electron microscopy. By shifting a pair of diffraction extinction spots and superimposing the reconstructed images before and after the shift, screw dislocations with a Burgers vector of 1 / 2 [ 01 1 − ] were successfully observed in electro-deposited Cu thin films. [ABSTRACT FROM AUTHOR]

Fault diagnosis of analog circuits is a classical problem, and its difficulty lies in the similarity between fault features. To address the issue, an end-to-end mutually exclusive autoencoder (EEMEAE) fault diagnosis method for analog circuits is proposed. In order to make full use of the advantages of Fourier transform(FT) and wavelet packet transform(WPT) for extracting signal features, the original signals processed by FT and WPT are fed into two autoencoders respectively. The hidden layers of the autoencoders are mutually exclusive by Euclidean distance restriction. And the reconstruction layer is replaced by a softmax layer and 1-norm combined with cross-entropy that can effectively enhance the discriminability of features. Finally, the learning rate is adjusted adaptively by the difference of loss function to further improve the convergence speed and diagnostic performance of the model. The proposed method is verified by the simulation circuit and actual circuit and the experimental results illustrate that it is effective. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is a distributed machine learning framework that enables scattered participants to collaboratively train machine learning models without revealing information to other participants. Due to its distributed nature, FL is susceptible to being manipulated by malicious clients. These malicious clients can launch backdoor attacks by contaminating local data or tampering with local model gradients, thereby damaging the global model. However, existing backdoor attacks in distributed scenarios have several vulnerabilities. For example, (1) the triggers in distributed backdoor attacks are mostly visible and easily perceivable by humans; (2) these triggers are mostly applied in the spatial domain, inevitably corrupting the semantic information of the contaminated pixels. To address these issues, this paper introduces a frequency-domain injection-based backdoor attack in FL. Specifically, by performing a Fourier transform, the trigger and the clean image are linearly mixed in the frequency domain, injecting the low-frequency information of the trigger into the clean image while preserving its semantic information. Experiments on multiple image classification datasets demonstrate that the attack method proposed in this paper is stealthier and more effective in FL scenarios compared to existing attack methods. [ABSTRACT FROM AUTHOR]

We consider estimates for the Fourier transform of measures concentrated on smooth surfaces given by the graph of a smooth function with simple Arnold singularities such that both principal curvatures of the surface vanish at some point. We prove that if the multiplicity of the critical point of the function does not exceed , then the Fourier transforms of the corresponding surface measures belong to for any . Note that for any smooth surface the Fourier transform of a nontrivial surface measure with compact support does not belong to ; i.e., the -estimate obtained is sharp. Moreover, there exists a function with an singularity (the multiplicity of the critical point of the function is equal to ) such that the Fourier transform of the corresponding surface measure does not belong to , which shows the sharpness of the results for the multiplicity of the critical point. [ABSTRACT FROM AUTHOR]

Load forecasting is a research hotspot in academia; in the context of new power systems, the prediction and determination of load reserve capacity is also important. In order to adapt to new forms of power systems, a day-ahead automatic generation control (AGC) reserve capacity demand prediction method based on the Fourier transform and the attention mechanism combined with a bidirectional long and short-term memory neural network model (Attention-BiLSTM) optimized by an improved whale optimization algorithm (IWOA) is proposed. Firstly, based on the response time, Fourier transform is used to refine the distinction between various types of load reserve demand, and the power of the AGC reserve band is calculated using Parseval's theorem to obtain the reserve capacity demand sequence. The maximum mutual information coefficient method is used to explore the relevant influencing factors of the AGC reserve sequence concerning the data characteristics of the AGC reserve sequence. Then, the historical daily AGC reserve demand sequences with relevant features are input into the Attention-BiLSTM prediction model, and the improved whale algorithm is used to automatically find the optimal hyperparameters to obtain better prediction results. Finally, the arithmetic simulation results show that the model proposed in this paper has the best prediction performance with the upper (0.8810) and lower (0.6651) bounds of the coefficient of determination ( R 2 ) higher than the other models, and it has the smallest mean absolute percentage error ( M A P E ) and root mean square error ( R M S E ). [ABSTRACT FROM AUTHOR]

This paper discussed the fracture analysis of two collinear cracks under a thermo-magnetic-electric-elastic field. Taking advantage of the permeable crack models and the singular integral equation, the analytical solutions of important parameters around two collinear cracks are obtained. An example is used to demonstrate the method provided in this paper. The effects of the dimensionless quantities between the upper and lower crack surfaces, such as heat flux on the crack surface, electric displacement, magnetic induction per unit thickness, and the corresponding intensity factors near the inner and outer crack tips, are shown in the case analysis. It should be emphasized that because the theoretical solution obtained in this paper has an explicit form, it is convenient to solve the stress intensity factor. In particular, it is very convenient to solve the influence of various physical quantities on the stress intensity factor of the crack tip. [ABSTRACT FROM AUTHOR]

The utilization of broadband quantization data increases the possibility of practical applications for fish target recognition based on the acoustic scattering theory. However, the quantification of broadband data is more complex than that of narrowband systems, requiring consideration of the broadband characteristics of split-beam transducers, seawater absorption, and circuits. This paper elucidates the scatterer acoustic field equation, transducer power equation, and signal processing flow in split-beam broadband quantization technology for engineering applications. A broadband calculation model based on transducer parameters is proposed to enhance the generalization ability of broadband quantization technology to different types of sonar. The classical echo integration method is combined with Fourier transform to meet the requirements of target strength (TS) estimation under broadband signals. This paper includes a series of experiments to prove the rationality and effectiveness of the method. The results demonstrate that the provided calculation model can more accurately reflect the backscattering characteristics of the scatterer, but certain errors remain. This article analyzes the sources of errors and validates the effectiveness of the new TS calculation method. [ABSTRACT FROM AUTHOR]

In this paper we consider the Fourier transform of the convolution of a distribution and a function which is an element of the space S0(ℝ). Also, we give an application of the obtained result to the sequences that converge in the same space, and we give their analytic representation. [ABSTRACT FROM AUTHOR]

The paper concerns problems of the recovery of operators from noisy information in weighted L q -spaces with homogeneous weights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the L p -metric. [ABSTRACT FROM AUTHOR]

The product q · q in Section 4 and Appendix should be replaced by qq. [ABSTRACT FROM AUTHOR]

This paper studies thermo-hydro-mechanical (T-H-M) coupled responses of layered transversely isotropic (TI) saturated media under moving thermal and mechanical loads. Firstly, governing equations including dynamic balance equations, T-H-M coupled constitutive equations, and generalized energy equations are established based on the thermodynamics and poroelastic mechanics. Next, the Fourier transform technology is utilized to transform complex coupled partial differential equations into ordinary ones in the wavenumber domain. With the help of a moving coordinate system, the key matrix equation of the moving load problem is derived. Then, combining with boundary, external load and interlayer continuity conditions, the extended precise integration method (PIM) is used to derive the solution in the wavenumber domain. After using the Gauss-Legendre numerical integration technique, the physical solution is obtained by programming on the MATLAB platform. Finally, numerical examples are designed to verify the proposed method, and further explore the influences of thermal loads, TI permeability and stratification on the T-H-M response. [ABSTRACT FROM AUTHOR]

Through optimization of terminal frequencies and effective sampling rates, we have developed nonlinear sawtooth-shaped frequency sweeps for efficient Fourier transform ion mobility mass spectrometry (FT-IM-MS) experiments. This is in contrast to conventional FT-IM-MS experiments where ion gates are modulated according to a linear frequency sweep. Linear frequency sweeps are effective but can be hindered by the amount of useful signal obtained using a single sweep over a large frequency range imposed by ion gating inefficiencies, particularly small ion packets, and gate depletion. These negative factors are direct consequences of the inherently low gate pulse widths of high-frequency ion gating events, placing an upper bound on FT-IM-MS performance. Here, we report alternative ion modulation strategies. Sawtooth frequency sweeps may be constructed for the purpose of either extending high-SNR transients or conducting efficient signal-averaging experiments for low-SNR transients. The data obtained using this approach show high-SNR signals for a set of low-mass tetraalkylammonium salts (<1000 m / z) where resolving powers in excess of 500 are achieved. Data for low-SNR obtained for multimeric protein complexes streptavidin (53 kDa) and GroEL (800 kDa) also reveal large increases in the signal-to-noise ratio for reconstructed arrival time distributions. [Display omitted] • Nonlinear frequency modulation increases efficiency and performance for atmospheric pressure ion mobility mass spectrometry. • Resolving power increases for low-mass analytes with high-SNR transients. • SNR increases for large multimeric proteins with low-SNR transients. [ABSTRACT FROM AUTHOR]

• Semi-analytic methods are used to solve 3D DPL problems. • Compared with FEM, the semi-analytic method has higher computational efficiency. • The phase lag of heat flow and the phase lag of temperature gradient have influence on the temperature response speed and the formation of temperature field. With the development of picosecond laser technology, the dual-phase-lagging (DPL) model is more suitable to describe the heat transfer problem with micro-scale effect and micro-time effect. In this paper, a three-dimensional dual-phase-lagging heat transfer model for picosecond laser processing is established. Then Fourier transform (FT) and Laplace transform (LT) are used to derive the frequency response functions (FRFs) of the problem in the frequency domain, and the inverse Laplace transform (ILT) and discrete-convolution fast Fourier transform (DC-FFT) algorithm are used to solve the temperature field. The calculation accuracy of this method is verified and the effect of phase lag constants on temperature field is studied. The results show that the semi-analytical method has a high accuracy for solving the dual-phase-lagging heat conduction model, and the phase lag of heat flux will affect the heating rate in the heating stage, and the phase lag of temperature gradient will delay the formation of temperature field. The effect of phase lag constants on temperature-time history is investigated and the related phenomena are explained by using the two-step heat transfer theory. This semi-analytical method provides a new approach to solve the problem of three-dimensional dual-phase-lagging heat transfer. [ABSTRACT FROM AUTHOR]