Explore the vast range of titles available.

Intelligent fault diagnosis methods based on signal analysis have been widely used for bearing fault diagnosis. These methods use a pre-determined transformation (such as empirical mode decomposition, fast Fourier transform, discrete wavelet transform) to convert time-series signals into frequency domain signals, the performance of dignostic system is significantly rely on the extracted features. However, extracting signal characteristic is fairly time consuming and depends on specialized signal processing knowledge. Although some studies have developed highly accurate algorithms, the diagnostic results rely heavily on large data sets and unreliable human analysis. This study proposes an automatic feature learning neural network that utilizes raw vibration signals as inputs, and uses two convolutional neural networks with different kernel sizes to automatically extract different frequency signal characteristics from raw data. Then long short-term memory was used to identify the fault type according to learned features. The data is down-sampled before inputting into the network, greatly reducing the number of parameters. The experiment shows that the proposed method can not only achieve 98.46% average accuracy, exceeding some state-of-the-art intelligent algorithms based on prior knowledge and having better performance in noisy environments.

Positive definiteness is determined for a wide class of functions relevant in the study of operator means and their norm comparisons. Then, this information is used to obtain an abundance of new sharp (unitarily) norm inequalities comparing various operator means and sometimes other related operators.

Die Dissertation beschreibt die Synthese und Charakterisierung verschiedener Münzmetallkomplexe an einem strukturgebenden tetradentaten monoanionischen PNNP Liganden. Von Interesse war die Frage nach einer möglichen Korrelation der lumineszenten Eigenschaften mit ausgewählten strukturellen Parametern. Es wurden daher selektiv Komplexe mit verschiedenen Kombinationen aus Art und Anzahl an Metallatomen innerhalb des Ligandensystems realisiert. Nach der Vorstellung von homometallischen zwei- und dreikernigen Komplexen, konnten, ausgehend von der zweikernigen Goldverbindung, verschiedene vierkernige und ein sechskerniger Goldkomplex synthetisiert werden. Die Verbindungen wurden intensiv bezüglich ihrer lumineszenten Eigenschaften, einige davon in verschiedenen Phasen, und zudem teilweise theoretisch untersucht. Aufbauend darauf gelang die Darstellung mehrerer Lanthanoid-Münzmetallkomplexe, die ebenfalls bezüglich ihrer lumineszenten Eigenschaften analysiert wurden. Außerdem wurden in einem kleinen Teil der Arbeit Münzmetallkomplexe mit einem Ferrocenylbisamidinatliganden vorgestellt, die teilweise eine kurze Fe M Distanz aufweisen.

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe\"Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

It's challenging to measure non-repetitive events in real time in the field of instrumentation and measurement. Dispersive Fourier transformation is an emerging method that permits capture of rare events, such as optical rogue waves and rare cancer cells in blood. This Review article covers the principle of dispersive Fourier transformation and its implementation in diverse applications. Dispersive Fourier transformation is an emerging measurement technique that overcomes the speed limitations of traditional optical instruments and enables fast continuous single-shot measurements in optical sensing, spectroscopy and imaging. Using chromatic dispersion, dispersive Fourier transformation maps the spectrum of an optical pulse to a temporal waveform whose intensity mimics the spectrum, thus allowing a single-pixel photodetector to capture the spectrum at a scan rate significantly beyond what is possible with conventional space-domain spectrometers. Over the past decade, this method has brought us a new class of real-time instruments that permit the capture of rare events such as optical rogue waves and rare cancer cells in blood, which would otherwise be missed using conventional instruments. In this Review, we discuss the principle of dispersive Fourier transformation and its implementation across a wide range of diverse applications.

Background Advancements in high-throughput sequencing and deep learning have boosted single-cell RNA studies. However, current methods for annotating single-cell data face challenges due to high data sparsity and tedious manual annotation on large-scale data. Results Thus, we proposed a novel annotation model integrating FFT (Fast Fourier Transform) and an enhanced Transformer, named scFTAT. Initially, it reduces data sparsity using LDA (Linear Discriminant Analysis). Subsequently, automatic cell annotation is achieved through a proposed module integrating FFT and an enhanced Transformer. Moreover, the model is fine-tuned to improve training performance by effectively incorporating such techniques as kernel approximation, position encoding enhancement, and attention enhancement modules. Compared to existing popular annotation tools, scFTAT maintains high accuracy and robustness on six typical datasets. Specifically, the model achieves an accuracy of 0.93 on the human kidney data, with an F1 score of 0.84, precision of 0.96, recall rate of 0.80, and Matthews correlation coefficient of 0.89. The highest accuracy of the compared methods is 0.92, with an F1 score of 0.71, precision of 0.75, recall rate of 0.73, and Matthews correlation coefficient of 0.85. The compiled codes and supplements are available at: https://github.com/gladex/scFTAT . Conclusion In summary, the proposed scFTAT effectively integrates FFT and enhanced Transformer for automatic feature learning, addressing the challenges of high sparsity and tedious manual annotation in single-cell profiling data. Experiments on six typical scRNA-seq datasets from human and mouse tissues evaluate the model using five metrics as accuracy, F1 score, precision, recall, and Matthews correlation coefficient. Performance comparisons with existing methods further demonstrate the efficiency and robustness of our proposed method.

The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain. When the sampling is uniform, the fast Fourier transform (FFT) allows this calculation to be computed in O(N log N) operations rather than O(N²) operations. Unfortunately, when the sampling is nonuniform, the FFT does not apply. Over the last few years, a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform FFTs (NUFFTs). These rely on a mixture of interpolation and the judicious use of the FFT on an oversampled grid [A. Dutt and V. Rokhlin, \"SIAM J. Sci. Comput.\", 14 (1993), pp. 1368-1383]. In this paper, we observe that one of the standard interpolation or \"gridding\" schemes, based on Gaussians, can be accelerated by a significant factor without precomputation and storage of the interpolation weights. This is of particular value in two- and three-dimensional settings, saving either$10^{d}N$in storage in d dimensions or a factor of about 5-10 in CPU time (independent of dimension).

The radio spectrum is a scarce and extremely valuable resource that demands careful real-time monitoring and dynamic resource allocation. Dynamic spectrum access (DSA) is a new paradigm for managing the radio spectrum, which requires AI/ML-driven algorithms for optimum performance under rapidly changing channel conditions and possible cyber-attacks in the electromagnetic domain. Fast sensing across multiple directions using array processors, with subsequent AI/ML-based algorithms for the sensing and perception of waveforms that are measured from the environment is critical for providing decision support in DSA. As part of directional and wideband spectrum perception, the ability to finely channelize wideband inputs using efficient Fourier analysis is much needed. However, a fine-grain fast Fourier transform (FFT) across a large number of directions is computationally intensive and leads to a high chip area and power consumption. We address this issue by exploiting the recently proposed approximate discrete Fourier transform (ADFT), which has its own sparse factorization for real-time implementation at a low complexity and power consumption. The ADFT is used to create a wideband multibeam RF digital beamformer and temporal spectrum-based attention unit that monitors 32 discrete directions across 32 sub-bands in real-time using a multiplierless algorithm with low computational complexity. The output of this spectral attention unit is applied as a decision variable to an intelligent receiver that adapts its center frequency and frequency resolution via FFT channelizers that are custom-built for real-time monitoring at high resolution. This two-step process allows the fine-gain FFT to be applied only to directions and bands of interest as determined by the ADFT-based low-complexity 2D spacetime attention unit. The fine-grain FFT provides a spectral signature that can find future use cases in neural network engines for achieving modulation recognition, IoT device identification, and RFI identification. Beamforming and spectral channelization algorithms, a digital computer architecture, and early prototypes using a 32-element fully digital multichannel receiver and field programmable gate array (FPGA)-based high-speed software-defined radio (SDR) are presented.

Waveform design is a crucial factor in electronic surveillance (ES) systems. In this paper, we introduce an algorithm that designs a low probability of intercept (LPI) radar waveform. Our approach directly minimizes the detection probability of summation detectors based on FFT filter banks. The algorithm is derived from the general quadratic optimization framework, which inherits the monotonic properties of such methods. To expedite overall convergence, we have integrated acceleration schemes based on the squared iterative method (SQUAREM). Additionally, the proposed algorithm can be executed through fast Fourier transform (FFT) operations, enhancing computational efficiency. With some modifications, the algorithm can be adjusted to incorporate spectral constraints, increasing its flexibility. Numerical experiments indicate that our proposed algorithm outperforms existing ones in terms of both intercept properties and computational complexity.