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With quaternion matrices and quaternion tensors being gradually used in the color image and color video processing, the block diagonalization of block circulant quaternion matrices has become a key issue in the establishment of T-product based methods for quaternion tensors. Out of this consideration, we aim at establishing a fast calculation approach for the block diagonalization of block circulant quaternion matrices with the help of the fast Fourier transform (FFT). We first show that the discrete Fourier matrix F p cannot diagonalize p × p circulant quaternion matrices, nor can the unitary quaternion matrices F p j and F p (1 + j) / 2 with j being an imaginary unit of quaternion algebra. Then we prove that the unitary octonion matrix F p p with p = l , il or (l + il) / 2 ( l , il being imaginary units of octonion algebra) can diagonalize a circulant quaternion matrix of size p × p , which further means that a block circulant quaternion matrix of size m p × n p can be block diagonalized at the cost of O (m n p log p) via the FFT. As one of applications, we give a fast algorithm to speed up the calculation of the T-product between m × n × p and n × s × p third-order quaternion tensors via FFTs, whose computational magnitude is almost 1/p of the original one. As another application, we propose an effective compression strategy for third-order quaternion tensors with a certain low-rankness. Simulations on the color image and color video compression demonstrate that our compression strategy with no QSVD involved, can achieve higher quality compression in terms of PSNR values at much less time costs, compared with the QSVD-based methods. [ABSTRACT FROM AUTHOR]

UNICEF reports that health workers frequently use the child's breath count to diagnose pneumonia in nations with weak health care systems (i.e., few doctors, limited access to laboratories, and chest x-rays). Counting a child's respiratory rate (RR) manually using an acute respiratory infection timer is a challenging task among health workers. The misclassification of an observed rate would lead to improper treatment. In the work, a low-cost noncontact automatic counter was proposed to estimate the RR using a Time of Flight (ToF) sensor. Here, the ToF sensor is pointed at the chest of the human body with clothes to capture chest wall expansion and contraction. This chest wall movement can be related to the inhalation and exhalation of breathing, which can be related to respiration activity. Clear breathing patterns were observed in the extracted respiration signal and standard signal processing techniques were employed to estimate the respiration rate. The device can measure the subject's respiration rate at a wide range of frequencies (slow, normal, and rapid), ranging from 4 to 100 breaths per minute (bpm). The single-pixel ToF sensor with a 940 nm wavelength is illumination-invariant in indoor applications and robust against clothes. The device's performance was assessed by comparing the attained real-time signals with the ground truth signals. The proposed device's estimated mean absolute error (MAE) has an error of less than 2 bpm for any frequency range. The device is computationally efficient, taking less than 36 ms to estimate and display the RR readings in the user interface. [ABSTRACT FROM AUTHOR]

In this paper, we consider solutions for discrete systems arising from multi-term time-fractional diffusion equations. Using discrete sine transform techniques, we find that all-at-once systems of such equations have a structure similar to that of diagonal-plus-Toeplitz matrices. We establish a generalized circulant approximate inverse preconditioner for the all-at-once systems. Through a detailed analysis of the preconditioned matrices, we show that the spectrum of the obtained preconditioned matrices is clustered around one. We give some numerical examples to demonstrate the effectiveness of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

Human activity recognition (HAR) with wearable inertial sensors is a burgeoning field, propelled by advances in sensor technology. Deep learning methods for HAR have notably enhanced recognition accuracy in recent years. Nonetheless, the complexity of previous models often impedes their use in real-life scenarios, particularly in online applications. Addressing this gap, we introduce SenseMLP, a novel approach employing a multi-layer perceptron (MLP) neural network architecture. SenseMLP features three parallel MLP branches that independently process and integrate features across the time, channel, and frequency dimensions. This structure not only simplifies the model but also significantly reduces the number of required parameters compared to previous deep learning HAR frameworks. We conducted comprehensive evaluations of SenseMLP against benchmark HAR datasets, including PAMAP2, OPPORTUNITY, USC-HAD, and SKODA. Our findings demonstrate that SenseMLP not only achieves state-of-the-art performance in terms of accuracy but also boasts fewer parameters and lower floating-point operations per second. For further research and application in the field, the source code of SenseMLP is available at [ABSTRACT FROM AUTHOR]

In IoT applications, prediction models have fundamental challenges such as real-time processing, producing results with considerable/without delay, and taking action against pattern drift. While existing models can excel when data statistics remain relatively stable, real-time systems may encounter difficulties, particularly when confronted with dynamic shifts in data behavior. Analyzing data streams generated by different IoT applications and detecting complex pattern on the fly has become an open area of research. Complex event processing with adaptivity is a must to get desired features in such models. To address this issue, a comprehensive model for prediction has been proposed in this paper. It consists of two phases: (1) the basic model is constructed using historical data, (2) a fast Fourier transform-based adaptive support vector regression (FFT-ASVR) approach is proposed to predict events embedded in IoT data streams. FFT-ASVR predicts abnormal events by experiencing a change in data streams with real-time model updation. The performance of FFT-ASVR with a similar existing method SVM-RBF is presented using real-time traffic data of Madrid city. The proposed approach has significant improvement in terms of mean absolute percentage error (MAPE) for prediction, is adaptive in nature, and is also capable of handling the issue of pattern drift. [ABSTRACT FROM AUTHOR]

Surface plasmon resonance (SPR) sensor is a fast, label-free and real-time optical sensing technology. In this paper, an improved data-processing method of centroid algorithm was employed and the Fast Fourier Transform Algorithm (FFT) was also adopted to improve the standard deviation (SD) of resonance angle, a representative of sensing precision. The significant parameters in this study are the height ratio and selected spectrum width of centroid algorithm and the FFT cut-off frequency. To generate a RI change of sensing medium, pure water and 3 g/L NaCl solution were prepared for experiments. The SD was optimized in case of pure water, and then the RI sensitivity was also calculated for comparison. As results, two optimized regions were obtained, those are upper and under regions. The upper region is related with the selected spectrum width, and a low FFT cut-off frequency was suitable. The under region has a little change with the spectrum width and the FFT cut-off frequency. In experiments, the resolution of 2.11 × 10− 6 RIU was obtained with samples of ultrapure water and 3 g/L NaCl solution. Furthermore, the limit of detection for BSA molecule as low as 8.36 pM was achieved without any other noise reduction method. This study aims to provide a new design idea and theoretical support for the optimal design of SPR sensor, and has an important research significance and application prospect in the fields of environmental monitoring and biochemical sensing. [ABSTRACT FROM AUTHOR]

In this study, we propose a method for recommending appropriate combinations of stocks based on the waveforms of stock price changes. Many Japanese prefer to maintain stability when managing their assets. Specialized knowledge is required to invest in stocks while reducing risk. Hence, stock recommendation methods with different characteristics are required. Stock price movements can be captured as waveforms. Dynamic time warping (DTW), cross–correlation functions, and fast Fourier transforms (FFTs) are used to compare the features of the waveforms. A combination of stocks with different waveforms avoids the risk of simultaneous crashes. In the current experiment, one–year stock waveforms are used to obtain the recommended stock. The combined stocks selected using the DTW, cross–correlation functions, and FFT are shown to be suitable. [ABSTRACT FROM AUTHOR]

Based on contact data, the dynamics of the abundance (N) and biomass (B) of phytoplankton in 2013–2014 and the concentration of chlorophyll a (Cсhl) in 2000–2003 and 2008–2021 were analyzed using fast Fourier transform (FFT) under conditions of changing water temperature (T) in the vicinity of Sevastopol in the Black Sea. Estimates of the contribution made by the variability of the annual and semiannual harmonics of N, B, Cchl, T to the seasonal cycle amounted to more than 56% for all parameters. A significant relationship between B and Cchl (r < –0.83) at two stations indicates the aging of microalgae. The dominance of different groups of microalgae in the phytoplankton biomass has been detected. A typical period of 2–4 years is distinguished in the interannual variability of Cchl and T in different seasons. [ABSTRACT FROM AUTHOR]

Purpose: Probe-based confocal laser endomicroscopy (pCLE) enables visualization of cellular tissue morphology during surgical procedures. To capture high-quality pCLE images during tissue scanning, it is important to maintain close contact between the probe and the tissue, while also keeping the probe perpendicular to the tissue surface. Existing robotic pCLE tissue scanning systems, which rely on macroscopic vision, struggle to accurately place the probe at the optimal position on the tissue surface. As a result, the need arises for regression of longitudinal distance and orientation via endomicroscopic vision. Method: This paper introduces a novel method for automatically regressing the orientation between a pCLE probe and the tissue surface during robotic scanning, utilizing the fast Fourier vision transformer (FF-ViT) to extract local frequency representations and use them for probe orientation regression. Additionally, the FF-ViT incorporates a blur mapping attention (BMA) module to refine latent representations, which is combined with the pyramid angle regressor (PAR) to precisely estimate probe orientation. Result: A first of its kind dataset for pCLE probe-tissue orientation (pCLE-PTO) has been created. The performance evaluation demonstrates that our proposed network surpasses other top regression networks in accuracy, stability, and generalizability, while maintaining low computational complexity (1.8G FLOPs) and high inference speed (90 fps). Conclusion: The performance evaluation study verifies the clinical value of the proposed framework and its potential to be integrated into surgical robotic platforms for intraoperative tissue scanning. [ABSTRACT FROM AUTHOR]

Ptychography today is considered the most natural and effective method for approaching the diffraction limit of optical resolution. The principal scheme of a ptychoscope does not contain refractive or focusing elements and includes a coherent light source, a platform for moving (macroscopic) object, and a detector for registering radiation passed through or reflected by the object associated with a computer for processing diffraction patterns. In classical optics, the main task in achieving high spatial resolution is the correction and elimination of aberrations of optical systems, while in ptychography spatial resolution mainly depends on the reliability of registration and computer processing of diffraction patterns with large numerical apertures. The key idea of ptychography is to obtain an image by computer processing of overlapping diffraction patterns (scans). When moving the object it is assumed that the illuminating beam and the position of the detector remain unchanged. Ptychography is used in a wide range of radiation wavelengths from infrared to X-ray, and it is possible to do without imaging optics. In this work, the possibility of obtaining an amplitude-phase image of the surface relief of an object inclined to the incident one was studied. [ABSTRACT FROM AUTHOR]

We present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009), which we extend by incorporating seasonal stochastic volatility represented with two different sinusoidal expressions. We obtain a quasi-analytical representation of the characteristic function of the futures log-prices and closed-form expressions for standard European options' prices using the fast Fourier transform algorithm. We price plain vanilla options on the Henry Hub natural gas futures contracts, using our model and extant models. We obtain higher accuracy levels with our model than with the extant models. [ABSTRACT FROM AUTHOR]

As one of the main components of the Earth orientation parameters, short-term prediction of the geodetic polar motion series is crucial in the field of deep-space exploration, high-precision positioning, and timing services, which require high real-time performance. Additionally, its middle- and long-term prediction is equally important in climate forecasting and geodynamics research. In this study, we propose the combined BiLSTM+ARIMA model, which is based on bidirectional long- and short-term memory (BiLSTM) and autoregression integrated moving average (ARIMA). First, ensemble empirical mode decomposition (EEMD) is performed as a filter to decompose the polar motion time series to obtain low- and high-frequency signals. The EOP14 C04 time series provided by International Earth Rotation and Reference Systems Service and decomposed by EEMD includes low-frequency signals like the long-term trend, decadal oscillation, Chandler wobble, and prograde annual wobble, along with shorter-period high-frequency signals. Second, low- and high-frequency signals are predicted using BiLSTM and ARIMA models, respectively. Finally, the low- and high-frequency signal forecast components are reconstructed to obtain geodetic polar motion predictions. In middle- and long-term polar motion prediction, the results show that the proposed model can improve the prediction accuracy by up to 42% and 17%, respectively. This demonstrated that the BiLSTM+ARIMA model can effectively improve the accuracy of polar motion prediction. [ABSTRACT FROM AUTHOR]

Electrochemical impedance spectroscopy (EIS) is a measurement method widely used for non-destructive analysis and diagnostics in various electrochemical fields. From the measured dependence of the battery impedance on the frequency, it is possible to determine the parameters of various equivalent electrical circuit models of the battery. The conventional method of battery measurement using single-sine EIS is currently one of the most widely used methods for the analysis of lithium-ion batteries. However, its most significant disadvantage is the relatively long measurement time. For this reason, there is a growing demand for faster methods using fast-Fourier transform or pseudo-random sequences. A description of various EIS methods applications is provided in this paper. [ABSTRACT FROM AUTHOR]

Purpose: The current study focuses on measuring the level of vibration and noise produced by a direct injection diesel engine when running on a mixture of molybdenum trioxide (MoO3) nanoparticles and Calophyllum inophyllum biodiesel (B20). Methods: The nanoparticles were used in an amount of 75 ppm and mixed with a surfactant and dispersant. In addition, the prepared fuel samples were tested on a diesel engine to investigate the vibration and noise characteristics by changing the injection pressures to 200 bar, 220 bar and 240 bar. Results and conclusion: The addition of nanoparticles to B20 has significantly reduced vibration and noise, especially when using nanofuel enriched with dispersants. In addition, the increased pressure during fuel injection resulted in reduced vibration and noise levels. Using B20 + MoO3 75 ppm + Dispersant 75 ppm fuel blend gave the most favourable results regarding RMS velocity and noise levels compared to the base diesel fuel. The progressive reduction in vibration and noise levels was seen as a result of the increased injection pressure. At a pressure of 240 bar, the B20 + MoO3 75 ppm + dispersant 75 ppm has shown a lower vibration and noise intensity than diesel and other fuel samples. The RMS velocity of RMS noise of B20 + MoO3 75 ppm + dispersant 75 ppm are 0.591 m/s, 0.568 m/s, and 0.491 m/s at 200 bar, 220 bar and 240 bar while the RMS noise is 68.266 dB (A), 66.283 dB (A), and 65.857 dB (A) respectively. The most decrease in vibration and noise was 28.76% and 9.78%, respectively compared to regular diesel for B20 + MoO3 75 ppm + dispersant 75 ppm at 240 bar. Finally, the kurtosis and skewness of the vibration data are within the normal range, which indicates that the distribution corresponds to the ideal normal distribution. [ABSTRACT FROM AUTHOR]

Purpose: This work designs a procedure for structural damage assessment in beams under moving loads. The proposal is based on the respective alterations of hybrid vibrational factors with respect to the structural changes, whereby matching them for accurate predictions. These hybrid factors are extracted from the vibrational responses and then are employed for an artificial neural network (ANN) to assess the structural condition. Methods: An experiment is deployed to generate a databank for evaluation as well as ANN training. The maximal overlap discrete wavelet transform (MODWT) and the fast Fourier transform (FFT) are incorporated to split original signals into several power bands, which helps to exploit characteristics of individual vibrational modes: centroids and comparative powers of allocated spectra. The extracted hybrid factors are then fed into an ANN to predict the damage condition of the beam. The training process of this ANN uses a databank of extracted features from measured signals. Results: The paper successfully finds out the damage-sensitive feature through signal processing. Alternatively, the implemented experiment provides a rich databank for the ANN training, and the training performance reaches a high accuracy. Moreover, the testing results reveal the superior generalization of the ANN because of automatic predictions with high precision. This proves the contribution of the study that the exploited features are proper for structural assessment, and the trained ANN learns the correlation of vibration features and structural state well. Conclusions: The automation and effectiveness of the proposed approach are endorsed, which has high applicability and accuracy for damage assessment in beams. The proposed method is mainly devoted to identifying, quantifying, and localizing damage. [ABSTRACT FROM AUTHOR]

One of the most crucial components of music is accompaniment creation and chord arrangement is essential to accompanying development. A greater level of musical skill and a thorough knowledge of music theory are often required for competent accompaniment production. To organise and provide space for additional chords, a Bengio Nesterov Momentum optimizer to Bidirectional Encoder Representations from Transformers (BNM-BERT) intuitive computer approach is provided. To replace manual chord creation for accompaniment, the work has generated Optimised Intellectual Natural Language Processing Music Accompaniment. An Overlapping Segmentation based Independent Component Analysis (OS-ICA) technique, which ensuring the frame interval signals are continuous and smoothness is used to begin the procedure after segmentation. Then, theme signal feature extraction is performed using the Dual Fast Transform (DFT), which combines the Continues Wavelet Transform (CWT) and Fast Fourier Transform (FFT) for feature extraction from music audio signals. This results in coefficients for the timbral texture, tonal texture, Pitch class Profile (PCP), and rhythmic activity, among other features of musical information that are specific to the sound spectrum. Then, to enhance the musical accompaniment, very pertinent rhythmic signals are chosen employing HE instated Jellyfish inquiry advancement (HEinit-JSO). The unlabeled audio stream is labelled using average linkage based on hierarchical divisive clustering after the feature is chosen. Finally, automatic chord label creation is done using the BNM- BERT model. The examination reveals that the well-before algorithm outperforms the standards in terms of reconstructive probability and generating effectiveness. Additionally, it shows how cascading effects can be used for accompaniment improvement, texture generation from chord circumstances, and chord analysis. [ABSTRACT FROM AUTHOR]

Purpose: Data preprocessing is one of the key steps in any fault diagnosis process. The real data obtained from machines carry a lot of noise and inferred signals from other parts of the machine or environment. The intensity of this contamination varies with the sampling rate of data acquisition. To filter out these components and enhance the quality of the features generated from these data, several data preprocessing techniques are described in the literature. But the major concerns are the limitations of these techniques and the proper selection of sampling rates for data acquisition. Methods: This paper presents a comprehensive overview of parametric and non-parametric data preprocessing techniques for gearbox fault diagnosis and how these techniques preserve their properties under different sampling rates. Both analytically simulated signals and experimental signals are used in this work to check the effectiveness of these techniques at different sampling rates. Results and Conclusions: The obtained results clearly show that data preprocessed by a non-parametric filter contains significantly more information than data preprocessed by a parametric filter or without a filter. Even for a low (affordable) sampling rate, the non-parametric filter works well as compared to the parametric filter and with no filter. The proposed work has potential relevance in the industrial IoT for online condition monitoring of gearboxes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general notion of convolution. Let D be a finite domain and let D n be the set of n-length vectors (tuples) of D . Let f : D × D → D be a function and let ⊕ f be a coordinate-wise application of f. The f -Convolution of two functions g , h : D n → { - M , ... , M } is (g ⊛ f h) (v) : = ∑ v g , v h ∈ D n s.t. v = v g ⊕ f v h g (v g) · h (v h) for every v ∈ D n . This problem generalizes many fundamental convolutions such as Subset Convolution, XOR Product, Covering Product or Packing Product, etc. For arbitrary function f and domain D we can compute f -Convolution via brute-force enumeration in O ~ (| D | 2 n · polylog (M)) time. Our main result is an improvement over this naive algorithm. We show that f -Convolution can be computed exactly in O ~ ((c · | D | 2 ) n · polylog (M)) for constant c : = 3 / 4 when D has even cardinality. Our main observation is that a cyclic partition of a function f : D × D → D can be used to speed up the computation of f -Convolution, and we show that an appropriate cyclic partition exists for every f. Furthermore, we demonstrate that a single entry of the f -Convolution can be computed more efficiently. In this variant, we are given two functions g , h : D n → { - M , ... , M } alongside with a vector v ∈ D n and the task of the f -Query problem is to compute integer (g ⊛ f h) (v) . This is a generalization of the well-known Orthogonal Vectors problem. We show that f -Query can be computed in O ~ (| D | ω 2 n · polylog (M)) time, where ω ∈ [ 2 , 2.372) is the exponent of currently fastest matrix multiplication algorithm. [ABSTRACT FROM AUTHOR]

Background: Piston rings are one of the most vital and critical components of ICEs. The purpose of the piston rings is to provide effective sealing so that the heat from the piston can be transferred to the cylinder wall and oil from the crankcase should be kept away from the combustion chamber. The wear of piston rings directly affects the efficiency and performance of the engine. As a result, to diagnose piston rings faults, an effective condition monitoring and fault diagnosis methodology must be adopted. Purpose: In this study, an attempt has been carried out to diagnose piston ring scuffing faults using vibration signature analysis. Methods: An accelerometer sensor was used to collect time domain vibration signals from the healthy and all faulty engine operating conditions. Spectral feature analysis techniques such as the fast Fourier transform (FFT), power spectrum density (PSD), and empirical mode decomposition (EMD) were used to post-process the acquired signals. Further, a neural network technique known as multi-layer perceptron (MLP) was employed to develop the model for the classification of piston ring scuffing faults. In the end, the outcomes of signal processing and machine learning techniques were evaluated for both engine operating conditions. Results: The results showed clear shreds of fault diagnostic information using FFT, PSD, and EMD analyses whereas the MLP technique provided the best neural network architecture with the least mean squared error value. Conclusion: The results obtained using the signal processing techniques can be considered as a reference for the diagnosis of various engine component faults viz. gudgeon pin, gears, bearings, camshaft, etc. Further, the classification models created with these signals may be utilized in the automobile sector to forecast faults in the previously stated engine components. [ABSTRACT FROM AUTHOR]

This contribution details the effective and accurate determination of the time-domain harmonic state estimation (TDHSE) of power networks interconnecting wind generation sources. The TDHSE method obtains the state variables of power networks and the system inputs. The algorithm uses a limited number of measuring devices, which can be contaminated with noise and/or gross errors. The wind generation source model represents the dynamic operation of a wind energy conversion system. It is based on a type-4 wind turbine and a direct-drive permanent magnet synchronous generator with a full scale back-to-back power converter. The wind generation source assumes wind fluctuations and changes in the angular speed control drive to estimate its dynamic behaviour and the effect on the power network. Case studies are considered for the analysis of a three-phase power network, i.e. with harmonic injections, with a wind generation source and with a wind farm. The TDHSE results of the analysed case studies are validated through direct comparison against the PSCAD/EMTDC® solution, obtaining a close agreement between the TDHSE and simulator responses. [ABSTRACT FROM AUTHOR]

Apples are susceptible to various types of damage during the production process. Such damage not only affects the appearance and edibility of the apples but also can result in the infection of healthy apples, leading to secondary economic losses. Therefore, it is crucial to properly handle damaged apples and re-sort them to enhance their utilization value and optimize resource use. To quickly and accurately identify apple damage and perform sorting in real time, addressing the resource limitations of mobile devices and the difficulty of extracting deep network image features, this study proposes a lightweight real-time apple damage classification network, Fast Fourier Transform Channel Attention (FFTCA)-YOLOv8n-cls. The FFTCA module focuses on the frequency domain feature information of images in deep networks, enhancing the network’s feature extraction capabilities. Additionally, it integrates Convolutional Block Attention Module (CBAM) and Distribution Shifting Convolution to capture channel and spatial information of images in shallow networks and accelerate network inference. Finally, FFTCA-YOLOv8n-cls is compared with typical lightweight classification networks. Experimental results show that this network has better classification accuracy and faster inference speed. Specifically, the FFTCA-YOLOv8n-cls network is only 0.601 MB in size, achieving a classification accuracy of 96.03%, a recall of 96.08%, and an F1-score of 96.05%, demonstrating its feasibility in real-time apple damage sorting. Moreover, this study applies the network to sorting robots, completing backend inference on servers and real-time inference on embedded devices to adapt to different working environments, achieving real-time sorting of damaged apples and validating the network’s application effectiveness. [ABSTRACT FROM AUTHOR]

Tauc plots have been massively used to determine the band gap energy Eg\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {E_{{\text{g}}} } \right)$$\end{document} of semiconductors, but its implementation still possibility of erroneous estimates, which can be attributed by the straight-line method that involving subjective analysis of the researcher's own judgment. Here, we have collaborated Kubelka–Munk, Taylor expansion, and density functional theory calculation as general method and fast Fourier transform (FFT) as a fresh technique for determining more accurately band gap. Based on UV–Vis spectra analysis and QE simulation, the band gap range of TiO2 from our calculation can be reported to be (3.26 ± 0.3) eV for a purity (~ 97.23%) with a crystallinity (~ 75%). It was found that FFT is a new viable comparison method to identify the suitable Eg\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$E_{{\text{g}}}$$\end{document} of semiconductors, which is crucial for optimizing material design and tailoring their functionality for various applications. [ABSTRACT FROM AUTHOR]

Consider a multivariate polynomial f∈K[x1,…,xn]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f \in K [x_1, \ldots , x_n]$$\end{document} over a field K, which is given through a black box capable of evaluating f at points in Kn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$K^n$$\end{document}, or possibly at points in An\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$A^n$$\end{document} for any K-algebra A. The problem of sparse interpolation is to express f in its usual form with respect to the monomial basis. We analyze the complexity of various old and new algorithms for this task in terms of bounds D and T for the total degree of f and its number of terms. We mainly focus on the case when K is a finite field and explore possible speed-ups. [ABSTRACT FROM AUTHOR]

In this contribution, the time-domain harmonic state estimation is evaluated using the real-time digital simulation, Kalman filter, an optimal measurement algorithm and a physical scaled-down laboratory implementation. This methodology is implemented using MATLAB/Simulink® and runs on RT-LAB® platform in real time. The optimal placement algorithm of measurement devices is used to obtain full observability of the system. This measurement algorithm finds the optimal placement with a limited number of measurement devices, whose measurements may be contaminated with noise. The measurement model is implemented in the physical test power system. Besides, the state estimator assesses the system inputs (internal generator voltages, nonlinear electrical load variables) whose dynamics are totally unknown. The harmonic content of the waveforms is obtained through the fast Fourier transform. The estimated responses in the case studies using the RT-LAB® platform are validated through direct comparison against those obtained in the physical implementation of the electrical power system, obtaining satisfactory results. [ABSTRACT FROM AUTHOR]