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Independent component analysis (ICA), as a statistical and computational approach, has been successfully applied to digital signal processing. Performance analysis for the ICA approach is perceived as a challenging task to work on. This contribution concerns the complex-valued FastICA algorithm in the range of ICA over the complex number domain. The focus is on the robust and equivariant behavior analysis of the complex-valued FastICA estimator. Although the complex-valued FastICA algorithm as well as its derivatives have been widely used methods for approaching the complex blind signal separation problem, rigorous mathematical treatments of the robust measurement and equivariance for the complex-valued FastICA estimator are still missing. This paper strictly analyzes the robustness against outliers and separation performance depending on the global system. We begin with defining the influence function (IF) of complex-valued FastICA functional and followed by deriving its closed-form expression. Then, we prove that the complex-valued FastICA algorithm based on the optimizing cost function is linear-equivariant, depending only on the source signals. [ABSTRACT FROM AUTHOR]

In practical applications, the temporal completeness of knowledge graphs is of great importance. However, previous studies have mostly focused on static knowledge graphs, generally neglecting the dynamic evolutionary properties of facts. Moreover, the unpredictable and limited availability of temporal knowledge graphs, together with the complex temporal dependency patterns, make current models inadequate for effectively describing facts that experience temporal transitions. To better represent the evolution of things over time, we provide a learning technique that uses quaternion rotation to describe temporal knowledge graphs. This technique describes the evolution of entities as a temporal rotation change in quaternion space. Compared to the Ermitian inner product in complex number space, the Hamiltonian product in quaternion space is better at showing how things might be connected. This leads to a learning process that is both more effective and more articulate. Experimental results demonstrate that our learning method significantly outperforms existing methods in capturing the dynamic evolution of temporal knowledge graphs, with improved accuracy and robustness across a range of benchmark datasets. [ABSTRACT FROM AUTHOR]

Since the product of complex numbers and rectangular fuzzy complex numbers (RFCN) is not necessarily a RFCN in the former fuzzy complex linear system (FCLS), the scalar multiplication and addition operations of complex numbers and fuzzy complex numbers (FCN) based on a new representation of FCN are proposed. We also introduce a new method for solving FCLS, which can convert FCLS into two distinct linear systems. One is an n × n complex linear system, and the other is an (m n) × (m n) real linear system, where n is the number of unknown variables, and m is the number of substitutional cyclic sets composed of coefficients of FCLS. In particular, using this method to solve one-dimensional fuzzy linear systems, a (2 n) × (2 n) RLS is obtained, which is consistent with Friedman's method. Finally, FCLS based on the RFCN as a special case are also investigated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a membership function used to form the fuzzy Mandelbric set and investigate the structural effects of additive and multiplicative dynamic noises on it. The newly defined membership function of this fuzzy set and its perturbations is a generalization of the indicator function for the classical Mandelbric set. We present an algorithm for detecting each complex number's fuzzy membership degree. Through the use of the membership degrees of each complex number and experimental mathematics based on the visualizations of a variety of versions by utilizing computer-aided design, we gain a deep foresight for the structure characteristics of the additive and multiplicative perturbed fuzzy Mandelbric sets. Our novel approach allows us to identify the symmetry states of the Mandelbric set and its perturbations by the membership degrees of complex numbers, unlike the existing methods described in the literature. [ABSTRACT FROM AUTHOR]

In this study, we propose the CVMFCC-DR (Complex-Valued Mel-Frequency Cepstral Coefficients Dimensionality Reduction) algorithm as an efficient method for reducing the dimensionality of speech signals. By utilizing the complex-valued MFCC technique, which considers both real and imaginary components, our algorithm enables dimensionality reduction without information loss while decreasing computational costs. The efficacy of the proposed algorithm is validated through experiments which demonstrate its effectiveness in building a speech recognition model using a complex-valued neural network. Additionally, a complex-valued softmax interpretation method for complex numbers is introduced. The experimental results indicate that the approach yields enhanced performance compared to traditional MFCC-based techniques, thereby highlighting its potential in the field of speech recognition. [ABSTRACT FROM AUTHOR]

The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model. [ABSTRACT FROM AUTHOR]

The location identification of dynamic load is an important part of load-identification technology. Traditional methods are mostly aimed at the identification of dynamic load's amplitude and phase. A new method for dynamic load location identification is proposed in this paper. An amplitude ratio or a phase difference between structural dynamic response signals is only related to the frequency response function (FRF), which is a complex-valued function that implies the location information of the load to be identified. In this method, the amplitude and phase variables of the excitation can be eliminated with symbolic calculations, and the location variables can be extracted from the FRF in a complex-number field. An excitation location can be identified quickly with parameter optimization using a Genetic Algorithm (GA), avoiding the ill-posed problem caused by matrix inversion. Numerical simulations and experiments demonstrate that this method can realize the fast recognition of several excitation positions, and has a high recognition accuracy, a short calculation time and a strong anti-noise ability. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to analyze the heat transfer mechanism of a new type of regenerator with a low temperature difference and low current resistance under oscillatory flow at room temperature. Taking the single tube of the regenerator as the research object, the exact analytical solution of the radial heat transfer characteristics of the regenerator is obtained by studying its analytical model. The factors affecting the heat transfer characteristics are analyzed, and then the regenerator is optimized to improve the performance and efficiency of the regenerator system. In this study, we systematically analyzed the radial heat transfer characteristics of a regenerator under isochoric process conditions. A closed-system physical model of the incompressible isochoric process under oscillating flow was established. Then, the radial analytical solutions of pressure fluctuation, fluid velocity, fluid-solid temperature, and heat were derived in the complex number field. Furthermore, the fluid velocity, fluid-solid coupling wall temperature, heat, and equivalent heat transfer coefficient were assessed. Furthermore, the influences of frequency, inner diameter R1 of the regenerator, and different working medium and materials on the above parameters were discussed. It was found that the analysis and evaluation of fluid velocity, fluid-structure coupling wall temperature, heat, and equivalent heat transfer coefficient are helpful in understanding the dynamic characteristics of radial heat transfer in a regenerator system. Through the study of radial heat transfer under oscillating flow, it was found that the working medium, frequency, inner diameter of the regenerator, and material quality of the regenerator are helpful for the design optimization of the regenerator. Furthermore, our investigations established that the variation law of wall fluid-solid coupling temperature amplitude could be divided into three parts: the unidirectional flow part; the low-frequency part, where the temperature amplitude falls rapidly with increasing frequency; and the high-frequency part, where the temperature amplitude increases with the frequency. In addition, the variation of radial heat transfer of the fluid-solid coupling surface is similar to the changes in the temperature amplitude. We also discovered that the equivalent heat transfer coefficient of the fluid-solid surface is related to thermal conductivity of the material. Specifically, larger thermal conductivity values result in greater equivalent heat transfer coefficients. Based on the research into the radial heat transfer characteristics, the new regenerator has great application potential in the Stirling air conditioning system at room temperature. [ABSTRACT FROM AUTHOR]

Accurate attitude determination is crucial for satellites and spacecraft. Among attitude determination devices, star sensors are the most accurate. Solving the lost-in-space problem is the most critical function of the star sensor. Our research introduces a novel star-identification system that utilizes a polygon-recognition algorithm to assign a unique complex number to polygons created by stars. This system aims to solve the lost-in-space problem. Our system includes a full solution with a lens, image sensor, processing unit, and algorithm implementation. To test the system's performance, we analyzed 100 night sky images that resembled what a real star sensor in orbit would experience. We used a k-d tree algorithm to accelerate the search in the star catalog of complex numbers. We implemented various verification methods, including internal polygon verification and a voting mechanism, to ensure the system's reliability. We obtained the star database used as a reference from the Gaia DR2 catalog, which we filtered, to eliminate irrelevant stars, and which we arranged by apparent magnitude. Despite manually introducing up to three false stars, the system successfully identified at least one star in 97% of the analyzed images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a methodology for computing the square root of a complex number based on a piecewise linear (PWL) approximation method. The proposed method relies on a software-based segmentor that automatically divides the three real square root functions used in complex square root computation into the fewest segments with a predefined fractional bit width and maximum absolute error (MAE). The coefficients, including the start point, end point, slope and y-intercept of each segment, are stored for use in the implementation of the hardware design. The proposed fully pipelined circuit is coded in the Verilog hardware description language (HDL). The results of synthesis in TSMC (Taiwan Semiconductor Manufacturing Company) 65-nm CMOS technology show that our design achieves savings of 64.21% in area, 16.67% in delay and 65.08% in power compared to the existing methods. Moreover, implementation results on an FPGA (Field-Programmable Gate Array) platform (XC7Z020-CLG400) show that the proposed design reduces the number of LUTs by 29.38%, delay by 28.57% and power consumption by 53.47%. [ABSTRACT FROM AUTHOR]

Quaternion is a four-dimensional and an extension of the complex number system. It is often viewed from various fields, such as analysis, algebra, and geometry. Several applications of quaternions are related to an object's rotation and motion in three-dimensional space in the form of a differential equation. In this paper, we do a systematic literature review on the development of quaternion differential equations. We utilize PRISMA (preferred reporting items for systematic review and meta-analyses) framework in the review process as well as content analysis. The expected result is a state-of-the-art and the gap of concepts or problems that still need to develop or answer. It was concluded that there are still some opportunities to develop a quaternion differential equation using a quaternion function domain. [ABSTRACT FROM AUTHOR]

This paper introduces one unique price motion process with fractional Brownian motion. We introduce the imaginary number into the agent's subjective probability for the reason of convergence; further, the result similar to Ito Lemma is proved. As an application, this result is applied to Merton's dynamic asset pricing framework. We find that the four order moment of fractional Brownian motion is entered into the agent's decision-making. The decomposition of variance of economic indexes supports the possibility of the complex number in price movement. [ABSTRACT FROM AUTHOR]

This paper demonstrates how a classical detector that collects non-interacting individual classical massive free particles can generate a quantum interference pattern. The proposed classical picture requires that particles carry the information of a phase equal to an action integral along their trajectory. At the point of their detection, a special type of detector collects the phases from all individual particles reaching it, adds them up over time as complex numbers, and divides them by the square root of their number. The detector announces a number of detections equal to the square of the amplitude of the resulting complex number. An interference pattern is gradually built from the collection of particle phases in the detection bins of the detector after several repetitions of the experiment. We obtain perfect agreement with three solutions of the Schrödinger equation for free particles: a Gaussian wavepacket, two Gaussian wavepackets approaching each other, and a Gaussian wavepacket reflecting off a wall. The main conclusion of the present work is that the interference of quantum mechanics is basically due to the detectors that collect the particles when there are macroscopic detectors operating as proposed. Finally, a simple physical experiment with a single-photon detector is proposed that will be able to test our theory. [ABSTRACT FROM AUTHOR]

Methods for solving planar dyads and triads in kinematic synthesis are scattered throughout the literature. A review of and a new compilation of the complex number synthesis method for planar dyads and triads is presented. The motivation of this paper is to formulate uniform solution procedures, pointing out the commonalities of various approaches and emphasizing a consistent method for synthesizing mechanisms defined by specified precision positions. Particular emphasis is given to the solution method using compatibility linkages. The textbook Advanced Mechanism Design Vol II by Erdman and Sandor (1984) only includes a small portion of the available information on this method, and several researchers have added to the basic knowledge in the years since. In some cases, the approach and nomenclature were not consistent, yielding a need to describe and chart a generic formulation and solution procedure for dyads/triads using compatibility linkages and solution structures. The present method offers benefits for solving for exact dyad/triad solutions for complex multiloop mechanisms and could be a promising tool for reducing the computational load of finding complex mechanisms, and for visualizing properties of the solution space. [ABSTRACT FROM AUTHOR]

Gears are foundational tools used to transmit or modify mechanical energy or motion. Implementing gears into planar linkage mechanisms is less common but can be a similarly valuable technique that takes advantage of the high efficiency of gears while producing complex and precise motions. While recent numerical methods for designing these geared planar linkage mechanisms (GPLMs) have proliferated in the literature, analytical approaches have their merits and have received less attention. Here, an analytical alternative is presented as a modification of the complex-number loop-based synthesis method for designing multiloop mechanisms. Some of the base topologies for geared dyad, triad, and quadriad chains are presented, along with a numerical example demonstrating the solution procedure's effectiveness. [ABSTRACT FROM AUTHOR]

Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green's function. In a paper, the problem is treated in distribution theory, and in another paper, the formulation is given on the basis of nonstandard analysis, where fractional derivative of degree, which is a complex number added by an infinitesimal number, is used. In the present paper, a simple recipe based on nonstandard analysis, which is closely related with distribution theory, is presented, where in place of Heaviside's step function H (t) and Dirac's delta function δ (t) in distribution theory, functions H ϵ (t) : = 1 Γ (1 + ϵ) t ϵ H (t) and δ ϵ (t) : = d d t H ϵ (t) = 1 Γ (ϵ) t ϵ − 1 H (t) for a positive infinitesimal number ϵ , are used. As an example, it is applied to Kummer's differential equation. [ABSTRACT FROM AUTHOR]

The wave passage effect is a measure of the wave passage delay due to the apparent velocity of waves, which is one of spatially varying properties of multivariate random processes. The phase of coherence function reflects the wave passage effect of wind fields. In the wind field, simulation by the spectral representation method, the classical phase formula, is not rigorous. This may affect the accuracy of simulation results and even cause incorrect simulations. In this study, the influences of the phase on stationary and nonstationary wind field simulations are researched and discussed in detail. Two schemes containing the classical phase formula and the separated phase scheme are compared in four types of wind field simulation. The qualitative analysis based on theoretical correlation function formula is first made to study the influence of the phase. Then, four numerical examples are utilized to quantitatively study the magnitude of the influence on the sample time history and correlation function of the simulated wind field. Results show that the classical phase formula will result in considerable simulation error for all four types of wind fields because it cannot completely represent the phase angle of a complex number. [ABSTRACT FROM AUTHOR]

The Ohtsuka–Vălean sum is extended to evaluate an extensive number of trigonometric and hyperbolic sums and products. The sums are taken over finite and infinite domains defined in terms of the Hurwitz–Lerch zeta function, which can be simplified to composite functions in special cases of integer values of the parameters involved. The results obtained include generalizations of finite and infinite products and sums of tangent, cotangent, hyperbolic tangent and hyperbolic cotangent functions, in certain cases raised to a complex number power. [ABSTRACT FROM AUTHOR]

The solution of a complex-valued matrix pseudoinverse is one of the key steps in various science and engineering fields. Owing to its important roles, researchers had put forward many related algorithms. With the development of research, a time-varying matrix pseudoinverse received more attention than a time-invarying one, as we know that a zeroing neural network (ZNN) is an efficient method to calculate a pseudoinverse of a complex-valued time-varying matrix. Due to the initial ZNN (IZNN) and its extensions lacking a mechanism to deal with both convergence and robustness, that is, most existing research on ZNN models only studied the convergence and robustness, respectively. In order to simultaneously improve the double features (i.e., convergence and robustness) of ZNN in solving a complex-valued time-varying pseudoinverse, this paper puts forward a double features ZNN (DFZNN) model by adopting a specially designed time-varying parameter and a novel nonlinear activation function. Moreover, two nonlinear activation types of complex number are investigated. The global convergence, predefined time convergence, and robustness are proven in theory, and the upper bound of the predefined convergence time is formulated exactly. The results of the numerical simulation verify the theoretical proof, in contrast to the existing complex-valued ZNN models, the DFZNN model has shorter predefined convergence time in a zero noise state, and enhances robustness in different noise states. Both the theoretical and the empirical results show that the DFZNN model has better ability in solving a time-varying complex-valued matrix pseudoinverse. Finally, the proposed DFZNN model is used to track the trajectory of a manipulator, which further verifies the reliability of the model. [ABSTRACT FROM AUTHOR]

There are two probabilistic algebras: one for classical probability and the other for quantum mechanics. Naturally, it is the relation to the object that decides, as in the case of logic, which algebra is to be used. From a paraconsistent multivalued logic therefore, one can derive a probability theory, adding the correspondence between truth value and fortuity. [ABSTRACT FROM AUTHOR]

Knowledge representation learning achieves the automatic completion of knowledge graphs (KGs) by embedding entities into continuous low-dimensional vector space. In knowledge graph completion (KGC) tasks, the inter-dependencies and hierarchical information in KGs have gained attention. Existing methods do not well capture the latent dependencies between all components of entities and relations. To address this, we introduce the mathematical theories of octonion, a more expressive generalized form of complex number and quaternion, and propose a translation-based KGC model with octonion (TransO). TransO models entities as octonion coordinate vectors, relations as the combination of octonion component matrices and coordinate vectors, and uses specific grouping calculation rules to interact between entities and relations. In addition, since hyperbolic Poincaré space in non-Euclidean mathematics can represent hierarchical data more accurately and effectively than traditional Euclidean space, we propose a Poincaré-extended TransO model (PTransO). PTransO transforms octonion coordinate vectors into hyperbolic embeddings by exponential mapping, and integrates the Euclidean-based calculations into hyperbolic space by operations such as Möbius addition and hyperbolic distance. The experimental results of link prediction indicate that TransO outperforms other translation-based models on the WN18 benchmark, and PTransO further achieves state-of-the-art performance in low-dimensional space on the well-established WN18RR and FB15k-237 benchmarks. [ABSTRACT FROM AUTHOR]

When studying the control problems of nonlinear systems, there are always uncertainties and disturbances. The existence of this phenomenon will increase the error in production engineering and reduce work efficiency. In order to reduce the nonlinear asymmetric control, the control method of a laser hyperchaotic system is designed in this paper. The system is a complex number system, with remarkable nonlinear characteristics. The system is divided into two parts by calculating the state transformation matrix, which shows that the system can realize simultaneous synchronization and anti-synchronization. Firstly, in the ideal case, the stabilization, synchronization, and anti-synchronization of the system are studied by using the dynamic gain feedback method, and a dynamic feedback controller is designed. Secondly, in the case of uncertainty and disturbance, a dynamic feedback control strategy based on uncertainty and disturbance estimator (UDE) is proposed. With the aim to solve the control problem of the system, the corresponding controller is designed to modify the system. Finally, through simulation and comparison, it is verified that the effect of this method is remarkable. [ABSTRACT FROM AUTHOR]

References 1 Martin Bueno J., Sáez-Plaza P., Ramos-Escudero F., Jiménez A.M., Fett R., Asuero A.G. Analysis and Antioxidant Capacity of Anthocyanin Pigments. Chlorophylls and carotenoids are two families of antioxidants that include a large and complex number of compounds, present in daily food intake, with added value ingredients and functional properties. Total polyphenol content (Folin-Cioculteau) and antioxidant capacity (DPPH, FRAP, and ORAC) were estimated, and the anthocyanin profile was assessed by ultra-high-performance liquid chromatography (UHPL-MS/MS). Anthocyanins [[1]], chlorophylls, and carotenoids [[3]] are pigments responsible for the colour of many fruits, flowers, and plant tissues. [Extracted from the article]

Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems. [ABSTRACT FROM AUTHOR]

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands. [ABSTRACT FROM AUTHOR]

This manuscript presents an analysis of machine learning (ML) usage in the Frequency Symbolic Method (FSM) to enhance the diagnosis of faults in parametric circuit analysis and optimization, with a particular focus on Linear Periodically Time-Variable (LPTV) systems. We put forth a few ML-based approaches for fault diagnosis (including anomaly detection), invisible feature detection, and the prediction of FSM output. These methodologies concentrate on identifying and diagnosing faults by evaluating particular ML techniques, extracting pertinent features, and determining the desired diagnostic outputs. The use cases of ML application considered in this paper demonstrate that machine learning can enhance fault detection and diagnosis, reduce human errors and identify previously unnoticed anomalies within the FSM framework. ML has never been used in FSM before, so the key aim of this paper is to consider possible use cases of AI application in FSM. Additionally, feature extraction, required as an input stage for the ML model, is proposed based on FSM peculiarities. This work can be considered a study of ML application in FSM. [ABSTRACT FROM AUTHOR]

The range-Doppler algorithm (RDA), a key technique for generating synthetic aperture radar (SAR) images, offers high-resolution images but requires significant memory resources and involves complex signal processing. Moreover, the multitude of fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) operations in RDA necessitates high bandwidth and lacks data reuse, leading to bottlenecks. This paper introduces a synthetic aperture radar dual in-line memory module (SARDIMM), which executes RDA operations near memory via near-memory processing (NMP), thereby effectively reducing memory accesses, execution time, and energy consumption. The embedded NMP module in SARDIMM optionally supports a combination of FFT, IFFT, and matched filter operations of the RDA for range and azimuth compression. The operator within the NMP module accelerates the FFT by performing two radix-2 single butterfly operations in parallel. The NMP module was implemented and validated on a Xilinx UltraScale+ field-programmable gate array (FPGA) using Verilog-HDL. The acceleration performance of RDA for images of various sizes was evaluated through a simulator modified with gem5 and DRAMSim3 and achieved a 6.34–6.93× speedup and 41.9–48.2% energy savings. [ABSTRACT FROM AUTHOR]

Because of the substantial progress in quantum computing technology, the safety of traditional cryptologic schemes is facing serious challenges. In this study, we explore the quantum safety of the lightweight cipher MIBS and propose quantum key-recovery attacks on the MIBS cipher by utilizing Grover's algorithm and Bernstein–Vazirani algorithm. We first construct linear-structure functions based on the 5-round MIBS cipher according to the characteristics of the linear transformations, and then we obtain a quantum distinguisher of the 5-round MIBS cipher by applying Bernstein–Vazirani algorithm to the constructed functions. Finally, utilizing this distinguisher and Grover's algorithm, we realize a 7-round key-recovery attack on the MIBS cipher, and then we expand the attack to more rounds of MIBS based on a similar idea. The quantum attack on the 7-round MIBS requires 156 qubits and has a time complexity of 2 10.5 . An 8-round attack requires 179 qubits and has a time complexity of 2 22 . Compared with existing quantum attacks, our attacks have better time complexity when attacking the same number of rounds. [ABSTRACT FROM AUTHOR]

The eigenvalues of complex q-Sturm–Liouville boundary value problems are the focus of this paper. The coefficients of the corresponding q-Sturm–Liouville equation provide the lower bounds on the real parts of all eigenvalues, and the real part of the eigenvalue and the coefficients of this q-Sturm–Liouville equation provide the bounds on the imaginary part of each eigenvalue. [ABSTRACT FROM AUTHOR]

Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev's estimates, etc.) particularly valuable. These methods also offer avenues for number-theoretic exploration through analytical manipulation. In this work, we introduce a novel approximation function, ϕ(n), which adds to the existing repertoire of approximation methods and provides a fresh perspective for number-theoretic studies. Deeper analytical investigation of ϕ(n) reveals modified representations of the Chebyshev function, prime number theorem, and Riemann zeta function. Computational studies indicate that the difference between ϕ(n) and the logarithmic integral at magnitudes greater than 10100 is less than 1%. [ABSTRACT FROM AUTHOR]

Rail surface defect detection is vital for railway safety. Traditional methods falter with varying defect sizes and complex backgrounds, while two-stage deep learning models, though accurate, lack real-time capabilities. To overcome these challenges, we propose an enhanced one-stage detection model based on CenterNet. We replace ResNet with ResNeXt and implement a multi-branch structure for better low-level feature extraction. Additionally, we integrate SKNet attention mechanism with the C2f structure from YOLOv8, improving the model's focus on critical image regions and enhancing the detection of minor defects. We also introduce an elliptical Gaussian kernel for size regression loss, better representing the aspect ratio of rail defects. This approach enhances detection accuracy and speeds up training. Our model achieves a mean accuracy (mAP) of 0.952 on the rail defects dataset, outperforming other models with a 6.6% improvement over the original and a 35.5% increase in training speed. These results demonstrate the efficiency and reliability of our method for rail defect detection. [ABSTRACT FROM AUTHOR]

An extremely large-scale antenna array (ELAA) can potentially provide significantly increased spatial multiplexing and beamforming gains, as well as enhanced localization capability. While presenting new potential, its near-field propagation and spatial non-stationary properties also impose a great challenge on the receiver design. This paper focuses on the receiver design in an uplink orthogonal frequency-division multiplexing system with a planar ELAA deployed at the base station. To solve the challenging problem of 3D user localization and channel estimation with the planar ELAA, a space-frequency user localization and channel reconstruction (SF-ULCR) receiver is proposed. Under the Bayesian framework, an extended probability model is first established, to capture the channel structural information comprehensively, based on which an iterative receiver consisting of three modules is derived: element-wise line spectrum estimation (ELSE), distance parameter estimation (DPE), and near-field localization (NFL). In particular, the ELSE module handles the line spectrum relationships among multiple subcarriers in the frequency domain, the DPE module extracts and integrates the distance information from the line spectrum parameters, and the NFL module utilizes the messages of distances for user localization based on near-field spatial characteristics. Our numerical results demonstrate that the proposed SF-ULCR algorithm outperforms existing baselines in terms of channel estimation and localization performance, and that it approaches the Cramèr–Rao bound. [ABSTRACT FROM AUTHOR]

Monitoring human activities, such as walking, falling, and jumping, provides valuable information for personalized health assistants. Existing solutions require the user to carry/wear certain smart devices to capture motion/audio data, use a high-definition camera to record video data, or deploy dedicated devices to collect wireless data. However, none of these solutions are widely adopted for reasons such as discomfort, privacy, and overheads. Therefore, an effective solution to provide non-intrusive, secure, and low-cost human activity monitoring is needed. In this study, we developed a contactless human activity monitoring system that utilizes channel state information (CSI) of the existing ubiquitous WiFi signals. Specifically, we deployed a low-cost commercial off-the-shelf (COTS) router as a transmitter and reused a desktop equipped with an Intel WiFi Link 5300 NIC as a receiver, allowing us to obtain CSI data that recorded human activities. To remove the outliers and ambient noise existing in raw CSI signals, an integrated filter consisting of Hampel, wavelet, and moving average filters was designed. Then, a new metric based on kurtosis and standard deviation was designed to obtain an optimal set of subcarriers that is sensitive to all target activities from the candidate 30 subcarriers. Finally, we selected a group of features, including time- and frequency-domain features, and trained a classification model to recognize different indoor human activities. Our experimental results demonstrate that the proposed system can achieve a mean accuracy of above 93%, even in the face of a long sensing distance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new data-aided (DA) joint angle and delay (JADE) maximum likelihood (ML) estimator. The latter consists of a substantially modified and, hence, significantly improved gray wolf optimization (GWO) technique by fully integrating and embedding within it the powerful importance sampling (IS) concept. This new approach, referred to hereafter as GWOEIS (for "GWO embedding IS"), guarantees global optimality, and offers higher resolution capabilities over orthogonal frequency division multiplex (OFDM) (i.e., multi-carrier and multi-path) single-input multiple-output (SIMO) channels. The traditional GWO randomly initializes the wolfs' positions (angles and delays) and, hence, requires larger packs and longer hunting (iterations) to catch the prey, i.e., find the correct angles of arrival (AoAs) and time delays (TDs), thereby affecting its search efficiency, whereas GWOEIS ensures faster convergence by providing reliable initial estimates based on a simplified importance function. More importantly, and beyond simple initialization of GWO with IS (coined as IS-GWO hereafter), we modify and dynamically update the conventional simple expression for the convergence factor of the GWO algorithm that entirely drives its hunting and tracking mechanisms by accounting for new cumulative distribution functions (CDFs) derived from the IS technique. Simulations unequivocally confirm these significant benefits in terms of increased accuracy and speed Moreover, GWOEIS reaches the Cramér–Rao lower bound (CRLB), even at low SNR levels. [ABSTRACT FROM AUTHOR]

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method. [ABSTRACT FROM AUTHOR]

Short-range MEMS-based (Micro Electronical Mechanical System) LiDAR provides precise point cloud datasets for rock fragment surfaces. However, there is more vibrational noise in MEMS-based LiDAR signals, which cannot guarantee that the reconstructed point cloud data are not distorted with a high compression ratio. Many studies have illustrated that wavelet-based clustered compressive sensing can improve reconstruction precision. The k-means clustering algorithm can be conveniently employed to obtain clusters; however, estimating a meaningful k value (i.e., the number of clusters) is challenging. An excessive quantity of clusters is not necessary for dense point clouds, as this leads to elevated consumption of memory and CPU resources. For sparser point clouds, fewer clusters lead to more distortions, while excessive clusters lead to more voids in reconstructed point clouds. This study proposes a local clustering method to determine a number of clusters closer to the actual number based on GMM (Gaussian Mixture Model) observation distances and density peaks. Experimental results illustrate that the estimated number of clusters is closer to the actual number in four datasets from the KEEL public repository. In point cloud compression and recovery experiments, our proposed approach compresses and recovers the Bunny and Armadillo datasets in the Stanford 3D repository; the experimental results illustrate that our proposed approach improves reconstructed point clouds' geometry and curvature similarity. Furthermore, the geometric similarity increases to 0.9 above in our complete rock fragment surface datasets after selecting a better wavelet basis for each dimension of MEMS-based LiDAR signals. In both experiments, the sparsity of signals was 0.8 and the sampling ratio was 0.4. Finally, a rock outcrop point cloud data experiment is utilized to verify that the proposed approach is applicable for large-scale research objects. All of our experiments illustrate that the proposed adaptive clustered compressive sensing approach can better reconstruct MEMS-based LiDAR point clouds with a lower sampling ratio. [ABSTRACT FROM AUTHOR]

Traditional methods of hologram generation, such as point-, polygon-, and layer-based physical simulation approaches, suffer from substantial computational overhead and generate low-fidelity holograms. Deep learning-based computer-generated holography demonstrates effective performance in terms of speed and hologram fidelity. There is potential to enhance the network's capacity for fitting and modeling in the context of computer-generated holography utilizing deep learning methods. Specifically, the ability of the proposed network to simulate Fresnel diffraction based on the provided hologram dataset requires further improvement to meet expectations for high-fidelity holograms. We propose a neural architecture called Holo-U2Net to address the challenge of generating a high-fidelity hologram within an acceptable time frame. Holo-U2Net shows notable performance in hologram evaluation metrics, including an average structural similarity of 0.9988, an average peak signal-to-noise ratio of 46.75 dB, an enhanced correlation coefficient of 0.9996, and a learned perceptual image patch similarity of 0.0008 on the MIT-CGH-4K large-scale hologram dataset. [ABSTRACT FROM AUTHOR]

In this paper, we combine simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) with rate-splitting multiple access (RSMA) technology and investigate the ergodic rate performance of an STAR-assisted RSMA system. Considering the discrete phase shifts of the STAR-RIS in practice, the downlink performance of STAR-RIS-assisted RSMA with discrete phase shifts is compared to that with continuous phase shifts. Firstly, the cumulative distribution function of signal-to-interference-plus-noise ratio (SINR) of users is analyzed. Then, the total ergodic rate of the system and its approximate closed-form solution are, respectively, derived based on the cumulative distribution function of users. The simulation results validate the effectiveness of the theoretical analysis, showing good agreement between the derived theoretical ergodic rate and the corresponding simulations. Although the system performance with discrete phase shifts is inferior to that with continuous phase shifts due to quantization errors, the performance of the continuous phase shift system is well approximated when the quantization bit of the phase shift system reaches 3 in the simulations. Additionally, the impact of the number of STAR-RIS elements on the system's performance is analyzed. [ABSTRACT FROM AUTHOR]

Buildings worldwide are becoming more thermally insulated, and air circulation is being reduced to a minimum. As a result, measuring indoor air quality is important to prevent harmful concentrations of various gases that can lead to safety risks and health problems. To measure such gases, it is necessary to produce low-cost and low-power-consuming sensors. Researchers have been focusing on semiconducting metal oxide (SMOx) gas sensors that can be combined with intelligent technologies such as smart homes, smart phones or smart watches to enable gas sensing anywhere and at any time. As a type of SMOx, p-type gas sensors are promising candidates and have attracted more interest in recent years due to their excellent electrical properties and stability. This review paper gives a short overview of the main development of sensors based on copper oxides and their composites, highlighting their potential for detecting CO2 and the factors influencing their performance. [ABSTRACT FROM AUTHOR]

Induction motors are the most common type of motor in power systems, constituting approximately 70–90% of the dynamic loads, making them significant contributors to system dynamics. In transient voltage stability analysis, dynamic equivalent models are commonly used to simplify the representation of a group of induction motors. This paper presents a method for the grouping and aggregation of induction motors at a common bus. Firstly, grouping rules are provided for clustering induction motors into several subgroups based on the mechanical principles of rotor force and motion, and aggregation rules are provided for aggregating a motor subgroup into a single-unit model based on the relationship between voltage drop and power transmission in distribution networks. Secondly, guided by the grouping rules, high-speed remaining electromagnetic torque and low-speed remaining electromagnetic torque are defined as new clustering indicators, and an adaptive K-means clustering method using silhouette coefficient verification is introduced to obtain the optimal motor subgroups. Thirdly, guided by the aggregation rules, a dynamic equivalent method is further introduced to obtain the equivalent single-unit model from a motor subgroup. Lastly, a transient voltage stability simulation in a typical distribution network is presented to illustrate that the proposed clustering and equivalent methods are more reasonable, accurate, and effective than traditional methods, as the obtained model has better dynamic characteristics and can more accurately reproduce the process of voltage collapse. [ABSTRACT FROM AUTHOR]

Under the condition of grid voltage imbalance, the circulation of the bridge arm inside the modular multilevel converter (MMC) increases significantly, which leads to the aggravation of the distortion of the bridge arm current, and, thus, increases the system loss and reduces the power quality. To address this problem, this paper analyzes the mechanism of circulating current generation and proposes a circulating current suppression strategy based on a reduced-order generalized integrator (ROGI), which firstly uses the ROGI system to separate the second-harmonic positive- and negative-sequence components in the circulating current from the DC, and then converts the rotating coordinates of the circulating current's second octave component into the DC to be fed into the proportional–integral quasi-resonance (PIR) controller for suppression. A simulation model of a 23-level MMC inverter is built in MATLAB/Simulink, and the control strategy proposed in this paper is compared with the classical proportional–integral (PI) control in simulation experiments. The simulation results show that the amplitude of the circulating current fluctuation of the classical PI control is reduced from 90 A to 22 A, and the harmonic distortion rate of the bridge arm current is reduced from 32.56% to 5.57%; the amplitude of the circulating current fluctuation of the control strategy proposed in this paper is reduced from 90 A to 5.7 A, and the harmonic distortion rate of the bridge arm current is reduced from 20.2% to 1.13%, which verifies the effectiveness of the pro-posed control strategy. [ABSTRACT FROM AUTHOR]

An atmospheric pressure plasma source of the microwave plasma pencil type utilizing a coaxial line is presented. The generated plasma takes the form of a cylinder up to about 30 mm long and up to 5 mm in diameter. It is suitable for surface sterilization, surface treatment, and material processing. This study numerically analyzes the electromagnetic radiation emitted by the plasma pencil, which compromises performance and poses safety risks. Electric field distributions, radiation patterns, the ratio of the power entering the discharge to the incident wave power, and the ratio of radiated power to entering power were numerically investigated for different plasma parameters and pencil lengths. Results indicate that increasing electron density, gas temperature, plasma length, and pencil length increases the radiated power by up to more than 60% of the entering power, and the radiation patterns can be highly non-uniform with strong backward lobe. The numerical finding were qualitatively confirmed experimentally. It was also found that it is possible to reduce radiation from the device by using appropriately designed cones, the presence of which does not impede its performance. [ABSTRACT FROM AUTHOR]

Interferometric radars are widely used sensors for structural health monitoring. They are able to perform dynamic measurements of displacement with sub-millimeter precision. Today, the Ku-band is the most common, due to the spread of commercial systems operating in this band. At the same time, the W-band sensors are gaining ever more interest. Other popular systems work in the X-band. Since the characteristics of the measurements dramatically depend on the operative frequency, it is essential to highlight their differences. For instance, higher frequency allows for high displacement resolution, but it is more subject to phase wrapping and decorrelation effects. In this paper, a direct comparison between radars operating in X, Ku, and W-band for bridge monitoring is carried out. The radars provide frequency-modulated continuous-wave signals. Experimental campaigns were performed both in controlled and realistic scenarios (a stayed bridge). The results of the experiments demonstrate that all the three sensors are suitable for performing dynamic structure monitoring despite their differences. It is worth noting that this comparative analysis has highlighted the role of amplitude variation in phase/displacement measurement. Regarding this point, the three different bands exhibit significant differences. [ABSTRACT FROM AUTHOR]

Utilizing spatial diversity, the distributed multiple-input multiple-output (MIMO) radar has the potential advantage of improving system detection performance. In this paper, the incoherent detection performance of distributed multiple-input multiple-output (MIMO) radars is investigated for Rice fluctuating targets. To calculate the incoherent detection probability, the moment generating function (MGF) of the Rice variable is expanded as the infinite series form. By inverting the product of MGFs of multiple independent Rice variables, new closed-form expressions for the probability density function (PDF) of the sum of independent and weighted squares of Rice variables are proposed. The proposed PDF expression for the sum of independent, non-identically distributed (i.n.i.d.) Rice variables involves an infinite series in terms of the confluent Lauricella function. Specially, the PDF for the sum of independent identically distributed (i.i.d.) Rice is expressed as the confluent hypergeometric function-based infinite series. In addition, the uniform convergence of the proposed PDF expression is also validated. Using this proposed expression, the closed-form and approximate expressions of the incoherent detection probability of MIMO radar are derived, respectively. Numerically evaluated results are illustrated and compared with Monte Carlo (MC) simulations to validate the accuracy of the derivations. [ABSTRACT FROM AUTHOR]

The transmit/receive-receive (T/R-R) synergetic High Frequency Surface Wave Radar (HFSWR) has increasingly attracted attention due to its high localization accuracy, but multi-target pairing needs to be performed before localization in multi-target scenarios. However, existing multi-target parameter matching methods have primarily focused on track association, which falls under the category of information-level fusion techniques, with few methods based on detected points. In this paper, we propose a multi-target pairing method with high computational efficiency based on angle information for T/R-R synergetic HFSWR. To be more specific, a dual-receiving array signal model under long baseline condition is firstly constructed. Then, the amplitude and phase differences of the same target reaching two subarrays are calculated to establish the cross-correlation matrix. Subsequently, in order to extract the rotation factor matrices containing pairing information and improve angle estimation performance, we utilize the conjugate symmetry properties of the uniform linear array (ULA) manifold matrix for generalized virtual aperture extension. Ultimately, azimuths estimation and multi-target pairing are accomplished by combining the propagator method (PM) and the ESPRIT algorithm. The proposed method relies solely on angle information for multi-target pairing and leverages the rotational invariance property of Vandermonde matrices to avoid peak searching or iterations, making it computationally efficient. Furthermore, the proposed method maintains superb performance regardless of whether the spatial angles are widely separated or very close. Simulation results validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an invariant by image viewpoint changes by applying an important theorem in conformal geometry stating that every surface of the Minkowski space R 3 , 1 leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ∐ α H α of R 3 , 1 by means of the powerful tools of the conformal Clifford algebras. We explain that every viewpoint change is given by a planar similarity and a perspective distortion encoded by the latitude angle of the camera. We model the perspective distortion by the point at infinity of the conformal model of the Euclidean plane described by D. Hestenesand we clarify the spinor representations of the similarities of the Euclidean plane. This leads us to represent the viewpoint changes by conformal transformations of ∐ α H α for the Minkowski metric of the ambient space. [ABSTRACT FROM AUTHOR]

We offer intriguing new insights into parameterized finite binomial sums, revealing elegant identities such as ∑ k = 0 , k ≠ n m + n (− 1) k n − k m + n k = (− 1) n m + n n (H m − H n) , where n , m are non-negative integers and H n is the harmonic number. These formulas beautifully capture the intricate relationship between harmonic numbers and binomial coefficients, providing a fresh and captivating perspective on combinatorial sums. [ABSTRACT FROM AUTHOR]

This paper considers a terahertz (THz) dual-function multi-input multi-output (MIMO) radar and communication system with the assistance of a reconfigurable intelligent surface (RIS) and jointly designs the constant modulus (CM) waveform and RIS phase shifts. A weighted optimization scheme is presented, to minimize the weighted sum of three objectives, including communication multi-user interference (MUI) energy, the negative of multi-target illumination power and the MIMO radar waveform similarity error under a CM constraint. For the formulated non-convex problem, a novel alternating coordinate descent (ACD) algorithm is introduced, to transform it into two subproblems for waveform and phase shift design. Unlike the existing optimization algorithms that solve each subproblem by iteratively approximating the optimal solution with iteration stepsize selection, the ACD algorithm can alternately solve each subproblem by dividing it into multiple simpler problems, to achieve closed-form solutions. Our numerical simulations demonstrate the superiorities of the ACD algorithm over the existing methods. In addition, the impacts of the weighting coefficients, RIS and channel conditions on the radar communication performance of the THz system are analyzed. [ABSTRACT FROM AUTHOR]

In this study, the impact of principal stress states on the stress characteristics and initial failure of the rock mass surrounding a three-center arch opening was investigated using complex variable function methods and Discrete Element Method (DEM) numerical modeling. First, the mapping function of the opening was determined using the trigonometric interpolation method, and the influence of the number of terms in the mapping function on its accuracy was revealed. Based on this, the far-field stress state of the underground rock mass was characterized by the ratio of the minimum to maximum principal stress (λ) and the angle (β) between the principal stress and the vertical direction. This stress state was then converted into normal and shear stresses. Using complex variable function theory, the stress characteristics at the boundary of the opening under different stress states were analyzed. Finally, DEM numerical modeling was employed to study the initial failure characteristics at the boundary of the opening and its relationship with the stress distribution. The results indicate that the lateral pressure coefficient significantly affects the stability of the opening by influencing stress concentration around the surrounding rock. Low lateral pressure coefficients lead to tensile stress concentration at the boundary perpendicular to the maximum principal stress. As the coefficient increases, tensile stress decreases, and compressive stress areas expand. While the principal stress direction has a minor effect on stress concentration, it notably impacts stress distribution at the boundary. When λ < 1.0 and β = 45°, stress distribution asymmetry is most pronounced, with the highest compressive stress. The early failure distribution aligns with stress concentration areas, validating the use of stress analysis in predicting opening stability and failure characteristics. [ABSTRACT FROM AUTHOR]

Featured Application: Featured Application: Seismic design of steel moment-resisting frames equipped with viscoelastic dampers in the framework of the Eurocode 8 provisions. The effectiveness of viscoelastic dampers as passive control devices has been demonstrated in the past through both experimental and numerical investigations. Based on the Modal Strain Energy Method, some authors have also proposed design procedures to size the viscoelastic dampers assuming a fist-mode behavior of the structure. However, even if the damped structure is governed by the first mode of vibration, viscoelastic dampers are sensitive to the frequencies of the upper modes and transmit unexpected internal forces to braces. This paper aims to develop a simple design procedure for steel moment-resisting frames equipped with viscoelastic dampers considering the effects of the higher modes of vibrations on the internal forces transmitted from the dampers to the braces. In the perspective of a designer-oriented study, the seismic demand is evaluated through simple analytical tools, such as the lateral force method or the response spectrum analysis. The design procedure is applied to a set of steel moment-resisting frames considering two levels of seismic hazard and two types of soil. Finally, the effectiveness of the proposed procedure is verified through nonlinear dynamic analysis. Based on the results, it is found that the proposed design procedure ensures the control of the story drift below prefixed limits and to predict accurately the internal forces that arise in the braces. [ABSTRACT FROM AUTHOR]