Search Results (60)

The Wigner function plays a central role in QCD as a phase-space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent work based on the Koopman–von Neumann–Sudarshan (KvNS) Hilbert space formulation of classical mechanics suggests the Wigner function arises as a quantum probability amplitude projected onto classical phase space, rather than a quasiprobability density. In the classical limit, this amplitude reduces to the classical Koopman wavefunction. In this work, we extend this perspective to relativistic QCD by constructing a Koopman description of the quark Wigner operator. We show that the Wigner operator is naturally isomorphic to a phase-space spinor, providing a unified framework in which both classical and quantum dynamics are expressed. Within this formulation, the Wigner function retains its interpretation as an amplitude even in the relativistic regime. This viewpoint clarifies the origin of negativity and other nonclassical features, and provides a more transparent foundation for parton distribution functions in QCD. Remarkably, the relativistic Koopman framework reproduces the classical limit of QCD. Full article

Accurately characterizing the statistical fluctuations of vehicle radar cross sections (RCSs) across polarization states and azimuthal sectors is essential for evaluating detection performance, conducting probabilistic simulations, and analyzing target features in millimeter-wave radar systems. Existing one-dimensional RCS statistical models, including Weibull, Chi-square, Lognormal, Rice, and Gaussian distributions, are often limited by their restricted functional expressiveness, making it difficult to simultaneously capture skewness, tail thickness, and azimuthal dependence under narrow angular-domain conditions. In addition, purely nonparametric approaches tend to produce spurious modes under finite-sample conditions and lack interpretable structural priors. To address these limitations, this paper proposes a Unimodal RCS Semiparametric Density Estimator (URCS-SDE) tailored for ground-vehicle targets. The proposed approach adopts kernel density estimation (KDE) as a data-driven baseline representation and incorporates physically plausible structural constraints through unimodal shape projection. Then a beta-type tail template is further introduced in the normalized amplitude domain to regulate boundary decay behavior. Finally, weighted least-squares calibration is performed on the histogram grid of the empirical probability density function (PDF), achieving a balanced trade-off between fitting accuracy and stability in both the peak and tail regions. Using multi-azimuth RCS measurements of two representative ground vehicles, the URCS-SDE is systematically compared with five classical parametric distributions and a representative regularized mixture density network (MDN) baseline. Performance is evaluated under both full-azimuth and directional-window conditions using the sum of squared errors (SSE), root mean squared error (RMSE), coefficient of determination (R-square) and held-out negative log-likelihood (NLL). The results show that the URCS-SDE consistently provides the most accurate and stable density estimates, especially in narrow angular windows. In addition, a threshold-based detection-support example derived from the fitted PDFs demonstrates that the advantage of the URCS-SDE transfers from density reconstruction to a directly engineering-relevant downstream quantity. Full article

Sensing mutual information (SMI) is widely adopted as a performance metric for integrated sensing and communication (ISAC) to enhance both sensing and communication capabilities. However, conventional approaches derive SMI from amplitude and phase, whereas an explicit evaluation of range mutual information (RMI) remains absent. In this paper, we investigate a novel closed-form approximation of RMI for ISAC. We first derive an explicit expression for the posterior probability density function (PDF) of the target range, which is formulated as a function of the signal’s autocorrelation and cross-correlation. Furthermore, we show that under high signal-to-noise ratio (SNR), the estimated range PDF approximates a Gaussian distribution in the sensing-unconstrained scenario and a truncated Gaussian distribution in the sensing-constrained scenario. Finally, we derive closed-form approximations of the RMI in both scenarios under high SNR. In the sensing-unconstrained scenario, the RMI is proportional to the delay interval, root-mean-square bandwidth, and SNR. In the constrained scenario, we obtain a closed-form RMI approximation by introducing an entropy correction term that quantifies the impact of boundary constraints. Additionally, we employ a maximum likelihood estimation (MLE) method to assess range estimation performance. Simulation results validate the accuracy of the theoretical results and the effectiveness of the proposed approximations. Full article

We investigate a stochastic coupled nonlinear Schrödinger (Manakov-type) system for option price and volatility wave fields within the Ivancevic adaptive-wave option-pricing paradigm, and derive exact wave families together with statistical diagnostics of the resulting dynamics. This system combines behavioral market effects with classical efficient-market dynamics and incorporates a controlled stochastic volatility component. Randomness in both the option price and volatility is incorporated via white noise, and a system of stochastic partial differential equations (PDEs) is developed that governs the joint evolution of option prices and stock price volatility. We derive advanced solutions of the proposed system using a newly created methodology. The obtained solutions are expressions of cnoidal, snoidal, dnoidal, hyperbolic, trigonometric, and exponential functions. The stochastic dynamical investigation, together with the statistical measures are presented. The autocorrelation function (ACF) of squared returns for the obtained analytical solutions is demonstrated to show distinct differences in second-order temporal dependence, while asymmetries in the temporal evolution of the fluctuations are depicted via leverage correlation (LC). The probability distribution function (PDF) dynamics of the soliton solutions illustrate prominent temporal variability and non-stationary statistical dynamics. Differences in dynamical coupling between the two components of the considered system are presented via phase velocity cross-correlation analysis and are supported by phase difference dynamics visualizations. The strength and structure of coupling between components are displayed via the amplitude cross-correlation function. Mean amplitude dynamics and variance as a function of noise intensity $\sigma$, provide a systematic influence of stochastic forcing on their energy and a quantitative measure of stochastic dispersion of soliton solutions. All the results are displayed in 3D and 2D graphs of the stochastics and statistical dynamics of the obtained solutions. Full article

This study aims to fill the existing gap in laser detection research, particularly regarding how the waveform of outgoing laser pulses affects detection performance. Based on the mechanism of light cone beam expansion, this study emits three different laser pulse signals to detect short-range targets. A theoretical model for short-range ranging of these lasers is established, and the effects of emission power, divergence angle, and equivalent root mean square noise voltage on circumferential detection accuracy are simulated and experimentally measured. As emission power decreases, both echo amplitude and detection accuracy decline for all three pulsed lasers. Additionally, except for the inverted parabolic function, both echo amplitude and detection accuracy decrease with reduced divergence angle. An increase in equivalent root mean square noise voltage broadens the half-width of the probability density distribution for pulsed laser detection. The mean central position deviation between the ideal and measured detection probability density distributions of the heavy-tailed function laser pulses shows the best performance and the highest fidelity, which are +0.01 m, +0.05 m, and +0.02 m, respectively, which is of great significance for the development of laser detection technology. Full article

This paper discusses whether the principal response features of composites subjected to fatigue loadings, including residual strength and lifetime statistics under variable amplitude (VA) loadings, can be resolved based on constant amplitude (CA) fatigue life data. The approach is based on the strength-residual strength-life equal-rank assumption (SRSLERA), providing a statistical correspondence between the static strength, residual strength, and fatigue life distribution functions under CA loadings. Under VA loadings, the strength degradation progression and then the fatigue lifetime are calculated by dividing the loading spectrum into a sequence of CA block loadings of given extents (including one cycle), and assuming that the strength at the end of a generic block loading equals the strength at the start of the consecutive one, namely the equivalent residual strength assumption (ERSA). The consequences of SRSLERA and ERSA are first discussed by re-elaborating a series of uniaxial, statistically sound CA residual strength and fatigue life data obtained under different loading ratios, R, ranging from pure tension to mixed tension–compression to pure compression. It is shown that the static strength Weibull’s shape and scale parameters, as well as the fatigue formulation parameters recovered under pure compression or tension loadings, represent the fingerprint of composite materials subjected to fatigue and characterize their uniqueness. The residual strength statistics, fatigue probability density functions (PDFs), and constant life diagram (CLD) construction are theoretically reported. Then, based on ERSA, the statistical lifetimes under VA loadings and the cycle-by-cycle damage progressions of block repeated loadings are analyzed, and a residual strength-based damage rule is compared to Miner’s rule. Full article

To analyze the dynamic response of tension leg platform (TLP) tendons under irregular ocean wave action, the governing equations of coupled vibration between the platform and tendon under irregular wave action are established based on Hamilton’s principle and the Kirchhoff hypothesis. Using the spectrum representation–random function method, the power spectral density function of the irregular wave load is derived, and the lateral wave forces at different tendon locations are calculated. The coupled lateral and axial responses of the tendon system are obtained through the fourth-order Runge–Kutta method. Considering the parametric vibrations of both the platform and tendon, the extreme lateral deflection of the tendon is employed as the control index to derive the probability density curves of the tendon deflection under irregular wave load. The results show that the amplitude of the wave load increases gradually along the height of the tendon, with a faster growth rate at locations closer to the water surface. The tendon’s lateral deflection response changes more drastically due to coupled parametric vibration of the platform. Based on 628 complete samples of irregular wave loads, the probability density curve and cumulative distribution curve of the extreme lateral deflection of the tendon under irregular wave loads are obtained. Under typical sea state conditions generated from the P-M wave spectrum, the reliability of the tendon under irregular wave load increases with the initial tension force. Full article

We propose an amplitude encoding of the traveling salesperson problem along with a method for calculating the cost function using a probability distribution obtained on a quantum computer. Our encoding requires a number of qubits that grows logarithmically with the number of cities. We propose to calculate the cost function using a nonlinear function of expectation values of quantum operators. This is in contrast to the typical method of evaluating the cost function by summing expectation values of quantum operators. We demonstrate our method using a variational quantum eigensolver algorithm to find the shortest route for a given graph. We find that there is a broad range in the hyperparameters of the optimization procedure for which the best route is found. Full article

To thoroughly analyze the high-frequency and high-amplitude electromagnetic disturbances generated during disconnector operation, this paper proposes an equivalent modeling approach based on dynamic arc behavior. The model incorporates the resistance, inductance, and capacitance characteristics of the arc and consists of four main modules: arc reignition, arc extinction, arc resistance control, and switch control. Complete logical coordination among these modules is designed to enhance the model’s performance in terms of dynamic response and modeling accuracy compared to traditional methods. By systematically comparing simulation results with experimental data and conventional model outputs, the effectiveness and reliability of the proposed model in accurately reflecting the operational characteristics of disconnectors are validated. Furthermore, a comparative analysis of transient waveform characteristics from both experiment and simulation is conducted, with key parameters extracted and probability density functions constructed. The results demonstrate the high-precision fitting capability of the model and further reveal the statistical distribution patterns of very fast transient overvoltage single-pulse characteristics. Full article

Prolonged periods of standing are linked to low back pain (LBP). Evaluating lumbar spine biomechanics in real-world contexts can provide novel insights into these links. This study aimed to determine if standing behaviour can be quantified, in individuals with LBP, in real-world environments. A three-stage design was used, (i) Verification of a bespoke algorithm characterising lumbar standing behaviour, (ii) Day-long assessment of standing behaviours of individuals with posture-related low back discomfort, and (iii) Case study application to individuals with clinical LBP. Analysis of standing posture across time included variability, fidgeting, and amplitude probability distribution function analysis. The study demonstrated that accelerometers are a valid method for extracting standing posture from everyday activity data. There was a wide variety of postures throughout the day in people with posture-related low back discomfort and people with clinical LBP. Frequency profiles ranged from slightly flexed to slightly extended postures, with skewed bell-shaped distributions common. Postural variability ranged from 3.4° to 7.7°, and fidgeting from 1.0° to 3.0°. This work presents a validated accelerometer-based method to capture, identify, and quantify real-world lumbar standing postures. The distinct characteristics of people with low back discomfort or pain highlight the importance of individualised approaches. Full article

Reconfigurable Intelligent Surfaces (RISs) and Non-Orthogonal Multiple Access (NOMA) have emerged as key technologies for next-generation (6G) wireless networks, attracting significant attention from researchers. As an advanced extension of RISs, Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surfaces (STAR-RISs) offer superior geometric and functional symmetry due to their capability to simultaneously reflect and transmit signals, thereby achieving full 360° spatial coverage. This symmetry not only ensures balanced energy distribution between the Transmission (T) and Reflection (R) regions but also facilitates interference cancellation through phase alignment. Furthermore, in NOMA networks, the symmetric allocation of power coefficients and the tunable transmission and reflection coefficients of STAR-RIS elements aligns with the principle of resource fairness in multi-user systems, which is crucial for maintaining fairness under asymmetric channel conditions. In this study, key factors, such as interference sources and distance effects, are considered in order to conduct a detailed analysis of the performance of STAR-RIS-assisted NOMA wireless education networks under multiple interference devices. Specifically, a comprehensive analysis of the Signal-to-Interference-plus-Noise Ratio (SINR) for both near-end and far-end devices is conducted, considering various scenarios, such as whether or not the direct communication link exists between the base station and the near-end device, and whether or not the near-end device is affected by interference. Based on these analyses, closed-form approximate expressions for the outage probabilities of the near-end and far-end devices, as well as the closed-form approximation for the system’s Spectral Efficiency (SE), are derived. Notably, the Gamma distribution is used to approximate the square of the composite channel amplitude between the base station and the near-end device, effectively reducing computational complexity. Finally, simulation results validate the accuracy of our analytical results. Both numerical and simulation results show that adjusting the base station’s power allocation, and the transmission and reflection coefficients of the STAR-RIS, can effectively mitigate the impact of interference devices on the near-end device and enhance the communication performance of receiving devices. Additionally, increasing the number of STAR-RIS elements can effectively improve the overall performance of the near-end device, far-end device, and the entire system. Full article

To address the challenges of slow convergence speed, poor convergence precision, and getting stuck in local optima for unmanned aerial vehicle (UAV) three-dimensional path planning, this paper proposes a path planning method based on an Improved Human Evolution Optimization Algorithm (IHEOA). First, a mathematical model is used to construct a three-dimensional terrain environment, and a multi-constraint path cost model is established, framing path planning as a multidimensional function optimization problem. Second, recognizing the sensitivity of population diversity to Logistic Chaotic Mapping in a traditional Human Evolution Optimization Algorithm (HEOA), an opposition-based learning strategy is employed to uniformly initialize the population distribution, thereby enhancing the algorithm’s global optimization capability. Additionally, a guidance factor strategy is introduced into the leader role during the development stage, providing clear directionality for the search process, which increases the probability of selecting optimal paths and accelerates the convergence speed. Furthermore, in the loser update strategy, an adaptive t-distribution perturbation strategy is utilized for its small mutation amplitude, which enhances the local search capability and robustness of the algorithm. Evaluations using 12 standard test functions demonstrate that these improvement strategies effectively enhance convergence precision and algorithm stability, with the IHEOA, which integrates multiple strategies, performing particularly well. Experimental comparative research on three different terrain environments and five traditional algorithms shows that the IHEOA not only exhibits excellent performance in terms of convergence speed and precision but also generates superior paths while demonstrating exceptional global optimization capability and robustness in complex environments. These results validate the significant advantages of the proposed improved algorithm in effectively addressing UAV path planning challenges. Full article

The limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality of different coherent-state signal constellations used in quantum communications, namely phase-shift keying (PSK), quadrature-amplitude modulation (QAM), and a newly defined signal named the sunflower-like (SUN) coherent-state signal. The non-orthogonality index (NOI) and the average probability of correct detection (detection probability) are numerically computed. Results show that PSK NOI increases faster than QAM and SUN as the number of signals increases for a given number of signal photons. QAM and SUN exhibit similar NOI and detection probability, behaving similarly to randomly generated signals for a larger number of signals. Approximation formulas are provided for the detection probability as a function of NOI for each signal type. While similar to QAM, SUN signal offers potential advantages for applications requiring uniform signal-space distribution. The findings provide valuable insights for designing useful quantum signal constellations. Full article

The radar monopulse angle measurement can obtain a target’s angle information within a single pulse, meaning that factors such as target motion and amplitude fluctuations, which vary over time, do not affect the angle measurement accuracy. However, in practical applications, when a target’s signal-to-noise ratio (SNR) is low, the single pulse signal is severely affected by noise, leading to a significant deterioration in angle measurement accuracy. Therefore, it is usually necessary to coherently integrate multiple pulses before estimating the angle. This paper constructs an angle expansion model for a multi-pulse angle measurement under coherent integration. The analysis reveals that even under noise-free conditions, after coherently integrating multiple pulses, the coupling of target amplitude fluctuations and motion state can still cause significant errors in the angle measurement. Subsequently, this paper conducts a detailed analysis of the impact of the amplitude fluctuations and target maneuvers on the random angle measurement error. It also derives approximate probability density functions of angle measurement errors under various fluctuation and motion scenarios based on the Lindeberg–Feller central limit theorem. In addition, based on the angle expansion model and the random error distribution, this paper proposes an angle correction algorithm based on multi-pulse integration and long-term estimation. Numerical experiments and radar data in the field verify the impact of target characteristics on the angle measurement under multi-pulse integration and the effectiveness of the angle correction algorithm. Full article

Low back pain affects 619 million people worldwide and is commonly provoked by sitting. Current assessment methods constrain task variability, removing real-world, task-switching behaviors. This study utilized accelerometers to provide an original validated method of in vivo real-world assessment of lumbar sitting behavior throughout a full day. A three-stage study design was used, which involved (1) blinded verification of our sitting detection algorithm, (2) full-day data collection from participants with low back discomfort, quantifying lumbar angles, and end-user acceptability explored, (3) case study application to two clinical low back pain (LBP) patients, incorporating measurement of provocative sitting. Focus group discussions demonstrated that data collection methods were acceptable. Sitting ‘windows’ were created and analyzed using novel histograms, amplitude probability distribution functions, and variability, demonstrating that sitting behavior was unique and varied across individuals. One LBP patient demonstrated two frequent lumbar postures (<15% flexion and ~75% flexion), with pain provocation at 62% lumbar flexion. The second patient demonstrated a single dominant posture (~90% flexion), with pain provoked at 86% lumbar flexion. Our in vivo approach offers an acceptable method to gain new insights into provocative sitting behavior in individuals with LBP, allowing individualized unconstrained data for full-day postures and pain provocation behaviors to be quantified, which are otherwise unattainable. Full article